From 3c1888b3480bf47b98e7a478aee5c5cffe5c0edd Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 1 Mar 2024 11:11:36 +0100
Subject: [PATCH 001/114] feat: mul by linear factor ok

---
 ecc/bn254/shplonk/shplonk.go | 54 ++++++++++++++++++++++++++++++++++++
 1 file changed, 54 insertions(+)
 create mode 100644 ecc/bn254/shplonk/shplonk.go

diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
new file mode 100644
index 0000000000..963663f623
--- /dev/null
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -0,0 +1,54 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+//cf https://eprint.iacr.org/2020/081.pdf
+
+package shplonk
+
+import (
+	"github.com/consensys/gnark-crypto/ecc/bn254"
+	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
+	"github.com/consensys/gnark-crypto/ecc/bn254/kzg"
+)
+
+// OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
+//
+// implements io.ReaderFrom and io.WriterTo
+type OpeningProof struct {
+
+	// W = ∑ᵢ γⁱZ_{T\xᵢ}(f_i(X)-f(x_i))
+	W bn254.G1Affine
+
+	// (fᵢ(xᵢ))_{i}
+	ClaimedValues []fr.Element
+}
+
+func BatchOpen(p [][]fr.Element, points []fr.Element, pk kzg.ProvingKey) {}
+
+// ------------------------------
+// utils
+
+// computes f <- (x-a)*f (in place if the capacity of f is correctly set)
+func multiplyLinearFactor(f []fr.Element, a fr.Element) []fr.Element {
+	s := len(f)
+	var tmp fr.Element
+	f = append(f, fr.NewElement(0))
+	f[s] = f[s-1]
+	for i := s - 1; i >= 1; i-- {
+		tmp.Mul(&f[i], &a)
+		f[i].Sub(&f[i-1], &tmp)
+	}
+	f[0].Mul(&f[0], &a).Neg(&f[0])
+	return f
+}

From b9aeda23fc26188604e5a6e72d2471e250c7efcd Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 1 Mar 2024 15:47:06 +0100
Subject: [PATCH 002/114] feat: division ok

---
 ecc/bn254/shplonk/shplonk.go      | 26 +++++++++
 ecc/bn254/shplonk/shplonk_test.go | 91 +++++++++++++++++++++++++++++++
 2 files changed, 117 insertions(+)
 create mode 100644 ecc/bn254/shplonk/shplonk_test.go

diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
index 963663f623..45c3997111 100644
--- a/ecc/bn254/shplonk/shplonk.go
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -39,6 +39,14 @@ func BatchOpen(p [][]fr.Element, points []fr.Element, pk kzg.ProvingKey) {}
 // ------------------------------
 // utils
 
+func eval(f []fr.Element, x fr.Element) fr.Element {
+	var y fr.Element
+	for i := len(f) - 1; i >= 0; i-- {
+		y.Mul(&y, &x).Add(&y, &f[i])
+	}
+	return y
+}
+
 // computes f <- (x-a)*f (in place if the capacity of f is correctly set)
 func multiplyLinearFactor(f []fr.Element, a fr.Element) []fr.Element {
 	s := len(f)
@@ -52,3 +60,21 @@ func multiplyLinearFactor(f []fr.Element, a fr.Element) []fr.Element {
 	f[0].Mul(&f[0], &a).Neg(&f[0])
 	return f
 }
+
+// returns f/g (assuming g divides f)
+// OK to not use fft if deg(g) is small
+// g's leading coefficient is assumed to be 1
+// f memory is re-used for the result
+func div(f, g []fr.Element) []fr.Element {
+	sizef := len(f)
+	sizeg := len(g)
+	stop := sizeg - +1
+	var t fr.Element
+	for i := sizef - 2; i >= stop; i-- {
+		for j := 0; j < sizeg-1; j++ {
+			t.Mul(&f[i+1], &g[sizeg-2-j])
+			f[i-j].Sub(&f[i-j], &t)
+		}
+	}
+	return f[sizeg-1:]
+}
diff --git a/ecc/bn254/shplonk/shplonk_test.go b/ecc/bn254/shplonk/shplonk_test.go
new file mode 100644
index 0000000000..1d49374f27
--- /dev/null
+++ b/ecc/bn254/shplonk/shplonk_test.go
@@ -0,0 +1,91 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package shplonk
+
+import (
+	"fmt"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
+)
+
+func TestMultiplyLinearFactor(t *testing.T) {
+
+	s := 10
+	f := make([]fr.Element, s, s+1)
+	for i := 0; i < 10; i++ {
+		f[i].SetRandom()
+	}
+
+	var a, y fr.Element
+	a.SetRandom()
+	y = eval(f, a)
+	if y.IsZero() {
+		t.Fatal("result should not be zero")
+	}
+
+	f = multiplyLinearFactor(f, a)
+	y = eval(f, a)
+	if !y.IsZero() {
+		t.Fatal("(X-a)f(X) should be zero at a")
+	}
+}
+
+func TestDiv(t *testing.T) {
+
+	nbPoints := 10
+	s := 10
+	f := make([]fr.Element, s, s+nbPoints)
+	for i := 0; i < s; i++ {
+		f[i].SetRandom()
+	}
+
+	// backup
+	g := make([]fr.Element, s)
+	copy(g, f)
+	for i := 0; i < len(g); i++ {
+		fmt.Printf("%s\n", g[i].String())
+	}
+	fmt.Println("--")
+
+	x := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		f = multiplyLinearFactor(f, x[i])
+	}
+	fmt.Println("--")
+	q := make([][2]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		q[i][1].SetOne()
+		q[i][0].Neg(&x[i])
+		f = div(f, q[i][:])
+	}
+
+	for i := 0; i < len(f); i++ {
+		fmt.Printf("%s\n", f[i].String())
+	}
+	fmt.Println("--")
+
+	// g should be equal to f
+	if len(f) != len(g) {
+		t.Fatal("lengths don't match")
+	}
+	for i := 0; i < len(g); i++ {
+		if !f[i].Equal(&g[i]) {
+			t.Fatal("f(x)(x-a)/(x-a) should be equal to f(x)")
+		}
+	}
+
+}

From c6fdec20aafc2bebd3b35b09fb7971f4c558fe91 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 1 Mar 2024 16:11:46 +0100
Subject: [PATCH 003/114] feat: build vanishing poly ok

---
 ecc/bn254/shplonk/shplonk.go      |  9 +++++++++
 ecc/bn254/shplonk/shplonk_test.go | 33 ++++++++++++++++++++-----------
 2 files changed, 30 insertions(+), 12 deletions(-)

diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
index 45c3997111..14a72a3ac7 100644
--- a/ecc/bn254/shplonk/shplonk.go
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -61,6 +61,15 @@ func multiplyLinearFactor(f []fr.Element, a fr.Element) []fr.Element {
 	return f
 }
 
+// returns πᵢ(X-xᵢ)
+func buildVanishingPoly(x []fr.Element) []fr.Element {
+	res := make([]fr.Element, 1, len(x)+1)
+	for i := 0; i < len(x); i++ {
+		res = multiplyLinearFactor(res, x[i])
+	}
+	return res
+}
+
 // returns f/g (assuming g divides f)
 // OK to not use fft if deg(g) is small
 // g's leading coefficient is assumed to be 1
diff --git a/ecc/bn254/shplonk/shplonk_test.go b/ecc/bn254/shplonk/shplonk_test.go
index 1d49374f27..62de573db4 100644
--- a/ecc/bn254/shplonk/shplonk_test.go
+++ b/ecc/bn254/shplonk/shplonk_test.go
@@ -15,12 +15,32 @@
 package shplonk
 
 import (
-	"fmt"
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
 )
 
+func TestBuildVanishingPoly(t *testing.T) {
+	s := 10
+	x := make([]fr.Element, s)
+	for i := 0; i < s; i++ {
+		x[i].SetRandom()
+	}
+	r := buildVanishingPoly(x)
+
+	if len(r) != s+1 {
+		t.Fatal("error degree r")
+	}
+
+	// check that r(x_{i})=0 for all i
+	for i := 0; i < len(x); i++ {
+		y := eval(r, x[i])
+		if !y.IsZero() {
+			t.Fatal("πᵢ(X-xᵢ) at xᵢ should be zero")
+		}
+	}
+}
+
 func TestMultiplyLinearFactor(t *testing.T) {
 
 	s := 10
@@ -55,17 +75,12 @@ func TestDiv(t *testing.T) {
 	// backup
 	g := make([]fr.Element, s)
 	copy(g, f)
-	for i := 0; i < len(g); i++ {
-		fmt.Printf("%s\n", g[i].String())
-	}
-	fmt.Println("--")
 
 	x := make([]fr.Element, nbPoints)
 	for i := 0; i < nbPoints; i++ {
 		x[i].SetRandom()
 		f = multiplyLinearFactor(f, x[i])
 	}
-	fmt.Println("--")
 	q := make([][2]fr.Element, nbPoints)
 	for i := 0; i < nbPoints; i++ {
 		q[i][1].SetOne()
@@ -73,11 +88,6 @@ func TestDiv(t *testing.T) {
 		f = div(f, q[i][:])
 	}
 
-	for i := 0; i < len(f); i++ {
-		fmt.Printf("%s\n", f[i].String())
-	}
-	fmt.Println("--")
-
 	// g should be equal to f
 	if len(f) != len(g) {
 		t.Fatal("lengths don't match")
@@ -87,5 +97,4 @@ func TestDiv(t *testing.T) {
 			t.Fatal("f(x)(x-a)/(x-a) should be equal to f(x)")
 		}
 	}
-
 }

From 34702b922bccc3e7acf671696eb6e4248fe38d8a Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 1 Mar 2024 19:06:24 +0100
Subject: [PATCH 004/114] fix: fixed vanishing poly

---
 ecc/bn254/shplonk/shplonk.go      |  1 +
 ecc/bn254/shplonk/shplonk_test.go | 28 ++++++++++++++++++++++++++++
 2 files changed, 29 insertions(+)

diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
index 14a72a3ac7..b434796c9e 100644
--- a/ecc/bn254/shplonk/shplonk.go
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -64,6 +64,7 @@ func multiplyLinearFactor(f []fr.Element, a fr.Element) []fr.Element {
 // returns πᵢ(X-xᵢ)
 func buildVanishingPoly(x []fr.Element) []fr.Element {
 	res := make([]fr.Element, 1, len(x)+1)
+	res[0].SetOne()
 	for i := 0; i < len(x); i++ {
 		res = multiplyLinearFactor(res, x[i])
 	}
diff --git a/ecc/bn254/shplonk/shplonk_test.go b/ecc/bn254/shplonk/shplonk_test.go
index 62de573db4..e2d47e63ce 100644
--- a/ecc/bn254/shplonk/shplonk_test.go
+++ b/ecc/bn254/shplonk/shplonk_test.go
@@ -39,6 +39,14 @@ func TestBuildVanishingPoly(t *testing.T) {
 			t.Fatal("πᵢ(X-xᵢ) at xᵢ should be zero")
 		}
 	}
+
+	// check that r(y)!=0 for a random point
+	var a fr.Element
+	a.SetRandom()
+	y := eval(r, a)
+	if y.IsZero() {
+		t.Fatal("πᵢ(X-xᵢ) at r \neq xᵢ should not be zero")
+	}
 }
 
 func TestMultiplyLinearFactor(t *testing.T) {
@@ -76,6 +84,7 @@ func TestDiv(t *testing.T) {
 	g := make([]fr.Element, s)
 	copy(g, f)
 
+	// successive divions of linear terms
 	x := make([]fr.Element, nbPoints)
 	for i := 0; i < nbPoints; i++ {
 		x[i].SetRandom()
@@ -97,4 +106,23 @@ func TestDiv(t *testing.T) {
 			t.Fatal("f(x)(x-a)/(x-a) should be equal to f(x)")
 		}
 	}
+
+	// division by a degree > 1 polynomial
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		f = multiplyLinearFactor(f, x[i])
+	}
+	r := buildVanishingPoly(x)
+	f = div(f, r)
+
+	// g should be equal to f
+	if len(f) != len(g) {
+		t.Fatal("lengths don't match")
+	}
+	for i := 0; i < len(g); i++ {
+		if !f[i].Equal(&g[i]) {
+			t.Fatal("f(x)(x-a)/(x-a) should be equal to f(x)")
+		}
+	}
+
 }

From 2dbe9e6efc08f7f3c42c011f7a050f8cd3ed6619 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 1 Mar 2024 19:17:45 +0100
Subject: [PATCH 005/114] fix: fixed test TestMultiplyLinearFactor

---
 ecc/bn254/shplonk/shplonk_test.go | 11 ++++++-----
 1 file changed, 6 insertions(+), 5 deletions(-)

diff --git a/ecc/bn254/shplonk/shplonk_test.go b/ecc/bn254/shplonk/shplonk_test.go
index e2d47e63ce..991e37cab1 100644
--- a/ecc/bn254/shplonk/shplonk_test.go
+++ b/ecc/bn254/shplonk/shplonk_test.go
@@ -59,16 +59,17 @@ func TestMultiplyLinearFactor(t *testing.T) {
 
 	var a, y fr.Element
 	a.SetRandom()
-	y = eval(f, a)
-	if y.IsZero() {
-		t.Fatal("result should not be zero")
-	}
-
 	f = multiplyLinearFactor(f, a)
 	y = eval(f, a)
 	if !y.IsZero() {
 		t.Fatal("(X-a)f(X) should be zero at a")
 	}
+	a.SetRandom()
+	y = eval(f, a)
+	if y.IsZero() {
+		t.Fatal("(X-1)f(X) at a random point should not be zero")
+	}
+
 }
 
 func TestDiv(t *testing.T) {

From d35544df58d7ceab54534f9b9dab49948c67fd8e Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Tue, 5 Mar 2024 16:56:48 +0100
Subject: [PATCH 006/114] feat: naive mul (for combinings polynomials) ok

---
 ecc/bn254/shplonk/shplonk.go      | 116 +++++++++++++++++++++++++++++-
 ecc/bn254/shplonk/shplonk_test.go |  36 ++++++++++
 2 files changed, 150 insertions(+), 2 deletions(-)

diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
index b434796c9e..2f6a7b0948 100644
--- a/ecc/bn254/shplonk/shplonk.go
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -17,9 +17,17 @@
 package shplonk
 
 import (
+	"errors"
+	"hash"
+
 	"github.com/consensys/gnark-crypto/ecc/bn254"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
 	"github.com/consensys/gnark-crypto/ecc/bn254/kzg"
+	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
+)
+
+var (
+	ErrInvalidNumberOfPoints = errors.New("number of digests should be equal to the number of points")
 )
 
 // OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
@@ -27,14 +35,94 @@ import (
 // implements io.ReaderFrom and io.WriterTo
 type OpeningProof struct {
 
-	// W = ∑ᵢ γⁱZ_{T\xᵢ}(f_i(X)-f(x_i))
+	// W = ∑ᵢ γⁱZ_{T\xᵢ}(f_i(X)-f(x_i)) where Z_{T} is the vanishing polynomial on the (xᵢ)_{i}
 	W bn254.G1Affine
 
+	// L(X)/(X-z) where L(X)=∑ᵢγⁱZ_{T\xᵢ}(f_i(X)-rᵢ) - Z_{T}W(X)
+	WPrime bn254.G1Affine
+
 	// (fᵢ(xᵢ))_{i}
 	ClaimedValues []fr.Element
 }
 
-func BatchOpen(p [][]fr.Element, points []fr.Element, pk kzg.ProvingKey) {}
+// func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points []fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
+
+// 	var res OpeningProof
+
+// 	if len(polynomials) != len(points) {
+// 		return res, ErrInvalidNumberOfPoints
+// 	}
+
+// 	// derive γ
+// 	gamma, err := deriveGamma(points, digests, hf, dataTranscript...)
+// 	if err != nil {
+// 		return res, err
+// 	}
+
+// 	// compute the claimed evaluations
+// 	maxSize := len(polynomials[0])
+// 	for i := 1; i < len(polynomials); i++ {
+// 		if maxSize < len(polynomials[i]) {
+// 			maxSize = len(polynomials[i])
+// 		}
+// 	}
+
+// 	totalSize := maxSize + len(points) // maxSize+len(points)-1 is the max degree among the polynomials Z_{T\xᵢ}fᵢ
+// 	buf := make([]fr.Element, totalSize)
+// 	f := make([]fr.Element, totalSize)
+// 	copy(buf, polynomials[0])
+// 	v := buildVanishingPoly(points[1:])
+
+// 	for i := 1; i<len(polynomials); i++ {
+
+// 	}
+
+// 	// derive z
+
+// 	return res, nil
+// }
+
+// BatchVerify uses proof to check that the commitments correctly open to proof.ClaimedValues
+// at points. The order mattes: the proof validates that the i-th commitment is correctly opened
+// at the i-th point
+func BatchVerify(proof OpeningProof, commitments []kzg.Digest, points []fr.Element) error {
+
+	// compute γ
+
+	return nil
+}
+
+// deriveGamma derives a challenge using Fiat Shamir to polynomials.
+func deriveGamma(points []fr.Element, digests []kzg.Digest, hf hash.Hash, dataTranscript ...[]byte) (fr.Element, error) {
+
+	// derive the challenge gamma, binded to the point and the commitments
+	fs := fiatshamir.NewTranscript(hf, "gamma")
+	for i := range points {
+		if err := fs.Bind("gamma", points[i].Marshal()); err != nil {
+			return fr.Element{}, err
+		}
+	}
+	for i := range digests {
+		if err := fs.Bind("gamma", digests[i].Marshal()); err != nil {
+			return fr.Element{}, err
+		}
+	}
+
+	for i := 0; i < len(dataTranscript); i++ {
+		if err := fs.Bind("gamma", dataTranscript[i]); err != nil {
+			return fr.Element{}, err
+		}
+	}
+
+	gammaByte, err := fs.ComputeChallenge("gamma")
+	if err != nil {
+		return fr.Element{}, err
+	}
+	var gamma fr.Element
+	gamma.SetBytes(gammaByte)
+
+	return gamma, nil
+}
 
 // ------------------------------
 // utils
@@ -71,6 +159,30 @@ func buildVanishingPoly(x []fr.Element) []fr.Element {
 	return res
 }
 
+// returns f*g using naive multiplication
+// deg(big)>>deg(small), deg(small) =~ 10 max
+// buf is used as a buffer
+func mul(big, small []fr.Element, buf []fr.Element) []fr.Element {
+
+	sizeRes := len(big) + len(small) - 1
+	if len(buf) < sizeRes {
+		s := make([]fr.Element, sizeRes-len(buf))
+		buf = append(buf, s...)
+	}
+	for i := 0; i < len(buf); i++ {
+		buf[i].SetZero()
+	}
+
+	var tmp fr.Element
+	for i := 0; i < len(small); i++ {
+		for j := 0; j < len(big); j++ {
+			tmp.Mul(&big[j], &small[i])
+			buf[j+i].Add(&buf[j+i], &tmp)
+		}
+	}
+	return buf
+}
+
 // returns f/g (assuming g divides f)
 // OK to not use fft if deg(g) is small
 // g's leading coefficient is assumed to be 1
diff --git a/ecc/bn254/shplonk/shplonk_test.go b/ecc/bn254/shplonk/shplonk_test.go
index 991e37cab1..62bec6a864 100644
--- a/ecc/bn254/shplonk/shplonk_test.go
+++ b/ecc/bn254/shplonk/shplonk_test.go
@@ -72,6 +72,42 @@ func TestMultiplyLinearFactor(t *testing.T) {
 
 }
 
+func TestNaiveMul(t *testing.T) {
+
+	size := 10
+	f := make([]fr.Element, size)
+	for i := 0; i < size; i++ {
+		f[i].SetRandom()
+	}
+
+	nbPoints := 10
+	points := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		points[i].SetRandom()
+	}
+
+	v := buildVanishingPoly(points)
+	buf := make([]fr.Element, size+nbPoints-1)
+	g := mul(f, v, buf)
+
+	// check that g(x_{i}) = 0
+	for i := 0; i < nbPoints; i++ {
+		y := eval(g, points[i])
+		if !y.IsZero() {
+			t.Fatal("f(X)(X-x_{1})..(X-x_{n}) at x_{i} should be zero")
+		}
+	}
+
+	// check that g(r) != 0 for a random point
+	var a fr.Element
+	a.SetRandom()
+	y := eval(g, a)
+	if y.IsZero() {
+		t.Fatal("f(X)(X-x_{1})..(X-x_{n}) at a random point should not be zero")
+	}
+
+}
+
 func TestDiv(t *testing.T) {
 
 	nbPoints := 10

From c7810044bc8de2c5260012c64ba73eab7107c0f7 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Tue, 5 Mar 2024 17:20:15 +0100
Subject: [PATCH 007/114] feat: add poly

---
 ecc/bn254/shplonk/shplonk.go | 82 ++++++++++++++++++++++++------------
 1 file changed, 55 insertions(+), 27 deletions(-)

diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
index 2f6a7b0948..e7d1cf8f9b 100644
--- a/ecc/bn254/shplonk/shplonk.go
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -45,42 +45,42 @@ type OpeningProof struct {
 	ClaimedValues []fr.Element
 }
 
-// func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points []fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
+func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points []fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
 
-// 	var res OpeningProof
+	var res OpeningProof
 
-// 	if len(polynomials) != len(points) {
-// 		return res, ErrInvalidNumberOfPoints
-// 	}
+	if len(polynomials) != len(points) {
+		return res, ErrInvalidNumberOfPoints
+	}
 
-// 	// derive γ
-// 	gamma, err := deriveGamma(points, digests, hf, dataTranscript...)
-// 	if err != nil {
-// 		return res, err
-// 	}
+	// derive γ
+	gamma, err := deriveGamma(points, digests, hf, dataTranscript...)
+	if err != nil {
+		return res, err
+	}
 
-// 	// compute the claimed evaluations
-// 	maxSize := len(polynomials[0])
-// 	for i := 1; i < len(polynomials); i++ {
-// 		if maxSize < len(polynomials[i]) {
-// 			maxSize = len(polynomials[i])
-// 		}
-// 	}
+	// compute the claimed evaluations
+	maxSize := len(polynomials[0])
+	for i := 1; i < len(polynomials); i++ {
+		if maxSize < len(polynomials[i]) {
+			maxSize = len(polynomials[i])
+		}
+	}
 
-// 	totalSize := maxSize + len(points) // maxSize+len(points)-1 is the max degree among the polynomials Z_{T\xᵢ}fᵢ
-// 	buf := make([]fr.Element, totalSize)
-// 	f := make([]fr.Element, totalSize)
-// 	copy(buf, polynomials[0])
-// 	v := buildVanishingPoly(points[1:])
+	totalSize := maxSize + len(points) // maxSize+len(points)-1 is the max degree among the polynomials Z_{T\xᵢ}fᵢ
+	buf := make([]fr.Element, totalSize)
+	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
+	copy(buf, polynomials[0])
+	v := buildVanishingPoly(points[1:])
 
-// 	for i := 1; i<len(polynomials); i++ {
+	for i := 1; i < len(polynomials); i++ {
 
-// 	}
+	}
 
-// 	// derive z
+	// derive z
 
-// 	return res, nil
-// }
+	return res, nil
+}
 
 // BatchVerify uses proof to check that the commitments correctly open to proof.ClaimedValues
 // at points. The order mattes: the proof validates that the i-th commitment is correctly opened
@@ -135,6 +135,34 @@ func eval(f []fr.Element, x fr.Element) fr.Element {
 	return y
 }
 
+// sets buf= f+g and returns buf (memory of f is re-used)
+func add(f, g, buf []fr.Element) []fr.Element {
+	maxSize := len(f)
+	if maxSize < len(g) {
+		maxSize = len(g)
+	}
+	if len(buf) < maxSize {
+		s := make([]fr.Element, maxSize-len(buf))
+		buf = append(buf, s...)
+	}
+	for i := 0; i < len(buf); i++ {
+		buf[i].SetZero()
+	}
+	copy(buf, f)
+	for i := 0; i < len(g); i++ {
+		buf[i].Add(&buf[i], &g[i])
+	}
+	return buf
+}
+
+// returns \gamma*f, re-using f
+func mulByConstant(f []fr.Element, gamma fr.Element) []fr.Element {
+	for i := 0; i < len(f); i++ {
+		f[i].Mul(&f[i], &gamma)
+	}
+	return f
+}
+
 // computes f <- (x-a)*f (in place if the capacity of f is correctly set)
 func multiplyLinearFactor(f []fr.Element, a fr.Element) []fr.Element {
 	s := len(f)

From c51d33296a32a5d09fe56564af154acfbc9ea3ba Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Thu, 7 Mar 2024 10:23:05 +0100
Subject: [PATCH 008/114] feat: wrpime ok

---
 ecc/bn254/shplonk/shplonk.go | 152 ++++++++++++++++++++++++-----------
 1 file changed, 104 insertions(+), 48 deletions(-)

diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
index e7d1cf8f9b..f51318b09f 100644
--- a/ecc/bn254/shplonk/shplonk.go
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -49,35 +49,106 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points []fr.Ele
 
 	var res OpeningProof
 
+	nbInstances := len(polynomials)
 	if len(polynomials) != len(points) {
 		return res, ErrInvalidNumberOfPoints
 	}
 
+	// transcript
+	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
+
 	// derive γ
-	gamma, err := deriveGamma(points, digests, hf, dataTranscript...)
+	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
 	if err != nil {
 		return res, err
 	}
 
 	// compute the claimed evaluations
-	maxSize := len(polynomials[0])
+	maxSizePolys := len(polynomials[0])
 	for i := 1; i < len(polynomials); i++ {
-		if maxSize < len(polynomials[i]) {
-			maxSize = len(polynomials[i])
+		if maxSizePolys < len(polynomials[i]) {
+			maxSizePolys = len(polynomials[i])
 		}
 	}
-
-	totalSize := maxSize + len(points) // maxSize+len(points)-1 is the max degree among the polynomials Z_{T\xᵢ}fᵢ
-	buf := make([]fr.Element, totalSize)
+	totalSize := maxSizePolys + len(points) - 1 // maxSizePolys+len(points)-2 is the max degree among the polynomials Z_{T\xᵢ}fᵢ
+	bufTotalSize := make([]fr.Element, totalSize)
+	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
 	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
-	copy(buf, polynomials[0])
-	v := buildVanishingPoly(points[1:])
+	bufPoints := make([]fr.Element, nbInstances-1)
+	ztMinusXi := make([][]fr.Element, nbInstances)
+	res.ClaimedValues = make([]fr.Element, nbInstances)
+	var accGamma fr.Element
+	accGamma.SetOne()
+	for i := 0; i < nbInstances; i++ {
+
+		res.ClaimedValues[i] = eval(polynomials[i], points[i])
+
+		copy(bufPoints, points[:i])
+		copy(bufPoints[i:], points[i+1:])
+
+		ztMinusXi[i] = buildVanishingPoly(bufPoints)
+		copy(bufMaxSizePolynomials, polynomials[i])
+		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &res.ClaimedValues[i]) // f-f(xᵢ)
+		bufTotalSize = mul(bufMaxSizePolynomials, ztMinusXi[i], bufTotalSize)
+		bufTotalSize = mulByConstant(bufTotalSize, accGamma)
+		for j := 0; j < len(bufTotalSize); j++ {
+			f[j].Add(&f[j], &bufTotalSize[j])
+		}
 
-	for i := 1; i < len(polynomials); i++ {
+		accGamma.Mul(&accGamma, &gamma)
+		setZero(bufMaxSizePolynomials)
+	}
 
+	zt := buildVanishingPoly(points)
+	w := div(f, zt) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
+	res.W, err = kzg.Commit(w, pk)
+	if err != nil {
+		return res, err
 	}
 
 	// derive z
+	z, err := deriveChallenge("z", nil, []kzg.Digest{res.W}, fs)
+	if err != nil {
+		return res, err
+	}
+
+	// compute L = ∑ᵢγⁱZ_{T\xᵢ}(z)(fᵢ-rᵢ(z))-Z_{T}(z)W
+	accGamma.SetOne()
+	var gammaiZtMinusXi fr.Element
+	l := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
+	for i := 0; i < len(polynomials); i++ {
+
+		zi := eval(ztMinusXi[i], z)
+		gammaiZtMinusXi.Mul(&accGamma, &zi)
+		copy(bufMaxSizePolynomials, polynomials[i])
+		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &res.ClaimedValues[i])
+		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusXi)
+		for j := 0; j < len(bufMaxSizePolynomials); j++ {
+			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
+		}
+
+		setZero(bufMaxSizePolynomials)
+		accGamma.Mul(&accGamma, &gamma)
+	}
+	ztz := eval(zt, z)
+	setZero(bufTotalSize)
+	copy(bufTotalSize, w)
+	mulByConstant(bufTotalSize, ztz)
+	for i := 0; i < totalSize-maxSizePolys; i++ {
+		bufTotalSize[totalSize-1-i].Neg(&bufTotalSize[totalSize-1-i])
+	}
+	for i := 0; i < maxSizePolys; i++ {
+		bufTotalSize[i].Sub(&l[i], &bufTotalSize[i])
+	}
+
+	lz := eval(l, z)
+	l[0].Sub(&l[0], &lz)
+	xMinusZ := buildVanishingPoly([]fr.Element{z})
+	wPrime := div(l, xMinusZ)
+	res.WPrime, err = kzg.Commit(wPrime, pk)
+	if err != nil {
+		return res, err
+	}
 
 	return res, nil
 }
@@ -92,29 +163,29 @@ func BatchVerify(proof OpeningProof, commitments []kzg.Digest, points []fr.Eleme
 	return nil
 }
 
-// deriveGamma derives a challenge using Fiat Shamir to polynomials.
-func deriveGamma(points []fr.Element, digests []kzg.Digest, hf hash.Hash, dataTranscript ...[]byte) (fr.Element, error) {
+// deriveChallenge derives a challenge using Fiat Shamir to polynomials.
+// The arguments are added to the transcript in the order in which they are given.
+func deriveChallenge(name string, points []fr.Element, digests []kzg.Digest, t *fiatshamir.Transcript, dataTranscript ...[]byte) (fr.Element, error) {
 
 	// derive the challenge gamma, binded to the point and the commitments
-	fs := fiatshamir.NewTranscript(hf, "gamma")
 	for i := range points {
-		if err := fs.Bind("gamma", points[i].Marshal()); err != nil {
+		if err := t.Bind(name, points[i].Marshal()); err != nil {
 			return fr.Element{}, err
 		}
 	}
 	for i := range digests {
-		if err := fs.Bind("gamma", digests[i].Marshal()); err != nil {
+		if err := t.Bind(name, digests[i].Marshal()); err != nil {
 			return fr.Element{}, err
 		}
 	}
 
 	for i := 0; i < len(dataTranscript); i++ {
-		if err := fs.Bind("gamma", dataTranscript[i]); err != nil {
+		if err := t.Bind(name, dataTranscript[i]); err != nil {
 			return fr.Element{}, err
 		}
 	}
 
-	gammaByte, err := fs.ComputeChallenge("gamma")
+	gammaByte, err := t.ComputeChallenge(name)
 	if err != nil {
 		return fr.Element{}, err
 	}
@@ -127,6 +198,13 @@ func deriveGamma(points []fr.Element, digests []kzg.Digest, hf hash.Hash, dataTr
 // ------------------------------
 // utils
 
+// sets f to zero
+func setZero(f []fr.Element) {
+	for i := 0; i < len(f); i++ {
+		f[i].SetZero()
+	}
+}
+
 func eval(f []fr.Element, x fr.Element) fr.Element {
 	var y fr.Element
 	for i := len(f) - 1; i >= 0; i-- {
@@ -135,27 +213,7 @@ func eval(f []fr.Element, x fr.Element) fr.Element {
 	return y
 }
 
-// sets buf= f+g and returns buf (memory of f is re-used)
-func add(f, g, buf []fr.Element) []fr.Element {
-	maxSize := len(f)
-	if maxSize < len(g) {
-		maxSize = len(g)
-	}
-	if len(buf) < maxSize {
-		s := make([]fr.Element, maxSize-len(buf))
-		buf = append(buf, s...)
-	}
-	for i := 0; i < len(buf); i++ {
-		buf[i].SetZero()
-	}
-	copy(buf, f)
-	for i := 0; i < len(g); i++ {
-		buf[i].Add(&buf[i], &g[i])
-	}
-	return buf
-}
-
-// returns \gamma*f, re-using f
+// returns γ*f, re-using f
 func mulByConstant(f []fr.Element, gamma fr.Element) []fr.Element {
 	for i := 0; i < len(f); i++ {
 		f[i].Mul(&f[i], &gamma)
@@ -188,23 +246,21 @@ func buildVanishingPoly(x []fr.Element) []fr.Element {
 }
 
 // returns f*g using naive multiplication
-// deg(big)>>deg(small), deg(small) =~ 10 max
-// buf is used as a buffer
-func mul(big, small []fr.Element, buf []fr.Element) []fr.Element {
+// deg(f)>>deg(g), deg(small) =~ 10 max
+// buf is used as a buffer and should not be f or g
+func mul(f, g []fr.Element, buf []fr.Element) []fr.Element {
 
-	sizeRes := len(big) + len(small) - 1
+	sizeRes := len(f) + len(g) - 1
 	if len(buf) < sizeRes {
 		s := make([]fr.Element, sizeRes-len(buf))
 		buf = append(buf, s...)
 	}
-	for i := 0; i < len(buf); i++ {
-		buf[i].SetZero()
-	}
+	setZero(buf)
 
 	var tmp fr.Element
-	for i := 0; i < len(small); i++ {
-		for j := 0; j < len(big); j++ {
-			tmp.Mul(&big[j], &small[i])
+	for i := 0; i < len(g); i++ {
+		for j := 0; j < len(f); j++ {
+			tmp.Mul(&f[j], &g[i])
 			buf[j+i].Add(&buf[j+i], &tmp)
 		}
 	}

From bd81fc9fe7cf99d075a0e4b5309573b212f5b105 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 8 Mar 2024 14:45:22 +0100
Subject: [PATCH 009/114] feat: sage debugging, open ok

---
 ecc/bn254/shplonk/shplonk.go      | 123 +++++++++++++++++++++++++++---
 ecc/bn254/shplonk/shplonk_test.go |  64 ++++++++++++++++
 2 files changed, 178 insertions(+), 9 deletions(-)

diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
index f51318b09f..5c791a75d1 100644
--- a/ecc/bn254/shplonk/shplonk.go
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -18,8 +18,11 @@ package shplonk
 
 import (
 	"errors"
+	"fmt"
 	"hash"
+	"math/big"
 
+	"github.com/consensys/gnark-crypto/ecc"
 	"github.com/consensys/gnark-crypto/ecc/bn254"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
 	"github.com/consensys/gnark-crypto/ecc/bn254/kzg"
@@ -28,6 +31,7 @@ import (
 
 var (
 	ErrInvalidNumberOfPoints = errors.New("number of digests should be equal to the number of points")
+	ErrVerifyOpeningProof    = errors.New("can't verify batch opening proof")
 )
 
 // OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
@@ -45,6 +49,13 @@ type OpeningProof struct {
 	ClaimedValues []fr.Element
 }
 
+func prettyPrintPoly(f []fr.Element) {
+	for i := 0; i < len(f)-1; i++ {
+		fmt.Printf("%s*x**%d+", f[i].String(), i)
+	}
+	fmt.Printf("%s*x**%d\n", f[len(f)-1].String(), len(f)-1)
+}
+
 func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points []fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
 
 	var res OpeningProof
@@ -71,6 +82,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points []fr.Ele
 		}
 	}
 	totalSize := maxSizePolys + len(points) - 1 // maxSizePolys+len(points)-2 is the max degree among the polynomials Z_{T\xᵢ}fᵢ
+
 	bufTotalSize := make([]fr.Element, totalSize)
 	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
 	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
@@ -79,16 +91,18 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points []fr.Ele
 	res.ClaimedValues = make([]fr.Element, nbInstances)
 	var accGamma fr.Element
 	accGamma.SetOne()
+
+	fmt.Printf("gamma = Fr(%s)\n", gamma.String())
 	for i := 0; i < nbInstances; i++ {
 
 		res.ClaimedValues[i] = eval(polynomials[i], points[i])
 
 		copy(bufPoints, points[:i])
 		copy(bufPoints[i:], points[i+1:])
-
 		ztMinusXi[i] = buildVanishingPoly(bufPoints)
+
 		copy(bufMaxSizePolynomials, polynomials[i])
-		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &res.ClaimedValues[i]) // f-f(xᵢ)
+		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &res.ClaimedValues[i])
 		bufTotalSize = mul(bufMaxSizePolynomials, ztMinusXi[i], bufTotalSize)
 		bufTotalSize = mulByConstant(bufTotalSize, accGamma)
 		for j := 0; j < len(bufTotalSize); j++ {
@@ -98,6 +112,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points []fr.Ele
 		accGamma.Mul(&accGamma, &gamma)
 		setZero(bufMaxSizePolynomials)
 	}
+	// prettyPrintPoly(f)
 
 	zt := buildVanishingPoly(points)
 	w := div(f, zt) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
@@ -111,6 +126,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points []fr.Ele
 	if err != nil {
 		return res, err
 	}
+	fmt.Printf("z = Fr(%s)\n", z.String())
 
 	// compute L = ∑ᵢγⁱZ_{T\xᵢ}(z)(fᵢ-rᵢ(z))-Z_{T}(z)W
 	accGamma.SetOne()
@@ -135,16 +151,16 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points []fr.Ele
 	copy(bufTotalSize, w)
 	mulByConstant(bufTotalSize, ztz)
 	for i := 0; i < totalSize-maxSizePolys; i++ {
-		bufTotalSize[totalSize-1-i].Neg(&bufTotalSize[totalSize-1-i])
+		l[totalSize-1-i].Neg(&bufTotalSize[totalSize-1-i])
 	}
 	for i := 0; i < maxSizePolys; i++ {
-		bufTotalSize[i].Sub(&l[i], &bufTotalSize[i])
+		l[i].Sub(&l[i], &bufTotalSize[i])
 	}
 
-	lz := eval(l, z)
-	l[0].Sub(&l[0], &lz)
 	xMinusZ := buildVanishingPoly([]fr.Element{z})
 	wPrime := div(l, xMinusZ)
+	prettyPrintPoly(wPrime)
+
 	res.WPrime, err = kzg.Commit(wPrime, pk)
 	if err != nil {
 		return res, err
@@ -154,11 +170,100 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points []fr.Ele
 }
 
 // BatchVerify uses proof to check that the commitments correctly open to proof.ClaimedValues
-// at points. The order mattes: the proof validates that the i-th commitment is correctly opened
+// at points. The order matters: the proof validates that the i-th commitment is correctly opened
 // at the i-th point
-func BatchVerify(proof OpeningProof, commitments []kzg.Digest, points []fr.Element) error {
+// dataTranscript is some extra data that might be needed for Fiat Shamir, and is appended at the end
+// of the original transcript.
+func BatchVerify(proof OpeningProof, digests []kzg.Digest, points []fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
+
+	if len(digests) != len(proof.ClaimedValues) {
+		return ErrInvalidNumberOfPoints
+	}
+	if len(digests) != len(points) {
+		return ErrInvalidNumberOfPoints
+	}
+
+	// transcript
+	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
+
+	// derive γ
+	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
+	if err != nil {
+		return err
+	}
+
+	// derive z
+	// TODO seems ok that z depend only on W, need to check that carefully
+	z, err := deriveChallenge("z", nil, []kzg.Digest{proof.W}, fs)
+	if err != nil {
+		return err
+	}
 
-	// compute γ
+	// check that e(F + zW', [1]_{2})=e(W',[x]_{2})
+	// where F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}-[∑ᵢγⁱZ_{T\xᵢ}(z)fᵢ(z)]_{1}-Z_{T}(z)[W]
+	var sumGammaiZTminusXiFiz, tmp, accGamma fr.Element
+	nbInstances := len(points)
+	gammaiZTminusXiz := make([]fr.Element, nbInstances)
+	accGamma.SetOne()
+	bufPoints := make([]fr.Element, len(points)-1)
+	for i := 0; i < len(points); i++ {
+
+		copy(bufPoints, points[:i])
+		copy(bufPoints[i:], points[i+1:])
+
+		ztMinusXi := buildVanishingPoly(bufPoints)
+		gammaiZTminusXiz[i] = eval(ztMinusXi, z)
+		gammaiZTminusXiz[i].Mul(&accGamma, &gammaiZTminusXiz[i])
+
+		tmp.Mul(&gammaiZTminusXiz[i], &proof.ClaimedValues[i])
+		sumGammaiZTminusXiFiz.Add(&sumGammaiZTminusXiFiz, &tmp)
+
+		accGamma.Mul(&accGamma, &gamma)
+	}
+
+	// ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}
+	config := ecc.MultiExpConfig{}
+	var sumGammaiZtMinusXiComi kzg.Digest
+	_, err = sumGammaiZtMinusXiComi.MultiExp(digests, gammaiZTminusXiz, config)
+	if err != nil {
+		return err
+	}
+
+	var bufBigInt big.Int
+
+	// [∑ᵢZ_{T\xᵢ}fᵢ(z)]_{1}
+	var sumGammaiZTminusXiFizCom kzg.Digest
+	var sumGammaiZTminusXiFizBigInt big.Int
+	sumGammaiZTminusXiFiz.BigInt(&sumGammaiZTminusXiFizBigInt)
+	sumGammaiZTminusXiFizCom.ScalarMultiplication(&vk.G1, &sumGammaiZTminusXiFizBigInt)
+
+	// Z_{T}(z)[W]
+	zt := buildVanishingPoly(points)
+	ztz := eval(zt, z)
+	var ztW kzg.Digest
+	ztz.BigInt(&bufBigInt)
+	ztW.ScalarMultiplication(&proof.W, &bufBigInt)
+
+	// F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i} - [∑ᵢZ_{T\xᵢ}fᵢ(z)]_{1} - Z_{T}(z)[W]
+	var f kzg.Digest
+	f.Sub(&sumGammaiZtMinusXiComi, &sumGammaiZTminusXiFizCom).
+		Sub(&f, &ztW)
+
+	// F+zW'
+	var zWPrime kzg.Digest
+	z.BigInt(&bufBigInt)
+	zWPrime.ScalarMultiplication(&zWPrime, &bufBigInt)
+	f.Add(&f, &zWPrime)
+
+	// check that e(F+zW',[1]_{2})=e(W',[x]_{2})
+	check, err := bn254.PairingCheckFixedQ(
+		[]bn254.G1Affine{f, proof.WPrime},
+		vk.Lines[:],
+	)
+
+	if !check {
+		return ErrVerifyOpeningProof
+	}
 
 	return nil
 }
diff --git a/ecc/bn254/shplonk/shplonk_test.go b/ecc/bn254/shplonk/shplonk_test.go
index 62bec6a864..a7aa8ed20c 100644
--- a/ecc/bn254/shplonk/shplonk_test.go
+++ b/ecc/bn254/shplonk/shplonk_test.go
@@ -15,11 +15,75 @@
 package shplonk
 
 import (
+	"crypto/sha256"
+	"fmt"
+	"math/big"
 	"testing"
 
+	"github.com/consensys/gnark-crypto/ecc"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
+	"github.com/consensys/gnark-crypto/ecc/bn254/kzg"
+	"github.com/stretchr/testify/require"
 )
 
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *kzg.SRS
+var bAlpha *big.Int
+
+func init() {
+	const srsSize = 230
+	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+}
+
+func TestOpening(t *testing.T) {
+
+	assert := require.New(t)
+
+	nbPolys := 2
+	sizePoly := make([]int, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		sizePoly[i] = 5 + i
+	}
+	polys := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		polys[i] = make([]fr.Element, sizePoly[i])
+		for j := 0; j < sizePoly[i]; j++ {
+			polys[i][j].SetRandom()
+		}
+	}
+
+	for i := 0; i < nbPolys; i++ {
+		prettyPrintPoly(polys[i])
+	}
+	fmt.Println("--")
+
+	digests := make([]kzg.Digest, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		digests[i], _ = kzg.Commit(polys[i], testSrs.Pk)
+	}
+
+	points := make([]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		points[i].SetRandom()
+	}
+
+	fmt.Println("[")
+	for i := 0; i < len(points); i++ {
+		fmt.Printf("Fr(%s), ", points[i].String())
+	}
+	fmt.Println("]")
+
+	hf := sha256.New()
+
+	openingProof, err := BatchOpen(polys, digests, points, hf, testSrs.Pk)
+	assert.NoError(err)
+
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	assert.NoError(err)
+
+}
+
 func TestBuildVanishingPoly(t *testing.T) {
 	s := 10
 	x := make([]fr.Element, s)

From 390621f28e71abe11359b38a4217297697e69e90 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 8 Mar 2024 19:10:10 +0100
Subject: [PATCH 010/114] feat: debugged neg pairing

---
 ecc/bn254/shplonk/shplonk.go      | 23 +++++++----------------
 ecc/bn254/shplonk/shplonk_test.go | 12 ------------
 2 files changed, 7 insertions(+), 28 deletions(-)

diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
index 5c791a75d1..c7e6a4d6eb 100644
--- a/ecc/bn254/shplonk/shplonk.go
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -18,7 +18,6 @@ package shplonk
 
 import (
 	"errors"
-	"fmt"
 	"hash"
 	"math/big"
 
@@ -49,13 +48,6 @@ type OpeningProof struct {
 	ClaimedValues []fr.Element
 }
 
-func prettyPrintPoly(f []fr.Element) {
-	for i := 0; i < len(f)-1; i++ {
-		fmt.Printf("%s*x**%d+", f[i].String(), i)
-	}
-	fmt.Printf("%s*x**%d\n", f[len(f)-1].String(), len(f)-1)
-}
-
 func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points []fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
 
 	var res OpeningProof
@@ -92,7 +84,6 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points []fr.Ele
 	var accGamma fr.Element
 	accGamma.SetOne()
 
-	fmt.Printf("gamma = Fr(%s)\n", gamma.String())
 	for i := 0; i < nbInstances; i++ {
 
 		res.ClaimedValues[i] = eval(polynomials[i], points[i])
@@ -112,7 +103,6 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points []fr.Ele
 		accGamma.Mul(&accGamma, &gamma)
 		setZero(bufMaxSizePolynomials)
 	}
-	// prettyPrintPoly(f)
 
 	zt := buildVanishingPoly(points)
 	w := div(f, zt) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
@@ -126,7 +116,6 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points []fr.Ele
 	if err != nil {
 		return res, err
 	}
-	fmt.Printf("z = Fr(%s)\n", z.String())
 
 	// compute L = ∑ᵢγⁱZ_{T\xᵢ}(z)(fᵢ-rᵢ(z))-Z_{T}(z)W
 	accGamma.SetOne()
@@ -159,7 +148,6 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points []fr.Ele
 
 	xMinusZ := buildVanishingPoly([]fr.Element{z})
 	wPrime := div(l, xMinusZ)
-	prettyPrintPoly(wPrime)
 
 	res.WPrime, err = kzg.Commit(wPrime, pk)
 	if err != nil {
@@ -244,7 +232,7 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points []fr.Element,
 	ztz.BigInt(&bufBigInt)
 	ztW.ScalarMultiplication(&proof.W, &bufBigInt)
 
-	// F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i} - [∑ᵢZ_{T\xᵢ}fᵢ(z)]_{1} - Z_{T}(z)[W]
+	// F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i} - [∑ᵢ\gamma^{i}Z_{T\xᵢ}fᵢ(z)]_{1} - Z_{T}(z)[W]
 	var f kzg.Digest
 	f.Sub(&sumGammaiZtMinusXiComi, &sumGammaiZTminusXiFizCom).
 		Sub(&f, &ztW)
@@ -252,8 +240,9 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points []fr.Element,
 	// F+zW'
 	var zWPrime kzg.Digest
 	z.BigInt(&bufBigInt)
-	zWPrime.ScalarMultiplication(&zWPrime, &bufBigInt)
+	zWPrime.ScalarMultiplication(&proof.WPrime, &bufBigInt)
 	f.Add(&f, &zWPrime)
+	f.Neg(&f)
 
 	// check that e(F+zW',[1]_{2})=e(W',[x]_{2})
 	check, err := bn254.PairingCheckFixedQ(
@@ -326,7 +315,8 @@ func mulByConstant(f []fr.Element, gamma fr.Element) []fr.Element {
 	return f
 }
 
-// computes f <- (x-a)*f (in place if the capacity of f is correctly set)
+// computes f <- (x-a)*f
+// memory of f is re used, need to pass a copy to not modify it
 func multiplyLinearFactor(f []fr.Element, a fr.Element) []fr.Element {
 	s := len(f)
 	var tmp fr.Element
@@ -353,6 +343,7 @@ func buildVanishingPoly(x []fr.Element) []fr.Element {
 // returns f*g using naive multiplication
 // deg(f)>>deg(g), deg(small) =~ 10 max
 // buf is used as a buffer and should not be f or g
+// f and g are not modified
 func mul(f, g []fr.Element, buf []fr.Element) []fr.Element {
 
 	sizeRes := len(f) + len(g) - 1
@@ -375,7 +366,7 @@ func mul(f, g []fr.Element, buf []fr.Element) []fr.Element {
 // returns f/g (assuming g divides f)
 // OK to not use fft if deg(g) is small
 // g's leading coefficient is assumed to be 1
-// f memory is re-used for the result
+// f memory is re-used for the result, need to pass a copy to not modify it
 func div(f, g []fr.Element) []fr.Element {
 	sizef := len(f)
 	sizeg := len(g)
diff --git a/ecc/bn254/shplonk/shplonk_test.go b/ecc/bn254/shplonk/shplonk_test.go
index a7aa8ed20c..8945160b7b 100644
--- a/ecc/bn254/shplonk/shplonk_test.go
+++ b/ecc/bn254/shplonk/shplonk_test.go
@@ -16,7 +16,6 @@ package shplonk
 
 import (
 	"crypto/sha256"
-	"fmt"
 	"math/big"
 	"testing"
 
@@ -53,11 +52,6 @@ func TestOpening(t *testing.T) {
 		}
 	}
 
-	for i := 0; i < nbPolys; i++ {
-		prettyPrintPoly(polys[i])
-	}
-	fmt.Println("--")
-
 	digests := make([]kzg.Digest, nbPolys)
 	for i := 0; i < nbPolys; i++ {
 		digests[i], _ = kzg.Commit(polys[i], testSrs.Pk)
@@ -68,12 +62,6 @@ func TestOpening(t *testing.T) {
 		points[i].SetRandom()
 	}
 
-	fmt.Println("[")
-	for i := 0; i < len(points); i++ {
-		fmt.Printf("Fr(%s), ", points[i].String())
-	}
-	fmt.Println("]")
-
 	hf := sha256.New()
 
 	openingProof, err := BatchOpen(polys, digests, points, hf, testSrs.Pk)

From 50c6a26e2c2d6602573a02740e79427c79e96de7 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Sun, 10 Mar 2024 13:50:32 +0100
Subject: [PATCH 011/114] feat: interpolator ok

---
 ecc/bn254/shplonk/shplonk.go      | 14 +++++++++++-
 ecc/bn254/shplonk/shplonk_test.go | 38 +++++++++++++++++++++++++++++--
 2 files changed, 49 insertions(+), 3 deletions(-)

diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
index c7e6a4d6eb..7d8b250c38 100644
--- a/ecc/bn254/shplonk/shplonk.go
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -232,7 +232,7 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points []fr.Element,
 	ztz.BigInt(&bufBigInt)
 	ztW.ScalarMultiplication(&proof.W, &bufBigInt)
 
-	// F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i} - [∑ᵢ\gamma^{i}Z_{T\xᵢ}fᵢ(z)]_{1} - Z_{T}(z)[W]
+	// F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i} - [∑ᵢγⁱZ_{T\xᵢ}fᵢ(z)]_{1} - Z_{T}(z)[W]
 	var f kzg.Digest
 	f.Sub(&sumGammaiZtMinusXiComi, &sumGammaiZTminusXiFizCom).
 		Sub(&f, &ztW)
@@ -340,6 +340,18 @@ func buildVanishingPoly(x []fr.Element) []fr.Element {
 	return res
 }
 
+// returns f such that f(xⱼ)=δⁱⱼ
+func buildLagrangeFromDomain(x []fr.Element, i int) []fr.Element {
+	xx := make([]fr.Element, len(x)-1)
+	copy(xx, x[:i])
+	copy(xx[i:], x[i+1:])
+	res := buildVanishingPoly(xx)
+	d := eval(res, x[i])
+	d.Inverse(&d)
+	res = mulByConstant(res, d)
+	return res
+}
+
 // returns f*g using naive multiplication
 // deg(f)>>deg(g), deg(small) =~ 10 max
 // buf is used as a buffer and should not be f or g
diff --git a/ecc/bn254/shplonk/shplonk_test.go b/ecc/bn254/shplonk/shplonk_test.go
index 8945160b7b..f70ba9bb58 100644
--- a/ecc/bn254/shplonk/shplonk_test.go
+++ b/ecc/bn254/shplonk/shplonk_test.go
@@ -72,6 +72,40 @@ func TestOpening(t *testing.T) {
 
 }
 
+func TestBuildLagrangeFromDomain(t *testing.T) {
+
+	nbPoints := 10
+	points := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		points[i].SetRandom()
+	}
+	var r fr.Element
+	for i := 0; i < nbPoints; i++ {
+
+		l := buildLagrangeFromDomain(points, i)
+
+		// check that l(xᵢ)=1 and l(xⱼ)=0 for j!=i
+		for j := 0; j < nbPoints; j++ {
+			y := eval(l, points[j])
+			if i == j {
+				if !y.IsOne() {
+					t.Fatal("l_{i}(x_{i}) should be equal to 1")
+				}
+			} else {
+				if !y.IsZero() {
+					t.Fatal("l_{i}(x_{j}) where i!=j should be equal to 0")
+				}
+			}
+		}
+		r.SetRandom()
+		y := eval(l, r)
+		if y.IsZero() {
+			t.Fatal("l_{i}(x) should not be zero if x is random")
+		}
+	}
+
+}
+
 func TestBuildVanishingPoly(t *testing.T) {
 	s := 10
 	x := make([]fr.Element, s)
@@ -84,7 +118,7 @@ func TestBuildVanishingPoly(t *testing.T) {
 		t.Fatal("error degree r")
 	}
 
-	// check that r(x_{i})=0 for all i
+	// check that r(xᵢ)=0 for all i
 	for i := 0; i < len(x); i++ {
 		y := eval(r, x[i])
 		if !y.IsZero() {
@@ -142,7 +176,7 @@ func TestNaiveMul(t *testing.T) {
 	buf := make([]fr.Element, size+nbPoints-1)
 	g := mul(f, v, buf)
 
-	// check that g(x_{i}) = 0
+	// check that g(xᵢ) = 0
 	for i := 0; i < nbPoints; i++ {
 		y := eval(g, points[i])
 		if !y.IsZero() {

From 505f8fea366b6fb17b9426ca9110605d8df35be4 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Sun, 10 Mar 2024 18:46:29 +0100
Subject: [PATCH 012/114] feat: interpolate ok

---
 ecc/bn254/shplonk/shplonk.go      | 15 +++++++++++++++
 ecc/bn254/shplonk/shplonk_test.go | 19 +++++++++++++++++++
 2 files changed, 34 insertions(+)

diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
index 7d8b250c38..31e44c9052 100644
--- a/ecc/bn254/shplonk/shplonk.go
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -340,6 +340,21 @@ func buildVanishingPoly(x []fr.Element) []fr.Element {
 	return res
 }
 
+// returns f such that f(xᵢ)=yᵢ, x and y are assumed to be of the same size
+func interpolate(x, y []fr.Element) []fr.Element {
+
+	res := make([]fr.Element, len(x))
+	for i := 0; i < len(x); i++ {
+		li := buildLagrangeFromDomain(x, i)
+		li = mulByConstant(li, y[i])
+		for j := 0; j < len(x); j++ {
+			res[j].Add(&res[j], &li[j])
+		}
+	}
+
+	return res
+}
+
 // returns f such that f(xⱼ)=δⁱⱼ
 func buildLagrangeFromDomain(x []fr.Element, i int) []fr.Element {
 	xx := make([]fr.Element, len(x)-1)
diff --git a/ecc/bn254/shplonk/shplonk_test.go b/ecc/bn254/shplonk/shplonk_test.go
index f70ba9bb58..6a81569bbe 100644
--- a/ecc/bn254/shplonk/shplonk_test.go
+++ b/ecc/bn254/shplonk/shplonk_test.go
@@ -72,6 +72,25 @@ func TestOpening(t *testing.T) {
 
 }
 
+func TestInterpolate(t *testing.T) {
+
+	nbPoints := 10
+	x := make([]fr.Element, nbPoints)
+	y := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		y[i].SetRandom()
+	}
+	f := interpolate(x, y)
+	for i := 0; i < nbPoints; i++ {
+		fx := eval(f, x[i])
+		if !fx.Equal(&y[i]) {
+			t.Fatal("f(x_{i})!=y_{i}")
+		}
+	}
+
+}
+
 func TestBuildLagrangeFromDomain(t *testing.T) {
 
 	nbPoints := 10

From 9c726c593a6b5d6e117808a1133237df926524c0 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Sun, 10 Mar 2024 19:55:18 +0100
Subject: [PATCH 013/114] feat: TestBuildZtMinusSi ok

---
 ecc/bn254/shplonk/shplonk.go      | 458 ++++++++++++++++--------------
 ecc/bn254/shplonk/shplonk_test.go | 104 ++++---
 2 files changed, 319 insertions(+), 243 deletions(-)

diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
index 31e44c9052..887533f050 100644
--- a/ecc/bn254/shplonk/shplonk.go
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -18,10 +18,7 @@ package shplonk
 
 import (
 	"errors"
-	"hash"
-	"math/big"
 
-	"github.com/consensys/gnark-crypto/ecc"
 	"github.com/consensys/gnark-crypto/ecc/bn254"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
 	"github.com/consensys/gnark-crypto/ecc/bn254/kzg"
@@ -44,227 +41,251 @@ type OpeningProof struct {
 	// L(X)/(X-z) where L(X)=∑ᵢγⁱZ_{T\xᵢ}(f_i(X)-rᵢ) - Z_{T}W(X)
 	WPrime bn254.G1Affine
 
-	// (fᵢ(xᵢ))_{i}
-	ClaimedValues []fr.Element
+	// ClaimedValues[i] are the values of fᵢ on Sᵢ
+	ClaimedValues [][]fr.Element
 }
 
-func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points []fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
-
-	var res OpeningProof
-
-	nbInstances := len(polynomials)
-	if len(polynomials) != len(points) {
-		return res, ErrInvalidNumberOfPoints
-	}
-
-	// transcript
-	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
-
-	// derive γ
-	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
-	if err != nil {
-		return res, err
-	}
-
-	// compute the claimed evaluations
-	maxSizePolys := len(polynomials[0])
-	for i := 1; i < len(polynomials); i++ {
-		if maxSizePolys < len(polynomials[i]) {
-			maxSizePolys = len(polynomials[i])
-		}
-	}
-	totalSize := maxSizePolys + len(points) - 1 // maxSizePolys+len(points)-2 is the max degree among the polynomials Z_{T\xᵢ}fᵢ
-
-	bufTotalSize := make([]fr.Element, totalSize)
-	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
-	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
-	bufPoints := make([]fr.Element, nbInstances-1)
-	ztMinusXi := make([][]fr.Element, nbInstances)
-	res.ClaimedValues = make([]fr.Element, nbInstances)
-	var accGamma fr.Element
-	accGamma.SetOne()
-
-	for i := 0; i < nbInstances; i++ {
-
-		res.ClaimedValues[i] = eval(polynomials[i], points[i])
-
-		copy(bufPoints, points[:i])
-		copy(bufPoints[i:], points[i+1:])
-		ztMinusXi[i] = buildVanishingPoly(bufPoints)
-
-		copy(bufMaxSizePolynomials, polynomials[i])
-		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &res.ClaimedValues[i])
-		bufTotalSize = mul(bufMaxSizePolynomials, ztMinusXi[i], bufTotalSize)
-		bufTotalSize = mulByConstant(bufTotalSize, accGamma)
-		for j := 0; j < len(bufTotalSize); j++ {
-			f[j].Add(&f[j], &bufTotalSize[j])
-		}
-
-		accGamma.Mul(&accGamma, &gamma)
-		setZero(bufMaxSizePolynomials)
-	}
-
-	zt := buildVanishingPoly(points)
-	w := div(f, zt) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
-	res.W, err = kzg.Commit(w, pk)
-	if err != nil {
-		return res, err
-	}
-
-	// derive z
-	z, err := deriveChallenge("z", nil, []kzg.Digest{res.W}, fs)
-	if err != nil {
-		return res, err
-	}
-
-	// compute L = ∑ᵢγⁱZ_{T\xᵢ}(z)(fᵢ-rᵢ(z))-Z_{T}(z)W
-	accGamma.SetOne()
-	var gammaiZtMinusXi fr.Element
-	l := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
-	for i := 0; i < len(polynomials); i++ {
-
-		zi := eval(ztMinusXi[i], z)
-		gammaiZtMinusXi.Mul(&accGamma, &zi)
-		copy(bufMaxSizePolynomials, polynomials[i])
-		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &res.ClaimedValues[i])
-		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusXi)
-		for j := 0; j < len(bufMaxSizePolynomials); j++ {
-			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
-		}
-
-		setZero(bufMaxSizePolynomials)
-		accGamma.Mul(&accGamma, &gamma)
-	}
-	ztz := eval(zt, z)
-	setZero(bufTotalSize)
-	copy(bufTotalSize, w)
-	mulByConstant(bufTotalSize, ztz)
-	for i := 0; i < totalSize-maxSizePolys; i++ {
-		l[totalSize-1-i].Neg(&bufTotalSize[totalSize-1-i])
-	}
-	for i := 0; i < maxSizePolys; i++ {
-		l[i].Sub(&l[i], &bufTotalSize[i])
-	}
-
-	xMinusZ := buildVanishingPoly([]fr.Element{z})
-	wPrime := div(l, xMinusZ)
-
-	res.WPrime, err = kzg.Commit(wPrime, pk)
-	if err != nil {
-		return res, err
-	}
-
-	return res, nil
-}
+// BatchOpen opens the list of polynomials on points, where the i-th polynomials is opend at points[i].
+// func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
+
+// 	var res OpeningProof
+
+// 	nbInstances := len(polynomials)
+// 	if len(polynomials) != len(points) {
+// 		return res, ErrInvalidNumberOfPoints
+// 	}
+
+// 	// transcript
+// 	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
+
+// 	// derive γ
+// 	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
+// 	if err != nil {
+// 		return res, err
+// 	}
+
+// 	// compute the size of the linear combination
+// 	maxSizePolys := len(polynomials[0])
+// 	for i := 1; i < len(polynomials); i++ {
+// 		if maxSizePolys < len(polynomials[i]) {
+// 			maxSizePolys = len(polynomials[i])
+// 		}
+// 	}
+// 	nbPoints := 0
+// 	sizeSi := make([]int, len(points))
+// 	for i := 0; i < nbInstances; i++ {
+// 		nbPoints += len(points[i])
+// 		sizeSi[i] = len(points[i])
+// 	}
+// 	totalSize := 0
+// 	for i := 0; i < nbInstances; i++ {
+// 		sizeIthTerm := len(polynomials[i]) + nbPoints - len(points[i]) // the degree of the i-th term is len(polynomials[i])-1+nbPoints-len(points[i])
+// 		if totalSize < sizeIthTerm {
+// 			totalSize = sizeIthTerm
+// 		}
+// 	}
+
+// 	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
+// 	bufTotalSize := make([]fr.Element, totalSize)
+// 	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
+// 	res.ClaimedValues = make([][]fr.Element, nbInstances)
+// 	for i := 0; i < nbPoints; i++ {
+// 		res.ClaimedValues[i] = make([]fr.Element, len(points[i]))
+// 	}
+// 	var accGamma fr.Element
+// 	accGamma.SetOne()
+
+// 	ztMinusSi := make([][]fr.Element, nbInstances)
+// 	for i := 0; i < nbInstances; i++ {
+
+// 		for j := 0; j < len(points[i]); j++ {
+// 			res.ClaimedValues[i][j] = eval(polynomials[i], points[i][j])
+// 		}
+
+// 		bufPoints := make([]fr.Element, 0, nbPoints-sizeSi[i])
+// 		for j := 0; j < i; j++ {
+// 			bufPoints = append(bufPoints, points[j]...)
+// 		}
+// 		for j := i + 1; j < nbInstances; j++ {
+// 			bufPoints = append(bufPoints, points[j]...)
+// 		}
+// 		ztMinusSi[i] = buildVanishingPoly(bufPoints)
+
+// 		copy(bufMaxSizePolynomials, polynomials[i])
+// 		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &res.ClaimedValues[i])
+// 		bufTotalSize = mul(bufMaxSizePolynomials, ztMinusXi[i], bufTotalSize)
+// 		bufTotalSize = mulByConstant(bufTotalSize, accGamma)
+// 		for j := 0; j < len(bufTotalSize); j++ {
+// 			f[j].Add(&f[j], &bufTotalSize[j])
+// 		}
+
+// 		accGamma.Mul(&accGamma, &gamma)
+// 		setZero(bufMaxSizePolynomials)
+// 	}
+
+// 	zt := buildVanishingPoly(points)
+// 	w := div(f, zt) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
+// 	res.W, err = kzg.Commit(w, pk)
+// 	if err != nil {
+// 		return res, err
+// 	}
+
+// 	// derive z
+// 	z, err := deriveChallenge("z", nil, []kzg.Digest{res.W}, fs)
+// 	if err != nil {
+// 		return res, err
+// 	}
+
+// 	// compute L = ∑ᵢγⁱZ_{T\xᵢ}(z)(fᵢ-rᵢ(z))-Z_{T}(z)W
+// 	accGamma.SetOne()
+// 	var gammaiZtMinusXi fr.Element
+// 	l := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
+// 	for i := 0; i < len(polynomials); i++ {
+
+// 		zi := eval(ztMinusXi[i], z)
+// 		gammaiZtMinusXi.Mul(&accGamma, &zi)
+// 		copy(bufMaxSizePolynomials, polynomials[i])
+// 		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &res.ClaimedValues[i])
+// 		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusXi)
+// 		for j := 0; j < len(bufMaxSizePolynomials); j++ {
+// 			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
+// 		}
+
+// 		setZero(bufMaxSizePolynomials)
+// 		accGamma.Mul(&accGamma, &gamma)
+// 	}
+// 	ztz := eval(zt, z)
+// 	setZero(bufTotalSize)
+// 	copy(bufTotalSize, w)
+// 	mulByConstant(bufTotalSize, ztz)
+// 	for i := 0; i < totalSize-maxSizePolys; i++ {
+// 		l[totalSize-1-i].Neg(&bufTotalSize[totalSize-1-i])
+// 	}
+// 	for i := 0; i < maxSizePolys; i++ {
+// 		l[i].Sub(&l[i], &bufTotalSize[i])
+// 	}
+
+// 	xMinusZ := buildVanishingPoly([]fr.Element{z})
+// 	wPrime := div(l, xMinusZ)
+
+// 	res.WPrime, err = kzg.Commit(wPrime, pk)
+// 	if err != nil {
+// 		return res, err
+// 	}
+
+// 	return res, nil
+// }
 
 // BatchVerify uses proof to check that the commitments correctly open to proof.ClaimedValues
 // at points. The order matters: the proof validates that the i-th commitment is correctly opened
 // at the i-th point
 // dataTranscript is some extra data that might be needed for Fiat Shamir, and is appended at the end
 // of the original transcript.
-func BatchVerify(proof OpeningProof, digests []kzg.Digest, points []fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
-
-	if len(digests) != len(proof.ClaimedValues) {
-		return ErrInvalidNumberOfPoints
-	}
-	if len(digests) != len(points) {
-		return ErrInvalidNumberOfPoints
-	}
-
-	// transcript
-	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
-
-	// derive γ
-	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
-	if err != nil {
-		return err
-	}
-
-	// derive z
-	// TODO seems ok that z depend only on W, need to check that carefully
-	z, err := deriveChallenge("z", nil, []kzg.Digest{proof.W}, fs)
-	if err != nil {
-		return err
-	}
-
-	// check that e(F + zW', [1]_{2})=e(W',[x]_{2})
-	// where F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}-[∑ᵢγⁱZ_{T\xᵢ}(z)fᵢ(z)]_{1}-Z_{T}(z)[W]
-	var sumGammaiZTminusXiFiz, tmp, accGamma fr.Element
-	nbInstances := len(points)
-	gammaiZTminusXiz := make([]fr.Element, nbInstances)
-	accGamma.SetOne()
-	bufPoints := make([]fr.Element, len(points)-1)
-	for i := 0; i < len(points); i++ {
-
-		copy(bufPoints, points[:i])
-		copy(bufPoints[i:], points[i+1:])
-
-		ztMinusXi := buildVanishingPoly(bufPoints)
-		gammaiZTminusXiz[i] = eval(ztMinusXi, z)
-		gammaiZTminusXiz[i].Mul(&accGamma, &gammaiZTminusXiz[i])
-
-		tmp.Mul(&gammaiZTminusXiz[i], &proof.ClaimedValues[i])
-		sumGammaiZTminusXiFiz.Add(&sumGammaiZTminusXiFiz, &tmp)
-
-		accGamma.Mul(&accGamma, &gamma)
-	}
-
-	// ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}
-	config := ecc.MultiExpConfig{}
-	var sumGammaiZtMinusXiComi kzg.Digest
-	_, err = sumGammaiZtMinusXiComi.MultiExp(digests, gammaiZTminusXiz, config)
-	if err != nil {
-		return err
-	}
-
-	var bufBigInt big.Int
-
-	// [∑ᵢZ_{T\xᵢ}fᵢ(z)]_{1}
-	var sumGammaiZTminusXiFizCom kzg.Digest
-	var sumGammaiZTminusXiFizBigInt big.Int
-	sumGammaiZTminusXiFiz.BigInt(&sumGammaiZTminusXiFizBigInt)
-	sumGammaiZTminusXiFizCom.ScalarMultiplication(&vk.G1, &sumGammaiZTminusXiFizBigInt)
-
-	// Z_{T}(z)[W]
-	zt := buildVanishingPoly(points)
-	ztz := eval(zt, z)
-	var ztW kzg.Digest
-	ztz.BigInt(&bufBigInt)
-	ztW.ScalarMultiplication(&proof.W, &bufBigInt)
-
-	// F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i} - [∑ᵢγⁱZ_{T\xᵢ}fᵢ(z)]_{1} - Z_{T}(z)[W]
-	var f kzg.Digest
-	f.Sub(&sumGammaiZtMinusXiComi, &sumGammaiZTminusXiFizCom).
-		Sub(&f, &ztW)
-
-	// F+zW'
-	var zWPrime kzg.Digest
-	z.BigInt(&bufBigInt)
-	zWPrime.ScalarMultiplication(&proof.WPrime, &bufBigInt)
-	f.Add(&f, &zWPrime)
-	f.Neg(&f)
-
-	// check that e(F+zW',[1]_{2})=e(W',[x]_{2})
-	check, err := bn254.PairingCheckFixedQ(
-		[]bn254.G1Affine{f, proof.WPrime},
-		vk.Lines[:],
-	)
-
-	if !check {
-		return ErrVerifyOpeningProof
-	}
-
-	return nil
-}
+// func BatchVerify(proof OpeningProof, digests []kzg.Digest, points []fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
+
+// 	if len(digests) != len(proof.ClaimedValues) {
+// 		return ErrInvalidNumberOfPoints
+// 	}
+// 	if len(digests) != len(points) {
+// 		return ErrInvalidNumberOfPoints
+// 	}
+
+// 	// transcript
+// 	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
+
+// 	// derive γ
+// 	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
+// 	if err != nil {
+// 		return err
+// 	}
+
+// 	// derive z
+// 	// TODO seems ok that z depend only on W, need to check that carefully
+// 	z, err := deriveChallenge("z", nil, []kzg.Digest{proof.W}, fs)
+// 	if err != nil {
+// 		return err
+// 	}
+
+// 	// check that e(F + zW', [1]_{2})=e(W',[x]_{2})
+// 	// where F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}-[∑ᵢγⁱZ_{T\xᵢ}(z)fᵢ(z)]_{1}-Z_{T}(z)[W]
+// 	var sumGammaiZTminusXiFiz, tmp, accGamma fr.Element
+// 	nbInstances := len(points)
+// 	gammaiZTminusXiz := make([]fr.Element, nbInstances)
+// 	accGamma.SetOne()
+// 	bufPoints := make([]fr.Element, len(points)-1)
+// 	for i := 0; i < len(points); i++ {
+
+// 		copy(bufPoints, points[:i])
+// 		copy(bufPoints[i:], points[i+1:])
+
+// 		ztMinusXi := buildVanishingPoly(bufPoints)
+// 		gammaiZTminusXiz[i] = eval(ztMinusXi, z)
+// 		gammaiZTminusXiz[i].Mul(&accGamma, &gammaiZTminusXiz[i])
+
+// 		tmp.Mul(&gammaiZTminusXiz[i], &proof.ClaimedValues[i])
+// 		sumGammaiZTminusXiFiz.Add(&sumGammaiZTminusXiFiz, &tmp)
+
+// 		accGamma.Mul(&accGamma, &gamma)
+// 	}
+
+// 	// ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}
+// 	config := ecc.MultiExpConfig{}
+// 	var sumGammaiZtMinusXiComi kzg.Digest
+// 	_, err = sumGammaiZtMinusXiComi.MultiExp(digests, gammaiZTminusXiz, config)
+// 	if err != nil {
+// 		return err
+// 	}
+
+// 	var bufBigInt big.Int
+
+// 	// [∑ᵢZ_{T\xᵢ}fᵢ(z)]_{1}
+// 	var sumGammaiZTminusXiFizCom kzg.Digest
+// 	var sumGammaiZTminusXiFizBigInt big.Int
+// 	sumGammaiZTminusXiFiz.BigInt(&sumGammaiZTminusXiFizBigInt)
+// 	sumGammaiZTminusXiFizCom.ScalarMultiplication(&vk.G1, &sumGammaiZTminusXiFizBigInt)
+
+// 	// Z_{T}(z)[W]
+// 	zt := buildVanishingPoly(points)
+// 	ztz := eval(zt, z)
+// 	var ztW kzg.Digest
+// 	ztz.BigInt(&bufBigInt)
+// 	ztW.ScalarMultiplication(&proof.W, &bufBigInt)
+
+// 	// F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i} - [∑ᵢγⁱZ_{T\xᵢ}fᵢ(z)]_{1} - Z_{T}(z)[W]
+// 	var f kzg.Digest
+// 	f.Sub(&sumGammaiZtMinusXiComi, &sumGammaiZTminusXiFizCom).
+// 		Sub(&f, &ztW)
+
+// 	// F+zW'
+// 	var zWPrime kzg.Digest
+// 	z.BigInt(&bufBigInt)
+// 	zWPrime.ScalarMultiplication(&proof.WPrime, &bufBigInt)
+// 	f.Add(&f, &zWPrime)
+// 	f.Neg(&f)
+
+// 	// check that e(F+zW',[1]_{2})=e(W',[x]_{2})
+// 	check, err := bn254.PairingCheckFixedQ(
+// 		[]bn254.G1Affine{f, proof.WPrime},
+// 		vk.Lines[:],
+// 	)
+
+// 	if !check {
+// 		return ErrVerifyOpeningProof
+// 	}
+
+// 	return nil
+// }
 
 // deriveChallenge derives a challenge using Fiat Shamir to polynomials.
 // The arguments are added to the transcript in the order in which they are given.
-func deriveChallenge(name string, points []fr.Element, digests []kzg.Digest, t *fiatshamir.Transcript, dataTranscript ...[]byte) (fr.Element, error) {
+func deriveChallenge(name string, points [][]fr.Element, digests []kzg.Digest, t *fiatshamir.Transcript, dataTranscript ...[]byte) (fr.Element, error) {
 
 	// derive the challenge gamma, binded to the point and the commitments
 	for i := range points {
-		if err := t.Bind(name, points[i].Marshal()); err != nil {
-			return fr.Element{}, err
+		for j := range points[i] {
+			if err := t.Bind(name, points[i][j].Marshal()); err != nil {
+				return fr.Element{}, err
+			}
 		}
 	}
 	for i := range digests {
@@ -330,6 +351,23 @@ func multiplyLinearFactor(f []fr.Element, a fr.Element) []fr.Element {
 	return f
 }
 
+// returns S_{T\S_{i}} where S_{i}=x[i]
+func buildZtMinusSi(x [][]fr.Element, i int) []fr.Element {
+	nbPoints := 0
+	for i := 0; i < len(x); i++ {
+		nbPoints += len(x[i])
+	}
+	bufPoints := make([]fr.Element, 0, nbPoints-len(x[i]))
+	for j := 0; j < i; j++ {
+		bufPoints = append(bufPoints, x[j]...)
+	}
+	for j := i + 1; j < len(x); j++ {
+		bufPoints = append(bufPoints, x[j]...)
+	}
+	ztMinusSi := buildVanishingPoly(bufPoints)
+	return ztMinusSi
+}
+
 // returns πᵢ(X-xᵢ)
 func buildVanishingPoly(x []fr.Element) []fr.Element {
 	res := make([]fr.Element, 1, len(x)+1)
diff --git a/ecc/bn254/shplonk/shplonk_test.go b/ecc/bn254/shplonk/shplonk_test.go
index 6a81569bbe..dcc4912947 100644
--- a/ecc/bn254/shplonk/shplonk_test.go
+++ b/ecc/bn254/shplonk/shplonk_test.go
@@ -15,14 +15,12 @@
 package shplonk
 
 import (
-	"crypto/sha256"
 	"math/big"
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
 	"github.com/consensys/gnark-crypto/ecc/bn254/kzg"
-	"github.com/stretchr/testify/require"
 )
 
 // Test SRS re-used across tests of the KZG scheme
@@ -35,41 +33,81 @@ func init() {
 	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
 }
 
-func TestOpening(t *testing.T) {
-
-	assert := require.New(t)
-
-	nbPolys := 2
-	sizePoly := make([]int, nbPolys)
-	for i := 0; i < nbPolys; i++ {
-		sizePoly[i] = 5 + i
-	}
-	polys := make([][]fr.Element, nbPolys)
-	for i := 0; i < nbPolys; i++ {
-		polys[i] = make([]fr.Element, sizePoly[i])
-		for j := 0; j < sizePoly[i]; j++ {
-			polys[i][j].SetRandom()
+// func TestOpening(t *testing.T) {
+
+// 	assert := require.New(t)
+
+// 	nbPolys := 2
+// 	sizePoly := make([]int, nbPolys)
+// 	for i := 0; i < nbPolys; i++ {
+// 		sizePoly[i] = 5 + i
+// 	}
+// 	polys := make([][]fr.Element, nbPolys)
+// 	for i := 0; i < nbPolys; i++ {
+// 		polys[i] = make([]fr.Element, sizePoly[i])
+// 		for j := 0; j < sizePoly[i]; j++ {
+// 			polys[i][j].SetRandom()
+// 		}
+// 	}
+
+// 	digests := make([]kzg.Digest, nbPolys)
+// 	for i := 0; i < nbPolys; i++ {
+// 		digests[i], _ = kzg.Commit(polys[i], testSrs.Pk)
+// 	}
+
+// 	points := make([]fr.Element, nbPolys)
+// 	for i := 0; i < nbPolys; i++ {
+// 		points[i].SetRandom()
+// 	}
+
+// 	hf := sha256.New()
+
+// 	openingProof, err := BatchOpen(polys, digests, points, hf, testSrs.Pk)
+// 	assert.NoError(err)
+
+// 	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+// 	assert.NoError(err)
+
+// }
+
+func TestBuildZtMinusSi(t *testing.T) {
+
+	nbSi := 10
+	points := make([][]fr.Element, nbSi)
+	sizeSi := make([]int, nbSi)
+	nbPoints := 0
+	for i := 0; i < nbSi; i++ {
+		sizeSi[i] = 5 + i
+		nbPoints += sizeSi[i]
+		points[i] = make([]fr.Element, sizeSi[i])
+		for j := 0; j < sizeSi[i]; j++ {
+			points[i][j].SetRandom()
 		}
 	}
-
-	digests := make([]kzg.Digest, nbPolys)
-	for i := 0; i < nbPolys; i++ {
-		digests[i], _ = kzg.Commit(polys[i], testSrs.Pk)
-	}
-
-	points := make([]fr.Element, nbPolys)
-	for i := 0; i < nbPolys; i++ {
-		points[i].SetRandom()
+	for i := 0; i < nbSi; i++ {
+		ztMinusSi := buildZtMinusSi(points, i)
+		if len(ztMinusSi) != nbPoints-sizeSi[i]+1 {
+			t.Fatal("deg(Z_{T-S_{i}}) should be nbPoints-size(S_{i})")
+		}
+		for j := 0; j < nbSi; j++ {
+			if j == i {
+				for k := 0; k < sizeSi[j]; k++ {
+					y := eval(ztMinusSi, points[j][k])
+					if y.IsZero() {
+						t.Fatal("Z_{T-S_{i}}(S_{i}) should not be zero")
+					}
+				}
+				continue
+			}
+			for k := 0; k < sizeSi[j]; k++ {
+				y := eval(ztMinusSi, points[j][k])
+				if !y.IsZero() {
+					t.Fatal("Z_{T-S_{i}}(S_{j}) should be zero")
+				}
+			}
+		}
 	}
 
-	hf := sha256.New()
-
-	openingProof, err := BatchOpen(polys, digests, points, hf, testSrs.Pk)
-	assert.NoError(err)
-
-	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
-	assert.NoError(err)
-
 }
 
 func TestInterpolate(t *testing.T) {

From 05b330d65cbfd8da0fdb7da3e56ff5c7fa7b374a Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Sun, 10 Mar 2024 23:12:43 +0100
Subject: [PATCH 014/114] feat: single point to set in open

---
 ecc/bn254/shplonk/shplonk.go | 268 +++++++++++++++++++----------------
 1 file changed, 144 insertions(+), 124 deletions(-)

diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
index 887533f050..c9eb8b3bce 100644
--- a/ecc/bn254/shplonk/shplonk.go
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -18,6 +18,7 @@ package shplonk
 
 import (
 	"errors"
+	"hash"
 
 	"github.com/consensys/gnark-crypto/ecc/bn254"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
@@ -35,7 +36,8 @@ var (
 // implements io.ReaderFrom and io.WriterTo
 type OpeningProof struct {
 
-	// W = ∑ᵢ γⁱZ_{T\xᵢ}(f_i(X)-f(x_i)) where Z_{T} is the vanishing polynomial on the (xᵢ)_{i}
+	// W = ∑ᵢ γⁱZ_{T\Sᵢ}(f_i(X)-r)/Z_{T} where Z_{T} is the vanishing polynomial on the (Sᵢ)_{i}
+	// and r interpolates fᵢ(Sᵢ) on (Sᵢ)
 	W bn254.G1Affine
 
 	// L(X)/(X-z) where L(X)=∑ᵢγⁱZ_{T\xᵢ}(f_i(X)-rᵢ) - Z_{T}W(X)
@@ -46,135 +48,133 @@ type OpeningProof struct {
 }
 
 // BatchOpen opens the list of polynomials on points, where the i-th polynomials is opend at points[i].
-// func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
+func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
 
-// 	var res OpeningProof
+	var res OpeningProof
 
-// 	nbInstances := len(polynomials)
-// 	if len(polynomials) != len(points) {
-// 		return res, ErrInvalidNumberOfPoints
-// 	}
+	nbInstances := len(polynomials)
+	if len(polynomials) != len(points) {
+		return res, ErrInvalidNumberOfPoints
+	}
 
-// 	// transcript
-// 	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
+	// transcript
+	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
 
-// 	// derive γ
-// 	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
-// 	if err != nil {
-// 		return res, err
-// 	}
+	// derive γ
+	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
+	if err != nil {
+		return res, err
+	}
 
-// 	// compute the size of the linear combination
-// 	maxSizePolys := len(polynomials[0])
-// 	for i := 1; i < len(polynomials); i++ {
-// 		if maxSizePolys < len(polynomials[i]) {
-// 			maxSizePolys = len(polynomials[i])
-// 		}
-// 	}
-// 	nbPoints := 0
-// 	sizeSi := make([]int, len(points))
-// 	for i := 0; i < nbInstances; i++ {
-// 		nbPoints += len(points[i])
-// 		sizeSi[i] = len(points[i])
-// 	}
-// 	totalSize := 0
-// 	for i := 0; i < nbInstances; i++ {
-// 		sizeIthTerm := len(polynomials[i]) + nbPoints - len(points[i]) // the degree of the i-th term is len(polynomials[i])-1+nbPoints-len(points[i])
-// 		if totalSize < sizeIthTerm {
-// 			totalSize = sizeIthTerm
-// 		}
-// 	}
+	// compute the size of the linear combination
+	maxSizePolys := len(polynomials[0])
+	for i := 1; i < len(polynomials); i++ {
+		if maxSizePolys < len(polynomials[i]) {
+			maxSizePolys = len(polynomials[i])
+		}
+	}
+	nbPoints := 0
+	sizeSi := make([]int, len(points))
+	for i := 0; i < nbInstances; i++ {
+		nbPoints += len(points[i])
+		sizeSi[i] = len(points[i])
+	}
+	totalSize := 0 // size of f := ∑ᵢ γⁱZ_{T\Sᵢ}(f_i(X)-r)
+	for i := 0; i < nbInstances; i++ {
+		sizeIthTerm := len(polynomials[i]) + nbPoints - len(points[i]) // the degree of the i-th term is len(polynomials[i])-1+nbPoints-len(points[i])
+		if totalSize < sizeIthTerm {
+			totalSize = sizeIthTerm
+		}
+	}
 
-// 	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
-// 	bufTotalSize := make([]fr.Element, totalSize)
-// 	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
-// 	res.ClaimedValues = make([][]fr.Element, nbInstances)
-// 	for i := 0; i < nbPoints; i++ {
-// 		res.ClaimedValues[i] = make([]fr.Element, len(points[i]))
-// 	}
-// 	var accGamma fr.Element
-// 	accGamma.SetOne()
+	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
+	bufTotalSize := make([]fr.Element, totalSize)
+	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
+	res.ClaimedValues = make([][]fr.Element, nbInstances)
+	for i := 0; i < nbPoints; i++ {
+		res.ClaimedValues[i] = make([]fr.Element, len(points[i]))
+	}
+	var accGamma fr.Element
+	accGamma.SetOne()
 
-// 	ztMinusSi := make([][]fr.Element, nbInstances)
-// 	for i := 0; i < nbInstances; i++ {
-
-// 		for j := 0; j < len(points[i]); j++ {
-// 			res.ClaimedValues[i][j] = eval(polynomials[i], points[i][j])
-// 		}
-
-// 		bufPoints := make([]fr.Element, 0, nbPoints-sizeSi[i])
-// 		for j := 0; j < i; j++ {
-// 			bufPoints = append(bufPoints, points[j]...)
-// 		}
-// 		for j := i + 1; j < nbInstances; j++ {
-// 			bufPoints = append(bufPoints, points[j]...)
-// 		}
-// 		ztMinusSi[i] = buildVanishingPoly(bufPoints)
-
-// 		copy(bufMaxSizePolynomials, polynomials[i])
-// 		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &res.ClaimedValues[i])
-// 		bufTotalSize = mul(bufMaxSizePolynomials, ztMinusXi[i], bufTotalSize)
-// 		bufTotalSize = mulByConstant(bufTotalSize, accGamma)
-// 		for j := 0; j < len(bufTotalSize); j++ {
-// 			f[j].Add(&f[j], &bufTotalSize[j])
-// 		}
+	ztMinusSi := make([][]fr.Element, nbInstances)
+	ri := make([][]fr.Element, nbInstances)
+	for i := 0; i < nbInstances; i++ {
 
-// 		accGamma.Mul(&accGamma, &gamma)
-// 		setZero(bufMaxSizePolynomials)
-// 	}
+		for j := 0; j < len(points[i]); j++ {
+			res.ClaimedValues[i][j] = eval(polynomials[i], points[i][j])
+		}
 
-// 	zt := buildVanishingPoly(points)
-// 	w := div(f, zt) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
-// 	res.W, err = kzg.Commit(w, pk)
-// 	if err != nil {
-// 		return res, err
-// 	}
+		ztMinusSi[i] = buildZtMinusSi(points, i)
 
-// 	// derive z
-// 	z, err := deriveChallenge("z", nil, []kzg.Digest{res.W}, fs)
-// 	if err != nil {
-// 		return res, err
-// 	}
+		copy(bufMaxSizePolynomials, polynomials[i])
+		ri[i] = interpolate(points[i], res.ClaimedValues[i])
+		sub(bufMaxSizePolynomials, ri[i])
+		bufTotalSize = mul(bufMaxSizePolynomials, ztMinusSi[i], bufTotalSize)
+		bufTotalSize = mulByConstant(bufTotalSize, accGamma)
+		for j := 0; j < len(bufTotalSize); j++ {
+			f[j].Add(&f[j], &bufTotalSize[j])
+		}
 
-// 	// compute L = ∑ᵢγⁱZ_{T\xᵢ}(z)(fᵢ-rᵢ(z))-Z_{T}(z)W
-// 	accGamma.SetOne()
-// 	var gammaiZtMinusXi fr.Element
-// 	l := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
-// 	for i := 0; i < len(polynomials); i++ {
-
-// 		zi := eval(ztMinusXi[i], z)
-// 		gammaiZtMinusXi.Mul(&accGamma, &zi)
-// 		copy(bufMaxSizePolynomials, polynomials[i])
-// 		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &res.ClaimedValues[i])
-// 		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusXi)
-// 		for j := 0; j < len(bufMaxSizePolynomials); j++ {
-// 			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
-// 		}
-
-// 		setZero(bufMaxSizePolynomials)
-// 		accGamma.Mul(&accGamma, &gamma)
-// 	}
-// 	ztz := eval(zt, z)
-// 	setZero(bufTotalSize)
-// 	copy(bufTotalSize, w)
-// 	mulByConstant(bufTotalSize, ztz)
-// 	for i := 0; i < totalSize-maxSizePolys; i++ {
-// 		l[totalSize-1-i].Neg(&bufTotalSize[totalSize-1-i])
-// 	}
-// 	for i := 0; i < maxSizePolys; i++ {
-// 		l[i].Sub(&l[i], &bufTotalSize[i])
-// 	}
+		accGamma.Mul(&accGamma, &gamma)
+		setZero(bufMaxSizePolynomials)
+	}
 
-// 	xMinusZ := buildVanishingPoly([]fr.Element{z})
-// 	wPrime := div(l, xMinusZ)
+	zt := buildVanishingPoly(flatten(points))
+	w := div(f, zt) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
+	res.W, err = kzg.Commit(w, pk)
+	if err != nil {
+		return res, err
+	}
 
-// 	res.WPrime, err = kzg.Commit(wPrime, pk)
-// 	if err != nil {
-// 		return res, err
-// 	}
+	// derive z
+	z, err := deriveChallenge("z", nil, []kzg.Digest{res.W}, fs)
+	if err != nil {
+		return res, err
+	}
 
-// 	return res, nil
-// }
+	// compute L = ∑ᵢγⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))-Z_{T}(z)W
+	accGamma.SetOne()
+	var gammaiZtMinusSiZ fr.Element
+	l := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
+	for i := 0; i < len(polynomials); i++ {
+
+		ztMinusSiZ := eval(ztMinusSi[i], z)
+
+		gammaiZtMinusSiZ.Mul(&accGamma, &ztMinusSiZ)
+
+		copy(bufMaxSizePolynomials, polynomials[i])
+		riz := eval(ri[i], z)
+		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz)
+		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusSiZ)
+		for j := 0; j < len(bufMaxSizePolynomials); j++ {
+			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
+		}
+
+		setZero(bufMaxSizePolynomials)
+		accGamma.Mul(&accGamma, &gamma)
+	}
+	ztz := eval(zt, z)
+	setZero(bufTotalSize)
+	copy(bufTotalSize, w)
+	mulByConstant(bufTotalSize, ztz)
+	for i := 0; i < totalSize-maxSizePolys; i++ {
+		l[totalSize-1-i].Neg(&bufTotalSize[totalSize-1-i])
+	}
+	for i := 0; i < maxSizePolys; i++ {
+		l[i].Sub(&l[i], &bufTotalSize[i])
+	}
+
+	xMinusZ := buildVanishingPoly([]fr.Element{z})
+	wPrime := div(l, xMinusZ)
+
+	res.WPrime, err = kzg.Commit(wPrime, pk)
+	if err != nil {
+		return res, err
+	}
+
+	return res, nil
+}
 
 // BatchVerify uses proof to check that the commitments correctly open to proof.ClaimedValues
 // at points. The order matters: the proof validates that the i-th commitment is correctly opened
@@ -313,6 +313,18 @@ func deriveChallenge(name string, points [][]fr.Element, digests []kzg.Digest, t
 // ------------------------------
 // utils
 
+func flatten(x [][]fr.Element) []fr.Element {
+	nbPoints := 0
+	for i := 0; i < len(x); i++ {
+		nbPoints += len(x[i])
+	}
+	res := make([]fr.Element, 0, nbPoints)
+	for i := 0; i < len(x); i++ {
+		res = append(res, x[i]...)
+	}
+	return res
+}
+
 // sets f to zero
 func setZero(f []fr.Element) {
 	for i := 0; i < len(f); i++ {
@@ -351,7 +363,7 @@ func multiplyLinearFactor(f []fr.Element, a fr.Element) []fr.Element {
 	return f
 }
 
-// returns S_{T\S_{i}} where S_{i}=x[i]
+// returns S_{T\Sᵢ} where Sᵢ=x[i]
 func buildZtMinusSi(x [][]fr.Element, i int) []fr.Element {
 	nbPoints := 0
 	for i := 0; i < len(x); i++ {
@@ -405,27 +417,35 @@ func buildLagrangeFromDomain(x []fr.Element, i int) []fr.Element {
 	return res
 }
 
+// returns f-g, the memory of f is re used, deg(g) << deg(f) here
+func sub(f, g []fr.Element) []fr.Element {
+	for i := 0; i < len(g); i++ {
+		f[i].Sub(&f[i], &g[i])
+	}
+	return f
+}
+
 // returns f*g using naive multiplication
 // deg(f)>>deg(g), deg(small) =~ 10 max
 // buf is used as a buffer and should not be f or g
 // f and g are not modified
-func mul(f, g []fr.Element, buf []fr.Element) []fr.Element {
+func mul(f, g []fr.Element, res []fr.Element) []fr.Element {
 
 	sizeRes := len(f) + len(g) - 1
-	if len(buf) < sizeRes {
-		s := make([]fr.Element, sizeRes-len(buf))
-		buf = append(buf, s...)
+	if len(res) < sizeRes {
+		s := make([]fr.Element, sizeRes-len(res))
+		res = append(res, s...)
 	}
-	setZero(buf)
+	setZero(res)
 
 	var tmp fr.Element
 	for i := 0; i < len(g); i++ {
 		for j := 0; j < len(f); j++ {
 			tmp.Mul(&f[j], &g[i])
-			buf[j+i].Add(&buf[j+i], &tmp)
+			res[j+i].Add(&res[j+i], &tmp)
 		}
 	}
-	return buf
+	return res
 }
 
 // returns f/g (assuming g divides f)

From 23cc6fa3169c9eafaf9281c892eeeaf071c1d6ca Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Mon, 11 Mar 2024 11:38:43 +0100
Subject: [PATCH 015/114] fix: used upper bound of the total size in buf

---
 ecc/bn254/shplonk/shplonk.go      | 11 ++----
 ecc/bn254/shplonk/shplonk_test.go | 61 +++++++++++++++++--------------
 2 files changed, 36 insertions(+), 36 deletions(-)

diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
index c9eb8b3bce..2ab9fc95e1 100644
--- a/ecc/bn254/shplonk/shplonk.go
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -79,19 +79,13 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 		nbPoints += len(points[i])
 		sizeSi[i] = len(points[i])
 	}
-	totalSize := 0 // size of f := ∑ᵢ γⁱZ_{T\Sᵢ}(f_i(X)-r)
-	for i := 0; i < nbInstances; i++ {
-		sizeIthTerm := len(polynomials[i]) + nbPoints - len(points[i]) // the degree of the i-th term is len(polynomials[i])-1+nbPoints-len(points[i])
-		if totalSize < sizeIthTerm {
-			totalSize = sizeIthTerm
-		}
-	}
+	totalSize := maxSizePolys + nbPoints // upper bound of the size of f := ∑ᵢ γⁱZ_{T\Sᵢ}(f_i(X)-r)
 
 	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
 	bufTotalSize := make([]fr.Element, totalSize)
 	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
 	res.ClaimedValues = make([][]fr.Element, nbInstances)
-	for i := 0; i < nbPoints; i++ {
+	for i := 0; i < nbInstances; i++ {
 		res.ClaimedValues[i] = make([]fr.Element, len(points[i]))
 	}
 	var accGamma fr.Element
@@ -110,6 +104,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 		copy(bufMaxSizePolynomials, polynomials[i])
 		ri[i] = interpolate(points[i], res.ClaimedValues[i])
 		sub(bufMaxSizePolynomials, ri[i])
+
 		bufTotalSize = mul(bufMaxSizePolynomials, ztMinusSi[i], bufTotalSize)
 		bufTotalSize = mulByConstant(bufTotalSize, accGamma)
 		for j := 0; j < len(bufTotalSize); j++ {
diff --git a/ecc/bn254/shplonk/shplonk_test.go b/ecc/bn254/shplonk/shplonk_test.go
index dcc4912947..4a718bea51 100644
--- a/ecc/bn254/shplonk/shplonk_test.go
+++ b/ecc/bn254/shplonk/shplonk_test.go
@@ -15,12 +15,14 @@
 package shplonk
 
 import (
+	"crypto/sha256"
 	"math/big"
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
 	"github.com/consensys/gnark-crypto/ecc/bn254/kzg"
+	"github.com/stretchr/testify/require"
 )
 
 // Test SRS re-used across tests of the KZG scheme
@@ -33,42 +35,45 @@ func init() {
 	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
 }
 
-// func TestOpening(t *testing.T) {
+func TestOpening(t *testing.T) {
 
-// 	assert := require.New(t)
+	assert := require.New(t)
 
-// 	nbPolys := 2
-// 	sizePoly := make([]int, nbPolys)
-// 	for i := 0; i < nbPolys; i++ {
-// 		sizePoly[i] = 5 + i
-// 	}
-// 	polys := make([][]fr.Element, nbPolys)
-// 	for i := 0; i < nbPolys; i++ {
-// 		polys[i] = make([]fr.Element, sizePoly[i])
-// 		for j := 0; j < sizePoly[i]; j++ {
-// 			polys[i][j].SetRandom()
-// 		}
-// 	}
+	nbPolys := 2
+	sizePoly := make([]int, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		sizePoly[i] = 10 + i
+	}
+	polys := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		polys[i] = make([]fr.Element, sizePoly[i])
+		for j := 0; j < sizePoly[i]; j++ {
+			polys[i][j].SetRandom()
+		}
+	}
 
-// 	digests := make([]kzg.Digest, nbPolys)
-// 	for i := 0; i < nbPolys; i++ {
-// 		digests[i], _ = kzg.Commit(polys[i], testSrs.Pk)
-// 	}
+	digests := make([]kzg.Digest, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		digests[i], _ = kzg.Commit(polys[i], testSrs.Pk)
+	}
 
-// 	points := make([]fr.Element, nbPolys)
-// 	for i := 0; i < nbPolys; i++ {
-// 		points[i].SetRandom()
-// 	}
+	points := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		points[i] = make([]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			points[i][j].SetRandom()
+		}
+	}
 
-// 	hf := sha256.New()
+	hf := sha256.New()
 
-// 	openingProof, err := BatchOpen(polys, digests, points, hf, testSrs.Pk)
-// 	assert.NoError(err)
+	_, err := BatchOpen(polys, digests, points, hf, testSrs.Pk)
+	assert.NoError(err)
 
-// 	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
-// 	assert.NoError(err)
+	// err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	// assert.NoError(err)
 
-// }
+}
 
 func TestBuildZtMinusSi(t *testing.T) {
 

From aa57e6a71eac45a8d128f89e9099ee5dc03ffdf0 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Tue, 12 Mar 2024 09:39:55 +0100
Subject: [PATCH 016/114] feat: test ok

---
 ecc/bn254/shplonk/shplonk.go      | 202 +++++++++++++++---------------
 ecc/bn254/shplonk/shplonk_test.go |  11 +-
 2 files changed, 109 insertions(+), 104 deletions(-)

diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
index 2ab9fc95e1..b8b3cc1a25 100644
--- a/ecc/bn254/shplonk/shplonk.go
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -19,7 +19,9 @@ package shplonk
 import (
 	"errors"
 	"hash"
+	"math/big"
 
+	"github.com/consensys/gnark-crypto/ecc"
 	"github.com/consensys/gnark-crypto/ecc/bn254"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
 	"github.com/consensys/gnark-crypto/ecc/bn254/kzg"
@@ -134,14 +136,13 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	l := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
 	for i := 0; i < len(polynomials); i++ {
 
-		ztMinusSiZ := eval(ztMinusSi[i], z)
-
-		gammaiZtMinusSiZ.Mul(&accGamma, &ztMinusSiZ)
+		ztMinusSiZ := eval(ztMinusSi[i], z)          // Z_{T\Sᵢ}(z)
+		gammaiZtMinusSiZ.Mul(&accGamma, &ztMinusSiZ) // γⁱZ_{T\Sᵢ}(z)
 
 		copy(bufMaxSizePolynomials, polynomials[i])
 		riz := eval(ri[i], z)
-		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz)
-		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusSiZ)
+		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz) // (fᵢ-rᵢ(z))
+		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusSiZ)        // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
 		for j := 0; j < len(bufMaxSizePolynomials); j++ {
 			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
 		}
@@ -152,13 +153,13 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	ztz := eval(zt, z)
 	setZero(bufTotalSize)
 	copy(bufTotalSize, w)
-	mulByConstant(bufTotalSize, ztz)
+	mulByConstant(bufTotalSize, ztz) // Z_{T}(z)W
 	for i := 0; i < totalSize-maxSizePolys; i++ {
 		l[totalSize-1-i].Neg(&bufTotalSize[totalSize-1-i])
 	}
 	for i := 0; i < maxSizePolys; i++ {
 		l[i].Sub(&l[i], &bufTotalSize[i])
-	}
+	} // L <- L-Z_{T}(z)W
 
 	xMinusZ := buildVanishingPoly([]fr.Element{z})
 	wPrime := div(l, xMinusZ)
@@ -176,100 +177,99 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 // at the i-th point
 // dataTranscript is some extra data that might be needed for Fiat Shamir, and is appended at the end
 // of the original transcript.
-// func BatchVerify(proof OpeningProof, digests []kzg.Digest, points []fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
-
-// 	if len(digests) != len(proof.ClaimedValues) {
-// 		return ErrInvalidNumberOfPoints
-// 	}
-// 	if len(digests) != len(points) {
-// 		return ErrInvalidNumberOfPoints
-// 	}
-
-// 	// transcript
-// 	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
-
-// 	// derive γ
-// 	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
-// 	if err != nil {
-// 		return err
-// 	}
-
-// 	// derive z
-// 	// TODO seems ok that z depend only on W, need to check that carefully
-// 	z, err := deriveChallenge("z", nil, []kzg.Digest{proof.W}, fs)
-// 	if err != nil {
-// 		return err
-// 	}
-
-// 	// check that e(F + zW', [1]_{2})=e(W',[x]_{2})
-// 	// where F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}-[∑ᵢγⁱZ_{T\xᵢ}(z)fᵢ(z)]_{1}-Z_{T}(z)[W]
-// 	var sumGammaiZTminusXiFiz, tmp, accGamma fr.Element
-// 	nbInstances := len(points)
-// 	gammaiZTminusXiz := make([]fr.Element, nbInstances)
-// 	accGamma.SetOne()
-// 	bufPoints := make([]fr.Element, len(points)-1)
-// 	for i := 0; i < len(points); i++ {
-
-// 		copy(bufPoints, points[:i])
-// 		copy(bufPoints[i:], points[i+1:])
-
-// 		ztMinusXi := buildVanishingPoly(bufPoints)
-// 		gammaiZTminusXiz[i] = eval(ztMinusXi, z)
-// 		gammaiZTminusXiz[i].Mul(&accGamma, &gammaiZTminusXiz[i])
-
-// 		tmp.Mul(&gammaiZTminusXiz[i], &proof.ClaimedValues[i])
-// 		sumGammaiZTminusXiFiz.Add(&sumGammaiZTminusXiFiz, &tmp)
-
-// 		accGamma.Mul(&accGamma, &gamma)
-// 	}
-
-// 	// ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}
-// 	config := ecc.MultiExpConfig{}
-// 	var sumGammaiZtMinusXiComi kzg.Digest
-// 	_, err = sumGammaiZtMinusXiComi.MultiExp(digests, gammaiZTminusXiz, config)
-// 	if err != nil {
-// 		return err
-// 	}
-
-// 	var bufBigInt big.Int
-
-// 	// [∑ᵢZ_{T\xᵢ}fᵢ(z)]_{1}
-// 	var sumGammaiZTminusXiFizCom kzg.Digest
-// 	var sumGammaiZTminusXiFizBigInt big.Int
-// 	sumGammaiZTminusXiFiz.BigInt(&sumGammaiZTminusXiFizBigInt)
-// 	sumGammaiZTminusXiFizCom.ScalarMultiplication(&vk.G1, &sumGammaiZTminusXiFizBigInt)
-
-// 	// Z_{T}(z)[W]
-// 	zt := buildVanishingPoly(points)
-// 	ztz := eval(zt, z)
-// 	var ztW kzg.Digest
-// 	ztz.BigInt(&bufBigInt)
-// 	ztW.ScalarMultiplication(&proof.W, &bufBigInt)
-
-// 	// F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i} - [∑ᵢγⁱZ_{T\xᵢ}fᵢ(z)]_{1} - Z_{T}(z)[W]
-// 	var f kzg.Digest
-// 	f.Sub(&sumGammaiZtMinusXiComi, &sumGammaiZTminusXiFizCom).
-// 		Sub(&f, &ztW)
-
-// 	// F+zW'
-// 	var zWPrime kzg.Digest
-// 	z.BigInt(&bufBigInt)
-// 	zWPrime.ScalarMultiplication(&proof.WPrime, &bufBigInt)
-// 	f.Add(&f, &zWPrime)
-// 	f.Neg(&f)
-
-// 	// check that e(F+zW',[1]_{2})=e(W',[x]_{2})
-// 	check, err := bn254.PairingCheckFixedQ(
-// 		[]bn254.G1Affine{f, proof.WPrime},
-// 		vk.Lines[:],
-// 	)
-
-// 	if !check {
-// 		return ErrVerifyOpeningProof
-// 	}
-
-// 	return nil
-// }
+func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
+
+	if len(digests) != len(proof.ClaimedValues) {
+		return ErrInvalidNumberOfPoints
+	}
+	if len(digests) != len(points) {
+		return ErrInvalidNumberOfPoints
+	}
+
+	// transcript
+	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
+
+	// derive γ
+	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
+	if err != nil {
+		return err
+	}
+
+	// derive z
+	// TODO seems ok that z depend only on W, need to check that carefully
+	z, err := deriveChallenge("z", nil, []kzg.Digest{proof.W}, fs)
+	if err != nil {
+		return err
+	}
+
+	// check that e(F + zW', [1]_{2})=e(W',[x]_{2})
+	// where F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}-[∑ᵢγⁱZ_{T\xᵢ}(z)fᵢ(z)]_{1}-Z_{T}(z)[W]
+	var sumGammaiZTminusSiRiz, tmp, accGamma fr.Element
+	nbInstances := len(points)
+	gammaiZTminusSiz := make([]fr.Element, nbInstances)
+	accGamma.SetOne()
+	ri := make([][]fr.Element, nbInstances)
+	for i := 0; i < len(points); i++ {
+
+		ztMinusSi := buildZtMinusSi(points, i)                   // Z_{T-S_{i}}(X)
+		gammaiZTminusSiz[i] = eval(ztMinusSi, z)                 // Z_{T-S_{i}}(z)
+		gammaiZTminusSiz[i].Mul(&accGamma, &gammaiZTminusSiz[i]) // \gamma^{i} Z_{T-S_{i}}(z)
+
+		ri[i] = interpolate(points[i], proof.ClaimedValues[i])
+		riz := eval(ri[i], z)               // r_{i}(z)
+		tmp.Mul(&gammaiZTminusSiz[i], &riz) // Z_{T-S_{i}}(z)r_{i}(z)
+		sumGammaiZTminusSiRiz.Add(&sumGammaiZTminusSiRiz, &tmp)
+
+		accGamma.Mul(&accGamma, &gamma)
+	}
+
+	// ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}
+	config := ecc.MultiExpConfig{}
+	var sumGammaiZtMinusSiComi kzg.Digest
+	_, err = sumGammaiZtMinusSiComi.MultiExp(digests, gammaiZTminusSiz, config)
+	if err != nil {
+		return err
+	}
+
+	var bufBigInt big.Int
+
+	// [∑ᵢZ_{T\xᵢ}fᵢ(z)]_{1}
+	var sumGammaiZTminusSiRizCom kzg.Digest
+	var sumGammaiZTminusSiRizBigInt big.Int
+	sumGammaiZTminusSiRiz.BigInt(&sumGammaiZTminusSiRizBigInt)
+	sumGammaiZTminusSiRizCom.ScalarMultiplication(&vk.G1, &sumGammaiZTminusSiRizBigInt)
+
+	// Z_{T}(z)[W]
+	zt := buildVanishingPoly(flatten(points))
+	ztz := eval(zt, z)
+	var ztW kzg.Digest
+	ztz.BigInt(&bufBigInt)
+	ztW.ScalarMultiplication(&proof.W, &bufBigInt)
+
+	// F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i} - [∑ᵢγⁱZ_{T\xᵢ}fᵢ(z)]_{1} - Z_{T}(z)[W]
+	var f kzg.Digest
+	f.Sub(&sumGammaiZtMinusSiComi, &sumGammaiZTminusSiRizCom).
+		Sub(&f, &ztW)
+
+	// F+zW'
+	var zWPrime kzg.Digest
+	z.BigInt(&bufBigInt)
+	zWPrime.ScalarMultiplication(&proof.WPrime, &bufBigInt)
+	f.Add(&f, &zWPrime)
+	f.Neg(&f)
+
+	// check that e(F+zW',[1]_{2})=e(W',[x]_{2})
+	check, err := bn254.PairingCheckFixedQ(
+		[]bn254.G1Affine{f, proof.WPrime},
+		vk.Lines[:],
+	)
+
+	if !check {
+		return ErrVerifyOpeningProof
+	}
+
+	return nil
+}
 
 // deriveChallenge derives a challenge using Fiat Shamir to polynomials.
 // The arguments are added to the transcript in the order in which they are given.
diff --git a/ecc/bn254/shplonk/shplonk_test.go b/ecc/bn254/shplonk/shplonk_test.go
index 4a718bea51..2b082d16c8 100644
--- a/ecc/bn254/shplonk/shplonk_test.go
+++ b/ecc/bn254/shplonk/shplonk_test.go
@@ -67,11 +67,16 @@ func TestOpening(t *testing.T) {
 
 	hf := sha256.New()
 
-	_, err := BatchOpen(polys, digests, points, hf, testSrs.Pk)
+	// correct proof
+	openingProof, err := BatchOpen(polys, digests, points, hf, testSrs.Pk)
+	assert.NoError(err)
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
 	assert.NoError(err)
 
-	// err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
-	// assert.NoError(err)
+	// tampered proof
+	openingProof.ClaimedValues[0][0].SetRandom()
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	assert.Error(err)
 
 }
 

From 3c068623b62584b2425836a52ff51a46b0acf746 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Tue, 12 Mar 2024 15:42:44 +0100
Subject: [PATCH 017/114] feat: generator ok

---
 internal/generator/main.go                    |   4 +
 internal/generator/shplonk/generator.go       |  23 +
 .../generator/shplonk/template/doc.go.tmpl    |   2 +
 .../shplonk/template/shplonk.go.tmpl          | 444 ++++++++++++++++++
 .../shplonk/template/shplonk.test.go.tmpl     | 302 ++++++++++++
 5 files changed, 775 insertions(+)
 create mode 100644 internal/generator/shplonk/generator.go
 create mode 100644 internal/generator/shplonk/template/doc.go.tmpl
 create mode 100644 internal/generator/shplonk/template/shplonk.go.tmpl
 create mode 100644 internal/generator/shplonk/template/shplonk.test.go.tmpl

diff --git a/internal/generator/main.go b/internal/generator/main.go
index 389f96c2e0..32802d3fee 100644
--- a/internal/generator/main.go
+++ b/internal/generator/main.go
@@ -27,6 +27,7 @@ import (
 	"github.com/consensys/gnark-crypto/internal/generator/permutation"
 	"github.com/consensys/gnark-crypto/internal/generator/plookup"
 	"github.com/consensys/gnark-crypto/internal/generator/polynomial"
+	"github.com/consensys/gnark-crypto/internal/generator/shplonk"
 	"github.com/consensys/gnark-crypto/internal/generator/sis"
 	"github.com/consensys/gnark-crypto/internal/generator/sumcheck"
 	"github.com/consensys/gnark-crypto/internal/generator/test_vector_utils"
@@ -99,6 +100,9 @@ func main() {
 			// generate kzg on fr
 			assertNoError(kzg.Generate(conf, filepath.Join(curveDir, "kzg"), bgen))
 
+			// generate shplonk on fr
+			assertNoError(shplonk.Generate(conf, filepath.Join(curveDir, "shplonk"), bgen))
+
 			// generate pedersen on fr
 			assertNoError(pedersen.Generate(conf, filepath.Join(curveDir, "fr", "pedersen"), bgen))
 
diff --git a/internal/generator/shplonk/generator.go b/internal/generator/shplonk/generator.go
new file mode 100644
index 0000000000..789ab126b4
--- /dev/null
+++ b/internal/generator/shplonk/generator.go
@@ -0,0 +1,23 @@
+package shplonk
+
+import (
+	"path/filepath"
+
+	"github.com/consensys/bavard"
+	"github.com/consensys/gnark-crypto/internal/generator/config"
+)
+
+func Generate(conf config.Curve, baseDir string, bgen *bavard.BatchGenerator) error {
+
+	// kzg commitment scheme
+	conf.Package = "shplonk"
+	entries := []bavard.Entry{
+		{File: filepath.Join(baseDir, "doc.go"), Templates: []string{"doc.go.tmpl"}},
+		{File: filepath.Join(baseDir, "shplonk.go"), Templates: []string{"shplonk.go.tmpl"}},
+		{File: filepath.Join(baseDir, "shplonk_test.go"), Templates: []string{"shplonk.test.go.tmpl"}},
+		// {File: filepath.Join(baseDir, "marshal.go"), Templates: []string{"marshal.go.tmpl"}},
+		// {File: filepath.Join(baseDir, "utils.go"), Templates: []string{"utils.go.tmpl"}},
+	}
+	return bgen.Generate(conf, conf.Package, "./shplonk/template/", entries...)
+
+}
diff --git a/internal/generator/shplonk/template/doc.go.tmpl b/internal/generator/shplonk/template/doc.go.tmpl
new file mode 100644
index 0000000000..3a63b76f90
--- /dev/null
+++ b/internal/generator/shplonk/template/doc.go.tmpl
@@ -0,0 +1,2 @@
+// Package {{.Package}} provides a SHPLONK commitment scheme, cf https://eprint.iacr.org/2020/081.pdf
+package {{.Package}}
\ No newline at end of file
diff --git a/internal/generator/shplonk/template/shplonk.go.tmpl b/internal/generator/shplonk/template/shplonk.go.tmpl
new file mode 100644
index 0000000000..c5f8fcbee4
--- /dev/null
+++ b/internal/generator/shplonk/template/shplonk.go.tmpl
@@ -0,0 +1,444 @@
+import (
+	"errors"
+	"hash"
+	"math/big"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}"
+	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/fr"
+	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/kzg"
+	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
+)
+
+var (
+	ErrInvalidNumberOfPoints = errors.New("number of digests should be equal to the number of points")
+	ErrVerifyOpeningProof    = errors.New("can't verify batch opening proof")
+)
+
+// OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
+//
+// implements io.ReaderFrom and io.WriterTo
+type OpeningProof struct {
+
+	// W = ∑ᵢ γⁱZ_{T\Sᵢ}(f_i(X)-r)/Z_{T} where Z_{T} is the vanishing polynomial on the (Sᵢ)_{i}
+	// and r interpolates fᵢ(Sᵢ) on (Sᵢ)
+	W {{ .CurvePackage }}.G1Affine
+
+	// L(X)/(X-z) where L(X)=∑ᵢγⁱZ_{T\xᵢ}(f_i(X)-rᵢ) - Z_{T}W(X)
+	WPrime {{ .CurvePackage }}.G1Affine
+
+	// ClaimedValues[i] are the values of fᵢ on Sᵢ
+	ClaimedValues [][]fr.Element
+}
+
+// BatchOpen opens the list of polynomials on points, where the i-th polynomials is opend at points[i].
+func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
+
+	var res OpeningProof
+
+	nbInstances := len(polynomials)
+	if len(polynomials) != len(points) {
+		return res, ErrInvalidNumberOfPoints
+	}
+
+	// transcript
+	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
+
+	// derive γ
+	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
+	if err != nil {
+		return res, err
+	}
+
+	// compute the size of the linear combination
+	maxSizePolys := len(polynomials[0])
+	for i := 1; i < len(polynomials); i++ {
+		if maxSizePolys < len(polynomials[i]) {
+			maxSizePolys = len(polynomials[i])
+		}
+	}
+	nbPoints := 0
+	sizeSi := make([]int, len(points))
+	for i := 0; i < nbInstances; i++ {
+		nbPoints += len(points[i])
+		sizeSi[i] = len(points[i])
+	}
+	totalSize := maxSizePolys + nbPoints // upper bound of the size of f := ∑ᵢ γⁱZ_{T\Sᵢ}(f_i(X)-r)
+
+	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
+	bufTotalSize := make([]fr.Element, totalSize)
+	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
+	res.ClaimedValues = make([][]fr.Element, nbInstances)
+	for i := 0; i < nbInstances; i++ {
+		res.ClaimedValues[i] = make([]fr.Element, len(points[i]))
+	}
+	var accGamma fr.Element
+	accGamma.SetOne()
+
+	ztMinusSi := make([][]fr.Element, nbInstances)
+	ri := make([][]fr.Element, nbInstances)
+	for i := 0; i < nbInstances; i++ {
+
+		for j := 0; j < len(points[i]); j++ {
+			res.ClaimedValues[i][j] = eval(polynomials[i], points[i][j])
+		}
+
+		ztMinusSi[i] = buildZtMinusSi(points, i)
+
+		copy(bufMaxSizePolynomials, polynomials[i])
+		ri[i] = interpolate(points[i], res.ClaimedValues[i])
+		sub(bufMaxSizePolynomials, ri[i])
+
+		bufTotalSize = mul(bufMaxSizePolynomials, ztMinusSi[i], bufTotalSize)
+		bufTotalSize = mulByConstant(bufTotalSize, accGamma)
+		for j := 0; j < len(bufTotalSize); j++ {
+			f[j].Add(&f[j], &bufTotalSize[j])
+		}
+
+		accGamma.Mul(&accGamma, &gamma)
+		setZero(bufMaxSizePolynomials)
+	}
+
+	zt := buildVanishingPoly(flatten(points))
+	w := div(f, zt) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
+	res.W, err = kzg.Commit(w, pk)
+	if err != nil {
+		return res, err
+	}
+
+	// derive z
+	z, err := deriveChallenge("z", nil, []kzg.Digest{res.W}, fs)
+	if err != nil {
+		return res, err
+	}
+
+	// compute L = ∑ᵢγⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))-Z_{T}(z)W
+	accGamma.SetOne()
+	var gammaiZtMinusSiZ fr.Element
+	l := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
+	for i := 0; i < len(polynomials); i++ {
+
+		ztMinusSiZ := eval(ztMinusSi[i], z)          // Z_{T\Sᵢ}(z)
+		gammaiZtMinusSiZ.Mul(&accGamma, &ztMinusSiZ) // γⁱZ_{T\Sᵢ}(z)
+
+		copy(bufMaxSizePolynomials, polynomials[i])
+		riz := eval(ri[i], z)
+		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz) // (fᵢ-rᵢ(z))
+		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusSiZ)        // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
+		for j := 0; j < len(bufMaxSizePolynomials); j++ {
+			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
+		}
+
+		setZero(bufMaxSizePolynomials)
+		accGamma.Mul(&accGamma, &gamma)
+	}
+	ztz := eval(zt, z)
+	setZero(bufTotalSize)
+	copy(bufTotalSize, w)
+	mulByConstant(bufTotalSize, ztz) // Z_{T}(z)W
+	for i := 0; i < totalSize-maxSizePolys; i++ {
+		l[totalSize-1-i].Neg(&bufTotalSize[totalSize-1-i])
+	}
+	for i := 0; i < maxSizePolys; i++ {
+		l[i].Sub(&l[i], &bufTotalSize[i])
+	} // L <- L-Z_{T}(z)W
+
+	xMinusZ := buildVanishingPoly([]fr.Element{z})
+	wPrime := div(l, xMinusZ)
+
+	res.WPrime, err = kzg.Commit(wPrime, pk)
+	if err != nil {
+		return res, err
+	}
+
+	return res, nil
+}
+
+// BatchVerify uses proof to check that the commitments correctly open to proof.ClaimedValues
+// at points. The order matters: the proof validates that the i-th commitment is correctly opened
+// at the i-th point
+// dataTranscript is some extra data that might be needed for Fiat Shamir, and is appended at the end
+// of the original transcript.
+func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
+
+	if len(digests) != len(proof.ClaimedValues) {
+		return ErrInvalidNumberOfPoints
+	}
+	if len(digests) != len(points) {
+		return ErrInvalidNumberOfPoints
+	}
+
+	// transcript
+	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
+
+	// derive γ
+	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
+	if err != nil {
+		return err
+	}
+
+	// derive z
+	// TODO seems ok that z depend only on W, need to check that carefully
+	z, err := deriveChallenge("z", nil, []kzg.Digest{proof.W}, fs)
+	if err != nil {
+		return err
+	}
+
+	// check that e(F + zW', [1]_{2})=e(W',[x]_{2})
+	// where F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}-[∑ᵢγⁱZ_{T\xᵢ}(z)fᵢ(z)]_{1}-Z_{T}(z)[W]
+	var sumGammaiZTminusSiRiz, tmp, accGamma fr.Element
+	nbInstances := len(points)
+	gammaiZTminusSiz := make([]fr.Element, nbInstances)
+	accGamma.SetOne()
+	ri := make([][]fr.Element, nbInstances)
+	for i := 0; i < len(points); i++ {
+
+		ztMinusSi := buildZtMinusSi(points, i)                   // Z_{T-S_{i}}(X)
+		gammaiZTminusSiz[i] = eval(ztMinusSi, z)                 // Z_{T-S_{i}}(z)
+		gammaiZTminusSiz[i].Mul(&accGamma, &gammaiZTminusSiz[i]) // \gamma^{i} Z_{T-S_{i}}(z)
+
+		ri[i] = interpolate(points[i], proof.ClaimedValues[i])
+		riz := eval(ri[i], z)               // r_{i}(z)
+		tmp.Mul(&gammaiZTminusSiz[i], &riz) // Z_{T-S_{i}}(z)r_{i}(z)
+		sumGammaiZTminusSiRiz.Add(&sumGammaiZTminusSiRiz, &tmp)
+
+		accGamma.Mul(&accGamma, &gamma)
+	}
+
+	// ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}
+	config := ecc.MultiExpConfig{}
+	var sumGammaiZtMinusSiComi kzg.Digest
+	_, err = sumGammaiZtMinusSiComi.MultiExp(digests, gammaiZTminusSiz, config)
+	if err != nil {
+		return err
+	}
+
+	var bufBigInt big.Int
+
+	// [∑ᵢZ_{T\xᵢ}fᵢ(z)]_{1}
+	var sumGammaiZTminusSiRizCom kzg.Digest
+	var sumGammaiZTminusSiRizBigInt big.Int
+	sumGammaiZTminusSiRiz.BigInt(&sumGammaiZTminusSiRizBigInt)
+	sumGammaiZTminusSiRizCom.ScalarMultiplication(&vk.G1, &sumGammaiZTminusSiRizBigInt)
+
+	// Z_{T}(z)[W]
+	zt := buildVanishingPoly(flatten(points))
+	ztz := eval(zt, z)
+	var ztW kzg.Digest
+	ztz.BigInt(&bufBigInt)
+	ztW.ScalarMultiplication(&proof.W, &bufBigInt)
+
+	// F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i} - [∑ᵢγⁱZ_{T\xᵢ}fᵢ(z)]_{1} - Z_{T}(z)[W]
+	var f kzg.Digest
+	f.Sub(&sumGammaiZtMinusSiComi, &sumGammaiZTminusSiRizCom).
+		Sub(&f, &ztW)
+
+	// F+zW'
+	var zWPrime kzg.Digest
+	z.BigInt(&bufBigInt)
+	zWPrime.ScalarMultiplication(&proof.WPrime, &bufBigInt)
+	f.Add(&f, &zWPrime)
+	f.Neg(&f)
+
+	// check that e(F+zW',[1]_{2})=e(W',[x]_{2})
+	check, err := {{ .CurvePackage }}.PairingCheckFixedQ(
+		[]{{ .CurvePackage }}.G1Affine{f, proof.WPrime},
+		vk.Lines[:],
+	)
+
+	if !check {
+		return ErrVerifyOpeningProof
+	}
+
+	return nil
+}
+
+// deriveChallenge derives a challenge using Fiat Shamir to polynomials.
+// The arguments are added to the transcript in the order in which they are given.
+func deriveChallenge(name string, points [][]fr.Element, digests []kzg.Digest, t *fiatshamir.Transcript, dataTranscript ...[]byte) (fr.Element, error) {
+
+	// derive the challenge gamma, binded to the point and the commitments
+	for i := range points {
+		for j := range points[i] {
+			if err := t.Bind(name, points[i][j].Marshal()); err != nil {
+				return fr.Element{}, err
+			}
+		}
+	}
+	for i := range digests {
+		if err := t.Bind(name, digests[i].Marshal()); err != nil {
+			return fr.Element{}, err
+		}
+	}
+
+	for i := 0; i < len(dataTranscript); i++ {
+		if err := t.Bind(name, dataTranscript[i]); err != nil {
+			return fr.Element{}, err
+		}
+	}
+
+	gammaByte, err := t.ComputeChallenge(name)
+	if err != nil {
+		return fr.Element{}, err
+	}
+	var gamma fr.Element
+	gamma.SetBytes(gammaByte)
+
+	return gamma, nil
+}
+
+// ------------------------------
+// utils
+
+func flatten(x [][]fr.Element) []fr.Element {
+	nbPoints := 0
+	for i := 0; i < len(x); i++ {
+		nbPoints += len(x[i])
+	}
+	res := make([]fr.Element, 0, nbPoints)
+	for i := 0; i < len(x); i++ {
+		res = append(res, x[i]...)
+	}
+	return res
+}
+
+// sets f to zero
+func setZero(f []fr.Element) {
+	for i := 0; i < len(f); i++ {
+		f[i].SetZero()
+	}
+}
+
+func eval(f []fr.Element, x fr.Element) fr.Element {
+	var y fr.Element
+	for i := len(f) - 1; i >= 0; i-- {
+		y.Mul(&y, &x).Add(&y, &f[i])
+	}
+	return y
+}
+
+// returns γ*f, re-using f
+func mulByConstant(f []fr.Element, gamma fr.Element) []fr.Element {
+	for i := 0; i < len(f); i++ {
+		f[i].Mul(&f[i], &gamma)
+	}
+	return f
+}
+
+// computes f <- (x-a)*f
+// memory of f is re used, need to pass a copy to not modify it
+func multiplyLinearFactor(f []fr.Element, a fr.Element) []fr.Element {
+	s := len(f)
+	var tmp fr.Element
+	f = append(f, fr.NewElement(0))
+	f[s] = f[s-1]
+	for i := s - 1; i >= 1; i-- {
+		tmp.Mul(&f[i], &a)
+		f[i].Sub(&f[i-1], &tmp)
+	}
+	f[0].Mul(&f[0], &a).Neg(&f[0])
+	return f
+}
+
+// returns S_{T\Sᵢ} where Sᵢ=x[i]
+func buildZtMinusSi(x [][]fr.Element, i int) []fr.Element {
+	nbPoints := 0
+	for i := 0; i < len(x); i++ {
+		nbPoints += len(x[i])
+	}
+	bufPoints := make([]fr.Element, 0, nbPoints-len(x[i]))
+	for j := 0; j < i; j++ {
+		bufPoints = append(bufPoints, x[j]...)
+	}
+	for j := i + 1; j < len(x); j++ {
+		bufPoints = append(bufPoints, x[j]...)
+	}
+	ztMinusSi := buildVanishingPoly(bufPoints)
+	return ztMinusSi
+}
+
+// returns πᵢ(X-xᵢ)
+func buildVanishingPoly(x []fr.Element) []fr.Element {
+	res := make([]fr.Element, 1, len(x)+1)
+	res[0].SetOne()
+	for i := 0; i < len(x); i++ {
+		res = multiplyLinearFactor(res, x[i])
+	}
+	return res
+}
+
+// returns f such that f(xᵢ)=yᵢ, x and y are assumed to be of the same size
+func interpolate(x, y []fr.Element) []fr.Element {
+
+	res := make([]fr.Element, len(x))
+	for i := 0; i < len(x); i++ {
+		li := buildLagrangeFromDomain(x, i)
+		li = mulByConstant(li, y[i])
+		for j := 0; j < len(x); j++ {
+			res[j].Add(&res[j], &li[j])
+		}
+	}
+
+	return res
+}
+
+// returns f such that f(xⱼ)=δⁱⱼ
+func buildLagrangeFromDomain(x []fr.Element, i int) []fr.Element {
+	xx := make([]fr.Element, len(x)-1)
+	copy(xx, x[:i])
+	copy(xx[i:], x[i+1:])
+	res := buildVanishingPoly(xx)
+	d := eval(res, x[i])
+	d.Inverse(&d)
+	res = mulByConstant(res, d)
+	return res
+}
+
+// returns f-g, the memory of f is re used, deg(g) << deg(f) here
+func sub(f, g []fr.Element) []fr.Element {
+	for i := 0; i < len(g); i++ {
+		f[i].Sub(&f[i], &g[i])
+	}
+	return f
+}
+
+// returns f*g using naive multiplication
+// deg(f)>>deg(g), deg(small) =~ 10 max
+// buf is used as a buffer and should not be f or g
+// f and g are not modified
+func mul(f, g []fr.Element, res []fr.Element) []fr.Element {
+
+	sizeRes := len(f) + len(g) - 1
+	if len(res) < sizeRes {
+		s := make([]fr.Element, sizeRes-len(res))
+		res = append(res, s...)
+	}
+	setZero(res)
+
+	var tmp fr.Element
+	for i := 0; i < len(g); i++ {
+		for j := 0; j < len(f); j++ {
+			tmp.Mul(&f[j], &g[i])
+			res[j+i].Add(&res[j+i], &tmp)
+		}
+	}
+	return res
+}
+
+// returns f/g (assuming g divides f)
+// OK to not use fft if deg(g) is small
+// g's leading coefficient is assumed to be 1
+// f memory is re-used for the result, need to pass a copy to not modify it
+func div(f, g []fr.Element) []fr.Element {
+	sizef := len(f)
+	sizeg := len(g)
+	stop := sizeg - +1
+	var t fr.Element
+	for i := sizef - 2; i >= stop; i-- {
+		for j := 0; j < sizeg-1; j++ {
+			t.Mul(&f[i+1], &g[sizeg-2-j])
+			f[i-j].Sub(&f[i-j], &t)
+		}
+	}
+	return f[sizeg-1:]
+}
diff --git a/internal/generator/shplonk/template/shplonk.test.go.tmpl b/internal/generator/shplonk/template/shplonk.test.go.tmpl
new file mode 100644
index 0000000000..d3f6611b64
--- /dev/null
+++ b/internal/generator/shplonk/template/shplonk.test.go.tmpl
@@ -0,0 +1,302 @@
+import (
+	"crypto/sha256"
+	"math/big"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/fr"
+	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/kzg"
+	"github.com/stretchr/testify/require"
+)
+
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *kzg.SRS
+var bAlpha *big.Int
+
+func init() {
+	const srsSize = 230
+	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+}
+
+func TestOpening(t *testing.T) {
+
+	assert := require.New(t)
+
+	nbPolys := 2
+	sizePoly := make([]int, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		sizePoly[i] = 10 + i
+	}
+	polys := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		polys[i] = make([]fr.Element, sizePoly[i])
+		for j := 0; j < sizePoly[i]; j++ {
+			polys[i][j].SetRandom()
+		}
+	}
+
+	digests := make([]kzg.Digest, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		digests[i], _ = kzg.Commit(polys[i], testSrs.Pk)
+	}
+
+	points := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		points[i] = make([]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+
+	hf := sha256.New()
+
+	// correct proof
+	openingProof, err := BatchOpen(polys, digests, points, hf, testSrs.Pk)
+	assert.NoError(err)
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	assert.NoError(err)
+
+	// tampered proof
+	openingProof.ClaimedValues[0][0].SetRandom()
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	assert.Error(err)
+
+}
+
+func TestBuildZtMinusSi(t *testing.T) {
+
+	nbSi := 10
+	points := make([][]fr.Element, nbSi)
+	sizeSi := make([]int, nbSi)
+	nbPoints := 0
+	for i := 0; i < nbSi; i++ {
+		sizeSi[i] = 5 + i
+		nbPoints += sizeSi[i]
+		points[i] = make([]fr.Element, sizeSi[i])
+		for j := 0; j < sizeSi[i]; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+	for i := 0; i < nbSi; i++ {
+		ztMinusSi := buildZtMinusSi(points, i)
+		if len(ztMinusSi) != nbPoints-sizeSi[i]+1 {
+			t.Fatal("deg(Z_{T-S_{i}}) should be nbPoints-size(S_{i})")
+		}
+		for j := 0; j < nbSi; j++ {
+			if j == i {
+				for k := 0; k < sizeSi[j]; k++ {
+					y := eval(ztMinusSi, points[j][k])
+					if y.IsZero() {
+						t.Fatal("Z_{T-S_{i}}(S_{i}) should not be zero")
+					}
+				}
+				continue
+			}
+			for k := 0; k < sizeSi[j]; k++ {
+				y := eval(ztMinusSi, points[j][k])
+				if !y.IsZero() {
+					t.Fatal("Z_{T-S_{i}}(S_{j}) should be zero")
+				}
+			}
+		}
+	}
+
+}
+
+func TestInterpolate(t *testing.T) {
+
+	nbPoints := 10
+	x := make([]fr.Element, nbPoints)
+	y := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		y[i].SetRandom()
+	}
+	f := interpolate(x, y)
+	for i := 0; i < nbPoints; i++ {
+		fx := eval(f, x[i])
+		if !fx.Equal(&y[i]) {
+			t.Fatal("f(x_{i})!=y_{i}")
+		}
+	}
+
+}
+
+func TestBuildLagrangeFromDomain(t *testing.T) {
+
+	nbPoints := 10
+	points := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		points[i].SetRandom()
+	}
+	var r fr.Element
+	for i := 0; i < nbPoints; i++ {
+
+		l := buildLagrangeFromDomain(points, i)
+
+		// check that l(xᵢ)=1 and l(xⱼ)=0 for j!=i
+		for j := 0; j < nbPoints; j++ {
+			y := eval(l, points[j])
+			if i == j {
+				if !y.IsOne() {
+					t.Fatal("l_{i}(x_{i}) should be equal to 1")
+				}
+			} else {
+				if !y.IsZero() {
+					t.Fatal("l_{i}(x_{j}) where i!=j should be equal to 0")
+				}
+			}
+		}
+		r.SetRandom()
+		y := eval(l, r)
+		if y.IsZero() {
+			t.Fatal("l_{i}(x) should not be zero if x is random")
+		}
+	}
+
+}
+
+func TestBuildVanishingPoly(t *testing.T) {
+	s := 10
+	x := make([]fr.Element, s)
+	for i := 0; i < s; i++ {
+		x[i].SetRandom()
+	}
+	r := buildVanishingPoly(x)
+
+	if len(r) != s+1 {
+		t.Fatal("error degree r")
+	}
+
+	// check that r(xᵢ)=0 for all i
+	for i := 0; i < len(x); i++ {
+		y := eval(r, x[i])
+		if !y.IsZero() {
+			t.Fatal("πᵢ(X-xᵢ) at xᵢ should be zero")
+		}
+	}
+
+	// check that r(y)!=0 for a random point
+	var a fr.Element
+	a.SetRandom()
+	y := eval(r, a)
+	if y.IsZero() {
+		t.Fatal("πᵢ(X-xᵢ) at r \neq xᵢ should not be zero")
+	}
+}
+
+func TestMultiplyLinearFactor(t *testing.T) {
+
+	s := 10
+	f := make([]fr.Element, s, s+1)
+	for i := 0; i < 10; i++ {
+		f[i].SetRandom()
+	}
+
+	var a, y fr.Element
+	a.SetRandom()
+	f = multiplyLinearFactor(f, a)
+	y = eval(f, a)
+	if !y.IsZero() {
+		t.Fatal("(X-a)f(X) should be zero at a")
+	}
+	a.SetRandom()
+	y = eval(f, a)
+	if y.IsZero() {
+		t.Fatal("(X-1)f(X) at a random point should not be zero")
+	}
+
+}
+
+func TestNaiveMul(t *testing.T) {
+
+	size := 10
+	f := make([]fr.Element, size)
+	for i := 0; i < size; i++ {
+		f[i].SetRandom()
+	}
+
+	nbPoints := 10
+	points := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		points[i].SetRandom()
+	}
+
+	v := buildVanishingPoly(points)
+	buf := make([]fr.Element, size+nbPoints-1)
+	g := mul(f, v, buf)
+
+	// check that g(xᵢ) = 0
+	for i := 0; i < nbPoints; i++ {
+		y := eval(g, points[i])
+		if !y.IsZero() {
+			t.Fatal("f(X)(X-x_{1})..(X-x_{n}) at x_{i} should be zero")
+		}
+	}
+
+	// check that g(r) != 0 for a random point
+	var a fr.Element
+	a.SetRandom()
+	y := eval(g, a)
+	if y.IsZero() {
+		t.Fatal("f(X)(X-x_{1})..(X-x_{n}) at a random point should not be zero")
+	}
+
+}
+
+func TestDiv(t *testing.T) {
+
+	nbPoints := 10
+	s := 10
+	f := make([]fr.Element, s, s+nbPoints)
+	for i := 0; i < s; i++ {
+		f[i].SetRandom()
+	}
+
+	// backup
+	g := make([]fr.Element, s)
+	copy(g, f)
+
+	// successive divions of linear terms
+	x := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		f = multiplyLinearFactor(f, x[i])
+	}
+	q := make([][2]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		q[i][1].SetOne()
+		q[i][0].Neg(&x[i])
+		f = div(f, q[i][:])
+	}
+
+	// g should be equal to f
+	if len(f) != len(g) {
+		t.Fatal("lengths don't match")
+	}
+	for i := 0; i < len(g); i++ {
+		if !f[i].Equal(&g[i]) {
+			t.Fatal("f(x)(x-a)/(x-a) should be equal to f(x)")
+		}
+	}
+
+	// division by a degree > 1 polynomial
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		f = multiplyLinearFactor(f, x[i])
+	}
+	r := buildVanishingPoly(x)
+	f = div(f, r)
+
+	// g should be equal to f
+	if len(f) != len(g) {
+		t.Fatal("lengths don't match")
+	}
+	for i := 0; i < len(g); i++ {
+		if !f[i].Equal(&g[i]) {
+			t.Fatal("f(x)(x-a)/(x-a) should be equal to f(x)")
+		}
+	}
+
+}

From 1f69dbce9ff37429f7a0a6969cb8bec0790be728 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Tue, 12 Mar 2024 16:05:11 +0100
Subject: [PATCH 018/114] feat: marshal ok

---
 ecc/bn254/shplonk/marshal.go | 60 ++++++++++++++++++++++++++++++++++++
 1 file changed, 60 insertions(+)
 create mode 100644 ecc/bn254/shplonk/marshal.go

diff --git a/ecc/bn254/shplonk/marshal.go b/ecc/bn254/shplonk/marshal.go
new file mode 100644
index 0000000000..66eaf0302f
--- /dev/null
+++ b/ecc/bn254/shplonk/marshal.go
@@ -0,0 +1,60 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package shplonk
+
+import (
+	"io"
+
+	"github.com/consensys/gnark-crypto/ecc/bn254"
+)
+
+func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
+
+	dec := bn254.NewDecoder(r)
+
+	toDecode := []interface{}{
+		&proof.W,
+		&proof.WPrime,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toDecode {
+		if err := dec.Decode(v); err != nil {
+			return dec.BytesRead(), err
+		}
+	}
+
+	return dec.BytesRead(), nil
+}
+
+// WriteTo writes binary encoding of a OpeningProof
+func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
+
+	enc := bn254.NewEncoder(w)
+
+	toEncode := []interface{}{
+		&proof.W,
+		&proof.WPrime,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toEncode {
+		if err := enc.Encode(v); err != nil {
+			return enc.BytesWritten(), err
+		}
+	}
+
+	return enc.BytesWritten(), nil
+}

From 8a58a0921ac7b3dc5d93c64c13fadbd58522a50d Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Tue, 12 Mar 2024 16:10:12 +0100
Subject: [PATCH 019/114] feat: additions of template files  marshal shplonk

---
 internal/generator/shplonk/generator.go       |  2 +-
 .../shplonk/template/marshal.go.tmpl          | 44 +++++++++++++++++++
 2 files changed, 45 insertions(+), 1 deletion(-)
 create mode 100644 internal/generator/shplonk/template/marshal.go.tmpl

diff --git a/internal/generator/shplonk/generator.go b/internal/generator/shplonk/generator.go
index 789ab126b4..94e1118300 100644
--- a/internal/generator/shplonk/generator.go
+++ b/internal/generator/shplonk/generator.go
@@ -15,7 +15,7 @@ func Generate(conf config.Curve, baseDir string, bgen *bavard.BatchGenerator) er
 		{File: filepath.Join(baseDir, "doc.go"), Templates: []string{"doc.go.tmpl"}},
 		{File: filepath.Join(baseDir, "shplonk.go"), Templates: []string{"shplonk.go.tmpl"}},
 		{File: filepath.Join(baseDir, "shplonk_test.go"), Templates: []string{"shplonk.test.go.tmpl"}},
-		// {File: filepath.Join(baseDir, "marshal.go"), Templates: []string{"marshal.go.tmpl"}},
+		{File: filepath.Join(baseDir, "marshal.go"), Templates: []string{"marshal.go.tmpl"}},
 		// {File: filepath.Join(baseDir, "utils.go"), Templates: []string{"utils.go.tmpl"}},
 	}
 	return bgen.Generate(conf, conf.Package, "./shplonk/template/", entries...)
diff --git a/internal/generator/shplonk/template/marshal.go.tmpl b/internal/generator/shplonk/template/marshal.go.tmpl
new file mode 100644
index 0000000000..316f852ef5
--- /dev/null
+++ b/internal/generator/shplonk/template/marshal.go.tmpl
@@ -0,0 +1,44 @@
+import (
+	"io"
+
+	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}"
+)
+
+func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
+
+	dec := {{ .CurvePackage }}.NewDecoder(r)
+
+	toDecode := []interface{}{
+		&proof.W,
+		&proof.WPrime,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toDecode {
+		if err := dec.Decode(v); err != nil {
+			return dec.BytesRead(), err
+		}
+	}
+
+	return dec.BytesRead(), nil
+}   
+
+// WriteTo writes binary encoding of a OpeningProof
+func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
+
+	enc := {{ .CurvePackage }}.NewEncoder(w)
+
+	toEncode := []interface{}{
+		&proof.W,
+		&proof.WPrime,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toEncode {
+		if err := enc.Encode(v); err != nil {
+			return enc.BytesWritten(), err
+		}
+	}
+
+	return enc.BytesWritten(), nil
+}

From 39a4e67ddf1b3a782ea4a983fe90fe540c7c18cd Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Tue, 12 Mar 2024 16:11:11 +0100
Subject: [PATCH 020/114] feat: code gen ok

---
 ecc/bls12-377/shplonk/doc.go          |  18 +
 ecc/bls12-377/shplonk/marshal.go      |  62 ++++
 ecc/bls12-377/shplonk/shplonk.go      | 462 ++++++++++++++++++++++++++
 ecc/bls12-377/shplonk/shplonk_test.go | 320 ++++++++++++++++++
 ecc/bls12-378/shplonk/doc.go          |  18 +
 ecc/bls12-378/shplonk/marshal.go      |  62 ++++
 ecc/bls12-378/shplonk/shplonk.go      | 462 ++++++++++++++++++++++++++
 ecc/bls12-378/shplonk/shplonk_test.go | 320 ++++++++++++++++++
 ecc/bls12-381/shplonk/doc.go          |  18 +
 ecc/bls12-381/shplonk/marshal.go      |  62 ++++
 ecc/bls12-381/shplonk/shplonk.go      | 462 ++++++++++++++++++++++++++
 ecc/bls12-381/shplonk/shplonk_test.go | 320 ++++++++++++++++++
 ecc/bls24-315/shplonk/doc.go          |  18 +
 ecc/bls24-315/shplonk/marshal.go      |  62 ++++
 ecc/bls24-315/shplonk/shplonk.go      | 462 ++++++++++++++++++++++++++
 ecc/bls24-315/shplonk/shplonk_test.go | 320 ++++++++++++++++++
 ecc/bls24-317/shplonk/doc.go          |  18 +
 ecc/bls24-317/shplonk/marshal.go      |  62 ++++
 ecc/bls24-317/shplonk/shplonk.go      | 462 ++++++++++++++++++++++++++
 ecc/bls24-317/shplonk/shplonk_test.go | 320 ++++++++++++++++++
 ecc/bn254/shplonk/doc.go              |  18 +
 ecc/bn254/shplonk/marshal.go          |   2 +
 ecc/bn254/shplonk/shplonk.go          |   2 +-
 ecc/bn254/shplonk/shplonk_test.go     |   2 +
 ecc/bw6-633/shplonk/doc.go            |  18 +
 ecc/bw6-633/shplonk/marshal.go        |  62 ++++
 ecc/bw6-633/shplonk/shplonk.go        | 462 ++++++++++++++++++++++++++
 ecc/bw6-633/shplonk/shplonk_test.go   | 320 ++++++++++++++++++
 ecc/bw6-756/shplonk/doc.go            |  18 +
 ecc/bw6-756/shplonk/marshal.go        |  62 ++++
 ecc/bw6-756/shplonk/shplonk.go        | 462 ++++++++++++++++++++++++++
 ecc/bw6-756/shplonk/shplonk_test.go   | 320 ++++++++++++++++++
 ecc/bw6-761/shplonk/doc.go            |  18 +
 ecc/bw6-761/shplonk/marshal.go        |  62 ++++
 ecc/bw6-761/shplonk/shplonk.go        | 462 ++++++++++++++++++++++++++
 ecc/bw6-761/shplonk/shplonk_test.go   | 320 ++++++++++++++++++
 36 files changed, 6919 insertions(+), 1 deletion(-)
 create mode 100644 ecc/bls12-377/shplonk/doc.go
 create mode 100644 ecc/bls12-377/shplonk/marshal.go
 create mode 100644 ecc/bls12-377/shplonk/shplonk.go
 create mode 100644 ecc/bls12-377/shplonk/shplonk_test.go
 create mode 100644 ecc/bls12-378/shplonk/doc.go
 create mode 100644 ecc/bls12-378/shplonk/marshal.go
 create mode 100644 ecc/bls12-378/shplonk/shplonk.go
 create mode 100644 ecc/bls12-378/shplonk/shplonk_test.go
 create mode 100644 ecc/bls12-381/shplonk/doc.go
 create mode 100644 ecc/bls12-381/shplonk/marshal.go
 create mode 100644 ecc/bls12-381/shplonk/shplonk.go
 create mode 100644 ecc/bls12-381/shplonk/shplonk_test.go
 create mode 100644 ecc/bls24-315/shplonk/doc.go
 create mode 100644 ecc/bls24-315/shplonk/marshal.go
 create mode 100644 ecc/bls24-315/shplonk/shplonk.go
 create mode 100644 ecc/bls24-315/shplonk/shplonk_test.go
 create mode 100644 ecc/bls24-317/shplonk/doc.go
 create mode 100644 ecc/bls24-317/shplonk/marshal.go
 create mode 100644 ecc/bls24-317/shplonk/shplonk.go
 create mode 100644 ecc/bls24-317/shplonk/shplonk_test.go
 create mode 100644 ecc/bn254/shplonk/doc.go
 create mode 100644 ecc/bw6-633/shplonk/doc.go
 create mode 100644 ecc/bw6-633/shplonk/marshal.go
 create mode 100644 ecc/bw6-633/shplonk/shplonk.go
 create mode 100644 ecc/bw6-633/shplonk/shplonk_test.go
 create mode 100644 ecc/bw6-756/shplonk/doc.go
 create mode 100644 ecc/bw6-756/shplonk/marshal.go
 create mode 100644 ecc/bw6-756/shplonk/shplonk.go
 create mode 100644 ecc/bw6-756/shplonk/shplonk_test.go
 create mode 100644 ecc/bw6-761/shplonk/doc.go
 create mode 100644 ecc/bw6-761/shplonk/marshal.go
 create mode 100644 ecc/bw6-761/shplonk/shplonk.go
 create mode 100644 ecc/bw6-761/shplonk/shplonk_test.go

diff --git a/ecc/bls12-377/shplonk/doc.go b/ecc/bls12-377/shplonk/doc.go
new file mode 100644
index 0000000000..e048f46009
--- /dev/null
+++ b/ecc/bls12-377/shplonk/doc.go
@@ -0,0 +1,18 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// Package shplonk provides a SHPLONK commitment scheme, cf https://eprint.iacr.org/2020/081.pdf
+package shplonk
diff --git a/ecc/bls12-377/shplonk/marshal.go b/ecc/bls12-377/shplonk/marshal.go
new file mode 100644
index 0000000000..9e03a86d06
--- /dev/null
+++ b/ecc/bls12-377/shplonk/marshal.go
@@ -0,0 +1,62 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"io"
+
+	"github.com/consensys/gnark-crypto/ecc/bls12-377"
+)
+
+func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
+
+	dec := bls12377.NewDecoder(r)
+
+	toDecode := []interface{}{
+		&proof.W,
+		&proof.WPrime,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toDecode {
+		if err := dec.Decode(v); err != nil {
+			return dec.BytesRead(), err
+		}
+	}
+
+	return dec.BytesRead(), nil
+}
+
+// WriteTo writes binary encoding of a OpeningProof
+func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
+
+	enc := bls12377.NewEncoder(w)
+
+	toEncode := []interface{}{
+		&proof.W,
+		&proof.WPrime,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toEncode {
+		if err := enc.Encode(v); err != nil {
+			return enc.BytesWritten(), err
+		}
+	}
+
+	return enc.BytesWritten(), nil
+}
diff --git a/ecc/bls12-377/shplonk/shplonk.go b/ecc/bls12-377/shplonk/shplonk.go
new file mode 100644
index 0000000000..13faee07d4
--- /dev/null
+++ b/ecc/bls12-377/shplonk/shplonk.go
@@ -0,0 +1,462 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"errors"
+	"hash"
+	"math/big"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bls12-377"
+	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls12-377/kzg"
+	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
+)
+
+var (
+	ErrInvalidNumberOfPoints = errors.New("number of digests should be equal to the number of points")
+	ErrVerifyOpeningProof    = errors.New("can't verify batch opening proof")
+)
+
+// OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
+//
+// implements io.ReaderFrom and io.WriterTo
+type OpeningProof struct {
+
+	// W = ∑ᵢ γⁱZ_{T\Sᵢ}(f_i(X)-r)/Z_{T} where Z_{T} is the vanishing polynomial on the (Sᵢ)_{i}
+	// and r interpolates fᵢ(Sᵢ) on (Sᵢ)
+	W bls12377.G1Affine
+
+	// L(X)/(X-z) where L(X)=∑ᵢγⁱZ_{T\xᵢ}(f_i(X)-rᵢ) - Z_{T}W(X)
+	WPrime bls12377.G1Affine
+
+	// ClaimedValues[i] are the values of fᵢ on Sᵢ
+	ClaimedValues [][]fr.Element
+}
+
+// BatchOpen opens the list of polynomials on points, where the i-th polynomials is opend at points[i].
+func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
+
+	var res OpeningProof
+
+	nbInstances := len(polynomials)
+	if len(polynomials) != len(points) {
+		return res, ErrInvalidNumberOfPoints
+	}
+
+	// transcript
+	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
+
+	// derive γ
+	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
+	if err != nil {
+		return res, err
+	}
+
+	// compute the size of the linear combination
+	maxSizePolys := len(polynomials[0])
+	for i := 1; i < len(polynomials); i++ {
+		if maxSizePolys < len(polynomials[i]) {
+			maxSizePolys = len(polynomials[i])
+		}
+	}
+	nbPoints := 0
+	sizeSi := make([]int, len(points))
+	for i := 0; i < nbInstances; i++ {
+		nbPoints += len(points[i])
+		sizeSi[i] = len(points[i])
+	}
+	totalSize := maxSizePolys + nbPoints // upper bound of the size of f := ∑ᵢ γⁱZ_{T\Sᵢ}(f_i(X)-r)
+
+	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
+	bufTotalSize := make([]fr.Element, totalSize)
+	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
+	res.ClaimedValues = make([][]fr.Element, nbInstances)
+	for i := 0; i < nbInstances; i++ {
+		res.ClaimedValues[i] = make([]fr.Element, len(points[i]))
+	}
+	var accGamma fr.Element
+	accGamma.SetOne()
+
+	ztMinusSi := make([][]fr.Element, nbInstances)
+	ri := make([][]fr.Element, nbInstances)
+	for i := 0; i < nbInstances; i++ {
+
+		for j := 0; j < len(points[i]); j++ {
+			res.ClaimedValues[i][j] = eval(polynomials[i], points[i][j])
+		}
+
+		ztMinusSi[i] = buildZtMinusSi(points, i)
+
+		copy(bufMaxSizePolynomials, polynomials[i])
+		ri[i] = interpolate(points[i], res.ClaimedValues[i])
+		sub(bufMaxSizePolynomials, ri[i])
+
+		bufTotalSize = mul(bufMaxSizePolynomials, ztMinusSi[i], bufTotalSize)
+		bufTotalSize = mulByConstant(bufTotalSize, accGamma)
+		for j := 0; j < len(bufTotalSize); j++ {
+			f[j].Add(&f[j], &bufTotalSize[j])
+		}
+
+		accGamma.Mul(&accGamma, &gamma)
+		setZero(bufMaxSizePolynomials)
+	}
+
+	zt := buildVanishingPoly(flatten(points))
+	w := div(f, zt) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
+	res.W, err = kzg.Commit(w, pk)
+	if err != nil {
+		return res, err
+	}
+
+	// derive z
+	z, err := deriveChallenge("z", nil, []kzg.Digest{res.W}, fs)
+	if err != nil {
+		return res, err
+	}
+
+	// compute L = ∑ᵢγⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))-Z_{T}(z)W
+	accGamma.SetOne()
+	var gammaiZtMinusSiZ fr.Element
+	l := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
+	for i := 0; i < len(polynomials); i++ {
+
+		ztMinusSiZ := eval(ztMinusSi[i], z)          // Z_{T\Sᵢ}(z)
+		gammaiZtMinusSiZ.Mul(&accGamma, &ztMinusSiZ) // γⁱZ_{T\Sᵢ}(z)
+
+		copy(bufMaxSizePolynomials, polynomials[i])
+		riz := eval(ri[i], z)
+		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz) // (fᵢ-rᵢ(z))
+		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusSiZ)        // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
+		for j := 0; j < len(bufMaxSizePolynomials); j++ {
+			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
+		}
+
+		setZero(bufMaxSizePolynomials)
+		accGamma.Mul(&accGamma, &gamma)
+	}
+	ztz := eval(zt, z)
+	setZero(bufTotalSize)
+	copy(bufTotalSize, w)
+	mulByConstant(bufTotalSize, ztz) // Z_{T}(z)W
+	for i := 0; i < totalSize-maxSizePolys; i++ {
+		l[totalSize-1-i].Neg(&bufTotalSize[totalSize-1-i])
+	}
+	for i := 0; i < maxSizePolys; i++ {
+		l[i].Sub(&l[i], &bufTotalSize[i])
+	} // L <- L-Z_{T}(z)W
+
+	xMinusZ := buildVanishingPoly([]fr.Element{z})
+	wPrime := div(l, xMinusZ)
+
+	res.WPrime, err = kzg.Commit(wPrime, pk)
+	if err != nil {
+		return res, err
+	}
+
+	return res, nil
+}
+
+// BatchVerify uses proof to check that the commitments correctly open to proof.ClaimedValues
+// at points. The order matters: the proof validates that the i-th commitment is correctly opened
+// at the i-th point
+// dataTranscript is some extra data that might be needed for Fiat Shamir, and is appended at the end
+// of the original transcript.
+func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
+
+	if len(digests) != len(proof.ClaimedValues) {
+		return ErrInvalidNumberOfPoints
+	}
+	if len(digests) != len(points) {
+		return ErrInvalidNumberOfPoints
+	}
+
+	// transcript
+	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
+
+	// derive γ
+	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
+	if err != nil {
+		return err
+	}
+
+	// derive z
+	// TODO seems ok that z depend only on W, need to check that carefully
+	z, err := deriveChallenge("z", nil, []kzg.Digest{proof.W}, fs)
+	if err != nil {
+		return err
+	}
+
+	// check that e(F + zW', [1]_{2})=e(W',[x]_{2})
+	// where F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}-[∑ᵢγⁱZ_{T\xᵢ}(z)fᵢ(z)]_{1}-Z_{T}(z)[W]
+	var sumGammaiZTminusSiRiz, tmp, accGamma fr.Element
+	nbInstances := len(points)
+	gammaiZTminusSiz := make([]fr.Element, nbInstances)
+	accGamma.SetOne()
+	ri := make([][]fr.Element, nbInstances)
+	for i := 0; i < len(points); i++ {
+
+		ztMinusSi := buildZtMinusSi(points, i)                   // Z_{T-S_{i}}(X)
+		gammaiZTminusSiz[i] = eval(ztMinusSi, z)                 // Z_{T-S_{i}}(z)
+		gammaiZTminusSiz[i].Mul(&accGamma, &gammaiZTminusSiz[i]) // \gamma^{i} Z_{T-S_{i}}(z)
+
+		ri[i] = interpolate(points[i], proof.ClaimedValues[i])
+		riz := eval(ri[i], z)               // r_{i}(z)
+		tmp.Mul(&gammaiZTminusSiz[i], &riz) // Z_{T-S_{i}}(z)r_{i}(z)
+		sumGammaiZTminusSiRiz.Add(&sumGammaiZTminusSiRiz, &tmp)
+
+		accGamma.Mul(&accGamma, &gamma)
+	}
+
+	// ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}
+	config := ecc.MultiExpConfig{}
+	var sumGammaiZtMinusSiComi kzg.Digest
+	_, err = sumGammaiZtMinusSiComi.MultiExp(digests, gammaiZTminusSiz, config)
+	if err != nil {
+		return err
+	}
+
+	var bufBigInt big.Int
+
+	// [∑ᵢZ_{T\xᵢ}fᵢ(z)]_{1}
+	var sumGammaiZTminusSiRizCom kzg.Digest
+	var sumGammaiZTminusSiRizBigInt big.Int
+	sumGammaiZTminusSiRiz.BigInt(&sumGammaiZTminusSiRizBigInt)
+	sumGammaiZTminusSiRizCom.ScalarMultiplication(&vk.G1, &sumGammaiZTminusSiRizBigInt)
+
+	// Z_{T}(z)[W]
+	zt := buildVanishingPoly(flatten(points))
+	ztz := eval(zt, z)
+	var ztW kzg.Digest
+	ztz.BigInt(&bufBigInt)
+	ztW.ScalarMultiplication(&proof.W, &bufBigInt)
+
+	// F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i} - [∑ᵢγⁱZ_{T\xᵢ}fᵢ(z)]_{1} - Z_{T}(z)[W]
+	var f kzg.Digest
+	f.Sub(&sumGammaiZtMinusSiComi, &sumGammaiZTminusSiRizCom).
+		Sub(&f, &ztW)
+
+	// F+zW'
+	var zWPrime kzg.Digest
+	z.BigInt(&bufBigInt)
+	zWPrime.ScalarMultiplication(&proof.WPrime, &bufBigInt)
+	f.Add(&f, &zWPrime)
+	f.Neg(&f)
+
+	// check that e(F+zW',[1]_{2})=e(W',[x]_{2})
+	check, err := bls12377.PairingCheckFixedQ(
+		[]bls12377.G1Affine{f, proof.WPrime},
+		vk.Lines[:],
+	)
+
+	if !check {
+		return ErrVerifyOpeningProof
+	}
+
+	return nil
+}
+
+// deriveChallenge derives a challenge using Fiat Shamir to polynomials.
+// The arguments are added to the transcript in the order in which they are given.
+func deriveChallenge(name string, points [][]fr.Element, digests []kzg.Digest, t *fiatshamir.Transcript, dataTranscript ...[]byte) (fr.Element, error) {
+
+	// derive the challenge gamma, binded to the point and the commitments
+	for i := range points {
+		for j := range points[i] {
+			if err := t.Bind(name, points[i][j].Marshal()); err != nil {
+				return fr.Element{}, err
+			}
+		}
+	}
+	for i := range digests {
+		if err := t.Bind(name, digests[i].Marshal()); err != nil {
+			return fr.Element{}, err
+		}
+	}
+
+	for i := 0; i < len(dataTranscript); i++ {
+		if err := t.Bind(name, dataTranscript[i]); err != nil {
+			return fr.Element{}, err
+		}
+	}
+
+	gammaByte, err := t.ComputeChallenge(name)
+	if err != nil {
+		return fr.Element{}, err
+	}
+	var gamma fr.Element
+	gamma.SetBytes(gammaByte)
+
+	return gamma, nil
+}
+
+// ------------------------------
+// utils
+
+func flatten(x [][]fr.Element) []fr.Element {
+	nbPoints := 0
+	for i := 0; i < len(x); i++ {
+		nbPoints += len(x[i])
+	}
+	res := make([]fr.Element, 0, nbPoints)
+	for i := 0; i < len(x); i++ {
+		res = append(res, x[i]...)
+	}
+	return res
+}
+
+// sets f to zero
+func setZero(f []fr.Element) {
+	for i := 0; i < len(f); i++ {
+		f[i].SetZero()
+	}
+}
+
+func eval(f []fr.Element, x fr.Element) fr.Element {
+	var y fr.Element
+	for i := len(f) - 1; i >= 0; i-- {
+		y.Mul(&y, &x).Add(&y, &f[i])
+	}
+	return y
+}
+
+// returns γ*f, re-using f
+func mulByConstant(f []fr.Element, gamma fr.Element) []fr.Element {
+	for i := 0; i < len(f); i++ {
+		f[i].Mul(&f[i], &gamma)
+	}
+	return f
+}
+
+// computes f <- (x-a)*f
+// memory of f is re used, need to pass a copy to not modify it
+func multiplyLinearFactor(f []fr.Element, a fr.Element) []fr.Element {
+	s := len(f)
+	var tmp fr.Element
+	f = append(f, fr.NewElement(0))
+	f[s] = f[s-1]
+	for i := s - 1; i >= 1; i-- {
+		tmp.Mul(&f[i], &a)
+		f[i].Sub(&f[i-1], &tmp)
+	}
+	f[0].Mul(&f[0], &a).Neg(&f[0])
+	return f
+}
+
+// returns S_{T\Sᵢ} where Sᵢ=x[i]
+func buildZtMinusSi(x [][]fr.Element, i int) []fr.Element {
+	nbPoints := 0
+	for i := 0; i < len(x); i++ {
+		nbPoints += len(x[i])
+	}
+	bufPoints := make([]fr.Element, 0, nbPoints-len(x[i]))
+	for j := 0; j < i; j++ {
+		bufPoints = append(bufPoints, x[j]...)
+	}
+	for j := i + 1; j < len(x); j++ {
+		bufPoints = append(bufPoints, x[j]...)
+	}
+	ztMinusSi := buildVanishingPoly(bufPoints)
+	return ztMinusSi
+}
+
+// returns πᵢ(X-xᵢ)
+func buildVanishingPoly(x []fr.Element) []fr.Element {
+	res := make([]fr.Element, 1, len(x)+1)
+	res[0].SetOne()
+	for i := 0; i < len(x); i++ {
+		res = multiplyLinearFactor(res, x[i])
+	}
+	return res
+}
+
+// returns f such that f(xᵢ)=yᵢ, x and y are assumed to be of the same size
+func interpolate(x, y []fr.Element) []fr.Element {
+
+	res := make([]fr.Element, len(x))
+	for i := 0; i < len(x); i++ {
+		li := buildLagrangeFromDomain(x, i)
+		li = mulByConstant(li, y[i])
+		for j := 0; j < len(x); j++ {
+			res[j].Add(&res[j], &li[j])
+		}
+	}
+
+	return res
+}
+
+// returns f such that f(xⱼ)=δⁱⱼ
+func buildLagrangeFromDomain(x []fr.Element, i int) []fr.Element {
+	xx := make([]fr.Element, len(x)-1)
+	copy(xx, x[:i])
+	copy(xx[i:], x[i+1:])
+	res := buildVanishingPoly(xx)
+	d := eval(res, x[i])
+	d.Inverse(&d)
+	res = mulByConstant(res, d)
+	return res
+}
+
+// returns f-g, the memory of f is re used, deg(g) << deg(f) here
+func sub(f, g []fr.Element) []fr.Element {
+	for i := 0; i < len(g); i++ {
+		f[i].Sub(&f[i], &g[i])
+	}
+	return f
+}
+
+// returns f*g using naive multiplication
+// deg(f)>>deg(g), deg(small) =~ 10 max
+// buf is used as a buffer and should not be f or g
+// f and g are not modified
+func mul(f, g []fr.Element, res []fr.Element) []fr.Element {
+
+	sizeRes := len(f) + len(g) - 1
+	if len(res) < sizeRes {
+		s := make([]fr.Element, sizeRes-len(res))
+		res = append(res, s...)
+	}
+	setZero(res)
+
+	var tmp fr.Element
+	for i := 0; i < len(g); i++ {
+		for j := 0; j < len(f); j++ {
+			tmp.Mul(&f[j], &g[i])
+			res[j+i].Add(&res[j+i], &tmp)
+		}
+	}
+	return res
+}
+
+// returns f/g (assuming g divides f)
+// OK to not use fft if deg(g) is small
+// g's leading coefficient is assumed to be 1
+// f memory is re-used for the result, need to pass a copy to not modify it
+func div(f, g []fr.Element) []fr.Element {
+	sizef := len(f)
+	sizeg := len(g)
+	stop := sizeg - +1
+	var t fr.Element
+	for i := sizef - 2; i >= stop; i-- {
+		for j := 0; j < sizeg-1; j++ {
+			t.Mul(&f[i+1], &g[sizeg-2-j])
+			f[i-j].Sub(&f[i-j], &t)
+		}
+	}
+	return f[sizeg-1:]
+}
diff --git a/ecc/bls12-377/shplonk/shplonk_test.go b/ecc/bls12-377/shplonk/shplonk_test.go
new file mode 100644
index 0000000000..69a26be1b8
--- /dev/null
+++ b/ecc/bls12-377/shplonk/shplonk_test.go
@@ -0,0 +1,320 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"crypto/sha256"
+	"math/big"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls12-377/kzg"
+	"github.com/stretchr/testify/require"
+)
+
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *kzg.SRS
+var bAlpha *big.Int
+
+func init() {
+	const srsSize = 230
+	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+}
+
+func TestOpening(t *testing.T) {
+
+	assert := require.New(t)
+
+	nbPolys := 2
+	sizePoly := make([]int, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		sizePoly[i] = 10 + i
+	}
+	polys := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		polys[i] = make([]fr.Element, sizePoly[i])
+		for j := 0; j < sizePoly[i]; j++ {
+			polys[i][j].SetRandom()
+		}
+	}
+
+	digests := make([]kzg.Digest, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		digests[i], _ = kzg.Commit(polys[i], testSrs.Pk)
+	}
+
+	points := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		points[i] = make([]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+
+	hf := sha256.New()
+
+	// correct proof
+	openingProof, err := BatchOpen(polys, digests, points, hf, testSrs.Pk)
+	assert.NoError(err)
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	assert.NoError(err)
+
+	// tampered proof
+	openingProof.ClaimedValues[0][0].SetRandom()
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	assert.Error(err)
+
+}
+
+func TestBuildZtMinusSi(t *testing.T) {
+
+	nbSi := 10
+	points := make([][]fr.Element, nbSi)
+	sizeSi := make([]int, nbSi)
+	nbPoints := 0
+	for i := 0; i < nbSi; i++ {
+		sizeSi[i] = 5 + i
+		nbPoints += sizeSi[i]
+		points[i] = make([]fr.Element, sizeSi[i])
+		for j := 0; j < sizeSi[i]; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+	for i := 0; i < nbSi; i++ {
+		ztMinusSi := buildZtMinusSi(points, i)
+		if len(ztMinusSi) != nbPoints-sizeSi[i]+1 {
+			t.Fatal("deg(Z_{T-S_{i}}) should be nbPoints-size(S_{i})")
+		}
+		for j := 0; j < nbSi; j++ {
+			if j == i {
+				for k := 0; k < sizeSi[j]; k++ {
+					y := eval(ztMinusSi, points[j][k])
+					if y.IsZero() {
+						t.Fatal("Z_{T-S_{i}}(S_{i}) should not be zero")
+					}
+				}
+				continue
+			}
+			for k := 0; k < sizeSi[j]; k++ {
+				y := eval(ztMinusSi, points[j][k])
+				if !y.IsZero() {
+					t.Fatal("Z_{T-S_{i}}(S_{j}) should be zero")
+				}
+			}
+		}
+	}
+
+}
+
+func TestInterpolate(t *testing.T) {
+
+	nbPoints := 10
+	x := make([]fr.Element, nbPoints)
+	y := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		y[i].SetRandom()
+	}
+	f := interpolate(x, y)
+	for i := 0; i < nbPoints; i++ {
+		fx := eval(f, x[i])
+		if !fx.Equal(&y[i]) {
+			t.Fatal("f(x_{i})!=y_{i}")
+		}
+	}
+
+}
+
+func TestBuildLagrangeFromDomain(t *testing.T) {
+
+	nbPoints := 10
+	points := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		points[i].SetRandom()
+	}
+	var r fr.Element
+	for i := 0; i < nbPoints; i++ {
+
+		l := buildLagrangeFromDomain(points, i)
+
+		// check that l(xᵢ)=1 and l(xⱼ)=0 for j!=i
+		for j := 0; j < nbPoints; j++ {
+			y := eval(l, points[j])
+			if i == j {
+				if !y.IsOne() {
+					t.Fatal("l_{i}(x_{i}) should be equal to 1")
+				}
+			} else {
+				if !y.IsZero() {
+					t.Fatal("l_{i}(x_{j}) where i!=j should be equal to 0")
+				}
+			}
+		}
+		r.SetRandom()
+		y := eval(l, r)
+		if y.IsZero() {
+			t.Fatal("l_{i}(x) should not be zero if x is random")
+		}
+	}
+
+}
+
+func TestBuildVanishingPoly(t *testing.T) {
+	s := 10
+	x := make([]fr.Element, s)
+	for i := 0; i < s; i++ {
+		x[i].SetRandom()
+	}
+	r := buildVanishingPoly(x)
+
+	if len(r) != s+1 {
+		t.Fatal("error degree r")
+	}
+
+	// check that r(xᵢ)=0 for all i
+	for i := 0; i < len(x); i++ {
+		y := eval(r, x[i])
+		if !y.IsZero() {
+			t.Fatal("πᵢ(X-xᵢ) at xᵢ should be zero")
+		}
+	}
+
+	// check that r(y)!=0 for a random point
+	var a fr.Element
+	a.SetRandom()
+	y := eval(r, a)
+	if y.IsZero() {
+		t.Fatal("πᵢ(X-xᵢ) at r \neq xᵢ should not be zero")
+	}
+}
+
+func TestMultiplyLinearFactor(t *testing.T) {
+
+	s := 10
+	f := make([]fr.Element, s, s+1)
+	for i := 0; i < 10; i++ {
+		f[i].SetRandom()
+	}
+
+	var a, y fr.Element
+	a.SetRandom()
+	f = multiplyLinearFactor(f, a)
+	y = eval(f, a)
+	if !y.IsZero() {
+		t.Fatal("(X-a)f(X) should be zero at a")
+	}
+	a.SetRandom()
+	y = eval(f, a)
+	if y.IsZero() {
+		t.Fatal("(X-1)f(X) at a random point should not be zero")
+	}
+
+}
+
+func TestNaiveMul(t *testing.T) {
+
+	size := 10
+	f := make([]fr.Element, size)
+	for i := 0; i < size; i++ {
+		f[i].SetRandom()
+	}
+
+	nbPoints := 10
+	points := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		points[i].SetRandom()
+	}
+
+	v := buildVanishingPoly(points)
+	buf := make([]fr.Element, size+nbPoints-1)
+	g := mul(f, v, buf)
+
+	// check that g(xᵢ) = 0
+	for i := 0; i < nbPoints; i++ {
+		y := eval(g, points[i])
+		if !y.IsZero() {
+			t.Fatal("f(X)(X-x_{1})..(X-x_{n}) at x_{i} should be zero")
+		}
+	}
+
+	// check that g(r) != 0 for a random point
+	var a fr.Element
+	a.SetRandom()
+	y := eval(g, a)
+	if y.IsZero() {
+		t.Fatal("f(X)(X-x_{1})..(X-x_{n}) at a random point should not be zero")
+	}
+
+}
+
+func TestDiv(t *testing.T) {
+
+	nbPoints := 10
+	s := 10
+	f := make([]fr.Element, s, s+nbPoints)
+	for i := 0; i < s; i++ {
+		f[i].SetRandom()
+	}
+
+	// backup
+	g := make([]fr.Element, s)
+	copy(g, f)
+
+	// successive divions of linear terms
+	x := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		f = multiplyLinearFactor(f, x[i])
+	}
+	q := make([][2]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		q[i][1].SetOne()
+		q[i][0].Neg(&x[i])
+		f = div(f, q[i][:])
+	}
+
+	// g should be equal to f
+	if len(f) != len(g) {
+		t.Fatal("lengths don't match")
+	}
+	for i := 0; i < len(g); i++ {
+		if !f[i].Equal(&g[i]) {
+			t.Fatal("f(x)(x-a)/(x-a) should be equal to f(x)")
+		}
+	}
+
+	// division by a degree > 1 polynomial
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		f = multiplyLinearFactor(f, x[i])
+	}
+	r := buildVanishingPoly(x)
+	f = div(f, r)
+
+	// g should be equal to f
+	if len(f) != len(g) {
+		t.Fatal("lengths don't match")
+	}
+	for i := 0; i < len(g); i++ {
+		if !f[i].Equal(&g[i]) {
+			t.Fatal("f(x)(x-a)/(x-a) should be equal to f(x)")
+		}
+	}
+
+}
diff --git a/ecc/bls12-378/shplonk/doc.go b/ecc/bls12-378/shplonk/doc.go
new file mode 100644
index 0000000000..e048f46009
--- /dev/null
+++ b/ecc/bls12-378/shplonk/doc.go
@@ -0,0 +1,18 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// Package shplonk provides a SHPLONK commitment scheme, cf https://eprint.iacr.org/2020/081.pdf
+package shplonk
diff --git a/ecc/bls12-378/shplonk/marshal.go b/ecc/bls12-378/shplonk/marshal.go
new file mode 100644
index 0000000000..6774448de5
--- /dev/null
+++ b/ecc/bls12-378/shplonk/marshal.go
@@ -0,0 +1,62 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"io"
+
+	"github.com/consensys/gnark-crypto/ecc/bls12-378"
+)
+
+func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
+
+	dec := bls12378.NewDecoder(r)
+
+	toDecode := []interface{}{
+		&proof.W,
+		&proof.WPrime,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toDecode {
+		if err := dec.Decode(v); err != nil {
+			return dec.BytesRead(), err
+		}
+	}
+
+	return dec.BytesRead(), nil
+}
+
+// WriteTo writes binary encoding of a OpeningProof
+func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
+
+	enc := bls12378.NewEncoder(w)
+
+	toEncode := []interface{}{
+		&proof.W,
+		&proof.WPrime,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toEncode {
+		if err := enc.Encode(v); err != nil {
+			return enc.BytesWritten(), err
+		}
+	}
+
+	return enc.BytesWritten(), nil
+}
diff --git a/ecc/bls12-378/shplonk/shplonk.go b/ecc/bls12-378/shplonk/shplonk.go
new file mode 100644
index 0000000000..1f447522ab
--- /dev/null
+++ b/ecc/bls12-378/shplonk/shplonk.go
@@ -0,0 +1,462 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"errors"
+	"hash"
+	"math/big"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bls12-378"
+	"github.com/consensys/gnark-crypto/ecc/bls12-378/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls12-378/kzg"
+	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
+)
+
+var (
+	ErrInvalidNumberOfPoints = errors.New("number of digests should be equal to the number of points")
+	ErrVerifyOpeningProof    = errors.New("can't verify batch opening proof")
+)
+
+// OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
+//
+// implements io.ReaderFrom and io.WriterTo
+type OpeningProof struct {
+
+	// W = ∑ᵢ γⁱZ_{T\Sᵢ}(f_i(X)-r)/Z_{T} where Z_{T} is the vanishing polynomial on the (Sᵢ)_{i}
+	// and r interpolates fᵢ(Sᵢ) on (Sᵢ)
+	W bls12378.G1Affine
+
+	// L(X)/(X-z) where L(X)=∑ᵢγⁱZ_{T\xᵢ}(f_i(X)-rᵢ) - Z_{T}W(X)
+	WPrime bls12378.G1Affine
+
+	// ClaimedValues[i] are the values of fᵢ on Sᵢ
+	ClaimedValues [][]fr.Element
+}
+
+// BatchOpen opens the list of polynomials on points, where the i-th polynomials is opend at points[i].
+func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
+
+	var res OpeningProof
+
+	nbInstances := len(polynomials)
+	if len(polynomials) != len(points) {
+		return res, ErrInvalidNumberOfPoints
+	}
+
+	// transcript
+	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
+
+	// derive γ
+	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
+	if err != nil {
+		return res, err
+	}
+
+	// compute the size of the linear combination
+	maxSizePolys := len(polynomials[0])
+	for i := 1; i < len(polynomials); i++ {
+		if maxSizePolys < len(polynomials[i]) {
+			maxSizePolys = len(polynomials[i])
+		}
+	}
+	nbPoints := 0
+	sizeSi := make([]int, len(points))
+	for i := 0; i < nbInstances; i++ {
+		nbPoints += len(points[i])
+		sizeSi[i] = len(points[i])
+	}
+	totalSize := maxSizePolys + nbPoints // upper bound of the size of f := ∑ᵢ γⁱZ_{T\Sᵢ}(f_i(X)-r)
+
+	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
+	bufTotalSize := make([]fr.Element, totalSize)
+	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
+	res.ClaimedValues = make([][]fr.Element, nbInstances)
+	for i := 0; i < nbInstances; i++ {
+		res.ClaimedValues[i] = make([]fr.Element, len(points[i]))
+	}
+	var accGamma fr.Element
+	accGamma.SetOne()
+
+	ztMinusSi := make([][]fr.Element, nbInstances)
+	ri := make([][]fr.Element, nbInstances)
+	for i := 0; i < nbInstances; i++ {
+
+		for j := 0; j < len(points[i]); j++ {
+			res.ClaimedValues[i][j] = eval(polynomials[i], points[i][j])
+		}
+
+		ztMinusSi[i] = buildZtMinusSi(points, i)
+
+		copy(bufMaxSizePolynomials, polynomials[i])
+		ri[i] = interpolate(points[i], res.ClaimedValues[i])
+		sub(bufMaxSizePolynomials, ri[i])
+
+		bufTotalSize = mul(bufMaxSizePolynomials, ztMinusSi[i], bufTotalSize)
+		bufTotalSize = mulByConstant(bufTotalSize, accGamma)
+		for j := 0; j < len(bufTotalSize); j++ {
+			f[j].Add(&f[j], &bufTotalSize[j])
+		}
+
+		accGamma.Mul(&accGamma, &gamma)
+		setZero(bufMaxSizePolynomials)
+	}
+
+	zt := buildVanishingPoly(flatten(points))
+	w := div(f, zt) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
+	res.W, err = kzg.Commit(w, pk)
+	if err != nil {
+		return res, err
+	}
+
+	// derive z
+	z, err := deriveChallenge("z", nil, []kzg.Digest{res.W}, fs)
+	if err != nil {
+		return res, err
+	}
+
+	// compute L = ∑ᵢγⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))-Z_{T}(z)W
+	accGamma.SetOne()
+	var gammaiZtMinusSiZ fr.Element
+	l := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
+	for i := 0; i < len(polynomials); i++ {
+
+		ztMinusSiZ := eval(ztMinusSi[i], z)          // Z_{T\Sᵢ}(z)
+		gammaiZtMinusSiZ.Mul(&accGamma, &ztMinusSiZ) // γⁱZ_{T\Sᵢ}(z)
+
+		copy(bufMaxSizePolynomials, polynomials[i])
+		riz := eval(ri[i], z)
+		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz) // (fᵢ-rᵢ(z))
+		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusSiZ)        // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
+		for j := 0; j < len(bufMaxSizePolynomials); j++ {
+			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
+		}
+
+		setZero(bufMaxSizePolynomials)
+		accGamma.Mul(&accGamma, &gamma)
+	}
+	ztz := eval(zt, z)
+	setZero(bufTotalSize)
+	copy(bufTotalSize, w)
+	mulByConstant(bufTotalSize, ztz) // Z_{T}(z)W
+	for i := 0; i < totalSize-maxSizePolys; i++ {
+		l[totalSize-1-i].Neg(&bufTotalSize[totalSize-1-i])
+	}
+	for i := 0; i < maxSizePolys; i++ {
+		l[i].Sub(&l[i], &bufTotalSize[i])
+	} // L <- L-Z_{T}(z)W
+
+	xMinusZ := buildVanishingPoly([]fr.Element{z})
+	wPrime := div(l, xMinusZ)
+
+	res.WPrime, err = kzg.Commit(wPrime, pk)
+	if err != nil {
+		return res, err
+	}
+
+	return res, nil
+}
+
+// BatchVerify uses proof to check that the commitments correctly open to proof.ClaimedValues
+// at points. The order matters: the proof validates that the i-th commitment is correctly opened
+// at the i-th point
+// dataTranscript is some extra data that might be needed for Fiat Shamir, and is appended at the end
+// of the original transcript.
+func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
+
+	if len(digests) != len(proof.ClaimedValues) {
+		return ErrInvalidNumberOfPoints
+	}
+	if len(digests) != len(points) {
+		return ErrInvalidNumberOfPoints
+	}
+
+	// transcript
+	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
+
+	// derive γ
+	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
+	if err != nil {
+		return err
+	}
+
+	// derive z
+	// TODO seems ok that z depend only on W, need to check that carefully
+	z, err := deriveChallenge("z", nil, []kzg.Digest{proof.W}, fs)
+	if err != nil {
+		return err
+	}
+
+	// check that e(F + zW', [1]_{2})=e(W',[x]_{2})
+	// where F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}-[∑ᵢγⁱZ_{T\xᵢ}(z)fᵢ(z)]_{1}-Z_{T}(z)[W]
+	var sumGammaiZTminusSiRiz, tmp, accGamma fr.Element
+	nbInstances := len(points)
+	gammaiZTminusSiz := make([]fr.Element, nbInstances)
+	accGamma.SetOne()
+	ri := make([][]fr.Element, nbInstances)
+	for i := 0; i < len(points); i++ {
+
+		ztMinusSi := buildZtMinusSi(points, i)                   // Z_{T-S_{i}}(X)
+		gammaiZTminusSiz[i] = eval(ztMinusSi, z)                 // Z_{T-S_{i}}(z)
+		gammaiZTminusSiz[i].Mul(&accGamma, &gammaiZTminusSiz[i]) // \gamma^{i} Z_{T-S_{i}}(z)
+
+		ri[i] = interpolate(points[i], proof.ClaimedValues[i])
+		riz := eval(ri[i], z)               // r_{i}(z)
+		tmp.Mul(&gammaiZTminusSiz[i], &riz) // Z_{T-S_{i}}(z)r_{i}(z)
+		sumGammaiZTminusSiRiz.Add(&sumGammaiZTminusSiRiz, &tmp)
+
+		accGamma.Mul(&accGamma, &gamma)
+	}
+
+	// ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}
+	config := ecc.MultiExpConfig{}
+	var sumGammaiZtMinusSiComi kzg.Digest
+	_, err = sumGammaiZtMinusSiComi.MultiExp(digests, gammaiZTminusSiz, config)
+	if err != nil {
+		return err
+	}
+
+	var bufBigInt big.Int
+
+	// [∑ᵢZ_{T\xᵢ}fᵢ(z)]_{1}
+	var sumGammaiZTminusSiRizCom kzg.Digest
+	var sumGammaiZTminusSiRizBigInt big.Int
+	sumGammaiZTminusSiRiz.BigInt(&sumGammaiZTminusSiRizBigInt)
+	sumGammaiZTminusSiRizCom.ScalarMultiplication(&vk.G1, &sumGammaiZTminusSiRizBigInt)
+
+	// Z_{T}(z)[W]
+	zt := buildVanishingPoly(flatten(points))
+	ztz := eval(zt, z)
+	var ztW kzg.Digest
+	ztz.BigInt(&bufBigInt)
+	ztW.ScalarMultiplication(&proof.W, &bufBigInt)
+
+	// F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i} - [∑ᵢγⁱZ_{T\xᵢ}fᵢ(z)]_{1} - Z_{T}(z)[W]
+	var f kzg.Digest
+	f.Sub(&sumGammaiZtMinusSiComi, &sumGammaiZTminusSiRizCom).
+		Sub(&f, &ztW)
+
+	// F+zW'
+	var zWPrime kzg.Digest
+	z.BigInt(&bufBigInt)
+	zWPrime.ScalarMultiplication(&proof.WPrime, &bufBigInt)
+	f.Add(&f, &zWPrime)
+	f.Neg(&f)
+
+	// check that e(F+zW',[1]_{2})=e(W',[x]_{2})
+	check, err := bls12378.PairingCheckFixedQ(
+		[]bls12378.G1Affine{f, proof.WPrime},
+		vk.Lines[:],
+	)
+
+	if !check {
+		return ErrVerifyOpeningProof
+	}
+
+	return nil
+}
+
+// deriveChallenge derives a challenge using Fiat Shamir to polynomials.
+// The arguments are added to the transcript in the order in which they are given.
+func deriveChallenge(name string, points [][]fr.Element, digests []kzg.Digest, t *fiatshamir.Transcript, dataTranscript ...[]byte) (fr.Element, error) {
+
+	// derive the challenge gamma, binded to the point and the commitments
+	for i := range points {
+		for j := range points[i] {
+			if err := t.Bind(name, points[i][j].Marshal()); err != nil {
+				return fr.Element{}, err
+			}
+		}
+	}
+	for i := range digests {
+		if err := t.Bind(name, digests[i].Marshal()); err != nil {
+			return fr.Element{}, err
+		}
+	}
+
+	for i := 0; i < len(dataTranscript); i++ {
+		if err := t.Bind(name, dataTranscript[i]); err != nil {
+			return fr.Element{}, err
+		}
+	}
+
+	gammaByte, err := t.ComputeChallenge(name)
+	if err != nil {
+		return fr.Element{}, err
+	}
+	var gamma fr.Element
+	gamma.SetBytes(gammaByte)
+
+	return gamma, nil
+}
+
+// ------------------------------
+// utils
+
+func flatten(x [][]fr.Element) []fr.Element {
+	nbPoints := 0
+	for i := 0; i < len(x); i++ {
+		nbPoints += len(x[i])
+	}
+	res := make([]fr.Element, 0, nbPoints)
+	for i := 0; i < len(x); i++ {
+		res = append(res, x[i]...)
+	}
+	return res
+}
+
+// sets f to zero
+func setZero(f []fr.Element) {
+	for i := 0; i < len(f); i++ {
+		f[i].SetZero()
+	}
+}
+
+func eval(f []fr.Element, x fr.Element) fr.Element {
+	var y fr.Element
+	for i := len(f) - 1; i >= 0; i-- {
+		y.Mul(&y, &x).Add(&y, &f[i])
+	}
+	return y
+}
+
+// returns γ*f, re-using f
+func mulByConstant(f []fr.Element, gamma fr.Element) []fr.Element {
+	for i := 0; i < len(f); i++ {
+		f[i].Mul(&f[i], &gamma)
+	}
+	return f
+}
+
+// computes f <- (x-a)*f
+// memory of f is re used, need to pass a copy to not modify it
+func multiplyLinearFactor(f []fr.Element, a fr.Element) []fr.Element {
+	s := len(f)
+	var tmp fr.Element
+	f = append(f, fr.NewElement(0))
+	f[s] = f[s-1]
+	for i := s - 1; i >= 1; i-- {
+		tmp.Mul(&f[i], &a)
+		f[i].Sub(&f[i-1], &tmp)
+	}
+	f[0].Mul(&f[0], &a).Neg(&f[0])
+	return f
+}
+
+// returns S_{T\Sᵢ} where Sᵢ=x[i]
+func buildZtMinusSi(x [][]fr.Element, i int) []fr.Element {
+	nbPoints := 0
+	for i := 0; i < len(x); i++ {
+		nbPoints += len(x[i])
+	}
+	bufPoints := make([]fr.Element, 0, nbPoints-len(x[i]))
+	for j := 0; j < i; j++ {
+		bufPoints = append(bufPoints, x[j]...)
+	}
+	for j := i + 1; j < len(x); j++ {
+		bufPoints = append(bufPoints, x[j]...)
+	}
+	ztMinusSi := buildVanishingPoly(bufPoints)
+	return ztMinusSi
+}
+
+// returns πᵢ(X-xᵢ)
+func buildVanishingPoly(x []fr.Element) []fr.Element {
+	res := make([]fr.Element, 1, len(x)+1)
+	res[0].SetOne()
+	for i := 0; i < len(x); i++ {
+		res = multiplyLinearFactor(res, x[i])
+	}
+	return res
+}
+
+// returns f such that f(xᵢ)=yᵢ, x and y are assumed to be of the same size
+func interpolate(x, y []fr.Element) []fr.Element {
+
+	res := make([]fr.Element, len(x))
+	for i := 0; i < len(x); i++ {
+		li := buildLagrangeFromDomain(x, i)
+		li = mulByConstant(li, y[i])
+		for j := 0; j < len(x); j++ {
+			res[j].Add(&res[j], &li[j])
+		}
+	}
+
+	return res
+}
+
+// returns f such that f(xⱼ)=δⁱⱼ
+func buildLagrangeFromDomain(x []fr.Element, i int) []fr.Element {
+	xx := make([]fr.Element, len(x)-1)
+	copy(xx, x[:i])
+	copy(xx[i:], x[i+1:])
+	res := buildVanishingPoly(xx)
+	d := eval(res, x[i])
+	d.Inverse(&d)
+	res = mulByConstant(res, d)
+	return res
+}
+
+// returns f-g, the memory of f is re used, deg(g) << deg(f) here
+func sub(f, g []fr.Element) []fr.Element {
+	for i := 0; i < len(g); i++ {
+		f[i].Sub(&f[i], &g[i])
+	}
+	return f
+}
+
+// returns f*g using naive multiplication
+// deg(f)>>deg(g), deg(small) =~ 10 max
+// buf is used as a buffer and should not be f or g
+// f and g are not modified
+func mul(f, g []fr.Element, res []fr.Element) []fr.Element {
+
+	sizeRes := len(f) + len(g) - 1
+	if len(res) < sizeRes {
+		s := make([]fr.Element, sizeRes-len(res))
+		res = append(res, s...)
+	}
+	setZero(res)
+
+	var tmp fr.Element
+	for i := 0; i < len(g); i++ {
+		for j := 0; j < len(f); j++ {
+			tmp.Mul(&f[j], &g[i])
+			res[j+i].Add(&res[j+i], &tmp)
+		}
+	}
+	return res
+}
+
+// returns f/g (assuming g divides f)
+// OK to not use fft if deg(g) is small
+// g's leading coefficient is assumed to be 1
+// f memory is re-used for the result, need to pass a copy to not modify it
+func div(f, g []fr.Element) []fr.Element {
+	sizef := len(f)
+	sizeg := len(g)
+	stop := sizeg - +1
+	var t fr.Element
+	for i := sizef - 2; i >= stop; i-- {
+		for j := 0; j < sizeg-1; j++ {
+			t.Mul(&f[i+1], &g[sizeg-2-j])
+			f[i-j].Sub(&f[i-j], &t)
+		}
+	}
+	return f[sizeg-1:]
+}
diff --git a/ecc/bls12-378/shplonk/shplonk_test.go b/ecc/bls12-378/shplonk/shplonk_test.go
new file mode 100644
index 0000000000..dcb5f69421
--- /dev/null
+++ b/ecc/bls12-378/shplonk/shplonk_test.go
@@ -0,0 +1,320 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"crypto/sha256"
+	"math/big"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bls12-378/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls12-378/kzg"
+	"github.com/stretchr/testify/require"
+)
+
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *kzg.SRS
+var bAlpha *big.Int
+
+func init() {
+	const srsSize = 230
+	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+}
+
+func TestOpening(t *testing.T) {
+
+	assert := require.New(t)
+
+	nbPolys := 2
+	sizePoly := make([]int, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		sizePoly[i] = 10 + i
+	}
+	polys := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		polys[i] = make([]fr.Element, sizePoly[i])
+		for j := 0; j < sizePoly[i]; j++ {
+			polys[i][j].SetRandom()
+		}
+	}
+
+	digests := make([]kzg.Digest, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		digests[i], _ = kzg.Commit(polys[i], testSrs.Pk)
+	}
+
+	points := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		points[i] = make([]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+
+	hf := sha256.New()
+
+	// correct proof
+	openingProof, err := BatchOpen(polys, digests, points, hf, testSrs.Pk)
+	assert.NoError(err)
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	assert.NoError(err)
+
+	// tampered proof
+	openingProof.ClaimedValues[0][0].SetRandom()
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	assert.Error(err)
+
+}
+
+func TestBuildZtMinusSi(t *testing.T) {
+
+	nbSi := 10
+	points := make([][]fr.Element, nbSi)
+	sizeSi := make([]int, nbSi)
+	nbPoints := 0
+	for i := 0; i < nbSi; i++ {
+		sizeSi[i] = 5 + i
+		nbPoints += sizeSi[i]
+		points[i] = make([]fr.Element, sizeSi[i])
+		for j := 0; j < sizeSi[i]; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+	for i := 0; i < nbSi; i++ {
+		ztMinusSi := buildZtMinusSi(points, i)
+		if len(ztMinusSi) != nbPoints-sizeSi[i]+1 {
+			t.Fatal("deg(Z_{T-S_{i}}) should be nbPoints-size(S_{i})")
+		}
+		for j := 0; j < nbSi; j++ {
+			if j == i {
+				for k := 0; k < sizeSi[j]; k++ {
+					y := eval(ztMinusSi, points[j][k])
+					if y.IsZero() {
+						t.Fatal("Z_{T-S_{i}}(S_{i}) should not be zero")
+					}
+				}
+				continue
+			}
+			for k := 0; k < sizeSi[j]; k++ {
+				y := eval(ztMinusSi, points[j][k])
+				if !y.IsZero() {
+					t.Fatal("Z_{T-S_{i}}(S_{j}) should be zero")
+				}
+			}
+		}
+	}
+
+}
+
+func TestInterpolate(t *testing.T) {
+
+	nbPoints := 10
+	x := make([]fr.Element, nbPoints)
+	y := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		y[i].SetRandom()
+	}
+	f := interpolate(x, y)
+	for i := 0; i < nbPoints; i++ {
+		fx := eval(f, x[i])
+		if !fx.Equal(&y[i]) {
+			t.Fatal("f(x_{i})!=y_{i}")
+		}
+	}
+
+}
+
+func TestBuildLagrangeFromDomain(t *testing.T) {
+
+	nbPoints := 10
+	points := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		points[i].SetRandom()
+	}
+	var r fr.Element
+	for i := 0; i < nbPoints; i++ {
+
+		l := buildLagrangeFromDomain(points, i)
+
+		// check that l(xᵢ)=1 and l(xⱼ)=0 for j!=i
+		for j := 0; j < nbPoints; j++ {
+			y := eval(l, points[j])
+			if i == j {
+				if !y.IsOne() {
+					t.Fatal("l_{i}(x_{i}) should be equal to 1")
+				}
+			} else {
+				if !y.IsZero() {
+					t.Fatal("l_{i}(x_{j}) where i!=j should be equal to 0")
+				}
+			}
+		}
+		r.SetRandom()
+		y := eval(l, r)
+		if y.IsZero() {
+			t.Fatal("l_{i}(x) should not be zero if x is random")
+		}
+	}
+
+}
+
+func TestBuildVanishingPoly(t *testing.T) {
+	s := 10
+	x := make([]fr.Element, s)
+	for i := 0; i < s; i++ {
+		x[i].SetRandom()
+	}
+	r := buildVanishingPoly(x)
+
+	if len(r) != s+1 {
+		t.Fatal("error degree r")
+	}
+
+	// check that r(xᵢ)=0 for all i
+	for i := 0; i < len(x); i++ {
+		y := eval(r, x[i])
+		if !y.IsZero() {
+			t.Fatal("πᵢ(X-xᵢ) at xᵢ should be zero")
+		}
+	}
+
+	// check that r(y)!=0 for a random point
+	var a fr.Element
+	a.SetRandom()
+	y := eval(r, a)
+	if y.IsZero() {
+		t.Fatal("πᵢ(X-xᵢ) at r \neq xᵢ should not be zero")
+	}
+}
+
+func TestMultiplyLinearFactor(t *testing.T) {
+
+	s := 10
+	f := make([]fr.Element, s, s+1)
+	for i := 0; i < 10; i++ {
+		f[i].SetRandom()
+	}
+
+	var a, y fr.Element
+	a.SetRandom()
+	f = multiplyLinearFactor(f, a)
+	y = eval(f, a)
+	if !y.IsZero() {
+		t.Fatal("(X-a)f(X) should be zero at a")
+	}
+	a.SetRandom()
+	y = eval(f, a)
+	if y.IsZero() {
+		t.Fatal("(X-1)f(X) at a random point should not be zero")
+	}
+
+}
+
+func TestNaiveMul(t *testing.T) {
+
+	size := 10
+	f := make([]fr.Element, size)
+	for i := 0; i < size; i++ {
+		f[i].SetRandom()
+	}
+
+	nbPoints := 10
+	points := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		points[i].SetRandom()
+	}
+
+	v := buildVanishingPoly(points)
+	buf := make([]fr.Element, size+nbPoints-1)
+	g := mul(f, v, buf)
+
+	// check that g(xᵢ) = 0
+	for i := 0; i < nbPoints; i++ {
+		y := eval(g, points[i])
+		if !y.IsZero() {
+			t.Fatal("f(X)(X-x_{1})..(X-x_{n}) at x_{i} should be zero")
+		}
+	}
+
+	// check that g(r) != 0 for a random point
+	var a fr.Element
+	a.SetRandom()
+	y := eval(g, a)
+	if y.IsZero() {
+		t.Fatal("f(X)(X-x_{1})..(X-x_{n}) at a random point should not be zero")
+	}
+
+}
+
+func TestDiv(t *testing.T) {
+
+	nbPoints := 10
+	s := 10
+	f := make([]fr.Element, s, s+nbPoints)
+	for i := 0; i < s; i++ {
+		f[i].SetRandom()
+	}
+
+	// backup
+	g := make([]fr.Element, s)
+	copy(g, f)
+
+	// successive divions of linear terms
+	x := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		f = multiplyLinearFactor(f, x[i])
+	}
+	q := make([][2]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		q[i][1].SetOne()
+		q[i][0].Neg(&x[i])
+		f = div(f, q[i][:])
+	}
+
+	// g should be equal to f
+	if len(f) != len(g) {
+		t.Fatal("lengths don't match")
+	}
+	for i := 0; i < len(g); i++ {
+		if !f[i].Equal(&g[i]) {
+			t.Fatal("f(x)(x-a)/(x-a) should be equal to f(x)")
+		}
+	}
+
+	// division by a degree > 1 polynomial
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		f = multiplyLinearFactor(f, x[i])
+	}
+	r := buildVanishingPoly(x)
+	f = div(f, r)
+
+	// g should be equal to f
+	if len(f) != len(g) {
+		t.Fatal("lengths don't match")
+	}
+	for i := 0; i < len(g); i++ {
+		if !f[i].Equal(&g[i]) {
+			t.Fatal("f(x)(x-a)/(x-a) should be equal to f(x)")
+		}
+	}
+
+}
diff --git a/ecc/bls12-381/shplonk/doc.go b/ecc/bls12-381/shplonk/doc.go
new file mode 100644
index 0000000000..e048f46009
--- /dev/null
+++ b/ecc/bls12-381/shplonk/doc.go
@@ -0,0 +1,18 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// Package shplonk provides a SHPLONK commitment scheme, cf https://eprint.iacr.org/2020/081.pdf
+package shplonk
diff --git a/ecc/bls12-381/shplonk/marshal.go b/ecc/bls12-381/shplonk/marshal.go
new file mode 100644
index 0000000000..b609b73266
--- /dev/null
+++ b/ecc/bls12-381/shplonk/marshal.go
@@ -0,0 +1,62 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"io"
+
+	"github.com/consensys/gnark-crypto/ecc/bls12-381"
+)
+
+func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
+
+	dec := bls12381.NewDecoder(r)
+
+	toDecode := []interface{}{
+		&proof.W,
+		&proof.WPrime,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toDecode {
+		if err := dec.Decode(v); err != nil {
+			return dec.BytesRead(), err
+		}
+	}
+
+	return dec.BytesRead(), nil
+}
+
+// WriteTo writes binary encoding of a OpeningProof
+func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
+
+	enc := bls12381.NewEncoder(w)
+
+	toEncode := []interface{}{
+		&proof.W,
+		&proof.WPrime,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toEncode {
+		if err := enc.Encode(v); err != nil {
+			return enc.BytesWritten(), err
+		}
+	}
+
+	return enc.BytesWritten(), nil
+}
diff --git a/ecc/bls12-381/shplonk/shplonk.go b/ecc/bls12-381/shplonk/shplonk.go
new file mode 100644
index 0000000000..43d624ae23
--- /dev/null
+++ b/ecc/bls12-381/shplonk/shplonk.go
@@ -0,0 +1,462 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"errors"
+	"hash"
+	"math/big"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bls12-381"
+	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls12-381/kzg"
+	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
+)
+
+var (
+	ErrInvalidNumberOfPoints = errors.New("number of digests should be equal to the number of points")
+	ErrVerifyOpeningProof    = errors.New("can't verify batch opening proof")
+)
+
+// OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
+//
+// implements io.ReaderFrom and io.WriterTo
+type OpeningProof struct {
+
+	// W = ∑ᵢ γⁱZ_{T\Sᵢ}(f_i(X)-r)/Z_{T} where Z_{T} is the vanishing polynomial on the (Sᵢ)_{i}
+	// and r interpolates fᵢ(Sᵢ) on (Sᵢ)
+	W bls12381.G1Affine
+
+	// L(X)/(X-z) where L(X)=∑ᵢγⁱZ_{T\xᵢ}(f_i(X)-rᵢ) - Z_{T}W(X)
+	WPrime bls12381.G1Affine
+
+	// ClaimedValues[i] are the values of fᵢ on Sᵢ
+	ClaimedValues [][]fr.Element
+}
+
+// BatchOpen opens the list of polynomials on points, where the i-th polynomials is opend at points[i].
+func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
+
+	var res OpeningProof
+
+	nbInstances := len(polynomials)
+	if len(polynomials) != len(points) {
+		return res, ErrInvalidNumberOfPoints
+	}
+
+	// transcript
+	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
+
+	// derive γ
+	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
+	if err != nil {
+		return res, err
+	}
+
+	// compute the size of the linear combination
+	maxSizePolys := len(polynomials[0])
+	for i := 1; i < len(polynomials); i++ {
+		if maxSizePolys < len(polynomials[i]) {
+			maxSizePolys = len(polynomials[i])
+		}
+	}
+	nbPoints := 0
+	sizeSi := make([]int, len(points))
+	for i := 0; i < nbInstances; i++ {
+		nbPoints += len(points[i])
+		sizeSi[i] = len(points[i])
+	}
+	totalSize := maxSizePolys + nbPoints // upper bound of the size of f := ∑ᵢ γⁱZ_{T\Sᵢ}(f_i(X)-r)
+
+	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
+	bufTotalSize := make([]fr.Element, totalSize)
+	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
+	res.ClaimedValues = make([][]fr.Element, nbInstances)
+	for i := 0; i < nbInstances; i++ {
+		res.ClaimedValues[i] = make([]fr.Element, len(points[i]))
+	}
+	var accGamma fr.Element
+	accGamma.SetOne()
+
+	ztMinusSi := make([][]fr.Element, nbInstances)
+	ri := make([][]fr.Element, nbInstances)
+	for i := 0; i < nbInstances; i++ {
+
+		for j := 0; j < len(points[i]); j++ {
+			res.ClaimedValues[i][j] = eval(polynomials[i], points[i][j])
+		}
+
+		ztMinusSi[i] = buildZtMinusSi(points, i)
+
+		copy(bufMaxSizePolynomials, polynomials[i])
+		ri[i] = interpolate(points[i], res.ClaimedValues[i])
+		sub(bufMaxSizePolynomials, ri[i])
+
+		bufTotalSize = mul(bufMaxSizePolynomials, ztMinusSi[i], bufTotalSize)
+		bufTotalSize = mulByConstant(bufTotalSize, accGamma)
+		for j := 0; j < len(bufTotalSize); j++ {
+			f[j].Add(&f[j], &bufTotalSize[j])
+		}
+
+		accGamma.Mul(&accGamma, &gamma)
+		setZero(bufMaxSizePolynomials)
+	}
+
+	zt := buildVanishingPoly(flatten(points))
+	w := div(f, zt) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
+	res.W, err = kzg.Commit(w, pk)
+	if err != nil {
+		return res, err
+	}
+
+	// derive z
+	z, err := deriveChallenge("z", nil, []kzg.Digest{res.W}, fs)
+	if err != nil {
+		return res, err
+	}
+
+	// compute L = ∑ᵢγⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))-Z_{T}(z)W
+	accGamma.SetOne()
+	var gammaiZtMinusSiZ fr.Element
+	l := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
+	for i := 0; i < len(polynomials); i++ {
+
+		ztMinusSiZ := eval(ztMinusSi[i], z)          // Z_{T\Sᵢ}(z)
+		gammaiZtMinusSiZ.Mul(&accGamma, &ztMinusSiZ) // γⁱZ_{T\Sᵢ}(z)
+
+		copy(bufMaxSizePolynomials, polynomials[i])
+		riz := eval(ri[i], z)
+		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz) // (fᵢ-rᵢ(z))
+		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusSiZ)        // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
+		for j := 0; j < len(bufMaxSizePolynomials); j++ {
+			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
+		}
+
+		setZero(bufMaxSizePolynomials)
+		accGamma.Mul(&accGamma, &gamma)
+	}
+	ztz := eval(zt, z)
+	setZero(bufTotalSize)
+	copy(bufTotalSize, w)
+	mulByConstant(bufTotalSize, ztz) // Z_{T}(z)W
+	for i := 0; i < totalSize-maxSizePolys; i++ {
+		l[totalSize-1-i].Neg(&bufTotalSize[totalSize-1-i])
+	}
+	for i := 0; i < maxSizePolys; i++ {
+		l[i].Sub(&l[i], &bufTotalSize[i])
+	} // L <- L-Z_{T}(z)W
+
+	xMinusZ := buildVanishingPoly([]fr.Element{z})
+	wPrime := div(l, xMinusZ)
+
+	res.WPrime, err = kzg.Commit(wPrime, pk)
+	if err != nil {
+		return res, err
+	}
+
+	return res, nil
+}
+
+// BatchVerify uses proof to check that the commitments correctly open to proof.ClaimedValues
+// at points. The order matters: the proof validates that the i-th commitment is correctly opened
+// at the i-th point
+// dataTranscript is some extra data that might be needed for Fiat Shamir, and is appended at the end
+// of the original transcript.
+func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
+
+	if len(digests) != len(proof.ClaimedValues) {
+		return ErrInvalidNumberOfPoints
+	}
+	if len(digests) != len(points) {
+		return ErrInvalidNumberOfPoints
+	}
+
+	// transcript
+	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
+
+	// derive γ
+	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
+	if err != nil {
+		return err
+	}
+
+	// derive z
+	// TODO seems ok that z depend only on W, need to check that carefully
+	z, err := deriveChallenge("z", nil, []kzg.Digest{proof.W}, fs)
+	if err != nil {
+		return err
+	}
+
+	// check that e(F + zW', [1]_{2})=e(W',[x]_{2})
+	// where F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}-[∑ᵢγⁱZ_{T\xᵢ}(z)fᵢ(z)]_{1}-Z_{T}(z)[W]
+	var sumGammaiZTminusSiRiz, tmp, accGamma fr.Element
+	nbInstances := len(points)
+	gammaiZTminusSiz := make([]fr.Element, nbInstances)
+	accGamma.SetOne()
+	ri := make([][]fr.Element, nbInstances)
+	for i := 0; i < len(points); i++ {
+
+		ztMinusSi := buildZtMinusSi(points, i)                   // Z_{T-S_{i}}(X)
+		gammaiZTminusSiz[i] = eval(ztMinusSi, z)                 // Z_{T-S_{i}}(z)
+		gammaiZTminusSiz[i].Mul(&accGamma, &gammaiZTminusSiz[i]) // \gamma^{i} Z_{T-S_{i}}(z)
+
+		ri[i] = interpolate(points[i], proof.ClaimedValues[i])
+		riz := eval(ri[i], z)               // r_{i}(z)
+		tmp.Mul(&gammaiZTminusSiz[i], &riz) // Z_{T-S_{i}}(z)r_{i}(z)
+		sumGammaiZTminusSiRiz.Add(&sumGammaiZTminusSiRiz, &tmp)
+
+		accGamma.Mul(&accGamma, &gamma)
+	}
+
+	// ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}
+	config := ecc.MultiExpConfig{}
+	var sumGammaiZtMinusSiComi kzg.Digest
+	_, err = sumGammaiZtMinusSiComi.MultiExp(digests, gammaiZTminusSiz, config)
+	if err != nil {
+		return err
+	}
+
+	var bufBigInt big.Int
+
+	// [∑ᵢZ_{T\xᵢ}fᵢ(z)]_{1}
+	var sumGammaiZTminusSiRizCom kzg.Digest
+	var sumGammaiZTminusSiRizBigInt big.Int
+	sumGammaiZTminusSiRiz.BigInt(&sumGammaiZTminusSiRizBigInt)
+	sumGammaiZTminusSiRizCom.ScalarMultiplication(&vk.G1, &sumGammaiZTminusSiRizBigInt)
+
+	// Z_{T}(z)[W]
+	zt := buildVanishingPoly(flatten(points))
+	ztz := eval(zt, z)
+	var ztW kzg.Digest
+	ztz.BigInt(&bufBigInt)
+	ztW.ScalarMultiplication(&proof.W, &bufBigInt)
+
+	// F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i} - [∑ᵢγⁱZ_{T\xᵢ}fᵢ(z)]_{1} - Z_{T}(z)[W]
+	var f kzg.Digest
+	f.Sub(&sumGammaiZtMinusSiComi, &sumGammaiZTminusSiRizCom).
+		Sub(&f, &ztW)
+
+	// F+zW'
+	var zWPrime kzg.Digest
+	z.BigInt(&bufBigInt)
+	zWPrime.ScalarMultiplication(&proof.WPrime, &bufBigInt)
+	f.Add(&f, &zWPrime)
+	f.Neg(&f)
+
+	// check that e(F+zW',[1]_{2})=e(W',[x]_{2})
+	check, err := bls12381.PairingCheckFixedQ(
+		[]bls12381.G1Affine{f, proof.WPrime},
+		vk.Lines[:],
+	)
+
+	if !check {
+		return ErrVerifyOpeningProof
+	}
+
+	return nil
+}
+
+// deriveChallenge derives a challenge using Fiat Shamir to polynomials.
+// The arguments are added to the transcript in the order in which they are given.
+func deriveChallenge(name string, points [][]fr.Element, digests []kzg.Digest, t *fiatshamir.Transcript, dataTranscript ...[]byte) (fr.Element, error) {
+
+	// derive the challenge gamma, binded to the point and the commitments
+	for i := range points {
+		for j := range points[i] {
+			if err := t.Bind(name, points[i][j].Marshal()); err != nil {
+				return fr.Element{}, err
+			}
+		}
+	}
+	for i := range digests {
+		if err := t.Bind(name, digests[i].Marshal()); err != nil {
+			return fr.Element{}, err
+		}
+	}
+
+	for i := 0; i < len(dataTranscript); i++ {
+		if err := t.Bind(name, dataTranscript[i]); err != nil {
+			return fr.Element{}, err
+		}
+	}
+
+	gammaByte, err := t.ComputeChallenge(name)
+	if err != nil {
+		return fr.Element{}, err
+	}
+	var gamma fr.Element
+	gamma.SetBytes(gammaByte)
+
+	return gamma, nil
+}
+
+// ------------------------------
+// utils
+
+func flatten(x [][]fr.Element) []fr.Element {
+	nbPoints := 0
+	for i := 0; i < len(x); i++ {
+		nbPoints += len(x[i])
+	}
+	res := make([]fr.Element, 0, nbPoints)
+	for i := 0; i < len(x); i++ {
+		res = append(res, x[i]...)
+	}
+	return res
+}
+
+// sets f to zero
+func setZero(f []fr.Element) {
+	for i := 0; i < len(f); i++ {
+		f[i].SetZero()
+	}
+}
+
+func eval(f []fr.Element, x fr.Element) fr.Element {
+	var y fr.Element
+	for i := len(f) - 1; i >= 0; i-- {
+		y.Mul(&y, &x).Add(&y, &f[i])
+	}
+	return y
+}
+
+// returns γ*f, re-using f
+func mulByConstant(f []fr.Element, gamma fr.Element) []fr.Element {
+	for i := 0; i < len(f); i++ {
+		f[i].Mul(&f[i], &gamma)
+	}
+	return f
+}
+
+// computes f <- (x-a)*f
+// memory of f is re used, need to pass a copy to not modify it
+func multiplyLinearFactor(f []fr.Element, a fr.Element) []fr.Element {
+	s := len(f)
+	var tmp fr.Element
+	f = append(f, fr.NewElement(0))
+	f[s] = f[s-1]
+	for i := s - 1; i >= 1; i-- {
+		tmp.Mul(&f[i], &a)
+		f[i].Sub(&f[i-1], &tmp)
+	}
+	f[0].Mul(&f[0], &a).Neg(&f[0])
+	return f
+}
+
+// returns S_{T\Sᵢ} where Sᵢ=x[i]
+func buildZtMinusSi(x [][]fr.Element, i int) []fr.Element {
+	nbPoints := 0
+	for i := 0; i < len(x); i++ {
+		nbPoints += len(x[i])
+	}
+	bufPoints := make([]fr.Element, 0, nbPoints-len(x[i]))
+	for j := 0; j < i; j++ {
+		bufPoints = append(bufPoints, x[j]...)
+	}
+	for j := i + 1; j < len(x); j++ {
+		bufPoints = append(bufPoints, x[j]...)
+	}
+	ztMinusSi := buildVanishingPoly(bufPoints)
+	return ztMinusSi
+}
+
+// returns πᵢ(X-xᵢ)
+func buildVanishingPoly(x []fr.Element) []fr.Element {
+	res := make([]fr.Element, 1, len(x)+1)
+	res[0].SetOne()
+	for i := 0; i < len(x); i++ {
+		res = multiplyLinearFactor(res, x[i])
+	}
+	return res
+}
+
+// returns f such that f(xᵢ)=yᵢ, x and y are assumed to be of the same size
+func interpolate(x, y []fr.Element) []fr.Element {
+
+	res := make([]fr.Element, len(x))
+	for i := 0; i < len(x); i++ {
+		li := buildLagrangeFromDomain(x, i)
+		li = mulByConstant(li, y[i])
+		for j := 0; j < len(x); j++ {
+			res[j].Add(&res[j], &li[j])
+		}
+	}
+
+	return res
+}
+
+// returns f such that f(xⱼ)=δⁱⱼ
+func buildLagrangeFromDomain(x []fr.Element, i int) []fr.Element {
+	xx := make([]fr.Element, len(x)-1)
+	copy(xx, x[:i])
+	copy(xx[i:], x[i+1:])
+	res := buildVanishingPoly(xx)
+	d := eval(res, x[i])
+	d.Inverse(&d)
+	res = mulByConstant(res, d)
+	return res
+}
+
+// returns f-g, the memory of f is re used, deg(g) << deg(f) here
+func sub(f, g []fr.Element) []fr.Element {
+	for i := 0; i < len(g); i++ {
+		f[i].Sub(&f[i], &g[i])
+	}
+	return f
+}
+
+// returns f*g using naive multiplication
+// deg(f)>>deg(g), deg(small) =~ 10 max
+// buf is used as a buffer and should not be f or g
+// f and g are not modified
+func mul(f, g []fr.Element, res []fr.Element) []fr.Element {
+
+	sizeRes := len(f) + len(g) - 1
+	if len(res) < sizeRes {
+		s := make([]fr.Element, sizeRes-len(res))
+		res = append(res, s...)
+	}
+	setZero(res)
+
+	var tmp fr.Element
+	for i := 0; i < len(g); i++ {
+		for j := 0; j < len(f); j++ {
+			tmp.Mul(&f[j], &g[i])
+			res[j+i].Add(&res[j+i], &tmp)
+		}
+	}
+	return res
+}
+
+// returns f/g (assuming g divides f)
+// OK to not use fft if deg(g) is small
+// g's leading coefficient is assumed to be 1
+// f memory is re-used for the result, need to pass a copy to not modify it
+func div(f, g []fr.Element) []fr.Element {
+	sizef := len(f)
+	sizeg := len(g)
+	stop := sizeg - +1
+	var t fr.Element
+	for i := sizef - 2; i >= stop; i-- {
+		for j := 0; j < sizeg-1; j++ {
+			t.Mul(&f[i+1], &g[sizeg-2-j])
+			f[i-j].Sub(&f[i-j], &t)
+		}
+	}
+	return f[sizeg-1:]
+}
diff --git a/ecc/bls12-381/shplonk/shplonk_test.go b/ecc/bls12-381/shplonk/shplonk_test.go
new file mode 100644
index 0000000000..043238b47d
--- /dev/null
+++ b/ecc/bls12-381/shplonk/shplonk_test.go
@@ -0,0 +1,320 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"crypto/sha256"
+	"math/big"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls12-381/kzg"
+	"github.com/stretchr/testify/require"
+)
+
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *kzg.SRS
+var bAlpha *big.Int
+
+func init() {
+	const srsSize = 230
+	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+}
+
+func TestOpening(t *testing.T) {
+
+	assert := require.New(t)
+
+	nbPolys := 2
+	sizePoly := make([]int, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		sizePoly[i] = 10 + i
+	}
+	polys := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		polys[i] = make([]fr.Element, sizePoly[i])
+		for j := 0; j < sizePoly[i]; j++ {
+			polys[i][j].SetRandom()
+		}
+	}
+
+	digests := make([]kzg.Digest, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		digests[i], _ = kzg.Commit(polys[i], testSrs.Pk)
+	}
+
+	points := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		points[i] = make([]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+
+	hf := sha256.New()
+
+	// correct proof
+	openingProof, err := BatchOpen(polys, digests, points, hf, testSrs.Pk)
+	assert.NoError(err)
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	assert.NoError(err)
+
+	// tampered proof
+	openingProof.ClaimedValues[0][0].SetRandom()
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	assert.Error(err)
+
+}
+
+func TestBuildZtMinusSi(t *testing.T) {
+
+	nbSi := 10
+	points := make([][]fr.Element, nbSi)
+	sizeSi := make([]int, nbSi)
+	nbPoints := 0
+	for i := 0; i < nbSi; i++ {
+		sizeSi[i] = 5 + i
+		nbPoints += sizeSi[i]
+		points[i] = make([]fr.Element, sizeSi[i])
+		for j := 0; j < sizeSi[i]; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+	for i := 0; i < nbSi; i++ {
+		ztMinusSi := buildZtMinusSi(points, i)
+		if len(ztMinusSi) != nbPoints-sizeSi[i]+1 {
+			t.Fatal("deg(Z_{T-S_{i}}) should be nbPoints-size(S_{i})")
+		}
+		for j := 0; j < nbSi; j++ {
+			if j == i {
+				for k := 0; k < sizeSi[j]; k++ {
+					y := eval(ztMinusSi, points[j][k])
+					if y.IsZero() {
+						t.Fatal("Z_{T-S_{i}}(S_{i}) should not be zero")
+					}
+				}
+				continue
+			}
+			for k := 0; k < sizeSi[j]; k++ {
+				y := eval(ztMinusSi, points[j][k])
+				if !y.IsZero() {
+					t.Fatal("Z_{T-S_{i}}(S_{j}) should be zero")
+				}
+			}
+		}
+	}
+
+}
+
+func TestInterpolate(t *testing.T) {
+
+	nbPoints := 10
+	x := make([]fr.Element, nbPoints)
+	y := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		y[i].SetRandom()
+	}
+	f := interpolate(x, y)
+	for i := 0; i < nbPoints; i++ {
+		fx := eval(f, x[i])
+		if !fx.Equal(&y[i]) {
+			t.Fatal("f(x_{i})!=y_{i}")
+		}
+	}
+
+}
+
+func TestBuildLagrangeFromDomain(t *testing.T) {
+
+	nbPoints := 10
+	points := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		points[i].SetRandom()
+	}
+	var r fr.Element
+	for i := 0; i < nbPoints; i++ {
+
+		l := buildLagrangeFromDomain(points, i)
+
+		// check that l(xᵢ)=1 and l(xⱼ)=0 for j!=i
+		for j := 0; j < nbPoints; j++ {
+			y := eval(l, points[j])
+			if i == j {
+				if !y.IsOne() {
+					t.Fatal("l_{i}(x_{i}) should be equal to 1")
+				}
+			} else {
+				if !y.IsZero() {
+					t.Fatal("l_{i}(x_{j}) where i!=j should be equal to 0")
+				}
+			}
+		}
+		r.SetRandom()
+		y := eval(l, r)
+		if y.IsZero() {
+			t.Fatal("l_{i}(x) should not be zero if x is random")
+		}
+	}
+
+}
+
+func TestBuildVanishingPoly(t *testing.T) {
+	s := 10
+	x := make([]fr.Element, s)
+	for i := 0; i < s; i++ {
+		x[i].SetRandom()
+	}
+	r := buildVanishingPoly(x)
+
+	if len(r) != s+1 {
+		t.Fatal("error degree r")
+	}
+
+	// check that r(xᵢ)=0 for all i
+	for i := 0; i < len(x); i++ {
+		y := eval(r, x[i])
+		if !y.IsZero() {
+			t.Fatal("πᵢ(X-xᵢ) at xᵢ should be zero")
+		}
+	}
+
+	// check that r(y)!=0 for a random point
+	var a fr.Element
+	a.SetRandom()
+	y := eval(r, a)
+	if y.IsZero() {
+		t.Fatal("πᵢ(X-xᵢ) at r \neq xᵢ should not be zero")
+	}
+}
+
+func TestMultiplyLinearFactor(t *testing.T) {
+
+	s := 10
+	f := make([]fr.Element, s, s+1)
+	for i := 0; i < 10; i++ {
+		f[i].SetRandom()
+	}
+
+	var a, y fr.Element
+	a.SetRandom()
+	f = multiplyLinearFactor(f, a)
+	y = eval(f, a)
+	if !y.IsZero() {
+		t.Fatal("(X-a)f(X) should be zero at a")
+	}
+	a.SetRandom()
+	y = eval(f, a)
+	if y.IsZero() {
+		t.Fatal("(X-1)f(X) at a random point should not be zero")
+	}
+
+}
+
+func TestNaiveMul(t *testing.T) {
+
+	size := 10
+	f := make([]fr.Element, size)
+	for i := 0; i < size; i++ {
+		f[i].SetRandom()
+	}
+
+	nbPoints := 10
+	points := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		points[i].SetRandom()
+	}
+
+	v := buildVanishingPoly(points)
+	buf := make([]fr.Element, size+nbPoints-1)
+	g := mul(f, v, buf)
+
+	// check that g(xᵢ) = 0
+	for i := 0; i < nbPoints; i++ {
+		y := eval(g, points[i])
+		if !y.IsZero() {
+			t.Fatal("f(X)(X-x_{1})..(X-x_{n}) at x_{i} should be zero")
+		}
+	}
+
+	// check that g(r) != 0 for a random point
+	var a fr.Element
+	a.SetRandom()
+	y := eval(g, a)
+	if y.IsZero() {
+		t.Fatal("f(X)(X-x_{1})..(X-x_{n}) at a random point should not be zero")
+	}
+
+}
+
+func TestDiv(t *testing.T) {
+
+	nbPoints := 10
+	s := 10
+	f := make([]fr.Element, s, s+nbPoints)
+	for i := 0; i < s; i++ {
+		f[i].SetRandom()
+	}
+
+	// backup
+	g := make([]fr.Element, s)
+	copy(g, f)
+
+	// successive divions of linear terms
+	x := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		f = multiplyLinearFactor(f, x[i])
+	}
+	q := make([][2]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		q[i][1].SetOne()
+		q[i][0].Neg(&x[i])
+		f = div(f, q[i][:])
+	}
+
+	// g should be equal to f
+	if len(f) != len(g) {
+		t.Fatal("lengths don't match")
+	}
+	for i := 0; i < len(g); i++ {
+		if !f[i].Equal(&g[i]) {
+			t.Fatal("f(x)(x-a)/(x-a) should be equal to f(x)")
+		}
+	}
+
+	// division by a degree > 1 polynomial
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		f = multiplyLinearFactor(f, x[i])
+	}
+	r := buildVanishingPoly(x)
+	f = div(f, r)
+
+	// g should be equal to f
+	if len(f) != len(g) {
+		t.Fatal("lengths don't match")
+	}
+	for i := 0; i < len(g); i++ {
+		if !f[i].Equal(&g[i]) {
+			t.Fatal("f(x)(x-a)/(x-a) should be equal to f(x)")
+		}
+	}
+
+}
diff --git a/ecc/bls24-315/shplonk/doc.go b/ecc/bls24-315/shplonk/doc.go
new file mode 100644
index 0000000000..e048f46009
--- /dev/null
+++ b/ecc/bls24-315/shplonk/doc.go
@@ -0,0 +1,18 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// Package shplonk provides a SHPLONK commitment scheme, cf https://eprint.iacr.org/2020/081.pdf
+package shplonk
diff --git a/ecc/bls24-315/shplonk/marshal.go b/ecc/bls24-315/shplonk/marshal.go
new file mode 100644
index 0000000000..a57a90679f
--- /dev/null
+++ b/ecc/bls24-315/shplonk/marshal.go
@@ -0,0 +1,62 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"io"
+
+	"github.com/consensys/gnark-crypto/ecc/bls24-315"
+)
+
+func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
+
+	dec := bls24315.NewDecoder(r)
+
+	toDecode := []interface{}{
+		&proof.W,
+		&proof.WPrime,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toDecode {
+		if err := dec.Decode(v); err != nil {
+			return dec.BytesRead(), err
+		}
+	}
+
+	return dec.BytesRead(), nil
+}
+
+// WriteTo writes binary encoding of a OpeningProof
+func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
+
+	enc := bls24315.NewEncoder(w)
+
+	toEncode := []interface{}{
+		&proof.W,
+		&proof.WPrime,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toEncode {
+		if err := enc.Encode(v); err != nil {
+			return enc.BytesWritten(), err
+		}
+	}
+
+	return enc.BytesWritten(), nil
+}
diff --git a/ecc/bls24-315/shplonk/shplonk.go b/ecc/bls24-315/shplonk/shplonk.go
new file mode 100644
index 0000000000..f3be3f5bfa
--- /dev/null
+++ b/ecc/bls24-315/shplonk/shplonk.go
@@ -0,0 +1,462 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"errors"
+	"hash"
+	"math/big"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bls24-315"
+	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls24-315/kzg"
+	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
+)
+
+var (
+	ErrInvalidNumberOfPoints = errors.New("number of digests should be equal to the number of points")
+	ErrVerifyOpeningProof    = errors.New("can't verify batch opening proof")
+)
+
+// OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
+//
+// implements io.ReaderFrom and io.WriterTo
+type OpeningProof struct {
+
+	// W = ∑ᵢ γⁱZ_{T\Sᵢ}(f_i(X)-r)/Z_{T} where Z_{T} is the vanishing polynomial on the (Sᵢ)_{i}
+	// and r interpolates fᵢ(Sᵢ) on (Sᵢ)
+	W bls24315.G1Affine
+
+	// L(X)/(X-z) where L(X)=∑ᵢγⁱZ_{T\xᵢ}(f_i(X)-rᵢ) - Z_{T}W(X)
+	WPrime bls24315.G1Affine
+
+	// ClaimedValues[i] are the values of fᵢ on Sᵢ
+	ClaimedValues [][]fr.Element
+}
+
+// BatchOpen opens the list of polynomials on points, where the i-th polynomials is opend at points[i].
+func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
+
+	var res OpeningProof
+
+	nbInstances := len(polynomials)
+	if len(polynomials) != len(points) {
+		return res, ErrInvalidNumberOfPoints
+	}
+
+	// transcript
+	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
+
+	// derive γ
+	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
+	if err != nil {
+		return res, err
+	}
+
+	// compute the size of the linear combination
+	maxSizePolys := len(polynomials[0])
+	for i := 1; i < len(polynomials); i++ {
+		if maxSizePolys < len(polynomials[i]) {
+			maxSizePolys = len(polynomials[i])
+		}
+	}
+	nbPoints := 0
+	sizeSi := make([]int, len(points))
+	for i := 0; i < nbInstances; i++ {
+		nbPoints += len(points[i])
+		sizeSi[i] = len(points[i])
+	}
+	totalSize := maxSizePolys + nbPoints // upper bound of the size of f := ∑ᵢ γⁱZ_{T\Sᵢ}(f_i(X)-r)
+
+	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
+	bufTotalSize := make([]fr.Element, totalSize)
+	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
+	res.ClaimedValues = make([][]fr.Element, nbInstances)
+	for i := 0; i < nbInstances; i++ {
+		res.ClaimedValues[i] = make([]fr.Element, len(points[i]))
+	}
+	var accGamma fr.Element
+	accGamma.SetOne()
+
+	ztMinusSi := make([][]fr.Element, nbInstances)
+	ri := make([][]fr.Element, nbInstances)
+	for i := 0; i < nbInstances; i++ {
+
+		for j := 0; j < len(points[i]); j++ {
+			res.ClaimedValues[i][j] = eval(polynomials[i], points[i][j])
+		}
+
+		ztMinusSi[i] = buildZtMinusSi(points, i)
+
+		copy(bufMaxSizePolynomials, polynomials[i])
+		ri[i] = interpolate(points[i], res.ClaimedValues[i])
+		sub(bufMaxSizePolynomials, ri[i])
+
+		bufTotalSize = mul(bufMaxSizePolynomials, ztMinusSi[i], bufTotalSize)
+		bufTotalSize = mulByConstant(bufTotalSize, accGamma)
+		for j := 0; j < len(bufTotalSize); j++ {
+			f[j].Add(&f[j], &bufTotalSize[j])
+		}
+
+		accGamma.Mul(&accGamma, &gamma)
+		setZero(bufMaxSizePolynomials)
+	}
+
+	zt := buildVanishingPoly(flatten(points))
+	w := div(f, zt) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
+	res.W, err = kzg.Commit(w, pk)
+	if err != nil {
+		return res, err
+	}
+
+	// derive z
+	z, err := deriveChallenge("z", nil, []kzg.Digest{res.W}, fs)
+	if err != nil {
+		return res, err
+	}
+
+	// compute L = ∑ᵢγⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))-Z_{T}(z)W
+	accGamma.SetOne()
+	var gammaiZtMinusSiZ fr.Element
+	l := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
+	for i := 0; i < len(polynomials); i++ {
+
+		ztMinusSiZ := eval(ztMinusSi[i], z)          // Z_{T\Sᵢ}(z)
+		gammaiZtMinusSiZ.Mul(&accGamma, &ztMinusSiZ) // γⁱZ_{T\Sᵢ}(z)
+
+		copy(bufMaxSizePolynomials, polynomials[i])
+		riz := eval(ri[i], z)
+		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz) // (fᵢ-rᵢ(z))
+		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusSiZ)        // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
+		for j := 0; j < len(bufMaxSizePolynomials); j++ {
+			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
+		}
+
+		setZero(bufMaxSizePolynomials)
+		accGamma.Mul(&accGamma, &gamma)
+	}
+	ztz := eval(zt, z)
+	setZero(bufTotalSize)
+	copy(bufTotalSize, w)
+	mulByConstant(bufTotalSize, ztz) // Z_{T}(z)W
+	for i := 0; i < totalSize-maxSizePolys; i++ {
+		l[totalSize-1-i].Neg(&bufTotalSize[totalSize-1-i])
+	}
+	for i := 0; i < maxSizePolys; i++ {
+		l[i].Sub(&l[i], &bufTotalSize[i])
+	} // L <- L-Z_{T}(z)W
+
+	xMinusZ := buildVanishingPoly([]fr.Element{z})
+	wPrime := div(l, xMinusZ)
+
+	res.WPrime, err = kzg.Commit(wPrime, pk)
+	if err != nil {
+		return res, err
+	}
+
+	return res, nil
+}
+
+// BatchVerify uses proof to check that the commitments correctly open to proof.ClaimedValues
+// at points. The order matters: the proof validates that the i-th commitment is correctly opened
+// at the i-th point
+// dataTranscript is some extra data that might be needed for Fiat Shamir, and is appended at the end
+// of the original transcript.
+func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
+
+	if len(digests) != len(proof.ClaimedValues) {
+		return ErrInvalidNumberOfPoints
+	}
+	if len(digests) != len(points) {
+		return ErrInvalidNumberOfPoints
+	}
+
+	// transcript
+	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
+
+	// derive γ
+	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
+	if err != nil {
+		return err
+	}
+
+	// derive z
+	// TODO seems ok that z depend only on W, need to check that carefully
+	z, err := deriveChallenge("z", nil, []kzg.Digest{proof.W}, fs)
+	if err != nil {
+		return err
+	}
+
+	// check that e(F + zW', [1]_{2})=e(W',[x]_{2})
+	// where F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}-[∑ᵢγⁱZ_{T\xᵢ}(z)fᵢ(z)]_{1}-Z_{T}(z)[W]
+	var sumGammaiZTminusSiRiz, tmp, accGamma fr.Element
+	nbInstances := len(points)
+	gammaiZTminusSiz := make([]fr.Element, nbInstances)
+	accGamma.SetOne()
+	ri := make([][]fr.Element, nbInstances)
+	for i := 0; i < len(points); i++ {
+
+		ztMinusSi := buildZtMinusSi(points, i)                   // Z_{T-S_{i}}(X)
+		gammaiZTminusSiz[i] = eval(ztMinusSi, z)                 // Z_{T-S_{i}}(z)
+		gammaiZTminusSiz[i].Mul(&accGamma, &gammaiZTminusSiz[i]) // \gamma^{i} Z_{T-S_{i}}(z)
+
+		ri[i] = interpolate(points[i], proof.ClaimedValues[i])
+		riz := eval(ri[i], z)               // r_{i}(z)
+		tmp.Mul(&gammaiZTminusSiz[i], &riz) // Z_{T-S_{i}}(z)r_{i}(z)
+		sumGammaiZTminusSiRiz.Add(&sumGammaiZTminusSiRiz, &tmp)
+
+		accGamma.Mul(&accGamma, &gamma)
+	}
+
+	// ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}
+	config := ecc.MultiExpConfig{}
+	var sumGammaiZtMinusSiComi kzg.Digest
+	_, err = sumGammaiZtMinusSiComi.MultiExp(digests, gammaiZTminusSiz, config)
+	if err != nil {
+		return err
+	}
+
+	var bufBigInt big.Int
+
+	// [∑ᵢZ_{T\xᵢ}fᵢ(z)]_{1}
+	var sumGammaiZTminusSiRizCom kzg.Digest
+	var sumGammaiZTminusSiRizBigInt big.Int
+	sumGammaiZTminusSiRiz.BigInt(&sumGammaiZTminusSiRizBigInt)
+	sumGammaiZTminusSiRizCom.ScalarMultiplication(&vk.G1, &sumGammaiZTminusSiRizBigInt)
+
+	// Z_{T}(z)[W]
+	zt := buildVanishingPoly(flatten(points))
+	ztz := eval(zt, z)
+	var ztW kzg.Digest
+	ztz.BigInt(&bufBigInt)
+	ztW.ScalarMultiplication(&proof.W, &bufBigInt)
+
+	// F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i} - [∑ᵢγⁱZ_{T\xᵢ}fᵢ(z)]_{1} - Z_{T}(z)[W]
+	var f kzg.Digest
+	f.Sub(&sumGammaiZtMinusSiComi, &sumGammaiZTminusSiRizCom).
+		Sub(&f, &ztW)
+
+	// F+zW'
+	var zWPrime kzg.Digest
+	z.BigInt(&bufBigInt)
+	zWPrime.ScalarMultiplication(&proof.WPrime, &bufBigInt)
+	f.Add(&f, &zWPrime)
+	f.Neg(&f)
+
+	// check that e(F+zW',[1]_{2})=e(W',[x]_{2})
+	check, err := bls24315.PairingCheckFixedQ(
+		[]bls24315.G1Affine{f, proof.WPrime},
+		vk.Lines[:],
+	)
+
+	if !check {
+		return ErrVerifyOpeningProof
+	}
+
+	return nil
+}
+
+// deriveChallenge derives a challenge using Fiat Shamir to polynomials.
+// The arguments are added to the transcript in the order in which they are given.
+func deriveChallenge(name string, points [][]fr.Element, digests []kzg.Digest, t *fiatshamir.Transcript, dataTranscript ...[]byte) (fr.Element, error) {
+
+	// derive the challenge gamma, binded to the point and the commitments
+	for i := range points {
+		for j := range points[i] {
+			if err := t.Bind(name, points[i][j].Marshal()); err != nil {
+				return fr.Element{}, err
+			}
+		}
+	}
+	for i := range digests {
+		if err := t.Bind(name, digests[i].Marshal()); err != nil {
+			return fr.Element{}, err
+		}
+	}
+
+	for i := 0; i < len(dataTranscript); i++ {
+		if err := t.Bind(name, dataTranscript[i]); err != nil {
+			return fr.Element{}, err
+		}
+	}
+
+	gammaByte, err := t.ComputeChallenge(name)
+	if err != nil {
+		return fr.Element{}, err
+	}
+	var gamma fr.Element
+	gamma.SetBytes(gammaByte)
+
+	return gamma, nil
+}
+
+// ------------------------------
+// utils
+
+func flatten(x [][]fr.Element) []fr.Element {
+	nbPoints := 0
+	for i := 0; i < len(x); i++ {
+		nbPoints += len(x[i])
+	}
+	res := make([]fr.Element, 0, nbPoints)
+	for i := 0; i < len(x); i++ {
+		res = append(res, x[i]...)
+	}
+	return res
+}
+
+// sets f to zero
+func setZero(f []fr.Element) {
+	for i := 0; i < len(f); i++ {
+		f[i].SetZero()
+	}
+}
+
+func eval(f []fr.Element, x fr.Element) fr.Element {
+	var y fr.Element
+	for i := len(f) - 1; i >= 0; i-- {
+		y.Mul(&y, &x).Add(&y, &f[i])
+	}
+	return y
+}
+
+// returns γ*f, re-using f
+func mulByConstant(f []fr.Element, gamma fr.Element) []fr.Element {
+	for i := 0; i < len(f); i++ {
+		f[i].Mul(&f[i], &gamma)
+	}
+	return f
+}
+
+// computes f <- (x-a)*f
+// memory of f is re used, need to pass a copy to not modify it
+func multiplyLinearFactor(f []fr.Element, a fr.Element) []fr.Element {
+	s := len(f)
+	var tmp fr.Element
+	f = append(f, fr.NewElement(0))
+	f[s] = f[s-1]
+	for i := s - 1; i >= 1; i-- {
+		tmp.Mul(&f[i], &a)
+		f[i].Sub(&f[i-1], &tmp)
+	}
+	f[0].Mul(&f[0], &a).Neg(&f[0])
+	return f
+}
+
+// returns S_{T\Sᵢ} where Sᵢ=x[i]
+func buildZtMinusSi(x [][]fr.Element, i int) []fr.Element {
+	nbPoints := 0
+	for i := 0; i < len(x); i++ {
+		nbPoints += len(x[i])
+	}
+	bufPoints := make([]fr.Element, 0, nbPoints-len(x[i]))
+	for j := 0; j < i; j++ {
+		bufPoints = append(bufPoints, x[j]...)
+	}
+	for j := i + 1; j < len(x); j++ {
+		bufPoints = append(bufPoints, x[j]...)
+	}
+	ztMinusSi := buildVanishingPoly(bufPoints)
+	return ztMinusSi
+}
+
+// returns πᵢ(X-xᵢ)
+func buildVanishingPoly(x []fr.Element) []fr.Element {
+	res := make([]fr.Element, 1, len(x)+1)
+	res[0].SetOne()
+	for i := 0; i < len(x); i++ {
+		res = multiplyLinearFactor(res, x[i])
+	}
+	return res
+}
+
+// returns f such that f(xᵢ)=yᵢ, x and y are assumed to be of the same size
+func interpolate(x, y []fr.Element) []fr.Element {
+
+	res := make([]fr.Element, len(x))
+	for i := 0; i < len(x); i++ {
+		li := buildLagrangeFromDomain(x, i)
+		li = mulByConstant(li, y[i])
+		for j := 0; j < len(x); j++ {
+			res[j].Add(&res[j], &li[j])
+		}
+	}
+
+	return res
+}
+
+// returns f such that f(xⱼ)=δⁱⱼ
+func buildLagrangeFromDomain(x []fr.Element, i int) []fr.Element {
+	xx := make([]fr.Element, len(x)-1)
+	copy(xx, x[:i])
+	copy(xx[i:], x[i+1:])
+	res := buildVanishingPoly(xx)
+	d := eval(res, x[i])
+	d.Inverse(&d)
+	res = mulByConstant(res, d)
+	return res
+}
+
+// returns f-g, the memory of f is re used, deg(g) << deg(f) here
+func sub(f, g []fr.Element) []fr.Element {
+	for i := 0; i < len(g); i++ {
+		f[i].Sub(&f[i], &g[i])
+	}
+	return f
+}
+
+// returns f*g using naive multiplication
+// deg(f)>>deg(g), deg(small) =~ 10 max
+// buf is used as a buffer and should not be f or g
+// f and g are not modified
+func mul(f, g []fr.Element, res []fr.Element) []fr.Element {
+
+	sizeRes := len(f) + len(g) - 1
+	if len(res) < sizeRes {
+		s := make([]fr.Element, sizeRes-len(res))
+		res = append(res, s...)
+	}
+	setZero(res)
+
+	var tmp fr.Element
+	for i := 0; i < len(g); i++ {
+		for j := 0; j < len(f); j++ {
+			tmp.Mul(&f[j], &g[i])
+			res[j+i].Add(&res[j+i], &tmp)
+		}
+	}
+	return res
+}
+
+// returns f/g (assuming g divides f)
+// OK to not use fft if deg(g) is small
+// g's leading coefficient is assumed to be 1
+// f memory is re-used for the result, need to pass a copy to not modify it
+func div(f, g []fr.Element) []fr.Element {
+	sizef := len(f)
+	sizeg := len(g)
+	stop := sizeg - +1
+	var t fr.Element
+	for i := sizef - 2; i >= stop; i-- {
+		for j := 0; j < sizeg-1; j++ {
+			t.Mul(&f[i+1], &g[sizeg-2-j])
+			f[i-j].Sub(&f[i-j], &t)
+		}
+	}
+	return f[sizeg-1:]
+}
diff --git a/ecc/bls24-315/shplonk/shplonk_test.go b/ecc/bls24-315/shplonk/shplonk_test.go
new file mode 100644
index 0000000000..3e282d99a1
--- /dev/null
+++ b/ecc/bls24-315/shplonk/shplonk_test.go
@@ -0,0 +1,320 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"crypto/sha256"
+	"math/big"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls24-315/kzg"
+	"github.com/stretchr/testify/require"
+)
+
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *kzg.SRS
+var bAlpha *big.Int
+
+func init() {
+	const srsSize = 230
+	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+}
+
+func TestOpening(t *testing.T) {
+
+	assert := require.New(t)
+
+	nbPolys := 2
+	sizePoly := make([]int, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		sizePoly[i] = 10 + i
+	}
+	polys := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		polys[i] = make([]fr.Element, sizePoly[i])
+		for j := 0; j < sizePoly[i]; j++ {
+			polys[i][j].SetRandom()
+		}
+	}
+
+	digests := make([]kzg.Digest, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		digests[i], _ = kzg.Commit(polys[i], testSrs.Pk)
+	}
+
+	points := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		points[i] = make([]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+
+	hf := sha256.New()
+
+	// correct proof
+	openingProof, err := BatchOpen(polys, digests, points, hf, testSrs.Pk)
+	assert.NoError(err)
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	assert.NoError(err)
+
+	// tampered proof
+	openingProof.ClaimedValues[0][0].SetRandom()
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	assert.Error(err)
+
+}
+
+func TestBuildZtMinusSi(t *testing.T) {
+
+	nbSi := 10
+	points := make([][]fr.Element, nbSi)
+	sizeSi := make([]int, nbSi)
+	nbPoints := 0
+	for i := 0; i < nbSi; i++ {
+		sizeSi[i] = 5 + i
+		nbPoints += sizeSi[i]
+		points[i] = make([]fr.Element, sizeSi[i])
+		for j := 0; j < sizeSi[i]; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+	for i := 0; i < nbSi; i++ {
+		ztMinusSi := buildZtMinusSi(points, i)
+		if len(ztMinusSi) != nbPoints-sizeSi[i]+1 {
+			t.Fatal("deg(Z_{T-S_{i}}) should be nbPoints-size(S_{i})")
+		}
+		for j := 0; j < nbSi; j++ {
+			if j == i {
+				for k := 0; k < sizeSi[j]; k++ {
+					y := eval(ztMinusSi, points[j][k])
+					if y.IsZero() {
+						t.Fatal("Z_{T-S_{i}}(S_{i}) should not be zero")
+					}
+				}
+				continue
+			}
+			for k := 0; k < sizeSi[j]; k++ {
+				y := eval(ztMinusSi, points[j][k])
+				if !y.IsZero() {
+					t.Fatal("Z_{T-S_{i}}(S_{j}) should be zero")
+				}
+			}
+		}
+	}
+
+}
+
+func TestInterpolate(t *testing.T) {
+
+	nbPoints := 10
+	x := make([]fr.Element, nbPoints)
+	y := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		y[i].SetRandom()
+	}
+	f := interpolate(x, y)
+	for i := 0; i < nbPoints; i++ {
+		fx := eval(f, x[i])
+		if !fx.Equal(&y[i]) {
+			t.Fatal("f(x_{i})!=y_{i}")
+		}
+	}
+
+}
+
+func TestBuildLagrangeFromDomain(t *testing.T) {
+
+	nbPoints := 10
+	points := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		points[i].SetRandom()
+	}
+	var r fr.Element
+	for i := 0; i < nbPoints; i++ {
+
+		l := buildLagrangeFromDomain(points, i)
+
+		// check that l(xᵢ)=1 and l(xⱼ)=0 for j!=i
+		for j := 0; j < nbPoints; j++ {
+			y := eval(l, points[j])
+			if i == j {
+				if !y.IsOne() {
+					t.Fatal("l_{i}(x_{i}) should be equal to 1")
+				}
+			} else {
+				if !y.IsZero() {
+					t.Fatal("l_{i}(x_{j}) where i!=j should be equal to 0")
+				}
+			}
+		}
+		r.SetRandom()
+		y := eval(l, r)
+		if y.IsZero() {
+			t.Fatal("l_{i}(x) should not be zero if x is random")
+		}
+	}
+
+}
+
+func TestBuildVanishingPoly(t *testing.T) {
+	s := 10
+	x := make([]fr.Element, s)
+	for i := 0; i < s; i++ {
+		x[i].SetRandom()
+	}
+	r := buildVanishingPoly(x)
+
+	if len(r) != s+1 {
+		t.Fatal("error degree r")
+	}
+
+	// check that r(xᵢ)=0 for all i
+	for i := 0; i < len(x); i++ {
+		y := eval(r, x[i])
+		if !y.IsZero() {
+			t.Fatal("πᵢ(X-xᵢ) at xᵢ should be zero")
+		}
+	}
+
+	// check that r(y)!=0 for a random point
+	var a fr.Element
+	a.SetRandom()
+	y := eval(r, a)
+	if y.IsZero() {
+		t.Fatal("πᵢ(X-xᵢ) at r \neq xᵢ should not be zero")
+	}
+}
+
+func TestMultiplyLinearFactor(t *testing.T) {
+
+	s := 10
+	f := make([]fr.Element, s, s+1)
+	for i := 0; i < 10; i++ {
+		f[i].SetRandom()
+	}
+
+	var a, y fr.Element
+	a.SetRandom()
+	f = multiplyLinearFactor(f, a)
+	y = eval(f, a)
+	if !y.IsZero() {
+		t.Fatal("(X-a)f(X) should be zero at a")
+	}
+	a.SetRandom()
+	y = eval(f, a)
+	if y.IsZero() {
+		t.Fatal("(X-1)f(X) at a random point should not be zero")
+	}
+
+}
+
+func TestNaiveMul(t *testing.T) {
+
+	size := 10
+	f := make([]fr.Element, size)
+	for i := 0; i < size; i++ {
+		f[i].SetRandom()
+	}
+
+	nbPoints := 10
+	points := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		points[i].SetRandom()
+	}
+
+	v := buildVanishingPoly(points)
+	buf := make([]fr.Element, size+nbPoints-1)
+	g := mul(f, v, buf)
+
+	// check that g(xᵢ) = 0
+	for i := 0; i < nbPoints; i++ {
+		y := eval(g, points[i])
+		if !y.IsZero() {
+			t.Fatal("f(X)(X-x_{1})..(X-x_{n}) at x_{i} should be zero")
+		}
+	}
+
+	// check that g(r) != 0 for a random point
+	var a fr.Element
+	a.SetRandom()
+	y := eval(g, a)
+	if y.IsZero() {
+		t.Fatal("f(X)(X-x_{1})..(X-x_{n}) at a random point should not be zero")
+	}
+
+}
+
+func TestDiv(t *testing.T) {
+
+	nbPoints := 10
+	s := 10
+	f := make([]fr.Element, s, s+nbPoints)
+	for i := 0; i < s; i++ {
+		f[i].SetRandom()
+	}
+
+	// backup
+	g := make([]fr.Element, s)
+	copy(g, f)
+
+	// successive divions of linear terms
+	x := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		f = multiplyLinearFactor(f, x[i])
+	}
+	q := make([][2]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		q[i][1].SetOne()
+		q[i][0].Neg(&x[i])
+		f = div(f, q[i][:])
+	}
+
+	// g should be equal to f
+	if len(f) != len(g) {
+		t.Fatal("lengths don't match")
+	}
+	for i := 0; i < len(g); i++ {
+		if !f[i].Equal(&g[i]) {
+			t.Fatal("f(x)(x-a)/(x-a) should be equal to f(x)")
+		}
+	}
+
+	// division by a degree > 1 polynomial
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		f = multiplyLinearFactor(f, x[i])
+	}
+	r := buildVanishingPoly(x)
+	f = div(f, r)
+
+	// g should be equal to f
+	if len(f) != len(g) {
+		t.Fatal("lengths don't match")
+	}
+	for i := 0; i < len(g); i++ {
+		if !f[i].Equal(&g[i]) {
+			t.Fatal("f(x)(x-a)/(x-a) should be equal to f(x)")
+		}
+	}
+
+}
diff --git a/ecc/bls24-317/shplonk/doc.go b/ecc/bls24-317/shplonk/doc.go
new file mode 100644
index 0000000000..e048f46009
--- /dev/null
+++ b/ecc/bls24-317/shplonk/doc.go
@@ -0,0 +1,18 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// Package shplonk provides a SHPLONK commitment scheme, cf https://eprint.iacr.org/2020/081.pdf
+package shplonk
diff --git a/ecc/bls24-317/shplonk/marshal.go b/ecc/bls24-317/shplonk/marshal.go
new file mode 100644
index 0000000000..b69c0946ca
--- /dev/null
+++ b/ecc/bls24-317/shplonk/marshal.go
@@ -0,0 +1,62 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"io"
+
+	"github.com/consensys/gnark-crypto/ecc/bls24-317"
+)
+
+func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
+
+	dec := bls24317.NewDecoder(r)
+
+	toDecode := []interface{}{
+		&proof.W,
+		&proof.WPrime,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toDecode {
+		if err := dec.Decode(v); err != nil {
+			return dec.BytesRead(), err
+		}
+	}
+
+	return dec.BytesRead(), nil
+}
+
+// WriteTo writes binary encoding of a OpeningProof
+func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
+
+	enc := bls24317.NewEncoder(w)
+
+	toEncode := []interface{}{
+		&proof.W,
+		&proof.WPrime,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toEncode {
+		if err := enc.Encode(v); err != nil {
+			return enc.BytesWritten(), err
+		}
+	}
+
+	return enc.BytesWritten(), nil
+}
diff --git a/ecc/bls24-317/shplonk/shplonk.go b/ecc/bls24-317/shplonk/shplonk.go
new file mode 100644
index 0000000000..dc8cdfa14a
--- /dev/null
+++ b/ecc/bls24-317/shplonk/shplonk.go
@@ -0,0 +1,462 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"errors"
+	"hash"
+	"math/big"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bls24-317"
+	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls24-317/kzg"
+	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
+)
+
+var (
+	ErrInvalidNumberOfPoints = errors.New("number of digests should be equal to the number of points")
+	ErrVerifyOpeningProof    = errors.New("can't verify batch opening proof")
+)
+
+// OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
+//
+// implements io.ReaderFrom and io.WriterTo
+type OpeningProof struct {
+
+	// W = ∑ᵢ γⁱZ_{T\Sᵢ}(f_i(X)-r)/Z_{T} where Z_{T} is the vanishing polynomial on the (Sᵢ)_{i}
+	// and r interpolates fᵢ(Sᵢ) on (Sᵢ)
+	W bls24317.G1Affine
+
+	// L(X)/(X-z) where L(X)=∑ᵢγⁱZ_{T\xᵢ}(f_i(X)-rᵢ) - Z_{T}W(X)
+	WPrime bls24317.G1Affine
+
+	// ClaimedValues[i] are the values of fᵢ on Sᵢ
+	ClaimedValues [][]fr.Element
+}
+
+// BatchOpen opens the list of polynomials on points, where the i-th polynomials is opend at points[i].
+func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
+
+	var res OpeningProof
+
+	nbInstances := len(polynomials)
+	if len(polynomials) != len(points) {
+		return res, ErrInvalidNumberOfPoints
+	}
+
+	// transcript
+	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
+
+	// derive γ
+	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
+	if err != nil {
+		return res, err
+	}
+
+	// compute the size of the linear combination
+	maxSizePolys := len(polynomials[0])
+	for i := 1; i < len(polynomials); i++ {
+		if maxSizePolys < len(polynomials[i]) {
+			maxSizePolys = len(polynomials[i])
+		}
+	}
+	nbPoints := 0
+	sizeSi := make([]int, len(points))
+	for i := 0; i < nbInstances; i++ {
+		nbPoints += len(points[i])
+		sizeSi[i] = len(points[i])
+	}
+	totalSize := maxSizePolys + nbPoints // upper bound of the size of f := ∑ᵢ γⁱZ_{T\Sᵢ}(f_i(X)-r)
+
+	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
+	bufTotalSize := make([]fr.Element, totalSize)
+	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
+	res.ClaimedValues = make([][]fr.Element, nbInstances)
+	for i := 0; i < nbInstances; i++ {
+		res.ClaimedValues[i] = make([]fr.Element, len(points[i]))
+	}
+	var accGamma fr.Element
+	accGamma.SetOne()
+
+	ztMinusSi := make([][]fr.Element, nbInstances)
+	ri := make([][]fr.Element, nbInstances)
+	for i := 0; i < nbInstances; i++ {
+
+		for j := 0; j < len(points[i]); j++ {
+			res.ClaimedValues[i][j] = eval(polynomials[i], points[i][j])
+		}
+
+		ztMinusSi[i] = buildZtMinusSi(points, i)
+
+		copy(bufMaxSizePolynomials, polynomials[i])
+		ri[i] = interpolate(points[i], res.ClaimedValues[i])
+		sub(bufMaxSizePolynomials, ri[i])
+
+		bufTotalSize = mul(bufMaxSizePolynomials, ztMinusSi[i], bufTotalSize)
+		bufTotalSize = mulByConstant(bufTotalSize, accGamma)
+		for j := 0; j < len(bufTotalSize); j++ {
+			f[j].Add(&f[j], &bufTotalSize[j])
+		}
+
+		accGamma.Mul(&accGamma, &gamma)
+		setZero(bufMaxSizePolynomials)
+	}
+
+	zt := buildVanishingPoly(flatten(points))
+	w := div(f, zt) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
+	res.W, err = kzg.Commit(w, pk)
+	if err != nil {
+		return res, err
+	}
+
+	// derive z
+	z, err := deriveChallenge("z", nil, []kzg.Digest{res.W}, fs)
+	if err != nil {
+		return res, err
+	}
+
+	// compute L = ∑ᵢγⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))-Z_{T}(z)W
+	accGamma.SetOne()
+	var gammaiZtMinusSiZ fr.Element
+	l := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
+	for i := 0; i < len(polynomials); i++ {
+
+		ztMinusSiZ := eval(ztMinusSi[i], z)          // Z_{T\Sᵢ}(z)
+		gammaiZtMinusSiZ.Mul(&accGamma, &ztMinusSiZ) // γⁱZ_{T\Sᵢ}(z)
+
+		copy(bufMaxSizePolynomials, polynomials[i])
+		riz := eval(ri[i], z)
+		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz) // (fᵢ-rᵢ(z))
+		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusSiZ)        // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
+		for j := 0; j < len(bufMaxSizePolynomials); j++ {
+			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
+		}
+
+		setZero(bufMaxSizePolynomials)
+		accGamma.Mul(&accGamma, &gamma)
+	}
+	ztz := eval(zt, z)
+	setZero(bufTotalSize)
+	copy(bufTotalSize, w)
+	mulByConstant(bufTotalSize, ztz) // Z_{T}(z)W
+	for i := 0; i < totalSize-maxSizePolys; i++ {
+		l[totalSize-1-i].Neg(&bufTotalSize[totalSize-1-i])
+	}
+	for i := 0; i < maxSizePolys; i++ {
+		l[i].Sub(&l[i], &bufTotalSize[i])
+	} // L <- L-Z_{T}(z)W
+
+	xMinusZ := buildVanishingPoly([]fr.Element{z})
+	wPrime := div(l, xMinusZ)
+
+	res.WPrime, err = kzg.Commit(wPrime, pk)
+	if err != nil {
+		return res, err
+	}
+
+	return res, nil
+}
+
+// BatchVerify uses proof to check that the commitments correctly open to proof.ClaimedValues
+// at points. The order matters: the proof validates that the i-th commitment is correctly opened
+// at the i-th point
+// dataTranscript is some extra data that might be needed for Fiat Shamir, and is appended at the end
+// of the original transcript.
+func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
+
+	if len(digests) != len(proof.ClaimedValues) {
+		return ErrInvalidNumberOfPoints
+	}
+	if len(digests) != len(points) {
+		return ErrInvalidNumberOfPoints
+	}
+
+	// transcript
+	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
+
+	// derive γ
+	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
+	if err != nil {
+		return err
+	}
+
+	// derive z
+	// TODO seems ok that z depend only on W, need to check that carefully
+	z, err := deriveChallenge("z", nil, []kzg.Digest{proof.W}, fs)
+	if err != nil {
+		return err
+	}
+
+	// check that e(F + zW', [1]_{2})=e(W',[x]_{2})
+	// where F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}-[∑ᵢγⁱZ_{T\xᵢ}(z)fᵢ(z)]_{1}-Z_{T}(z)[W]
+	var sumGammaiZTminusSiRiz, tmp, accGamma fr.Element
+	nbInstances := len(points)
+	gammaiZTminusSiz := make([]fr.Element, nbInstances)
+	accGamma.SetOne()
+	ri := make([][]fr.Element, nbInstances)
+	for i := 0; i < len(points); i++ {
+
+		ztMinusSi := buildZtMinusSi(points, i)                   // Z_{T-S_{i}}(X)
+		gammaiZTminusSiz[i] = eval(ztMinusSi, z)                 // Z_{T-S_{i}}(z)
+		gammaiZTminusSiz[i].Mul(&accGamma, &gammaiZTminusSiz[i]) // \gamma^{i} Z_{T-S_{i}}(z)
+
+		ri[i] = interpolate(points[i], proof.ClaimedValues[i])
+		riz := eval(ri[i], z)               // r_{i}(z)
+		tmp.Mul(&gammaiZTminusSiz[i], &riz) // Z_{T-S_{i}}(z)r_{i}(z)
+		sumGammaiZTminusSiRiz.Add(&sumGammaiZTminusSiRiz, &tmp)
+
+		accGamma.Mul(&accGamma, &gamma)
+	}
+
+	// ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}
+	config := ecc.MultiExpConfig{}
+	var sumGammaiZtMinusSiComi kzg.Digest
+	_, err = sumGammaiZtMinusSiComi.MultiExp(digests, gammaiZTminusSiz, config)
+	if err != nil {
+		return err
+	}
+
+	var bufBigInt big.Int
+
+	// [∑ᵢZ_{T\xᵢ}fᵢ(z)]_{1}
+	var sumGammaiZTminusSiRizCom kzg.Digest
+	var sumGammaiZTminusSiRizBigInt big.Int
+	sumGammaiZTminusSiRiz.BigInt(&sumGammaiZTminusSiRizBigInt)
+	sumGammaiZTminusSiRizCom.ScalarMultiplication(&vk.G1, &sumGammaiZTminusSiRizBigInt)
+
+	// Z_{T}(z)[W]
+	zt := buildVanishingPoly(flatten(points))
+	ztz := eval(zt, z)
+	var ztW kzg.Digest
+	ztz.BigInt(&bufBigInt)
+	ztW.ScalarMultiplication(&proof.W, &bufBigInt)
+
+	// F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i} - [∑ᵢγⁱZ_{T\xᵢ}fᵢ(z)]_{1} - Z_{T}(z)[W]
+	var f kzg.Digest
+	f.Sub(&sumGammaiZtMinusSiComi, &sumGammaiZTminusSiRizCom).
+		Sub(&f, &ztW)
+
+	// F+zW'
+	var zWPrime kzg.Digest
+	z.BigInt(&bufBigInt)
+	zWPrime.ScalarMultiplication(&proof.WPrime, &bufBigInt)
+	f.Add(&f, &zWPrime)
+	f.Neg(&f)
+
+	// check that e(F+zW',[1]_{2})=e(W',[x]_{2})
+	check, err := bls24317.PairingCheckFixedQ(
+		[]bls24317.G1Affine{f, proof.WPrime},
+		vk.Lines[:],
+	)
+
+	if !check {
+		return ErrVerifyOpeningProof
+	}
+
+	return nil
+}
+
+// deriveChallenge derives a challenge using Fiat Shamir to polynomials.
+// The arguments are added to the transcript in the order in which they are given.
+func deriveChallenge(name string, points [][]fr.Element, digests []kzg.Digest, t *fiatshamir.Transcript, dataTranscript ...[]byte) (fr.Element, error) {
+
+	// derive the challenge gamma, binded to the point and the commitments
+	for i := range points {
+		for j := range points[i] {
+			if err := t.Bind(name, points[i][j].Marshal()); err != nil {
+				return fr.Element{}, err
+			}
+		}
+	}
+	for i := range digests {
+		if err := t.Bind(name, digests[i].Marshal()); err != nil {
+			return fr.Element{}, err
+		}
+	}
+
+	for i := 0; i < len(dataTranscript); i++ {
+		if err := t.Bind(name, dataTranscript[i]); err != nil {
+			return fr.Element{}, err
+		}
+	}
+
+	gammaByte, err := t.ComputeChallenge(name)
+	if err != nil {
+		return fr.Element{}, err
+	}
+	var gamma fr.Element
+	gamma.SetBytes(gammaByte)
+
+	return gamma, nil
+}
+
+// ------------------------------
+// utils
+
+func flatten(x [][]fr.Element) []fr.Element {
+	nbPoints := 0
+	for i := 0; i < len(x); i++ {
+		nbPoints += len(x[i])
+	}
+	res := make([]fr.Element, 0, nbPoints)
+	for i := 0; i < len(x); i++ {
+		res = append(res, x[i]...)
+	}
+	return res
+}
+
+// sets f to zero
+func setZero(f []fr.Element) {
+	for i := 0; i < len(f); i++ {
+		f[i].SetZero()
+	}
+}
+
+func eval(f []fr.Element, x fr.Element) fr.Element {
+	var y fr.Element
+	for i := len(f) - 1; i >= 0; i-- {
+		y.Mul(&y, &x).Add(&y, &f[i])
+	}
+	return y
+}
+
+// returns γ*f, re-using f
+func mulByConstant(f []fr.Element, gamma fr.Element) []fr.Element {
+	for i := 0; i < len(f); i++ {
+		f[i].Mul(&f[i], &gamma)
+	}
+	return f
+}
+
+// computes f <- (x-a)*f
+// memory of f is re used, need to pass a copy to not modify it
+func multiplyLinearFactor(f []fr.Element, a fr.Element) []fr.Element {
+	s := len(f)
+	var tmp fr.Element
+	f = append(f, fr.NewElement(0))
+	f[s] = f[s-1]
+	for i := s - 1; i >= 1; i-- {
+		tmp.Mul(&f[i], &a)
+		f[i].Sub(&f[i-1], &tmp)
+	}
+	f[0].Mul(&f[0], &a).Neg(&f[0])
+	return f
+}
+
+// returns S_{T\Sᵢ} where Sᵢ=x[i]
+func buildZtMinusSi(x [][]fr.Element, i int) []fr.Element {
+	nbPoints := 0
+	for i := 0; i < len(x); i++ {
+		nbPoints += len(x[i])
+	}
+	bufPoints := make([]fr.Element, 0, nbPoints-len(x[i]))
+	for j := 0; j < i; j++ {
+		bufPoints = append(bufPoints, x[j]...)
+	}
+	for j := i + 1; j < len(x); j++ {
+		bufPoints = append(bufPoints, x[j]...)
+	}
+	ztMinusSi := buildVanishingPoly(bufPoints)
+	return ztMinusSi
+}
+
+// returns πᵢ(X-xᵢ)
+func buildVanishingPoly(x []fr.Element) []fr.Element {
+	res := make([]fr.Element, 1, len(x)+1)
+	res[0].SetOne()
+	for i := 0; i < len(x); i++ {
+		res = multiplyLinearFactor(res, x[i])
+	}
+	return res
+}
+
+// returns f such that f(xᵢ)=yᵢ, x and y are assumed to be of the same size
+func interpolate(x, y []fr.Element) []fr.Element {
+
+	res := make([]fr.Element, len(x))
+	for i := 0; i < len(x); i++ {
+		li := buildLagrangeFromDomain(x, i)
+		li = mulByConstant(li, y[i])
+		for j := 0; j < len(x); j++ {
+			res[j].Add(&res[j], &li[j])
+		}
+	}
+
+	return res
+}
+
+// returns f such that f(xⱼ)=δⁱⱼ
+func buildLagrangeFromDomain(x []fr.Element, i int) []fr.Element {
+	xx := make([]fr.Element, len(x)-1)
+	copy(xx, x[:i])
+	copy(xx[i:], x[i+1:])
+	res := buildVanishingPoly(xx)
+	d := eval(res, x[i])
+	d.Inverse(&d)
+	res = mulByConstant(res, d)
+	return res
+}
+
+// returns f-g, the memory of f is re used, deg(g) << deg(f) here
+func sub(f, g []fr.Element) []fr.Element {
+	for i := 0; i < len(g); i++ {
+		f[i].Sub(&f[i], &g[i])
+	}
+	return f
+}
+
+// returns f*g using naive multiplication
+// deg(f)>>deg(g), deg(small) =~ 10 max
+// buf is used as a buffer and should not be f or g
+// f and g are not modified
+func mul(f, g []fr.Element, res []fr.Element) []fr.Element {
+
+	sizeRes := len(f) + len(g) - 1
+	if len(res) < sizeRes {
+		s := make([]fr.Element, sizeRes-len(res))
+		res = append(res, s...)
+	}
+	setZero(res)
+
+	var tmp fr.Element
+	for i := 0; i < len(g); i++ {
+		for j := 0; j < len(f); j++ {
+			tmp.Mul(&f[j], &g[i])
+			res[j+i].Add(&res[j+i], &tmp)
+		}
+	}
+	return res
+}
+
+// returns f/g (assuming g divides f)
+// OK to not use fft if deg(g) is small
+// g's leading coefficient is assumed to be 1
+// f memory is re-used for the result, need to pass a copy to not modify it
+func div(f, g []fr.Element) []fr.Element {
+	sizef := len(f)
+	sizeg := len(g)
+	stop := sizeg - +1
+	var t fr.Element
+	for i := sizef - 2; i >= stop; i-- {
+		for j := 0; j < sizeg-1; j++ {
+			t.Mul(&f[i+1], &g[sizeg-2-j])
+			f[i-j].Sub(&f[i-j], &t)
+		}
+	}
+	return f[sizeg-1:]
+}
diff --git a/ecc/bls24-317/shplonk/shplonk_test.go b/ecc/bls24-317/shplonk/shplonk_test.go
new file mode 100644
index 0000000000..14dd5af291
--- /dev/null
+++ b/ecc/bls24-317/shplonk/shplonk_test.go
@@ -0,0 +1,320 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"crypto/sha256"
+	"math/big"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls24-317/kzg"
+	"github.com/stretchr/testify/require"
+)
+
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *kzg.SRS
+var bAlpha *big.Int
+
+func init() {
+	const srsSize = 230
+	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+}
+
+func TestOpening(t *testing.T) {
+
+	assert := require.New(t)
+
+	nbPolys := 2
+	sizePoly := make([]int, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		sizePoly[i] = 10 + i
+	}
+	polys := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		polys[i] = make([]fr.Element, sizePoly[i])
+		for j := 0; j < sizePoly[i]; j++ {
+			polys[i][j].SetRandom()
+		}
+	}
+
+	digests := make([]kzg.Digest, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		digests[i], _ = kzg.Commit(polys[i], testSrs.Pk)
+	}
+
+	points := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		points[i] = make([]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+
+	hf := sha256.New()
+
+	// correct proof
+	openingProof, err := BatchOpen(polys, digests, points, hf, testSrs.Pk)
+	assert.NoError(err)
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	assert.NoError(err)
+
+	// tampered proof
+	openingProof.ClaimedValues[0][0].SetRandom()
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	assert.Error(err)
+
+}
+
+func TestBuildZtMinusSi(t *testing.T) {
+
+	nbSi := 10
+	points := make([][]fr.Element, nbSi)
+	sizeSi := make([]int, nbSi)
+	nbPoints := 0
+	for i := 0; i < nbSi; i++ {
+		sizeSi[i] = 5 + i
+		nbPoints += sizeSi[i]
+		points[i] = make([]fr.Element, sizeSi[i])
+		for j := 0; j < sizeSi[i]; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+	for i := 0; i < nbSi; i++ {
+		ztMinusSi := buildZtMinusSi(points, i)
+		if len(ztMinusSi) != nbPoints-sizeSi[i]+1 {
+			t.Fatal("deg(Z_{T-S_{i}}) should be nbPoints-size(S_{i})")
+		}
+		for j := 0; j < nbSi; j++ {
+			if j == i {
+				for k := 0; k < sizeSi[j]; k++ {
+					y := eval(ztMinusSi, points[j][k])
+					if y.IsZero() {
+						t.Fatal("Z_{T-S_{i}}(S_{i}) should not be zero")
+					}
+				}
+				continue
+			}
+			for k := 0; k < sizeSi[j]; k++ {
+				y := eval(ztMinusSi, points[j][k])
+				if !y.IsZero() {
+					t.Fatal("Z_{T-S_{i}}(S_{j}) should be zero")
+				}
+			}
+		}
+	}
+
+}
+
+func TestInterpolate(t *testing.T) {
+
+	nbPoints := 10
+	x := make([]fr.Element, nbPoints)
+	y := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		y[i].SetRandom()
+	}
+	f := interpolate(x, y)
+	for i := 0; i < nbPoints; i++ {
+		fx := eval(f, x[i])
+		if !fx.Equal(&y[i]) {
+			t.Fatal("f(x_{i})!=y_{i}")
+		}
+	}
+
+}
+
+func TestBuildLagrangeFromDomain(t *testing.T) {
+
+	nbPoints := 10
+	points := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		points[i].SetRandom()
+	}
+	var r fr.Element
+	for i := 0; i < nbPoints; i++ {
+
+		l := buildLagrangeFromDomain(points, i)
+
+		// check that l(xᵢ)=1 and l(xⱼ)=0 for j!=i
+		for j := 0; j < nbPoints; j++ {
+			y := eval(l, points[j])
+			if i == j {
+				if !y.IsOne() {
+					t.Fatal("l_{i}(x_{i}) should be equal to 1")
+				}
+			} else {
+				if !y.IsZero() {
+					t.Fatal("l_{i}(x_{j}) where i!=j should be equal to 0")
+				}
+			}
+		}
+		r.SetRandom()
+		y := eval(l, r)
+		if y.IsZero() {
+			t.Fatal("l_{i}(x) should not be zero if x is random")
+		}
+	}
+
+}
+
+func TestBuildVanishingPoly(t *testing.T) {
+	s := 10
+	x := make([]fr.Element, s)
+	for i := 0; i < s; i++ {
+		x[i].SetRandom()
+	}
+	r := buildVanishingPoly(x)
+
+	if len(r) != s+1 {
+		t.Fatal("error degree r")
+	}
+
+	// check that r(xᵢ)=0 for all i
+	for i := 0; i < len(x); i++ {
+		y := eval(r, x[i])
+		if !y.IsZero() {
+			t.Fatal("πᵢ(X-xᵢ) at xᵢ should be zero")
+		}
+	}
+
+	// check that r(y)!=0 for a random point
+	var a fr.Element
+	a.SetRandom()
+	y := eval(r, a)
+	if y.IsZero() {
+		t.Fatal("πᵢ(X-xᵢ) at r \neq xᵢ should not be zero")
+	}
+}
+
+func TestMultiplyLinearFactor(t *testing.T) {
+
+	s := 10
+	f := make([]fr.Element, s, s+1)
+	for i := 0; i < 10; i++ {
+		f[i].SetRandom()
+	}
+
+	var a, y fr.Element
+	a.SetRandom()
+	f = multiplyLinearFactor(f, a)
+	y = eval(f, a)
+	if !y.IsZero() {
+		t.Fatal("(X-a)f(X) should be zero at a")
+	}
+	a.SetRandom()
+	y = eval(f, a)
+	if y.IsZero() {
+		t.Fatal("(X-1)f(X) at a random point should not be zero")
+	}
+
+}
+
+func TestNaiveMul(t *testing.T) {
+
+	size := 10
+	f := make([]fr.Element, size)
+	for i := 0; i < size; i++ {
+		f[i].SetRandom()
+	}
+
+	nbPoints := 10
+	points := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		points[i].SetRandom()
+	}
+
+	v := buildVanishingPoly(points)
+	buf := make([]fr.Element, size+nbPoints-1)
+	g := mul(f, v, buf)
+
+	// check that g(xᵢ) = 0
+	for i := 0; i < nbPoints; i++ {
+		y := eval(g, points[i])
+		if !y.IsZero() {
+			t.Fatal("f(X)(X-x_{1})..(X-x_{n}) at x_{i} should be zero")
+		}
+	}
+
+	// check that g(r) != 0 for a random point
+	var a fr.Element
+	a.SetRandom()
+	y := eval(g, a)
+	if y.IsZero() {
+		t.Fatal("f(X)(X-x_{1})..(X-x_{n}) at a random point should not be zero")
+	}
+
+}
+
+func TestDiv(t *testing.T) {
+
+	nbPoints := 10
+	s := 10
+	f := make([]fr.Element, s, s+nbPoints)
+	for i := 0; i < s; i++ {
+		f[i].SetRandom()
+	}
+
+	// backup
+	g := make([]fr.Element, s)
+	copy(g, f)
+
+	// successive divions of linear terms
+	x := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		f = multiplyLinearFactor(f, x[i])
+	}
+	q := make([][2]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		q[i][1].SetOne()
+		q[i][0].Neg(&x[i])
+		f = div(f, q[i][:])
+	}
+
+	// g should be equal to f
+	if len(f) != len(g) {
+		t.Fatal("lengths don't match")
+	}
+	for i := 0; i < len(g); i++ {
+		if !f[i].Equal(&g[i]) {
+			t.Fatal("f(x)(x-a)/(x-a) should be equal to f(x)")
+		}
+	}
+
+	// division by a degree > 1 polynomial
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		f = multiplyLinearFactor(f, x[i])
+	}
+	r := buildVanishingPoly(x)
+	f = div(f, r)
+
+	// g should be equal to f
+	if len(f) != len(g) {
+		t.Fatal("lengths don't match")
+	}
+	for i := 0; i < len(g); i++ {
+		if !f[i].Equal(&g[i]) {
+			t.Fatal("f(x)(x-a)/(x-a) should be equal to f(x)")
+		}
+	}
+
+}
diff --git a/ecc/bn254/shplonk/doc.go b/ecc/bn254/shplonk/doc.go
new file mode 100644
index 0000000000..e048f46009
--- /dev/null
+++ b/ecc/bn254/shplonk/doc.go
@@ -0,0 +1,18 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// Package shplonk provides a SHPLONK commitment scheme, cf https://eprint.iacr.org/2020/081.pdf
+package shplonk
diff --git a/ecc/bn254/shplonk/marshal.go b/ecc/bn254/shplonk/marshal.go
index 66eaf0302f..050e1d6fdf 100644
--- a/ecc/bn254/shplonk/marshal.go
+++ b/ecc/bn254/shplonk/marshal.go
@@ -12,6 +12,8 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
 package shplonk
 
 import (
diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
index b8b3cc1a25..3ed334464e 100644
--- a/ecc/bn254/shplonk/shplonk.go
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -12,7 +12,7 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-//cf https://eprint.iacr.org/2020/081.pdf
+// Code generated by consensys/gnark-crypto DO NOT EDIT
 
 package shplonk
 
diff --git a/ecc/bn254/shplonk/shplonk_test.go b/ecc/bn254/shplonk/shplonk_test.go
index 2b082d16c8..6d2c2841b0 100644
--- a/ecc/bn254/shplonk/shplonk_test.go
+++ b/ecc/bn254/shplonk/shplonk_test.go
@@ -12,6 +12,8 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
 package shplonk
 
 import (
diff --git a/ecc/bw6-633/shplonk/doc.go b/ecc/bw6-633/shplonk/doc.go
new file mode 100644
index 0000000000..e048f46009
--- /dev/null
+++ b/ecc/bw6-633/shplonk/doc.go
@@ -0,0 +1,18 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// Package shplonk provides a SHPLONK commitment scheme, cf https://eprint.iacr.org/2020/081.pdf
+package shplonk
diff --git a/ecc/bw6-633/shplonk/marshal.go b/ecc/bw6-633/shplonk/marshal.go
new file mode 100644
index 0000000000..2c44c28a65
--- /dev/null
+++ b/ecc/bw6-633/shplonk/marshal.go
@@ -0,0 +1,62 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"io"
+
+	"github.com/consensys/gnark-crypto/ecc/bw6-633"
+)
+
+func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
+
+	dec := bw6633.NewDecoder(r)
+
+	toDecode := []interface{}{
+		&proof.W,
+		&proof.WPrime,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toDecode {
+		if err := dec.Decode(v); err != nil {
+			return dec.BytesRead(), err
+		}
+	}
+
+	return dec.BytesRead(), nil
+}
+
+// WriteTo writes binary encoding of a OpeningProof
+func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
+
+	enc := bw6633.NewEncoder(w)
+
+	toEncode := []interface{}{
+		&proof.W,
+		&proof.WPrime,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toEncode {
+		if err := enc.Encode(v); err != nil {
+			return enc.BytesWritten(), err
+		}
+	}
+
+	return enc.BytesWritten(), nil
+}
diff --git a/ecc/bw6-633/shplonk/shplonk.go b/ecc/bw6-633/shplonk/shplonk.go
new file mode 100644
index 0000000000..a3d6bd1999
--- /dev/null
+++ b/ecc/bw6-633/shplonk/shplonk.go
@@ -0,0 +1,462 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"errors"
+	"hash"
+	"math/big"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bw6-633"
+	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
+	"github.com/consensys/gnark-crypto/ecc/bw6-633/kzg"
+	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
+)
+
+var (
+	ErrInvalidNumberOfPoints = errors.New("number of digests should be equal to the number of points")
+	ErrVerifyOpeningProof    = errors.New("can't verify batch opening proof")
+)
+
+// OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
+//
+// implements io.ReaderFrom and io.WriterTo
+type OpeningProof struct {
+
+	// W = ∑ᵢ γⁱZ_{T\Sᵢ}(f_i(X)-r)/Z_{T} where Z_{T} is the vanishing polynomial on the (Sᵢ)_{i}
+	// and r interpolates fᵢ(Sᵢ) on (Sᵢ)
+	W bw6633.G1Affine
+
+	// L(X)/(X-z) where L(X)=∑ᵢγⁱZ_{T\xᵢ}(f_i(X)-rᵢ) - Z_{T}W(X)
+	WPrime bw6633.G1Affine
+
+	// ClaimedValues[i] are the values of fᵢ on Sᵢ
+	ClaimedValues [][]fr.Element
+}
+
+// BatchOpen opens the list of polynomials on points, where the i-th polynomials is opend at points[i].
+func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
+
+	var res OpeningProof
+
+	nbInstances := len(polynomials)
+	if len(polynomials) != len(points) {
+		return res, ErrInvalidNumberOfPoints
+	}
+
+	// transcript
+	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
+
+	// derive γ
+	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
+	if err != nil {
+		return res, err
+	}
+
+	// compute the size of the linear combination
+	maxSizePolys := len(polynomials[0])
+	for i := 1; i < len(polynomials); i++ {
+		if maxSizePolys < len(polynomials[i]) {
+			maxSizePolys = len(polynomials[i])
+		}
+	}
+	nbPoints := 0
+	sizeSi := make([]int, len(points))
+	for i := 0; i < nbInstances; i++ {
+		nbPoints += len(points[i])
+		sizeSi[i] = len(points[i])
+	}
+	totalSize := maxSizePolys + nbPoints // upper bound of the size of f := ∑ᵢ γⁱZ_{T\Sᵢ}(f_i(X)-r)
+
+	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
+	bufTotalSize := make([]fr.Element, totalSize)
+	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
+	res.ClaimedValues = make([][]fr.Element, nbInstances)
+	for i := 0; i < nbInstances; i++ {
+		res.ClaimedValues[i] = make([]fr.Element, len(points[i]))
+	}
+	var accGamma fr.Element
+	accGamma.SetOne()
+
+	ztMinusSi := make([][]fr.Element, nbInstances)
+	ri := make([][]fr.Element, nbInstances)
+	for i := 0; i < nbInstances; i++ {
+
+		for j := 0; j < len(points[i]); j++ {
+			res.ClaimedValues[i][j] = eval(polynomials[i], points[i][j])
+		}
+
+		ztMinusSi[i] = buildZtMinusSi(points, i)
+
+		copy(bufMaxSizePolynomials, polynomials[i])
+		ri[i] = interpolate(points[i], res.ClaimedValues[i])
+		sub(bufMaxSizePolynomials, ri[i])
+
+		bufTotalSize = mul(bufMaxSizePolynomials, ztMinusSi[i], bufTotalSize)
+		bufTotalSize = mulByConstant(bufTotalSize, accGamma)
+		for j := 0; j < len(bufTotalSize); j++ {
+			f[j].Add(&f[j], &bufTotalSize[j])
+		}
+
+		accGamma.Mul(&accGamma, &gamma)
+		setZero(bufMaxSizePolynomials)
+	}
+
+	zt := buildVanishingPoly(flatten(points))
+	w := div(f, zt) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
+	res.W, err = kzg.Commit(w, pk)
+	if err != nil {
+		return res, err
+	}
+
+	// derive z
+	z, err := deriveChallenge("z", nil, []kzg.Digest{res.W}, fs)
+	if err != nil {
+		return res, err
+	}
+
+	// compute L = ∑ᵢγⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))-Z_{T}(z)W
+	accGamma.SetOne()
+	var gammaiZtMinusSiZ fr.Element
+	l := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
+	for i := 0; i < len(polynomials); i++ {
+
+		ztMinusSiZ := eval(ztMinusSi[i], z)          // Z_{T\Sᵢ}(z)
+		gammaiZtMinusSiZ.Mul(&accGamma, &ztMinusSiZ) // γⁱZ_{T\Sᵢ}(z)
+
+		copy(bufMaxSizePolynomials, polynomials[i])
+		riz := eval(ri[i], z)
+		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz) // (fᵢ-rᵢ(z))
+		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusSiZ)        // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
+		for j := 0; j < len(bufMaxSizePolynomials); j++ {
+			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
+		}
+
+		setZero(bufMaxSizePolynomials)
+		accGamma.Mul(&accGamma, &gamma)
+	}
+	ztz := eval(zt, z)
+	setZero(bufTotalSize)
+	copy(bufTotalSize, w)
+	mulByConstant(bufTotalSize, ztz) // Z_{T}(z)W
+	for i := 0; i < totalSize-maxSizePolys; i++ {
+		l[totalSize-1-i].Neg(&bufTotalSize[totalSize-1-i])
+	}
+	for i := 0; i < maxSizePolys; i++ {
+		l[i].Sub(&l[i], &bufTotalSize[i])
+	} // L <- L-Z_{T}(z)W
+
+	xMinusZ := buildVanishingPoly([]fr.Element{z})
+	wPrime := div(l, xMinusZ)
+
+	res.WPrime, err = kzg.Commit(wPrime, pk)
+	if err != nil {
+		return res, err
+	}
+
+	return res, nil
+}
+
+// BatchVerify uses proof to check that the commitments correctly open to proof.ClaimedValues
+// at points. The order matters: the proof validates that the i-th commitment is correctly opened
+// at the i-th point
+// dataTranscript is some extra data that might be needed for Fiat Shamir, and is appended at the end
+// of the original transcript.
+func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
+
+	if len(digests) != len(proof.ClaimedValues) {
+		return ErrInvalidNumberOfPoints
+	}
+	if len(digests) != len(points) {
+		return ErrInvalidNumberOfPoints
+	}
+
+	// transcript
+	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
+
+	// derive γ
+	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
+	if err != nil {
+		return err
+	}
+
+	// derive z
+	// TODO seems ok that z depend only on W, need to check that carefully
+	z, err := deriveChallenge("z", nil, []kzg.Digest{proof.W}, fs)
+	if err != nil {
+		return err
+	}
+
+	// check that e(F + zW', [1]_{2})=e(W',[x]_{2})
+	// where F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}-[∑ᵢγⁱZ_{T\xᵢ}(z)fᵢ(z)]_{1}-Z_{T}(z)[W]
+	var sumGammaiZTminusSiRiz, tmp, accGamma fr.Element
+	nbInstances := len(points)
+	gammaiZTminusSiz := make([]fr.Element, nbInstances)
+	accGamma.SetOne()
+	ri := make([][]fr.Element, nbInstances)
+	for i := 0; i < len(points); i++ {
+
+		ztMinusSi := buildZtMinusSi(points, i)                   // Z_{T-S_{i}}(X)
+		gammaiZTminusSiz[i] = eval(ztMinusSi, z)                 // Z_{T-S_{i}}(z)
+		gammaiZTminusSiz[i].Mul(&accGamma, &gammaiZTminusSiz[i]) // \gamma^{i} Z_{T-S_{i}}(z)
+
+		ri[i] = interpolate(points[i], proof.ClaimedValues[i])
+		riz := eval(ri[i], z)               // r_{i}(z)
+		tmp.Mul(&gammaiZTminusSiz[i], &riz) // Z_{T-S_{i}}(z)r_{i}(z)
+		sumGammaiZTminusSiRiz.Add(&sumGammaiZTminusSiRiz, &tmp)
+
+		accGamma.Mul(&accGamma, &gamma)
+	}
+
+	// ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}
+	config := ecc.MultiExpConfig{}
+	var sumGammaiZtMinusSiComi kzg.Digest
+	_, err = sumGammaiZtMinusSiComi.MultiExp(digests, gammaiZTminusSiz, config)
+	if err != nil {
+		return err
+	}
+
+	var bufBigInt big.Int
+
+	// [∑ᵢZ_{T\xᵢ}fᵢ(z)]_{1}
+	var sumGammaiZTminusSiRizCom kzg.Digest
+	var sumGammaiZTminusSiRizBigInt big.Int
+	sumGammaiZTminusSiRiz.BigInt(&sumGammaiZTminusSiRizBigInt)
+	sumGammaiZTminusSiRizCom.ScalarMultiplication(&vk.G1, &sumGammaiZTminusSiRizBigInt)
+
+	// Z_{T}(z)[W]
+	zt := buildVanishingPoly(flatten(points))
+	ztz := eval(zt, z)
+	var ztW kzg.Digest
+	ztz.BigInt(&bufBigInt)
+	ztW.ScalarMultiplication(&proof.W, &bufBigInt)
+
+	// F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i} - [∑ᵢγⁱZ_{T\xᵢ}fᵢ(z)]_{1} - Z_{T}(z)[W]
+	var f kzg.Digest
+	f.Sub(&sumGammaiZtMinusSiComi, &sumGammaiZTminusSiRizCom).
+		Sub(&f, &ztW)
+
+	// F+zW'
+	var zWPrime kzg.Digest
+	z.BigInt(&bufBigInt)
+	zWPrime.ScalarMultiplication(&proof.WPrime, &bufBigInt)
+	f.Add(&f, &zWPrime)
+	f.Neg(&f)
+
+	// check that e(F+zW',[1]_{2})=e(W',[x]_{2})
+	check, err := bw6633.PairingCheckFixedQ(
+		[]bw6633.G1Affine{f, proof.WPrime},
+		vk.Lines[:],
+	)
+
+	if !check {
+		return ErrVerifyOpeningProof
+	}
+
+	return nil
+}
+
+// deriveChallenge derives a challenge using Fiat Shamir to polynomials.
+// The arguments are added to the transcript in the order in which they are given.
+func deriveChallenge(name string, points [][]fr.Element, digests []kzg.Digest, t *fiatshamir.Transcript, dataTranscript ...[]byte) (fr.Element, error) {
+
+	// derive the challenge gamma, binded to the point and the commitments
+	for i := range points {
+		for j := range points[i] {
+			if err := t.Bind(name, points[i][j].Marshal()); err != nil {
+				return fr.Element{}, err
+			}
+		}
+	}
+	for i := range digests {
+		if err := t.Bind(name, digests[i].Marshal()); err != nil {
+			return fr.Element{}, err
+		}
+	}
+
+	for i := 0; i < len(dataTranscript); i++ {
+		if err := t.Bind(name, dataTranscript[i]); err != nil {
+			return fr.Element{}, err
+		}
+	}
+
+	gammaByte, err := t.ComputeChallenge(name)
+	if err != nil {
+		return fr.Element{}, err
+	}
+	var gamma fr.Element
+	gamma.SetBytes(gammaByte)
+
+	return gamma, nil
+}
+
+// ------------------------------
+// utils
+
+func flatten(x [][]fr.Element) []fr.Element {
+	nbPoints := 0
+	for i := 0; i < len(x); i++ {
+		nbPoints += len(x[i])
+	}
+	res := make([]fr.Element, 0, nbPoints)
+	for i := 0; i < len(x); i++ {
+		res = append(res, x[i]...)
+	}
+	return res
+}
+
+// sets f to zero
+func setZero(f []fr.Element) {
+	for i := 0; i < len(f); i++ {
+		f[i].SetZero()
+	}
+}
+
+func eval(f []fr.Element, x fr.Element) fr.Element {
+	var y fr.Element
+	for i := len(f) - 1; i >= 0; i-- {
+		y.Mul(&y, &x).Add(&y, &f[i])
+	}
+	return y
+}
+
+// returns γ*f, re-using f
+func mulByConstant(f []fr.Element, gamma fr.Element) []fr.Element {
+	for i := 0; i < len(f); i++ {
+		f[i].Mul(&f[i], &gamma)
+	}
+	return f
+}
+
+// computes f <- (x-a)*f
+// memory of f is re used, need to pass a copy to not modify it
+func multiplyLinearFactor(f []fr.Element, a fr.Element) []fr.Element {
+	s := len(f)
+	var tmp fr.Element
+	f = append(f, fr.NewElement(0))
+	f[s] = f[s-1]
+	for i := s - 1; i >= 1; i-- {
+		tmp.Mul(&f[i], &a)
+		f[i].Sub(&f[i-1], &tmp)
+	}
+	f[0].Mul(&f[0], &a).Neg(&f[0])
+	return f
+}
+
+// returns S_{T\Sᵢ} where Sᵢ=x[i]
+func buildZtMinusSi(x [][]fr.Element, i int) []fr.Element {
+	nbPoints := 0
+	for i := 0; i < len(x); i++ {
+		nbPoints += len(x[i])
+	}
+	bufPoints := make([]fr.Element, 0, nbPoints-len(x[i]))
+	for j := 0; j < i; j++ {
+		bufPoints = append(bufPoints, x[j]...)
+	}
+	for j := i + 1; j < len(x); j++ {
+		bufPoints = append(bufPoints, x[j]...)
+	}
+	ztMinusSi := buildVanishingPoly(bufPoints)
+	return ztMinusSi
+}
+
+// returns πᵢ(X-xᵢ)
+func buildVanishingPoly(x []fr.Element) []fr.Element {
+	res := make([]fr.Element, 1, len(x)+1)
+	res[0].SetOne()
+	for i := 0; i < len(x); i++ {
+		res = multiplyLinearFactor(res, x[i])
+	}
+	return res
+}
+
+// returns f such that f(xᵢ)=yᵢ, x and y are assumed to be of the same size
+func interpolate(x, y []fr.Element) []fr.Element {
+
+	res := make([]fr.Element, len(x))
+	for i := 0; i < len(x); i++ {
+		li := buildLagrangeFromDomain(x, i)
+		li = mulByConstant(li, y[i])
+		for j := 0; j < len(x); j++ {
+			res[j].Add(&res[j], &li[j])
+		}
+	}
+
+	return res
+}
+
+// returns f such that f(xⱼ)=δⁱⱼ
+func buildLagrangeFromDomain(x []fr.Element, i int) []fr.Element {
+	xx := make([]fr.Element, len(x)-1)
+	copy(xx, x[:i])
+	copy(xx[i:], x[i+1:])
+	res := buildVanishingPoly(xx)
+	d := eval(res, x[i])
+	d.Inverse(&d)
+	res = mulByConstant(res, d)
+	return res
+}
+
+// returns f-g, the memory of f is re used, deg(g) << deg(f) here
+func sub(f, g []fr.Element) []fr.Element {
+	for i := 0; i < len(g); i++ {
+		f[i].Sub(&f[i], &g[i])
+	}
+	return f
+}
+
+// returns f*g using naive multiplication
+// deg(f)>>deg(g), deg(small) =~ 10 max
+// buf is used as a buffer and should not be f or g
+// f and g are not modified
+func mul(f, g []fr.Element, res []fr.Element) []fr.Element {
+
+	sizeRes := len(f) + len(g) - 1
+	if len(res) < sizeRes {
+		s := make([]fr.Element, sizeRes-len(res))
+		res = append(res, s...)
+	}
+	setZero(res)
+
+	var tmp fr.Element
+	for i := 0; i < len(g); i++ {
+		for j := 0; j < len(f); j++ {
+			tmp.Mul(&f[j], &g[i])
+			res[j+i].Add(&res[j+i], &tmp)
+		}
+	}
+	return res
+}
+
+// returns f/g (assuming g divides f)
+// OK to not use fft if deg(g) is small
+// g's leading coefficient is assumed to be 1
+// f memory is re-used for the result, need to pass a copy to not modify it
+func div(f, g []fr.Element) []fr.Element {
+	sizef := len(f)
+	sizeg := len(g)
+	stop := sizeg - +1
+	var t fr.Element
+	for i := sizef - 2; i >= stop; i-- {
+		for j := 0; j < sizeg-1; j++ {
+			t.Mul(&f[i+1], &g[sizeg-2-j])
+			f[i-j].Sub(&f[i-j], &t)
+		}
+	}
+	return f[sizeg-1:]
+}
diff --git a/ecc/bw6-633/shplonk/shplonk_test.go b/ecc/bw6-633/shplonk/shplonk_test.go
new file mode 100644
index 0000000000..807b263e08
--- /dev/null
+++ b/ecc/bw6-633/shplonk/shplonk_test.go
@@ -0,0 +1,320 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"crypto/sha256"
+	"math/big"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
+	"github.com/consensys/gnark-crypto/ecc/bw6-633/kzg"
+	"github.com/stretchr/testify/require"
+)
+
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *kzg.SRS
+var bAlpha *big.Int
+
+func init() {
+	const srsSize = 230
+	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+}
+
+func TestOpening(t *testing.T) {
+
+	assert := require.New(t)
+
+	nbPolys := 2
+	sizePoly := make([]int, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		sizePoly[i] = 10 + i
+	}
+	polys := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		polys[i] = make([]fr.Element, sizePoly[i])
+		for j := 0; j < sizePoly[i]; j++ {
+			polys[i][j].SetRandom()
+		}
+	}
+
+	digests := make([]kzg.Digest, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		digests[i], _ = kzg.Commit(polys[i], testSrs.Pk)
+	}
+
+	points := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		points[i] = make([]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+
+	hf := sha256.New()
+
+	// correct proof
+	openingProof, err := BatchOpen(polys, digests, points, hf, testSrs.Pk)
+	assert.NoError(err)
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	assert.NoError(err)
+
+	// tampered proof
+	openingProof.ClaimedValues[0][0].SetRandom()
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	assert.Error(err)
+
+}
+
+func TestBuildZtMinusSi(t *testing.T) {
+
+	nbSi := 10
+	points := make([][]fr.Element, nbSi)
+	sizeSi := make([]int, nbSi)
+	nbPoints := 0
+	for i := 0; i < nbSi; i++ {
+		sizeSi[i] = 5 + i
+		nbPoints += sizeSi[i]
+		points[i] = make([]fr.Element, sizeSi[i])
+		for j := 0; j < sizeSi[i]; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+	for i := 0; i < nbSi; i++ {
+		ztMinusSi := buildZtMinusSi(points, i)
+		if len(ztMinusSi) != nbPoints-sizeSi[i]+1 {
+			t.Fatal("deg(Z_{T-S_{i}}) should be nbPoints-size(S_{i})")
+		}
+		for j := 0; j < nbSi; j++ {
+			if j == i {
+				for k := 0; k < sizeSi[j]; k++ {
+					y := eval(ztMinusSi, points[j][k])
+					if y.IsZero() {
+						t.Fatal("Z_{T-S_{i}}(S_{i}) should not be zero")
+					}
+				}
+				continue
+			}
+			for k := 0; k < sizeSi[j]; k++ {
+				y := eval(ztMinusSi, points[j][k])
+				if !y.IsZero() {
+					t.Fatal("Z_{T-S_{i}}(S_{j}) should be zero")
+				}
+			}
+		}
+	}
+
+}
+
+func TestInterpolate(t *testing.T) {
+
+	nbPoints := 10
+	x := make([]fr.Element, nbPoints)
+	y := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		y[i].SetRandom()
+	}
+	f := interpolate(x, y)
+	for i := 0; i < nbPoints; i++ {
+		fx := eval(f, x[i])
+		if !fx.Equal(&y[i]) {
+			t.Fatal("f(x_{i})!=y_{i}")
+		}
+	}
+
+}
+
+func TestBuildLagrangeFromDomain(t *testing.T) {
+
+	nbPoints := 10
+	points := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		points[i].SetRandom()
+	}
+	var r fr.Element
+	for i := 0; i < nbPoints; i++ {
+
+		l := buildLagrangeFromDomain(points, i)
+
+		// check that l(xᵢ)=1 and l(xⱼ)=0 for j!=i
+		for j := 0; j < nbPoints; j++ {
+			y := eval(l, points[j])
+			if i == j {
+				if !y.IsOne() {
+					t.Fatal("l_{i}(x_{i}) should be equal to 1")
+				}
+			} else {
+				if !y.IsZero() {
+					t.Fatal("l_{i}(x_{j}) where i!=j should be equal to 0")
+				}
+			}
+		}
+		r.SetRandom()
+		y := eval(l, r)
+		if y.IsZero() {
+			t.Fatal("l_{i}(x) should not be zero if x is random")
+		}
+	}
+
+}
+
+func TestBuildVanishingPoly(t *testing.T) {
+	s := 10
+	x := make([]fr.Element, s)
+	for i := 0; i < s; i++ {
+		x[i].SetRandom()
+	}
+	r := buildVanishingPoly(x)
+
+	if len(r) != s+1 {
+		t.Fatal("error degree r")
+	}
+
+	// check that r(xᵢ)=0 for all i
+	for i := 0; i < len(x); i++ {
+		y := eval(r, x[i])
+		if !y.IsZero() {
+			t.Fatal("πᵢ(X-xᵢ) at xᵢ should be zero")
+		}
+	}
+
+	// check that r(y)!=0 for a random point
+	var a fr.Element
+	a.SetRandom()
+	y := eval(r, a)
+	if y.IsZero() {
+		t.Fatal("πᵢ(X-xᵢ) at r \neq xᵢ should not be zero")
+	}
+}
+
+func TestMultiplyLinearFactor(t *testing.T) {
+
+	s := 10
+	f := make([]fr.Element, s, s+1)
+	for i := 0; i < 10; i++ {
+		f[i].SetRandom()
+	}
+
+	var a, y fr.Element
+	a.SetRandom()
+	f = multiplyLinearFactor(f, a)
+	y = eval(f, a)
+	if !y.IsZero() {
+		t.Fatal("(X-a)f(X) should be zero at a")
+	}
+	a.SetRandom()
+	y = eval(f, a)
+	if y.IsZero() {
+		t.Fatal("(X-1)f(X) at a random point should not be zero")
+	}
+
+}
+
+func TestNaiveMul(t *testing.T) {
+
+	size := 10
+	f := make([]fr.Element, size)
+	for i := 0; i < size; i++ {
+		f[i].SetRandom()
+	}
+
+	nbPoints := 10
+	points := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		points[i].SetRandom()
+	}
+
+	v := buildVanishingPoly(points)
+	buf := make([]fr.Element, size+nbPoints-1)
+	g := mul(f, v, buf)
+
+	// check that g(xᵢ) = 0
+	for i := 0; i < nbPoints; i++ {
+		y := eval(g, points[i])
+		if !y.IsZero() {
+			t.Fatal("f(X)(X-x_{1})..(X-x_{n}) at x_{i} should be zero")
+		}
+	}
+
+	// check that g(r) != 0 for a random point
+	var a fr.Element
+	a.SetRandom()
+	y := eval(g, a)
+	if y.IsZero() {
+		t.Fatal("f(X)(X-x_{1})..(X-x_{n}) at a random point should not be zero")
+	}
+
+}
+
+func TestDiv(t *testing.T) {
+
+	nbPoints := 10
+	s := 10
+	f := make([]fr.Element, s, s+nbPoints)
+	for i := 0; i < s; i++ {
+		f[i].SetRandom()
+	}
+
+	// backup
+	g := make([]fr.Element, s)
+	copy(g, f)
+
+	// successive divions of linear terms
+	x := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		f = multiplyLinearFactor(f, x[i])
+	}
+	q := make([][2]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		q[i][1].SetOne()
+		q[i][0].Neg(&x[i])
+		f = div(f, q[i][:])
+	}
+
+	// g should be equal to f
+	if len(f) != len(g) {
+		t.Fatal("lengths don't match")
+	}
+	for i := 0; i < len(g); i++ {
+		if !f[i].Equal(&g[i]) {
+			t.Fatal("f(x)(x-a)/(x-a) should be equal to f(x)")
+		}
+	}
+
+	// division by a degree > 1 polynomial
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		f = multiplyLinearFactor(f, x[i])
+	}
+	r := buildVanishingPoly(x)
+	f = div(f, r)
+
+	// g should be equal to f
+	if len(f) != len(g) {
+		t.Fatal("lengths don't match")
+	}
+	for i := 0; i < len(g); i++ {
+		if !f[i].Equal(&g[i]) {
+			t.Fatal("f(x)(x-a)/(x-a) should be equal to f(x)")
+		}
+	}
+
+}
diff --git a/ecc/bw6-756/shplonk/doc.go b/ecc/bw6-756/shplonk/doc.go
new file mode 100644
index 0000000000..e048f46009
--- /dev/null
+++ b/ecc/bw6-756/shplonk/doc.go
@@ -0,0 +1,18 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// Package shplonk provides a SHPLONK commitment scheme, cf https://eprint.iacr.org/2020/081.pdf
+package shplonk
diff --git a/ecc/bw6-756/shplonk/marshal.go b/ecc/bw6-756/shplonk/marshal.go
new file mode 100644
index 0000000000..e7b0bf4ed8
--- /dev/null
+++ b/ecc/bw6-756/shplonk/marshal.go
@@ -0,0 +1,62 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"io"
+
+	"github.com/consensys/gnark-crypto/ecc/bw6-756"
+)
+
+func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
+
+	dec := bw6756.NewDecoder(r)
+
+	toDecode := []interface{}{
+		&proof.W,
+		&proof.WPrime,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toDecode {
+		if err := dec.Decode(v); err != nil {
+			return dec.BytesRead(), err
+		}
+	}
+
+	return dec.BytesRead(), nil
+}
+
+// WriteTo writes binary encoding of a OpeningProof
+func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
+
+	enc := bw6756.NewEncoder(w)
+
+	toEncode := []interface{}{
+		&proof.W,
+		&proof.WPrime,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toEncode {
+		if err := enc.Encode(v); err != nil {
+			return enc.BytesWritten(), err
+		}
+	}
+
+	return enc.BytesWritten(), nil
+}
diff --git a/ecc/bw6-756/shplonk/shplonk.go b/ecc/bw6-756/shplonk/shplonk.go
new file mode 100644
index 0000000000..d8353e303b
--- /dev/null
+++ b/ecc/bw6-756/shplonk/shplonk.go
@@ -0,0 +1,462 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"errors"
+	"hash"
+	"math/big"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bw6-756"
+	"github.com/consensys/gnark-crypto/ecc/bw6-756/fr"
+	"github.com/consensys/gnark-crypto/ecc/bw6-756/kzg"
+	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
+)
+
+var (
+	ErrInvalidNumberOfPoints = errors.New("number of digests should be equal to the number of points")
+	ErrVerifyOpeningProof    = errors.New("can't verify batch opening proof")
+)
+
+// OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
+//
+// implements io.ReaderFrom and io.WriterTo
+type OpeningProof struct {
+
+	// W = ∑ᵢ γⁱZ_{T\Sᵢ}(f_i(X)-r)/Z_{T} where Z_{T} is the vanishing polynomial on the (Sᵢ)_{i}
+	// and r interpolates fᵢ(Sᵢ) on (Sᵢ)
+	W bw6756.G1Affine
+
+	// L(X)/(X-z) where L(X)=∑ᵢγⁱZ_{T\xᵢ}(f_i(X)-rᵢ) - Z_{T}W(X)
+	WPrime bw6756.G1Affine
+
+	// ClaimedValues[i] are the values of fᵢ on Sᵢ
+	ClaimedValues [][]fr.Element
+}
+
+// BatchOpen opens the list of polynomials on points, where the i-th polynomials is opend at points[i].
+func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
+
+	var res OpeningProof
+
+	nbInstances := len(polynomials)
+	if len(polynomials) != len(points) {
+		return res, ErrInvalidNumberOfPoints
+	}
+
+	// transcript
+	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
+
+	// derive γ
+	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
+	if err != nil {
+		return res, err
+	}
+
+	// compute the size of the linear combination
+	maxSizePolys := len(polynomials[0])
+	for i := 1; i < len(polynomials); i++ {
+		if maxSizePolys < len(polynomials[i]) {
+			maxSizePolys = len(polynomials[i])
+		}
+	}
+	nbPoints := 0
+	sizeSi := make([]int, len(points))
+	for i := 0; i < nbInstances; i++ {
+		nbPoints += len(points[i])
+		sizeSi[i] = len(points[i])
+	}
+	totalSize := maxSizePolys + nbPoints // upper bound of the size of f := ∑ᵢ γⁱZ_{T\Sᵢ}(f_i(X)-r)
+
+	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
+	bufTotalSize := make([]fr.Element, totalSize)
+	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
+	res.ClaimedValues = make([][]fr.Element, nbInstances)
+	for i := 0; i < nbInstances; i++ {
+		res.ClaimedValues[i] = make([]fr.Element, len(points[i]))
+	}
+	var accGamma fr.Element
+	accGamma.SetOne()
+
+	ztMinusSi := make([][]fr.Element, nbInstances)
+	ri := make([][]fr.Element, nbInstances)
+	for i := 0; i < nbInstances; i++ {
+
+		for j := 0; j < len(points[i]); j++ {
+			res.ClaimedValues[i][j] = eval(polynomials[i], points[i][j])
+		}
+
+		ztMinusSi[i] = buildZtMinusSi(points, i)
+
+		copy(bufMaxSizePolynomials, polynomials[i])
+		ri[i] = interpolate(points[i], res.ClaimedValues[i])
+		sub(bufMaxSizePolynomials, ri[i])
+
+		bufTotalSize = mul(bufMaxSizePolynomials, ztMinusSi[i], bufTotalSize)
+		bufTotalSize = mulByConstant(bufTotalSize, accGamma)
+		for j := 0; j < len(bufTotalSize); j++ {
+			f[j].Add(&f[j], &bufTotalSize[j])
+		}
+
+		accGamma.Mul(&accGamma, &gamma)
+		setZero(bufMaxSizePolynomials)
+	}
+
+	zt := buildVanishingPoly(flatten(points))
+	w := div(f, zt) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
+	res.W, err = kzg.Commit(w, pk)
+	if err != nil {
+		return res, err
+	}
+
+	// derive z
+	z, err := deriveChallenge("z", nil, []kzg.Digest{res.W}, fs)
+	if err != nil {
+		return res, err
+	}
+
+	// compute L = ∑ᵢγⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))-Z_{T}(z)W
+	accGamma.SetOne()
+	var gammaiZtMinusSiZ fr.Element
+	l := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
+	for i := 0; i < len(polynomials); i++ {
+
+		ztMinusSiZ := eval(ztMinusSi[i], z)          // Z_{T\Sᵢ}(z)
+		gammaiZtMinusSiZ.Mul(&accGamma, &ztMinusSiZ) // γⁱZ_{T\Sᵢ}(z)
+
+		copy(bufMaxSizePolynomials, polynomials[i])
+		riz := eval(ri[i], z)
+		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz) // (fᵢ-rᵢ(z))
+		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusSiZ)        // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
+		for j := 0; j < len(bufMaxSizePolynomials); j++ {
+			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
+		}
+
+		setZero(bufMaxSizePolynomials)
+		accGamma.Mul(&accGamma, &gamma)
+	}
+	ztz := eval(zt, z)
+	setZero(bufTotalSize)
+	copy(bufTotalSize, w)
+	mulByConstant(bufTotalSize, ztz) // Z_{T}(z)W
+	for i := 0; i < totalSize-maxSizePolys; i++ {
+		l[totalSize-1-i].Neg(&bufTotalSize[totalSize-1-i])
+	}
+	for i := 0; i < maxSizePolys; i++ {
+		l[i].Sub(&l[i], &bufTotalSize[i])
+	} // L <- L-Z_{T}(z)W
+
+	xMinusZ := buildVanishingPoly([]fr.Element{z})
+	wPrime := div(l, xMinusZ)
+
+	res.WPrime, err = kzg.Commit(wPrime, pk)
+	if err != nil {
+		return res, err
+	}
+
+	return res, nil
+}
+
+// BatchVerify uses proof to check that the commitments correctly open to proof.ClaimedValues
+// at points. The order matters: the proof validates that the i-th commitment is correctly opened
+// at the i-th point
+// dataTranscript is some extra data that might be needed for Fiat Shamir, and is appended at the end
+// of the original transcript.
+func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
+
+	if len(digests) != len(proof.ClaimedValues) {
+		return ErrInvalidNumberOfPoints
+	}
+	if len(digests) != len(points) {
+		return ErrInvalidNumberOfPoints
+	}
+
+	// transcript
+	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
+
+	// derive γ
+	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
+	if err != nil {
+		return err
+	}
+
+	// derive z
+	// TODO seems ok that z depend only on W, need to check that carefully
+	z, err := deriveChallenge("z", nil, []kzg.Digest{proof.W}, fs)
+	if err != nil {
+		return err
+	}
+
+	// check that e(F + zW', [1]_{2})=e(W',[x]_{2})
+	// where F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}-[∑ᵢγⁱZ_{T\xᵢ}(z)fᵢ(z)]_{1}-Z_{T}(z)[W]
+	var sumGammaiZTminusSiRiz, tmp, accGamma fr.Element
+	nbInstances := len(points)
+	gammaiZTminusSiz := make([]fr.Element, nbInstances)
+	accGamma.SetOne()
+	ri := make([][]fr.Element, nbInstances)
+	for i := 0; i < len(points); i++ {
+
+		ztMinusSi := buildZtMinusSi(points, i)                   // Z_{T-S_{i}}(X)
+		gammaiZTminusSiz[i] = eval(ztMinusSi, z)                 // Z_{T-S_{i}}(z)
+		gammaiZTminusSiz[i].Mul(&accGamma, &gammaiZTminusSiz[i]) // \gamma^{i} Z_{T-S_{i}}(z)
+
+		ri[i] = interpolate(points[i], proof.ClaimedValues[i])
+		riz := eval(ri[i], z)               // r_{i}(z)
+		tmp.Mul(&gammaiZTminusSiz[i], &riz) // Z_{T-S_{i}}(z)r_{i}(z)
+		sumGammaiZTminusSiRiz.Add(&sumGammaiZTminusSiRiz, &tmp)
+
+		accGamma.Mul(&accGamma, &gamma)
+	}
+
+	// ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}
+	config := ecc.MultiExpConfig{}
+	var sumGammaiZtMinusSiComi kzg.Digest
+	_, err = sumGammaiZtMinusSiComi.MultiExp(digests, gammaiZTminusSiz, config)
+	if err != nil {
+		return err
+	}
+
+	var bufBigInt big.Int
+
+	// [∑ᵢZ_{T\xᵢ}fᵢ(z)]_{1}
+	var sumGammaiZTminusSiRizCom kzg.Digest
+	var sumGammaiZTminusSiRizBigInt big.Int
+	sumGammaiZTminusSiRiz.BigInt(&sumGammaiZTminusSiRizBigInt)
+	sumGammaiZTminusSiRizCom.ScalarMultiplication(&vk.G1, &sumGammaiZTminusSiRizBigInt)
+
+	// Z_{T}(z)[W]
+	zt := buildVanishingPoly(flatten(points))
+	ztz := eval(zt, z)
+	var ztW kzg.Digest
+	ztz.BigInt(&bufBigInt)
+	ztW.ScalarMultiplication(&proof.W, &bufBigInt)
+
+	// F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i} - [∑ᵢγⁱZ_{T\xᵢ}fᵢ(z)]_{1} - Z_{T}(z)[W]
+	var f kzg.Digest
+	f.Sub(&sumGammaiZtMinusSiComi, &sumGammaiZTminusSiRizCom).
+		Sub(&f, &ztW)
+
+	// F+zW'
+	var zWPrime kzg.Digest
+	z.BigInt(&bufBigInt)
+	zWPrime.ScalarMultiplication(&proof.WPrime, &bufBigInt)
+	f.Add(&f, &zWPrime)
+	f.Neg(&f)
+
+	// check that e(F+zW',[1]_{2})=e(W',[x]_{2})
+	check, err := bw6756.PairingCheckFixedQ(
+		[]bw6756.G1Affine{f, proof.WPrime},
+		vk.Lines[:],
+	)
+
+	if !check {
+		return ErrVerifyOpeningProof
+	}
+
+	return nil
+}
+
+// deriveChallenge derives a challenge using Fiat Shamir to polynomials.
+// The arguments are added to the transcript in the order in which they are given.
+func deriveChallenge(name string, points [][]fr.Element, digests []kzg.Digest, t *fiatshamir.Transcript, dataTranscript ...[]byte) (fr.Element, error) {
+
+	// derive the challenge gamma, binded to the point and the commitments
+	for i := range points {
+		for j := range points[i] {
+			if err := t.Bind(name, points[i][j].Marshal()); err != nil {
+				return fr.Element{}, err
+			}
+		}
+	}
+	for i := range digests {
+		if err := t.Bind(name, digests[i].Marshal()); err != nil {
+			return fr.Element{}, err
+		}
+	}
+
+	for i := 0; i < len(dataTranscript); i++ {
+		if err := t.Bind(name, dataTranscript[i]); err != nil {
+			return fr.Element{}, err
+		}
+	}
+
+	gammaByte, err := t.ComputeChallenge(name)
+	if err != nil {
+		return fr.Element{}, err
+	}
+	var gamma fr.Element
+	gamma.SetBytes(gammaByte)
+
+	return gamma, nil
+}
+
+// ------------------------------
+// utils
+
+func flatten(x [][]fr.Element) []fr.Element {
+	nbPoints := 0
+	for i := 0; i < len(x); i++ {
+		nbPoints += len(x[i])
+	}
+	res := make([]fr.Element, 0, nbPoints)
+	for i := 0; i < len(x); i++ {
+		res = append(res, x[i]...)
+	}
+	return res
+}
+
+// sets f to zero
+func setZero(f []fr.Element) {
+	for i := 0; i < len(f); i++ {
+		f[i].SetZero()
+	}
+}
+
+func eval(f []fr.Element, x fr.Element) fr.Element {
+	var y fr.Element
+	for i := len(f) - 1; i >= 0; i-- {
+		y.Mul(&y, &x).Add(&y, &f[i])
+	}
+	return y
+}
+
+// returns γ*f, re-using f
+func mulByConstant(f []fr.Element, gamma fr.Element) []fr.Element {
+	for i := 0; i < len(f); i++ {
+		f[i].Mul(&f[i], &gamma)
+	}
+	return f
+}
+
+// computes f <- (x-a)*f
+// memory of f is re used, need to pass a copy to not modify it
+func multiplyLinearFactor(f []fr.Element, a fr.Element) []fr.Element {
+	s := len(f)
+	var tmp fr.Element
+	f = append(f, fr.NewElement(0))
+	f[s] = f[s-1]
+	for i := s - 1; i >= 1; i-- {
+		tmp.Mul(&f[i], &a)
+		f[i].Sub(&f[i-1], &tmp)
+	}
+	f[0].Mul(&f[0], &a).Neg(&f[0])
+	return f
+}
+
+// returns S_{T\Sᵢ} where Sᵢ=x[i]
+func buildZtMinusSi(x [][]fr.Element, i int) []fr.Element {
+	nbPoints := 0
+	for i := 0; i < len(x); i++ {
+		nbPoints += len(x[i])
+	}
+	bufPoints := make([]fr.Element, 0, nbPoints-len(x[i]))
+	for j := 0; j < i; j++ {
+		bufPoints = append(bufPoints, x[j]...)
+	}
+	for j := i + 1; j < len(x); j++ {
+		bufPoints = append(bufPoints, x[j]...)
+	}
+	ztMinusSi := buildVanishingPoly(bufPoints)
+	return ztMinusSi
+}
+
+// returns πᵢ(X-xᵢ)
+func buildVanishingPoly(x []fr.Element) []fr.Element {
+	res := make([]fr.Element, 1, len(x)+1)
+	res[0].SetOne()
+	for i := 0; i < len(x); i++ {
+		res = multiplyLinearFactor(res, x[i])
+	}
+	return res
+}
+
+// returns f such that f(xᵢ)=yᵢ, x and y are assumed to be of the same size
+func interpolate(x, y []fr.Element) []fr.Element {
+
+	res := make([]fr.Element, len(x))
+	for i := 0; i < len(x); i++ {
+		li := buildLagrangeFromDomain(x, i)
+		li = mulByConstant(li, y[i])
+		for j := 0; j < len(x); j++ {
+			res[j].Add(&res[j], &li[j])
+		}
+	}
+
+	return res
+}
+
+// returns f such that f(xⱼ)=δⁱⱼ
+func buildLagrangeFromDomain(x []fr.Element, i int) []fr.Element {
+	xx := make([]fr.Element, len(x)-1)
+	copy(xx, x[:i])
+	copy(xx[i:], x[i+1:])
+	res := buildVanishingPoly(xx)
+	d := eval(res, x[i])
+	d.Inverse(&d)
+	res = mulByConstant(res, d)
+	return res
+}
+
+// returns f-g, the memory of f is re used, deg(g) << deg(f) here
+func sub(f, g []fr.Element) []fr.Element {
+	for i := 0; i < len(g); i++ {
+		f[i].Sub(&f[i], &g[i])
+	}
+	return f
+}
+
+// returns f*g using naive multiplication
+// deg(f)>>deg(g), deg(small) =~ 10 max
+// buf is used as a buffer and should not be f or g
+// f and g are not modified
+func mul(f, g []fr.Element, res []fr.Element) []fr.Element {
+
+	sizeRes := len(f) + len(g) - 1
+	if len(res) < sizeRes {
+		s := make([]fr.Element, sizeRes-len(res))
+		res = append(res, s...)
+	}
+	setZero(res)
+
+	var tmp fr.Element
+	for i := 0; i < len(g); i++ {
+		for j := 0; j < len(f); j++ {
+			tmp.Mul(&f[j], &g[i])
+			res[j+i].Add(&res[j+i], &tmp)
+		}
+	}
+	return res
+}
+
+// returns f/g (assuming g divides f)
+// OK to not use fft if deg(g) is small
+// g's leading coefficient is assumed to be 1
+// f memory is re-used for the result, need to pass a copy to not modify it
+func div(f, g []fr.Element) []fr.Element {
+	sizef := len(f)
+	sizeg := len(g)
+	stop := sizeg - +1
+	var t fr.Element
+	for i := sizef - 2; i >= stop; i-- {
+		for j := 0; j < sizeg-1; j++ {
+			t.Mul(&f[i+1], &g[sizeg-2-j])
+			f[i-j].Sub(&f[i-j], &t)
+		}
+	}
+	return f[sizeg-1:]
+}
diff --git a/ecc/bw6-756/shplonk/shplonk_test.go b/ecc/bw6-756/shplonk/shplonk_test.go
new file mode 100644
index 0000000000..c729294363
--- /dev/null
+++ b/ecc/bw6-756/shplonk/shplonk_test.go
@@ -0,0 +1,320 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"crypto/sha256"
+	"math/big"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bw6-756/fr"
+	"github.com/consensys/gnark-crypto/ecc/bw6-756/kzg"
+	"github.com/stretchr/testify/require"
+)
+
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *kzg.SRS
+var bAlpha *big.Int
+
+func init() {
+	const srsSize = 230
+	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+}
+
+func TestOpening(t *testing.T) {
+
+	assert := require.New(t)
+
+	nbPolys := 2
+	sizePoly := make([]int, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		sizePoly[i] = 10 + i
+	}
+	polys := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		polys[i] = make([]fr.Element, sizePoly[i])
+		for j := 0; j < sizePoly[i]; j++ {
+			polys[i][j].SetRandom()
+		}
+	}
+
+	digests := make([]kzg.Digest, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		digests[i], _ = kzg.Commit(polys[i], testSrs.Pk)
+	}
+
+	points := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		points[i] = make([]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+
+	hf := sha256.New()
+
+	// correct proof
+	openingProof, err := BatchOpen(polys, digests, points, hf, testSrs.Pk)
+	assert.NoError(err)
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	assert.NoError(err)
+
+	// tampered proof
+	openingProof.ClaimedValues[0][0].SetRandom()
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	assert.Error(err)
+
+}
+
+func TestBuildZtMinusSi(t *testing.T) {
+
+	nbSi := 10
+	points := make([][]fr.Element, nbSi)
+	sizeSi := make([]int, nbSi)
+	nbPoints := 0
+	for i := 0; i < nbSi; i++ {
+		sizeSi[i] = 5 + i
+		nbPoints += sizeSi[i]
+		points[i] = make([]fr.Element, sizeSi[i])
+		for j := 0; j < sizeSi[i]; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+	for i := 0; i < nbSi; i++ {
+		ztMinusSi := buildZtMinusSi(points, i)
+		if len(ztMinusSi) != nbPoints-sizeSi[i]+1 {
+			t.Fatal("deg(Z_{T-S_{i}}) should be nbPoints-size(S_{i})")
+		}
+		for j := 0; j < nbSi; j++ {
+			if j == i {
+				for k := 0; k < sizeSi[j]; k++ {
+					y := eval(ztMinusSi, points[j][k])
+					if y.IsZero() {
+						t.Fatal("Z_{T-S_{i}}(S_{i}) should not be zero")
+					}
+				}
+				continue
+			}
+			for k := 0; k < sizeSi[j]; k++ {
+				y := eval(ztMinusSi, points[j][k])
+				if !y.IsZero() {
+					t.Fatal("Z_{T-S_{i}}(S_{j}) should be zero")
+				}
+			}
+		}
+	}
+
+}
+
+func TestInterpolate(t *testing.T) {
+
+	nbPoints := 10
+	x := make([]fr.Element, nbPoints)
+	y := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		y[i].SetRandom()
+	}
+	f := interpolate(x, y)
+	for i := 0; i < nbPoints; i++ {
+		fx := eval(f, x[i])
+		if !fx.Equal(&y[i]) {
+			t.Fatal("f(x_{i})!=y_{i}")
+		}
+	}
+
+}
+
+func TestBuildLagrangeFromDomain(t *testing.T) {
+
+	nbPoints := 10
+	points := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		points[i].SetRandom()
+	}
+	var r fr.Element
+	for i := 0; i < nbPoints; i++ {
+
+		l := buildLagrangeFromDomain(points, i)
+
+		// check that l(xᵢ)=1 and l(xⱼ)=0 for j!=i
+		for j := 0; j < nbPoints; j++ {
+			y := eval(l, points[j])
+			if i == j {
+				if !y.IsOne() {
+					t.Fatal("l_{i}(x_{i}) should be equal to 1")
+				}
+			} else {
+				if !y.IsZero() {
+					t.Fatal("l_{i}(x_{j}) where i!=j should be equal to 0")
+				}
+			}
+		}
+		r.SetRandom()
+		y := eval(l, r)
+		if y.IsZero() {
+			t.Fatal("l_{i}(x) should not be zero if x is random")
+		}
+	}
+
+}
+
+func TestBuildVanishingPoly(t *testing.T) {
+	s := 10
+	x := make([]fr.Element, s)
+	for i := 0; i < s; i++ {
+		x[i].SetRandom()
+	}
+	r := buildVanishingPoly(x)
+
+	if len(r) != s+1 {
+		t.Fatal("error degree r")
+	}
+
+	// check that r(xᵢ)=0 for all i
+	for i := 0; i < len(x); i++ {
+		y := eval(r, x[i])
+		if !y.IsZero() {
+			t.Fatal("πᵢ(X-xᵢ) at xᵢ should be zero")
+		}
+	}
+
+	// check that r(y)!=0 for a random point
+	var a fr.Element
+	a.SetRandom()
+	y := eval(r, a)
+	if y.IsZero() {
+		t.Fatal("πᵢ(X-xᵢ) at r \neq xᵢ should not be zero")
+	}
+}
+
+func TestMultiplyLinearFactor(t *testing.T) {
+
+	s := 10
+	f := make([]fr.Element, s, s+1)
+	for i := 0; i < 10; i++ {
+		f[i].SetRandom()
+	}
+
+	var a, y fr.Element
+	a.SetRandom()
+	f = multiplyLinearFactor(f, a)
+	y = eval(f, a)
+	if !y.IsZero() {
+		t.Fatal("(X-a)f(X) should be zero at a")
+	}
+	a.SetRandom()
+	y = eval(f, a)
+	if y.IsZero() {
+		t.Fatal("(X-1)f(X) at a random point should not be zero")
+	}
+
+}
+
+func TestNaiveMul(t *testing.T) {
+
+	size := 10
+	f := make([]fr.Element, size)
+	for i := 0; i < size; i++ {
+		f[i].SetRandom()
+	}
+
+	nbPoints := 10
+	points := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		points[i].SetRandom()
+	}
+
+	v := buildVanishingPoly(points)
+	buf := make([]fr.Element, size+nbPoints-1)
+	g := mul(f, v, buf)
+
+	// check that g(xᵢ) = 0
+	for i := 0; i < nbPoints; i++ {
+		y := eval(g, points[i])
+		if !y.IsZero() {
+			t.Fatal("f(X)(X-x_{1})..(X-x_{n}) at x_{i} should be zero")
+		}
+	}
+
+	// check that g(r) != 0 for a random point
+	var a fr.Element
+	a.SetRandom()
+	y := eval(g, a)
+	if y.IsZero() {
+		t.Fatal("f(X)(X-x_{1})..(X-x_{n}) at a random point should not be zero")
+	}
+
+}
+
+func TestDiv(t *testing.T) {
+
+	nbPoints := 10
+	s := 10
+	f := make([]fr.Element, s, s+nbPoints)
+	for i := 0; i < s; i++ {
+		f[i].SetRandom()
+	}
+
+	// backup
+	g := make([]fr.Element, s)
+	copy(g, f)
+
+	// successive divions of linear terms
+	x := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		f = multiplyLinearFactor(f, x[i])
+	}
+	q := make([][2]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		q[i][1].SetOne()
+		q[i][0].Neg(&x[i])
+		f = div(f, q[i][:])
+	}
+
+	// g should be equal to f
+	if len(f) != len(g) {
+		t.Fatal("lengths don't match")
+	}
+	for i := 0; i < len(g); i++ {
+		if !f[i].Equal(&g[i]) {
+			t.Fatal("f(x)(x-a)/(x-a) should be equal to f(x)")
+		}
+	}
+
+	// division by a degree > 1 polynomial
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		f = multiplyLinearFactor(f, x[i])
+	}
+	r := buildVanishingPoly(x)
+	f = div(f, r)
+
+	// g should be equal to f
+	if len(f) != len(g) {
+		t.Fatal("lengths don't match")
+	}
+	for i := 0; i < len(g); i++ {
+		if !f[i].Equal(&g[i]) {
+			t.Fatal("f(x)(x-a)/(x-a) should be equal to f(x)")
+		}
+	}
+
+}
diff --git a/ecc/bw6-761/shplonk/doc.go b/ecc/bw6-761/shplonk/doc.go
new file mode 100644
index 0000000000..e048f46009
--- /dev/null
+++ b/ecc/bw6-761/shplonk/doc.go
@@ -0,0 +1,18 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// Package shplonk provides a SHPLONK commitment scheme, cf https://eprint.iacr.org/2020/081.pdf
+package shplonk
diff --git a/ecc/bw6-761/shplonk/marshal.go b/ecc/bw6-761/shplonk/marshal.go
new file mode 100644
index 0000000000..f931b1dd51
--- /dev/null
+++ b/ecc/bw6-761/shplonk/marshal.go
@@ -0,0 +1,62 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"io"
+
+	"github.com/consensys/gnark-crypto/ecc/bw6-761"
+)
+
+func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
+
+	dec := bw6761.NewDecoder(r)
+
+	toDecode := []interface{}{
+		&proof.W,
+		&proof.WPrime,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toDecode {
+		if err := dec.Decode(v); err != nil {
+			return dec.BytesRead(), err
+		}
+	}
+
+	return dec.BytesRead(), nil
+}
+
+// WriteTo writes binary encoding of a OpeningProof
+func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
+
+	enc := bw6761.NewEncoder(w)
+
+	toEncode := []interface{}{
+		&proof.W,
+		&proof.WPrime,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toEncode {
+		if err := enc.Encode(v); err != nil {
+			return enc.BytesWritten(), err
+		}
+	}
+
+	return enc.BytesWritten(), nil
+}
diff --git a/ecc/bw6-761/shplonk/shplonk.go b/ecc/bw6-761/shplonk/shplonk.go
new file mode 100644
index 0000000000..a4d81d6def
--- /dev/null
+++ b/ecc/bw6-761/shplonk/shplonk.go
@@ -0,0 +1,462 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"errors"
+	"hash"
+	"math/big"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bw6-761"
+	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
+	"github.com/consensys/gnark-crypto/ecc/bw6-761/kzg"
+	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
+)
+
+var (
+	ErrInvalidNumberOfPoints = errors.New("number of digests should be equal to the number of points")
+	ErrVerifyOpeningProof    = errors.New("can't verify batch opening proof")
+)
+
+// OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
+//
+// implements io.ReaderFrom and io.WriterTo
+type OpeningProof struct {
+
+	// W = ∑ᵢ γⁱZ_{T\Sᵢ}(f_i(X)-r)/Z_{T} where Z_{T} is the vanishing polynomial on the (Sᵢ)_{i}
+	// and r interpolates fᵢ(Sᵢ) on (Sᵢ)
+	W bw6761.G1Affine
+
+	// L(X)/(X-z) where L(X)=∑ᵢγⁱZ_{T\xᵢ}(f_i(X)-rᵢ) - Z_{T}W(X)
+	WPrime bw6761.G1Affine
+
+	// ClaimedValues[i] are the values of fᵢ on Sᵢ
+	ClaimedValues [][]fr.Element
+}
+
+// BatchOpen opens the list of polynomials on points, where the i-th polynomials is opend at points[i].
+func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
+
+	var res OpeningProof
+
+	nbInstances := len(polynomials)
+	if len(polynomials) != len(points) {
+		return res, ErrInvalidNumberOfPoints
+	}
+
+	// transcript
+	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
+
+	// derive γ
+	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
+	if err != nil {
+		return res, err
+	}
+
+	// compute the size of the linear combination
+	maxSizePolys := len(polynomials[0])
+	for i := 1; i < len(polynomials); i++ {
+		if maxSizePolys < len(polynomials[i]) {
+			maxSizePolys = len(polynomials[i])
+		}
+	}
+	nbPoints := 0
+	sizeSi := make([]int, len(points))
+	for i := 0; i < nbInstances; i++ {
+		nbPoints += len(points[i])
+		sizeSi[i] = len(points[i])
+	}
+	totalSize := maxSizePolys + nbPoints // upper bound of the size of f := ∑ᵢ γⁱZ_{T\Sᵢ}(f_i(X)-r)
+
+	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
+	bufTotalSize := make([]fr.Element, totalSize)
+	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
+	res.ClaimedValues = make([][]fr.Element, nbInstances)
+	for i := 0; i < nbInstances; i++ {
+		res.ClaimedValues[i] = make([]fr.Element, len(points[i]))
+	}
+	var accGamma fr.Element
+	accGamma.SetOne()
+
+	ztMinusSi := make([][]fr.Element, nbInstances)
+	ri := make([][]fr.Element, nbInstances)
+	for i := 0; i < nbInstances; i++ {
+
+		for j := 0; j < len(points[i]); j++ {
+			res.ClaimedValues[i][j] = eval(polynomials[i], points[i][j])
+		}
+
+		ztMinusSi[i] = buildZtMinusSi(points, i)
+
+		copy(bufMaxSizePolynomials, polynomials[i])
+		ri[i] = interpolate(points[i], res.ClaimedValues[i])
+		sub(bufMaxSizePolynomials, ri[i])
+
+		bufTotalSize = mul(bufMaxSizePolynomials, ztMinusSi[i], bufTotalSize)
+		bufTotalSize = mulByConstant(bufTotalSize, accGamma)
+		for j := 0; j < len(bufTotalSize); j++ {
+			f[j].Add(&f[j], &bufTotalSize[j])
+		}
+
+		accGamma.Mul(&accGamma, &gamma)
+		setZero(bufMaxSizePolynomials)
+	}
+
+	zt := buildVanishingPoly(flatten(points))
+	w := div(f, zt) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
+	res.W, err = kzg.Commit(w, pk)
+	if err != nil {
+		return res, err
+	}
+
+	// derive z
+	z, err := deriveChallenge("z", nil, []kzg.Digest{res.W}, fs)
+	if err != nil {
+		return res, err
+	}
+
+	// compute L = ∑ᵢγⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))-Z_{T}(z)W
+	accGamma.SetOne()
+	var gammaiZtMinusSiZ fr.Element
+	l := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation page 11 for notation
+	for i := 0; i < len(polynomials); i++ {
+
+		ztMinusSiZ := eval(ztMinusSi[i], z)          // Z_{T\Sᵢ}(z)
+		gammaiZtMinusSiZ.Mul(&accGamma, &ztMinusSiZ) // γⁱZ_{T\Sᵢ}(z)
+
+		copy(bufMaxSizePolynomials, polynomials[i])
+		riz := eval(ri[i], z)
+		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz) // (fᵢ-rᵢ(z))
+		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusSiZ)        // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
+		for j := 0; j < len(bufMaxSizePolynomials); j++ {
+			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
+		}
+
+		setZero(bufMaxSizePolynomials)
+		accGamma.Mul(&accGamma, &gamma)
+	}
+	ztz := eval(zt, z)
+	setZero(bufTotalSize)
+	copy(bufTotalSize, w)
+	mulByConstant(bufTotalSize, ztz) // Z_{T}(z)W
+	for i := 0; i < totalSize-maxSizePolys; i++ {
+		l[totalSize-1-i].Neg(&bufTotalSize[totalSize-1-i])
+	}
+	for i := 0; i < maxSizePolys; i++ {
+		l[i].Sub(&l[i], &bufTotalSize[i])
+	} // L <- L-Z_{T}(z)W
+
+	xMinusZ := buildVanishingPoly([]fr.Element{z})
+	wPrime := div(l, xMinusZ)
+
+	res.WPrime, err = kzg.Commit(wPrime, pk)
+	if err != nil {
+		return res, err
+	}
+
+	return res, nil
+}
+
+// BatchVerify uses proof to check that the commitments correctly open to proof.ClaimedValues
+// at points. The order matters: the proof validates that the i-th commitment is correctly opened
+// at the i-th point
+// dataTranscript is some extra data that might be needed for Fiat Shamir, and is appended at the end
+// of the original transcript.
+func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
+
+	if len(digests) != len(proof.ClaimedValues) {
+		return ErrInvalidNumberOfPoints
+	}
+	if len(digests) != len(points) {
+		return ErrInvalidNumberOfPoints
+	}
+
+	// transcript
+	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
+
+	// derive γ
+	gamma, err := deriveChallenge("gamma", points, digests, fs, dataTranscript...)
+	if err != nil {
+		return err
+	}
+
+	// derive z
+	// TODO seems ok that z depend only on W, need to check that carefully
+	z, err := deriveChallenge("z", nil, []kzg.Digest{proof.W}, fs)
+	if err != nil {
+		return err
+	}
+
+	// check that e(F + zW', [1]_{2})=e(W',[x]_{2})
+	// where F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}-[∑ᵢγⁱZ_{T\xᵢ}(z)fᵢ(z)]_{1}-Z_{T}(z)[W]
+	var sumGammaiZTminusSiRiz, tmp, accGamma fr.Element
+	nbInstances := len(points)
+	gammaiZTminusSiz := make([]fr.Element, nbInstances)
+	accGamma.SetOne()
+	ri := make([][]fr.Element, nbInstances)
+	for i := 0; i < len(points); i++ {
+
+		ztMinusSi := buildZtMinusSi(points, i)                   // Z_{T-S_{i}}(X)
+		gammaiZTminusSiz[i] = eval(ztMinusSi, z)                 // Z_{T-S_{i}}(z)
+		gammaiZTminusSiz[i].Mul(&accGamma, &gammaiZTminusSiz[i]) // \gamma^{i} Z_{T-S_{i}}(z)
+
+		ri[i] = interpolate(points[i], proof.ClaimedValues[i])
+		riz := eval(ri[i], z)               // r_{i}(z)
+		tmp.Mul(&gammaiZTminusSiz[i], &riz) // Z_{T-S_{i}}(z)r_{i}(z)
+		sumGammaiZTminusSiRiz.Add(&sumGammaiZTminusSiRiz, &tmp)
+
+		accGamma.Mul(&accGamma, &gamma)
+	}
+
+	// ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i}
+	config := ecc.MultiExpConfig{}
+	var sumGammaiZtMinusSiComi kzg.Digest
+	_, err = sumGammaiZtMinusSiComi.MultiExp(digests, gammaiZTminusSiz, config)
+	if err != nil {
+		return err
+	}
+
+	var bufBigInt big.Int
+
+	// [∑ᵢZ_{T\xᵢ}fᵢ(z)]_{1}
+	var sumGammaiZTminusSiRizCom kzg.Digest
+	var sumGammaiZTminusSiRizBigInt big.Int
+	sumGammaiZTminusSiRiz.BigInt(&sumGammaiZTminusSiRizBigInt)
+	sumGammaiZTminusSiRizCom.ScalarMultiplication(&vk.G1, &sumGammaiZTminusSiRizBigInt)
+
+	// Z_{T}(z)[W]
+	zt := buildVanishingPoly(flatten(points))
+	ztz := eval(zt, z)
+	var ztW kzg.Digest
+	ztz.BigInt(&bufBigInt)
+	ztW.ScalarMultiplication(&proof.W, &bufBigInt)
+
+	// F = ∑ᵢγⁱZ_{T\xᵢ}[Com]_{i} - [∑ᵢγⁱZ_{T\xᵢ}fᵢ(z)]_{1} - Z_{T}(z)[W]
+	var f kzg.Digest
+	f.Sub(&sumGammaiZtMinusSiComi, &sumGammaiZTminusSiRizCom).
+		Sub(&f, &ztW)
+
+	// F+zW'
+	var zWPrime kzg.Digest
+	z.BigInt(&bufBigInt)
+	zWPrime.ScalarMultiplication(&proof.WPrime, &bufBigInt)
+	f.Add(&f, &zWPrime)
+	f.Neg(&f)
+
+	// check that e(F+zW',[1]_{2})=e(W',[x]_{2})
+	check, err := bw6761.PairingCheckFixedQ(
+		[]bw6761.G1Affine{f, proof.WPrime},
+		vk.Lines[:],
+	)
+
+	if !check {
+		return ErrVerifyOpeningProof
+	}
+
+	return nil
+}
+
+// deriveChallenge derives a challenge using Fiat Shamir to polynomials.
+// The arguments are added to the transcript in the order in which they are given.
+func deriveChallenge(name string, points [][]fr.Element, digests []kzg.Digest, t *fiatshamir.Transcript, dataTranscript ...[]byte) (fr.Element, error) {
+
+	// derive the challenge gamma, binded to the point and the commitments
+	for i := range points {
+		for j := range points[i] {
+			if err := t.Bind(name, points[i][j].Marshal()); err != nil {
+				return fr.Element{}, err
+			}
+		}
+	}
+	for i := range digests {
+		if err := t.Bind(name, digests[i].Marshal()); err != nil {
+			return fr.Element{}, err
+		}
+	}
+
+	for i := 0; i < len(dataTranscript); i++ {
+		if err := t.Bind(name, dataTranscript[i]); err != nil {
+			return fr.Element{}, err
+		}
+	}
+
+	gammaByte, err := t.ComputeChallenge(name)
+	if err != nil {
+		return fr.Element{}, err
+	}
+	var gamma fr.Element
+	gamma.SetBytes(gammaByte)
+
+	return gamma, nil
+}
+
+// ------------------------------
+// utils
+
+func flatten(x [][]fr.Element) []fr.Element {
+	nbPoints := 0
+	for i := 0; i < len(x); i++ {
+		nbPoints += len(x[i])
+	}
+	res := make([]fr.Element, 0, nbPoints)
+	for i := 0; i < len(x); i++ {
+		res = append(res, x[i]...)
+	}
+	return res
+}
+
+// sets f to zero
+func setZero(f []fr.Element) {
+	for i := 0; i < len(f); i++ {
+		f[i].SetZero()
+	}
+}
+
+func eval(f []fr.Element, x fr.Element) fr.Element {
+	var y fr.Element
+	for i := len(f) - 1; i >= 0; i-- {
+		y.Mul(&y, &x).Add(&y, &f[i])
+	}
+	return y
+}
+
+// returns γ*f, re-using f
+func mulByConstant(f []fr.Element, gamma fr.Element) []fr.Element {
+	for i := 0; i < len(f); i++ {
+		f[i].Mul(&f[i], &gamma)
+	}
+	return f
+}
+
+// computes f <- (x-a)*f
+// memory of f is re used, need to pass a copy to not modify it
+func multiplyLinearFactor(f []fr.Element, a fr.Element) []fr.Element {
+	s := len(f)
+	var tmp fr.Element
+	f = append(f, fr.NewElement(0))
+	f[s] = f[s-1]
+	for i := s - 1; i >= 1; i-- {
+		tmp.Mul(&f[i], &a)
+		f[i].Sub(&f[i-1], &tmp)
+	}
+	f[0].Mul(&f[0], &a).Neg(&f[0])
+	return f
+}
+
+// returns S_{T\Sᵢ} where Sᵢ=x[i]
+func buildZtMinusSi(x [][]fr.Element, i int) []fr.Element {
+	nbPoints := 0
+	for i := 0; i < len(x); i++ {
+		nbPoints += len(x[i])
+	}
+	bufPoints := make([]fr.Element, 0, nbPoints-len(x[i]))
+	for j := 0; j < i; j++ {
+		bufPoints = append(bufPoints, x[j]...)
+	}
+	for j := i + 1; j < len(x); j++ {
+		bufPoints = append(bufPoints, x[j]...)
+	}
+	ztMinusSi := buildVanishingPoly(bufPoints)
+	return ztMinusSi
+}
+
+// returns πᵢ(X-xᵢ)
+func buildVanishingPoly(x []fr.Element) []fr.Element {
+	res := make([]fr.Element, 1, len(x)+1)
+	res[0].SetOne()
+	for i := 0; i < len(x); i++ {
+		res = multiplyLinearFactor(res, x[i])
+	}
+	return res
+}
+
+// returns f such that f(xᵢ)=yᵢ, x and y are assumed to be of the same size
+func interpolate(x, y []fr.Element) []fr.Element {
+
+	res := make([]fr.Element, len(x))
+	for i := 0; i < len(x); i++ {
+		li := buildLagrangeFromDomain(x, i)
+		li = mulByConstant(li, y[i])
+		for j := 0; j < len(x); j++ {
+			res[j].Add(&res[j], &li[j])
+		}
+	}
+
+	return res
+}
+
+// returns f such that f(xⱼ)=δⁱⱼ
+func buildLagrangeFromDomain(x []fr.Element, i int) []fr.Element {
+	xx := make([]fr.Element, len(x)-1)
+	copy(xx, x[:i])
+	copy(xx[i:], x[i+1:])
+	res := buildVanishingPoly(xx)
+	d := eval(res, x[i])
+	d.Inverse(&d)
+	res = mulByConstant(res, d)
+	return res
+}
+
+// returns f-g, the memory of f is re used, deg(g) << deg(f) here
+func sub(f, g []fr.Element) []fr.Element {
+	for i := 0; i < len(g); i++ {
+		f[i].Sub(&f[i], &g[i])
+	}
+	return f
+}
+
+// returns f*g using naive multiplication
+// deg(f)>>deg(g), deg(small) =~ 10 max
+// buf is used as a buffer and should not be f or g
+// f and g are not modified
+func mul(f, g []fr.Element, res []fr.Element) []fr.Element {
+
+	sizeRes := len(f) + len(g) - 1
+	if len(res) < sizeRes {
+		s := make([]fr.Element, sizeRes-len(res))
+		res = append(res, s...)
+	}
+	setZero(res)
+
+	var tmp fr.Element
+	for i := 0; i < len(g); i++ {
+		for j := 0; j < len(f); j++ {
+			tmp.Mul(&f[j], &g[i])
+			res[j+i].Add(&res[j+i], &tmp)
+		}
+	}
+	return res
+}
+
+// returns f/g (assuming g divides f)
+// OK to not use fft if deg(g) is small
+// g's leading coefficient is assumed to be 1
+// f memory is re-used for the result, need to pass a copy to not modify it
+func div(f, g []fr.Element) []fr.Element {
+	sizef := len(f)
+	sizeg := len(g)
+	stop := sizeg - +1
+	var t fr.Element
+	for i := sizef - 2; i >= stop; i-- {
+		for j := 0; j < sizeg-1; j++ {
+			t.Mul(&f[i+1], &g[sizeg-2-j])
+			f[i-j].Sub(&f[i-j], &t)
+		}
+	}
+	return f[sizeg-1:]
+}
diff --git a/ecc/bw6-761/shplonk/shplonk_test.go b/ecc/bw6-761/shplonk/shplonk_test.go
new file mode 100644
index 0000000000..e962fe6dff
--- /dev/null
+++ b/ecc/bw6-761/shplonk/shplonk_test.go
@@ -0,0 +1,320 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"crypto/sha256"
+	"math/big"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
+	"github.com/consensys/gnark-crypto/ecc/bw6-761/kzg"
+	"github.com/stretchr/testify/require"
+)
+
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *kzg.SRS
+var bAlpha *big.Int
+
+func init() {
+	const srsSize = 230
+	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+}
+
+func TestOpening(t *testing.T) {
+
+	assert := require.New(t)
+
+	nbPolys := 2
+	sizePoly := make([]int, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		sizePoly[i] = 10 + i
+	}
+	polys := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		polys[i] = make([]fr.Element, sizePoly[i])
+		for j := 0; j < sizePoly[i]; j++ {
+			polys[i][j].SetRandom()
+		}
+	}
+
+	digests := make([]kzg.Digest, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		digests[i], _ = kzg.Commit(polys[i], testSrs.Pk)
+	}
+
+	points := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		points[i] = make([]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+
+	hf := sha256.New()
+
+	// correct proof
+	openingProof, err := BatchOpen(polys, digests, points, hf, testSrs.Pk)
+	assert.NoError(err)
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	assert.NoError(err)
+
+	// tampered proof
+	openingProof.ClaimedValues[0][0].SetRandom()
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	assert.Error(err)
+
+}
+
+func TestBuildZtMinusSi(t *testing.T) {
+
+	nbSi := 10
+	points := make([][]fr.Element, nbSi)
+	sizeSi := make([]int, nbSi)
+	nbPoints := 0
+	for i := 0; i < nbSi; i++ {
+		sizeSi[i] = 5 + i
+		nbPoints += sizeSi[i]
+		points[i] = make([]fr.Element, sizeSi[i])
+		for j := 0; j < sizeSi[i]; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+	for i := 0; i < nbSi; i++ {
+		ztMinusSi := buildZtMinusSi(points, i)
+		if len(ztMinusSi) != nbPoints-sizeSi[i]+1 {
+			t.Fatal("deg(Z_{T-S_{i}}) should be nbPoints-size(S_{i})")
+		}
+		for j := 0; j < nbSi; j++ {
+			if j == i {
+				for k := 0; k < sizeSi[j]; k++ {
+					y := eval(ztMinusSi, points[j][k])
+					if y.IsZero() {
+						t.Fatal("Z_{T-S_{i}}(S_{i}) should not be zero")
+					}
+				}
+				continue
+			}
+			for k := 0; k < sizeSi[j]; k++ {
+				y := eval(ztMinusSi, points[j][k])
+				if !y.IsZero() {
+					t.Fatal("Z_{T-S_{i}}(S_{j}) should be zero")
+				}
+			}
+		}
+	}
+
+}
+
+func TestInterpolate(t *testing.T) {
+
+	nbPoints := 10
+	x := make([]fr.Element, nbPoints)
+	y := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		y[i].SetRandom()
+	}
+	f := interpolate(x, y)
+	for i := 0; i < nbPoints; i++ {
+		fx := eval(f, x[i])
+		if !fx.Equal(&y[i]) {
+			t.Fatal("f(x_{i})!=y_{i}")
+		}
+	}
+
+}
+
+func TestBuildLagrangeFromDomain(t *testing.T) {
+
+	nbPoints := 10
+	points := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		points[i].SetRandom()
+	}
+	var r fr.Element
+	for i := 0; i < nbPoints; i++ {
+
+		l := buildLagrangeFromDomain(points, i)
+
+		// check that l(xᵢ)=1 and l(xⱼ)=0 for j!=i
+		for j := 0; j < nbPoints; j++ {
+			y := eval(l, points[j])
+			if i == j {
+				if !y.IsOne() {
+					t.Fatal("l_{i}(x_{i}) should be equal to 1")
+				}
+			} else {
+				if !y.IsZero() {
+					t.Fatal("l_{i}(x_{j}) where i!=j should be equal to 0")
+				}
+			}
+		}
+		r.SetRandom()
+		y := eval(l, r)
+		if y.IsZero() {
+			t.Fatal("l_{i}(x) should not be zero if x is random")
+		}
+	}
+
+}
+
+func TestBuildVanishingPoly(t *testing.T) {
+	s := 10
+	x := make([]fr.Element, s)
+	for i := 0; i < s; i++ {
+		x[i].SetRandom()
+	}
+	r := buildVanishingPoly(x)
+
+	if len(r) != s+1 {
+		t.Fatal("error degree r")
+	}
+
+	// check that r(xᵢ)=0 for all i
+	for i := 0; i < len(x); i++ {
+		y := eval(r, x[i])
+		if !y.IsZero() {
+			t.Fatal("πᵢ(X-xᵢ) at xᵢ should be zero")
+		}
+	}
+
+	// check that r(y)!=0 for a random point
+	var a fr.Element
+	a.SetRandom()
+	y := eval(r, a)
+	if y.IsZero() {
+		t.Fatal("πᵢ(X-xᵢ) at r \neq xᵢ should not be zero")
+	}
+}
+
+func TestMultiplyLinearFactor(t *testing.T) {
+
+	s := 10
+	f := make([]fr.Element, s, s+1)
+	for i := 0; i < 10; i++ {
+		f[i].SetRandom()
+	}
+
+	var a, y fr.Element
+	a.SetRandom()
+	f = multiplyLinearFactor(f, a)
+	y = eval(f, a)
+	if !y.IsZero() {
+		t.Fatal("(X-a)f(X) should be zero at a")
+	}
+	a.SetRandom()
+	y = eval(f, a)
+	if y.IsZero() {
+		t.Fatal("(X-1)f(X) at a random point should not be zero")
+	}
+
+}
+
+func TestNaiveMul(t *testing.T) {
+
+	size := 10
+	f := make([]fr.Element, size)
+	for i := 0; i < size; i++ {
+		f[i].SetRandom()
+	}
+
+	nbPoints := 10
+	points := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		points[i].SetRandom()
+	}
+
+	v := buildVanishingPoly(points)
+	buf := make([]fr.Element, size+nbPoints-1)
+	g := mul(f, v, buf)
+
+	// check that g(xᵢ) = 0
+	for i := 0; i < nbPoints; i++ {
+		y := eval(g, points[i])
+		if !y.IsZero() {
+			t.Fatal("f(X)(X-x_{1})..(X-x_{n}) at x_{i} should be zero")
+		}
+	}
+
+	// check that g(r) != 0 for a random point
+	var a fr.Element
+	a.SetRandom()
+	y := eval(g, a)
+	if y.IsZero() {
+		t.Fatal("f(X)(X-x_{1})..(X-x_{n}) at a random point should not be zero")
+	}
+
+}
+
+func TestDiv(t *testing.T) {
+
+	nbPoints := 10
+	s := 10
+	f := make([]fr.Element, s, s+nbPoints)
+	for i := 0; i < s; i++ {
+		f[i].SetRandom()
+	}
+
+	// backup
+	g := make([]fr.Element, s)
+	copy(g, f)
+
+	// successive divions of linear terms
+	x := make([]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		f = multiplyLinearFactor(f, x[i])
+	}
+	q := make([][2]fr.Element, nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		q[i][1].SetOne()
+		q[i][0].Neg(&x[i])
+		f = div(f, q[i][:])
+	}
+
+	// g should be equal to f
+	if len(f) != len(g) {
+		t.Fatal("lengths don't match")
+	}
+	for i := 0; i < len(g); i++ {
+		if !f[i].Equal(&g[i]) {
+			t.Fatal("f(x)(x-a)/(x-a) should be equal to f(x)")
+		}
+	}
+
+	// division by a degree > 1 polynomial
+	for i := 0; i < nbPoints; i++ {
+		x[i].SetRandom()
+		f = multiplyLinearFactor(f, x[i])
+	}
+	r := buildVanishingPoly(x)
+	f = div(f, r)
+
+	// g should be equal to f
+	if len(f) != len(g) {
+		t.Fatal("lengths don't match")
+	}
+	for i := 0; i < len(g); i++ {
+		if !f[i].Equal(&g[i]) {
+			t.Fatal("f(x)(x-a)/(x-a) should be equal to f(x)")
+		}
+	}
+
+}

From 18554885c18beba07c660d23447dae2bc9b1ba19 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Thu, 14 Mar 2024 11:54:58 +0100
Subject: [PATCH 021/114] fix: added condition for existence of t-th roots

---
 ecc/bn254/fflonk/fflonk.go | 71 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 71 insertions(+)
 create mode 100644 ecc/bn254/fflonk/fflonk.go

diff --git a/ecc/bn254/fflonk/fflonk.go b/ecc/bn254/fflonk/fflonk.go
new file mode 100644
index 0000000000..ca44cb8b41
--- /dev/null
+++ b/ecc/bn254/fflonk/fflonk.go
@@ -0,0 +1,71 @@
+package fflonk
+
+import (
+	"errors"
+	"math/big"
+
+	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
+)
+
+var (
+	ErrRootsOne = errors.New("Fr does not contain all the t-th roots of 1")
+	ErrRootsX   = errors.New("Fr does not contain all the t-th roots of the input")
+)
+
+// utils
+
+// getGenFrStar returns a generator of Fr^{*}
+func getGenFrStar() fr.Element {
+	var res fr.Element
+	res.SetUint64(5)
+	return res
+}
+
+// returns the t t-th roots of x, return an error if they do not exist in Fr
+func extractRoots(x fr.Element, t int) ([]fr.Element, error) {
+
+	// for the t-th roots of x to exist we need
+	// * t | r-1
+	// * t² | p - (t-1)
+	r := fr.Modulus()
+	tBigInt := big.NewInt(int64(t))
+	oneBigInt := big.NewInt(1)
+	var a, b big.Int
+	a.Sub(r, oneBigInt)
+	a.Mod(&a, tBigInt)
+	zeroBigInt := big.NewInt(0)
+	if a.Cmp(zeroBigInt) != 0 {
+		return nil, ErrRootsOne
+	}
+	a.SetUint64(uint64(t)).Mul(tBigInt, tBigInt)
+	b.Sub(r, tBigInt).Add(&b, oneBigInt)
+	a.Mod(&b, &a)
+	if b.Cmp(zeroBigInt) != 0 {
+		return nil, ErrRootsX
+	}
+
+	// ᵗ√(x) = x^{(p-1)/t + 1}
+	var expo big.Int
+	var tthRoot fr.Element
+	r = fr.Modulus()
+	tBigInt = big.NewInt(int64(t))
+	expo.Sub(r, oneBigInt).
+		Div(&expo, tBigInt).
+		Add(&expo, oneBigInt)
+	tthRoot.Exp(x, &expo)
+
+	// compute the t-th roots of 1
+	r.Sub(r, oneBigInt)
+	tBigInt.Div(r, tBigInt)
+	gen := getGenFrStar()
+	gen.Exp(gen, tBigInt)
+
+	res := make([]fr.Element, t)
+	res[0].Set(&tthRoot)
+	for i := 1; i < t; i++ {
+		res[i].Mul(&res[i-1], &gen)
+	}
+
+	return res, nil
+
+}

From 77f4a854078396b438f8c17295fc3472ef11f2a2 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Thu, 14 Mar 2024 11:55:19 +0100
Subject: [PATCH 022/114] feat: test roots extraction

---
 ecc/bn254/fflonk/fflonk_test.go | 36 +++++++++++++++++++++++++++++++++
 1 file changed, 36 insertions(+)
 create mode 100644 ecc/bn254/fflonk/fflonk_test.go

diff --git a/ecc/bn254/fflonk/fflonk_test.go b/ecc/bn254/fflonk/fflonk_test.go
new file mode 100644
index 0000000000..f345c2a04b
--- /dev/null
+++ b/ecc/bn254/fflonk/fflonk_test.go
@@ -0,0 +1,36 @@
+package fflonk
+
+import (
+	"math/big"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
+	"github.com/stretchr/testify/require"
+)
+
+func TestExtractRoots(t *testing.T) {
+
+	assert := require.New(t)
+
+	m := 9
+	var x fr.Element
+	x.SetRandom()
+	roots, err := extractRoots(x, m)
+	assert.NoError(err)
+
+	// check that (yᵐ-x)=Πᵢ(y-ωⁱᵗ√(x)) for a random y
+	var y fr.Element
+	y.SetRandom()
+	expo := big.NewInt(int64(m))
+	y.Exp(x, expo).Sub(&y, &x)
+	var rhs, tmp fr.Element
+	rhs.SetOne()
+	for i := 0; i < m; i++ {
+		tmp.Sub(&y, &roots[i])
+		rhs.Mul(&rhs, &tmp)
+	}
+	if !rhs.Equal(&y) {
+		assert.Fail("(yᵐ-x) != Πᵢ(y-ωⁱᵗ√(x)))")
+	}
+
+}

From 70781a5668524eb004282e70a308333a7debbe35 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Thu, 14 Mar 2024 18:48:22 +0100
Subject: [PATCH 023/114] feat: folding ok

---
 ecc/bn254/fflonk/fflonk.go      | 117 +++++++++++++++++++++-----------
 ecc/bn254/fflonk/fflonk_test.go |  52 +++++++++-----
 2 files changed, 111 insertions(+), 58 deletions(-)

diff --git a/ecc/bn254/fflonk/fflonk.go b/ecc/bn254/fflonk/fflonk.go
index ca44cb8b41..b3aadcb1b8 100644
--- a/ecc/bn254/fflonk/fflonk.go
+++ b/ecc/bn254/fflonk/fflonk.go
@@ -2,9 +2,9 @@ package fflonk
 
 import (
 	"errors"
-	"math/big"
 
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
+	"github.com/consensys/gnark-crypto/ecc/bn254/kzg"
 )
 
 var (
@@ -21,51 +21,86 @@ func getGenFrStar() fr.Element {
 	return res
 }
 
-// returns the t t-th roots of x, return an error if they do not exist in Fr
-func extractRoots(x fr.Element, t int) ([]fr.Element, error) {
+// Commit commits to a list of polynomial by intertwinning them like in the FFT, that is
+// returns ∑_{i<t}Pᵢ(Xᵗ)Xⁱ for t polynomials
+func Commit(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
+	buf := Fold(p)
+	com, err := kzg.Commit(buf, pk, nbTasks...)
+	return com, err
+}
 
-	// for the t-th roots of x to exist we need
-	// * t | r-1
-	// * t² | p - (t-1)
-	r := fr.Modulus()
-	tBigInt := big.NewInt(int64(t))
-	oneBigInt := big.NewInt(1)
-	var a, b big.Int
-	a.Sub(r, oneBigInt)
-	a.Mod(&a, tBigInt)
-	zeroBigInt := big.NewInt(0)
-	if a.Cmp(zeroBigInt) != 0 {
-		return nil, ErrRootsOne
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ
+func Fold(p [][]fr.Element) []fr.Element {
+	t := len(p)
+	sizeResult := 0
+	for i := range p {
+		if sizeResult < len(p[i]) {
+			sizeResult = len(p[i])
+		}
 	}
-	a.SetUint64(uint64(t)).Mul(tBigInt, tBigInt)
-	b.Sub(r, tBigInt).Add(&b, oneBigInt)
-	a.Mod(&b, &a)
-	if b.Cmp(zeroBigInt) != 0 {
-		return nil, ErrRootsX
+	sizeResult = sizeResult*len(p) + len(p) - 1
+	buf := make([]fr.Element, sizeResult)
+	for i := range p {
+		for j := range p[i] {
+			buf[j*t+i].Set(&p[i][j])
+		}
 	}
+	return buf
+}
 
-	// ᵗ√(x) = x^{(p-1)/t + 1}
-	var expo big.Int
-	var tthRoot fr.Element
-	r = fr.Modulus()
-	tBigInt = big.NewInt(int64(t))
-	expo.Sub(r, oneBigInt).
-		Div(&expo, tBigInt).
-		Add(&expo, oneBigInt)
-	tthRoot.Exp(x, &expo)
+func eval(f []fr.Element, x fr.Element) fr.Element {
+	var y fr.Element
+	for i := len(f) - 1; i >= 0; i-- {
+		y.Mul(&y, &x).Add(&y, &f[i])
+	}
+	return y
+}
 
-	// compute the t-th roots of 1
-	r.Sub(r, oneBigInt)
-	tBigInt.Div(r, tBigInt)
-	gen := getGenFrStar()
-	gen.Exp(gen, tBigInt)
+// returns the t t-th roots of x, return an error if they do not exist in Fr
+// func extractRoots(x fr.Element, t int) ([]fr.Element, error) {
 
-	res := make([]fr.Element, t)
-	res[0].Set(&tthRoot)
-	for i := 1; i < t; i++ {
-		res[i].Mul(&res[i-1], &gen)
-	}
+// 	// for the t-th roots of x to exist we need
+// 	// * t | r-1
+// 	// * t² | p - (t-1)
+// 	r := fr.Modulus()
+// 	tBigInt := big.NewInt(int64(t))
+// 	oneBigInt := big.NewInt(1)
+// 	var a, b big.Int
+// 	a.Sub(r, oneBigInt)
+// 	a.Mod(&a, tBigInt)
+// 	zeroBigInt := big.NewInt(0)
+// 	if a.Cmp(zeroBigInt) != 0 {
+// 		return nil, ErrRootsOne
+// 	}
+// 	a.SetUint64(uint64(t)).Mul(tBigInt, tBigInt)
+// 	b.Sub(r, tBigInt).Add(&b, oneBigInt)
+// 	a.Mod(&b, &a)
+// 	if b.Cmp(zeroBigInt) != 0 {
+// 		return nil, ErrRootsX
+// 	}
 
-	return res, nil
+// 	// ᵗ√(x) = x^{(p-1)/t + 1}
+// 	var expo big.Int
+// 	var tthRoot fr.Element
+// 	r = fr.Modulus()
+// 	tBigInt = big.NewInt(int64(t))
+// 	expo.Sub(r, oneBigInt).
+// 		Div(&expo, tBigInt).
+// 		Add(&expo, oneBigInt)
+// 	tthRoot.Exp(x, &expo)
 
-}
+// 	// compute the t-th roots of 1
+// 	r.Sub(r, oneBigInt)
+// 	tBigInt.Div(r, tBigInt)
+// 	gen := getGenFrStar()
+// 	gen.Exp(gen, tBigInt)
+
+// 	res := make([]fr.Element, t)
+// 	res[0].Set(&tthRoot)
+// 	for i := 1; i < t; i++ {
+// 		res[i].Mul(&res[i-1], &gen)
+// 	}
+
+// 	return res, nil
+
+// }
diff --git a/ecc/bn254/fflonk/fflonk_test.go b/ecc/bn254/fflonk/fflonk_test.go
index f345c2a04b..75370984f1 100644
--- a/ecc/bn254/fflonk/fflonk_test.go
+++ b/ecc/bn254/fflonk/fflonk_test.go
@@ -4,33 +4,51 @@ import (
 	"math/big"
 	"testing"
 
+	"github.com/consensys/gnark-crypto/ecc"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
+	"github.com/consensys/gnark-crypto/ecc/bn254/kzg"
 	"github.com/stretchr/testify/require"
 )
 
-func TestExtractRoots(t *testing.T) {
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *kzg.SRS
+var bAlpha *big.Int
+
+func init() {
+	const srsSize = 230
+	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+}
+
+func TestCommit(t *testing.T) {
 
 	assert := require.New(t)
 
-	m := 9
+	// sample polynomials
+	nbPolys := 2
+	p := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		p[i] = make([]fr.Element, i+10)
+		for j := 0; j < i+10; j++ {
+			p[i][j].SetRandom()
+		}
+	}
+
+	// fflonk commit to them
 	var x fr.Element
 	x.SetRandom()
-	roots, err := extractRoots(x, m)
+	proof, err := kzg.Open(Fold(p), x, testSrs.Pk)
 	assert.NoError(err)
 
-	// check that (yᵐ-x)=Πᵢ(y-ωⁱᵗ√(x)) for a random y
-	var y fr.Element
-	y.SetRandom()
-	expo := big.NewInt(int64(m))
-	y.Exp(x, expo).Sub(&y, &x)
-	var rhs, tmp fr.Element
-	rhs.SetOne()
-	for i := 0; i < m; i++ {
-		tmp.Sub(&y, &roots[i])
-		rhs.Mul(&rhs, &tmp)
-	}
-	if !rhs.Equal(&y) {
-		assert.Fail("(yᵐ-x) != Πᵢ(y-ωⁱᵗ√(x)))")
+	// check that Open(C, x) = ∑_{i<t}Pᵢ(xᵗ)xⁱ
+	var xt fr.Element
+	var expo big.Int
+	expo.SetUint64(uint64(nbPolys))
+	xt.Exp(x, &expo)
+	px := make([]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		px[i] = eval(p[i], xt)
 	}
-
+	y := eval(px, x)
+	assert.True(y.Equal(&proof.ClaimedValue))
 }

From 19ecdf8fa4821165a4d4bcc210a8747aa4852548 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 15 Mar 2024 16:36:25 +0100
Subject: [PATCH 024/114] feat: fflonk fold and open

---
 ecc/bn254/fflonk/fflonk.go | 126 ++++++++++++++++++++++++++++++++++---
 1 file changed, 116 insertions(+), 10 deletions(-)

diff --git a/ecc/bn254/fflonk/fflonk.go b/ecc/bn254/fflonk/fflonk.go
index b3aadcb1b8..3878fc51d0 100644
--- a/ecc/bn254/fflonk/fflonk.go
+++ b/ecc/bn254/fflonk/fflonk.go
@@ -2,28 +2,37 @@ package fflonk
 
 import (
 	"errors"
+	"hash"
+	"math/big"
 
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
 	"github.com/consensys/gnark-crypto/ecc/bn254/kzg"
+	"github.com/consensys/gnark-crypto/ecc/bn254/shplonk"
 )
 
 var (
-	ErrRootsOne = errors.New("Fr does not contain all the t-th roots of 1")
-	ErrRootsX   = errors.New("Fr does not contain all the t-th roots of the input")
+	ErrRootsOne              = errors.New("Fr does not contain all the t-th roots of 1")
+	ErrNbPolynomialsNbPoints = errors.New("the number of packs of polynomials should be the same as the number of pack of points")
 )
 
-// utils
+// Opening fflonk proof for opening a list of list of polynomials ((fʲᵢ)ᵢ)ⱼ where each
+// pack of polynomials (fʲᵢ)ᵢ (the pack is indexed by j) is opened on a powers of elements in
+// the set (Sʲᵢ)ᵢ (indexed by j), where the power is |(fʲᵢ)ᵢ|.
+//
+// implements io.ReaderFrom and io.WriterTo
+type OpeningProof struct {
 
-// getGenFrStar returns a generator of Fr^{*}
-func getGenFrStar() fr.Element {
-	var res fr.Element
-	res.SetUint64(5)
-	return res
+	// shplonk opening proof of the folded polynomials
+	SOpeningProof shplonk.OpeningProof
+
+	// ClaimedValues ClaimedValues[i][j] contains the values
+	// of fʲᵢ on Sⱼ^{|(fʲᵢ)ᵢ|}
+	ClaimedValues [][][]fr.Element
 }
 
-// Commit commits to a list of polynomial by intertwinning them like in the FFT, that is
+// CommitAndFold commits to a list of polynomial by intertwinning them like in the FFT, that is
 // returns ∑_{i<t}Pᵢ(Xᵗ)Xⁱ for t polynomials
-func Commit(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
+func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
 	buf := Fold(p)
 	com, err := kzg.Commit(buf, pk, nbTasks...)
 	return com, err
@@ -48,6 +57,98 @@ func Fold(p [][]fr.Element) []fr.Element {
 	return buf
 }
 
+// BatchOpen computes a batch opening proof of p (the (fʲᵢ)ᵢ ) on powers of points (the ((Sʲᵢ)ᵢ)ⱼ).
+// The j-th pack of polynomials is opened on the power |(fʲᵢ)ᵢ| of (Sʲᵢ)ᵢ.
+// digests is the list (CommitAndFold(p[i]))ᵢ. It is assumed that the list has been computed beforehand
+// and provided as an input to not duplicate computations.
+func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
+
+	var res OpeningProof
+
+	if len(p) != len(points) {
+		return res, ErrNbPolynomialsNbPoints
+	}
+
+	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
+	nbPolysPerPack := make([]int, len(p))
+	for i := 0; i < len(p); i++ {
+		nbPolysPerPack[i] = len(p[i])
+	}
+	pointsPowerM := make([][]fr.Element, len(points))
+	var tmpBigInt big.Int
+	for i := 0; i < len(p); i++ {
+		tmpBigInt.SetUint64(uint64(nbPolysPerPack[i]))
+		pointsPowerM[i] = make([]fr.Element, len(points[i]))
+		for j := 0; j < len(points[i]); j++ {
+			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
+		}
+	}
+
+	// step 1: compute the claimed values, that is the evaluations of the polynomials
+	// on the relevant powers of the sets
+	res.ClaimedValues = make([][][]fr.Element, len(p))
+	for i := 0; i < len(p); i++ {
+		res.ClaimedValues[i] = make([][]fr.Element, len(p[i]))
+		for j := 0; j < len(points[i]); j++ {
+			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
+			for k := 0; k < len(points[i]); k++ {
+				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
+			}
+		}
+	}
+
+	// step 2: fold polynomials
+	foldedPolynomials := make([][]fr.Element, len(p))
+	for i := 0; i < len(p); i++ {
+		foldedPolynomials[i] = Fold(p[i])
+	}
+
+	// step 4: compute the associated roots, that is for each point p corresponding
+	// to a pack i of polynomials, we extend to <p, ω p, .., ωᵗ⁻¹p> if
+	// the i-th pack contains t polynomials where ω is a t-th root of 1
+	var omega fr.Element
+	zeroBigInt := big.NewInt(0)
+	genFrStar := getGenFrStar()
+	rMinusOneBigInt := fr.Modulus()
+	oneBigInt := big.NewInt(1)
+	rMinusOneBigInt.Sub(rMinusOneBigInt, oneBigInt)
+	newPoints := make([][]fr.Element, len(points))
+	for i := 0; i < len(p); i++ {
+		tmpBigInt.SetUint64(uint64(len(p[i])))
+		tmpBigInt.Mod(rMinusOneBigInt, &tmpBigInt)
+		if tmpBigInt.Cmp(zeroBigInt) != 0 {
+			return res, ErrRootsOne
+		}
+		tmpBigInt.SetUint64(uint64(len(p[i])))
+		tmpBigInt.Div(rMinusOneBigInt, &tmpBigInt)
+		omega.Exp(genFrStar, &tmpBigInt)
+		t := len(p[i])
+		newPoints[i] = make([]fr.Element, t*len(points[i]))
+		for j := 0; j < len(points[i]); j++ {
+			newPoints[i][j*t].Set(&points[i][j])
+			for k := 1; k < t; k++ {
+				newPoints[i][j*t+k].Mul(&newPoints[i][j*t+k-1], &omega)
+			}
+		}
+	}
+
+	// step 5: shplonk open the list of single polynomials on the new sets
+	var err error
+	res.SOpeningProof, err = shplonk.BatchOpen(foldedPolynomials, digests, points, hf, pk, dataTranscript...)
+
+	return res, err
+
+}
+
+// utils
+
+// getGenFrStar returns a generator of Fr^{*}
+func getGenFrStar() fr.Element {
+	var res fr.Element
+	res.SetUint64(5)
+	return res
+}
+
 func eval(f []fr.Element, x fr.Element) fr.Element {
 	var y fr.Element
 	for i := len(f) - 1; i >= 0; i-- {
@@ -56,6 +157,11 @@ func eval(f []fr.Element, x fr.Element) fr.Element {
 	return y
 }
 
+// Open
+// func Open(polynomials [][]fr.Element, digests []kzg.Digest, points []fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (shplonk.OpeningProof, error) {
+
+// }
+
 // returns the t t-th roots of x, return an error if they do not exist in Fr
 // func extractRoots(x fr.Element, t int) ([]fr.Element, error) {
 

From 5bf6194cf9b4e025f89b5c7534772b6f77758a27 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 15 Mar 2024 17:44:03 +0100
Subject: [PATCH 025/114] feat: getIthRootOne ok

---
 ecc/bn254/fflonk/fflonk.go      | 28 ++++++++++++++++++++++++++++
 ecc/bn254/fflonk/fflonk_test.go | 17 +++++++++++++++++
 2 files changed, 45 insertions(+)

diff --git a/ecc/bn254/fflonk/fflonk.go b/ecc/bn254/fflonk/fflonk.go
index 3878fc51d0..aa4789a425 100644
--- a/ecc/bn254/fflonk/fflonk.go
+++ b/ecc/bn254/fflonk/fflonk.go
@@ -140,6 +140,14 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 
 }
 
+// BatchVerify uses a proof to check that each digest digests[i] is correctly opened on the set points[i].
+// The digests are the commitments to the folded underlying polynomials. The shplonk proof is
+// verified directly using the embedded shplonk proof, and the claimed values consistency between the underlying
+// shplonk proof
+func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
+	return nil
+}
+
 // utils
 
 // getGenFrStar returns a generator of Fr^{*}
@@ -149,6 +157,26 @@ func getGenFrStar() fr.Element {
 	return res
 }
 
+// getIthRootOne returns a generator of Z/iZ
+func getIthRootOne(i int) (fr.Element, error) {
+	var omega fr.Element
+	var tmpBigInt, zeroBigInt big.Int
+	oneBigInt := big.NewInt(1)
+	zeroBigInt.SetUint64(0)
+	rMinusOneBigInt := fr.Modulus()
+	rMinusOneBigInt.Sub(rMinusOneBigInt, oneBigInt)
+	tmpBigInt.SetUint64(uint64(i))
+	tmpBigInt.Mod(rMinusOneBigInt, &tmpBigInt)
+	if tmpBigInt.Cmp(&zeroBigInt) != 0 {
+		return omega, ErrRootsOne
+	}
+	genFrStar := getGenFrStar()
+	tmpBigInt.SetUint64(uint64(i))
+	tmpBigInt.Div(rMinusOneBigInt, &tmpBigInt)
+	omega.Exp(genFrStar, &tmpBigInt)
+	return omega, nil
+}
+
 func eval(f []fr.Element, x fr.Element) fr.Element {
 	var y fr.Element
 	for i := len(f) - 1; i >= 0; i-- {
diff --git a/ecc/bn254/fflonk/fflonk_test.go b/ecc/bn254/fflonk/fflonk_test.go
index 75370984f1..29a2b28587 100644
--- a/ecc/bn254/fflonk/fflonk_test.go
+++ b/ecc/bn254/fflonk/fflonk_test.go
@@ -52,3 +52,20 @@ func TestCommit(t *testing.T) {
 	y := eval(px, x)
 	assert.True(y.Equal(&proof.ClaimedValue))
 }
+
+func TestGetIthRootOne(t *testing.T) {
+
+	assert := require.New(t)
+
+	order := 9
+	omega, err := getIthRootOne(order)
+	assert.NoError(err)
+	var orderBigInt big.Int
+	orderBigInt.SetUint64(uint64(order))
+	omega.Exp(omega, &orderBigInt)
+	assert.True(omega.IsOne())
+
+	order = 7
+	_, err = getIthRootOne(order)
+	assert.Error(err)
+}

From 69b626124528cc498572525188c3f5f98637de90 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Mon, 18 Mar 2024 13:12:13 +0100
Subject: [PATCH 026/114] feat: factored extended set

---
 ecc/bn254/fflonk/fflonk.go | 171 +++++++++++++++++++------------------
 1 file changed, 90 insertions(+), 81 deletions(-)

diff --git a/ecc/bn254/fflonk/fflonk.go b/ecc/bn254/fflonk/fflonk.go
index aa4789a425..34f6b300a9 100644
--- a/ecc/bn254/fflonk/fflonk.go
+++ b/ecc/bn254/fflonk/fflonk.go
@@ -11,13 +11,15 @@ import (
 )
 
 var (
-	ErrRootsOne              = errors.New("Fr does not contain all the t-th roots of 1")
-	ErrNbPolynomialsNbPoints = errors.New("the number of packs of polynomials should be the same as the number of pack of points")
+	ErrRootsOne                       = errors.New("Fr does not contain all the t-th roots of 1")
+	ErrNbPolynomialsNbPoints          = errors.New("the number of packs of polynomials should be the same as the number of pack of points")
+	ErrInonsistentFolding             = errors.New("the outer claimed values are not consistent with the shplonk proof")
+	ErrInconsistentNumberFoldedPoints = errors.New("the number of outer claimed values is inconsistent with the number of claimed values in the shplonk proof")
 )
 
 // Opening fflonk proof for opening a list of list of polynomials ((fʲᵢ)ᵢ)ⱼ where each
 // pack of polynomials (fʲᵢ)ᵢ (the pack is indexed by j) is opened on a powers of elements in
-// the set (Sʲᵢ)ᵢ (indexed by j), where the power is |(fʲᵢ)ᵢ|.
+// the set Sʲ (indexed by j), where the power is |(fʲᵢ)ᵢ|.
 //
 // implements io.ReaderFrom and io.WriterTo
 type OpeningProof struct {
@@ -89,7 +91,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	res.ClaimedValues = make([][][]fr.Element, len(p))
 	for i := 0; i < len(p); i++ {
 		res.ClaimedValues[i] = make([][]fr.Element, len(p[i]))
-		for j := 0; j < len(points[i]); j++ {
+		for j := 0; j < len(p[i]); j++ {
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 			for k := 0; k < len(points[i]); k++ {
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
@@ -106,34 +108,17 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	// step 4: compute the associated roots, that is for each point p corresponding
 	// to a pack i of polynomials, we extend to <p, ω p, .., ωᵗ⁻¹p> if
 	// the i-th pack contains t polynomials where ω is a t-th root of 1
-	var omega fr.Element
-	zeroBigInt := big.NewInt(0)
-	genFrStar := getGenFrStar()
-	rMinusOneBigInt := fr.Modulus()
-	oneBigInt := big.NewInt(1)
-	rMinusOneBigInt.Sub(rMinusOneBigInt, oneBigInt)
 	newPoints := make([][]fr.Element, len(points))
+	var err error
 	for i := 0; i < len(p); i++ {
-		tmpBigInt.SetUint64(uint64(len(p[i])))
-		tmpBigInt.Mod(rMinusOneBigInt, &tmpBigInt)
-		if tmpBigInt.Cmp(zeroBigInt) != 0 {
-			return res, ErrRootsOne
-		}
-		tmpBigInt.SetUint64(uint64(len(p[i])))
-		tmpBigInt.Div(rMinusOneBigInt, &tmpBigInt)
-		omega.Exp(genFrStar, &tmpBigInt)
 		t := len(p[i])
-		newPoints[i] = make([]fr.Element, t*len(points[i]))
-		for j := 0; j < len(points[i]); j++ {
-			newPoints[i][j*t].Set(&points[i][j])
-			for k := 1; k < t; k++ {
-				newPoints[i][j*t+k].Mul(&newPoints[i][j*t+k-1], &omega)
-			}
+		newPoints[i], err = extendSet(points[i], t)
+		if err != nil {
+			return res, err
 		}
 	}
 
 	// step 5: shplonk open the list of single polynomials on the new sets
-	var err error
 	res.SOpeningProof, err = shplonk.BatchOpen(foldedPolynomials, digests, points, hf, pk, dataTranscript...)
 
 	return res, err
@@ -142,9 +127,68 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 
 // BatchVerify uses a proof to check that each digest digests[i] is correctly opened on the set points[i].
 // The digests are the commitments to the folded underlying polynomials. The shplonk proof is
-// verified directly using the embedded shplonk proof, and the claimed values consistency between the underlying
-// shplonk proof
+// verified directly using the embedded shplonk proof. This function only computes the consistency
+// between the claimed values of the underlying shplonk proof and the outer claimed values, using the fft-like
+// folding. Namely, the outer claimed values are the evaluation of the original polynomials (so before they
+// were folded) at the relevant powers of the points.
 func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
+
+	// step 0: consistency checks between the folded claimed values of shplonk and the claimed
+	// values at the powers of the Sᵢ
+	for i := 0; i < len(proof.ClaimedValues); i++ {
+		sizeSi := len(proof.ClaimedValues[i][0])
+		for j := 1; j < len(proof.ClaimedValues[i]); j++ {
+			// each set of opening must be of the same size (opeings on powers of Si)
+			if sizeSi != len(proof.ClaimedValues[i][j]) {
+				return ErrNbPolynomialsNbPoints
+			}
+		}
+		currNbPolynomials := len(proof.ClaimedValues[i])
+		sizeSi = sizeSi * currNbPolynomials
+		// |originalPolynomials_{i}|x|Sᵢ| == |foldedPolynomials|x|folded Sᵢ|
+		if sizeSi != len(proof.SOpeningProof.ClaimedValues[i]) {
+			return ErrInconsistentNumberFoldedPoints
+		}
+	}
+
+	// step 1: fold the outer claimed values and check that they correspond to the
+	// shplonk claimed values
+	var curFoldedClaimedValue, accOmega fr.Element
+	for i := 0; i < len(proof.ClaimedValues); i++ {
+		t := len(proof.ClaimedValues[i])
+		omega, err := getIthRootOne(t)
+		if err != nil {
+			return err
+		}
+		sizeSi := len(proof.ClaimedValues[i][0])
+		polyClaimedValues := make([]fr.Element, t)
+		accOmega.SetOne()
+		for j := 0; j < sizeSi; j++ {
+			for k := 0; k < t; k++ {
+				polyClaimedValues[k].Set(&proof.ClaimedValues[i][k][j])
+			}
+			for l := 0; l < t; l++ {
+				curFoldedClaimedValue = eval(polyClaimedValues, accOmega)
+				if !curFoldedClaimedValue.Equal(&proof.SOpeningProof.ClaimedValues[i][j*t+l]) {
+					return ErrInonsistentFolding
+				}
+				accOmega.Mul(&accOmega, &omega)
+			}
+		}
+	}
+
+	// step 2: verify the embedded shplonk proof
+	extendedPoints := make([][]fr.Element, len(points))
+	var err error
+	for i := 0; i < len(points); i++ {
+		t := len(proof.ClaimedValues[i])
+		extendedPoints[i], err = extendSet(points[i], t)
+		if err != nil {
+			return err
+		}
+	}
+	err = shplonk.BatchVerify(proof.SOpeningProof, digests, extendedPoints, hf, vk, dataTranscript...)
+
 	return nil
 }
 
@@ -177,6 +221,25 @@ func getIthRootOne(i int) (fr.Element, error) {
 	return omega, nil
 }
 
+// extendSet returns [p[0], ω p[0], .. ,ωᵗ⁻¹p[0],p[1],..,ωᵗ⁻¹p[1],..]
+func extendSet(p []fr.Element, t int) ([]fr.Element, error) {
+
+	omega, err := getIthRootOne(t)
+	if err != nil {
+		return nil, err
+	}
+	nbPoints := len(p)
+	newPoints := make([]fr.Element, t*nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		newPoints[i*t].Set(&p[i])
+		for k := 1; k < t; k++ {
+			newPoints[i*t+k].Mul(&newPoints[i*t+k-1], &omega)
+		}
+	}
+
+	return newPoints, nil
+}
+
 func eval(f []fr.Element, x fr.Element) fr.Element {
 	var y fr.Element
 	for i := len(f) - 1; i >= 0; i-- {
@@ -184,57 +247,3 @@ func eval(f []fr.Element, x fr.Element) fr.Element {
 	}
 	return y
 }
-
-// Open
-// func Open(polynomials [][]fr.Element, digests []kzg.Digest, points []fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (shplonk.OpeningProof, error) {
-
-// }
-
-// returns the t t-th roots of x, return an error if they do not exist in Fr
-// func extractRoots(x fr.Element, t int) ([]fr.Element, error) {
-
-// 	// for the t-th roots of x to exist we need
-// 	// * t | r-1
-// 	// * t² | p - (t-1)
-// 	r := fr.Modulus()
-// 	tBigInt := big.NewInt(int64(t))
-// 	oneBigInt := big.NewInt(1)
-// 	var a, b big.Int
-// 	a.Sub(r, oneBigInt)
-// 	a.Mod(&a, tBigInt)
-// 	zeroBigInt := big.NewInt(0)
-// 	if a.Cmp(zeroBigInt) != 0 {
-// 		return nil, ErrRootsOne
-// 	}
-// 	a.SetUint64(uint64(t)).Mul(tBigInt, tBigInt)
-// 	b.Sub(r, tBigInt).Add(&b, oneBigInt)
-// 	a.Mod(&b, &a)
-// 	if b.Cmp(zeroBigInt) != 0 {
-// 		return nil, ErrRootsX
-// 	}
-
-// 	// ᵗ√(x) = x^{(p-1)/t + 1}
-// 	var expo big.Int
-// 	var tthRoot fr.Element
-// 	r = fr.Modulus()
-// 	tBigInt = big.NewInt(int64(t))
-// 	expo.Sub(r, oneBigInt).
-// 		Div(&expo, tBigInt).
-// 		Add(&expo, oneBigInt)
-// 	tthRoot.Exp(x, &expo)
-
-// 	// compute the t-th roots of 1
-// 	r.Sub(r, oneBigInt)
-// 	tBigInt.Div(r, tBigInt)
-// 	gen := getGenFrStar()
-// 	gen.Exp(gen, tBigInt)
-
-// 	res := make([]fr.Element, t)
-// 	res[0].Set(&tthRoot)
-// 	for i := 1; i < t; i++ {
-// 		res[i].Mul(&res[i-1], &gen)
-// 	}
-
-// 	return res, nil
-
-// }

From 0b73a022467034e7eb8e6418ecf17270edb13284 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Mon, 18 Mar 2024 18:25:11 +0100
Subject: [PATCH 027/114] feat: fixed fflonk folding

---
 ecc/bn254/fflonk/fflonk.go      | 10 +++---
 ecc/bn254/fflonk/fflonk_test.go | 56 ++++++++++++++++++++++++++++++++-
 2 files changed, 60 insertions(+), 6 deletions(-)

diff --git a/ecc/bn254/fflonk/fflonk.go b/ecc/bn254/fflonk/fflonk.go
index 34f6b300a9..3f8533e51b 100644
--- a/ecc/bn254/fflonk/fflonk.go
+++ b/ecc/bn254/fflonk/fflonk.go
@@ -119,7 +119,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	}
 
 	// step 5: shplonk open the list of single polynomials on the new sets
-	res.SOpeningProof, err = shplonk.BatchOpen(foldedPolynomials, digests, points, hf, pk, dataTranscript...)
+	res.SOpeningProof, err = shplonk.BatchOpen(foldedPolynomials, digests, newPoints, hf, pk, dataTranscript...)
 
 	return res, err
 
@@ -153,7 +153,7 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 
 	// step 1: fold the outer claimed values and check that they correspond to the
 	// shplonk claimed values
-	var curFoldedClaimedValue, accOmega fr.Element
+	var curFoldedClaimedValue, omgeaiPoint fr.Element
 	for i := 0; i < len(proof.ClaimedValues); i++ {
 		t := len(proof.ClaimedValues[i])
 		omega, err := getIthRootOne(t)
@@ -162,17 +162,17 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 		}
 		sizeSi := len(proof.ClaimedValues[i][0])
 		polyClaimedValues := make([]fr.Element, t)
-		accOmega.SetOne()
 		for j := 0; j < sizeSi; j++ {
 			for k := 0; k < t; k++ {
 				polyClaimedValues[k].Set(&proof.ClaimedValues[i][k][j])
 			}
+			omgeaiPoint.Set(&points[i][j])
 			for l := 0; l < t; l++ {
-				curFoldedClaimedValue = eval(polyClaimedValues, accOmega)
+				curFoldedClaimedValue = eval(polyClaimedValues, omgeaiPoint)
 				if !curFoldedClaimedValue.Equal(&proof.SOpeningProof.ClaimedValues[i][j*t+l]) {
 					return ErrInonsistentFolding
 				}
-				accOmega.Mul(&accOmega, &omega)
+				omgeaiPoint.Mul(&omgeaiPoint, &omega)
 			}
 		}
 	}
diff --git a/ecc/bn254/fflonk/fflonk_test.go b/ecc/bn254/fflonk/fflonk_test.go
index 29a2b28587..e5409a602a 100644
--- a/ecc/bn254/fflonk/fflonk_test.go
+++ b/ecc/bn254/fflonk/fflonk_test.go
@@ -1,6 +1,7 @@
 package fflonk
 
 import (
+	"crypto/sha256"
 	"math/big"
 	"testing"
 
@@ -15,11 +16,64 @@ var testSrs *kzg.SRS
 var bAlpha *big.Int
 
 func init() {
-	const srsSize = 230
+	const srsSize = 400
 	bAlpha = new(big.Int).SetInt64(42) // randomise ?
 	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
 }
 
+func TestFflonk(t *testing.T) {
+
+	assert := require.New(t)
+
+	// sample random polynomials of various sizes
+	nbSets := 5
+	p := make([][][]fr.Element, nbSets)
+	for i := 0; i < nbSets; i++ {
+		nbPolysInSet := 9
+		p[i] = make([][]fr.Element, nbPolysInSet)
+		for j := 0; j < nbPolysInSet; j++ {
+			curSizePoly := j + 10
+			p[i][j] = make([]fr.Element, curSizePoly)
+			for k := 0; k < curSizePoly; k++ {
+				p[i][j][k].SetRandom()
+			}
+		}
+	}
+
+	// sample random sets Sᵢ
+	x := make([][]fr.Element, nbSets)
+	for i := 0; i < nbSets; i++ {
+		curSetSize := i + 4
+		x[i] = make([]fr.Element, curSetSize)
+		for j := 0; j < curSetSize; j++ {
+			x[i][j].SetRandom()
+		}
+	}
+
+	// commit to the folded polynomials
+	digests := make([]kzg.Digest, nbSets)
+	var err error
+	for i := 0; i < nbSets; i++ {
+		digests[i], err = CommitAndFold(p[i], testSrs.Pk)
+		assert.NoError(err)
+	}
+
+	// compute flonk opening proof
+	hf := sha256.New()
+	proof, err := BatchOpen(p, digests, x, hf, testSrs.Pk)
+	assert.NoError(err)
+
+	// check opening proof
+	err = BatchVerify(proof, digests, x, hf, testSrs.Vk)
+	assert.NoError(err)
+
+	// tamper the proof
+	proof.ClaimedValues[0][0][0].SetRandom()
+	err = BatchVerify(proof, digests, x, hf, testSrs.Vk)
+	assert.Error(err)
+
+}
+
 func TestCommit(t *testing.T) {
 
 	assert := require.New(t)

From 24ac555295c429f2c9b98111db6593371ae56e20 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Mon, 18 Mar 2024 18:35:36 +0100
Subject: [PATCH 028/114] feat: addition of templates for fflonk

---
 internal/generator/fflonk/generator.go        |  23 ++
 .../generator/fflonk/template/fflonk.go.tmpl  | 265 ++++++++++++++++++
 .../fflonk/template/fflonk.test.go.tmpl       | 123 ++++++++
 internal/generator/main.go                    |   3 +
 4 files changed, 414 insertions(+)
 create mode 100644 internal/generator/fflonk/generator.go
 create mode 100644 internal/generator/fflonk/template/fflonk.go.tmpl
 create mode 100644 internal/generator/fflonk/template/fflonk.test.go.tmpl

diff --git a/internal/generator/fflonk/generator.go b/internal/generator/fflonk/generator.go
new file mode 100644
index 0000000000..2bc2897afb
--- /dev/null
+++ b/internal/generator/fflonk/generator.go
@@ -0,0 +1,23 @@
+package fflonk
+
+import (
+	"path/filepath"
+
+	"github.com/consensys/bavard"
+	"github.com/consensys/gnark-crypto/internal/generator/config"
+)
+
+func Generate(conf config.Curve, baseDir string, bgen *bavard.BatchGenerator) error {
+
+	// kzg commitment scheme
+	conf.Package = "fflonk"
+	entries := []bavard.Entry{
+		// {File: filepath.Join(baseDir, "doc.go"), Templates: []string{"doc.go.tmpl"}},
+		{File: filepath.Join(baseDir, "fflonk.go"), Templates: []string{"fflonk.go.tmpl"}},
+		{File: filepath.Join(baseDir, "fflonk_test.go"), Templates: []string{"fflonk.test.go.tmpl"}},
+		// {File: filepath.Join(baseDir, "marshal.go"), Templates: []string{"marshal.go.tmpl"}},
+		// {File: filepath.Join(baseDir, "utils.go"), Templates: []string{"utils.go.tmpl"}},
+	}
+	return bgen.Generate(conf, conf.Package, "./fflonk/template/", entries...)
+
+}
diff --git a/internal/generator/fflonk/template/fflonk.go.tmpl b/internal/generator/fflonk/template/fflonk.go.tmpl
new file mode 100644
index 0000000000..f9ee38a06b
--- /dev/null
+++ b/internal/generator/fflonk/template/fflonk.go.tmpl
@@ -0,0 +1,265 @@
+import (
+	"errors"
+	"hash"
+	"math/big"
+
+	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/fr"
+	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/kzg"
+	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/shplonk"
+)
+
+var (
+	ErrRootsOne                       = errors.New("Fr does not contain all the t-th roots of 1")
+	ErrNbPolynomialsNbPoints          = errors.New("the number of packs of polynomials should be the same as the number of pack of points")
+	ErrInonsistentFolding             = errors.New("the outer claimed values are not consistent with the shplonk proof")
+	ErrInconsistentNumberFoldedPoints = errors.New("the number of outer claimed values is inconsistent with the number of claimed values in the shplonk proof")
+)
+
+// Opening fflonk proof for opening a list of list of polynomials ((fʲᵢ)ᵢ)ⱼ where each
+// pack of polynomials (fʲᵢ)ᵢ (the pack is indexed by j) is opened on a powers of elements in
+// the set Sʲ (indexed by j), where the power is |(fʲᵢ)ᵢ|.
+//
+// implements io.ReaderFrom and io.WriterTo
+type OpeningProof struct {
+
+	// shplonk opening proof of the folded polynomials
+	SOpeningProof shplonk.OpeningProof
+
+	// ClaimedValues ClaimedValues[i][j] contains the values
+	// of fʲᵢ on Sⱼ^{|(fʲᵢ)ᵢ|}
+	ClaimedValues [][][]fr.Element
+}
+
+// CommitAndFold commits to a list of polynomial by intertwinning them like in the FFT, that is
+// returns ∑_{i<t}Pᵢ(Xᵗ)Xⁱ for t polynomials
+func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
+	buf := Fold(p)
+	com, err := kzg.Commit(buf, pk, nbTasks...)
+	return com, err
+}
+
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ
+func Fold(p [][]fr.Element) []fr.Element {
+	t := len(p)
+	sizeResult := 0
+	for i := range p {
+		if sizeResult < len(p[i]) {
+			sizeResult = len(p[i])
+		}
+	}
+	sizeResult = sizeResult*len(p) + len(p) - 1
+	buf := make([]fr.Element, sizeResult)
+	for i := range p {
+		for j := range p[i] {
+			buf[j*t+i].Set(&p[i][j])
+		}
+	}
+	return buf
+}
+
+// BatchOpen computes a batch opening proof of p (the (fʲᵢ)ᵢ ) on powers of points (the ((Sʲᵢ)ᵢ)ⱼ).
+// The j-th pack of polynomials is opened on the power |(fʲᵢ)ᵢ| of (Sʲᵢ)ᵢ.
+// digests is the list (CommitAndFold(p[i]))ᵢ. It is assumed that the list has been computed beforehand
+// and provided as an input to not duplicate computations.
+func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
+
+	var res OpeningProof
+
+	if len(p) != len(points) {
+		return res, ErrNbPolynomialsNbPoints
+	}
+
+	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
+	nbPolysPerPack := make([]int, len(p))
+	for i := 0; i < len(p); i++ {
+		nbPolysPerPack[i] = len(p[i])
+	}
+	pointsPowerM := make([][]fr.Element, len(points))
+	var tmpBigInt big.Int
+	for i := 0; i < len(p); i++ {
+		tmpBigInt.SetUint64(uint64(nbPolysPerPack[i]))
+		pointsPowerM[i] = make([]fr.Element, len(points[i]))
+		for j := 0; j < len(points[i]); j++ {
+			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
+		}
+	}
+
+	// step 1: compute the claimed values, that is the evaluations of the polynomials
+	// on the relevant powers of the sets
+	res.ClaimedValues = make([][][]fr.Element, len(p))
+	for i := 0; i < len(p); i++ {
+		res.ClaimedValues[i] = make([][]fr.Element, len(p[i]))
+		for j := 0; j < len(p[i]); j++ {
+			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
+			for k := 0; k < len(points[i]); k++ {
+				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
+			}
+		}
+	}
+
+	// step 2: fold polynomials
+	foldedPolynomials := make([][]fr.Element, len(p))
+	for i := 0; i < len(p); i++ {
+		foldedPolynomials[i] = Fold(p[i])
+	}
+
+	// step 4: compute the associated roots, that is for each point p corresponding
+	// to a pack i of polynomials, we extend to <p, ω p, .., ωᵗ⁻¹p> if
+	// the i-th pack contains t polynomials where ω is a t-th root of 1
+	newPoints := make([][]fr.Element, len(points))
+	var err error
+	for i := 0; i < len(p); i++ {
+		t := len(p[i])
+		newPoints[i], err = extendSet(points[i], t)
+		if err != nil {
+			return res, err
+		}
+	}
+
+	// step 5: shplonk open the list of single polynomials on the new sets
+	res.SOpeningProof, err = shplonk.BatchOpen(foldedPolynomials, digests, newPoints, hf, pk, dataTranscript...)
+
+	return res, err
+
+}
+
+// BatchVerify uses a proof to check that each digest digests[i] is correctly opened on the set points[i].
+// The digests are the commitments to the folded underlying polynomials. The shplonk proof is
+// verified directly using the embedded shplonk proof. This function only computes the consistency
+// between the claimed values of the underlying shplonk proof and the outer claimed values, using the fft-like
+// folding. Namely, the outer claimed values are the evaluation of the original polynomials (so before they
+// were folded) at the relevant powers of the points.
+func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
+
+	// step 0: consistency checks between the folded claimed values of shplonk and the claimed
+	// values at the powers of the Sᵢ
+	for i := 0; i < len(proof.ClaimedValues); i++ {
+		sizeSi := len(proof.ClaimedValues[i][0])
+		for j := 1; j < len(proof.ClaimedValues[i]); j++ {
+			// each set of opening must be of the same size (opeings on powers of Si)
+			if sizeSi != len(proof.ClaimedValues[i][j]) {
+				return ErrNbPolynomialsNbPoints
+			}
+		}
+		currNbPolynomials := len(proof.ClaimedValues[i])
+		sizeSi = sizeSi * currNbPolynomials
+		// |originalPolynomials_{i}|x|Sᵢ| == |foldedPolynomials|x|folded Sᵢ|
+		if sizeSi != len(proof.SOpeningProof.ClaimedValues[i]) {
+			return ErrInconsistentNumberFoldedPoints
+		}
+	}
+
+	// step 1: fold the outer claimed values and check that they correspond to the
+	// shplonk claimed values
+	var curFoldedClaimedValue, omgeaiPoint fr.Element
+	for i := 0; i < len(proof.ClaimedValues); i++ {
+		t := len(proof.ClaimedValues[i])
+		omega, err := getIthRootOne(t)
+		if err != nil {
+			return err
+		}
+		sizeSi := len(proof.ClaimedValues[i][0])
+		polyClaimedValues := make([]fr.Element, t)
+		for j := 0; j < sizeSi; j++ {
+			for k := 0; k < t; k++ {
+				polyClaimedValues[k].Set(&proof.ClaimedValues[i][k][j])
+			}
+			omgeaiPoint.Set(&points[i][j])
+			for l := 0; l < t; l++ {
+				curFoldedClaimedValue = eval(polyClaimedValues, omgeaiPoint)
+				if !curFoldedClaimedValue.Equal(&proof.SOpeningProof.ClaimedValues[i][j*t+l]) {
+					return ErrInonsistentFolding
+				}
+				omgeaiPoint.Mul(&omgeaiPoint, &omega)
+			}
+		}
+	}
+
+	// step 2: verify the embedded shplonk proof
+	extendedPoints := make([][]fr.Element, len(points))
+	var err error
+	for i := 0; i < len(points); i++ {
+		t := len(proof.ClaimedValues[i])
+		extendedPoints[i], err = extendSet(points[i], t)
+		if err != nil {
+			return err
+		}
+	}
+	err = shplonk.BatchVerify(proof.SOpeningProof, digests, extendedPoints, hf, vk, dataTranscript...)
+
+	return nil
+}
+
+// utils
+
+// getGenFrStar returns a generator of Fr^{*}
+func getGenFrStar() fr.Element {
+	var res fr.Element
+    {{if eq .Name "bls12-378"}}
+        res.SetUint64(22)
+	{{else if eq .Name "bls12-377"}}
+        res.SetUint64(22)
+	{{else if eq .Name "bls12-381"}}
+        res.SetUint64(7)
+	{{else if eq .Name "bn254"}}
+        res.SetUint64(5)
+	{{else if eq .Name "bw6-761"}}
+        res.SetUint64(15)
+	{{else if eq .Name "bw6-756"}}
+        res.SetUint64(5)
+    {{else if eq .Name "bw6-633"}}
+        res.SetUint64(13)
+	{{else if eq .Name "bls24-315"}}
+        res.SetUint64(7)
+	{{else if eq .Name "bls24-317"}}
+        res.SetUint64(7)
+	{{end}}
+	return res
+}
+
+// getIthRootOne returns a generator of Z/iZ
+func getIthRootOne(i int) (fr.Element, error) {
+	var omega fr.Element
+	var tmpBigInt, zeroBigInt big.Int
+	oneBigInt := big.NewInt(1)
+	zeroBigInt.SetUint64(0)
+	rMinusOneBigInt := fr.Modulus()
+	rMinusOneBigInt.Sub(rMinusOneBigInt, oneBigInt)
+	tmpBigInt.SetUint64(uint64(i))
+	tmpBigInt.Mod(rMinusOneBigInt, &tmpBigInt)
+	if tmpBigInt.Cmp(&zeroBigInt) != 0 {
+		return omega, ErrRootsOne
+	}
+	genFrStar := getGenFrStar()
+	tmpBigInt.SetUint64(uint64(i))
+	tmpBigInt.Div(rMinusOneBigInt, &tmpBigInt)
+	omega.Exp(genFrStar, &tmpBigInt)
+	return omega, nil
+}
+
+// extendSet returns [p[0], ω p[0], .. ,ωᵗ⁻¹p[0],p[1],..,ωᵗ⁻¹p[1],..]
+func extendSet(p []fr.Element, t int) ([]fr.Element, error) {
+
+	omega, err := getIthRootOne(t)
+	if err != nil {
+		return nil, err
+	}
+	nbPoints := len(p)
+	newPoints := make([]fr.Element, t*nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		newPoints[i*t].Set(&p[i])
+		for k := 1; k < t; k++ {
+			newPoints[i*t+k].Mul(&newPoints[i*t+k-1], &omega)
+		}
+	}
+
+	return newPoints, nil
+}
+
+func eval(f []fr.Element, x fr.Element) fr.Element {
+	var y fr.Element
+	for i := len(f) - 1; i >= 0; i-- {
+		y.Mul(&y, &x).Add(&y, &f[i])
+	}
+	return y
+}
diff --git a/internal/generator/fflonk/template/fflonk.test.go.tmpl b/internal/generator/fflonk/template/fflonk.test.go.tmpl
new file mode 100644
index 0000000000..c65b2afa17
--- /dev/null
+++ b/internal/generator/fflonk/template/fflonk.test.go.tmpl
@@ -0,0 +1,123 @@
+import (
+	"crypto/sha256"
+	"math/big"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/fr"
+	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/kzg"
+	"github.com/stretchr/testify/require"
+)
+
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *kzg.SRS
+var bAlpha *big.Int
+
+func init() {
+	const srsSize = 400
+	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+}
+
+func TestFflonk(t *testing.T) {
+
+	assert := require.New(t)
+
+	// sample random polynomials of various sizes
+	nbSets := 5
+	p := make([][][]fr.Element, nbSets)
+	for i := 0; i < nbSets; i++ {
+		nbPolysInSet := 9
+		p[i] = make([][]fr.Element, nbPolysInSet)
+		for j := 0; j < nbPolysInSet; j++ {
+			curSizePoly := j + 10
+			p[i][j] = make([]fr.Element, curSizePoly)
+			for k := 0; k < curSizePoly; k++ {
+				p[i][j][k].SetRandom()
+			}
+		}
+	}
+
+	// sample random sets Sᵢ
+	x := make([][]fr.Element, nbSets)
+	for i := 0; i < nbSets; i++ {
+		curSetSize := i + 4
+		x[i] = make([]fr.Element, curSetSize)
+		for j := 0; j < curSetSize; j++ {
+			x[i][j].SetRandom()
+		}
+	}
+
+	// commit to the folded polynomials
+	digests := make([]kzg.Digest, nbSets)
+	var err error
+	for i := 0; i < nbSets; i++ {
+		digests[i], err = CommitAndFold(p[i], testSrs.Pk)
+		assert.NoError(err)
+	}
+
+	// compute flonk opening proof
+	hf := sha256.New()
+	proof, err := BatchOpen(p, digests, x, hf, testSrs.Pk)
+	assert.NoError(err)
+
+	// check opening proof
+	err = BatchVerify(proof, digests, x, hf, testSrs.Vk)
+	assert.NoError(err)
+
+	// tamper the proof
+	proof.ClaimedValues[0][0][0].SetRandom()
+	err = BatchVerify(proof, digests, x, hf, testSrs.Vk)
+	assert.Error(err)
+
+}
+
+func TestCommit(t *testing.T) {
+
+	assert := require.New(t)
+
+	// sample polynomials
+	nbPolys := 2
+	p := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		p[i] = make([]fr.Element, i+10)
+		for j := 0; j < i+10; j++ {
+			p[i][j].SetRandom()
+		}
+	}
+
+	// fflonk commit to them
+	var x fr.Element
+	x.SetRandom()
+	proof, err := kzg.Open(Fold(p), x, testSrs.Pk)
+	assert.NoError(err)
+
+	// check that Open(C, x) = ∑_{i<t}Pᵢ(xᵗ)xⁱ
+	var xt fr.Element
+	var expo big.Int
+	expo.SetUint64(uint64(nbPolys))
+	xt.Exp(x, &expo)
+	px := make([]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		px[i] = eval(p[i], xt)
+	}
+	y := eval(px, x)
+	assert.True(y.Equal(&proof.ClaimedValue))
+}
+
+func TestGetIthRootOne(t *testing.T) {
+
+	assert := require.New(t)
+
+	order := 9
+	omega, err := getIthRootOne(order)
+	assert.NoError(err)
+	var orderBigInt big.Int
+	orderBigInt.SetUint64(uint64(order))
+	omega.Exp(omega, &orderBigInt)
+	assert.True(omega.IsOne())
+
+	order = 7
+	_, err = getIthRootOne(order)
+	assert.Error(err)
+}
diff --git a/internal/generator/main.go b/internal/generator/main.go
index 32802d3fee..7522a0c7bc 100644
--- a/internal/generator/main.go
+++ b/internal/generator/main.go
@@ -103,6 +103,9 @@ func main() {
 			// generate shplonk on fr
 			assertNoError(shplonk.Generate(conf, filepath.Join(curveDir, "shplonk"), bgen))
 
+			// generate fflonk on fr
+			assertNoError(shplonk.Generate(conf, filepath.Join(curveDir, "fflonk"), bgen))
+
 			// generate pedersen on fr
 			assertNoError(pedersen.Generate(conf, filepath.Join(curveDir, "fr", "pedersen"), bgen))
 

From 8af301d90ee3c84340856798962312e68096791e Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Mon, 18 Mar 2024 18:37:43 +0100
Subject: [PATCH 029/114] feat: add doc for fflonk

---
 internal/generator/fflonk/generator.go         | 3 +--
 internal/generator/fflonk/template/doc.go.tmpl | 5 +++++
 2 files changed, 6 insertions(+), 2 deletions(-)
 create mode 100644 internal/generator/fflonk/template/doc.go.tmpl

diff --git a/internal/generator/fflonk/generator.go b/internal/generator/fflonk/generator.go
index 2bc2897afb..40ee17daf3 100644
--- a/internal/generator/fflonk/generator.go
+++ b/internal/generator/fflonk/generator.go
@@ -12,11 +12,10 @@ func Generate(conf config.Curve, baseDir string, bgen *bavard.BatchGenerator) er
 	// kzg commitment scheme
 	conf.Package = "fflonk"
 	entries := []bavard.Entry{
-		// {File: filepath.Join(baseDir, "doc.go"), Templates: []string{"doc.go.tmpl"}},
+		{File: filepath.Join(baseDir, "doc.go"), Templates: []string{"doc.go.tmpl"}},
 		{File: filepath.Join(baseDir, "fflonk.go"), Templates: []string{"fflonk.go.tmpl"}},
 		{File: filepath.Join(baseDir, "fflonk_test.go"), Templates: []string{"fflonk.test.go.tmpl"}},
 		// {File: filepath.Join(baseDir, "marshal.go"), Templates: []string{"marshal.go.tmpl"}},
-		// {File: filepath.Join(baseDir, "utils.go"), Templates: []string{"utils.go.tmpl"}},
 	}
 	return bgen.Generate(conf, conf.Package, "./fflonk/template/", entries...)
 
diff --git a/internal/generator/fflonk/template/doc.go.tmpl b/internal/generator/fflonk/template/doc.go.tmpl
new file mode 100644
index 0000000000..382fe8636e
--- /dev/null
+++ b/internal/generator/fflonk/template/doc.go.tmpl
@@ -0,0 +1,5 @@
+// Package {{.Package}} provides fflonk commitment, based on shplonk.
+// 
+// See https://eprint.iacr.org/2020/081.pdf for shplonk
+// See https://eprint.iacr.org/2021/1167.pdf for fflonk.
+package {{.Package}}
\ No newline at end of file

From 68c09521781df17adcdd8f936346bd3408e47512 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Mon, 18 Mar 2024 18:46:26 +0100
Subject: [PATCH 030/114] feat: added fflonk in code gen main

---
 internal/generator/main.go | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/internal/generator/main.go b/internal/generator/main.go
index 7522a0c7bc..ee5e072a5f 100644
--- a/internal/generator/main.go
+++ b/internal/generator/main.go
@@ -16,6 +16,7 @@ import (
 	"github.com/consensys/gnark-crypto/internal/generator/ecdsa"
 	"github.com/consensys/gnark-crypto/internal/generator/edwards"
 	"github.com/consensys/gnark-crypto/internal/generator/edwards/eddsa"
+	"github.com/consensys/gnark-crypto/internal/generator/fflonk"
 	"github.com/consensys/gnark-crypto/internal/generator/fft"
 	fri "github.com/consensys/gnark-crypto/internal/generator/fri/template"
 	"github.com/consensys/gnark-crypto/internal/generator/gkr"
@@ -104,7 +105,7 @@ func main() {
 			assertNoError(shplonk.Generate(conf, filepath.Join(curveDir, "shplonk"), bgen))
 
 			// generate fflonk on fr
-			assertNoError(shplonk.Generate(conf, filepath.Join(curveDir, "fflonk"), bgen))
+			assertNoError(fflonk.Generate(conf, filepath.Join(curveDir, "fflonk"), bgen))
 
 			// generate pedersen on fr
 			assertNoError(pedersen.Generate(conf, filepath.Join(curveDir, "fr", "pedersen"), bgen))

From e4e4a39c17b7b2da22a844a4da3398603d2e9406 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Mon, 18 Mar 2024 18:48:07 +0100
Subject: [PATCH 031/114] feat: code gen, tests for existence of roots of 1
 need to be tuned

---
 ecc/bls12-377/fflonk/doc.go         |  21 +++
 ecc/bls12-377/fflonk/fflonk.go      | 267 ++++++++++++++++++++++++++++
 ecc/bls12-377/fflonk/fflonk_test.go | 141 +++++++++++++++
 ecc/bls12-378/fflonk/doc.go         |  21 +++
 ecc/bls12-378/fflonk/fflonk.go      | 267 ++++++++++++++++++++++++++++
 ecc/bls12-378/fflonk/fflonk_test.go | 141 +++++++++++++++
 ecc/bls12-381/fflonk/doc.go         |  21 +++
 ecc/bls12-381/fflonk/fflonk.go      | 267 ++++++++++++++++++++++++++++
 ecc/bls12-381/fflonk/fflonk_test.go | 141 +++++++++++++++
 ecc/bls24-315/fflonk/doc.go         |  21 +++
 ecc/bls24-315/fflonk/fflonk.go      | 267 ++++++++++++++++++++++++++++
 ecc/bls24-315/fflonk/fflonk_test.go | 141 +++++++++++++++
 ecc/bls24-317/fflonk/doc.go         |  21 +++
 ecc/bls24-317/fflonk/fflonk.go      | 267 ++++++++++++++++++++++++++++
 ecc/bls24-317/fflonk/fflonk_test.go | 141 +++++++++++++++
 ecc/bn254/fflonk/doc.go             |  21 +++
 ecc/bn254/fflonk/fflonk.go          |  18 ++
 ecc/bn254/fflonk/fflonk_test.go     |  16 ++
 ecc/bw6-633/fflonk/doc.go           |  21 +++
 ecc/bw6-633/fflonk/fflonk.go        | 267 ++++++++++++++++++++++++++++
 ecc/bw6-633/fflonk/fflonk_test.go   | 141 +++++++++++++++
 ecc/bw6-756/fflonk/doc.go           |  21 +++
 ecc/bw6-756/fflonk/fflonk.go        | 267 ++++++++++++++++++++++++++++
 ecc/bw6-756/fflonk/fflonk_test.go   | 141 +++++++++++++++
 ecc/bw6-761/fflonk/doc.go           |  21 +++
 ecc/bw6-761/fflonk/fflonk.go        | 267 ++++++++++++++++++++++++++++
 ecc/bw6-761/fflonk/fflonk_test.go   | 141 +++++++++++++++
 27 files changed, 3487 insertions(+)
 create mode 100644 ecc/bls12-377/fflonk/doc.go
 create mode 100644 ecc/bls12-377/fflonk/fflonk.go
 create mode 100644 ecc/bls12-377/fflonk/fflonk_test.go
 create mode 100644 ecc/bls12-378/fflonk/doc.go
 create mode 100644 ecc/bls12-378/fflonk/fflonk.go
 create mode 100644 ecc/bls12-378/fflonk/fflonk_test.go
 create mode 100644 ecc/bls12-381/fflonk/doc.go
 create mode 100644 ecc/bls12-381/fflonk/fflonk.go
 create mode 100644 ecc/bls12-381/fflonk/fflonk_test.go
 create mode 100644 ecc/bls24-315/fflonk/doc.go
 create mode 100644 ecc/bls24-315/fflonk/fflonk.go
 create mode 100644 ecc/bls24-315/fflonk/fflonk_test.go
 create mode 100644 ecc/bls24-317/fflonk/doc.go
 create mode 100644 ecc/bls24-317/fflonk/fflonk.go
 create mode 100644 ecc/bls24-317/fflonk/fflonk_test.go
 create mode 100644 ecc/bn254/fflonk/doc.go
 create mode 100644 ecc/bw6-633/fflonk/doc.go
 create mode 100644 ecc/bw6-633/fflonk/fflonk.go
 create mode 100644 ecc/bw6-633/fflonk/fflonk_test.go
 create mode 100644 ecc/bw6-756/fflonk/doc.go
 create mode 100644 ecc/bw6-756/fflonk/fflonk.go
 create mode 100644 ecc/bw6-756/fflonk/fflonk_test.go
 create mode 100644 ecc/bw6-761/fflonk/doc.go
 create mode 100644 ecc/bw6-761/fflonk/fflonk.go
 create mode 100644 ecc/bw6-761/fflonk/fflonk_test.go

diff --git a/ecc/bls12-377/fflonk/doc.go b/ecc/bls12-377/fflonk/doc.go
new file mode 100644
index 0000000000..694eaa9734
--- /dev/null
+++ b/ecc/bls12-377/fflonk/doc.go
@@ -0,0 +1,21 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// Package fflonk provides fflonk commitment, based on shplonk.
+//
+// See https://eprint.iacr.org/2020/081.pdf for shplonk
+// See https://eprint.iacr.org/2021/1167.pdf for fflonk.
+package fflonk
diff --git a/ecc/bls12-377/fflonk/fflonk.go b/ecc/bls12-377/fflonk/fflonk.go
new file mode 100644
index 0000000000..31176422e0
--- /dev/null
+++ b/ecc/bls12-377/fflonk/fflonk.go
@@ -0,0 +1,267 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"errors"
+	"hash"
+	"math/big"
+
+	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls12-377/kzg"
+	"github.com/consensys/gnark-crypto/ecc/bls12-377/shplonk"
+)
+
+var (
+	ErrRootsOne                       = errors.New("Fr does not contain all the t-th roots of 1")
+	ErrNbPolynomialsNbPoints          = errors.New("the number of packs of polynomials should be the same as the number of pack of points")
+	ErrInonsistentFolding             = errors.New("the outer claimed values are not consistent with the shplonk proof")
+	ErrInconsistentNumberFoldedPoints = errors.New("the number of outer claimed values is inconsistent with the number of claimed values in the shplonk proof")
+)
+
+// Opening fflonk proof for opening a list of list of polynomials ((fʲᵢ)ᵢ)ⱼ where each
+// pack of polynomials (fʲᵢ)ᵢ (the pack is indexed by j) is opened on a powers of elements in
+// the set Sʲ (indexed by j), where the power is |(fʲᵢ)ᵢ|.
+//
+// implements io.ReaderFrom and io.WriterTo
+type OpeningProof struct {
+
+	// shplonk opening proof of the folded polynomials
+	SOpeningProof shplonk.OpeningProof
+
+	// ClaimedValues ClaimedValues[i][j] contains the values
+	// of fʲᵢ on Sⱼ^{|(fʲᵢ)ᵢ|}
+	ClaimedValues [][][]fr.Element
+}
+
+// CommitAndFold commits to a list of polynomial by intertwinning them like in the FFT, that is
+// returns ∑_{i<t}Pᵢ(Xᵗ)Xⁱ for t polynomials
+func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
+	buf := Fold(p)
+	com, err := kzg.Commit(buf, pk, nbTasks...)
+	return com, err
+}
+
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ
+func Fold(p [][]fr.Element) []fr.Element {
+	t := len(p)
+	sizeResult := 0
+	for i := range p {
+		if sizeResult < len(p[i]) {
+			sizeResult = len(p[i])
+		}
+	}
+	sizeResult = sizeResult*len(p) + len(p) - 1
+	buf := make([]fr.Element, sizeResult)
+	for i := range p {
+		for j := range p[i] {
+			buf[j*t+i].Set(&p[i][j])
+		}
+	}
+	return buf
+}
+
+// BatchOpen computes a batch opening proof of p (the (fʲᵢ)ᵢ ) on powers of points (the ((Sʲᵢ)ᵢ)ⱼ).
+// The j-th pack of polynomials is opened on the power |(fʲᵢ)ᵢ| of (Sʲᵢ)ᵢ.
+// digests is the list (CommitAndFold(p[i]))ᵢ. It is assumed that the list has been computed beforehand
+// and provided as an input to not duplicate computations.
+func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
+
+	var res OpeningProof
+
+	if len(p) != len(points) {
+		return res, ErrNbPolynomialsNbPoints
+	}
+
+	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
+	nbPolysPerPack := make([]int, len(p))
+	for i := 0; i < len(p); i++ {
+		nbPolysPerPack[i] = len(p[i])
+	}
+	pointsPowerM := make([][]fr.Element, len(points))
+	var tmpBigInt big.Int
+	for i := 0; i < len(p); i++ {
+		tmpBigInt.SetUint64(uint64(nbPolysPerPack[i]))
+		pointsPowerM[i] = make([]fr.Element, len(points[i]))
+		for j := 0; j < len(points[i]); j++ {
+			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
+		}
+	}
+
+	// step 1: compute the claimed values, that is the evaluations of the polynomials
+	// on the relevant powers of the sets
+	res.ClaimedValues = make([][][]fr.Element, len(p))
+	for i := 0; i < len(p); i++ {
+		res.ClaimedValues[i] = make([][]fr.Element, len(p[i]))
+		for j := 0; j < len(p[i]); j++ {
+			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
+			for k := 0; k < len(points[i]); k++ {
+				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
+			}
+		}
+	}
+
+	// step 2: fold polynomials
+	foldedPolynomials := make([][]fr.Element, len(p))
+	for i := 0; i < len(p); i++ {
+		foldedPolynomials[i] = Fold(p[i])
+	}
+
+	// step 4: compute the associated roots, that is for each point p corresponding
+	// to a pack i of polynomials, we extend to <p, ω p, .., ωᵗ⁻¹p> if
+	// the i-th pack contains t polynomials where ω is a t-th root of 1
+	newPoints := make([][]fr.Element, len(points))
+	var err error
+	for i := 0; i < len(p); i++ {
+		t := len(p[i])
+		newPoints[i], err = extendSet(points[i], t)
+		if err != nil {
+			return res, err
+		}
+	}
+
+	// step 5: shplonk open the list of single polynomials on the new sets
+	res.SOpeningProof, err = shplonk.BatchOpen(foldedPolynomials, digests, newPoints, hf, pk, dataTranscript...)
+
+	return res, err
+
+}
+
+// BatchVerify uses a proof to check that each digest digests[i] is correctly opened on the set points[i].
+// The digests are the commitments to the folded underlying polynomials. The shplonk proof is
+// verified directly using the embedded shplonk proof. This function only computes the consistency
+// between the claimed values of the underlying shplonk proof and the outer claimed values, using the fft-like
+// folding. Namely, the outer claimed values are the evaluation of the original polynomials (so before they
+// were folded) at the relevant powers of the points.
+func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
+
+	// step 0: consistency checks between the folded claimed values of shplonk and the claimed
+	// values at the powers of the Sᵢ
+	for i := 0; i < len(proof.ClaimedValues); i++ {
+		sizeSi := len(proof.ClaimedValues[i][0])
+		for j := 1; j < len(proof.ClaimedValues[i]); j++ {
+			// each set of opening must be of the same size (opeings on powers of Si)
+			if sizeSi != len(proof.ClaimedValues[i][j]) {
+				return ErrNbPolynomialsNbPoints
+			}
+		}
+		currNbPolynomials := len(proof.ClaimedValues[i])
+		sizeSi = sizeSi * currNbPolynomials
+		// |originalPolynomials_{i}|x|Sᵢ| == |foldedPolynomials|x|folded Sᵢ|
+		if sizeSi != len(proof.SOpeningProof.ClaimedValues[i]) {
+			return ErrInconsistentNumberFoldedPoints
+		}
+	}
+
+	// step 1: fold the outer claimed values and check that they correspond to the
+	// shplonk claimed values
+	var curFoldedClaimedValue, omgeaiPoint fr.Element
+	for i := 0; i < len(proof.ClaimedValues); i++ {
+		t := len(proof.ClaimedValues[i])
+		omega, err := getIthRootOne(t)
+		if err != nil {
+			return err
+		}
+		sizeSi := len(proof.ClaimedValues[i][0])
+		polyClaimedValues := make([]fr.Element, t)
+		for j := 0; j < sizeSi; j++ {
+			for k := 0; k < t; k++ {
+				polyClaimedValues[k].Set(&proof.ClaimedValues[i][k][j])
+			}
+			omgeaiPoint.Set(&points[i][j])
+			for l := 0; l < t; l++ {
+				curFoldedClaimedValue = eval(polyClaimedValues, omgeaiPoint)
+				if !curFoldedClaimedValue.Equal(&proof.SOpeningProof.ClaimedValues[i][j*t+l]) {
+					return ErrInonsistentFolding
+				}
+				omgeaiPoint.Mul(&omgeaiPoint, &omega)
+			}
+		}
+	}
+
+	// step 2: verify the embedded shplonk proof
+	extendedPoints := make([][]fr.Element, len(points))
+	var err error
+	for i := 0; i < len(points); i++ {
+		t := len(proof.ClaimedValues[i])
+		extendedPoints[i], err = extendSet(points[i], t)
+		if err != nil {
+			return err
+		}
+	}
+	err = shplonk.BatchVerify(proof.SOpeningProof, digests, extendedPoints, hf, vk, dataTranscript...)
+
+	return nil
+}
+
+// utils
+
+// getGenFrStar returns a generator of Fr^{*}
+func getGenFrStar() fr.Element {
+	var res fr.Element
+
+	res.SetUint64(22)
+
+	return res
+}
+
+// getIthRootOne returns a generator of Z/iZ
+func getIthRootOne(i int) (fr.Element, error) {
+	var omega fr.Element
+	var tmpBigInt, zeroBigInt big.Int
+	oneBigInt := big.NewInt(1)
+	zeroBigInt.SetUint64(0)
+	rMinusOneBigInt := fr.Modulus()
+	rMinusOneBigInt.Sub(rMinusOneBigInt, oneBigInt)
+	tmpBigInt.SetUint64(uint64(i))
+	tmpBigInt.Mod(rMinusOneBigInt, &tmpBigInt)
+	if tmpBigInt.Cmp(&zeroBigInt) != 0 {
+		return omega, ErrRootsOne
+	}
+	genFrStar := getGenFrStar()
+	tmpBigInt.SetUint64(uint64(i))
+	tmpBigInt.Div(rMinusOneBigInt, &tmpBigInt)
+	omega.Exp(genFrStar, &tmpBigInt)
+	return omega, nil
+}
+
+// extendSet returns [p[0], ω p[0], .. ,ωᵗ⁻¹p[0],p[1],..,ωᵗ⁻¹p[1],..]
+func extendSet(p []fr.Element, t int) ([]fr.Element, error) {
+
+	omega, err := getIthRootOne(t)
+	if err != nil {
+		return nil, err
+	}
+	nbPoints := len(p)
+	newPoints := make([]fr.Element, t*nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		newPoints[i*t].Set(&p[i])
+		for k := 1; k < t; k++ {
+			newPoints[i*t+k].Mul(&newPoints[i*t+k-1], &omega)
+		}
+	}
+
+	return newPoints, nil
+}
+
+func eval(f []fr.Element, x fr.Element) fr.Element {
+	var y fr.Element
+	for i := len(f) - 1; i >= 0; i-- {
+		y.Mul(&y, &x).Add(&y, &f[i])
+	}
+	return y
+}
diff --git a/ecc/bls12-377/fflonk/fflonk_test.go b/ecc/bls12-377/fflonk/fflonk_test.go
new file mode 100644
index 0000000000..4caddc248d
--- /dev/null
+++ b/ecc/bls12-377/fflonk/fflonk_test.go
@@ -0,0 +1,141 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"crypto/sha256"
+	"math/big"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls12-377/kzg"
+	"github.com/stretchr/testify/require"
+)
+
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *kzg.SRS
+var bAlpha *big.Int
+
+func init() {
+	const srsSize = 400
+	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+}
+
+func TestFflonk(t *testing.T) {
+
+	assert := require.New(t)
+
+	// sample random polynomials of various sizes
+	nbSets := 5
+	p := make([][][]fr.Element, nbSets)
+	for i := 0; i < nbSets; i++ {
+		nbPolysInSet := 9
+		p[i] = make([][]fr.Element, nbPolysInSet)
+		for j := 0; j < nbPolysInSet; j++ {
+			curSizePoly := j + 10
+			p[i][j] = make([]fr.Element, curSizePoly)
+			for k := 0; k < curSizePoly; k++ {
+				p[i][j][k].SetRandom()
+			}
+		}
+	}
+
+	// sample random sets Sᵢ
+	x := make([][]fr.Element, nbSets)
+	for i := 0; i < nbSets; i++ {
+		curSetSize := i + 4
+		x[i] = make([]fr.Element, curSetSize)
+		for j := 0; j < curSetSize; j++ {
+			x[i][j].SetRandom()
+		}
+	}
+
+	// commit to the folded polynomials
+	digests := make([]kzg.Digest, nbSets)
+	var err error
+	for i := 0; i < nbSets; i++ {
+		digests[i], err = CommitAndFold(p[i], testSrs.Pk)
+		assert.NoError(err)
+	}
+
+	// compute flonk opening proof
+	hf := sha256.New()
+	proof, err := BatchOpen(p, digests, x, hf, testSrs.Pk)
+	assert.NoError(err)
+
+	// check opening proof
+	err = BatchVerify(proof, digests, x, hf, testSrs.Vk)
+	assert.NoError(err)
+
+	// tamper the proof
+	proof.ClaimedValues[0][0][0].SetRandom()
+	err = BatchVerify(proof, digests, x, hf, testSrs.Vk)
+	assert.Error(err)
+
+}
+
+func TestCommit(t *testing.T) {
+
+	assert := require.New(t)
+
+	// sample polynomials
+	nbPolys := 2
+	p := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		p[i] = make([]fr.Element, i+10)
+		for j := 0; j < i+10; j++ {
+			p[i][j].SetRandom()
+		}
+	}
+
+	// fflonk commit to them
+	var x fr.Element
+	x.SetRandom()
+	proof, err := kzg.Open(Fold(p), x, testSrs.Pk)
+	assert.NoError(err)
+
+	// check that Open(C, x) = ∑_{i<t}Pᵢ(xᵗ)xⁱ
+	var xt fr.Element
+	var expo big.Int
+	expo.SetUint64(uint64(nbPolys))
+	xt.Exp(x, &expo)
+	px := make([]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		px[i] = eval(p[i], xt)
+	}
+	y := eval(px, x)
+	assert.True(y.Equal(&proof.ClaimedValue))
+}
+
+func TestGetIthRootOne(t *testing.T) {
+
+	assert := require.New(t)
+
+	order := 9
+	omega, err := getIthRootOne(order)
+	assert.NoError(err)
+	var orderBigInt big.Int
+	orderBigInt.SetUint64(uint64(order))
+	omega.Exp(omega, &orderBigInt)
+	assert.True(omega.IsOne())
+
+	order = 7
+	_, err = getIthRootOne(order)
+	assert.Error(err)
+}
diff --git a/ecc/bls12-378/fflonk/doc.go b/ecc/bls12-378/fflonk/doc.go
new file mode 100644
index 0000000000..694eaa9734
--- /dev/null
+++ b/ecc/bls12-378/fflonk/doc.go
@@ -0,0 +1,21 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// Package fflonk provides fflonk commitment, based on shplonk.
+//
+// See https://eprint.iacr.org/2020/081.pdf for shplonk
+// See https://eprint.iacr.org/2021/1167.pdf for fflonk.
+package fflonk
diff --git a/ecc/bls12-378/fflonk/fflonk.go b/ecc/bls12-378/fflonk/fflonk.go
new file mode 100644
index 0000000000..967a45d404
--- /dev/null
+++ b/ecc/bls12-378/fflonk/fflonk.go
@@ -0,0 +1,267 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"errors"
+	"hash"
+	"math/big"
+
+	"github.com/consensys/gnark-crypto/ecc/bls12-378/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls12-378/kzg"
+	"github.com/consensys/gnark-crypto/ecc/bls12-378/shplonk"
+)
+
+var (
+	ErrRootsOne                       = errors.New("Fr does not contain all the t-th roots of 1")
+	ErrNbPolynomialsNbPoints          = errors.New("the number of packs of polynomials should be the same as the number of pack of points")
+	ErrInonsistentFolding             = errors.New("the outer claimed values are not consistent with the shplonk proof")
+	ErrInconsistentNumberFoldedPoints = errors.New("the number of outer claimed values is inconsistent with the number of claimed values in the shplonk proof")
+)
+
+// Opening fflonk proof for opening a list of list of polynomials ((fʲᵢ)ᵢ)ⱼ where each
+// pack of polynomials (fʲᵢ)ᵢ (the pack is indexed by j) is opened on a powers of elements in
+// the set Sʲ (indexed by j), where the power is |(fʲᵢ)ᵢ|.
+//
+// implements io.ReaderFrom and io.WriterTo
+type OpeningProof struct {
+
+	// shplonk opening proof of the folded polynomials
+	SOpeningProof shplonk.OpeningProof
+
+	// ClaimedValues ClaimedValues[i][j] contains the values
+	// of fʲᵢ on Sⱼ^{|(fʲᵢ)ᵢ|}
+	ClaimedValues [][][]fr.Element
+}
+
+// CommitAndFold commits to a list of polynomial by intertwinning them like in the FFT, that is
+// returns ∑_{i<t}Pᵢ(Xᵗ)Xⁱ for t polynomials
+func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
+	buf := Fold(p)
+	com, err := kzg.Commit(buf, pk, nbTasks...)
+	return com, err
+}
+
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ
+func Fold(p [][]fr.Element) []fr.Element {
+	t := len(p)
+	sizeResult := 0
+	for i := range p {
+		if sizeResult < len(p[i]) {
+			sizeResult = len(p[i])
+		}
+	}
+	sizeResult = sizeResult*len(p) + len(p) - 1
+	buf := make([]fr.Element, sizeResult)
+	for i := range p {
+		for j := range p[i] {
+			buf[j*t+i].Set(&p[i][j])
+		}
+	}
+	return buf
+}
+
+// BatchOpen computes a batch opening proof of p (the (fʲᵢ)ᵢ ) on powers of points (the ((Sʲᵢ)ᵢ)ⱼ).
+// The j-th pack of polynomials is opened on the power |(fʲᵢ)ᵢ| of (Sʲᵢ)ᵢ.
+// digests is the list (CommitAndFold(p[i]))ᵢ. It is assumed that the list has been computed beforehand
+// and provided as an input to not duplicate computations.
+func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
+
+	var res OpeningProof
+
+	if len(p) != len(points) {
+		return res, ErrNbPolynomialsNbPoints
+	}
+
+	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
+	nbPolysPerPack := make([]int, len(p))
+	for i := 0; i < len(p); i++ {
+		nbPolysPerPack[i] = len(p[i])
+	}
+	pointsPowerM := make([][]fr.Element, len(points))
+	var tmpBigInt big.Int
+	for i := 0; i < len(p); i++ {
+		tmpBigInt.SetUint64(uint64(nbPolysPerPack[i]))
+		pointsPowerM[i] = make([]fr.Element, len(points[i]))
+		for j := 0; j < len(points[i]); j++ {
+			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
+		}
+	}
+
+	// step 1: compute the claimed values, that is the evaluations of the polynomials
+	// on the relevant powers of the sets
+	res.ClaimedValues = make([][][]fr.Element, len(p))
+	for i := 0; i < len(p); i++ {
+		res.ClaimedValues[i] = make([][]fr.Element, len(p[i]))
+		for j := 0; j < len(p[i]); j++ {
+			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
+			for k := 0; k < len(points[i]); k++ {
+				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
+			}
+		}
+	}
+
+	// step 2: fold polynomials
+	foldedPolynomials := make([][]fr.Element, len(p))
+	for i := 0; i < len(p); i++ {
+		foldedPolynomials[i] = Fold(p[i])
+	}
+
+	// step 4: compute the associated roots, that is for each point p corresponding
+	// to a pack i of polynomials, we extend to <p, ω p, .., ωᵗ⁻¹p> if
+	// the i-th pack contains t polynomials where ω is a t-th root of 1
+	newPoints := make([][]fr.Element, len(points))
+	var err error
+	for i := 0; i < len(p); i++ {
+		t := len(p[i])
+		newPoints[i], err = extendSet(points[i], t)
+		if err != nil {
+			return res, err
+		}
+	}
+
+	// step 5: shplonk open the list of single polynomials on the new sets
+	res.SOpeningProof, err = shplonk.BatchOpen(foldedPolynomials, digests, newPoints, hf, pk, dataTranscript...)
+
+	return res, err
+
+}
+
+// BatchVerify uses a proof to check that each digest digests[i] is correctly opened on the set points[i].
+// The digests are the commitments to the folded underlying polynomials. The shplonk proof is
+// verified directly using the embedded shplonk proof. This function only computes the consistency
+// between the claimed values of the underlying shplonk proof and the outer claimed values, using the fft-like
+// folding. Namely, the outer claimed values are the evaluation of the original polynomials (so before they
+// were folded) at the relevant powers of the points.
+func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
+
+	// step 0: consistency checks between the folded claimed values of shplonk and the claimed
+	// values at the powers of the Sᵢ
+	for i := 0; i < len(proof.ClaimedValues); i++ {
+		sizeSi := len(proof.ClaimedValues[i][0])
+		for j := 1; j < len(proof.ClaimedValues[i]); j++ {
+			// each set of opening must be of the same size (opeings on powers of Si)
+			if sizeSi != len(proof.ClaimedValues[i][j]) {
+				return ErrNbPolynomialsNbPoints
+			}
+		}
+		currNbPolynomials := len(proof.ClaimedValues[i])
+		sizeSi = sizeSi * currNbPolynomials
+		// |originalPolynomials_{i}|x|Sᵢ| == |foldedPolynomials|x|folded Sᵢ|
+		if sizeSi != len(proof.SOpeningProof.ClaimedValues[i]) {
+			return ErrInconsistentNumberFoldedPoints
+		}
+	}
+
+	// step 1: fold the outer claimed values and check that they correspond to the
+	// shplonk claimed values
+	var curFoldedClaimedValue, omgeaiPoint fr.Element
+	for i := 0; i < len(proof.ClaimedValues); i++ {
+		t := len(proof.ClaimedValues[i])
+		omega, err := getIthRootOne(t)
+		if err != nil {
+			return err
+		}
+		sizeSi := len(proof.ClaimedValues[i][0])
+		polyClaimedValues := make([]fr.Element, t)
+		for j := 0; j < sizeSi; j++ {
+			for k := 0; k < t; k++ {
+				polyClaimedValues[k].Set(&proof.ClaimedValues[i][k][j])
+			}
+			omgeaiPoint.Set(&points[i][j])
+			for l := 0; l < t; l++ {
+				curFoldedClaimedValue = eval(polyClaimedValues, omgeaiPoint)
+				if !curFoldedClaimedValue.Equal(&proof.SOpeningProof.ClaimedValues[i][j*t+l]) {
+					return ErrInonsistentFolding
+				}
+				omgeaiPoint.Mul(&omgeaiPoint, &omega)
+			}
+		}
+	}
+
+	// step 2: verify the embedded shplonk proof
+	extendedPoints := make([][]fr.Element, len(points))
+	var err error
+	for i := 0; i < len(points); i++ {
+		t := len(proof.ClaimedValues[i])
+		extendedPoints[i], err = extendSet(points[i], t)
+		if err != nil {
+			return err
+		}
+	}
+	err = shplonk.BatchVerify(proof.SOpeningProof, digests, extendedPoints, hf, vk, dataTranscript...)
+
+	return nil
+}
+
+// utils
+
+// getGenFrStar returns a generator of Fr^{*}
+func getGenFrStar() fr.Element {
+	var res fr.Element
+
+	res.SetUint64(22)
+
+	return res
+}
+
+// getIthRootOne returns a generator of Z/iZ
+func getIthRootOne(i int) (fr.Element, error) {
+	var omega fr.Element
+	var tmpBigInt, zeroBigInt big.Int
+	oneBigInt := big.NewInt(1)
+	zeroBigInt.SetUint64(0)
+	rMinusOneBigInt := fr.Modulus()
+	rMinusOneBigInt.Sub(rMinusOneBigInt, oneBigInt)
+	tmpBigInt.SetUint64(uint64(i))
+	tmpBigInt.Mod(rMinusOneBigInt, &tmpBigInt)
+	if tmpBigInt.Cmp(&zeroBigInt) != 0 {
+		return omega, ErrRootsOne
+	}
+	genFrStar := getGenFrStar()
+	tmpBigInt.SetUint64(uint64(i))
+	tmpBigInt.Div(rMinusOneBigInt, &tmpBigInt)
+	omega.Exp(genFrStar, &tmpBigInt)
+	return omega, nil
+}
+
+// extendSet returns [p[0], ω p[0], .. ,ωᵗ⁻¹p[0],p[1],..,ωᵗ⁻¹p[1],..]
+func extendSet(p []fr.Element, t int) ([]fr.Element, error) {
+
+	omega, err := getIthRootOne(t)
+	if err != nil {
+		return nil, err
+	}
+	nbPoints := len(p)
+	newPoints := make([]fr.Element, t*nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		newPoints[i*t].Set(&p[i])
+		for k := 1; k < t; k++ {
+			newPoints[i*t+k].Mul(&newPoints[i*t+k-1], &omega)
+		}
+	}
+
+	return newPoints, nil
+}
+
+func eval(f []fr.Element, x fr.Element) fr.Element {
+	var y fr.Element
+	for i := len(f) - 1; i >= 0; i-- {
+		y.Mul(&y, &x).Add(&y, &f[i])
+	}
+	return y
+}
diff --git a/ecc/bls12-378/fflonk/fflonk_test.go b/ecc/bls12-378/fflonk/fflonk_test.go
new file mode 100644
index 0000000000..e26d4f7380
--- /dev/null
+++ b/ecc/bls12-378/fflonk/fflonk_test.go
@@ -0,0 +1,141 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"crypto/sha256"
+	"math/big"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bls12-378/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls12-378/kzg"
+	"github.com/stretchr/testify/require"
+)
+
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *kzg.SRS
+var bAlpha *big.Int
+
+func init() {
+	const srsSize = 400
+	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+}
+
+func TestFflonk(t *testing.T) {
+
+	assert := require.New(t)
+
+	// sample random polynomials of various sizes
+	nbSets := 5
+	p := make([][][]fr.Element, nbSets)
+	for i := 0; i < nbSets; i++ {
+		nbPolysInSet := 9
+		p[i] = make([][]fr.Element, nbPolysInSet)
+		for j := 0; j < nbPolysInSet; j++ {
+			curSizePoly := j + 10
+			p[i][j] = make([]fr.Element, curSizePoly)
+			for k := 0; k < curSizePoly; k++ {
+				p[i][j][k].SetRandom()
+			}
+		}
+	}
+
+	// sample random sets Sᵢ
+	x := make([][]fr.Element, nbSets)
+	for i := 0; i < nbSets; i++ {
+		curSetSize := i + 4
+		x[i] = make([]fr.Element, curSetSize)
+		for j := 0; j < curSetSize; j++ {
+			x[i][j].SetRandom()
+		}
+	}
+
+	// commit to the folded polynomials
+	digests := make([]kzg.Digest, nbSets)
+	var err error
+	for i := 0; i < nbSets; i++ {
+		digests[i], err = CommitAndFold(p[i], testSrs.Pk)
+		assert.NoError(err)
+	}
+
+	// compute flonk opening proof
+	hf := sha256.New()
+	proof, err := BatchOpen(p, digests, x, hf, testSrs.Pk)
+	assert.NoError(err)
+
+	// check opening proof
+	err = BatchVerify(proof, digests, x, hf, testSrs.Vk)
+	assert.NoError(err)
+
+	// tamper the proof
+	proof.ClaimedValues[0][0][0].SetRandom()
+	err = BatchVerify(proof, digests, x, hf, testSrs.Vk)
+	assert.Error(err)
+
+}
+
+func TestCommit(t *testing.T) {
+
+	assert := require.New(t)
+
+	// sample polynomials
+	nbPolys := 2
+	p := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		p[i] = make([]fr.Element, i+10)
+		for j := 0; j < i+10; j++ {
+			p[i][j].SetRandom()
+		}
+	}
+
+	// fflonk commit to them
+	var x fr.Element
+	x.SetRandom()
+	proof, err := kzg.Open(Fold(p), x, testSrs.Pk)
+	assert.NoError(err)
+
+	// check that Open(C, x) = ∑_{i<t}Pᵢ(xᵗ)xⁱ
+	var xt fr.Element
+	var expo big.Int
+	expo.SetUint64(uint64(nbPolys))
+	xt.Exp(x, &expo)
+	px := make([]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		px[i] = eval(p[i], xt)
+	}
+	y := eval(px, x)
+	assert.True(y.Equal(&proof.ClaimedValue))
+}
+
+func TestGetIthRootOne(t *testing.T) {
+
+	assert := require.New(t)
+
+	order := 9
+	omega, err := getIthRootOne(order)
+	assert.NoError(err)
+	var orderBigInt big.Int
+	orderBigInt.SetUint64(uint64(order))
+	omega.Exp(omega, &orderBigInt)
+	assert.True(omega.IsOne())
+
+	order = 7
+	_, err = getIthRootOne(order)
+	assert.Error(err)
+}
diff --git a/ecc/bls12-381/fflonk/doc.go b/ecc/bls12-381/fflonk/doc.go
new file mode 100644
index 0000000000..694eaa9734
--- /dev/null
+++ b/ecc/bls12-381/fflonk/doc.go
@@ -0,0 +1,21 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// Package fflonk provides fflonk commitment, based on shplonk.
+//
+// See https://eprint.iacr.org/2020/081.pdf for shplonk
+// See https://eprint.iacr.org/2021/1167.pdf for fflonk.
+package fflonk
diff --git a/ecc/bls12-381/fflonk/fflonk.go b/ecc/bls12-381/fflonk/fflonk.go
new file mode 100644
index 0000000000..0709f6d803
--- /dev/null
+++ b/ecc/bls12-381/fflonk/fflonk.go
@@ -0,0 +1,267 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"errors"
+	"hash"
+	"math/big"
+
+	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls12-381/kzg"
+	"github.com/consensys/gnark-crypto/ecc/bls12-381/shplonk"
+)
+
+var (
+	ErrRootsOne                       = errors.New("Fr does not contain all the t-th roots of 1")
+	ErrNbPolynomialsNbPoints          = errors.New("the number of packs of polynomials should be the same as the number of pack of points")
+	ErrInonsistentFolding             = errors.New("the outer claimed values are not consistent with the shplonk proof")
+	ErrInconsistentNumberFoldedPoints = errors.New("the number of outer claimed values is inconsistent with the number of claimed values in the shplonk proof")
+)
+
+// Opening fflonk proof for opening a list of list of polynomials ((fʲᵢ)ᵢ)ⱼ where each
+// pack of polynomials (fʲᵢ)ᵢ (the pack is indexed by j) is opened on a powers of elements in
+// the set Sʲ (indexed by j), where the power is |(fʲᵢ)ᵢ|.
+//
+// implements io.ReaderFrom and io.WriterTo
+type OpeningProof struct {
+
+	// shplonk opening proof of the folded polynomials
+	SOpeningProof shplonk.OpeningProof
+
+	// ClaimedValues ClaimedValues[i][j] contains the values
+	// of fʲᵢ on Sⱼ^{|(fʲᵢ)ᵢ|}
+	ClaimedValues [][][]fr.Element
+}
+
+// CommitAndFold commits to a list of polynomial by intertwinning them like in the FFT, that is
+// returns ∑_{i<t}Pᵢ(Xᵗ)Xⁱ for t polynomials
+func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
+	buf := Fold(p)
+	com, err := kzg.Commit(buf, pk, nbTasks...)
+	return com, err
+}
+
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ
+func Fold(p [][]fr.Element) []fr.Element {
+	t := len(p)
+	sizeResult := 0
+	for i := range p {
+		if sizeResult < len(p[i]) {
+			sizeResult = len(p[i])
+		}
+	}
+	sizeResult = sizeResult*len(p) + len(p) - 1
+	buf := make([]fr.Element, sizeResult)
+	for i := range p {
+		for j := range p[i] {
+			buf[j*t+i].Set(&p[i][j])
+		}
+	}
+	return buf
+}
+
+// BatchOpen computes a batch opening proof of p (the (fʲᵢ)ᵢ ) on powers of points (the ((Sʲᵢ)ᵢ)ⱼ).
+// The j-th pack of polynomials is opened on the power |(fʲᵢ)ᵢ| of (Sʲᵢ)ᵢ.
+// digests is the list (CommitAndFold(p[i]))ᵢ. It is assumed that the list has been computed beforehand
+// and provided as an input to not duplicate computations.
+func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
+
+	var res OpeningProof
+
+	if len(p) != len(points) {
+		return res, ErrNbPolynomialsNbPoints
+	}
+
+	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
+	nbPolysPerPack := make([]int, len(p))
+	for i := 0; i < len(p); i++ {
+		nbPolysPerPack[i] = len(p[i])
+	}
+	pointsPowerM := make([][]fr.Element, len(points))
+	var tmpBigInt big.Int
+	for i := 0; i < len(p); i++ {
+		tmpBigInt.SetUint64(uint64(nbPolysPerPack[i]))
+		pointsPowerM[i] = make([]fr.Element, len(points[i]))
+		for j := 0; j < len(points[i]); j++ {
+			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
+		}
+	}
+
+	// step 1: compute the claimed values, that is the evaluations of the polynomials
+	// on the relevant powers of the sets
+	res.ClaimedValues = make([][][]fr.Element, len(p))
+	for i := 0; i < len(p); i++ {
+		res.ClaimedValues[i] = make([][]fr.Element, len(p[i]))
+		for j := 0; j < len(p[i]); j++ {
+			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
+			for k := 0; k < len(points[i]); k++ {
+				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
+			}
+		}
+	}
+
+	// step 2: fold polynomials
+	foldedPolynomials := make([][]fr.Element, len(p))
+	for i := 0; i < len(p); i++ {
+		foldedPolynomials[i] = Fold(p[i])
+	}
+
+	// step 4: compute the associated roots, that is for each point p corresponding
+	// to a pack i of polynomials, we extend to <p, ω p, .., ωᵗ⁻¹p> if
+	// the i-th pack contains t polynomials where ω is a t-th root of 1
+	newPoints := make([][]fr.Element, len(points))
+	var err error
+	for i := 0; i < len(p); i++ {
+		t := len(p[i])
+		newPoints[i], err = extendSet(points[i], t)
+		if err != nil {
+			return res, err
+		}
+	}
+
+	// step 5: shplonk open the list of single polynomials on the new sets
+	res.SOpeningProof, err = shplonk.BatchOpen(foldedPolynomials, digests, newPoints, hf, pk, dataTranscript...)
+
+	return res, err
+
+}
+
+// BatchVerify uses a proof to check that each digest digests[i] is correctly opened on the set points[i].
+// The digests are the commitments to the folded underlying polynomials. The shplonk proof is
+// verified directly using the embedded shplonk proof. This function only computes the consistency
+// between the claimed values of the underlying shplonk proof and the outer claimed values, using the fft-like
+// folding. Namely, the outer claimed values are the evaluation of the original polynomials (so before they
+// were folded) at the relevant powers of the points.
+func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
+
+	// step 0: consistency checks between the folded claimed values of shplonk and the claimed
+	// values at the powers of the Sᵢ
+	for i := 0; i < len(proof.ClaimedValues); i++ {
+		sizeSi := len(proof.ClaimedValues[i][0])
+		for j := 1; j < len(proof.ClaimedValues[i]); j++ {
+			// each set of opening must be of the same size (opeings on powers of Si)
+			if sizeSi != len(proof.ClaimedValues[i][j]) {
+				return ErrNbPolynomialsNbPoints
+			}
+		}
+		currNbPolynomials := len(proof.ClaimedValues[i])
+		sizeSi = sizeSi * currNbPolynomials
+		// |originalPolynomials_{i}|x|Sᵢ| == |foldedPolynomials|x|folded Sᵢ|
+		if sizeSi != len(proof.SOpeningProof.ClaimedValues[i]) {
+			return ErrInconsistentNumberFoldedPoints
+		}
+	}
+
+	// step 1: fold the outer claimed values and check that they correspond to the
+	// shplonk claimed values
+	var curFoldedClaimedValue, omgeaiPoint fr.Element
+	for i := 0; i < len(proof.ClaimedValues); i++ {
+		t := len(proof.ClaimedValues[i])
+		omega, err := getIthRootOne(t)
+		if err != nil {
+			return err
+		}
+		sizeSi := len(proof.ClaimedValues[i][0])
+		polyClaimedValues := make([]fr.Element, t)
+		for j := 0; j < sizeSi; j++ {
+			for k := 0; k < t; k++ {
+				polyClaimedValues[k].Set(&proof.ClaimedValues[i][k][j])
+			}
+			omgeaiPoint.Set(&points[i][j])
+			for l := 0; l < t; l++ {
+				curFoldedClaimedValue = eval(polyClaimedValues, omgeaiPoint)
+				if !curFoldedClaimedValue.Equal(&proof.SOpeningProof.ClaimedValues[i][j*t+l]) {
+					return ErrInonsistentFolding
+				}
+				omgeaiPoint.Mul(&omgeaiPoint, &omega)
+			}
+		}
+	}
+
+	// step 2: verify the embedded shplonk proof
+	extendedPoints := make([][]fr.Element, len(points))
+	var err error
+	for i := 0; i < len(points); i++ {
+		t := len(proof.ClaimedValues[i])
+		extendedPoints[i], err = extendSet(points[i], t)
+		if err != nil {
+			return err
+		}
+	}
+	err = shplonk.BatchVerify(proof.SOpeningProof, digests, extendedPoints, hf, vk, dataTranscript...)
+
+	return nil
+}
+
+// utils
+
+// getGenFrStar returns a generator of Fr^{*}
+func getGenFrStar() fr.Element {
+	var res fr.Element
+
+	res.SetUint64(7)
+
+	return res
+}
+
+// getIthRootOne returns a generator of Z/iZ
+func getIthRootOne(i int) (fr.Element, error) {
+	var omega fr.Element
+	var tmpBigInt, zeroBigInt big.Int
+	oneBigInt := big.NewInt(1)
+	zeroBigInt.SetUint64(0)
+	rMinusOneBigInt := fr.Modulus()
+	rMinusOneBigInt.Sub(rMinusOneBigInt, oneBigInt)
+	tmpBigInt.SetUint64(uint64(i))
+	tmpBigInt.Mod(rMinusOneBigInt, &tmpBigInt)
+	if tmpBigInt.Cmp(&zeroBigInt) != 0 {
+		return omega, ErrRootsOne
+	}
+	genFrStar := getGenFrStar()
+	tmpBigInt.SetUint64(uint64(i))
+	tmpBigInt.Div(rMinusOneBigInt, &tmpBigInt)
+	omega.Exp(genFrStar, &tmpBigInt)
+	return omega, nil
+}
+
+// extendSet returns [p[0], ω p[0], .. ,ωᵗ⁻¹p[0],p[1],..,ωᵗ⁻¹p[1],..]
+func extendSet(p []fr.Element, t int) ([]fr.Element, error) {
+
+	omega, err := getIthRootOne(t)
+	if err != nil {
+		return nil, err
+	}
+	nbPoints := len(p)
+	newPoints := make([]fr.Element, t*nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		newPoints[i*t].Set(&p[i])
+		for k := 1; k < t; k++ {
+			newPoints[i*t+k].Mul(&newPoints[i*t+k-1], &omega)
+		}
+	}
+
+	return newPoints, nil
+}
+
+func eval(f []fr.Element, x fr.Element) fr.Element {
+	var y fr.Element
+	for i := len(f) - 1; i >= 0; i-- {
+		y.Mul(&y, &x).Add(&y, &f[i])
+	}
+	return y
+}
diff --git a/ecc/bls12-381/fflonk/fflonk_test.go b/ecc/bls12-381/fflonk/fflonk_test.go
new file mode 100644
index 0000000000..417e22139d
--- /dev/null
+++ b/ecc/bls12-381/fflonk/fflonk_test.go
@@ -0,0 +1,141 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"crypto/sha256"
+	"math/big"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls12-381/kzg"
+	"github.com/stretchr/testify/require"
+)
+
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *kzg.SRS
+var bAlpha *big.Int
+
+func init() {
+	const srsSize = 400
+	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+}
+
+func TestFflonk(t *testing.T) {
+
+	assert := require.New(t)
+
+	// sample random polynomials of various sizes
+	nbSets := 5
+	p := make([][][]fr.Element, nbSets)
+	for i := 0; i < nbSets; i++ {
+		nbPolysInSet := 9
+		p[i] = make([][]fr.Element, nbPolysInSet)
+		for j := 0; j < nbPolysInSet; j++ {
+			curSizePoly := j + 10
+			p[i][j] = make([]fr.Element, curSizePoly)
+			for k := 0; k < curSizePoly; k++ {
+				p[i][j][k].SetRandom()
+			}
+		}
+	}
+
+	// sample random sets Sᵢ
+	x := make([][]fr.Element, nbSets)
+	for i := 0; i < nbSets; i++ {
+		curSetSize := i + 4
+		x[i] = make([]fr.Element, curSetSize)
+		for j := 0; j < curSetSize; j++ {
+			x[i][j].SetRandom()
+		}
+	}
+
+	// commit to the folded polynomials
+	digests := make([]kzg.Digest, nbSets)
+	var err error
+	for i := 0; i < nbSets; i++ {
+		digests[i], err = CommitAndFold(p[i], testSrs.Pk)
+		assert.NoError(err)
+	}
+
+	// compute flonk opening proof
+	hf := sha256.New()
+	proof, err := BatchOpen(p, digests, x, hf, testSrs.Pk)
+	assert.NoError(err)
+
+	// check opening proof
+	err = BatchVerify(proof, digests, x, hf, testSrs.Vk)
+	assert.NoError(err)
+
+	// tamper the proof
+	proof.ClaimedValues[0][0][0].SetRandom()
+	err = BatchVerify(proof, digests, x, hf, testSrs.Vk)
+	assert.Error(err)
+
+}
+
+func TestCommit(t *testing.T) {
+
+	assert := require.New(t)
+
+	// sample polynomials
+	nbPolys := 2
+	p := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		p[i] = make([]fr.Element, i+10)
+		for j := 0; j < i+10; j++ {
+			p[i][j].SetRandom()
+		}
+	}
+
+	// fflonk commit to them
+	var x fr.Element
+	x.SetRandom()
+	proof, err := kzg.Open(Fold(p), x, testSrs.Pk)
+	assert.NoError(err)
+
+	// check that Open(C, x) = ∑_{i<t}Pᵢ(xᵗ)xⁱ
+	var xt fr.Element
+	var expo big.Int
+	expo.SetUint64(uint64(nbPolys))
+	xt.Exp(x, &expo)
+	px := make([]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		px[i] = eval(p[i], xt)
+	}
+	y := eval(px, x)
+	assert.True(y.Equal(&proof.ClaimedValue))
+}
+
+func TestGetIthRootOne(t *testing.T) {
+
+	assert := require.New(t)
+
+	order := 9
+	omega, err := getIthRootOne(order)
+	assert.NoError(err)
+	var orderBigInt big.Int
+	orderBigInt.SetUint64(uint64(order))
+	omega.Exp(omega, &orderBigInt)
+	assert.True(omega.IsOne())
+
+	order = 7
+	_, err = getIthRootOne(order)
+	assert.Error(err)
+}
diff --git a/ecc/bls24-315/fflonk/doc.go b/ecc/bls24-315/fflonk/doc.go
new file mode 100644
index 0000000000..694eaa9734
--- /dev/null
+++ b/ecc/bls24-315/fflonk/doc.go
@@ -0,0 +1,21 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// Package fflonk provides fflonk commitment, based on shplonk.
+//
+// See https://eprint.iacr.org/2020/081.pdf for shplonk
+// See https://eprint.iacr.org/2021/1167.pdf for fflonk.
+package fflonk
diff --git a/ecc/bls24-315/fflonk/fflonk.go b/ecc/bls24-315/fflonk/fflonk.go
new file mode 100644
index 0000000000..c4f890596f
--- /dev/null
+++ b/ecc/bls24-315/fflonk/fflonk.go
@@ -0,0 +1,267 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"errors"
+	"hash"
+	"math/big"
+
+	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls24-315/kzg"
+	"github.com/consensys/gnark-crypto/ecc/bls24-315/shplonk"
+)
+
+var (
+	ErrRootsOne                       = errors.New("Fr does not contain all the t-th roots of 1")
+	ErrNbPolynomialsNbPoints          = errors.New("the number of packs of polynomials should be the same as the number of pack of points")
+	ErrInonsistentFolding             = errors.New("the outer claimed values are not consistent with the shplonk proof")
+	ErrInconsistentNumberFoldedPoints = errors.New("the number of outer claimed values is inconsistent with the number of claimed values in the shplonk proof")
+)
+
+// Opening fflonk proof for opening a list of list of polynomials ((fʲᵢ)ᵢ)ⱼ where each
+// pack of polynomials (fʲᵢ)ᵢ (the pack is indexed by j) is opened on a powers of elements in
+// the set Sʲ (indexed by j), where the power is |(fʲᵢ)ᵢ|.
+//
+// implements io.ReaderFrom and io.WriterTo
+type OpeningProof struct {
+
+	// shplonk opening proof of the folded polynomials
+	SOpeningProof shplonk.OpeningProof
+
+	// ClaimedValues ClaimedValues[i][j] contains the values
+	// of fʲᵢ on Sⱼ^{|(fʲᵢ)ᵢ|}
+	ClaimedValues [][][]fr.Element
+}
+
+// CommitAndFold commits to a list of polynomial by intertwinning them like in the FFT, that is
+// returns ∑_{i<t}Pᵢ(Xᵗ)Xⁱ for t polynomials
+func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
+	buf := Fold(p)
+	com, err := kzg.Commit(buf, pk, nbTasks...)
+	return com, err
+}
+
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ
+func Fold(p [][]fr.Element) []fr.Element {
+	t := len(p)
+	sizeResult := 0
+	for i := range p {
+		if sizeResult < len(p[i]) {
+			sizeResult = len(p[i])
+		}
+	}
+	sizeResult = sizeResult*len(p) + len(p) - 1
+	buf := make([]fr.Element, sizeResult)
+	for i := range p {
+		for j := range p[i] {
+			buf[j*t+i].Set(&p[i][j])
+		}
+	}
+	return buf
+}
+
+// BatchOpen computes a batch opening proof of p (the (fʲᵢ)ᵢ ) on powers of points (the ((Sʲᵢ)ᵢ)ⱼ).
+// The j-th pack of polynomials is opened on the power |(fʲᵢ)ᵢ| of (Sʲᵢ)ᵢ.
+// digests is the list (CommitAndFold(p[i]))ᵢ. It is assumed that the list has been computed beforehand
+// and provided as an input to not duplicate computations.
+func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
+
+	var res OpeningProof
+
+	if len(p) != len(points) {
+		return res, ErrNbPolynomialsNbPoints
+	}
+
+	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
+	nbPolysPerPack := make([]int, len(p))
+	for i := 0; i < len(p); i++ {
+		nbPolysPerPack[i] = len(p[i])
+	}
+	pointsPowerM := make([][]fr.Element, len(points))
+	var tmpBigInt big.Int
+	for i := 0; i < len(p); i++ {
+		tmpBigInt.SetUint64(uint64(nbPolysPerPack[i]))
+		pointsPowerM[i] = make([]fr.Element, len(points[i]))
+		for j := 0; j < len(points[i]); j++ {
+			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
+		}
+	}
+
+	// step 1: compute the claimed values, that is the evaluations of the polynomials
+	// on the relevant powers of the sets
+	res.ClaimedValues = make([][][]fr.Element, len(p))
+	for i := 0; i < len(p); i++ {
+		res.ClaimedValues[i] = make([][]fr.Element, len(p[i]))
+		for j := 0; j < len(p[i]); j++ {
+			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
+			for k := 0; k < len(points[i]); k++ {
+				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
+			}
+		}
+	}
+
+	// step 2: fold polynomials
+	foldedPolynomials := make([][]fr.Element, len(p))
+	for i := 0; i < len(p); i++ {
+		foldedPolynomials[i] = Fold(p[i])
+	}
+
+	// step 4: compute the associated roots, that is for each point p corresponding
+	// to a pack i of polynomials, we extend to <p, ω p, .., ωᵗ⁻¹p> if
+	// the i-th pack contains t polynomials where ω is a t-th root of 1
+	newPoints := make([][]fr.Element, len(points))
+	var err error
+	for i := 0; i < len(p); i++ {
+		t := len(p[i])
+		newPoints[i], err = extendSet(points[i], t)
+		if err != nil {
+			return res, err
+		}
+	}
+
+	// step 5: shplonk open the list of single polynomials on the new sets
+	res.SOpeningProof, err = shplonk.BatchOpen(foldedPolynomials, digests, newPoints, hf, pk, dataTranscript...)
+
+	return res, err
+
+}
+
+// BatchVerify uses a proof to check that each digest digests[i] is correctly opened on the set points[i].
+// The digests are the commitments to the folded underlying polynomials. The shplonk proof is
+// verified directly using the embedded shplonk proof. This function only computes the consistency
+// between the claimed values of the underlying shplonk proof and the outer claimed values, using the fft-like
+// folding. Namely, the outer claimed values are the evaluation of the original polynomials (so before they
+// were folded) at the relevant powers of the points.
+func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
+
+	// step 0: consistency checks between the folded claimed values of shplonk and the claimed
+	// values at the powers of the Sᵢ
+	for i := 0; i < len(proof.ClaimedValues); i++ {
+		sizeSi := len(proof.ClaimedValues[i][0])
+		for j := 1; j < len(proof.ClaimedValues[i]); j++ {
+			// each set of opening must be of the same size (opeings on powers of Si)
+			if sizeSi != len(proof.ClaimedValues[i][j]) {
+				return ErrNbPolynomialsNbPoints
+			}
+		}
+		currNbPolynomials := len(proof.ClaimedValues[i])
+		sizeSi = sizeSi * currNbPolynomials
+		// |originalPolynomials_{i}|x|Sᵢ| == |foldedPolynomials|x|folded Sᵢ|
+		if sizeSi != len(proof.SOpeningProof.ClaimedValues[i]) {
+			return ErrInconsistentNumberFoldedPoints
+		}
+	}
+
+	// step 1: fold the outer claimed values and check that they correspond to the
+	// shplonk claimed values
+	var curFoldedClaimedValue, omgeaiPoint fr.Element
+	for i := 0; i < len(proof.ClaimedValues); i++ {
+		t := len(proof.ClaimedValues[i])
+		omega, err := getIthRootOne(t)
+		if err != nil {
+			return err
+		}
+		sizeSi := len(proof.ClaimedValues[i][0])
+		polyClaimedValues := make([]fr.Element, t)
+		for j := 0; j < sizeSi; j++ {
+			for k := 0; k < t; k++ {
+				polyClaimedValues[k].Set(&proof.ClaimedValues[i][k][j])
+			}
+			omgeaiPoint.Set(&points[i][j])
+			for l := 0; l < t; l++ {
+				curFoldedClaimedValue = eval(polyClaimedValues, omgeaiPoint)
+				if !curFoldedClaimedValue.Equal(&proof.SOpeningProof.ClaimedValues[i][j*t+l]) {
+					return ErrInonsistentFolding
+				}
+				omgeaiPoint.Mul(&omgeaiPoint, &omega)
+			}
+		}
+	}
+
+	// step 2: verify the embedded shplonk proof
+	extendedPoints := make([][]fr.Element, len(points))
+	var err error
+	for i := 0; i < len(points); i++ {
+		t := len(proof.ClaimedValues[i])
+		extendedPoints[i], err = extendSet(points[i], t)
+		if err != nil {
+			return err
+		}
+	}
+	err = shplonk.BatchVerify(proof.SOpeningProof, digests, extendedPoints, hf, vk, dataTranscript...)
+
+	return nil
+}
+
+// utils
+
+// getGenFrStar returns a generator of Fr^{*}
+func getGenFrStar() fr.Element {
+	var res fr.Element
+
+	res.SetUint64(7)
+
+	return res
+}
+
+// getIthRootOne returns a generator of Z/iZ
+func getIthRootOne(i int) (fr.Element, error) {
+	var omega fr.Element
+	var tmpBigInt, zeroBigInt big.Int
+	oneBigInt := big.NewInt(1)
+	zeroBigInt.SetUint64(0)
+	rMinusOneBigInt := fr.Modulus()
+	rMinusOneBigInt.Sub(rMinusOneBigInt, oneBigInt)
+	tmpBigInt.SetUint64(uint64(i))
+	tmpBigInt.Mod(rMinusOneBigInt, &tmpBigInt)
+	if tmpBigInt.Cmp(&zeroBigInt) != 0 {
+		return omega, ErrRootsOne
+	}
+	genFrStar := getGenFrStar()
+	tmpBigInt.SetUint64(uint64(i))
+	tmpBigInt.Div(rMinusOneBigInt, &tmpBigInt)
+	omega.Exp(genFrStar, &tmpBigInt)
+	return omega, nil
+}
+
+// extendSet returns [p[0], ω p[0], .. ,ωᵗ⁻¹p[0],p[1],..,ωᵗ⁻¹p[1],..]
+func extendSet(p []fr.Element, t int) ([]fr.Element, error) {
+
+	omega, err := getIthRootOne(t)
+	if err != nil {
+		return nil, err
+	}
+	nbPoints := len(p)
+	newPoints := make([]fr.Element, t*nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		newPoints[i*t].Set(&p[i])
+		for k := 1; k < t; k++ {
+			newPoints[i*t+k].Mul(&newPoints[i*t+k-1], &omega)
+		}
+	}
+
+	return newPoints, nil
+}
+
+func eval(f []fr.Element, x fr.Element) fr.Element {
+	var y fr.Element
+	for i := len(f) - 1; i >= 0; i-- {
+		y.Mul(&y, &x).Add(&y, &f[i])
+	}
+	return y
+}
diff --git a/ecc/bls24-315/fflonk/fflonk_test.go b/ecc/bls24-315/fflonk/fflonk_test.go
new file mode 100644
index 0000000000..af7cc9faf7
--- /dev/null
+++ b/ecc/bls24-315/fflonk/fflonk_test.go
@@ -0,0 +1,141 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"crypto/sha256"
+	"math/big"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls24-315/kzg"
+	"github.com/stretchr/testify/require"
+)
+
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *kzg.SRS
+var bAlpha *big.Int
+
+func init() {
+	const srsSize = 400
+	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+}
+
+func TestFflonk(t *testing.T) {
+
+	assert := require.New(t)
+
+	// sample random polynomials of various sizes
+	nbSets := 5
+	p := make([][][]fr.Element, nbSets)
+	for i := 0; i < nbSets; i++ {
+		nbPolysInSet := 9
+		p[i] = make([][]fr.Element, nbPolysInSet)
+		for j := 0; j < nbPolysInSet; j++ {
+			curSizePoly := j + 10
+			p[i][j] = make([]fr.Element, curSizePoly)
+			for k := 0; k < curSizePoly; k++ {
+				p[i][j][k].SetRandom()
+			}
+		}
+	}
+
+	// sample random sets Sᵢ
+	x := make([][]fr.Element, nbSets)
+	for i := 0; i < nbSets; i++ {
+		curSetSize := i + 4
+		x[i] = make([]fr.Element, curSetSize)
+		for j := 0; j < curSetSize; j++ {
+			x[i][j].SetRandom()
+		}
+	}
+
+	// commit to the folded polynomials
+	digests := make([]kzg.Digest, nbSets)
+	var err error
+	for i := 0; i < nbSets; i++ {
+		digests[i], err = CommitAndFold(p[i], testSrs.Pk)
+		assert.NoError(err)
+	}
+
+	// compute flonk opening proof
+	hf := sha256.New()
+	proof, err := BatchOpen(p, digests, x, hf, testSrs.Pk)
+	assert.NoError(err)
+
+	// check opening proof
+	err = BatchVerify(proof, digests, x, hf, testSrs.Vk)
+	assert.NoError(err)
+
+	// tamper the proof
+	proof.ClaimedValues[0][0][0].SetRandom()
+	err = BatchVerify(proof, digests, x, hf, testSrs.Vk)
+	assert.Error(err)
+
+}
+
+func TestCommit(t *testing.T) {
+
+	assert := require.New(t)
+
+	// sample polynomials
+	nbPolys := 2
+	p := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		p[i] = make([]fr.Element, i+10)
+		for j := 0; j < i+10; j++ {
+			p[i][j].SetRandom()
+		}
+	}
+
+	// fflonk commit to them
+	var x fr.Element
+	x.SetRandom()
+	proof, err := kzg.Open(Fold(p), x, testSrs.Pk)
+	assert.NoError(err)
+
+	// check that Open(C, x) = ∑_{i<t}Pᵢ(xᵗ)xⁱ
+	var xt fr.Element
+	var expo big.Int
+	expo.SetUint64(uint64(nbPolys))
+	xt.Exp(x, &expo)
+	px := make([]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		px[i] = eval(p[i], xt)
+	}
+	y := eval(px, x)
+	assert.True(y.Equal(&proof.ClaimedValue))
+}
+
+func TestGetIthRootOne(t *testing.T) {
+
+	assert := require.New(t)
+
+	order := 9
+	omega, err := getIthRootOne(order)
+	assert.NoError(err)
+	var orderBigInt big.Int
+	orderBigInt.SetUint64(uint64(order))
+	omega.Exp(omega, &orderBigInt)
+	assert.True(omega.IsOne())
+
+	order = 7
+	_, err = getIthRootOne(order)
+	assert.Error(err)
+}
diff --git a/ecc/bls24-317/fflonk/doc.go b/ecc/bls24-317/fflonk/doc.go
new file mode 100644
index 0000000000..694eaa9734
--- /dev/null
+++ b/ecc/bls24-317/fflonk/doc.go
@@ -0,0 +1,21 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// Package fflonk provides fflonk commitment, based on shplonk.
+//
+// See https://eprint.iacr.org/2020/081.pdf for shplonk
+// See https://eprint.iacr.org/2021/1167.pdf for fflonk.
+package fflonk
diff --git a/ecc/bls24-317/fflonk/fflonk.go b/ecc/bls24-317/fflonk/fflonk.go
new file mode 100644
index 0000000000..37d6bbf592
--- /dev/null
+++ b/ecc/bls24-317/fflonk/fflonk.go
@@ -0,0 +1,267 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"errors"
+	"hash"
+	"math/big"
+
+	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls24-317/kzg"
+	"github.com/consensys/gnark-crypto/ecc/bls24-317/shplonk"
+)
+
+var (
+	ErrRootsOne                       = errors.New("Fr does not contain all the t-th roots of 1")
+	ErrNbPolynomialsNbPoints          = errors.New("the number of packs of polynomials should be the same as the number of pack of points")
+	ErrInonsistentFolding             = errors.New("the outer claimed values are not consistent with the shplonk proof")
+	ErrInconsistentNumberFoldedPoints = errors.New("the number of outer claimed values is inconsistent with the number of claimed values in the shplonk proof")
+)
+
+// Opening fflonk proof for opening a list of list of polynomials ((fʲᵢ)ᵢ)ⱼ where each
+// pack of polynomials (fʲᵢ)ᵢ (the pack is indexed by j) is opened on a powers of elements in
+// the set Sʲ (indexed by j), where the power is |(fʲᵢ)ᵢ|.
+//
+// implements io.ReaderFrom and io.WriterTo
+type OpeningProof struct {
+
+	// shplonk opening proof of the folded polynomials
+	SOpeningProof shplonk.OpeningProof
+
+	// ClaimedValues ClaimedValues[i][j] contains the values
+	// of fʲᵢ on Sⱼ^{|(fʲᵢ)ᵢ|}
+	ClaimedValues [][][]fr.Element
+}
+
+// CommitAndFold commits to a list of polynomial by intertwinning them like in the FFT, that is
+// returns ∑_{i<t}Pᵢ(Xᵗ)Xⁱ for t polynomials
+func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
+	buf := Fold(p)
+	com, err := kzg.Commit(buf, pk, nbTasks...)
+	return com, err
+}
+
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ
+func Fold(p [][]fr.Element) []fr.Element {
+	t := len(p)
+	sizeResult := 0
+	for i := range p {
+		if sizeResult < len(p[i]) {
+			sizeResult = len(p[i])
+		}
+	}
+	sizeResult = sizeResult*len(p) + len(p) - 1
+	buf := make([]fr.Element, sizeResult)
+	for i := range p {
+		for j := range p[i] {
+			buf[j*t+i].Set(&p[i][j])
+		}
+	}
+	return buf
+}
+
+// BatchOpen computes a batch opening proof of p (the (fʲᵢ)ᵢ ) on powers of points (the ((Sʲᵢ)ᵢ)ⱼ).
+// The j-th pack of polynomials is opened on the power |(fʲᵢ)ᵢ| of (Sʲᵢ)ᵢ.
+// digests is the list (CommitAndFold(p[i]))ᵢ. It is assumed that the list has been computed beforehand
+// and provided as an input to not duplicate computations.
+func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
+
+	var res OpeningProof
+
+	if len(p) != len(points) {
+		return res, ErrNbPolynomialsNbPoints
+	}
+
+	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
+	nbPolysPerPack := make([]int, len(p))
+	for i := 0; i < len(p); i++ {
+		nbPolysPerPack[i] = len(p[i])
+	}
+	pointsPowerM := make([][]fr.Element, len(points))
+	var tmpBigInt big.Int
+	for i := 0; i < len(p); i++ {
+		tmpBigInt.SetUint64(uint64(nbPolysPerPack[i]))
+		pointsPowerM[i] = make([]fr.Element, len(points[i]))
+		for j := 0; j < len(points[i]); j++ {
+			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
+		}
+	}
+
+	// step 1: compute the claimed values, that is the evaluations of the polynomials
+	// on the relevant powers of the sets
+	res.ClaimedValues = make([][][]fr.Element, len(p))
+	for i := 0; i < len(p); i++ {
+		res.ClaimedValues[i] = make([][]fr.Element, len(p[i]))
+		for j := 0; j < len(p[i]); j++ {
+			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
+			for k := 0; k < len(points[i]); k++ {
+				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
+			}
+		}
+	}
+
+	// step 2: fold polynomials
+	foldedPolynomials := make([][]fr.Element, len(p))
+	for i := 0; i < len(p); i++ {
+		foldedPolynomials[i] = Fold(p[i])
+	}
+
+	// step 4: compute the associated roots, that is for each point p corresponding
+	// to a pack i of polynomials, we extend to <p, ω p, .., ωᵗ⁻¹p> if
+	// the i-th pack contains t polynomials where ω is a t-th root of 1
+	newPoints := make([][]fr.Element, len(points))
+	var err error
+	for i := 0; i < len(p); i++ {
+		t := len(p[i])
+		newPoints[i], err = extendSet(points[i], t)
+		if err != nil {
+			return res, err
+		}
+	}
+
+	// step 5: shplonk open the list of single polynomials on the new sets
+	res.SOpeningProof, err = shplonk.BatchOpen(foldedPolynomials, digests, newPoints, hf, pk, dataTranscript...)
+
+	return res, err
+
+}
+
+// BatchVerify uses a proof to check that each digest digests[i] is correctly opened on the set points[i].
+// The digests are the commitments to the folded underlying polynomials. The shplonk proof is
+// verified directly using the embedded shplonk proof. This function only computes the consistency
+// between the claimed values of the underlying shplonk proof and the outer claimed values, using the fft-like
+// folding. Namely, the outer claimed values are the evaluation of the original polynomials (so before they
+// were folded) at the relevant powers of the points.
+func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
+
+	// step 0: consistency checks between the folded claimed values of shplonk and the claimed
+	// values at the powers of the Sᵢ
+	for i := 0; i < len(proof.ClaimedValues); i++ {
+		sizeSi := len(proof.ClaimedValues[i][0])
+		for j := 1; j < len(proof.ClaimedValues[i]); j++ {
+			// each set of opening must be of the same size (opeings on powers of Si)
+			if sizeSi != len(proof.ClaimedValues[i][j]) {
+				return ErrNbPolynomialsNbPoints
+			}
+		}
+		currNbPolynomials := len(proof.ClaimedValues[i])
+		sizeSi = sizeSi * currNbPolynomials
+		// |originalPolynomials_{i}|x|Sᵢ| == |foldedPolynomials|x|folded Sᵢ|
+		if sizeSi != len(proof.SOpeningProof.ClaimedValues[i]) {
+			return ErrInconsistentNumberFoldedPoints
+		}
+	}
+
+	// step 1: fold the outer claimed values and check that they correspond to the
+	// shplonk claimed values
+	var curFoldedClaimedValue, omgeaiPoint fr.Element
+	for i := 0; i < len(proof.ClaimedValues); i++ {
+		t := len(proof.ClaimedValues[i])
+		omega, err := getIthRootOne(t)
+		if err != nil {
+			return err
+		}
+		sizeSi := len(proof.ClaimedValues[i][0])
+		polyClaimedValues := make([]fr.Element, t)
+		for j := 0; j < sizeSi; j++ {
+			for k := 0; k < t; k++ {
+				polyClaimedValues[k].Set(&proof.ClaimedValues[i][k][j])
+			}
+			omgeaiPoint.Set(&points[i][j])
+			for l := 0; l < t; l++ {
+				curFoldedClaimedValue = eval(polyClaimedValues, omgeaiPoint)
+				if !curFoldedClaimedValue.Equal(&proof.SOpeningProof.ClaimedValues[i][j*t+l]) {
+					return ErrInonsistentFolding
+				}
+				omgeaiPoint.Mul(&omgeaiPoint, &omega)
+			}
+		}
+	}
+
+	// step 2: verify the embedded shplonk proof
+	extendedPoints := make([][]fr.Element, len(points))
+	var err error
+	for i := 0; i < len(points); i++ {
+		t := len(proof.ClaimedValues[i])
+		extendedPoints[i], err = extendSet(points[i], t)
+		if err != nil {
+			return err
+		}
+	}
+	err = shplonk.BatchVerify(proof.SOpeningProof, digests, extendedPoints, hf, vk, dataTranscript...)
+
+	return nil
+}
+
+// utils
+
+// getGenFrStar returns a generator of Fr^{*}
+func getGenFrStar() fr.Element {
+	var res fr.Element
+
+	res.SetUint64(7)
+
+	return res
+}
+
+// getIthRootOne returns a generator of Z/iZ
+func getIthRootOne(i int) (fr.Element, error) {
+	var omega fr.Element
+	var tmpBigInt, zeroBigInt big.Int
+	oneBigInt := big.NewInt(1)
+	zeroBigInt.SetUint64(0)
+	rMinusOneBigInt := fr.Modulus()
+	rMinusOneBigInt.Sub(rMinusOneBigInt, oneBigInt)
+	tmpBigInt.SetUint64(uint64(i))
+	tmpBigInt.Mod(rMinusOneBigInt, &tmpBigInt)
+	if tmpBigInt.Cmp(&zeroBigInt) != 0 {
+		return omega, ErrRootsOne
+	}
+	genFrStar := getGenFrStar()
+	tmpBigInt.SetUint64(uint64(i))
+	tmpBigInt.Div(rMinusOneBigInt, &tmpBigInt)
+	omega.Exp(genFrStar, &tmpBigInt)
+	return omega, nil
+}
+
+// extendSet returns [p[0], ω p[0], .. ,ωᵗ⁻¹p[0],p[1],..,ωᵗ⁻¹p[1],..]
+func extendSet(p []fr.Element, t int) ([]fr.Element, error) {
+
+	omega, err := getIthRootOne(t)
+	if err != nil {
+		return nil, err
+	}
+	nbPoints := len(p)
+	newPoints := make([]fr.Element, t*nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		newPoints[i*t].Set(&p[i])
+		for k := 1; k < t; k++ {
+			newPoints[i*t+k].Mul(&newPoints[i*t+k-1], &omega)
+		}
+	}
+
+	return newPoints, nil
+}
+
+func eval(f []fr.Element, x fr.Element) fr.Element {
+	var y fr.Element
+	for i := len(f) - 1; i >= 0; i-- {
+		y.Mul(&y, &x).Add(&y, &f[i])
+	}
+	return y
+}
diff --git a/ecc/bls24-317/fflonk/fflonk_test.go b/ecc/bls24-317/fflonk/fflonk_test.go
new file mode 100644
index 0000000000..5d964e4fda
--- /dev/null
+++ b/ecc/bls24-317/fflonk/fflonk_test.go
@@ -0,0 +1,141 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"crypto/sha256"
+	"math/big"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls24-317/kzg"
+	"github.com/stretchr/testify/require"
+)
+
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *kzg.SRS
+var bAlpha *big.Int
+
+func init() {
+	const srsSize = 400
+	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+}
+
+func TestFflonk(t *testing.T) {
+
+	assert := require.New(t)
+
+	// sample random polynomials of various sizes
+	nbSets := 5
+	p := make([][][]fr.Element, nbSets)
+	for i := 0; i < nbSets; i++ {
+		nbPolysInSet := 9
+		p[i] = make([][]fr.Element, nbPolysInSet)
+		for j := 0; j < nbPolysInSet; j++ {
+			curSizePoly := j + 10
+			p[i][j] = make([]fr.Element, curSizePoly)
+			for k := 0; k < curSizePoly; k++ {
+				p[i][j][k].SetRandom()
+			}
+		}
+	}
+
+	// sample random sets Sᵢ
+	x := make([][]fr.Element, nbSets)
+	for i := 0; i < nbSets; i++ {
+		curSetSize := i + 4
+		x[i] = make([]fr.Element, curSetSize)
+		for j := 0; j < curSetSize; j++ {
+			x[i][j].SetRandom()
+		}
+	}
+
+	// commit to the folded polynomials
+	digests := make([]kzg.Digest, nbSets)
+	var err error
+	for i := 0; i < nbSets; i++ {
+		digests[i], err = CommitAndFold(p[i], testSrs.Pk)
+		assert.NoError(err)
+	}
+
+	// compute flonk opening proof
+	hf := sha256.New()
+	proof, err := BatchOpen(p, digests, x, hf, testSrs.Pk)
+	assert.NoError(err)
+
+	// check opening proof
+	err = BatchVerify(proof, digests, x, hf, testSrs.Vk)
+	assert.NoError(err)
+
+	// tamper the proof
+	proof.ClaimedValues[0][0][0].SetRandom()
+	err = BatchVerify(proof, digests, x, hf, testSrs.Vk)
+	assert.Error(err)
+
+}
+
+func TestCommit(t *testing.T) {
+
+	assert := require.New(t)
+
+	// sample polynomials
+	nbPolys := 2
+	p := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		p[i] = make([]fr.Element, i+10)
+		for j := 0; j < i+10; j++ {
+			p[i][j].SetRandom()
+		}
+	}
+
+	// fflonk commit to them
+	var x fr.Element
+	x.SetRandom()
+	proof, err := kzg.Open(Fold(p), x, testSrs.Pk)
+	assert.NoError(err)
+
+	// check that Open(C, x) = ∑_{i<t}Pᵢ(xᵗ)xⁱ
+	var xt fr.Element
+	var expo big.Int
+	expo.SetUint64(uint64(nbPolys))
+	xt.Exp(x, &expo)
+	px := make([]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		px[i] = eval(p[i], xt)
+	}
+	y := eval(px, x)
+	assert.True(y.Equal(&proof.ClaimedValue))
+}
+
+func TestGetIthRootOne(t *testing.T) {
+
+	assert := require.New(t)
+
+	order := 9
+	omega, err := getIthRootOne(order)
+	assert.NoError(err)
+	var orderBigInt big.Int
+	orderBigInt.SetUint64(uint64(order))
+	omega.Exp(omega, &orderBigInt)
+	assert.True(omega.IsOne())
+
+	order = 7
+	_, err = getIthRootOne(order)
+	assert.Error(err)
+}
diff --git a/ecc/bn254/fflonk/doc.go b/ecc/bn254/fflonk/doc.go
new file mode 100644
index 0000000000..694eaa9734
--- /dev/null
+++ b/ecc/bn254/fflonk/doc.go
@@ -0,0 +1,21 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// Package fflonk provides fflonk commitment, based on shplonk.
+//
+// See https://eprint.iacr.org/2020/081.pdf for shplonk
+// See https://eprint.iacr.org/2021/1167.pdf for fflonk.
+package fflonk
diff --git a/ecc/bn254/fflonk/fflonk.go b/ecc/bn254/fflonk/fflonk.go
index 3f8533e51b..9062a8d2ca 100644
--- a/ecc/bn254/fflonk/fflonk.go
+++ b/ecc/bn254/fflonk/fflonk.go
@@ -1,3 +1,19 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
 package fflonk
 
 import (
@@ -197,7 +213,9 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 // getGenFrStar returns a generator of Fr^{*}
 func getGenFrStar() fr.Element {
 	var res fr.Element
+
 	res.SetUint64(5)
+
 	return res
 }
 
diff --git a/ecc/bn254/fflonk/fflonk_test.go b/ecc/bn254/fflonk/fflonk_test.go
index e5409a602a..c04a66ae2d 100644
--- a/ecc/bn254/fflonk/fflonk_test.go
+++ b/ecc/bn254/fflonk/fflonk_test.go
@@ -1,3 +1,19 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
 package fflonk
 
 import (
diff --git a/ecc/bw6-633/fflonk/doc.go b/ecc/bw6-633/fflonk/doc.go
new file mode 100644
index 0000000000..694eaa9734
--- /dev/null
+++ b/ecc/bw6-633/fflonk/doc.go
@@ -0,0 +1,21 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// Package fflonk provides fflonk commitment, based on shplonk.
+//
+// See https://eprint.iacr.org/2020/081.pdf for shplonk
+// See https://eprint.iacr.org/2021/1167.pdf for fflonk.
+package fflonk
diff --git a/ecc/bw6-633/fflonk/fflonk.go b/ecc/bw6-633/fflonk/fflonk.go
new file mode 100644
index 0000000000..fe88556e0e
--- /dev/null
+++ b/ecc/bw6-633/fflonk/fflonk.go
@@ -0,0 +1,267 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"errors"
+	"hash"
+	"math/big"
+
+	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
+	"github.com/consensys/gnark-crypto/ecc/bw6-633/kzg"
+	"github.com/consensys/gnark-crypto/ecc/bw6-633/shplonk"
+)
+
+var (
+	ErrRootsOne                       = errors.New("Fr does not contain all the t-th roots of 1")
+	ErrNbPolynomialsNbPoints          = errors.New("the number of packs of polynomials should be the same as the number of pack of points")
+	ErrInonsistentFolding             = errors.New("the outer claimed values are not consistent with the shplonk proof")
+	ErrInconsistentNumberFoldedPoints = errors.New("the number of outer claimed values is inconsistent with the number of claimed values in the shplonk proof")
+)
+
+// Opening fflonk proof for opening a list of list of polynomials ((fʲᵢ)ᵢ)ⱼ where each
+// pack of polynomials (fʲᵢ)ᵢ (the pack is indexed by j) is opened on a powers of elements in
+// the set Sʲ (indexed by j), where the power is |(fʲᵢ)ᵢ|.
+//
+// implements io.ReaderFrom and io.WriterTo
+type OpeningProof struct {
+
+	// shplonk opening proof of the folded polynomials
+	SOpeningProof shplonk.OpeningProof
+
+	// ClaimedValues ClaimedValues[i][j] contains the values
+	// of fʲᵢ on Sⱼ^{|(fʲᵢ)ᵢ|}
+	ClaimedValues [][][]fr.Element
+}
+
+// CommitAndFold commits to a list of polynomial by intertwinning them like in the FFT, that is
+// returns ∑_{i<t}Pᵢ(Xᵗ)Xⁱ for t polynomials
+func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
+	buf := Fold(p)
+	com, err := kzg.Commit(buf, pk, nbTasks...)
+	return com, err
+}
+
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ
+func Fold(p [][]fr.Element) []fr.Element {
+	t := len(p)
+	sizeResult := 0
+	for i := range p {
+		if sizeResult < len(p[i]) {
+			sizeResult = len(p[i])
+		}
+	}
+	sizeResult = sizeResult*len(p) + len(p) - 1
+	buf := make([]fr.Element, sizeResult)
+	for i := range p {
+		for j := range p[i] {
+			buf[j*t+i].Set(&p[i][j])
+		}
+	}
+	return buf
+}
+
+// BatchOpen computes a batch opening proof of p (the (fʲᵢ)ᵢ ) on powers of points (the ((Sʲᵢ)ᵢ)ⱼ).
+// The j-th pack of polynomials is opened on the power |(fʲᵢ)ᵢ| of (Sʲᵢ)ᵢ.
+// digests is the list (CommitAndFold(p[i]))ᵢ. It is assumed that the list has been computed beforehand
+// and provided as an input to not duplicate computations.
+func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
+
+	var res OpeningProof
+
+	if len(p) != len(points) {
+		return res, ErrNbPolynomialsNbPoints
+	}
+
+	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
+	nbPolysPerPack := make([]int, len(p))
+	for i := 0; i < len(p); i++ {
+		nbPolysPerPack[i] = len(p[i])
+	}
+	pointsPowerM := make([][]fr.Element, len(points))
+	var tmpBigInt big.Int
+	for i := 0; i < len(p); i++ {
+		tmpBigInt.SetUint64(uint64(nbPolysPerPack[i]))
+		pointsPowerM[i] = make([]fr.Element, len(points[i]))
+		for j := 0; j < len(points[i]); j++ {
+			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
+		}
+	}
+
+	// step 1: compute the claimed values, that is the evaluations of the polynomials
+	// on the relevant powers of the sets
+	res.ClaimedValues = make([][][]fr.Element, len(p))
+	for i := 0; i < len(p); i++ {
+		res.ClaimedValues[i] = make([][]fr.Element, len(p[i]))
+		for j := 0; j < len(p[i]); j++ {
+			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
+			for k := 0; k < len(points[i]); k++ {
+				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
+			}
+		}
+	}
+
+	// step 2: fold polynomials
+	foldedPolynomials := make([][]fr.Element, len(p))
+	for i := 0; i < len(p); i++ {
+		foldedPolynomials[i] = Fold(p[i])
+	}
+
+	// step 4: compute the associated roots, that is for each point p corresponding
+	// to a pack i of polynomials, we extend to <p, ω p, .., ωᵗ⁻¹p> if
+	// the i-th pack contains t polynomials where ω is a t-th root of 1
+	newPoints := make([][]fr.Element, len(points))
+	var err error
+	for i := 0; i < len(p); i++ {
+		t := len(p[i])
+		newPoints[i], err = extendSet(points[i], t)
+		if err != nil {
+			return res, err
+		}
+	}
+
+	// step 5: shplonk open the list of single polynomials on the new sets
+	res.SOpeningProof, err = shplonk.BatchOpen(foldedPolynomials, digests, newPoints, hf, pk, dataTranscript...)
+
+	return res, err
+
+}
+
+// BatchVerify uses a proof to check that each digest digests[i] is correctly opened on the set points[i].
+// The digests are the commitments to the folded underlying polynomials. The shplonk proof is
+// verified directly using the embedded shplonk proof. This function only computes the consistency
+// between the claimed values of the underlying shplonk proof and the outer claimed values, using the fft-like
+// folding. Namely, the outer claimed values are the evaluation of the original polynomials (so before they
+// were folded) at the relevant powers of the points.
+func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
+
+	// step 0: consistency checks between the folded claimed values of shplonk and the claimed
+	// values at the powers of the Sᵢ
+	for i := 0; i < len(proof.ClaimedValues); i++ {
+		sizeSi := len(proof.ClaimedValues[i][0])
+		for j := 1; j < len(proof.ClaimedValues[i]); j++ {
+			// each set of opening must be of the same size (opeings on powers of Si)
+			if sizeSi != len(proof.ClaimedValues[i][j]) {
+				return ErrNbPolynomialsNbPoints
+			}
+		}
+		currNbPolynomials := len(proof.ClaimedValues[i])
+		sizeSi = sizeSi * currNbPolynomials
+		// |originalPolynomials_{i}|x|Sᵢ| == |foldedPolynomials|x|folded Sᵢ|
+		if sizeSi != len(proof.SOpeningProof.ClaimedValues[i]) {
+			return ErrInconsistentNumberFoldedPoints
+		}
+	}
+
+	// step 1: fold the outer claimed values and check that they correspond to the
+	// shplonk claimed values
+	var curFoldedClaimedValue, omgeaiPoint fr.Element
+	for i := 0; i < len(proof.ClaimedValues); i++ {
+		t := len(proof.ClaimedValues[i])
+		omega, err := getIthRootOne(t)
+		if err != nil {
+			return err
+		}
+		sizeSi := len(proof.ClaimedValues[i][0])
+		polyClaimedValues := make([]fr.Element, t)
+		for j := 0; j < sizeSi; j++ {
+			for k := 0; k < t; k++ {
+				polyClaimedValues[k].Set(&proof.ClaimedValues[i][k][j])
+			}
+			omgeaiPoint.Set(&points[i][j])
+			for l := 0; l < t; l++ {
+				curFoldedClaimedValue = eval(polyClaimedValues, omgeaiPoint)
+				if !curFoldedClaimedValue.Equal(&proof.SOpeningProof.ClaimedValues[i][j*t+l]) {
+					return ErrInonsistentFolding
+				}
+				omgeaiPoint.Mul(&omgeaiPoint, &omega)
+			}
+		}
+	}
+
+	// step 2: verify the embedded shplonk proof
+	extendedPoints := make([][]fr.Element, len(points))
+	var err error
+	for i := 0; i < len(points); i++ {
+		t := len(proof.ClaimedValues[i])
+		extendedPoints[i], err = extendSet(points[i], t)
+		if err != nil {
+			return err
+		}
+	}
+	err = shplonk.BatchVerify(proof.SOpeningProof, digests, extendedPoints, hf, vk, dataTranscript...)
+
+	return nil
+}
+
+// utils
+
+// getGenFrStar returns a generator of Fr^{*}
+func getGenFrStar() fr.Element {
+	var res fr.Element
+
+	res.SetUint64(13)
+
+	return res
+}
+
+// getIthRootOne returns a generator of Z/iZ
+func getIthRootOne(i int) (fr.Element, error) {
+	var omega fr.Element
+	var tmpBigInt, zeroBigInt big.Int
+	oneBigInt := big.NewInt(1)
+	zeroBigInt.SetUint64(0)
+	rMinusOneBigInt := fr.Modulus()
+	rMinusOneBigInt.Sub(rMinusOneBigInt, oneBigInt)
+	tmpBigInt.SetUint64(uint64(i))
+	tmpBigInt.Mod(rMinusOneBigInt, &tmpBigInt)
+	if tmpBigInt.Cmp(&zeroBigInt) != 0 {
+		return omega, ErrRootsOne
+	}
+	genFrStar := getGenFrStar()
+	tmpBigInt.SetUint64(uint64(i))
+	tmpBigInt.Div(rMinusOneBigInt, &tmpBigInt)
+	omega.Exp(genFrStar, &tmpBigInt)
+	return omega, nil
+}
+
+// extendSet returns [p[0], ω p[0], .. ,ωᵗ⁻¹p[0],p[1],..,ωᵗ⁻¹p[1],..]
+func extendSet(p []fr.Element, t int) ([]fr.Element, error) {
+
+	omega, err := getIthRootOne(t)
+	if err != nil {
+		return nil, err
+	}
+	nbPoints := len(p)
+	newPoints := make([]fr.Element, t*nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		newPoints[i*t].Set(&p[i])
+		for k := 1; k < t; k++ {
+			newPoints[i*t+k].Mul(&newPoints[i*t+k-1], &omega)
+		}
+	}
+
+	return newPoints, nil
+}
+
+func eval(f []fr.Element, x fr.Element) fr.Element {
+	var y fr.Element
+	for i := len(f) - 1; i >= 0; i-- {
+		y.Mul(&y, &x).Add(&y, &f[i])
+	}
+	return y
+}
diff --git a/ecc/bw6-633/fflonk/fflonk_test.go b/ecc/bw6-633/fflonk/fflonk_test.go
new file mode 100644
index 0000000000..1d031a6929
--- /dev/null
+++ b/ecc/bw6-633/fflonk/fflonk_test.go
@@ -0,0 +1,141 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"crypto/sha256"
+	"math/big"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
+	"github.com/consensys/gnark-crypto/ecc/bw6-633/kzg"
+	"github.com/stretchr/testify/require"
+)
+
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *kzg.SRS
+var bAlpha *big.Int
+
+func init() {
+	const srsSize = 400
+	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+}
+
+func TestFflonk(t *testing.T) {
+
+	assert := require.New(t)
+
+	// sample random polynomials of various sizes
+	nbSets := 5
+	p := make([][][]fr.Element, nbSets)
+	for i := 0; i < nbSets; i++ {
+		nbPolysInSet := 9
+		p[i] = make([][]fr.Element, nbPolysInSet)
+		for j := 0; j < nbPolysInSet; j++ {
+			curSizePoly := j + 10
+			p[i][j] = make([]fr.Element, curSizePoly)
+			for k := 0; k < curSizePoly; k++ {
+				p[i][j][k].SetRandom()
+			}
+		}
+	}
+
+	// sample random sets Sᵢ
+	x := make([][]fr.Element, nbSets)
+	for i := 0; i < nbSets; i++ {
+		curSetSize := i + 4
+		x[i] = make([]fr.Element, curSetSize)
+		for j := 0; j < curSetSize; j++ {
+			x[i][j].SetRandom()
+		}
+	}
+
+	// commit to the folded polynomials
+	digests := make([]kzg.Digest, nbSets)
+	var err error
+	for i := 0; i < nbSets; i++ {
+		digests[i], err = CommitAndFold(p[i], testSrs.Pk)
+		assert.NoError(err)
+	}
+
+	// compute flonk opening proof
+	hf := sha256.New()
+	proof, err := BatchOpen(p, digests, x, hf, testSrs.Pk)
+	assert.NoError(err)
+
+	// check opening proof
+	err = BatchVerify(proof, digests, x, hf, testSrs.Vk)
+	assert.NoError(err)
+
+	// tamper the proof
+	proof.ClaimedValues[0][0][0].SetRandom()
+	err = BatchVerify(proof, digests, x, hf, testSrs.Vk)
+	assert.Error(err)
+
+}
+
+func TestCommit(t *testing.T) {
+
+	assert := require.New(t)
+
+	// sample polynomials
+	nbPolys := 2
+	p := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		p[i] = make([]fr.Element, i+10)
+		for j := 0; j < i+10; j++ {
+			p[i][j].SetRandom()
+		}
+	}
+
+	// fflonk commit to them
+	var x fr.Element
+	x.SetRandom()
+	proof, err := kzg.Open(Fold(p), x, testSrs.Pk)
+	assert.NoError(err)
+
+	// check that Open(C, x) = ∑_{i<t}Pᵢ(xᵗ)xⁱ
+	var xt fr.Element
+	var expo big.Int
+	expo.SetUint64(uint64(nbPolys))
+	xt.Exp(x, &expo)
+	px := make([]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		px[i] = eval(p[i], xt)
+	}
+	y := eval(px, x)
+	assert.True(y.Equal(&proof.ClaimedValue))
+}
+
+func TestGetIthRootOne(t *testing.T) {
+
+	assert := require.New(t)
+
+	order := 9
+	omega, err := getIthRootOne(order)
+	assert.NoError(err)
+	var orderBigInt big.Int
+	orderBigInt.SetUint64(uint64(order))
+	omega.Exp(omega, &orderBigInt)
+	assert.True(omega.IsOne())
+
+	order = 7
+	_, err = getIthRootOne(order)
+	assert.Error(err)
+}
diff --git a/ecc/bw6-756/fflonk/doc.go b/ecc/bw6-756/fflonk/doc.go
new file mode 100644
index 0000000000..694eaa9734
--- /dev/null
+++ b/ecc/bw6-756/fflonk/doc.go
@@ -0,0 +1,21 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// Package fflonk provides fflonk commitment, based on shplonk.
+//
+// See https://eprint.iacr.org/2020/081.pdf for shplonk
+// See https://eprint.iacr.org/2021/1167.pdf for fflonk.
+package fflonk
diff --git a/ecc/bw6-756/fflonk/fflonk.go b/ecc/bw6-756/fflonk/fflonk.go
new file mode 100644
index 0000000000..5942714f18
--- /dev/null
+++ b/ecc/bw6-756/fflonk/fflonk.go
@@ -0,0 +1,267 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"errors"
+	"hash"
+	"math/big"
+
+	"github.com/consensys/gnark-crypto/ecc/bw6-756/fr"
+	"github.com/consensys/gnark-crypto/ecc/bw6-756/kzg"
+	"github.com/consensys/gnark-crypto/ecc/bw6-756/shplonk"
+)
+
+var (
+	ErrRootsOne                       = errors.New("Fr does not contain all the t-th roots of 1")
+	ErrNbPolynomialsNbPoints          = errors.New("the number of packs of polynomials should be the same as the number of pack of points")
+	ErrInonsistentFolding             = errors.New("the outer claimed values are not consistent with the shplonk proof")
+	ErrInconsistentNumberFoldedPoints = errors.New("the number of outer claimed values is inconsistent with the number of claimed values in the shplonk proof")
+)
+
+// Opening fflonk proof for opening a list of list of polynomials ((fʲᵢ)ᵢ)ⱼ where each
+// pack of polynomials (fʲᵢ)ᵢ (the pack is indexed by j) is opened on a powers of elements in
+// the set Sʲ (indexed by j), where the power is |(fʲᵢ)ᵢ|.
+//
+// implements io.ReaderFrom and io.WriterTo
+type OpeningProof struct {
+
+	// shplonk opening proof of the folded polynomials
+	SOpeningProof shplonk.OpeningProof
+
+	// ClaimedValues ClaimedValues[i][j] contains the values
+	// of fʲᵢ on Sⱼ^{|(fʲᵢ)ᵢ|}
+	ClaimedValues [][][]fr.Element
+}
+
+// CommitAndFold commits to a list of polynomial by intertwinning them like in the FFT, that is
+// returns ∑_{i<t}Pᵢ(Xᵗ)Xⁱ for t polynomials
+func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
+	buf := Fold(p)
+	com, err := kzg.Commit(buf, pk, nbTasks...)
+	return com, err
+}
+
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ
+func Fold(p [][]fr.Element) []fr.Element {
+	t := len(p)
+	sizeResult := 0
+	for i := range p {
+		if sizeResult < len(p[i]) {
+			sizeResult = len(p[i])
+		}
+	}
+	sizeResult = sizeResult*len(p) + len(p) - 1
+	buf := make([]fr.Element, sizeResult)
+	for i := range p {
+		for j := range p[i] {
+			buf[j*t+i].Set(&p[i][j])
+		}
+	}
+	return buf
+}
+
+// BatchOpen computes a batch opening proof of p (the (fʲᵢ)ᵢ ) on powers of points (the ((Sʲᵢ)ᵢ)ⱼ).
+// The j-th pack of polynomials is opened on the power |(fʲᵢ)ᵢ| of (Sʲᵢ)ᵢ.
+// digests is the list (CommitAndFold(p[i]))ᵢ. It is assumed that the list has been computed beforehand
+// and provided as an input to not duplicate computations.
+func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
+
+	var res OpeningProof
+
+	if len(p) != len(points) {
+		return res, ErrNbPolynomialsNbPoints
+	}
+
+	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
+	nbPolysPerPack := make([]int, len(p))
+	for i := 0; i < len(p); i++ {
+		nbPolysPerPack[i] = len(p[i])
+	}
+	pointsPowerM := make([][]fr.Element, len(points))
+	var tmpBigInt big.Int
+	for i := 0; i < len(p); i++ {
+		tmpBigInt.SetUint64(uint64(nbPolysPerPack[i]))
+		pointsPowerM[i] = make([]fr.Element, len(points[i]))
+		for j := 0; j < len(points[i]); j++ {
+			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
+		}
+	}
+
+	// step 1: compute the claimed values, that is the evaluations of the polynomials
+	// on the relevant powers of the sets
+	res.ClaimedValues = make([][][]fr.Element, len(p))
+	for i := 0; i < len(p); i++ {
+		res.ClaimedValues[i] = make([][]fr.Element, len(p[i]))
+		for j := 0; j < len(p[i]); j++ {
+			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
+			for k := 0; k < len(points[i]); k++ {
+				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
+			}
+		}
+	}
+
+	// step 2: fold polynomials
+	foldedPolynomials := make([][]fr.Element, len(p))
+	for i := 0; i < len(p); i++ {
+		foldedPolynomials[i] = Fold(p[i])
+	}
+
+	// step 4: compute the associated roots, that is for each point p corresponding
+	// to a pack i of polynomials, we extend to <p, ω p, .., ωᵗ⁻¹p> if
+	// the i-th pack contains t polynomials where ω is a t-th root of 1
+	newPoints := make([][]fr.Element, len(points))
+	var err error
+	for i := 0; i < len(p); i++ {
+		t := len(p[i])
+		newPoints[i], err = extendSet(points[i], t)
+		if err != nil {
+			return res, err
+		}
+	}
+
+	// step 5: shplonk open the list of single polynomials on the new sets
+	res.SOpeningProof, err = shplonk.BatchOpen(foldedPolynomials, digests, newPoints, hf, pk, dataTranscript...)
+
+	return res, err
+
+}
+
+// BatchVerify uses a proof to check that each digest digests[i] is correctly opened on the set points[i].
+// The digests are the commitments to the folded underlying polynomials. The shplonk proof is
+// verified directly using the embedded shplonk proof. This function only computes the consistency
+// between the claimed values of the underlying shplonk proof and the outer claimed values, using the fft-like
+// folding. Namely, the outer claimed values are the evaluation of the original polynomials (so before they
+// were folded) at the relevant powers of the points.
+func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
+
+	// step 0: consistency checks between the folded claimed values of shplonk and the claimed
+	// values at the powers of the Sᵢ
+	for i := 0; i < len(proof.ClaimedValues); i++ {
+		sizeSi := len(proof.ClaimedValues[i][0])
+		for j := 1; j < len(proof.ClaimedValues[i]); j++ {
+			// each set of opening must be of the same size (opeings on powers of Si)
+			if sizeSi != len(proof.ClaimedValues[i][j]) {
+				return ErrNbPolynomialsNbPoints
+			}
+		}
+		currNbPolynomials := len(proof.ClaimedValues[i])
+		sizeSi = sizeSi * currNbPolynomials
+		// |originalPolynomials_{i}|x|Sᵢ| == |foldedPolynomials|x|folded Sᵢ|
+		if sizeSi != len(proof.SOpeningProof.ClaimedValues[i]) {
+			return ErrInconsistentNumberFoldedPoints
+		}
+	}
+
+	// step 1: fold the outer claimed values and check that they correspond to the
+	// shplonk claimed values
+	var curFoldedClaimedValue, omgeaiPoint fr.Element
+	for i := 0; i < len(proof.ClaimedValues); i++ {
+		t := len(proof.ClaimedValues[i])
+		omega, err := getIthRootOne(t)
+		if err != nil {
+			return err
+		}
+		sizeSi := len(proof.ClaimedValues[i][0])
+		polyClaimedValues := make([]fr.Element, t)
+		for j := 0; j < sizeSi; j++ {
+			for k := 0; k < t; k++ {
+				polyClaimedValues[k].Set(&proof.ClaimedValues[i][k][j])
+			}
+			omgeaiPoint.Set(&points[i][j])
+			for l := 0; l < t; l++ {
+				curFoldedClaimedValue = eval(polyClaimedValues, omgeaiPoint)
+				if !curFoldedClaimedValue.Equal(&proof.SOpeningProof.ClaimedValues[i][j*t+l]) {
+					return ErrInonsistentFolding
+				}
+				omgeaiPoint.Mul(&omgeaiPoint, &omega)
+			}
+		}
+	}
+
+	// step 2: verify the embedded shplonk proof
+	extendedPoints := make([][]fr.Element, len(points))
+	var err error
+	for i := 0; i < len(points); i++ {
+		t := len(proof.ClaimedValues[i])
+		extendedPoints[i], err = extendSet(points[i], t)
+		if err != nil {
+			return err
+		}
+	}
+	err = shplonk.BatchVerify(proof.SOpeningProof, digests, extendedPoints, hf, vk, dataTranscript...)
+
+	return nil
+}
+
+// utils
+
+// getGenFrStar returns a generator of Fr^{*}
+func getGenFrStar() fr.Element {
+	var res fr.Element
+
+	res.SetUint64(5)
+
+	return res
+}
+
+// getIthRootOne returns a generator of Z/iZ
+func getIthRootOne(i int) (fr.Element, error) {
+	var omega fr.Element
+	var tmpBigInt, zeroBigInt big.Int
+	oneBigInt := big.NewInt(1)
+	zeroBigInt.SetUint64(0)
+	rMinusOneBigInt := fr.Modulus()
+	rMinusOneBigInt.Sub(rMinusOneBigInt, oneBigInt)
+	tmpBigInt.SetUint64(uint64(i))
+	tmpBigInt.Mod(rMinusOneBigInt, &tmpBigInt)
+	if tmpBigInt.Cmp(&zeroBigInt) != 0 {
+		return omega, ErrRootsOne
+	}
+	genFrStar := getGenFrStar()
+	tmpBigInt.SetUint64(uint64(i))
+	tmpBigInt.Div(rMinusOneBigInt, &tmpBigInt)
+	omega.Exp(genFrStar, &tmpBigInt)
+	return omega, nil
+}
+
+// extendSet returns [p[0], ω p[0], .. ,ωᵗ⁻¹p[0],p[1],..,ωᵗ⁻¹p[1],..]
+func extendSet(p []fr.Element, t int) ([]fr.Element, error) {
+
+	omega, err := getIthRootOne(t)
+	if err != nil {
+		return nil, err
+	}
+	nbPoints := len(p)
+	newPoints := make([]fr.Element, t*nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		newPoints[i*t].Set(&p[i])
+		for k := 1; k < t; k++ {
+			newPoints[i*t+k].Mul(&newPoints[i*t+k-1], &omega)
+		}
+	}
+
+	return newPoints, nil
+}
+
+func eval(f []fr.Element, x fr.Element) fr.Element {
+	var y fr.Element
+	for i := len(f) - 1; i >= 0; i-- {
+		y.Mul(&y, &x).Add(&y, &f[i])
+	}
+	return y
+}
diff --git a/ecc/bw6-756/fflonk/fflonk_test.go b/ecc/bw6-756/fflonk/fflonk_test.go
new file mode 100644
index 0000000000..d17a5372d2
--- /dev/null
+++ b/ecc/bw6-756/fflonk/fflonk_test.go
@@ -0,0 +1,141 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"crypto/sha256"
+	"math/big"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bw6-756/fr"
+	"github.com/consensys/gnark-crypto/ecc/bw6-756/kzg"
+	"github.com/stretchr/testify/require"
+)
+
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *kzg.SRS
+var bAlpha *big.Int
+
+func init() {
+	const srsSize = 400
+	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+}
+
+func TestFflonk(t *testing.T) {
+
+	assert := require.New(t)
+
+	// sample random polynomials of various sizes
+	nbSets := 5
+	p := make([][][]fr.Element, nbSets)
+	for i := 0; i < nbSets; i++ {
+		nbPolysInSet := 9
+		p[i] = make([][]fr.Element, nbPolysInSet)
+		for j := 0; j < nbPolysInSet; j++ {
+			curSizePoly := j + 10
+			p[i][j] = make([]fr.Element, curSizePoly)
+			for k := 0; k < curSizePoly; k++ {
+				p[i][j][k].SetRandom()
+			}
+		}
+	}
+
+	// sample random sets Sᵢ
+	x := make([][]fr.Element, nbSets)
+	for i := 0; i < nbSets; i++ {
+		curSetSize := i + 4
+		x[i] = make([]fr.Element, curSetSize)
+		for j := 0; j < curSetSize; j++ {
+			x[i][j].SetRandom()
+		}
+	}
+
+	// commit to the folded polynomials
+	digests := make([]kzg.Digest, nbSets)
+	var err error
+	for i := 0; i < nbSets; i++ {
+		digests[i], err = CommitAndFold(p[i], testSrs.Pk)
+		assert.NoError(err)
+	}
+
+	// compute flonk opening proof
+	hf := sha256.New()
+	proof, err := BatchOpen(p, digests, x, hf, testSrs.Pk)
+	assert.NoError(err)
+
+	// check opening proof
+	err = BatchVerify(proof, digests, x, hf, testSrs.Vk)
+	assert.NoError(err)
+
+	// tamper the proof
+	proof.ClaimedValues[0][0][0].SetRandom()
+	err = BatchVerify(proof, digests, x, hf, testSrs.Vk)
+	assert.Error(err)
+
+}
+
+func TestCommit(t *testing.T) {
+
+	assert := require.New(t)
+
+	// sample polynomials
+	nbPolys := 2
+	p := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		p[i] = make([]fr.Element, i+10)
+		for j := 0; j < i+10; j++ {
+			p[i][j].SetRandom()
+		}
+	}
+
+	// fflonk commit to them
+	var x fr.Element
+	x.SetRandom()
+	proof, err := kzg.Open(Fold(p), x, testSrs.Pk)
+	assert.NoError(err)
+
+	// check that Open(C, x) = ∑_{i<t}Pᵢ(xᵗ)xⁱ
+	var xt fr.Element
+	var expo big.Int
+	expo.SetUint64(uint64(nbPolys))
+	xt.Exp(x, &expo)
+	px := make([]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		px[i] = eval(p[i], xt)
+	}
+	y := eval(px, x)
+	assert.True(y.Equal(&proof.ClaimedValue))
+}
+
+func TestGetIthRootOne(t *testing.T) {
+
+	assert := require.New(t)
+
+	order := 9
+	omega, err := getIthRootOne(order)
+	assert.NoError(err)
+	var orderBigInt big.Int
+	orderBigInt.SetUint64(uint64(order))
+	omega.Exp(omega, &orderBigInt)
+	assert.True(omega.IsOne())
+
+	order = 7
+	_, err = getIthRootOne(order)
+	assert.Error(err)
+}
diff --git a/ecc/bw6-761/fflonk/doc.go b/ecc/bw6-761/fflonk/doc.go
new file mode 100644
index 0000000000..694eaa9734
--- /dev/null
+++ b/ecc/bw6-761/fflonk/doc.go
@@ -0,0 +1,21 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// Package fflonk provides fflonk commitment, based on shplonk.
+//
+// See https://eprint.iacr.org/2020/081.pdf for shplonk
+// See https://eprint.iacr.org/2021/1167.pdf for fflonk.
+package fflonk
diff --git a/ecc/bw6-761/fflonk/fflonk.go b/ecc/bw6-761/fflonk/fflonk.go
new file mode 100644
index 0000000000..1c760fea0d
--- /dev/null
+++ b/ecc/bw6-761/fflonk/fflonk.go
@@ -0,0 +1,267 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"errors"
+	"hash"
+	"math/big"
+
+	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
+	"github.com/consensys/gnark-crypto/ecc/bw6-761/kzg"
+	"github.com/consensys/gnark-crypto/ecc/bw6-761/shplonk"
+)
+
+var (
+	ErrRootsOne                       = errors.New("Fr does not contain all the t-th roots of 1")
+	ErrNbPolynomialsNbPoints          = errors.New("the number of packs of polynomials should be the same as the number of pack of points")
+	ErrInonsistentFolding             = errors.New("the outer claimed values are not consistent with the shplonk proof")
+	ErrInconsistentNumberFoldedPoints = errors.New("the number of outer claimed values is inconsistent with the number of claimed values in the shplonk proof")
+)
+
+// Opening fflonk proof for opening a list of list of polynomials ((fʲᵢ)ᵢ)ⱼ where each
+// pack of polynomials (fʲᵢ)ᵢ (the pack is indexed by j) is opened on a powers of elements in
+// the set Sʲ (indexed by j), where the power is |(fʲᵢ)ᵢ|.
+//
+// implements io.ReaderFrom and io.WriterTo
+type OpeningProof struct {
+
+	// shplonk opening proof of the folded polynomials
+	SOpeningProof shplonk.OpeningProof
+
+	// ClaimedValues ClaimedValues[i][j] contains the values
+	// of fʲᵢ on Sⱼ^{|(fʲᵢ)ᵢ|}
+	ClaimedValues [][][]fr.Element
+}
+
+// CommitAndFold commits to a list of polynomial by intertwinning them like in the FFT, that is
+// returns ∑_{i<t}Pᵢ(Xᵗ)Xⁱ for t polynomials
+func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
+	buf := Fold(p)
+	com, err := kzg.Commit(buf, pk, nbTasks...)
+	return com, err
+}
+
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ
+func Fold(p [][]fr.Element) []fr.Element {
+	t := len(p)
+	sizeResult := 0
+	for i := range p {
+		if sizeResult < len(p[i]) {
+			sizeResult = len(p[i])
+		}
+	}
+	sizeResult = sizeResult*len(p) + len(p) - 1
+	buf := make([]fr.Element, sizeResult)
+	for i := range p {
+		for j := range p[i] {
+			buf[j*t+i].Set(&p[i][j])
+		}
+	}
+	return buf
+}
+
+// BatchOpen computes a batch opening proof of p (the (fʲᵢ)ᵢ ) on powers of points (the ((Sʲᵢ)ᵢ)ⱼ).
+// The j-th pack of polynomials is opened on the power |(fʲᵢ)ᵢ| of (Sʲᵢ)ᵢ.
+// digests is the list (CommitAndFold(p[i]))ᵢ. It is assumed that the list has been computed beforehand
+// and provided as an input to not duplicate computations.
+func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
+
+	var res OpeningProof
+
+	if len(p) != len(points) {
+		return res, ErrNbPolynomialsNbPoints
+	}
+
+	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
+	nbPolysPerPack := make([]int, len(p))
+	for i := 0; i < len(p); i++ {
+		nbPolysPerPack[i] = len(p[i])
+	}
+	pointsPowerM := make([][]fr.Element, len(points))
+	var tmpBigInt big.Int
+	for i := 0; i < len(p); i++ {
+		tmpBigInt.SetUint64(uint64(nbPolysPerPack[i]))
+		pointsPowerM[i] = make([]fr.Element, len(points[i]))
+		for j := 0; j < len(points[i]); j++ {
+			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
+		}
+	}
+
+	// step 1: compute the claimed values, that is the evaluations of the polynomials
+	// on the relevant powers of the sets
+	res.ClaimedValues = make([][][]fr.Element, len(p))
+	for i := 0; i < len(p); i++ {
+		res.ClaimedValues[i] = make([][]fr.Element, len(p[i]))
+		for j := 0; j < len(p[i]); j++ {
+			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
+			for k := 0; k < len(points[i]); k++ {
+				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
+			}
+		}
+	}
+
+	// step 2: fold polynomials
+	foldedPolynomials := make([][]fr.Element, len(p))
+	for i := 0; i < len(p); i++ {
+		foldedPolynomials[i] = Fold(p[i])
+	}
+
+	// step 4: compute the associated roots, that is for each point p corresponding
+	// to a pack i of polynomials, we extend to <p, ω p, .., ωᵗ⁻¹p> if
+	// the i-th pack contains t polynomials where ω is a t-th root of 1
+	newPoints := make([][]fr.Element, len(points))
+	var err error
+	for i := 0; i < len(p); i++ {
+		t := len(p[i])
+		newPoints[i], err = extendSet(points[i], t)
+		if err != nil {
+			return res, err
+		}
+	}
+
+	// step 5: shplonk open the list of single polynomials on the new sets
+	res.SOpeningProof, err = shplonk.BatchOpen(foldedPolynomials, digests, newPoints, hf, pk, dataTranscript...)
+
+	return res, err
+
+}
+
+// BatchVerify uses a proof to check that each digest digests[i] is correctly opened on the set points[i].
+// The digests are the commitments to the folded underlying polynomials. The shplonk proof is
+// verified directly using the embedded shplonk proof. This function only computes the consistency
+// between the claimed values of the underlying shplonk proof and the outer claimed values, using the fft-like
+// folding. Namely, the outer claimed values are the evaluation of the original polynomials (so before they
+// were folded) at the relevant powers of the points.
+func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, vk kzg.VerifyingKey, dataTranscript ...[]byte) error {
+
+	// step 0: consistency checks between the folded claimed values of shplonk and the claimed
+	// values at the powers of the Sᵢ
+	for i := 0; i < len(proof.ClaimedValues); i++ {
+		sizeSi := len(proof.ClaimedValues[i][0])
+		for j := 1; j < len(proof.ClaimedValues[i]); j++ {
+			// each set of opening must be of the same size (opeings on powers of Si)
+			if sizeSi != len(proof.ClaimedValues[i][j]) {
+				return ErrNbPolynomialsNbPoints
+			}
+		}
+		currNbPolynomials := len(proof.ClaimedValues[i])
+		sizeSi = sizeSi * currNbPolynomials
+		// |originalPolynomials_{i}|x|Sᵢ| == |foldedPolynomials|x|folded Sᵢ|
+		if sizeSi != len(proof.SOpeningProof.ClaimedValues[i]) {
+			return ErrInconsistentNumberFoldedPoints
+		}
+	}
+
+	// step 1: fold the outer claimed values and check that they correspond to the
+	// shplonk claimed values
+	var curFoldedClaimedValue, omgeaiPoint fr.Element
+	for i := 0; i < len(proof.ClaimedValues); i++ {
+		t := len(proof.ClaimedValues[i])
+		omega, err := getIthRootOne(t)
+		if err != nil {
+			return err
+		}
+		sizeSi := len(proof.ClaimedValues[i][0])
+		polyClaimedValues := make([]fr.Element, t)
+		for j := 0; j < sizeSi; j++ {
+			for k := 0; k < t; k++ {
+				polyClaimedValues[k].Set(&proof.ClaimedValues[i][k][j])
+			}
+			omgeaiPoint.Set(&points[i][j])
+			for l := 0; l < t; l++ {
+				curFoldedClaimedValue = eval(polyClaimedValues, omgeaiPoint)
+				if !curFoldedClaimedValue.Equal(&proof.SOpeningProof.ClaimedValues[i][j*t+l]) {
+					return ErrInonsistentFolding
+				}
+				omgeaiPoint.Mul(&omgeaiPoint, &omega)
+			}
+		}
+	}
+
+	// step 2: verify the embedded shplonk proof
+	extendedPoints := make([][]fr.Element, len(points))
+	var err error
+	for i := 0; i < len(points); i++ {
+		t := len(proof.ClaimedValues[i])
+		extendedPoints[i], err = extendSet(points[i], t)
+		if err != nil {
+			return err
+		}
+	}
+	err = shplonk.BatchVerify(proof.SOpeningProof, digests, extendedPoints, hf, vk, dataTranscript...)
+
+	return nil
+}
+
+// utils
+
+// getGenFrStar returns a generator of Fr^{*}
+func getGenFrStar() fr.Element {
+	var res fr.Element
+
+	res.SetUint64(15)
+
+	return res
+}
+
+// getIthRootOne returns a generator of Z/iZ
+func getIthRootOne(i int) (fr.Element, error) {
+	var omega fr.Element
+	var tmpBigInt, zeroBigInt big.Int
+	oneBigInt := big.NewInt(1)
+	zeroBigInt.SetUint64(0)
+	rMinusOneBigInt := fr.Modulus()
+	rMinusOneBigInt.Sub(rMinusOneBigInt, oneBigInt)
+	tmpBigInt.SetUint64(uint64(i))
+	tmpBigInt.Mod(rMinusOneBigInt, &tmpBigInt)
+	if tmpBigInt.Cmp(&zeroBigInt) != 0 {
+		return omega, ErrRootsOne
+	}
+	genFrStar := getGenFrStar()
+	tmpBigInt.SetUint64(uint64(i))
+	tmpBigInt.Div(rMinusOneBigInt, &tmpBigInt)
+	omega.Exp(genFrStar, &tmpBigInt)
+	return omega, nil
+}
+
+// extendSet returns [p[0], ω p[0], .. ,ωᵗ⁻¹p[0],p[1],..,ωᵗ⁻¹p[1],..]
+func extendSet(p []fr.Element, t int) ([]fr.Element, error) {
+
+	omega, err := getIthRootOne(t)
+	if err != nil {
+		return nil, err
+	}
+	nbPoints := len(p)
+	newPoints := make([]fr.Element, t*nbPoints)
+	for i := 0; i < nbPoints; i++ {
+		newPoints[i*t].Set(&p[i])
+		for k := 1; k < t; k++ {
+			newPoints[i*t+k].Mul(&newPoints[i*t+k-1], &omega)
+		}
+	}
+
+	return newPoints, nil
+}
+
+func eval(f []fr.Element, x fr.Element) fr.Element {
+	var y fr.Element
+	for i := len(f) - 1; i >= 0; i-- {
+		y.Mul(&y, &x).Add(&y, &f[i])
+	}
+	return y
+}
diff --git a/ecc/bw6-761/fflonk/fflonk_test.go b/ecc/bw6-761/fflonk/fflonk_test.go
new file mode 100644
index 0000000000..030b6e8db2
--- /dev/null
+++ b/ecc/bw6-761/fflonk/fflonk_test.go
@@ -0,0 +1,141 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"crypto/sha256"
+	"math/big"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
+	"github.com/consensys/gnark-crypto/ecc/bw6-761/kzg"
+	"github.com/stretchr/testify/require"
+)
+
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *kzg.SRS
+var bAlpha *big.Int
+
+func init() {
+	const srsSize = 400
+	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+}
+
+func TestFflonk(t *testing.T) {
+
+	assert := require.New(t)
+
+	// sample random polynomials of various sizes
+	nbSets := 5
+	p := make([][][]fr.Element, nbSets)
+	for i := 0; i < nbSets; i++ {
+		nbPolysInSet := 9
+		p[i] = make([][]fr.Element, nbPolysInSet)
+		for j := 0; j < nbPolysInSet; j++ {
+			curSizePoly := j + 10
+			p[i][j] = make([]fr.Element, curSizePoly)
+			for k := 0; k < curSizePoly; k++ {
+				p[i][j][k].SetRandom()
+			}
+		}
+	}
+
+	// sample random sets Sᵢ
+	x := make([][]fr.Element, nbSets)
+	for i := 0; i < nbSets; i++ {
+		curSetSize := i + 4
+		x[i] = make([]fr.Element, curSetSize)
+		for j := 0; j < curSetSize; j++ {
+			x[i][j].SetRandom()
+		}
+	}
+
+	// commit to the folded polynomials
+	digests := make([]kzg.Digest, nbSets)
+	var err error
+	for i := 0; i < nbSets; i++ {
+		digests[i], err = CommitAndFold(p[i], testSrs.Pk)
+		assert.NoError(err)
+	}
+
+	// compute flonk opening proof
+	hf := sha256.New()
+	proof, err := BatchOpen(p, digests, x, hf, testSrs.Pk)
+	assert.NoError(err)
+
+	// check opening proof
+	err = BatchVerify(proof, digests, x, hf, testSrs.Vk)
+	assert.NoError(err)
+
+	// tamper the proof
+	proof.ClaimedValues[0][0][0].SetRandom()
+	err = BatchVerify(proof, digests, x, hf, testSrs.Vk)
+	assert.Error(err)
+
+}
+
+func TestCommit(t *testing.T) {
+
+	assert := require.New(t)
+
+	// sample polynomials
+	nbPolys := 2
+	p := make([][]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		p[i] = make([]fr.Element, i+10)
+		for j := 0; j < i+10; j++ {
+			p[i][j].SetRandom()
+		}
+	}
+
+	// fflonk commit to them
+	var x fr.Element
+	x.SetRandom()
+	proof, err := kzg.Open(Fold(p), x, testSrs.Pk)
+	assert.NoError(err)
+
+	// check that Open(C, x) = ∑_{i<t}Pᵢ(xᵗ)xⁱ
+	var xt fr.Element
+	var expo big.Int
+	expo.SetUint64(uint64(nbPolys))
+	xt.Exp(x, &expo)
+	px := make([]fr.Element, nbPolys)
+	for i := 0; i < nbPolys; i++ {
+		px[i] = eval(p[i], xt)
+	}
+	y := eval(px, x)
+	assert.True(y.Equal(&proof.ClaimedValue))
+}
+
+func TestGetIthRootOne(t *testing.T) {
+
+	assert := require.New(t)
+
+	order := 9
+	omega, err := getIthRootOne(order)
+	assert.NoError(err)
+	var orderBigInt big.Int
+	orderBigInt.SetUint64(uint64(order))
+	omega.Exp(omega, &orderBigInt)
+	assert.True(omega.IsOne())
+
+	order = 7
+	_, err = getIthRootOne(order)
+	assert.Error(err)
+}

From 2a43132f585dfbd46c666fd09f67ad843cbbc834 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Tue, 19 Mar 2024 16:28:47 +0100
Subject: [PATCH 032/114] feat: marshal fflonk bn254

---
 ecc/bn254/fflonk/marshal.go | 49 +++++++++++++++++++++++++++++++++++++
 1 file changed, 49 insertions(+)
 create mode 100644 ecc/bn254/fflonk/marshal.go

diff --git a/ecc/bn254/fflonk/marshal.go b/ecc/bn254/fflonk/marshal.go
new file mode 100644
index 0000000000..034e00c6ff
--- /dev/null
+++ b/ecc/bn254/fflonk/marshal.go
@@ -0,0 +1,49 @@
+package fflonk
+
+import (
+	"io"
+
+	"github.com/consensys/gnark-crypto/ecc/bn254"
+)
+
+// ReadFrom decodes OpeningProof data from reader.
+func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
+
+	dec := bn254.NewDecoder(r)
+
+	toDecode := []interface{}{
+		&proof.SOpeningProof.W,
+		&proof.SOpeningProof.WPrime,
+		proof.SOpeningProof.ClaimedValues,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toDecode {
+		if err := dec.Decode(v); err != nil {
+			return dec.BytesRead(), err
+		}
+	}
+
+	return dec.BytesRead(), nil
+}
+
+// WriteTo writes binary encoding of OpeningProof.
+func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
+
+	enc := bn254.NewEncoder(w)
+
+	toEncode := []interface{}{
+		&proof.SOpeningProof.W,
+		&proof.SOpeningProof.WPrime,
+		proof.SOpeningProof.ClaimedValues,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toEncode {
+		if err := enc.Encode(v); err != nil {
+			return enc.BytesWritten(), err
+		}
+	}
+
+	return enc.BytesWritten(), nil
+}

From 6f3074bcfa6b7703b71b3324df567f6483c67ec5 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Tue, 19 Mar 2024 18:48:13 +0100
Subject: [PATCH 033/114] feat: marshal

---
 ecc/bls12-377/fflonk/marshal.go        | 65 ++++++++++++++++++++++++++
 ecc/bls12-378/fflonk/marshal.go        | 65 ++++++++++++++++++++++++++
 ecc/bls12-381/fflonk/marshal.go        | 65 ++++++++++++++++++++++++++
 ecc/bls24-315/fflonk/marshal.go        | 65 ++++++++++++++++++++++++++
 ecc/bls24-317/fflonk/marshal.go        | 65 ++++++++++++++++++++++++++
 ecc/bn254/fflonk/marshal.go            | 16 +++++++
 ecc/bw6-633/fflonk/marshal.go          | 65 ++++++++++++++++++++++++++
 ecc/bw6-756/fflonk/marshal.go          | 65 ++++++++++++++++++++++++++
 ecc/bw6-761/fflonk/marshal.go          | 65 ++++++++++++++++++++++++++
 internal/generator/fflonk/generator.go |  2 +-
 10 files changed, 537 insertions(+), 1 deletion(-)
 create mode 100644 ecc/bls12-377/fflonk/marshal.go
 create mode 100644 ecc/bls12-378/fflonk/marshal.go
 create mode 100644 ecc/bls12-381/fflonk/marshal.go
 create mode 100644 ecc/bls24-315/fflonk/marshal.go
 create mode 100644 ecc/bls24-317/fflonk/marshal.go
 create mode 100644 ecc/bw6-633/fflonk/marshal.go
 create mode 100644 ecc/bw6-756/fflonk/marshal.go
 create mode 100644 ecc/bw6-761/fflonk/marshal.go

diff --git a/ecc/bls12-377/fflonk/marshal.go b/ecc/bls12-377/fflonk/marshal.go
new file mode 100644
index 0000000000..b5dd8da92e
--- /dev/null
+++ b/ecc/bls12-377/fflonk/marshal.go
@@ -0,0 +1,65 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"io"
+
+	"github.com/consensys/gnark-crypto/ecc/bls12-377"
+)
+
+// ReadFrom decodes OpeningProof data from reader.
+func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
+
+	dec := bls12377.NewDecoder(r)
+
+	toDecode := []interface{}{
+		&proof.SOpeningProof.W,
+		&proof.SOpeningProof.WPrime,
+		proof.SOpeningProof.ClaimedValues,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toDecode {
+		if err := dec.Decode(v); err != nil {
+			return dec.BytesRead(), err
+		}
+	}
+
+	return dec.BytesRead(), nil
+}
+
+// WriteTo writes binary encoding of OpeningProof.
+func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
+
+	enc := bls12377.NewEncoder(w)
+
+	toEncode := []interface{}{
+		&proof.SOpeningProof.W,
+		&proof.SOpeningProof.WPrime,
+		proof.SOpeningProof.ClaimedValues,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toEncode {
+		if err := enc.Encode(v); err != nil {
+			return enc.BytesWritten(), err
+		}
+	}
+
+	return enc.BytesWritten(), nil
+}
diff --git a/ecc/bls12-378/fflonk/marshal.go b/ecc/bls12-378/fflonk/marshal.go
new file mode 100644
index 0000000000..bd46e96297
--- /dev/null
+++ b/ecc/bls12-378/fflonk/marshal.go
@@ -0,0 +1,65 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"io"
+
+	"github.com/consensys/gnark-crypto/ecc/bls12-378"
+)
+
+// ReadFrom decodes OpeningProof data from reader.
+func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
+
+	dec := bls12378.NewDecoder(r)
+
+	toDecode := []interface{}{
+		&proof.SOpeningProof.W,
+		&proof.SOpeningProof.WPrime,
+		proof.SOpeningProof.ClaimedValues,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toDecode {
+		if err := dec.Decode(v); err != nil {
+			return dec.BytesRead(), err
+		}
+	}
+
+	return dec.BytesRead(), nil
+}
+
+// WriteTo writes binary encoding of OpeningProof.
+func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
+
+	enc := bls12378.NewEncoder(w)
+
+	toEncode := []interface{}{
+		&proof.SOpeningProof.W,
+		&proof.SOpeningProof.WPrime,
+		proof.SOpeningProof.ClaimedValues,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toEncode {
+		if err := enc.Encode(v); err != nil {
+			return enc.BytesWritten(), err
+		}
+	}
+
+	return enc.BytesWritten(), nil
+}
diff --git a/ecc/bls12-381/fflonk/marshal.go b/ecc/bls12-381/fflonk/marshal.go
new file mode 100644
index 0000000000..cdf278f6f5
--- /dev/null
+++ b/ecc/bls12-381/fflonk/marshal.go
@@ -0,0 +1,65 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"io"
+
+	"github.com/consensys/gnark-crypto/ecc/bls12-381"
+)
+
+// ReadFrom decodes OpeningProof data from reader.
+func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
+
+	dec := bls12381.NewDecoder(r)
+
+	toDecode := []interface{}{
+		&proof.SOpeningProof.W,
+		&proof.SOpeningProof.WPrime,
+		proof.SOpeningProof.ClaimedValues,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toDecode {
+		if err := dec.Decode(v); err != nil {
+			return dec.BytesRead(), err
+		}
+	}
+
+	return dec.BytesRead(), nil
+}
+
+// WriteTo writes binary encoding of OpeningProof.
+func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
+
+	enc := bls12381.NewEncoder(w)
+
+	toEncode := []interface{}{
+		&proof.SOpeningProof.W,
+		&proof.SOpeningProof.WPrime,
+		proof.SOpeningProof.ClaimedValues,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toEncode {
+		if err := enc.Encode(v); err != nil {
+			return enc.BytesWritten(), err
+		}
+	}
+
+	return enc.BytesWritten(), nil
+}
diff --git a/ecc/bls24-315/fflonk/marshal.go b/ecc/bls24-315/fflonk/marshal.go
new file mode 100644
index 0000000000..f706558a7b
--- /dev/null
+++ b/ecc/bls24-315/fflonk/marshal.go
@@ -0,0 +1,65 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"io"
+
+	"github.com/consensys/gnark-crypto/ecc/bls24-315"
+)
+
+// ReadFrom decodes OpeningProof data from reader.
+func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
+
+	dec := bls24315.NewDecoder(r)
+
+	toDecode := []interface{}{
+		&proof.SOpeningProof.W,
+		&proof.SOpeningProof.WPrime,
+		proof.SOpeningProof.ClaimedValues,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toDecode {
+		if err := dec.Decode(v); err != nil {
+			return dec.BytesRead(), err
+		}
+	}
+
+	return dec.BytesRead(), nil
+}
+
+// WriteTo writes binary encoding of OpeningProof.
+func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
+
+	enc := bls24315.NewEncoder(w)
+
+	toEncode := []interface{}{
+		&proof.SOpeningProof.W,
+		&proof.SOpeningProof.WPrime,
+		proof.SOpeningProof.ClaimedValues,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toEncode {
+		if err := enc.Encode(v); err != nil {
+			return enc.BytesWritten(), err
+		}
+	}
+
+	return enc.BytesWritten(), nil
+}
diff --git a/ecc/bls24-317/fflonk/marshal.go b/ecc/bls24-317/fflonk/marshal.go
new file mode 100644
index 0000000000..1129b6a503
--- /dev/null
+++ b/ecc/bls24-317/fflonk/marshal.go
@@ -0,0 +1,65 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"io"
+
+	"github.com/consensys/gnark-crypto/ecc/bls24-317"
+)
+
+// ReadFrom decodes OpeningProof data from reader.
+func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
+
+	dec := bls24317.NewDecoder(r)
+
+	toDecode := []interface{}{
+		&proof.SOpeningProof.W,
+		&proof.SOpeningProof.WPrime,
+		proof.SOpeningProof.ClaimedValues,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toDecode {
+		if err := dec.Decode(v); err != nil {
+			return dec.BytesRead(), err
+		}
+	}
+
+	return dec.BytesRead(), nil
+}
+
+// WriteTo writes binary encoding of OpeningProof.
+func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
+
+	enc := bls24317.NewEncoder(w)
+
+	toEncode := []interface{}{
+		&proof.SOpeningProof.W,
+		&proof.SOpeningProof.WPrime,
+		proof.SOpeningProof.ClaimedValues,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toEncode {
+		if err := enc.Encode(v); err != nil {
+			return enc.BytesWritten(), err
+		}
+	}
+
+	return enc.BytesWritten(), nil
+}
diff --git a/ecc/bn254/fflonk/marshal.go b/ecc/bn254/fflonk/marshal.go
index 034e00c6ff..ff35b08e26 100644
--- a/ecc/bn254/fflonk/marshal.go
+++ b/ecc/bn254/fflonk/marshal.go
@@ -1,3 +1,19 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
 package fflonk
 
 import (
diff --git a/ecc/bw6-633/fflonk/marshal.go b/ecc/bw6-633/fflonk/marshal.go
new file mode 100644
index 0000000000..a8b354e6c4
--- /dev/null
+++ b/ecc/bw6-633/fflonk/marshal.go
@@ -0,0 +1,65 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"io"
+
+	"github.com/consensys/gnark-crypto/ecc/bw6-633"
+)
+
+// ReadFrom decodes OpeningProof data from reader.
+func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
+
+	dec := bw6633.NewDecoder(r)
+
+	toDecode := []interface{}{
+		&proof.SOpeningProof.W,
+		&proof.SOpeningProof.WPrime,
+		proof.SOpeningProof.ClaimedValues,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toDecode {
+		if err := dec.Decode(v); err != nil {
+			return dec.BytesRead(), err
+		}
+	}
+
+	return dec.BytesRead(), nil
+}
+
+// WriteTo writes binary encoding of OpeningProof.
+func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
+
+	enc := bw6633.NewEncoder(w)
+
+	toEncode := []interface{}{
+		&proof.SOpeningProof.W,
+		&proof.SOpeningProof.WPrime,
+		proof.SOpeningProof.ClaimedValues,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toEncode {
+		if err := enc.Encode(v); err != nil {
+			return enc.BytesWritten(), err
+		}
+	}
+
+	return enc.BytesWritten(), nil
+}
diff --git a/ecc/bw6-756/fflonk/marshal.go b/ecc/bw6-756/fflonk/marshal.go
new file mode 100644
index 0000000000..1d8be3fa12
--- /dev/null
+++ b/ecc/bw6-756/fflonk/marshal.go
@@ -0,0 +1,65 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"io"
+
+	"github.com/consensys/gnark-crypto/ecc/bw6-756"
+)
+
+// ReadFrom decodes OpeningProof data from reader.
+func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
+
+	dec := bw6756.NewDecoder(r)
+
+	toDecode := []interface{}{
+		&proof.SOpeningProof.W,
+		&proof.SOpeningProof.WPrime,
+		proof.SOpeningProof.ClaimedValues,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toDecode {
+		if err := dec.Decode(v); err != nil {
+			return dec.BytesRead(), err
+		}
+	}
+
+	return dec.BytesRead(), nil
+}
+
+// WriteTo writes binary encoding of OpeningProof.
+func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
+
+	enc := bw6756.NewEncoder(w)
+
+	toEncode := []interface{}{
+		&proof.SOpeningProof.W,
+		&proof.SOpeningProof.WPrime,
+		proof.SOpeningProof.ClaimedValues,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toEncode {
+		if err := enc.Encode(v); err != nil {
+			return enc.BytesWritten(), err
+		}
+	}
+
+	return enc.BytesWritten(), nil
+}
diff --git a/ecc/bw6-761/fflonk/marshal.go b/ecc/bw6-761/fflonk/marshal.go
new file mode 100644
index 0000000000..243d3035f1
--- /dev/null
+++ b/ecc/bw6-761/fflonk/marshal.go
@@ -0,0 +1,65 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"io"
+
+	"github.com/consensys/gnark-crypto/ecc/bw6-761"
+)
+
+// ReadFrom decodes OpeningProof data from reader.
+func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
+
+	dec := bw6761.NewDecoder(r)
+
+	toDecode := []interface{}{
+		&proof.SOpeningProof.W,
+		&proof.SOpeningProof.WPrime,
+		proof.SOpeningProof.ClaimedValues,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toDecode {
+		if err := dec.Decode(v); err != nil {
+			return dec.BytesRead(), err
+		}
+	}
+
+	return dec.BytesRead(), nil
+}
+
+// WriteTo writes binary encoding of OpeningProof.
+func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
+
+	enc := bw6761.NewEncoder(w)
+
+	toEncode := []interface{}{
+		&proof.SOpeningProof.W,
+		&proof.SOpeningProof.WPrime,
+		proof.SOpeningProof.ClaimedValues,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toEncode {
+		if err := enc.Encode(v); err != nil {
+			return enc.BytesWritten(), err
+		}
+	}
+
+	return enc.BytesWritten(), nil
+}
diff --git a/internal/generator/fflonk/generator.go b/internal/generator/fflonk/generator.go
index 40ee17daf3..875c129dd8 100644
--- a/internal/generator/fflonk/generator.go
+++ b/internal/generator/fflonk/generator.go
@@ -15,7 +15,7 @@ func Generate(conf config.Curve, baseDir string, bgen *bavard.BatchGenerator) er
 		{File: filepath.Join(baseDir, "doc.go"), Templates: []string{"doc.go.tmpl"}},
 		{File: filepath.Join(baseDir, "fflonk.go"), Templates: []string{"fflonk.go.tmpl"}},
 		{File: filepath.Join(baseDir, "fflonk_test.go"), Templates: []string{"fflonk.test.go.tmpl"}},
-		// {File: filepath.Join(baseDir, "marshal.go"), Templates: []string{"marshal.go.tmpl"}},
+		{File: filepath.Join(baseDir, "marshal.go"), Templates: []string{"marshal.go.tmpl"}},
 	}
 	return bgen.Generate(conf, conf.Package, "./fflonk/template/", entries...)
 

From 941631d402bfc341529b83c10f80a69f0bafc25a Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Tue, 19 Mar 2024 18:48:31 +0100
Subject: [PATCH 034/114] feat: template marshal

---
 .../generator/fflonk/template/marshal.go.tmpl | 47 +++++++++++++++++++
 1 file changed, 47 insertions(+)
 create mode 100644 internal/generator/fflonk/template/marshal.go.tmpl

diff --git a/internal/generator/fflonk/template/marshal.go.tmpl b/internal/generator/fflonk/template/marshal.go.tmpl
new file mode 100644
index 0000000000..e70d43bb7f
--- /dev/null
+++ b/internal/generator/fflonk/template/marshal.go.tmpl
@@ -0,0 +1,47 @@
+import (
+	"io"
+
+	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}"
+)
+
+// ReadFrom decodes OpeningProof data from reader.
+func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
+
+	dec := {{ .CurvePackage }}.NewDecoder(r)
+
+	toDecode := []interface{}{
+		&proof.SOpeningProof.W,
+		&proof.SOpeningProof.WPrime,
+		proof.SOpeningProof.ClaimedValues,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toDecode {
+		if err := dec.Decode(v); err != nil {
+			return dec.BytesRead(), err
+		}
+	}
+
+	return dec.BytesRead(), nil
+}
+
+// WriteTo writes binary encoding of OpeningProof.
+func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
+
+	enc := {{ .CurvePackage }}.NewEncoder(w)
+
+	toEncode := []interface{}{
+		&proof.SOpeningProof.W,
+		&proof.SOpeningProof.WPrime,
+		proof.SOpeningProof.ClaimedValues,
+		proof.ClaimedValues,
+	}
+
+	for _, v := range toEncode {
+		if err := enc.Encode(v); err != nil {
+			return enc.BytesWritten(), err
+		}
+	}
+
+	return enc.BytesWritten(), nil
+}

From e651058209cd0b4f62c842f31e2eb31c5bed5bba Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 29 Mar 2024 12:25:04 +0100
Subject: [PATCH 035/114] feat: add dummy polynomial so the number of poly
 divides r-1

---
 ecc/bn254/fflonk/fflonk.go | 40 +++++++++++++++++++++++++++++---------
 1 file changed, 31 insertions(+), 9 deletions(-)

diff --git a/ecc/bn254/fflonk/fflonk.go b/ecc/bn254/fflonk/fflonk.go
index 9062a8d2ca..5ec41acc8a 100644
--- a/ecc/bn254/fflonk/fflonk.go
+++ b/ecc/bn254/fflonk/fflonk.go
@@ -12,8 +12,6 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-// Code generated by consensys/gnark-crypto DO NOT EDIT
-
 package fflonk
 
 import (
@@ -56,16 +54,19 @@ func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Dig
 	return com, err
 }
 
-// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ. The
 func Fold(p [][]fr.Element) []fr.Element {
-	t := len(p)
+
+	// we first pick the smallest divisor of r-1 bounding above len(p)
+	t := getNextDivisorRMinusOne(len(p))
+
 	sizeResult := 0
 	for i := range p {
 		if sizeResult < len(p[i]) {
 			sizeResult = len(p[i])
 		}
 	}
-	sizeResult = sizeResult*len(p) + len(p) - 1
+	sizeResult = sizeResult*t + t - 1
 	buf := make([]fr.Element, sizeResult)
 	for i := range p {
 		for j := range p[i] {
@@ -89,13 +90,15 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 
 	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
 	nbPolysPerPack := make([]int, len(p))
+	nextPowerOfTwoPerPack := make([]int, len(p))
 	for i := 0; i < len(p); i++ {
 		nbPolysPerPack[i] = len(p[i])
+		nextPowerOfTwoPerPack[i] = getNextDivisorRMinusOne(len(p[i]))
 	}
 	pointsPowerM := make([][]fr.Element, len(points))
 	var tmpBigInt big.Int
 	for i := 0; i < len(p); i++ {
-		tmpBigInt.SetUint64(uint64(nbPolysPerPack[i]))
+		tmpBigInt.SetUint64(uint64(nextPowerOfTwoPerPack[i]))
 		pointsPowerM[i] = make([]fr.Element, len(points[i]))
 		for j := 0; j < len(points[i]); j++ {
 			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
@@ -106,13 +109,16 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	// on the relevant powers of the sets
 	res.ClaimedValues = make([][][]fr.Element, len(p))
 	for i := 0; i < len(p); i++ {
-		res.ClaimedValues[i] = make([][]fr.Element, len(p[i]))
+		res.ClaimedValues[i] = make([][]fr.Element, nextPowerOfTwoPerPack[i])
 		for j := 0; j < len(p[i]); j++ {
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 			for k := 0; k < len(points[i]); k++ {
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
+		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaing polynomials are zero
+			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
+		}
 	}
 
 	// step 2: fold polynomials
@@ -127,8 +133,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	newPoints := make([][]fr.Element, len(points))
 	var err error
 	for i := 0; i < len(p); i++ {
-		t := len(p[i])
-		newPoints[i], err = extendSet(points[i], t)
+		newPoints[i], err = extendSet(points[i], nextPowerOfTwoPerPack[i])
 		if err != nil {
 			return res, err
 		}
@@ -239,6 +244,23 @@ func getIthRootOne(i int) (fr.Element, error) {
 	return omega, nil
 }
 
+// computes the smallest i bounding above number_polynomials
+// and dividing r-1.
+func getNextDivisorRMinusOne(i int) int {
+	var zero, tmp, one big.Int
+	r := fr.Modulus()
+	one.SetUint64(1)
+	r.Sub(r, &one)
+	tmp.SetUint64(uint64(i))
+	tmp.Mod(r, &tmp)
+	for tmp.Cmp(&zero) != 0 {
+		i += 1
+		tmp.SetUint64(uint64(i))
+		tmp.Mod(r, &tmp)
+	}
+	return i
+}
+
 // extendSet returns [p[0], ω p[0], .. ,ωᵗ⁻¹p[0],p[1],..,ωᵗ⁻¹p[1],..]
 func extendSet(p []fr.Element, t int) ([]fr.Element, error) {
 

From 78bda2d2a276a82cc40a308c257cf79bb8dc49af Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 29 Mar 2024 18:14:36 +0100
Subject: [PATCH 036/114] feat: proof tunes the number of polynomial so it
 divides r-1

---
 ecc/bls12-377/fflonk/fflonk.go                | 56 ++++++++----
 ecc/bls12-378/fflonk/fflonk.go                | 56 ++++++++----
 ecc/bls12-381/fflonk/fflonk.go                | 56 ++++++++----
 ecc/bls24-315/fflonk/fflonk.go                | 56 ++++++++----
 ecc/bls24-317/fflonk/fflonk.go                | 56 ++++++++----
 ecc/bn254/fflonk/fflonk.go                    | 20 +++--
 ecc/bw6-633/fflonk/fflonk.go                  | 56 ++++++++----
 ecc/bw6-756/fflonk/fflonk.go                  | 56 ++++++++----
 ecc/bw6-761/fflonk/fflonk.go                  | 56 ++++++++----
 .../generator/fflonk/template/fflonk.go.tmpl  | 88 ++++++++++++-------
 10 files changed, 387 insertions(+), 169 deletions(-)

diff --git a/ecc/bls12-377/fflonk/fflonk.go b/ecc/bls12-377/fflonk/fflonk.go
index 31176422e0..75649f5e41 100644
--- a/ecc/bls12-377/fflonk/fflonk.go
+++ b/ecc/bls12-377/fflonk/fflonk.go
@@ -56,16 +56,19 @@ func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Dig
 	return com, err
 }
 
-// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ. The
 func Fold(p [][]fr.Element) []fr.Element {
-	t := len(p)
+
+	// we first pick the smallest divisor of r-1 bounding above len(p)
+	t := getNextDivisorRMinusOne(len(p))
+
 	sizeResult := 0
 	for i := range p {
 		if sizeResult < len(p[i]) {
 			sizeResult = len(p[i])
 		}
 	}
-	sizeResult = sizeResult*len(p) + len(p) - 1
+	sizeResult = sizeResult*t + t - 1
 	buf := make([]fr.Element, sizeResult)
 	for i := range p {
 		for j := range p[i] {
@@ -89,13 +92,15 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 
 	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
 	nbPolysPerPack := make([]int, len(p))
+	nextPowerOfTwoPerPack := make([]int, len(p))
 	for i := 0; i < len(p); i++ {
 		nbPolysPerPack[i] = len(p[i])
+		nextPowerOfTwoPerPack[i] = getNextDivisorRMinusOne(len(p[i]))
 	}
 	pointsPowerM := make([][]fr.Element, len(points))
 	var tmpBigInt big.Int
 	for i := 0; i < len(p); i++ {
-		tmpBigInt.SetUint64(uint64(nbPolysPerPack[i]))
+		tmpBigInt.SetUint64(uint64(nextPowerOfTwoPerPack[i]))
 		pointsPowerM[i] = make([]fr.Element, len(points[i]))
 		for j := 0; j < len(points[i]); j++ {
 			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
@@ -106,13 +111,16 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	// on the relevant powers of the sets
 	res.ClaimedValues = make([][][]fr.Element, len(p))
 	for i := 0; i < len(p); i++ {
-		res.ClaimedValues[i] = make([][]fr.Element, len(p[i]))
+		res.ClaimedValues[i] = make([][]fr.Element, nextPowerOfTwoPerPack[i])
 		for j := 0; j < len(p[i]); j++ {
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 			for k := 0; k < len(points[i]); k++ {
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
+		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaing polynomials are zero
+			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
+		}
 	}
 
 	// step 2: fold polynomials
@@ -127,8 +135,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	newPoints := make([][]fr.Element, len(points))
 	var err error
 	for i := 0; i < len(p); i++ {
-		t := len(p[i])
-		newPoints[i], err = extendSet(points[i], t)
+		newPoints[i], err = extendSet(points[i], nextPowerOfTwoPerPack[i])
 		if err != nil {
 			return res, err
 		}
@@ -210,15 +217,6 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 
 // utils
 
-// getGenFrStar returns a generator of Fr^{*}
-func getGenFrStar() fr.Element {
-	var res fr.Element
-
-	res.SetUint64(22)
-
-	return res
-}
-
 // getIthRootOne returns a generator of Z/iZ
 func getIthRootOne(i int) (fr.Element, error) {
 	var omega fr.Element
@@ -239,6 +237,23 @@ func getIthRootOne(i int) (fr.Element, error) {
 	return omega, nil
 }
 
+// computes the smallest i bounding above number_polynomials
+// and dividing r-1.
+func getNextDivisorRMinusOne(i int) int {
+	var zero, tmp, one big.Int
+	r := fr.Modulus()
+	one.SetUint64(1)
+	r.Sub(r, &one)
+	tmp.SetUint64(uint64(i))
+	tmp.Mod(r, &tmp)
+	for tmp.Cmp(&zero) != 0 {
+		i += 1
+		tmp.SetUint64(uint64(i))
+		tmp.Mod(r, &tmp)
+	}
+	return i
+}
+
 // extendSet returns [p[0], ω p[0], .. ,ωᵗ⁻¹p[0],p[1],..,ωᵗ⁻¹p[1],..]
 func extendSet(p []fr.Element, t int) ([]fr.Element, error) {
 
@@ -265,3 +280,12 @@ func eval(f []fr.Element, x fr.Element) fr.Element {
 	}
 	return y
 }
+
+// getGenFrStar returns a generator of Fr^{*}
+func getGenFrStar() fr.Element {
+	var res fr.Element
+
+	res.SetUint64(22)
+
+	return res
+}
diff --git a/ecc/bls12-378/fflonk/fflonk.go b/ecc/bls12-378/fflonk/fflonk.go
index 967a45d404..d1e276c167 100644
--- a/ecc/bls12-378/fflonk/fflonk.go
+++ b/ecc/bls12-378/fflonk/fflonk.go
@@ -56,16 +56,19 @@ func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Dig
 	return com, err
 }
 
-// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ. The
 func Fold(p [][]fr.Element) []fr.Element {
-	t := len(p)
+
+	// we first pick the smallest divisor of r-1 bounding above len(p)
+	t := getNextDivisorRMinusOne(len(p))
+
 	sizeResult := 0
 	for i := range p {
 		if sizeResult < len(p[i]) {
 			sizeResult = len(p[i])
 		}
 	}
-	sizeResult = sizeResult*len(p) + len(p) - 1
+	sizeResult = sizeResult*t + t - 1
 	buf := make([]fr.Element, sizeResult)
 	for i := range p {
 		for j := range p[i] {
@@ -89,13 +92,15 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 
 	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
 	nbPolysPerPack := make([]int, len(p))
+	nextPowerOfTwoPerPack := make([]int, len(p))
 	for i := 0; i < len(p); i++ {
 		nbPolysPerPack[i] = len(p[i])
+		nextPowerOfTwoPerPack[i] = getNextDivisorRMinusOne(len(p[i]))
 	}
 	pointsPowerM := make([][]fr.Element, len(points))
 	var tmpBigInt big.Int
 	for i := 0; i < len(p); i++ {
-		tmpBigInt.SetUint64(uint64(nbPolysPerPack[i]))
+		tmpBigInt.SetUint64(uint64(nextPowerOfTwoPerPack[i]))
 		pointsPowerM[i] = make([]fr.Element, len(points[i]))
 		for j := 0; j < len(points[i]); j++ {
 			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
@@ -106,13 +111,16 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	// on the relevant powers of the sets
 	res.ClaimedValues = make([][][]fr.Element, len(p))
 	for i := 0; i < len(p); i++ {
-		res.ClaimedValues[i] = make([][]fr.Element, len(p[i]))
+		res.ClaimedValues[i] = make([][]fr.Element, nextPowerOfTwoPerPack[i])
 		for j := 0; j < len(p[i]); j++ {
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 			for k := 0; k < len(points[i]); k++ {
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
+		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaing polynomials are zero
+			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
+		}
 	}
 
 	// step 2: fold polynomials
@@ -127,8 +135,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	newPoints := make([][]fr.Element, len(points))
 	var err error
 	for i := 0; i < len(p); i++ {
-		t := len(p[i])
-		newPoints[i], err = extendSet(points[i], t)
+		newPoints[i], err = extendSet(points[i], nextPowerOfTwoPerPack[i])
 		if err != nil {
 			return res, err
 		}
@@ -210,15 +217,6 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 
 // utils
 
-// getGenFrStar returns a generator of Fr^{*}
-func getGenFrStar() fr.Element {
-	var res fr.Element
-
-	res.SetUint64(22)
-
-	return res
-}
-
 // getIthRootOne returns a generator of Z/iZ
 func getIthRootOne(i int) (fr.Element, error) {
 	var omega fr.Element
@@ -239,6 +237,23 @@ func getIthRootOne(i int) (fr.Element, error) {
 	return omega, nil
 }
 
+// computes the smallest i bounding above number_polynomials
+// and dividing r-1.
+func getNextDivisorRMinusOne(i int) int {
+	var zero, tmp, one big.Int
+	r := fr.Modulus()
+	one.SetUint64(1)
+	r.Sub(r, &one)
+	tmp.SetUint64(uint64(i))
+	tmp.Mod(r, &tmp)
+	for tmp.Cmp(&zero) != 0 {
+		i += 1
+		tmp.SetUint64(uint64(i))
+		tmp.Mod(r, &tmp)
+	}
+	return i
+}
+
 // extendSet returns [p[0], ω p[0], .. ,ωᵗ⁻¹p[0],p[1],..,ωᵗ⁻¹p[1],..]
 func extendSet(p []fr.Element, t int) ([]fr.Element, error) {
 
@@ -265,3 +280,12 @@ func eval(f []fr.Element, x fr.Element) fr.Element {
 	}
 	return y
 }
+
+// getGenFrStar returns a generator of Fr^{*}
+func getGenFrStar() fr.Element {
+	var res fr.Element
+
+	res.SetUint64(22)
+
+	return res
+}
diff --git a/ecc/bls12-381/fflonk/fflonk.go b/ecc/bls12-381/fflonk/fflonk.go
index 0709f6d803..79b20c1a8e 100644
--- a/ecc/bls12-381/fflonk/fflonk.go
+++ b/ecc/bls12-381/fflonk/fflonk.go
@@ -56,16 +56,19 @@ func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Dig
 	return com, err
 }
 
-// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ. The
 func Fold(p [][]fr.Element) []fr.Element {
-	t := len(p)
+
+	// we first pick the smallest divisor of r-1 bounding above len(p)
+	t := getNextDivisorRMinusOne(len(p))
+
 	sizeResult := 0
 	for i := range p {
 		if sizeResult < len(p[i]) {
 			sizeResult = len(p[i])
 		}
 	}
-	sizeResult = sizeResult*len(p) + len(p) - 1
+	sizeResult = sizeResult*t + t - 1
 	buf := make([]fr.Element, sizeResult)
 	for i := range p {
 		for j := range p[i] {
@@ -89,13 +92,15 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 
 	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
 	nbPolysPerPack := make([]int, len(p))
+	nextPowerOfTwoPerPack := make([]int, len(p))
 	for i := 0; i < len(p); i++ {
 		nbPolysPerPack[i] = len(p[i])
+		nextPowerOfTwoPerPack[i] = getNextDivisorRMinusOne(len(p[i]))
 	}
 	pointsPowerM := make([][]fr.Element, len(points))
 	var tmpBigInt big.Int
 	for i := 0; i < len(p); i++ {
-		tmpBigInt.SetUint64(uint64(nbPolysPerPack[i]))
+		tmpBigInt.SetUint64(uint64(nextPowerOfTwoPerPack[i]))
 		pointsPowerM[i] = make([]fr.Element, len(points[i]))
 		for j := 0; j < len(points[i]); j++ {
 			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
@@ -106,13 +111,16 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	// on the relevant powers of the sets
 	res.ClaimedValues = make([][][]fr.Element, len(p))
 	for i := 0; i < len(p); i++ {
-		res.ClaimedValues[i] = make([][]fr.Element, len(p[i]))
+		res.ClaimedValues[i] = make([][]fr.Element, nextPowerOfTwoPerPack[i])
 		for j := 0; j < len(p[i]); j++ {
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 			for k := 0; k < len(points[i]); k++ {
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
+		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaing polynomials are zero
+			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
+		}
 	}
 
 	// step 2: fold polynomials
@@ -127,8 +135,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	newPoints := make([][]fr.Element, len(points))
 	var err error
 	for i := 0; i < len(p); i++ {
-		t := len(p[i])
-		newPoints[i], err = extendSet(points[i], t)
+		newPoints[i], err = extendSet(points[i], nextPowerOfTwoPerPack[i])
 		if err != nil {
 			return res, err
 		}
@@ -210,15 +217,6 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 
 // utils
 
-// getGenFrStar returns a generator of Fr^{*}
-func getGenFrStar() fr.Element {
-	var res fr.Element
-
-	res.SetUint64(7)
-
-	return res
-}
-
 // getIthRootOne returns a generator of Z/iZ
 func getIthRootOne(i int) (fr.Element, error) {
 	var omega fr.Element
@@ -239,6 +237,23 @@ func getIthRootOne(i int) (fr.Element, error) {
 	return omega, nil
 }
 
+// computes the smallest i bounding above number_polynomials
+// and dividing r-1.
+func getNextDivisorRMinusOne(i int) int {
+	var zero, tmp, one big.Int
+	r := fr.Modulus()
+	one.SetUint64(1)
+	r.Sub(r, &one)
+	tmp.SetUint64(uint64(i))
+	tmp.Mod(r, &tmp)
+	for tmp.Cmp(&zero) != 0 {
+		i += 1
+		tmp.SetUint64(uint64(i))
+		tmp.Mod(r, &tmp)
+	}
+	return i
+}
+
 // extendSet returns [p[0], ω p[0], .. ,ωᵗ⁻¹p[0],p[1],..,ωᵗ⁻¹p[1],..]
 func extendSet(p []fr.Element, t int) ([]fr.Element, error) {
 
@@ -265,3 +280,12 @@ func eval(f []fr.Element, x fr.Element) fr.Element {
 	}
 	return y
 }
+
+// getGenFrStar returns a generator of Fr^{*}
+func getGenFrStar() fr.Element {
+	var res fr.Element
+
+	res.SetUint64(7)
+
+	return res
+}
diff --git a/ecc/bls24-315/fflonk/fflonk.go b/ecc/bls24-315/fflonk/fflonk.go
index c4f890596f..708e50ca85 100644
--- a/ecc/bls24-315/fflonk/fflonk.go
+++ b/ecc/bls24-315/fflonk/fflonk.go
@@ -56,16 +56,19 @@ func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Dig
 	return com, err
 }
 
-// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ. The
 func Fold(p [][]fr.Element) []fr.Element {
-	t := len(p)
+
+	// we first pick the smallest divisor of r-1 bounding above len(p)
+	t := getNextDivisorRMinusOne(len(p))
+
 	sizeResult := 0
 	for i := range p {
 		if sizeResult < len(p[i]) {
 			sizeResult = len(p[i])
 		}
 	}
-	sizeResult = sizeResult*len(p) + len(p) - 1
+	sizeResult = sizeResult*t + t - 1
 	buf := make([]fr.Element, sizeResult)
 	for i := range p {
 		for j := range p[i] {
@@ -89,13 +92,15 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 
 	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
 	nbPolysPerPack := make([]int, len(p))
+	nextPowerOfTwoPerPack := make([]int, len(p))
 	for i := 0; i < len(p); i++ {
 		nbPolysPerPack[i] = len(p[i])
+		nextPowerOfTwoPerPack[i] = getNextDivisorRMinusOne(len(p[i]))
 	}
 	pointsPowerM := make([][]fr.Element, len(points))
 	var tmpBigInt big.Int
 	for i := 0; i < len(p); i++ {
-		tmpBigInt.SetUint64(uint64(nbPolysPerPack[i]))
+		tmpBigInt.SetUint64(uint64(nextPowerOfTwoPerPack[i]))
 		pointsPowerM[i] = make([]fr.Element, len(points[i]))
 		for j := 0; j < len(points[i]); j++ {
 			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
@@ -106,13 +111,16 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	// on the relevant powers of the sets
 	res.ClaimedValues = make([][][]fr.Element, len(p))
 	for i := 0; i < len(p); i++ {
-		res.ClaimedValues[i] = make([][]fr.Element, len(p[i]))
+		res.ClaimedValues[i] = make([][]fr.Element, nextPowerOfTwoPerPack[i])
 		for j := 0; j < len(p[i]); j++ {
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 			for k := 0; k < len(points[i]); k++ {
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
+		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaing polynomials are zero
+			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
+		}
 	}
 
 	// step 2: fold polynomials
@@ -127,8 +135,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	newPoints := make([][]fr.Element, len(points))
 	var err error
 	for i := 0; i < len(p); i++ {
-		t := len(p[i])
-		newPoints[i], err = extendSet(points[i], t)
+		newPoints[i], err = extendSet(points[i], nextPowerOfTwoPerPack[i])
 		if err != nil {
 			return res, err
 		}
@@ -210,15 +217,6 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 
 // utils
 
-// getGenFrStar returns a generator of Fr^{*}
-func getGenFrStar() fr.Element {
-	var res fr.Element
-
-	res.SetUint64(7)
-
-	return res
-}
-
 // getIthRootOne returns a generator of Z/iZ
 func getIthRootOne(i int) (fr.Element, error) {
 	var omega fr.Element
@@ -239,6 +237,23 @@ func getIthRootOne(i int) (fr.Element, error) {
 	return omega, nil
 }
 
+// computes the smallest i bounding above number_polynomials
+// and dividing r-1.
+func getNextDivisorRMinusOne(i int) int {
+	var zero, tmp, one big.Int
+	r := fr.Modulus()
+	one.SetUint64(1)
+	r.Sub(r, &one)
+	tmp.SetUint64(uint64(i))
+	tmp.Mod(r, &tmp)
+	for tmp.Cmp(&zero) != 0 {
+		i += 1
+		tmp.SetUint64(uint64(i))
+		tmp.Mod(r, &tmp)
+	}
+	return i
+}
+
 // extendSet returns [p[0], ω p[0], .. ,ωᵗ⁻¹p[0],p[1],..,ωᵗ⁻¹p[1],..]
 func extendSet(p []fr.Element, t int) ([]fr.Element, error) {
 
@@ -265,3 +280,12 @@ func eval(f []fr.Element, x fr.Element) fr.Element {
 	}
 	return y
 }
+
+// getGenFrStar returns a generator of Fr^{*}
+func getGenFrStar() fr.Element {
+	var res fr.Element
+
+	res.SetUint64(7)
+
+	return res
+}
diff --git a/ecc/bls24-317/fflonk/fflonk.go b/ecc/bls24-317/fflonk/fflonk.go
index 37d6bbf592..f9de5d74e5 100644
--- a/ecc/bls24-317/fflonk/fflonk.go
+++ b/ecc/bls24-317/fflonk/fflonk.go
@@ -56,16 +56,19 @@ func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Dig
 	return com, err
 }
 
-// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ. The
 func Fold(p [][]fr.Element) []fr.Element {
-	t := len(p)
+
+	// we first pick the smallest divisor of r-1 bounding above len(p)
+	t := getNextDivisorRMinusOne(len(p))
+
 	sizeResult := 0
 	for i := range p {
 		if sizeResult < len(p[i]) {
 			sizeResult = len(p[i])
 		}
 	}
-	sizeResult = sizeResult*len(p) + len(p) - 1
+	sizeResult = sizeResult*t + t - 1
 	buf := make([]fr.Element, sizeResult)
 	for i := range p {
 		for j := range p[i] {
@@ -89,13 +92,15 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 
 	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
 	nbPolysPerPack := make([]int, len(p))
+	nextPowerOfTwoPerPack := make([]int, len(p))
 	for i := 0; i < len(p); i++ {
 		nbPolysPerPack[i] = len(p[i])
+		nextPowerOfTwoPerPack[i] = getNextDivisorRMinusOne(len(p[i]))
 	}
 	pointsPowerM := make([][]fr.Element, len(points))
 	var tmpBigInt big.Int
 	for i := 0; i < len(p); i++ {
-		tmpBigInt.SetUint64(uint64(nbPolysPerPack[i]))
+		tmpBigInt.SetUint64(uint64(nextPowerOfTwoPerPack[i]))
 		pointsPowerM[i] = make([]fr.Element, len(points[i]))
 		for j := 0; j < len(points[i]); j++ {
 			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
@@ -106,13 +111,16 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	// on the relevant powers of the sets
 	res.ClaimedValues = make([][][]fr.Element, len(p))
 	for i := 0; i < len(p); i++ {
-		res.ClaimedValues[i] = make([][]fr.Element, len(p[i]))
+		res.ClaimedValues[i] = make([][]fr.Element, nextPowerOfTwoPerPack[i])
 		for j := 0; j < len(p[i]); j++ {
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 			for k := 0; k < len(points[i]); k++ {
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
+		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaing polynomials are zero
+			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
+		}
 	}
 
 	// step 2: fold polynomials
@@ -127,8 +135,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	newPoints := make([][]fr.Element, len(points))
 	var err error
 	for i := 0; i < len(p); i++ {
-		t := len(p[i])
-		newPoints[i], err = extendSet(points[i], t)
+		newPoints[i], err = extendSet(points[i], nextPowerOfTwoPerPack[i])
 		if err != nil {
 			return res, err
 		}
@@ -210,15 +217,6 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 
 // utils
 
-// getGenFrStar returns a generator of Fr^{*}
-func getGenFrStar() fr.Element {
-	var res fr.Element
-
-	res.SetUint64(7)
-
-	return res
-}
-
 // getIthRootOne returns a generator of Z/iZ
 func getIthRootOne(i int) (fr.Element, error) {
 	var omega fr.Element
@@ -239,6 +237,23 @@ func getIthRootOne(i int) (fr.Element, error) {
 	return omega, nil
 }
 
+// computes the smallest i bounding above number_polynomials
+// and dividing r-1.
+func getNextDivisorRMinusOne(i int) int {
+	var zero, tmp, one big.Int
+	r := fr.Modulus()
+	one.SetUint64(1)
+	r.Sub(r, &one)
+	tmp.SetUint64(uint64(i))
+	tmp.Mod(r, &tmp)
+	for tmp.Cmp(&zero) != 0 {
+		i += 1
+		tmp.SetUint64(uint64(i))
+		tmp.Mod(r, &tmp)
+	}
+	return i
+}
+
 // extendSet returns [p[0], ω p[0], .. ,ωᵗ⁻¹p[0],p[1],..,ωᵗ⁻¹p[1],..]
 func extendSet(p []fr.Element, t int) ([]fr.Element, error) {
 
@@ -265,3 +280,12 @@ func eval(f []fr.Element, x fr.Element) fr.Element {
 	}
 	return y
 }
+
+// getGenFrStar returns a generator of Fr^{*}
+func getGenFrStar() fr.Element {
+	var res fr.Element
+
+	res.SetUint64(7)
+
+	return res
+}
diff --git a/ecc/bn254/fflonk/fflonk.go b/ecc/bn254/fflonk/fflonk.go
index 5ec41acc8a..32fb98795f 100644
--- a/ecc/bn254/fflonk/fflonk.go
+++ b/ecc/bn254/fflonk/fflonk.go
@@ -12,6 +12,8 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
 package fflonk
 
 import (
@@ -215,15 +217,6 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 
 // utils
 
-// getGenFrStar returns a generator of Fr^{*}
-func getGenFrStar() fr.Element {
-	var res fr.Element
-
-	res.SetUint64(5)
-
-	return res
-}
-
 // getIthRootOne returns a generator of Z/iZ
 func getIthRootOne(i int) (fr.Element, error) {
 	var omega fr.Element
@@ -287,3 +280,12 @@ func eval(f []fr.Element, x fr.Element) fr.Element {
 	}
 	return y
 }
+
+// getGenFrStar returns a generator of Fr^{*}
+func getGenFrStar() fr.Element {
+	var res fr.Element
+
+	res.SetUint64(5)
+
+	return res
+}
diff --git a/ecc/bw6-633/fflonk/fflonk.go b/ecc/bw6-633/fflonk/fflonk.go
index fe88556e0e..2b07024ab3 100644
--- a/ecc/bw6-633/fflonk/fflonk.go
+++ b/ecc/bw6-633/fflonk/fflonk.go
@@ -56,16 +56,19 @@ func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Dig
 	return com, err
 }
 
-// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ. The
 func Fold(p [][]fr.Element) []fr.Element {
-	t := len(p)
+
+	// we first pick the smallest divisor of r-1 bounding above len(p)
+	t := getNextDivisorRMinusOne(len(p))
+
 	sizeResult := 0
 	for i := range p {
 		if sizeResult < len(p[i]) {
 			sizeResult = len(p[i])
 		}
 	}
-	sizeResult = sizeResult*len(p) + len(p) - 1
+	sizeResult = sizeResult*t + t - 1
 	buf := make([]fr.Element, sizeResult)
 	for i := range p {
 		for j := range p[i] {
@@ -89,13 +92,15 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 
 	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
 	nbPolysPerPack := make([]int, len(p))
+	nextPowerOfTwoPerPack := make([]int, len(p))
 	for i := 0; i < len(p); i++ {
 		nbPolysPerPack[i] = len(p[i])
+		nextPowerOfTwoPerPack[i] = getNextDivisorRMinusOne(len(p[i]))
 	}
 	pointsPowerM := make([][]fr.Element, len(points))
 	var tmpBigInt big.Int
 	for i := 0; i < len(p); i++ {
-		tmpBigInt.SetUint64(uint64(nbPolysPerPack[i]))
+		tmpBigInt.SetUint64(uint64(nextPowerOfTwoPerPack[i]))
 		pointsPowerM[i] = make([]fr.Element, len(points[i]))
 		for j := 0; j < len(points[i]); j++ {
 			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
@@ -106,13 +111,16 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	// on the relevant powers of the sets
 	res.ClaimedValues = make([][][]fr.Element, len(p))
 	for i := 0; i < len(p); i++ {
-		res.ClaimedValues[i] = make([][]fr.Element, len(p[i]))
+		res.ClaimedValues[i] = make([][]fr.Element, nextPowerOfTwoPerPack[i])
 		for j := 0; j < len(p[i]); j++ {
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 			for k := 0; k < len(points[i]); k++ {
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
+		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaing polynomials are zero
+			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
+		}
 	}
 
 	// step 2: fold polynomials
@@ -127,8 +135,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	newPoints := make([][]fr.Element, len(points))
 	var err error
 	for i := 0; i < len(p); i++ {
-		t := len(p[i])
-		newPoints[i], err = extendSet(points[i], t)
+		newPoints[i], err = extendSet(points[i], nextPowerOfTwoPerPack[i])
 		if err != nil {
 			return res, err
 		}
@@ -210,15 +217,6 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 
 // utils
 
-// getGenFrStar returns a generator of Fr^{*}
-func getGenFrStar() fr.Element {
-	var res fr.Element
-
-	res.SetUint64(13)
-
-	return res
-}
-
 // getIthRootOne returns a generator of Z/iZ
 func getIthRootOne(i int) (fr.Element, error) {
 	var omega fr.Element
@@ -239,6 +237,23 @@ func getIthRootOne(i int) (fr.Element, error) {
 	return omega, nil
 }
 
+// computes the smallest i bounding above number_polynomials
+// and dividing r-1.
+func getNextDivisorRMinusOne(i int) int {
+	var zero, tmp, one big.Int
+	r := fr.Modulus()
+	one.SetUint64(1)
+	r.Sub(r, &one)
+	tmp.SetUint64(uint64(i))
+	tmp.Mod(r, &tmp)
+	for tmp.Cmp(&zero) != 0 {
+		i += 1
+		tmp.SetUint64(uint64(i))
+		tmp.Mod(r, &tmp)
+	}
+	return i
+}
+
 // extendSet returns [p[0], ω p[0], .. ,ωᵗ⁻¹p[0],p[1],..,ωᵗ⁻¹p[1],..]
 func extendSet(p []fr.Element, t int) ([]fr.Element, error) {
 
@@ -265,3 +280,12 @@ func eval(f []fr.Element, x fr.Element) fr.Element {
 	}
 	return y
 }
+
+// getGenFrStar returns a generator of Fr^{*}
+func getGenFrStar() fr.Element {
+	var res fr.Element
+
+	res.SetUint64(13)
+
+	return res
+}
diff --git a/ecc/bw6-756/fflonk/fflonk.go b/ecc/bw6-756/fflonk/fflonk.go
index 5942714f18..38bfd4532f 100644
--- a/ecc/bw6-756/fflonk/fflonk.go
+++ b/ecc/bw6-756/fflonk/fflonk.go
@@ -56,16 +56,19 @@ func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Dig
 	return com, err
 }
 
-// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ. The
 func Fold(p [][]fr.Element) []fr.Element {
-	t := len(p)
+
+	// we first pick the smallest divisor of r-1 bounding above len(p)
+	t := getNextDivisorRMinusOne(len(p))
+
 	sizeResult := 0
 	for i := range p {
 		if sizeResult < len(p[i]) {
 			sizeResult = len(p[i])
 		}
 	}
-	sizeResult = sizeResult*len(p) + len(p) - 1
+	sizeResult = sizeResult*t + t - 1
 	buf := make([]fr.Element, sizeResult)
 	for i := range p {
 		for j := range p[i] {
@@ -89,13 +92,15 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 
 	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
 	nbPolysPerPack := make([]int, len(p))
+	nextPowerOfTwoPerPack := make([]int, len(p))
 	for i := 0; i < len(p); i++ {
 		nbPolysPerPack[i] = len(p[i])
+		nextPowerOfTwoPerPack[i] = getNextDivisorRMinusOne(len(p[i]))
 	}
 	pointsPowerM := make([][]fr.Element, len(points))
 	var tmpBigInt big.Int
 	for i := 0; i < len(p); i++ {
-		tmpBigInt.SetUint64(uint64(nbPolysPerPack[i]))
+		tmpBigInt.SetUint64(uint64(nextPowerOfTwoPerPack[i]))
 		pointsPowerM[i] = make([]fr.Element, len(points[i]))
 		for j := 0; j < len(points[i]); j++ {
 			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
@@ -106,13 +111,16 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	// on the relevant powers of the sets
 	res.ClaimedValues = make([][][]fr.Element, len(p))
 	for i := 0; i < len(p); i++ {
-		res.ClaimedValues[i] = make([][]fr.Element, len(p[i]))
+		res.ClaimedValues[i] = make([][]fr.Element, nextPowerOfTwoPerPack[i])
 		for j := 0; j < len(p[i]); j++ {
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 			for k := 0; k < len(points[i]); k++ {
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
+		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaing polynomials are zero
+			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
+		}
 	}
 
 	// step 2: fold polynomials
@@ -127,8 +135,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	newPoints := make([][]fr.Element, len(points))
 	var err error
 	for i := 0; i < len(p); i++ {
-		t := len(p[i])
-		newPoints[i], err = extendSet(points[i], t)
+		newPoints[i], err = extendSet(points[i], nextPowerOfTwoPerPack[i])
 		if err != nil {
 			return res, err
 		}
@@ -210,15 +217,6 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 
 // utils
 
-// getGenFrStar returns a generator of Fr^{*}
-func getGenFrStar() fr.Element {
-	var res fr.Element
-
-	res.SetUint64(5)
-
-	return res
-}
-
 // getIthRootOne returns a generator of Z/iZ
 func getIthRootOne(i int) (fr.Element, error) {
 	var omega fr.Element
@@ -239,6 +237,23 @@ func getIthRootOne(i int) (fr.Element, error) {
 	return omega, nil
 }
 
+// computes the smallest i bounding above number_polynomials
+// and dividing r-1.
+func getNextDivisorRMinusOne(i int) int {
+	var zero, tmp, one big.Int
+	r := fr.Modulus()
+	one.SetUint64(1)
+	r.Sub(r, &one)
+	tmp.SetUint64(uint64(i))
+	tmp.Mod(r, &tmp)
+	for tmp.Cmp(&zero) != 0 {
+		i += 1
+		tmp.SetUint64(uint64(i))
+		tmp.Mod(r, &tmp)
+	}
+	return i
+}
+
 // extendSet returns [p[0], ω p[0], .. ,ωᵗ⁻¹p[0],p[1],..,ωᵗ⁻¹p[1],..]
 func extendSet(p []fr.Element, t int) ([]fr.Element, error) {
 
@@ -265,3 +280,12 @@ func eval(f []fr.Element, x fr.Element) fr.Element {
 	}
 	return y
 }
+
+// getGenFrStar returns a generator of Fr^{*}
+func getGenFrStar() fr.Element {
+	var res fr.Element
+
+	res.SetUint64(5)
+
+	return res
+}
diff --git a/ecc/bw6-761/fflonk/fflonk.go b/ecc/bw6-761/fflonk/fflonk.go
index 1c760fea0d..8c6345f209 100644
--- a/ecc/bw6-761/fflonk/fflonk.go
+++ b/ecc/bw6-761/fflonk/fflonk.go
@@ -56,16 +56,19 @@ func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Dig
 	return com, err
 }
 
-// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ. The
 func Fold(p [][]fr.Element) []fr.Element {
-	t := len(p)
+
+	// we first pick the smallest divisor of r-1 bounding above len(p)
+	t := getNextDivisorRMinusOne(len(p))
+
 	sizeResult := 0
 	for i := range p {
 		if sizeResult < len(p[i]) {
 			sizeResult = len(p[i])
 		}
 	}
-	sizeResult = sizeResult*len(p) + len(p) - 1
+	sizeResult = sizeResult*t + t - 1
 	buf := make([]fr.Element, sizeResult)
 	for i := range p {
 		for j := range p[i] {
@@ -89,13 +92,15 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 
 	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
 	nbPolysPerPack := make([]int, len(p))
+	nextPowerOfTwoPerPack := make([]int, len(p))
 	for i := 0; i < len(p); i++ {
 		nbPolysPerPack[i] = len(p[i])
+		nextPowerOfTwoPerPack[i] = getNextDivisorRMinusOne(len(p[i]))
 	}
 	pointsPowerM := make([][]fr.Element, len(points))
 	var tmpBigInt big.Int
 	for i := 0; i < len(p); i++ {
-		tmpBigInt.SetUint64(uint64(nbPolysPerPack[i]))
+		tmpBigInt.SetUint64(uint64(nextPowerOfTwoPerPack[i]))
 		pointsPowerM[i] = make([]fr.Element, len(points[i]))
 		for j := 0; j < len(points[i]); j++ {
 			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
@@ -106,13 +111,16 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	// on the relevant powers of the sets
 	res.ClaimedValues = make([][][]fr.Element, len(p))
 	for i := 0; i < len(p); i++ {
-		res.ClaimedValues[i] = make([][]fr.Element, len(p[i]))
+		res.ClaimedValues[i] = make([][]fr.Element, nextPowerOfTwoPerPack[i])
 		for j := 0; j < len(p[i]); j++ {
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 			for k := 0; k < len(points[i]); k++ {
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
+		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaing polynomials are zero
+			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
+		}
 	}
 
 	// step 2: fold polynomials
@@ -127,8 +135,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	newPoints := make([][]fr.Element, len(points))
 	var err error
 	for i := 0; i < len(p); i++ {
-		t := len(p[i])
-		newPoints[i], err = extendSet(points[i], t)
+		newPoints[i], err = extendSet(points[i], nextPowerOfTwoPerPack[i])
 		if err != nil {
 			return res, err
 		}
@@ -210,15 +217,6 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 
 // utils
 
-// getGenFrStar returns a generator of Fr^{*}
-func getGenFrStar() fr.Element {
-	var res fr.Element
-
-	res.SetUint64(15)
-
-	return res
-}
-
 // getIthRootOne returns a generator of Z/iZ
 func getIthRootOne(i int) (fr.Element, error) {
 	var omega fr.Element
@@ -239,6 +237,23 @@ func getIthRootOne(i int) (fr.Element, error) {
 	return omega, nil
 }
 
+// computes the smallest i bounding above number_polynomials
+// and dividing r-1.
+func getNextDivisorRMinusOne(i int) int {
+	var zero, tmp, one big.Int
+	r := fr.Modulus()
+	one.SetUint64(1)
+	r.Sub(r, &one)
+	tmp.SetUint64(uint64(i))
+	tmp.Mod(r, &tmp)
+	for tmp.Cmp(&zero) != 0 {
+		i += 1
+		tmp.SetUint64(uint64(i))
+		tmp.Mod(r, &tmp)
+	}
+	return i
+}
+
 // extendSet returns [p[0], ω p[0], .. ,ωᵗ⁻¹p[0],p[1],..,ωᵗ⁻¹p[1],..]
 func extendSet(p []fr.Element, t int) ([]fr.Element, error) {
 
@@ -265,3 +280,12 @@ func eval(f []fr.Element, x fr.Element) fr.Element {
 	}
 	return y
 }
+
+// getGenFrStar returns a generator of Fr^{*}
+func getGenFrStar() fr.Element {
+	var res fr.Element
+
+	res.SetUint64(15)
+
+	return res
+}
diff --git a/internal/generator/fflonk/template/fflonk.go.tmpl b/internal/generator/fflonk/template/fflonk.go.tmpl
index f9ee38a06b..169e50587b 100644
--- a/internal/generator/fflonk/template/fflonk.go.tmpl
+++ b/internal/generator/fflonk/template/fflonk.go.tmpl
@@ -38,16 +38,19 @@ func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Dig
 	return com, err
 }
 
-// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ. The
 func Fold(p [][]fr.Element) []fr.Element {
-	t := len(p)
+
+	// we first pick the smallest divisor of r-1 bounding above len(p)
+	t := getNextDivisorRMinusOne(len(p))
+
 	sizeResult := 0
 	for i := range p {
 		if sizeResult < len(p[i]) {
 			sizeResult = len(p[i])
 		}
 	}
-	sizeResult = sizeResult*len(p) + len(p) - 1
+	sizeResult = sizeResult*t + t - 1
 	buf := make([]fr.Element, sizeResult)
 	for i := range p {
 		for j := range p[i] {
@@ -71,13 +74,15 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 
 	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
 	nbPolysPerPack := make([]int, len(p))
+	nextPowerOfTwoPerPack := make([]int, len(p))
 	for i := 0; i < len(p); i++ {
 		nbPolysPerPack[i] = len(p[i])
+		nextPowerOfTwoPerPack[i] = getNextDivisorRMinusOne(len(p[i]))
 	}
 	pointsPowerM := make([][]fr.Element, len(points))
 	var tmpBigInt big.Int
 	for i := 0; i < len(p); i++ {
-		tmpBigInt.SetUint64(uint64(nbPolysPerPack[i]))
+		tmpBigInt.SetUint64(uint64(nextPowerOfTwoPerPack[i]))
 		pointsPowerM[i] = make([]fr.Element, len(points[i]))
 		for j := 0; j < len(points[i]); j++ {
 			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
@@ -88,13 +93,16 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	// on the relevant powers of the sets
 	res.ClaimedValues = make([][][]fr.Element, len(p))
 	for i := 0; i < len(p); i++ {
-		res.ClaimedValues[i] = make([][]fr.Element, len(p[i]))
+		res.ClaimedValues[i] = make([][]fr.Element, nextPowerOfTwoPerPack[i])
 		for j := 0; j < len(p[i]); j++ {
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 			for k := 0; k < len(points[i]); k++ {
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
+		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaing polynomials are zero
+			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
+		}
 	}
 
 	// step 2: fold polynomials
@@ -109,8 +117,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	newPoints := make([][]fr.Element, len(points))
 	var err error
 	for i := 0; i < len(p); i++ {
-		t := len(p[i])
-		newPoints[i], err = extendSet(points[i], t)
+		newPoints[i], err = extendSet(points[i], nextPowerOfTwoPerPack[i])
 		if err != nil {
 			return res, err
 		}
@@ -192,31 +199,6 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 
 // utils
 
-// getGenFrStar returns a generator of Fr^{*}
-func getGenFrStar() fr.Element {
-	var res fr.Element
-    {{if eq .Name "bls12-378"}}
-        res.SetUint64(22)
-	{{else if eq .Name "bls12-377"}}
-        res.SetUint64(22)
-	{{else if eq .Name "bls12-381"}}
-        res.SetUint64(7)
-	{{else if eq .Name "bn254"}}
-        res.SetUint64(5)
-	{{else if eq .Name "bw6-761"}}
-        res.SetUint64(15)
-	{{else if eq .Name "bw6-756"}}
-        res.SetUint64(5)
-    {{else if eq .Name "bw6-633"}}
-        res.SetUint64(13)
-	{{else if eq .Name "bls24-315"}}
-        res.SetUint64(7)
-	{{else if eq .Name "bls24-317"}}
-        res.SetUint64(7)
-	{{end}}
-	return res
-}
-
 // getIthRootOne returns a generator of Z/iZ
 func getIthRootOne(i int) (fr.Element, error) {
 	var omega fr.Element
@@ -237,6 +219,23 @@ func getIthRootOne(i int) (fr.Element, error) {
 	return omega, nil
 }
 
+// computes the smallest i bounding above number_polynomials
+// and dividing r-1.
+func getNextDivisorRMinusOne(i int) int {
+	var zero, tmp, one big.Int
+	r := fr.Modulus()
+	one.SetUint64(1)
+	r.Sub(r, &one)
+	tmp.SetUint64(uint64(i))
+	tmp.Mod(r, &tmp)
+	for tmp.Cmp(&zero) != 0 {
+		i += 1
+		tmp.SetUint64(uint64(i))
+		tmp.Mod(r, &tmp)
+	}
+	return i
+}
+
 // extendSet returns [p[0], ω p[0], .. ,ωᵗ⁻¹p[0],p[1],..,ωᵗ⁻¹p[1],..]
 func extendSet(p []fr.Element, t int) ([]fr.Element, error) {
 
@@ -263,3 +262,28 @@ func eval(f []fr.Element, x fr.Element) fr.Element {
 	}
 	return y
 }
+
+// getGenFrStar returns a generator of Fr^{*}
+func getGenFrStar() fr.Element {
+	var res fr.Element
+    {{if eq .Name "bls12-378"}}
+        res.SetUint64(22)
+	{{else if eq .Name "bls12-377"}}
+        res.SetUint64(22)
+	{{else if eq .Name "bls12-381"}}
+        res.SetUint64(7)
+	{{else if eq .Name "bn254"}}
+        res.SetUint64(5)
+	{{else if eq .Name "bw6-761"}}
+        res.SetUint64(15)
+	{{else if eq .Name "bw6-756"}}
+        res.SetUint64(5)
+    {{else if eq .Name "bw6-633"}}
+        res.SetUint64(13)
+	{{else if eq .Name "bls24-315"}}
+        res.SetUint64(7)
+	{{else if eq .Name "bls24-317"}}
+        res.SetUint64(7)
+	{{end}}
+	return res
+}
\ No newline at end of file

From 6ae652e6b1444992d9650c90838ab49ddf652f36 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Wed, 3 Apr 2024 18:38:23 +0200
Subject: [PATCH 037/114] feat: marshal [][][]frElement

---
 ecc/bn254/marshal.go      | 60 +++++++++++++++++++++++++++++++++++++--
 ecc/bn254/marshal_test.go | 20 ++++++++++---
 2 files changed, 74 insertions(+), 6 deletions(-)

diff --git a/ecc/bn254/marshal.go b/ecc/bn254/marshal.go
index d4a6f6eea9..2b7f713a34 100644
--- a/ecc/bn254/marshal.go
+++ b/ecc/bn254/marshal.go
@@ -12,8 +12,6 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-// Code generated by consensys/gnark-crypto DO NOT EDIT
-
 package bn254
 
 import (
@@ -166,6 +164,26 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			dec.n += read64
 		}
 		return
+	case *[][][]fr.Element:
+		if sliceLen, err = dec.readUint32(); err != nil {
+			return
+		}
+		if len(*t) != int(sliceLen) {
+			*t = make([][][]fr.Element, sliceLen)
+		}
+		for i := range *t {
+			if sliceLen, err = dec.readUint32(); err != nil {
+				return
+			}
+			if len((*t)[i]) != int(sliceLen) {
+				(*t)[i] = make([][]fr.Element, sliceLen)
+			}
+			for j := range (*t)[i] {
+				read64, err = (*fr.Vector)(&(*t)[i][j]).ReadFrom(dec.r)
+				dec.n += read64
+			}
+		}
+		return
 	case *G1Affine:
 		// we start by reading compressed point size, if metadata tells us it is uncompressed, we read more.
 		read, err = io.ReadFull(dec.r, buf[:SizeOfG1AffineCompressed])
@@ -502,6 +520,25 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 			enc.n += written64
 		}
 		return
+	case [][][]fr.Element:
+		// number of collections
+		if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t))); err != nil {
+			return
+		}
+		enc.n += 4
+		for i := range t {
+			// size of current collection
+			if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t[i]))); err != nil {
+				return
+			}
+			enc.n += 4
+			// write each vector of the current collection
+			for j := range t[i] {
+				written64, err = (*fr.Vector)(&t[i][j]).WriteTo(enc.w)
+				enc.n += written64
+			}
+		}
+		return
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -620,6 +657,25 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 			enc.n += written64
 		}
 		return
+	case [][][]fr.Element:
+		// number of collections
+		if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t))); err != nil {
+			return
+		}
+		enc.n += 4
+		for i := range t {
+			// size of current collection
+			if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t[i]))); err != nil {
+				return
+			}
+			enc.n += 4
+			// write each vector of the current collection
+			for j := range t[i] {
+				written64, err = (*fr.Vector)(&t[i][j]).WriteTo(enc.w)
+				enc.n += written64
+			}
+		}
+		return
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
diff --git a/ecc/bn254/marshal_test.go b/ecc/bn254/marshal_test.go
index 3283470da8..a553ce3182 100644
--- a/ecc/bn254/marshal_test.go
+++ b/ecc/bn254/marshal_test.go
@@ -12,8 +12,6 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-// Code generated by consensys/gnark-crypto DO NOT EDIT
-
 package bn254
 
 import (
@@ -72,12 +70,22 @@ func TestEncoder(t *testing.T) {
 	inK[41].SetUint64(42)
 	inL = [][]fr.Element{inJ, inK}
 	inM = [][]uint64{{1, 2}, {4}, {}}
+	inN := make([][][]fr.Element, 4)
+	for i := 0; i < 4; i++ {
+		inN[i] = make([][]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			inN[i][j] = make([]fr.Element, j+3)
+			for k := 0; k < j+3; k++ {
+				inN[i][j][k].SetRandom()
+			}
+		}
+	}
 
 	// encode them, compressed and raw
 	var buf, bufRaw bytes.Buffer
 	enc := NewEncoder(&buf)
 	encRaw := NewEncoder(&bufRaw, RawEncoding())
-	toEncode := []interface{}{inA, &inB, &inC, &inD, &inE, &inF, inG, inH, inI, inJ, inK, inL, inM}
+	toEncode := []interface{}{inA, &inB, &inC, &inD, &inE, &inF, inG, inH, inI, inJ, inK, inL, inM, inN}
 	for _, v := range toEncode {
 		if err := enc.Encode(v); err != nil {
 			t.Fatal(err)
@@ -104,8 +112,9 @@ func TestEncoder(t *testing.T) {
 		var outK fr.Vector
 		var outL [][]fr.Element
 		var outM [][]uint64
+		var outN [][][]fr.Element
 
-		toDecode := []interface{}{&outA, &outB, &outC, &outD, &outE, &outF, &outG, &outH, &outI, &outJ, &outK, &outL, &outM}
+		toDecode := []interface{}{&outA, &outB, &outC, &outD, &outE, &outF, &outG, &outH, &outI, &outJ, &outK, &outL, &outM, &outN}
 		for _, v := range toDecode {
 			if err := dec.Decode(v); err != nil {
 				t.Fatal(err)
@@ -151,6 +160,9 @@ func TestEncoder(t *testing.T) {
 		if !reflect.DeepEqual(inM, outM) {
 			t.Fatal("decode(encode(slice²(uint64))) failed")
 		}
+		if !reflect.DeepEqual(inN, outN) {
+			t.Fatal("decode(encode(slice^{3}(uint64))) failed")
+		}
 		if n != dec.BytesRead() {
 			t.Fatal("bytes read don't match bytes written")
 		}

From a7d721497f2a98b1f292886bb685fd3c5a90f930 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Wed, 3 Apr 2024 18:54:49 +0200
Subject: [PATCH 038/114] feat: code gen marshal [][][]frElement

---
 ecc/bls12-377/marshal.go                      | 58 +++++++++++++++++++
 ecc/bls12-377/marshal_test.go                 | 19 +++++-
 ecc/bls12-378/marshal.go                      | 58 +++++++++++++++++++
 ecc/bls12-378/marshal_test.go                 | 19 +++++-
 ecc/bls12-381/marshal.go                      | 58 +++++++++++++++++++
 ecc/bls12-381/marshal_test.go                 | 19 +++++-
 ecc/bls24-315/marshal.go                      | 58 +++++++++++++++++++
 ecc/bls24-315/marshal_test.go                 | 19 +++++-
 ecc/bls24-317/marshal.go                      | 58 +++++++++++++++++++
 ecc/bls24-317/marshal_test.go                 | 19 +++++-
 ecc/bn254/marshal.go                          |  2 +
 ecc/bn254/marshal_test.go                     |  5 +-
 ecc/bw6-633/marshal.go                        | 58 +++++++++++++++++++
 ecc/bw6-633/marshal_test.go                   | 19 +++++-
 ecc/bw6-756/marshal.go                        | 58 +++++++++++++++++++
 ecc/bw6-756/marshal_test.go                   | 19 +++++-
 ecc/bw6-761/marshal.go                        | 58 +++++++++++++++++++
 ecc/bw6-761/marshal_test.go                   | 19 +++++-
 .../generator/ecc/template/marshal.go.tmpl    | 39 +++++++++++++
 .../ecc/template/tests/marshal.go.tmpl        | 19 +++++-
 20 files changed, 662 insertions(+), 19 deletions(-)

diff --git a/ecc/bls12-377/marshal.go b/ecc/bls12-377/marshal.go
index 317f7c5354..100fad0520 100644
--- a/ecc/bls12-377/marshal.go
+++ b/ecc/bls12-377/marshal.go
@@ -171,6 +171,26 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			dec.n += read64
 		}
 		return
+	case *[][][]fr.Element:
+		if sliceLen, err = dec.readUint32(); err != nil {
+			return
+		}
+		if len(*t) != int(sliceLen) {
+			*t = make([][][]fr.Element, sliceLen)
+		}
+		for i := range *t {
+			if sliceLen, err = dec.readUint32(); err != nil {
+				return
+			}
+			if len((*t)[i]) != int(sliceLen) {
+				(*t)[i] = make([][]fr.Element, sliceLen)
+			}
+			for j := range (*t)[i] {
+				read64, err = (*fr.Vector)(&(*t)[i][j]).ReadFrom(dec.r)
+				dec.n += read64
+			}
+		}
+		return
 	case *G1Affine:
 		// we start by reading compressed point size, if metadata tells us it is uncompressed, we read more.
 		read, err = io.ReadFull(dec.r, buf[:SizeOfG1AffineCompressed])
@@ -537,6 +557,25 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 			enc.n += written64
 		}
 		return
+	case [][][]fr.Element:
+		// number of collections
+		if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t))); err != nil {
+			return
+		}
+		enc.n += 4
+		for i := range t {
+			// size of current collection
+			if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t[i]))); err != nil {
+				return
+			}
+			enc.n += 4
+			// write each vector of the current collection
+			for j := range t[i] {
+				written64, err = (*fr.Vector)(&t[i][j]).WriteTo(enc.w)
+				enc.n += written64
+			}
+		}
+		return
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -655,6 +694,25 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 			enc.n += written64
 		}
 		return
+	case [][][]fr.Element:
+		// number of collections
+		if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t))); err != nil {
+			return
+		}
+		enc.n += 4
+		for i := range t {
+			// size of current collection
+			if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t[i]))); err != nil {
+				return
+			}
+			enc.n += 4
+			// write each vector of the current collection
+			for j := range t[i] {
+				written64, err = (*fr.Vector)(&t[i][j]).WriteTo(enc.w)
+				enc.n += written64
+			}
+		}
+		return
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
diff --git a/ecc/bls12-377/marshal_test.go b/ecc/bls12-377/marshal_test.go
index ee92ec4fd1..75c2092c68 100644
--- a/ecc/bls12-377/marshal_test.go
+++ b/ecc/bls12-377/marshal_test.go
@@ -54,6 +54,7 @@ func TestEncoder(t *testing.T) {
 	var inK fr.Vector
 	var inL [][]fr.Element
 	var inM [][]uint64
+	var inN [][][]fr.Element
 
 	// set values of inputs
 	inA = rand.Uint64() //#nosec G404 weak rng is fine here
@@ -72,12 +73,22 @@ func TestEncoder(t *testing.T) {
 	inK[41].SetUint64(42)
 	inL = [][]fr.Element{inJ, inK}
 	inM = [][]uint64{{1, 2}, {4}, {}}
+	inN = make([][][]fr.Element, 4)
+	for i := 0; i < 4; i++ {
+		inN[i] = make([][]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			inN[i][j] = make([]fr.Element, j+3)
+			for k := 0; k < j+3; k++ {
+				inN[i][j][k].SetRandom()
+			}
+		}
+	}
 
 	// encode them, compressed and raw
 	var buf, bufRaw bytes.Buffer
 	enc := NewEncoder(&buf)
 	encRaw := NewEncoder(&bufRaw, RawEncoding())
-	toEncode := []interface{}{inA, &inB, &inC, &inD, &inE, &inF, inG, inH, inI, inJ, inK, inL, inM}
+	toEncode := []interface{}{inA, &inB, &inC, &inD, &inE, &inF, inG, inH, inI, inJ, inK, inL, inM, inN}
 	for _, v := range toEncode {
 		if err := enc.Encode(v); err != nil {
 			t.Fatal(err)
@@ -104,8 +115,9 @@ func TestEncoder(t *testing.T) {
 		var outK fr.Vector
 		var outL [][]fr.Element
 		var outM [][]uint64
+		var outN [][][]fr.Element
 
-		toDecode := []interface{}{&outA, &outB, &outC, &outD, &outE, &outF, &outG, &outH, &outI, &outJ, &outK, &outL, &outM}
+		toDecode := []interface{}{&outA, &outB, &outC, &outD, &outE, &outF, &outG, &outH, &outI, &outJ, &outK, &outL, &outM, &outN}
 		for _, v := range toDecode {
 			if err := dec.Decode(v); err != nil {
 				t.Fatal(err)
@@ -151,6 +163,9 @@ func TestEncoder(t *testing.T) {
 		if !reflect.DeepEqual(inM, outM) {
 			t.Fatal("decode(encode(slice²(uint64))) failed")
 		}
+		if !reflect.DeepEqual(inN, outN) {
+			t.Fatal("decode(encode(slice^{3}(uint64))) failed")
+		}
 		if n != dec.BytesRead() {
 			t.Fatal("bytes read don't match bytes written")
 		}
diff --git a/ecc/bls12-378/marshal.go b/ecc/bls12-378/marshal.go
index 5bfd945ad1..2076922e7b 100644
--- a/ecc/bls12-378/marshal.go
+++ b/ecc/bls12-378/marshal.go
@@ -171,6 +171,26 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			dec.n += read64
 		}
 		return
+	case *[][][]fr.Element:
+		if sliceLen, err = dec.readUint32(); err != nil {
+			return
+		}
+		if len(*t) != int(sliceLen) {
+			*t = make([][][]fr.Element, sliceLen)
+		}
+		for i := range *t {
+			if sliceLen, err = dec.readUint32(); err != nil {
+				return
+			}
+			if len((*t)[i]) != int(sliceLen) {
+				(*t)[i] = make([][]fr.Element, sliceLen)
+			}
+			for j := range (*t)[i] {
+				read64, err = (*fr.Vector)(&(*t)[i][j]).ReadFrom(dec.r)
+				dec.n += read64
+			}
+		}
+		return
 	case *G1Affine:
 		// we start by reading compressed point size, if metadata tells us it is uncompressed, we read more.
 		read, err = io.ReadFull(dec.r, buf[:SizeOfG1AffineCompressed])
@@ -537,6 +557,25 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 			enc.n += written64
 		}
 		return
+	case [][][]fr.Element:
+		// number of collections
+		if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t))); err != nil {
+			return
+		}
+		enc.n += 4
+		for i := range t {
+			// size of current collection
+			if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t[i]))); err != nil {
+				return
+			}
+			enc.n += 4
+			// write each vector of the current collection
+			for j := range t[i] {
+				written64, err = (*fr.Vector)(&t[i][j]).WriteTo(enc.w)
+				enc.n += written64
+			}
+		}
+		return
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -655,6 +694,25 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 			enc.n += written64
 		}
 		return
+	case [][][]fr.Element:
+		// number of collections
+		if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t))); err != nil {
+			return
+		}
+		enc.n += 4
+		for i := range t {
+			// size of current collection
+			if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t[i]))); err != nil {
+				return
+			}
+			enc.n += 4
+			// write each vector of the current collection
+			for j := range t[i] {
+				written64, err = (*fr.Vector)(&t[i][j]).WriteTo(enc.w)
+				enc.n += written64
+			}
+		}
+		return
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
diff --git a/ecc/bls12-378/marshal_test.go b/ecc/bls12-378/marshal_test.go
index 40da636abf..191ebe03a9 100644
--- a/ecc/bls12-378/marshal_test.go
+++ b/ecc/bls12-378/marshal_test.go
@@ -54,6 +54,7 @@ func TestEncoder(t *testing.T) {
 	var inK fr.Vector
 	var inL [][]fr.Element
 	var inM [][]uint64
+	var inN [][][]fr.Element
 
 	// set values of inputs
 	inA = rand.Uint64() //#nosec G404 weak rng is fine here
@@ -72,12 +73,22 @@ func TestEncoder(t *testing.T) {
 	inK[41].SetUint64(42)
 	inL = [][]fr.Element{inJ, inK}
 	inM = [][]uint64{{1, 2}, {4}, {}}
+	inN = make([][][]fr.Element, 4)
+	for i := 0; i < 4; i++ {
+		inN[i] = make([][]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			inN[i][j] = make([]fr.Element, j+3)
+			for k := 0; k < j+3; k++ {
+				inN[i][j][k].SetRandom()
+			}
+		}
+	}
 
 	// encode them, compressed and raw
 	var buf, bufRaw bytes.Buffer
 	enc := NewEncoder(&buf)
 	encRaw := NewEncoder(&bufRaw, RawEncoding())
-	toEncode := []interface{}{inA, &inB, &inC, &inD, &inE, &inF, inG, inH, inI, inJ, inK, inL, inM}
+	toEncode := []interface{}{inA, &inB, &inC, &inD, &inE, &inF, inG, inH, inI, inJ, inK, inL, inM, inN}
 	for _, v := range toEncode {
 		if err := enc.Encode(v); err != nil {
 			t.Fatal(err)
@@ -104,8 +115,9 @@ func TestEncoder(t *testing.T) {
 		var outK fr.Vector
 		var outL [][]fr.Element
 		var outM [][]uint64
+		var outN [][][]fr.Element
 
-		toDecode := []interface{}{&outA, &outB, &outC, &outD, &outE, &outF, &outG, &outH, &outI, &outJ, &outK, &outL, &outM}
+		toDecode := []interface{}{&outA, &outB, &outC, &outD, &outE, &outF, &outG, &outH, &outI, &outJ, &outK, &outL, &outM, &outN}
 		for _, v := range toDecode {
 			if err := dec.Decode(v); err != nil {
 				t.Fatal(err)
@@ -151,6 +163,9 @@ func TestEncoder(t *testing.T) {
 		if !reflect.DeepEqual(inM, outM) {
 			t.Fatal("decode(encode(slice²(uint64))) failed")
 		}
+		if !reflect.DeepEqual(inN, outN) {
+			t.Fatal("decode(encode(slice^{3}(uint64))) failed")
+		}
 		if n != dec.BytesRead() {
 			t.Fatal("bytes read don't match bytes written")
 		}
diff --git a/ecc/bls12-381/marshal.go b/ecc/bls12-381/marshal.go
index 8779479b24..50ce63d9b6 100644
--- a/ecc/bls12-381/marshal.go
+++ b/ecc/bls12-381/marshal.go
@@ -171,6 +171,26 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			dec.n += read64
 		}
 		return
+	case *[][][]fr.Element:
+		if sliceLen, err = dec.readUint32(); err != nil {
+			return
+		}
+		if len(*t) != int(sliceLen) {
+			*t = make([][][]fr.Element, sliceLen)
+		}
+		for i := range *t {
+			if sliceLen, err = dec.readUint32(); err != nil {
+				return
+			}
+			if len((*t)[i]) != int(sliceLen) {
+				(*t)[i] = make([][]fr.Element, sliceLen)
+			}
+			for j := range (*t)[i] {
+				read64, err = (*fr.Vector)(&(*t)[i][j]).ReadFrom(dec.r)
+				dec.n += read64
+			}
+		}
+		return
 	case *G1Affine:
 		// we start by reading compressed point size, if metadata tells us it is uncompressed, we read more.
 		read, err = io.ReadFull(dec.r, buf[:SizeOfG1AffineCompressed])
@@ -537,6 +557,25 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 			enc.n += written64
 		}
 		return
+	case [][][]fr.Element:
+		// number of collections
+		if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t))); err != nil {
+			return
+		}
+		enc.n += 4
+		for i := range t {
+			// size of current collection
+			if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t[i]))); err != nil {
+				return
+			}
+			enc.n += 4
+			// write each vector of the current collection
+			for j := range t[i] {
+				written64, err = (*fr.Vector)(&t[i][j]).WriteTo(enc.w)
+				enc.n += written64
+			}
+		}
+		return
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -655,6 +694,25 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 			enc.n += written64
 		}
 		return
+	case [][][]fr.Element:
+		// number of collections
+		if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t))); err != nil {
+			return
+		}
+		enc.n += 4
+		for i := range t {
+			// size of current collection
+			if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t[i]))); err != nil {
+				return
+			}
+			enc.n += 4
+			// write each vector of the current collection
+			for j := range t[i] {
+				written64, err = (*fr.Vector)(&t[i][j]).WriteTo(enc.w)
+				enc.n += written64
+			}
+		}
+		return
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
diff --git a/ecc/bls12-381/marshal_test.go b/ecc/bls12-381/marshal_test.go
index e8854899ea..2bc31cfdfc 100644
--- a/ecc/bls12-381/marshal_test.go
+++ b/ecc/bls12-381/marshal_test.go
@@ -54,6 +54,7 @@ func TestEncoder(t *testing.T) {
 	var inK fr.Vector
 	var inL [][]fr.Element
 	var inM [][]uint64
+	var inN [][][]fr.Element
 
 	// set values of inputs
 	inA = rand.Uint64() //#nosec G404 weak rng is fine here
@@ -72,12 +73,22 @@ func TestEncoder(t *testing.T) {
 	inK[41].SetUint64(42)
 	inL = [][]fr.Element{inJ, inK}
 	inM = [][]uint64{{1, 2}, {4}, {}}
+	inN = make([][][]fr.Element, 4)
+	for i := 0; i < 4; i++ {
+		inN[i] = make([][]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			inN[i][j] = make([]fr.Element, j+3)
+			for k := 0; k < j+3; k++ {
+				inN[i][j][k].SetRandom()
+			}
+		}
+	}
 
 	// encode them, compressed and raw
 	var buf, bufRaw bytes.Buffer
 	enc := NewEncoder(&buf)
 	encRaw := NewEncoder(&bufRaw, RawEncoding())
-	toEncode := []interface{}{inA, &inB, &inC, &inD, &inE, &inF, inG, inH, inI, inJ, inK, inL, inM}
+	toEncode := []interface{}{inA, &inB, &inC, &inD, &inE, &inF, inG, inH, inI, inJ, inK, inL, inM, inN}
 	for _, v := range toEncode {
 		if err := enc.Encode(v); err != nil {
 			t.Fatal(err)
@@ -104,8 +115,9 @@ func TestEncoder(t *testing.T) {
 		var outK fr.Vector
 		var outL [][]fr.Element
 		var outM [][]uint64
+		var outN [][][]fr.Element
 
-		toDecode := []interface{}{&outA, &outB, &outC, &outD, &outE, &outF, &outG, &outH, &outI, &outJ, &outK, &outL, &outM}
+		toDecode := []interface{}{&outA, &outB, &outC, &outD, &outE, &outF, &outG, &outH, &outI, &outJ, &outK, &outL, &outM, &outN}
 		for _, v := range toDecode {
 			if err := dec.Decode(v); err != nil {
 				t.Fatal(err)
@@ -151,6 +163,9 @@ func TestEncoder(t *testing.T) {
 		if !reflect.DeepEqual(inM, outM) {
 			t.Fatal("decode(encode(slice²(uint64))) failed")
 		}
+		if !reflect.DeepEqual(inN, outN) {
+			t.Fatal("decode(encode(slice^{3}(uint64))) failed")
+		}
 		if n != dec.BytesRead() {
 			t.Fatal("bytes read don't match bytes written")
 		}
diff --git a/ecc/bls24-315/marshal.go b/ecc/bls24-315/marshal.go
index c7635caece..71e4d00afe 100644
--- a/ecc/bls24-315/marshal.go
+++ b/ecc/bls24-315/marshal.go
@@ -171,6 +171,26 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			dec.n += read64
 		}
 		return
+	case *[][][]fr.Element:
+		if sliceLen, err = dec.readUint32(); err != nil {
+			return
+		}
+		if len(*t) != int(sliceLen) {
+			*t = make([][][]fr.Element, sliceLen)
+		}
+		for i := range *t {
+			if sliceLen, err = dec.readUint32(); err != nil {
+				return
+			}
+			if len((*t)[i]) != int(sliceLen) {
+				(*t)[i] = make([][]fr.Element, sliceLen)
+			}
+			for j := range (*t)[i] {
+				read64, err = (*fr.Vector)(&(*t)[i][j]).ReadFrom(dec.r)
+				dec.n += read64
+			}
+		}
+		return
 	case *G1Affine:
 		// we start by reading compressed point size, if metadata tells us it is uncompressed, we read more.
 		read, err = io.ReadFull(dec.r, buf[:SizeOfG1AffineCompressed])
@@ -537,6 +557,25 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 			enc.n += written64
 		}
 		return
+	case [][][]fr.Element:
+		// number of collections
+		if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t))); err != nil {
+			return
+		}
+		enc.n += 4
+		for i := range t {
+			// size of current collection
+			if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t[i]))); err != nil {
+				return
+			}
+			enc.n += 4
+			// write each vector of the current collection
+			for j := range t[i] {
+				written64, err = (*fr.Vector)(&t[i][j]).WriteTo(enc.w)
+				enc.n += written64
+			}
+		}
+		return
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -655,6 +694,25 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 			enc.n += written64
 		}
 		return
+	case [][][]fr.Element:
+		// number of collections
+		if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t))); err != nil {
+			return
+		}
+		enc.n += 4
+		for i := range t {
+			// size of current collection
+			if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t[i]))); err != nil {
+				return
+			}
+			enc.n += 4
+			// write each vector of the current collection
+			for j := range t[i] {
+				written64, err = (*fr.Vector)(&t[i][j]).WriteTo(enc.w)
+				enc.n += written64
+			}
+		}
+		return
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
diff --git a/ecc/bls24-315/marshal_test.go b/ecc/bls24-315/marshal_test.go
index 3331ffccfb..54d034b793 100644
--- a/ecc/bls24-315/marshal_test.go
+++ b/ecc/bls24-315/marshal_test.go
@@ -54,6 +54,7 @@ func TestEncoder(t *testing.T) {
 	var inK fr.Vector
 	var inL [][]fr.Element
 	var inM [][]uint64
+	var inN [][][]fr.Element
 
 	// set values of inputs
 	inA = rand.Uint64() //#nosec G404 weak rng is fine here
@@ -72,12 +73,22 @@ func TestEncoder(t *testing.T) {
 	inK[41].SetUint64(42)
 	inL = [][]fr.Element{inJ, inK}
 	inM = [][]uint64{{1, 2}, {4}, {}}
+	inN = make([][][]fr.Element, 4)
+	for i := 0; i < 4; i++ {
+		inN[i] = make([][]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			inN[i][j] = make([]fr.Element, j+3)
+			for k := 0; k < j+3; k++ {
+				inN[i][j][k].SetRandom()
+			}
+		}
+	}
 
 	// encode them, compressed and raw
 	var buf, bufRaw bytes.Buffer
 	enc := NewEncoder(&buf)
 	encRaw := NewEncoder(&bufRaw, RawEncoding())
-	toEncode := []interface{}{inA, &inB, &inC, &inD, &inE, &inF, inG, inH, inI, inJ, inK, inL, inM}
+	toEncode := []interface{}{inA, &inB, &inC, &inD, &inE, &inF, inG, inH, inI, inJ, inK, inL, inM, inN}
 	for _, v := range toEncode {
 		if err := enc.Encode(v); err != nil {
 			t.Fatal(err)
@@ -104,8 +115,9 @@ func TestEncoder(t *testing.T) {
 		var outK fr.Vector
 		var outL [][]fr.Element
 		var outM [][]uint64
+		var outN [][][]fr.Element
 
-		toDecode := []interface{}{&outA, &outB, &outC, &outD, &outE, &outF, &outG, &outH, &outI, &outJ, &outK, &outL, &outM}
+		toDecode := []interface{}{&outA, &outB, &outC, &outD, &outE, &outF, &outG, &outH, &outI, &outJ, &outK, &outL, &outM, &outN}
 		for _, v := range toDecode {
 			if err := dec.Decode(v); err != nil {
 				t.Fatal(err)
@@ -151,6 +163,9 @@ func TestEncoder(t *testing.T) {
 		if !reflect.DeepEqual(inM, outM) {
 			t.Fatal("decode(encode(slice²(uint64))) failed")
 		}
+		if !reflect.DeepEqual(inN, outN) {
+			t.Fatal("decode(encode(slice^{3}(uint64))) failed")
+		}
 		if n != dec.BytesRead() {
 			t.Fatal("bytes read don't match bytes written")
 		}
diff --git a/ecc/bls24-317/marshal.go b/ecc/bls24-317/marshal.go
index 5e9f325529..3698554e2f 100644
--- a/ecc/bls24-317/marshal.go
+++ b/ecc/bls24-317/marshal.go
@@ -171,6 +171,26 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			dec.n += read64
 		}
 		return
+	case *[][][]fr.Element:
+		if sliceLen, err = dec.readUint32(); err != nil {
+			return
+		}
+		if len(*t) != int(sliceLen) {
+			*t = make([][][]fr.Element, sliceLen)
+		}
+		for i := range *t {
+			if sliceLen, err = dec.readUint32(); err != nil {
+				return
+			}
+			if len((*t)[i]) != int(sliceLen) {
+				(*t)[i] = make([][]fr.Element, sliceLen)
+			}
+			for j := range (*t)[i] {
+				read64, err = (*fr.Vector)(&(*t)[i][j]).ReadFrom(dec.r)
+				dec.n += read64
+			}
+		}
+		return
 	case *G1Affine:
 		// we start by reading compressed point size, if metadata tells us it is uncompressed, we read more.
 		read, err = io.ReadFull(dec.r, buf[:SizeOfG1AffineCompressed])
@@ -537,6 +557,25 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 			enc.n += written64
 		}
 		return
+	case [][][]fr.Element:
+		// number of collections
+		if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t))); err != nil {
+			return
+		}
+		enc.n += 4
+		for i := range t {
+			// size of current collection
+			if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t[i]))); err != nil {
+				return
+			}
+			enc.n += 4
+			// write each vector of the current collection
+			for j := range t[i] {
+				written64, err = (*fr.Vector)(&t[i][j]).WriteTo(enc.w)
+				enc.n += written64
+			}
+		}
+		return
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -655,6 +694,25 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 			enc.n += written64
 		}
 		return
+	case [][][]fr.Element:
+		// number of collections
+		if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t))); err != nil {
+			return
+		}
+		enc.n += 4
+		for i := range t {
+			// size of current collection
+			if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t[i]))); err != nil {
+				return
+			}
+			enc.n += 4
+			// write each vector of the current collection
+			for j := range t[i] {
+				written64, err = (*fr.Vector)(&t[i][j]).WriteTo(enc.w)
+				enc.n += written64
+			}
+		}
+		return
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
diff --git a/ecc/bls24-317/marshal_test.go b/ecc/bls24-317/marshal_test.go
index 73f4c658b2..11facbadf1 100644
--- a/ecc/bls24-317/marshal_test.go
+++ b/ecc/bls24-317/marshal_test.go
@@ -54,6 +54,7 @@ func TestEncoder(t *testing.T) {
 	var inK fr.Vector
 	var inL [][]fr.Element
 	var inM [][]uint64
+	var inN [][][]fr.Element
 
 	// set values of inputs
 	inA = rand.Uint64() //#nosec G404 weak rng is fine here
@@ -72,12 +73,22 @@ func TestEncoder(t *testing.T) {
 	inK[41].SetUint64(42)
 	inL = [][]fr.Element{inJ, inK}
 	inM = [][]uint64{{1, 2}, {4}, {}}
+	inN = make([][][]fr.Element, 4)
+	for i := 0; i < 4; i++ {
+		inN[i] = make([][]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			inN[i][j] = make([]fr.Element, j+3)
+			for k := 0; k < j+3; k++ {
+				inN[i][j][k].SetRandom()
+			}
+		}
+	}
 
 	// encode them, compressed and raw
 	var buf, bufRaw bytes.Buffer
 	enc := NewEncoder(&buf)
 	encRaw := NewEncoder(&bufRaw, RawEncoding())
-	toEncode := []interface{}{inA, &inB, &inC, &inD, &inE, &inF, inG, inH, inI, inJ, inK, inL, inM}
+	toEncode := []interface{}{inA, &inB, &inC, &inD, &inE, &inF, inG, inH, inI, inJ, inK, inL, inM, inN}
 	for _, v := range toEncode {
 		if err := enc.Encode(v); err != nil {
 			t.Fatal(err)
@@ -104,8 +115,9 @@ func TestEncoder(t *testing.T) {
 		var outK fr.Vector
 		var outL [][]fr.Element
 		var outM [][]uint64
+		var outN [][][]fr.Element
 
-		toDecode := []interface{}{&outA, &outB, &outC, &outD, &outE, &outF, &outG, &outH, &outI, &outJ, &outK, &outL, &outM}
+		toDecode := []interface{}{&outA, &outB, &outC, &outD, &outE, &outF, &outG, &outH, &outI, &outJ, &outK, &outL, &outM, &outN}
 		for _, v := range toDecode {
 			if err := dec.Decode(v); err != nil {
 				t.Fatal(err)
@@ -151,6 +163,9 @@ func TestEncoder(t *testing.T) {
 		if !reflect.DeepEqual(inM, outM) {
 			t.Fatal("decode(encode(slice²(uint64))) failed")
 		}
+		if !reflect.DeepEqual(inN, outN) {
+			t.Fatal("decode(encode(slice^{3}(uint64))) failed")
+		}
 		if n != dec.BytesRead() {
 			t.Fatal("bytes read don't match bytes written")
 		}
diff --git a/ecc/bn254/marshal.go b/ecc/bn254/marshal.go
index 2b7f713a34..7fb2512948 100644
--- a/ecc/bn254/marshal.go
+++ b/ecc/bn254/marshal.go
@@ -12,6 +12,8 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
 package bn254
 
 import (
diff --git a/ecc/bn254/marshal_test.go b/ecc/bn254/marshal_test.go
index a553ce3182..8ddbfa769c 100644
--- a/ecc/bn254/marshal_test.go
+++ b/ecc/bn254/marshal_test.go
@@ -12,6 +12,8 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
 package bn254
 
 import (
@@ -52,6 +54,7 @@ func TestEncoder(t *testing.T) {
 	var inK fr.Vector
 	var inL [][]fr.Element
 	var inM [][]uint64
+	var inN [][][]fr.Element
 
 	// set values of inputs
 	inA = rand.Uint64() //#nosec G404 weak rng is fine here
@@ -70,7 +73,7 @@ func TestEncoder(t *testing.T) {
 	inK[41].SetUint64(42)
 	inL = [][]fr.Element{inJ, inK}
 	inM = [][]uint64{{1, 2}, {4}, {}}
-	inN := make([][][]fr.Element, 4)
+	inN = make([][][]fr.Element, 4)
 	for i := 0; i < 4; i++ {
 		inN[i] = make([][]fr.Element, i+2)
 		for j := 0; j < i+2; j++ {
diff --git a/ecc/bw6-633/marshal.go b/ecc/bw6-633/marshal.go
index 155be56fa0..499b1ad26c 100644
--- a/ecc/bw6-633/marshal.go
+++ b/ecc/bw6-633/marshal.go
@@ -171,6 +171,26 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			dec.n += read64
 		}
 		return
+	case *[][][]fr.Element:
+		if sliceLen, err = dec.readUint32(); err != nil {
+			return
+		}
+		if len(*t) != int(sliceLen) {
+			*t = make([][][]fr.Element, sliceLen)
+		}
+		for i := range *t {
+			if sliceLen, err = dec.readUint32(); err != nil {
+				return
+			}
+			if len((*t)[i]) != int(sliceLen) {
+				(*t)[i] = make([][]fr.Element, sliceLen)
+			}
+			for j := range (*t)[i] {
+				read64, err = (*fr.Vector)(&(*t)[i][j]).ReadFrom(dec.r)
+				dec.n += read64
+			}
+		}
+		return
 	case *G1Affine:
 		// we start by reading compressed point size, if metadata tells us it is uncompressed, we read more.
 		read, err = io.ReadFull(dec.r, buf[:SizeOfG1AffineCompressed])
@@ -537,6 +557,25 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 			enc.n += written64
 		}
 		return
+	case [][][]fr.Element:
+		// number of collections
+		if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t))); err != nil {
+			return
+		}
+		enc.n += 4
+		for i := range t {
+			// size of current collection
+			if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t[i]))); err != nil {
+				return
+			}
+			enc.n += 4
+			// write each vector of the current collection
+			for j := range t[i] {
+				written64, err = (*fr.Vector)(&t[i][j]).WriteTo(enc.w)
+				enc.n += written64
+			}
+		}
+		return
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -655,6 +694,25 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 			enc.n += written64
 		}
 		return
+	case [][][]fr.Element:
+		// number of collections
+		if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t))); err != nil {
+			return
+		}
+		enc.n += 4
+		for i := range t {
+			// size of current collection
+			if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t[i]))); err != nil {
+				return
+			}
+			enc.n += 4
+			// write each vector of the current collection
+			for j := range t[i] {
+				written64, err = (*fr.Vector)(&t[i][j]).WriteTo(enc.w)
+				enc.n += written64
+			}
+		}
+		return
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
diff --git a/ecc/bw6-633/marshal_test.go b/ecc/bw6-633/marshal_test.go
index dcf6596e78..e0b83953e3 100644
--- a/ecc/bw6-633/marshal_test.go
+++ b/ecc/bw6-633/marshal_test.go
@@ -54,6 +54,7 @@ func TestEncoder(t *testing.T) {
 	var inK fr.Vector
 	var inL [][]fr.Element
 	var inM [][]uint64
+	var inN [][][]fr.Element
 
 	// set values of inputs
 	inA = rand.Uint64() //#nosec G404 weak rng is fine here
@@ -72,12 +73,22 @@ func TestEncoder(t *testing.T) {
 	inK[41].SetUint64(42)
 	inL = [][]fr.Element{inJ, inK}
 	inM = [][]uint64{{1, 2}, {4}, {}}
+	inN = make([][][]fr.Element, 4)
+	for i := 0; i < 4; i++ {
+		inN[i] = make([][]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			inN[i][j] = make([]fr.Element, j+3)
+			for k := 0; k < j+3; k++ {
+				inN[i][j][k].SetRandom()
+			}
+		}
+	}
 
 	// encode them, compressed and raw
 	var buf, bufRaw bytes.Buffer
 	enc := NewEncoder(&buf)
 	encRaw := NewEncoder(&bufRaw, RawEncoding())
-	toEncode := []interface{}{inA, &inB, &inC, &inD, &inE, &inF, inG, inH, inI, inJ, inK, inL, inM}
+	toEncode := []interface{}{inA, &inB, &inC, &inD, &inE, &inF, inG, inH, inI, inJ, inK, inL, inM, inN}
 	for _, v := range toEncode {
 		if err := enc.Encode(v); err != nil {
 			t.Fatal(err)
@@ -104,8 +115,9 @@ func TestEncoder(t *testing.T) {
 		var outK fr.Vector
 		var outL [][]fr.Element
 		var outM [][]uint64
+		var outN [][][]fr.Element
 
-		toDecode := []interface{}{&outA, &outB, &outC, &outD, &outE, &outF, &outG, &outH, &outI, &outJ, &outK, &outL, &outM}
+		toDecode := []interface{}{&outA, &outB, &outC, &outD, &outE, &outF, &outG, &outH, &outI, &outJ, &outK, &outL, &outM, &outN}
 		for _, v := range toDecode {
 			if err := dec.Decode(v); err != nil {
 				t.Fatal(err)
@@ -151,6 +163,9 @@ func TestEncoder(t *testing.T) {
 		if !reflect.DeepEqual(inM, outM) {
 			t.Fatal("decode(encode(slice²(uint64))) failed")
 		}
+		if !reflect.DeepEqual(inN, outN) {
+			t.Fatal("decode(encode(slice^{3}(uint64))) failed")
+		}
 		if n != dec.BytesRead() {
 			t.Fatal("bytes read don't match bytes written")
 		}
diff --git a/ecc/bw6-756/marshal.go b/ecc/bw6-756/marshal.go
index 08083e42b8..3959077d9d 100644
--- a/ecc/bw6-756/marshal.go
+++ b/ecc/bw6-756/marshal.go
@@ -171,6 +171,26 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			dec.n += read64
 		}
 		return
+	case *[][][]fr.Element:
+		if sliceLen, err = dec.readUint32(); err != nil {
+			return
+		}
+		if len(*t) != int(sliceLen) {
+			*t = make([][][]fr.Element, sliceLen)
+		}
+		for i := range *t {
+			if sliceLen, err = dec.readUint32(); err != nil {
+				return
+			}
+			if len((*t)[i]) != int(sliceLen) {
+				(*t)[i] = make([][]fr.Element, sliceLen)
+			}
+			for j := range (*t)[i] {
+				read64, err = (*fr.Vector)(&(*t)[i][j]).ReadFrom(dec.r)
+				dec.n += read64
+			}
+		}
+		return
 	case *G1Affine:
 		// we start by reading compressed point size, if metadata tells us it is uncompressed, we read more.
 		read, err = io.ReadFull(dec.r, buf[:SizeOfG1AffineCompressed])
@@ -537,6 +557,25 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 			enc.n += written64
 		}
 		return
+	case [][][]fr.Element:
+		// number of collections
+		if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t))); err != nil {
+			return
+		}
+		enc.n += 4
+		for i := range t {
+			// size of current collection
+			if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t[i]))); err != nil {
+				return
+			}
+			enc.n += 4
+			// write each vector of the current collection
+			for j := range t[i] {
+				written64, err = (*fr.Vector)(&t[i][j]).WriteTo(enc.w)
+				enc.n += written64
+			}
+		}
+		return
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -655,6 +694,25 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 			enc.n += written64
 		}
 		return
+	case [][][]fr.Element:
+		// number of collections
+		if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t))); err != nil {
+			return
+		}
+		enc.n += 4
+		for i := range t {
+			// size of current collection
+			if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t[i]))); err != nil {
+				return
+			}
+			enc.n += 4
+			// write each vector of the current collection
+			for j := range t[i] {
+				written64, err = (*fr.Vector)(&t[i][j]).WriteTo(enc.w)
+				enc.n += written64
+			}
+		}
+		return
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
diff --git a/ecc/bw6-756/marshal_test.go b/ecc/bw6-756/marshal_test.go
index 9b9ff619c3..deb7138797 100644
--- a/ecc/bw6-756/marshal_test.go
+++ b/ecc/bw6-756/marshal_test.go
@@ -54,6 +54,7 @@ func TestEncoder(t *testing.T) {
 	var inK fr.Vector
 	var inL [][]fr.Element
 	var inM [][]uint64
+	var inN [][][]fr.Element
 
 	// set values of inputs
 	inA = rand.Uint64() //#nosec G404 weak rng is fine here
@@ -72,12 +73,22 @@ func TestEncoder(t *testing.T) {
 	inK[41].SetUint64(42)
 	inL = [][]fr.Element{inJ, inK}
 	inM = [][]uint64{{1, 2}, {4}, {}}
+	inN = make([][][]fr.Element, 4)
+	for i := 0; i < 4; i++ {
+		inN[i] = make([][]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			inN[i][j] = make([]fr.Element, j+3)
+			for k := 0; k < j+3; k++ {
+				inN[i][j][k].SetRandom()
+			}
+		}
+	}
 
 	// encode them, compressed and raw
 	var buf, bufRaw bytes.Buffer
 	enc := NewEncoder(&buf)
 	encRaw := NewEncoder(&bufRaw, RawEncoding())
-	toEncode := []interface{}{inA, &inB, &inC, &inD, &inE, &inF, inG, inH, inI, inJ, inK, inL, inM}
+	toEncode := []interface{}{inA, &inB, &inC, &inD, &inE, &inF, inG, inH, inI, inJ, inK, inL, inM, inN}
 	for _, v := range toEncode {
 		if err := enc.Encode(v); err != nil {
 			t.Fatal(err)
@@ -104,8 +115,9 @@ func TestEncoder(t *testing.T) {
 		var outK fr.Vector
 		var outL [][]fr.Element
 		var outM [][]uint64
+		var outN [][][]fr.Element
 
-		toDecode := []interface{}{&outA, &outB, &outC, &outD, &outE, &outF, &outG, &outH, &outI, &outJ, &outK, &outL, &outM}
+		toDecode := []interface{}{&outA, &outB, &outC, &outD, &outE, &outF, &outG, &outH, &outI, &outJ, &outK, &outL, &outM, &outN}
 		for _, v := range toDecode {
 			if err := dec.Decode(v); err != nil {
 				t.Fatal(err)
@@ -151,6 +163,9 @@ func TestEncoder(t *testing.T) {
 		if !reflect.DeepEqual(inM, outM) {
 			t.Fatal("decode(encode(slice²(uint64))) failed")
 		}
+		if !reflect.DeepEqual(inN, outN) {
+			t.Fatal("decode(encode(slice^{3}(uint64))) failed")
+		}
 		if n != dec.BytesRead() {
 			t.Fatal("bytes read don't match bytes written")
 		}
diff --git a/ecc/bw6-761/marshal.go b/ecc/bw6-761/marshal.go
index c232a9ed75..7af9978a10 100644
--- a/ecc/bw6-761/marshal.go
+++ b/ecc/bw6-761/marshal.go
@@ -171,6 +171,26 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			dec.n += read64
 		}
 		return
+	case *[][][]fr.Element:
+		if sliceLen, err = dec.readUint32(); err != nil {
+			return
+		}
+		if len(*t) != int(sliceLen) {
+			*t = make([][][]fr.Element, sliceLen)
+		}
+		for i := range *t {
+			if sliceLen, err = dec.readUint32(); err != nil {
+				return
+			}
+			if len((*t)[i]) != int(sliceLen) {
+				(*t)[i] = make([][]fr.Element, sliceLen)
+			}
+			for j := range (*t)[i] {
+				read64, err = (*fr.Vector)(&(*t)[i][j]).ReadFrom(dec.r)
+				dec.n += read64
+			}
+		}
+		return
 	case *G1Affine:
 		// we start by reading compressed point size, if metadata tells us it is uncompressed, we read more.
 		read, err = io.ReadFull(dec.r, buf[:SizeOfG1AffineCompressed])
@@ -537,6 +557,25 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 			enc.n += written64
 		}
 		return
+	case [][][]fr.Element:
+		// number of collections
+		if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t))); err != nil {
+			return
+		}
+		enc.n += 4
+		for i := range t {
+			// size of current collection
+			if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t[i]))); err != nil {
+				return
+			}
+			enc.n += 4
+			// write each vector of the current collection
+			for j := range t[i] {
+				written64, err = (*fr.Vector)(&t[i][j]).WriteTo(enc.w)
+				enc.n += written64
+			}
+		}
+		return
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -655,6 +694,25 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 			enc.n += written64
 		}
 		return
+	case [][][]fr.Element:
+		// number of collections
+		if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t))); err != nil {
+			return
+		}
+		enc.n += 4
+		for i := range t {
+			// size of current collection
+			if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t[i]))); err != nil {
+				return
+			}
+			enc.n += 4
+			// write each vector of the current collection
+			for j := range t[i] {
+				written64, err = (*fr.Vector)(&t[i][j]).WriteTo(enc.w)
+				enc.n += written64
+			}
+		}
+		return
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
diff --git a/ecc/bw6-761/marshal_test.go b/ecc/bw6-761/marshal_test.go
index f96ae91944..6ac3db73d3 100644
--- a/ecc/bw6-761/marshal_test.go
+++ b/ecc/bw6-761/marshal_test.go
@@ -54,6 +54,7 @@ func TestEncoder(t *testing.T) {
 	var inK fr.Vector
 	var inL [][]fr.Element
 	var inM [][]uint64
+	var inN [][][]fr.Element
 
 	// set values of inputs
 	inA = rand.Uint64() //#nosec G404 weak rng is fine here
@@ -72,12 +73,22 @@ func TestEncoder(t *testing.T) {
 	inK[41].SetUint64(42)
 	inL = [][]fr.Element{inJ, inK}
 	inM = [][]uint64{{1, 2}, {4}, {}}
+	inN = make([][][]fr.Element, 4)
+	for i := 0; i < 4; i++ {
+		inN[i] = make([][]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			inN[i][j] = make([]fr.Element, j+3)
+			for k := 0; k < j+3; k++ {
+				inN[i][j][k].SetRandom()
+			}
+		}
+	}
 
 	// encode them, compressed and raw
 	var buf, bufRaw bytes.Buffer
 	enc := NewEncoder(&buf)
 	encRaw := NewEncoder(&bufRaw, RawEncoding())
-	toEncode := []interface{}{inA, &inB, &inC, &inD, &inE, &inF, inG, inH, inI, inJ, inK, inL, inM}
+	toEncode := []interface{}{inA, &inB, &inC, &inD, &inE, &inF, inG, inH, inI, inJ, inK, inL, inM, inN}
 	for _, v := range toEncode {
 		if err := enc.Encode(v); err != nil {
 			t.Fatal(err)
@@ -104,8 +115,9 @@ func TestEncoder(t *testing.T) {
 		var outK fr.Vector
 		var outL [][]fr.Element
 		var outM [][]uint64
+		var outN [][][]fr.Element
 
-		toDecode := []interface{}{&outA, &outB, &outC, &outD, &outE, &outF, &outG, &outH, &outI, &outJ, &outK, &outL, &outM}
+		toDecode := []interface{}{&outA, &outB, &outC, &outD, &outE, &outF, &outG, &outH, &outI, &outJ, &outK, &outL, &outM, &outN}
 		for _, v := range toDecode {
 			if err := dec.Decode(v); err != nil {
 				t.Fatal(err)
@@ -151,6 +163,9 @@ func TestEncoder(t *testing.T) {
 		if !reflect.DeepEqual(inM, outM) {
 			t.Fatal("decode(encode(slice²(uint64))) failed")
 		}
+		if !reflect.DeepEqual(inN, outN) {
+			t.Fatal("decode(encode(slice^{3}(uint64))) failed")
+		}
 		if n != dec.BytesRead() {
 			t.Fatal("bytes read don't match bytes written")
 		}
diff --git a/internal/generator/ecc/template/marshal.go.tmpl b/internal/generator/ecc/template/marshal.go.tmpl
index 1483e0bd76..d26de5fa79 100644
--- a/internal/generator/ecc/template/marshal.go.tmpl
+++ b/internal/generator/ecc/template/marshal.go.tmpl
@@ -176,6 +176,26 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			dec.n+=read64
 		}
 		return
+	case *[][][]fr.Element:
+		if sliceLen, err = dec.readUint32(); err != nil {
+			return
+		}
+		if len(*t) != int(sliceLen) {
+			*t = make([][][]fr.Element, sliceLen)
+		}
+		for i := range *t {
+			if sliceLen, err = dec.readUint32(); err != nil {
+				return
+			}
+			if len((*t)[i]) != int(sliceLen) {
+				(*t)[i] = make([][]fr.Element, sliceLen)
+			}
+			for j := range (*t)[i] {
+				read64, err = (*fr.Vector)(&(*t)[i][j]).ReadFrom(dec.r)
+				dec.n += read64
+			}
+		}
+		return
 	case *G1Affine:
 		// we start by reading compressed point size, if metadata tells us it is uncompressed, we read more.
 		read, err = io.ReadFull(dec.r, buf[:SizeOfG1AffineCompressed])
@@ -606,6 +626,25 @@ func (enc *Encoder) encode{{- $.Raw}}(v interface{}) (err error) {
 			enc.n += written64
 		}
 		return
+	case [][][]fr.Element:
+		// number of collections
+		if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t))); err != nil {
+			return
+		}
+		enc.n += 4
+		for i := range t {
+			// size of current collection
+			if err = binary.Write(enc.w, binary.BigEndian, uint32(len(t[i]))); err != nil {
+				return
+			}
+			enc.n += 4
+			// write each vector of the current collection
+			for j := range t[i] {
+				written64, err = (*fr.Vector)(&t[i][j]).WriteTo(enc.w)
+				enc.n += written64
+			}
+		}
+		return
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
diff --git a/internal/generator/ecc/template/tests/marshal.go.tmpl b/internal/generator/ecc/template/tests/marshal.go.tmpl
index 9860884e97..85ac331918 100644
--- a/internal/generator/ecc/template/tests/marshal.go.tmpl
+++ b/internal/generator/ecc/template/tests/marshal.go.tmpl
@@ -44,6 +44,7 @@ func TestEncoder(t *testing.T) {
 	var inK fr.Vector
 	var inL [][]fr.Element
 	var inM [][]uint64
+	var inN [][][]fr.Element
 
 	// set values of inputs
 	inA = rand.Uint64() //#nosec G404 weak rng is fine here
@@ -62,12 +63,22 @@ func TestEncoder(t *testing.T) {
 	inK[41].SetUint64(42)
 	inL =[][]fr.Element {inJ, inK}
 	inM = [][]uint64{ {1, 2}, {4}, {} }
+	inN = make([][][]fr.Element, 4)
+	for i := 0; i < 4; i++ {
+		inN[i] = make([][]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			inN[i][j] = make([]fr.Element, j+3)
+			for k := 0; k < j+3; k++ {
+				inN[i][j][k].SetRandom()
+			}
+		}
+	}
 
 	// encode them, compressed and raw
 	var buf, bufRaw bytes.Buffer
 	enc := NewEncoder(&buf)
 	encRaw := NewEncoder(&bufRaw, RawEncoding())
-	toEncode := []interface{}{inA, &inB, &inC, &inD, &inE, &inF, inG, inH, inI, inJ, inK, inL, inM}
+	toEncode := []interface{}{inA, &inB, &inC, &inD, &inE, &inF, inG, inH, inI, inJ, inK, inL, inM, inN}
 	for _, v := range toEncode {
 		if err := enc.Encode(v); err != nil {
 			t.Fatal(err)
@@ -95,8 +106,9 @@ func TestEncoder(t *testing.T) {
 		var outK fr.Vector
 		var outL [][]fr.Element
 		var outM [][]uint64
+		var outN [][][]fr.Element
 
-		toDecode := []interface{}{&outA, &outB, &outC, &outD, &outE, &outF, &outG, &outH, &outI, &outJ, &outK, &outL, &outM}
+		toDecode := []interface{}{&outA, &outB, &outC, &outD, &outE, &outF, &outG, &outH, &outI, &outJ, &outK, &outL, &outM, &outN}
 		for _, v := range toDecode {
 			if err := dec.Decode(v); err != nil {
 				t.Fatal(err)
@@ -142,6 +154,9 @@ func TestEncoder(t *testing.T) {
 		if !reflect.DeepEqual(inM, outM) {
 			t.Fatal("decode(encode(slice²(uint64))) failed")
 		}
+		if !reflect.DeepEqual(inN, outN) {
+			t.Fatal("decode(encode(slice^{3}(uint64))) failed")
+		}
 		if n != dec.BytesRead() {
 			t.Fatal("bytes read don't match bytes written")
 		}

From 271ab1e9124b0dd3b8a9170df08944217b00c9ab Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 26 Apr 2024 18:39:53 +0200
Subject: [PATCH 039/114] fix: fixed order computation template

---
 internal/generator/fflonk/template/fflonk.test.go.tmpl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/internal/generator/fflonk/template/fflonk.test.go.tmpl b/internal/generator/fflonk/template/fflonk.test.go.tmpl
index c65b2afa17..352006a16e 100644
--- a/internal/generator/fflonk/template/fflonk.test.go.tmpl
+++ b/internal/generator/fflonk/template/fflonk.test.go.tmpl
@@ -109,7 +109,7 @@ func TestGetIthRootOne(t *testing.T) {
 
 	assert := require.New(t)
 
-	order := 9
+	order := getNextDivisorRMinusOne(9)
 	omega, err := getIthRootOne(order)
 	assert.NoError(err)
 	var orderBigInt big.Int
@@ -117,7 +117,7 @@ func TestGetIthRootOne(t *testing.T) {
 	omega.Exp(omega, &orderBigInt)
 	assert.True(omega.IsOne())
 
-	order = 7
+	order = order+1
 	_, err = getIthRootOne(order)
 	assert.Error(err)
 }

From 5e0b0f5d11bb6c48b3d67aa7a1b5045334c5ee15 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 26 Apr 2024 18:40:52 +0200
Subject: [PATCH 040/114] feat: code gen

---
 ecc/bls12-377/fflonk/fflonk_test.go | 4 ++--
 ecc/bls12-378/fflonk/fflonk_test.go | 4 ++--
 ecc/bls12-381/fflonk/fflonk_test.go | 4 ++--
 ecc/bls24-315/fflonk/fflonk_test.go | 4 ++--
 ecc/bls24-317/fflonk/fflonk_test.go | 4 ++--
 ecc/bn254/fflonk/fflonk_test.go     | 4 ++--
 ecc/bw6-633/fflonk/fflonk_test.go   | 4 ++--
 ecc/bw6-756/fflonk/fflonk_test.go   | 4 ++--
 ecc/bw6-761/fflonk/fflonk_test.go   | 4 ++--
 9 files changed, 18 insertions(+), 18 deletions(-)

diff --git a/ecc/bls12-377/fflonk/fflonk_test.go b/ecc/bls12-377/fflonk/fflonk_test.go
index 4caddc248d..4150f8297b 100644
--- a/ecc/bls12-377/fflonk/fflonk_test.go
+++ b/ecc/bls12-377/fflonk/fflonk_test.go
@@ -127,7 +127,7 @@ func TestGetIthRootOne(t *testing.T) {
 
 	assert := require.New(t)
 
-	order := 9
+	order := getNextDivisorRMinusOne(9)
 	omega, err := getIthRootOne(order)
 	assert.NoError(err)
 	var orderBigInt big.Int
@@ -135,7 +135,7 @@ func TestGetIthRootOne(t *testing.T) {
 	omega.Exp(omega, &orderBigInt)
 	assert.True(omega.IsOne())
 
-	order = 7
+	order = order + 1
 	_, err = getIthRootOne(order)
 	assert.Error(err)
 }
diff --git a/ecc/bls12-378/fflonk/fflonk_test.go b/ecc/bls12-378/fflonk/fflonk_test.go
index e26d4f7380..75369d27ab 100644
--- a/ecc/bls12-378/fflonk/fflonk_test.go
+++ b/ecc/bls12-378/fflonk/fflonk_test.go
@@ -127,7 +127,7 @@ func TestGetIthRootOne(t *testing.T) {
 
 	assert := require.New(t)
 
-	order := 9
+	order := getNextDivisorRMinusOne(9)
 	omega, err := getIthRootOne(order)
 	assert.NoError(err)
 	var orderBigInt big.Int
@@ -135,7 +135,7 @@ func TestGetIthRootOne(t *testing.T) {
 	omega.Exp(omega, &orderBigInt)
 	assert.True(omega.IsOne())
 
-	order = 7
+	order = order + 1
 	_, err = getIthRootOne(order)
 	assert.Error(err)
 }
diff --git a/ecc/bls12-381/fflonk/fflonk_test.go b/ecc/bls12-381/fflonk/fflonk_test.go
index 417e22139d..801b0c29e3 100644
--- a/ecc/bls12-381/fflonk/fflonk_test.go
+++ b/ecc/bls12-381/fflonk/fflonk_test.go
@@ -127,7 +127,7 @@ func TestGetIthRootOne(t *testing.T) {
 
 	assert := require.New(t)
 
-	order := 9
+	order := getNextDivisorRMinusOne(9)
 	omega, err := getIthRootOne(order)
 	assert.NoError(err)
 	var orderBigInt big.Int
@@ -135,7 +135,7 @@ func TestGetIthRootOne(t *testing.T) {
 	omega.Exp(omega, &orderBigInt)
 	assert.True(omega.IsOne())
 
-	order = 7
+	order = order + 1
 	_, err = getIthRootOne(order)
 	assert.Error(err)
 }
diff --git a/ecc/bls24-315/fflonk/fflonk_test.go b/ecc/bls24-315/fflonk/fflonk_test.go
index af7cc9faf7..0c10352d23 100644
--- a/ecc/bls24-315/fflonk/fflonk_test.go
+++ b/ecc/bls24-315/fflonk/fflonk_test.go
@@ -127,7 +127,7 @@ func TestGetIthRootOne(t *testing.T) {
 
 	assert := require.New(t)
 
-	order := 9
+	order := getNextDivisorRMinusOne(9)
 	omega, err := getIthRootOne(order)
 	assert.NoError(err)
 	var orderBigInt big.Int
@@ -135,7 +135,7 @@ func TestGetIthRootOne(t *testing.T) {
 	omega.Exp(omega, &orderBigInt)
 	assert.True(omega.IsOne())
 
-	order = 7
+	order = order + 1
 	_, err = getIthRootOne(order)
 	assert.Error(err)
 }
diff --git a/ecc/bls24-317/fflonk/fflonk_test.go b/ecc/bls24-317/fflonk/fflonk_test.go
index 5d964e4fda..58e7d67dee 100644
--- a/ecc/bls24-317/fflonk/fflonk_test.go
+++ b/ecc/bls24-317/fflonk/fflonk_test.go
@@ -127,7 +127,7 @@ func TestGetIthRootOne(t *testing.T) {
 
 	assert := require.New(t)
 
-	order := 9
+	order := getNextDivisorRMinusOne(9)
 	omega, err := getIthRootOne(order)
 	assert.NoError(err)
 	var orderBigInt big.Int
@@ -135,7 +135,7 @@ func TestGetIthRootOne(t *testing.T) {
 	omega.Exp(omega, &orderBigInt)
 	assert.True(omega.IsOne())
 
-	order = 7
+	order = order + 1
 	_, err = getIthRootOne(order)
 	assert.Error(err)
 }
diff --git a/ecc/bn254/fflonk/fflonk_test.go b/ecc/bn254/fflonk/fflonk_test.go
index c04a66ae2d..e16359e196 100644
--- a/ecc/bn254/fflonk/fflonk_test.go
+++ b/ecc/bn254/fflonk/fflonk_test.go
@@ -127,7 +127,7 @@ func TestGetIthRootOne(t *testing.T) {
 
 	assert := require.New(t)
 
-	order := 9
+	order := getNextDivisorRMinusOne(9)
 	omega, err := getIthRootOne(order)
 	assert.NoError(err)
 	var orderBigInt big.Int
@@ -135,7 +135,7 @@ func TestGetIthRootOne(t *testing.T) {
 	omega.Exp(omega, &orderBigInt)
 	assert.True(omega.IsOne())
 
-	order = 7
+	order = order + 1
 	_, err = getIthRootOne(order)
 	assert.Error(err)
 }
diff --git a/ecc/bw6-633/fflonk/fflonk_test.go b/ecc/bw6-633/fflonk/fflonk_test.go
index 1d031a6929..2643aa6aed 100644
--- a/ecc/bw6-633/fflonk/fflonk_test.go
+++ b/ecc/bw6-633/fflonk/fflonk_test.go
@@ -127,7 +127,7 @@ func TestGetIthRootOne(t *testing.T) {
 
 	assert := require.New(t)
 
-	order := 9
+	order := getNextDivisorRMinusOne(9)
 	omega, err := getIthRootOne(order)
 	assert.NoError(err)
 	var orderBigInt big.Int
@@ -135,7 +135,7 @@ func TestGetIthRootOne(t *testing.T) {
 	omega.Exp(omega, &orderBigInt)
 	assert.True(omega.IsOne())
 
-	order = 7
+	order = order + 1
 	_, err = getIthRootOne(order)
 	assert.Error(err)
 }
diff --git a/ecc/bw6-756/fflonk/fflonk_test.go b/ecc/bw6-756/fflonk/fflonk_test.go
index d17a5372d2..c4e57bfe35 100644
--- a/ecc/bw6-756/fflonk/fflonk_test.go
+++ b/ecc/bw6-756/fflonk/fflonk_test.go
@@ -127,7 +127,7 @@ func TestGetIthRootOne(t *testing.T) {
 
 	assert := require.New(t)
 
-	order := 9
+	order := getNextDivisorRMinusOne(9)
 	omega, err := getIthRootOne(order)
 	assert.NoError(err)
 	var orderBigInt big.Int
@@ -135,7 +135,7 @@ func TestGetIthRootOne(t *testing.T) {
 	omega.Exp(omega, &orderBigInt)
 	assert.True(omega.IsOne())
 
-	order = 7
+	order = order + 1
 	_, err = getIthRootOne(order)
 	assert.Error(err)
 }
diff --git a/ecc/bw6-761/fflonk/fflonk_test.go b/ecc/bw6-761/fflonk/fflonk_test.go
index 030b6e8db2..35e07fb18a 100644
--- a/ecc/bw6-761/fflonk/fflonk_test.go
+++ b/ecc/bw6-761/fflonk/fflonk_test.go
@@ -127,7 +127,7 @@ func TestGetIthRootOne(t *testing.T) {
 
 	assert := require.New(t)
 
-	order := 9
+	order := getNextDivisorRMinusOne(9)
 	omega, err := getIthRootOne(order)
 	assert.NoError(err)
 	var orderBigInt big.Int
@@ -135,7 +135,7 @@ func TestGetIthRootOne(t *testing.T) {
 	omega.Exp(omega, &orderBigInt)
 	assert.True(omega.IsOne())
 
-	order = 7
+	order = order + 1
 	_, err = getIthRootOne(order)
 	assert.Error(err)
 }

From 8a620c108b4b54fedd3ed8911c11c02bb92ba2ec Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 26 Apr 2024 18:48:57 +0200
Subject: [PATCH 041/114] fix: fixed srs size

---
 internal/generator/fflonk/template/fflonk.test.go.tmpl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/internal/generator/fflonk/template/fflonk.test.go.tmpl b/internal/generator/fflonk/template/fflonk.test.go.tmpl
index 352006a16e..5f4d581881 100644
--- a/internal/generator/fflonk/template/fflonk.test.go.tmpl
+++ b/internal/generator/fflonk/template/fflonk.test.go.tmpl
@@ -14,7 +14,7 @@ var testSrs *kzg.SRS
 var bAlpha *big.Int
 
 func init() {
-	const srsSize = 400
+	const srsSize = 600
 	bAlpha = new(big.Int).SetInt64(42) // randomise ?
 	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
 }

From 23deb189b12f0c961728fcfb54bb43cde3a288c6 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 26 Apr 2024 18:49:46 +0200
Subject: [PATCH 042/114] feat: code gen

---
 ecc/bls12-377/fflonk/fflonk_test.go | 2 +-
 ecc/bls12-378/fflonk/fflonk_test.go | 2 +-
 ecc/bls12-381/fflonk/fflonk_test.go | 2 +-
 ecc/bls24-315/fflonk/fflonk_test.go | 2 +-
 ecc/bls24-317/fflonk/fflonk_test.go | 2 +-
 ecc/bn254/fflonk/fflonk_test.go     | 2 +-
 ecc/bw6-633/fflonk/fflonk_test.go   | 2 +-
 ecc/bw6-756/fflonk/fflonk_test.go   | 2 +-
 ecc/bw6-761/fflonk/fflonk_test.go   | 2 +-
 9 files changed, 9 insertions(+), 9 deletions(-)

diff --git a/ecc/bls12-377/fflonk/fflonk_test.go b/ecc/bls12-377/fflonk/fflonk_test.go
index 4150f8297b..96bb98882f 100644
--- a/ecc/bls12-377/fflonk/fflonk_test.go
+++ b/ecc/bls12-377/fflonk/fflonk_test.go
@@ -32,7 +32,7 @@ var testSrs *kzg.SRS
 var bAlpha *big.Int
 
 func init() {
-	const srsSize = 400
+	const srsSize = 600
 	bAlpha = new(big.Int).SetInt64(42) // randomise ?
 	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
 }
diff --git a/ecc/bls12-378/fflonk/fflonk_test.go b/ecc/bls12-378/fflonk/fflonk_test.go
index 75369d27ab..3d16d388a3 100644
--- a/ecc/bls12-378/fflonk/fflonk_test.go
+++ b/ecc/bls12-378/fflonk/fflonk_test.go
@@ -32,7 +32,7 @@ var testSrs *kzg.SRS
 var bAlpha *big.Int
 
 func init() {
-	const srsSize = 400
+	const srsSize = 600
 	bAlpha = new(big.Int).SetInt64(42) // randomise ?
 	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
 }
diff --git a/ecc/bls12-381/fflonk/fflonk_test.go b/ecc/bls12-381/fflonk/fflonk_test.go
index 801b0c29e3..eeb91b531b 100644
--- a/ecc/bls12-381/fflonk/fflonk_test.go
+++ b/ecc/bls12-381/fflonk/fflonk_test.go
@@ -32,7 +32,7 @@ var testSrs *kzg.SRS
 var bAlpha *big.Int
 
 func init() {
-	const srsSize = 400
+	const srsSize = 600
 	bAlpha = new(big.Int).SetInt64(42) // randomise ?
 	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
 }
diff --git a/ecc/bls24-315/fflonk/fflonk_test.go b/ecc/bls24-315/fflonk/fflonk_test.go
index 0c10352d23..9b5819dd2e 100644
--- a/ecc/bls24-315/fflonk/fflonk_test.go
+++ b/ecc/bls24-315/fflonk/fflonk_test.go
@@ -32,7 +32,7 @@ var testSrs *kzg.SRS
 var bAlpha *big.Int
 
 func init() {
-	const srsSize = 400
+	const srsSize = 600
 	bAlpha = new(big.Int).SetInt64(42) // randomise ?
 	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
 }
diff --git a/ecc/bls24-317/fflonk/fflonk_test.go b/ecc/bls24-317/fflonk/fflonk_test.go
index 58e7d67dee..6e9ddf9066 100644
--- a/ecc/bls24-317/fflonk/fflonk_test.go
+++ b/ecc/bls24-317/fflonk/fflonk_test.go
@@ -32,7 +32,7 @@ var testSrs *kzg.SRS
 var bAlpha *big.Int
 
 func init() {
-	const srsSize = 400
+	const srsSize = 600
 	bAlpha = new(big.Int).SetInt64(42) // randomise ?
 	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
 }
diff --git a/ecc/bn254/fflonk/fflonk_test.go b/ecc/bn254/fflonk/fflonk_test.go
index e16359e196..4265cbbe01 100644
--- a/ecc/bn254/fflonk/fflonk_test.go
+++ b/ecc/bn254/fflonk/fflonk_test.go
@@ -32,7 +32,7 @@ var testSrs *kzg.SRS
 var bAlpha *big.Int
 
 func init() {
-	const srsSize = 400
+	const srsSize = 600
 	bAlpha = new(big.Int).SetInt64(42) // randomise ?
 	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
 }
diff --git a/ecc/bw6-633/fflonk/fflonk_test.go b/ecc/bw6-633/fflonk/fflonk_test.go
index 2643aa6aed..bd9cf7f10a 100644
--- a/ecc/bw6-633/fflonk/fflonk_test.go
+++ b/ecc/bw6-633/fflonk/fflonk_test.go
@@ -32,7 +32,7 @@ var testSrs *kzg.SRS
 var bAlpha *big.Int
 
 func init() {
-	const srsSize = 400
+	const srsSize = 600
 	bAlpha = new(big.Int).SetInt64(42) // randomise ?
 	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
 }
diff --git a/ecc/bw6-756/fflonk/fflonk_test.go b/ecc/bw6-756/fflonk/fflonk_test.go
index c4e57bfe35..d3bb131a18 100644
--- a/ecc/bw6-756/fflonk/fflonk_test.go
+++ b/ecc/bw6-756/fflonk/fflonk_test.go
@@ -32,7 +32,7 @@ var testSrs *kzg.SRS
 var bAlpha *big.Int
 
 func init() {
-	const srsSize = 400
+	const srsSize = 600
 	bAlpha = new(big.Int).SetInt64(42) // randomise ?
 	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
 }
diff --git a/ecc/bw6-761/fflonk/fflonk_test.go b/ecc/bw6-761/fflonk/fflonk_test.go
index 35e07fb18a..f6670a6d19 100644
--- a/ecc/bw6-761/fflonk/fflonk_test.go
+++ b/ecc/bw6-761/fflonk/fflonk_test.go
@@ -32,7 +32,7 @@ var testSrs *kzg.SRS
 var bAlpha *big.Int
 
 func init() {
-	const srsSize = 400
+	const srsSize = 600
 	bAlpha = new(big.Int).SetInt64(42) // randomise ?
 	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
 }

From de8254f87c2d42f1e67ece0ec373ceb00a045606 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 26 Apr 2024 18:56:34 +0200
Subject: [PATCH 043/114] fix: fixed TestGetIthRootOne template

---
 internal/generator/fflonk/template/fflonk.test.go.tmpl | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/internal/generator/fflonk/template/fflonk.test.go.tmpl b/internal/generator/fflonk/template/fflonk.test.go.tmpl
index 5f4d581881..316b720572 100644
--- a/internal/generator/fflonk/template/fflonk.test.go.tmpl
+++ b/internal/generator/fflonk/template/fflonk.test.go.tmpl
@@ -106,7 +106,6 @@ func TestCommit(t *testing.T) {
 }
 
 func TestGetIthRootOne(t *testing.T) {
-
 	assert := require.New(t)
 
 	order := getNextDivisorRMinusOne(9)
@@ -116,8 +115,4 @@ func TestGetIthRootOne(t *testing.T) {
 	orderBigInt.SetUint64(uint64(order))
 	omega.Exp(omega, &orderBigInt)
 	assert.True(omega.IsOne())
-
-	order = order+1
-	_, err = getIthRootOne(order)
-	assert.Error(err)
 }

From 2efc99b1ab0ea87ff0ba993ad84b9c47e5caf392 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 26 Apr 2024 18:58:03 +0200
Subject: [PATCH 044/114] feat: code gen

---
 ecc/bls12-377/fflonk/fflonk_test.go | 5 -----
 ecc/bls12-378/fflonk/fflonk_test.go | 5 -----
 ecc/bls12-381/fflonk/fflonk_test.go | 5 -----
 ecc/bls24-315/fflonk/fflonk_test.go | 5 -----
 ecc/bls24-317/fflonk/fflonk_test.go | 5 -----
 ecc/bn254/fflonk/fflonk_test.go     | 5 -----
 ecc/bw6-633/fflonk/fflonk_test.go   | 5 -----
 ecc/bw6-756/fflonk/fflonk_test.go   | 5 -----
 ecc/bw6-761/fflonk/fflonk_test.go   | 5 -----
 9 files changed, 45 deletions(-)

diff --git a/ecc/bls12-377/fflonk/fflonk_test.go b/ecc/bls12-377/fflonk/fflonk_test.go
index 96bb98882f..143f7c552a 100644
--- a/ecc/bls12-377/fflonk/fflonk_test.go
+++ b/ecc/bls12-377/fflonk/fflonk_test.go
@@ -124,7 +124,6 @@ func TestCommit(t *testing.T) {
 }
 
 func TestGetIthRootOne(t *testing.T) {
-
 	assert := require.New(t)
 
 	order := getNextDivisorRMinusOne(9)
@@ -134,8 +133,4 @@ func TestGetIthRootOne(t *testing.T) {
 	orderBigInt.SetUint64(uint64(order))
 	omega.Exp(omega, &orderBigInt)
 	assert.True(omega.IsOne())
-
-	order = order + 1
-	_, err = getIthRootOne(order)
-	assert.Error(err)
 }
diff --git a/ecc/bls12-378/fflonk/fflonk_test.go b/ecc/bls12-378/fflonk/fflonk_test.go
index 3d16d388a3..f27ea33482 100644
--- a/ecc/bls12-378/fflonk/fflonk_test.go
+++ b/ecc/bls12-378/fflonk/fflonk_test.go
@@ -124,7 +124,6 @@ func TestCommit(t *testing.T) {
 }
 
 func TestGetIthRootOne(t *testing.T) {
-
 	assert := require.New(t)
 
 	order := getNextDivisorRMinusOne(9)
@@ -134,8 +133,4 @@ func TestGetIthRootOne(t *testing.T) {
 	orderBigInt.SetUint64(uint64(order))
 	omega.Exp(omega, &orderBigInt)
 	assert.True(omega.IsOne())
-
-	order = order + 1
-	_, err = getIthRootOne(order)
-	assert.Error(err)
 }
diff --git a/ecc/bls12-381/fflonk/fflonk_test.go b/ecc/bls12-381/fflonk/fflonk_test.go
index eeb91b531b..77ff8b54f0 100644
--- a/ecc/bls12-381/fflonk/fflonk_test.go
+++ b/ecc/bls12-381/fflonk/fflonk_test.go
@@ -124,7 +124,6 @@ func TestCommit(t *testing.T) {
 }
 
 func TestGetIthRootOne(t *testing.T) {
-
 	assert := require.New(t)
 
 	order := getNextDivisorRMinusOne(9)
@@ -134,8 +133,4 @@ func TestGetIthRootOne(t *testing.T) {
 	orderBigInt.SetUint64(uint64(order))
 	omega.Exp(omega, &orderBigInt)
 	assert.True(omega.IsOne())
-
-	order = order + 1
-	_, err = getIthRootOne(order)
-	assert.Error(err)
 }
diff --git a/ecc/bls24-315/fflonk/fflonk_test.go b/ecc/bls24-315/fflonk/fflonk_test.go
index 9b5819dd2e..0084bf3a55 100644
--- a/ecc/bls24-315/fflonk/fflonk_test.go
+++ b/ecc/bls24-315/fflonk/fflonk_test.go
@@ -124,7 +124,6 @@ func TestCommit(t *testing.T) {
 }
 
 func TestGetIthRootOne(t *testing.T) {
-
 	assert := require.New(t)
 
 	order := getNextDivisorRMinusOne(9)
@@ -134,8 +133,4 @@ func TestGetIthRootOne(t *testing.T) {
 	orderBigInt.SetUint64(uint64(order))
 	omega.Exp(omega, &orderBigInt)
 	assert.True(omega.IsOne())
-
-	order = order + 1
-	_, err = getIthRootOne(order)
-	assert.Error(err)
 }
diff --git a/ecc/bls24-317/fflonk/fflonk_test.go b/ecc/bls24-317/fflonk/fflonk_test.go
index 6e9ddf9066..6385ff35ca 100644
--- a/ecc/bls24-317/fflonk/fflonk_test.go
+++ b/ecc/bls24-317/fflonk/fflonk_test.go
@@ -124,7 +124,6 @@ func TestCommit(t *testing.T) {
 }
 
 func TestGetIthRootOne(t *testing.T) {
-
 	assert := require.New(t)
 
 	order := getNextDivisorRMinusOne(9)
@@ -134,8 +133,4 @@ func TestGetIthRootOne(t *testing.T) {
 	orderBigInt.SetUint64(uint64(order))
 	omega.Exp(omega, &orderBigInt)
 	assert.True(omega.IsOne())
-
-	order = order + 1
-	_, err = getIthRootOne(order)
-	assert.Error(err)
 }
diff --git a/ecc/bn254/fflonk/fflonk_test.go b/ecc/bn254/fflonk/fflonk_test.go
index 4265cbbe01..28a02458f8 100644
--- a/ecc/bn254/fflonk/fflonk_test.go
+++ b/ecc/bn254/fflonk/fflonk_test.go
@@ -124,7 +124,6 @@ func TestCommit(t *testing.T) {
 }
 
 func TestGetIthRootOne(t *testing.T) {
-
 	assert := require.New(t)
 
 	order := getNextDivisorRMinusOne(9)
@@ -134,8 +133,4 @@ func TestGetIthRootOne(t *testing.T) {
 	orderBigInt.SetUint64(uint64(order))
 	omega.Exp(omega, &orderBigInt)
 	assert.True(omega.IsOne())
-
-	order = order + 1
-	_, err = getIthRootOne(order)
-	assert.Error(err)
 }
diff --git a/ecc/bw6-633/fflonk/fflonk_test.go b/ecc/bw6-633/fflonk/fflonk_test.go
index bd9cf7f10a..7615629666 100644
--- a/ecc/bw6-633/fflonk/fflonk_test.go
+++ b/ecc/bw6-633/fflonk/fflonk_test.go
@@ -124,7 +124,6 @@ func TestCommit(t *testing.T) {
 }
 
 func TestGetIthRootOne(t *testing.T) {
-
 	assert := require.New(t)
 
 	order := getNextDivisorRMinusOne(9)
@@ -134,8 +133,4 @@ func TestGetIthRootOne(t *testing.T) {
 	orderBigInt.SetUint64(uint64(order))
 	omega.Exp(omega, &orderBigInt)
 	assert.True(omega.IsOne())
-
-	order = order + 1
-	_, err = getIthRootOne(order)
-	assert.Error(err)
 }
diff --git a/ecc/bw6-756/fflonk/fflonk_test.go b/ecc/bw6-756/fflonk/fflonk_test.go
index d3bb131a18..2bacfcdcc0 100644
--- a/ecc/bw6-756/fflonk/fflonk_test.go
+++ b/ecc/bw6-756/fflonk/fflonk_test.go
@@ -124,7 +124,6 @@ func TestCommit(t *testing.T) {
 }
 
 func TestGetIthRootOne(t *testing.T) {
-
 	assert := require.New(t)
 
 	order := getNextDivisorRMinusOne(9)
@@ -134,8 +133,4 @@ func TestGetIthRootOne(t *testing.T) {
 	orderBigInt.SetUint64(uint64(order))
 	omega.Exp(omega, &orderBigInt)
 	assert.True(omega.IsOne())
-
-	order = order + 1
-	_, err = getIthRootOne(order)
-	assert.Error(err)
 }
diff --git a/ecc/bw6-761/fflonk/fflonk_test.go b/ecc/bw6-761/fflonk/fflonk_test.go
index f6670a6d19..c1f726fc68 100644
--- a/ecc/bw6-761/fflonk/fflonk_test.go
+++ b/ecc/bw6-761/fflonk/fflonk_test.go
@@ -124,7 +124,6 @@ func TestCommit(t *testing.T) {
 }
 
 func TestGetIthRootOne(t *testing.T) {
-
 	assert := require.New(t)
 
 	order := getNextDivisorRMinusOne(9)
@@ -134,8 +133,4 @@ func TestGetIthRootOne(t *testing.T) {
 	orderBigInt.SetUint64(uint64(order))
 	omega.Exp(omega, &orderBigInt)
 	assert.True(omega.IsOne())
-
-	order = order + 1
-	_, err = getIthRootOne(order)
-	assert.Error(err)
 }

From 341ba5bffd7d4a3f52155b67a551de9a6acec09a Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 26 Apr 2024 19:04:26 +0200
Subject: [PATCH 045/114] style: remaing -> remaining

---
 internal/generator/fflonk/template/fflonk.go.tmpl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/internal/generator/fflonk/template/fflonk.go.tmpl b/internal/generator/fflonk/template/fflonk.go.tmpl
index 169e50587b..e20df4a656 100644
--- a/internal/generator/fflonk/template/fflonk.go.tmpl
+++ b/internal/generator/fflonk/template/fflonk.go.tmpl
@@ -100,7 +100,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
-		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaing polynomials are zero
+		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaining polynomials are zero
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 		}
 	}

From 46e95f8247ebc22a8536051abcc23c1b4f67915b Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 26 Apr 2024 19:07:26 +0200
Subject: [PATCH 046/114] feat: code gen

---
 ecc/bls12-377/fflonk/fflonk.go | 2 +-
 ecc/bls12-378/fflonk/fflonk.go | 2 +-
 ecc/bls12-381/fflonk/fflonk.go | 2 +-
 ecc/bls24-315/fflonk/fflonk.go | 2 +-
 ecc/bls24-317/fflonk/fflonk.go | 2 +-
 ecc/bn254/fflonk/fflonk.go     | 2 +-
 ecc/bw6-633/fflonk/fflonk.go   | 2 +-
 ecc/bw6-756/fflonk/fflonk.go   | 2 +-
 ecc/bw6-761/fflonk/fflonk.go   | 2 +-
 9 files changed, 9 insertions(+), 9 deletions(-)

diff --git a/ecc/bls12-377/fflonk/fflonk.go b/ecc/bls12-377/fflonk/fflonk.go
index 75649f5e41..6acd7bc79f 100644
--- a/ecc/bls12-377/fflonk/fflonk.go
+++ b/ecc/bls12-377/fflonk/fflonk.go
@@ -118,7 +118,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
-		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaing polynomials are zero
+		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaining polynomials are zero
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 		}
 	}
diff --git a/ecc/bls12-378/fflonk/fflonk.go b/ecc/bls12-378/fflonk/fflonk.go
index d1e276c167..2397f3fc77 100644
--- a/ecc/bls12-378/fflonk/fflonk.go
+++ b/ecc/bls12-378/fflonk/fflonk.go
@@ -118,7 +118,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
-		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaing polynomials are zero
+		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaining polynomials are zero
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 		}
 	}
diff --git a/ecc/bls12-381/fflonk/fflonk.go b/ecc/bls12-381/fflonk/fflonk.go
index 79b20c1a8e..037d45885f 100644
--- a/ecc/bls12-381/fflonk/fflonk.go
+++ b/ecc/bls12-381/fflonk/fflonk.go
@@ -118,7 +118,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
-		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaing polynomials are zero
+		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaining polynomials are zero
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 		}
 	}
diff --git a/ecc/bls24-315/fflonk/fflonk.go b/ecc/bls24-315/fflonk/fflonk.go
index 708e50ca85..dd7ce2d560 100644
--- a/ecc/bls24-315/fflonk/fflonk.go
+++ b/ecc/bls24-315/fflonk/fflonk.go
@@ -118,7 +118,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
-		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaing polynomials are zero
+		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaining polynomials are zero
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 		}
 	}
diff --git a/ecc/bls24-317/fflonk/fflonk.go b/ecc/bls24-317/fflonk/fflonk.go
index f9de5d74e5..c88257f32c 100644
--- a/ecc/bls24-317/fflonk/fflonk.go
+++ b/ecc/bls24-317/fflonk/fflonk.go
@@ -118,7 +118,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
-		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaing polynomials are zero
+		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaining polynomials are zero
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 		}
 	}
diff --git a/ecc/bn254/fflonk/fflonk.go b/ecc/bn254/fflonk/fflonk.go
index 32fb98795f..77b37730ba 100644
--- a/ecc/bn254/fflonk/fflonk.go
+++ b/ecc/bn254/fflonk/fflonk.go
@@ -118,7 +118,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
-		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaing polynomials are zero
+		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaining polynomials are zero
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 		}
 	}
diff --git a/ecc/bw6-633/fflonk/fflonk.go b/ecc/bw6-633/fflonk/fflonk.go
index 2b07024ab3..c009315e66 100644
--- a/ecc/bw6-633/fflonk/fflonk.go
+++ b/ecc/bw6-633/fflonk/fflonk.go
@@ -118,7 +118,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
-		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaing polynomials are zero
+		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaining polynomials are zero
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 		}
 	}
diff --git a/ecc/bw6-756/fflonk/fflonk.go b/ecc/bw6-756/fflonk/fflonk.go
index 38bfd4532f..6c687b4aef 100644
--- a/ecc/bw6-756/fflonk/fflonk.go
+++ b/ecc/bw6-756/fflonk/fflonk.go
@@ -118,7 +118,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
-		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaing polynomials are zero
+		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaining polynomials are zero
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 		}
 	}
diff --git a/ecc/bw6-761/fflonk/fflonk.go b/ecc/bw6-761/fflonk/fflonk.go
index 8c6345f209..fe58acc678 100644
--- a/ecc/bw6-761/fflonk/fflonk.go
+++ b/ecc/bw6-761/fflonk/fflonk.go
@@ -118,7 +118,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
-		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaing polynomials are zero
+		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaining polynomials are zero
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 		}
 	}

From ec436b4c2b525f8bc5b1138147bbce59026a8148 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Wed, 18 Sep 2024 18:54:28 +0200
Subject: [PATCH 047/114] fix: fixed panic

---
 ecc/bls12-377/shplonk/shplonk_test.go                    | 6 +++++-
 ecc/bls12-378/shplonk/shplonk_test.go                    | 6 +++++-
 ecc/bls12-381/shplonk/shplonk_test.go                    | 6 +++++-
 ecc/bls24-315/shplonk/shplonk_test.go                    | 6 +++++-
 ecc/bls24-317/shplonk/shplonk_test.go                    | 6 +++++-
 ecc/bn254/shplonk/shplonk_test.go                        | 6 +++++-
 ecc/bw6-633/shplonk/shplonk_test.go                      | 6 +++++-
 ecc/bw6-756/shplonk/shplonk_test.go                      | 6 +++++-
 ecc/bw6-761/shplonk/shplonk_test.go                      | 6 +++++-
 internal/generator/shplonk/template/shplonk.test.go.tmpl | 6 +++++-
 10 files changed, 50 insertions(+), 10 deletions(-)

diff --git a/ecc/bls12-377/shplonk/shplonk_test.go b/ecc/bls12-377/shplonk/shplonk_test.go
index 69a26be1b8..0b69e54a71 100644
--- a/ecc/bls12-377/shplonk/shplonk_test.go
+++ b/ecc/bls12-377/shplonk/shplonk_test.go
@@ -34,7 +34,11 @@ var bAlpha *big.Int
 func init() {
 	const srsSize = 230
 	bAlpha = new(big.Int).SetInt64(42) // randomise ?
-	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+	var err error
+	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+	if err != nil {
+		panic(err)
+	}
 }
 
 func TestOpening(t *testing.T) {
diff --git a/ecc/bls12-378/shplonk/shplonk_test.go b/ecc/bls12-378/shplonk/shplonk_test.go
index dcb5f69421..ac3d707cf5 100644
--- a/ecc/bls12-378/shplonk/shplonk_test.go
+++ b/ecc/bls12-378/shplonk/shplonk_test.go
@@ -34,7 +34,11 @@ var bAlpha *big.Int
 func init() {
 	const srsSize = 230
 	bAlpha = new(big.Int).SetInt64(42) // randomise ?
-	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+	var err error
+	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+	if err != nil {
+		panic(err)
+	}
 }
 
 func TestOpening(t *testing.T) {
diff --git a/ecc/bls12-381/shplonk/shplonk_test.go b/ecc/bls12-381/shplonk/shplonk_test.go
index 043238b47d..12468961cb 100644
--- a/ecc/bls12-381/shplonk/shplonk_test.go
+++ b/ecc/bls12-381/shplonk/shplonk_test.go
@@ -34,7 +34,11 @@ var bAlpha *big.Int
 func init() {
 	const srsSize = 230
 	bAlpha = new(big.Int).SetInt64(42) // randomise ?
-	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+	var err error
+	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+	if err != nil {
+		panic(err)
+	}
 }
 
 func TestOpening(t *testing.T) {
diff --git a/ecc/bls24-315/shplonk/shplonk_test.go b/ecc/bls24-315/shplonk/shplonk_test.go
index 3e282d99a1..9bc663dcf0 100644
--- a/ecc/bls24-315/shplonk/shplonk_test.go
+++ b/ecc/bls24-315/shplonk/shplonk_test.go
@@ -34,7 +34,11 @@ var bAlpha *big.Int
 func init() {
 	const srsSize = 230
 	bAlpha = new(big.Int).SetInt64(42) // randomise ?
-	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+	var err error
+	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+	if err != nil {
+		panic(err)
+	}
 }
 
 func TestOpening(t *testing.T) {
diff --git a/ecc/bls24-317/shplonk/shplonk_test.go b/ecc/bls24-317/shplonk/shplonk_test.go
index 14dd5af291..72c89c9629 100644
--- a/ecc/bls24-317/shplonk/shplonk_test.go
+++ b/ecc/bls24-317/shplonk/shplonk_test.go
@@ -34,7 +34,11 @@ var bAlpha *big.Int
 func init() {
 	const srsSize = 230
 	bAlpha = new(big.Int).SetInt64(42) // randomise ?
-	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+	var err error
+	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+	if err != nil {
+		panic(err)
+	}
 }
 
 func TestOpening(t *testing.T) {
diff --git a/ecc/bn254/shplonk/shplonk_test.go b/ecc/bn254/shplonk/shplonk_test.go
index 6d2c2841b0..be2a812dc6 100644
--- a/ecc/bn254/shplonk/shplonk_test.go
+++ b/ecc/bn254/shplonk/shplonk_test.go
@@ -34,7 +34,11 @@ var bAlpha *big.Int
 func init() {
 	const srsSize = 230
 	bAlpha = new(big.Int).SetInt64(42) // randomise ?
-	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+	var err error
+	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+	if err != nil {
+		panic(err)
+	}
 }
 
 func TestOpening(t *testing.T) {
diff --git a/ecc/bw6-633/shplonk/shplonk_test.go b/ecc/bw6-633/shplonk/shplonk_test.go
index 807b263e08..cde6f766c2 100644
--- a/ecc/bw6-633/shplonk/shplonk_test.go
+++ b/ecc/bw6-633/shplonk/shplonk_test.go
@@ -34,7 +34,11 @@ var bAlpha *big.Int
 func init() {
 	const srsSize = 230
 	bAlpha = new(big.Int).SetInt64(42) // randomise ?
-	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+	var err error
+	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+	if err != nil {
+		panic(err)
+	}
 }
 
 func TestOpening(t *testing.T) {
diff --git a/ecc/bw6-756/shplonk/shplonk_test.go b/ecc/bw6-756/shplonk/shplonk_test.go
index c729294363..2ada895dff 100644
--- a/ecc/bw6-756/shplonk/shplonk_test.go
+++ b/ecc/bw6-756/shplonk/shplonk_test.go
@@ -34,7 +34,11 @@ var bAlpha *big.Int
 func init() {
 	const srsSize = 230
 	bAlpha = new(big.Int).SetInt64(42) // randomise ?
-	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+	var err error
+	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+	if err != nil {
+		panic(err)
+	}
 }
 
 func TestOpening(t *testing.T) {
diff --git a/ecc/bw6-761/shplonk/shplonk_test.go b/ecc/bw6-761/shplonk/shplonk_test.go
index e962fe6dff..3fb7e0715c 100644
--- a/ecc/bw6-761/shplonk/shplonk_test.go
+++ b/ecc/bw6-761/shplonk/shplonk_test.go
@@ -34,7 +34,11 @@ var bAlpha *big.Int
 func init() {
 	const srsSize = 230
 	bAlpha = new(big.Int).SetInt64(42) // randomise ?
-	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+	var err error
+	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+	if err != nil {
+		panic(err)
+	}
 }
 
 func TestOpening(t *testing.T) {
diff --git a/internal/generator/shplonk/template/shplonk.test.go.tmpl b/internal/generator/shplonk/template/shplonk.test.go.tmpl
index d3f6611b64..c7e3514cfe 100644
--- a/internal/generator/shplonk/template/shplonk.test.go.tmpl
+++ b/internal/generator/shplonk/template/shplonk.test.go.tmpl
@@ -16,7 +16,11 @@ var bAlpha *big.Int
 func init() {
 	const srsSize = 230
 	bAlpha = new(big.Int).SetInt64(42) // randomise ?
-	testSrs, _ = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+	var err error
+	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
+	if err!=nil {
+		panic(err)
+	}
 }
 
 func TestOpening(t *testing.T) {

From d2074285b9a9fda508ba9f44ce6ef23d7840bcc3 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Wed, 18 Sep 2024 18:57:42 +0200
Subject: [PATCH 048/114] feat: randomise SRS

---
 ecc/bls12-377/shplonk/shplonk_test.go                    | 4 +++-
 ecc/bls12-378/shplonk/shplonk_test.go                    | 4 +++-
 ecc/bls12-381/shplonk/shplonk_test.go                    | 4 +++-
 ecc/bls24-315/shplonk/shplonk_test.go                    | 4 +++-
 ecc/bls24-317/shplonk/shplonk_test.go                    | 4 +++-
 ecc/bn254/shplonk/shplonk_test.go                        | 4 +++-
 ecc/bw6-633/shplonk/shplonk_test.go                      | 4 +++-
 ecc/bw6-756/shplonk/shplonk_test.go                      | 4 +++-
 ecc/bw6-761/shplonk/shplonk_test.go                      | 4 +++-
 internal/generator/shplonk/template/shplonk.test.go.tmpl | 5 ++++-
 10 files changed, 31 insertions(+), 10 deletions(-)

diff --git a/ecc/bls12-377/shplonk/shplonk_test.go b/ecc/bls12-377/shplonk/shplonk_test.go
index 0b69e54a71..b956361f86 100644
--- a/ecc/bls12-377/shplonk/shplonk_test.go
+++ b/ecc/bls12-377/shplonk/shplonk_test.go
@@ -33,7 +33,9 @@ var bAlpha *big.Int
 
 func init() {
 	const srsSize = 230
-	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	var frAlpha fr.Element
+	frAlpha.SetRandom()
+	frAlpha.BigInt(bAlpha)
 	var err error
 	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
 	if err != nil {
diff --git a/ecc/bls12-378/shplonk/shplonk_test.go b/ecc/bls12-378/shplonk/shplonk_test.go
index ac3d707cf5..5bbb9fc122 100644
--- a/ecc/bls12-378/shplonk/shplonk_test.go
+++ b/ecc/bls12-378/shplonk/shplonk_test.go
@@ -33,7 +33,9 @@ var bAlpha *big.Int
 
 func init() {
 	const srsSize = 230
-	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	var frAlpha fr.Element
+	frAlpha.SetRandom()
+	frAlpha.BigInt(bAlpha)
 	var err error
 	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
 	if err != nil {
diff --git a/ecc/bls12-381/shplonk/shplonk_test.go b/ecc/bls12-381/shplonk/shplonk_test.go
index 12468961cb..67eba49ba3 100644
--- a/ecc/bls12-381/shplonk/shplonk_test.go
+++ b/ecc/bls12-381/shplonk/shplonk_test.go
@@ -33,7 +33,9 @@ var bAlpha *big.Int
 
 func init() {
 	const srsSize = 230
-	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	var frAlpha fr.Element
+	frAlpha.SetRandom()
+	frAlpha.BigInt(bAlpha)
 	var err error
 	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
 	if err != nil {
diff --git a/ecc/bls24-315/shplonk/shplonk_test.go b/ecc/bls24-315/shplonk/shplonk_test.go
index 9bc663dcf0..93b6636857 100644
--- a/ecc/bls24-315/shplonk/shplonk_test.go
+++ b/ecc/bls24-315/shplonk/shplonk_test.go
@@ -33,7 +33,9 @@ var bAlpha *big.Int
 
 func init() {
 	const srsSize = 230
-	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	var frAlpha fr.Element
+	frAlpha.SetRandom()
+	frAlpha.BigInt(bAlpha)
 	var err error
 	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
 	if err != nil {
diff --git a/ecc/bls24-317/shplonk/shplonk_test.go b/ecc/bls24-317/shplonk/shplonk_test.go
index 72c89c9629..7afffeb886 100644
--- a/ecc/bls24-317/shplonk/shplonk_test.go
+++ b/ecc/bls24-317/shplonk/shplonk_test.go
@@ -33,7 +33,9 @@ var bAlpha *big.Int
 
 func init() {
 	const srsSize = 230
-	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	var frAlpha fr.Element
+	frAlpha.SetRandom()
+	frAlpha.BigInt(bAlpha)
 	var err error
 	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
 	if err != nil {
diff --git a/ecc/bn254/shplonk/shplonk_test.go b/ecc/bn254/shplonk/shplonk_test.go
index be2a812dc6..7b14e5544f 100644
--- a/ecc/bn254/shplonk/shplonk_test.go
+++ b/ecc/bn254/shplonk/shplonk_test.go
@@ -33,7 +33,9 @@ var bAlpha *big.Int
 
 func init() {
 	const srsSize = 230
-	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	var frAlpha fr.Element
+	frAlpha.SetRandom()
+	frAlpha.BigInt(bAlpha)
 	var err error
 	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
 	if err != nil {
diff --git a/ecc/bw6-633/shplonk/shplonk_test.go b/ecc/bw6-633/shplonk/shplonk_test.go
index cde6f766c2..c813a1bf53 100644
--- a/ecc/bw6-633/shplonk/shplonk_test.go
+++ b/ecc/bw6-633/shplonk/shplonk_test.go
@@ -33,7 +33,9 @@ var bAlpha *big.Int
 
 func init() {
 	const srsSize = 230
-	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	var frAlpha fr.Element
+	frAlpha.SetRandom()
+	frAlpha.BigInt(bAlpha)
 	var err error
 	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
 	if err != nil {
diff --git a/ecc/bw6-756/shplonk/shplonk_test.go b/ecc/bw6-756/shplonk/shplonk_test.go
index 2ada895dff..c72b57d7ec 100644
--- a/ecc/bw6-756/shplonk/shplonk_test.go
+++ b/ecc/bw6-756/shplonk/shplonk_test.go
@@ -33,7 +33,9 @@ var bAlpha *big.Int
 
 func init() {
 	const srsSize = 230
-	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	var frAlpha fr.Element
+	frAlpha.SetRandom()
+	frAlpha.BigInt(bAlpha)
 	var err error
 	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
 	if err != nil {
diff --git a/ecc/bw6-761/shplonk/shplonk_test.go b/ecc/bw6-761/shplonk/shplonk_test.go
index 3fb7e0715c..95702777e1 100644
--- a/ecc/bw6-761/shplonk/shplonk_test.go
+++ b/ecc/bw6-761/shplonk/shplonk_test.go
@@ -33,7 +33,9 @@ var bAlpha *big.Int
 
 func init() {
 	const srsSize = 230
-	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	var frAlpha fr.Element
+	frAlpha.SetRandom()
+	frAlpha.BigInt(bAlpha)
 	var err error
 	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
 	if err != nil {
diff --git a/internal/generator/shplonk/template/shplonk.test.go.tmpl b/internal/generator/shplonk/template/shplonk.test.go.tmpl
index c7e3514cfe..d6e8302b93 100644
--- a/internal/generator/shplonk/template/shplonk.test.go.tmpl
+++ b/internal/generator/shplonk/template/shplonk.test.go.tmpl
@@ -13,9 +13,12 @@ import (
 var testSrs *kzg.SRS
 var bAlpha *big.Int
 
+
 func init() {
 	const srsSize = 230
-	bAlpha = new(big.Int).SetInt64(42) // randomise ?
+	var frAlpha fr.Element
+	frAlpha.SetRandom()
+	frAlpha.BigInt(bAlpha)
 	var err error
 	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
 	if err!=nil {

From b4815d64b148817932e0c23d18ae2f778a7a5eda Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Wed, 18 Sep 2024 19:02:36 +0200
Subject: [PATCH 049/114] fix: raise error when nbDigest != number of
 polynomials

---
 ecc/bls12-377/shplonk/shplonk.go                    | 8 ++++++--
 ecc/bls12-378/shplonk/shplonk.go                    | 8 ++++++--
 ecc/bls12-381/shplonk/shplonk.go                    | 8 ++++++--
 ecc/bls24-315/shplonk/shplonk.go                    | 8 ++++++--
 ecc/bls24-317/shplonk/shplonk.go                    | 8 ++++++--
 ecc/bn254/shplonk/shplonk.go                        | 8 ++++++--
 ecc/bw6-633/shplonk/shplonk.go                      | 8 ++++++--
 ecc/bw6-756/shplonk/shplonk.go                      | 8 ++++++--
 ecc/bw6-761/shplonk/shplonk.go                      | 8 ++++++--
 internal/generator/shplonk/template/shplonk.go.tmpl | 4 ++++
 10 files changed, 58 insertions(+), 18 deletions(-)

diff --git a/ecc/bls12-377/shplonk/shplonk.go b/ecc/bls12-377/shplonk/shplonk.go
index 13faee07d4..fb17486b45 100644
--- a/ecc/bls12-377/shplonk/shplonk.go
+++ b/ecc/bls12-377/shplonk/shplonk.go
@@ -29,8 +29,9 @@ import (
 )
 
 var (
-	ErrInvalidNumberOfPoints = errors.New("number of digests should be equal to the number of points")
-	ErrVerifyOpeningProof    = errors.New("can't verify batch opening proof")
+	ErrInvalidNumberOfPoints  = errors.New("number of digests should be equal to the number of points")
+	ErrVerifyOpeningProof     = errors.New("can't verify batch opening proof")
+	ErrInvalidNumberOfDigests = errors.New("number of digests should be equal to the number of polynomials")
 )
 
 // OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
@@ -58,6 +59,9 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	if len(polynomials) != len(points) {
 		return res, ErrInvalidNumberOfPoints
 	}
+	if len(polynomials) != len(digests) {
+		return res, ErrInvalidNumberOfDigests
+	}
 
 	// transcript
 	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
diff --git a/ecc/bls12-378/shplonk/shplonk.go b/ecc/bls12-378/shplonk/shplonk.go
index 1f447522ab..6f464422c3 100644
--- a/ecc/bls12-378/shplonk/shplonk.go
+++ b/ecc/bls12-378/shplonk/shplonk.go
@@ -29,8 +29,9 @@ import (
 )
 
 var (
-	ErrInvalidNumberOfPoints = errors.New("number of digests should be equal to the number of points")
-	ErrVerifyOpeningProof    = errors.New("can't verify batch opening proof")
+	ErrInvalidNumberOfPoints  = errors.New("number of digests should be equal to the number of points")
+	ErrVerifyOpeningProof     = errors.New("can't verify batch opening proof")
+	ErrInvalidNumberOfDigests = errors.New("number of digests should be equal to the number of polynomials")
 )
 
 // OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
@@ -58,6 +59,9 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	if len(polynomials) != len(points) {
 		return res, ErrInvalidNumberOfPoints
 	}
+	if len(polynomials) != len(digests) {
+		return res, ErrInvalidNumberOfDigests
+	}
 
 	// transcript
 	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
diff --git a/ecc/bls12-381/shplonk/shplonk.go b/ecc/bls12-381/shplonk/shplonk.go
index 43d624ae23..09fc264dd9 100644
--- a/ecc/bls12-381/shplonk/shplonk.go
+++ b/ecc/bls12-381/shplonk/shplonk.go
@@ -29,8 +29,9 @@ import (
 )
 
 var (
-	ErrInvalidNumberOfPoints = errors.New("number of digests should be equal to the number of points")
-	ErrVerifyOpeningProof    = errors.New("can't verify batch opening proof")
+	ErrInvalidNumberOfPoints  = errors.New("number of digests should be equal to the number of points")
+	ErrVerifyOpeningProof     = errors.New("can't verify batch opening proof")
+	ErrInvalidNumberOfDigests = errors.New("number of digests should be equal to the number of polynomials")
 )
 
 // OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
@@ -58,6 +59,9 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	if len(polynomials) != len(points) {
 		return res, ErrInvalidNumberOfPoints
 	}
+	if len(polynomials) != len(digests) {
+		return res, ErrInvalidNumberOfDigests
+	}
 
 	// transcript
 	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
diff --git a/ecc/bls24-315/shplonk/shplonk.go b/ecc/bls24-315/shplonk/shplonk.go
index f3be3f5bfa..e0733e5d1c 100644
--- a/ecc/bls24-315/shplonk/shplonk.go
+++ b/ecc/bls24-315/shplonk/shplonk.go
@@ -29,8 +29,9 @@ import (
 )
 
 var (
-	ErrInvalidNumberOfPoints = errors.New("number of digests should be equal to the number of points")
-	ErrVerifyOpeningProof    = errors.New("can't verify batch opening proof")
+	ErrInvalidNumberOfPoints  = errors.New("number of digests should be equal to the number of points")
+	ErrVerifyOpeningProof     = errors.New("can't verify batch opening proof")
+	ErrInvalidNumberOfDigests = errors.New("number of digests should be equal to the number of polynomials")
 )
 
 // OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
@@ -58,6 +59,9 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	if len(polynomials) != len(points) {
 		return res, ErrInvalidNumberOfPoints
 	}
+	if len(polynomials) != len(digests) {
+		return res, ErrInvalidNumberOfDigests
+	}
 
 	// transcript
 	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
diff --git a/ecc/bls24-317/shplonk/shplonk.go b/ecc/bls24-317/shplonk/shplonk.go
index dc8cdfa14a..722ca208cd 100644
--- a/ecc/bls24-317/shplonk/shplonk.go
+++ b/ecc/bls24-317/shplonk/shplonk.go
@@ -29,8 +29,9 @@ import (
 )
 
 var (
-	ErrInvalidNumberOfPoints = errors.New("number of digests should be equal to the number of points")
-	ErrVerifyOpeningProof    = errors.New("can't verify batch opening proof")
+	ErrInvalidNumberOfPoints  = errors.New("number of digests should be equal to the number of points")
+	ErrVerifyOpeningProof     = errors.New("can't verify batch opening proof")
+	ErrInvalidNumberOfDigests = errors.New("number of digests should be equal to the number of polynomials")
 )
 
 // OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
@@ -58,6 +59,9 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	if len(polynomials) != len(points) {
 		return res, ErrInvalidNumberOfPoints
 	}
+	if len(polynomials) != len(digests) {
+		return res, ErrInvalidNumberOfDigests
+	}
 
 	// transcript
 	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
index 3ed334464e..c33fa05c4c 100644
--- a/ecc/bn254/shplonk/shplonk.go
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -29,8 +29,9 @@ import (
 )
 
 var (
-	ErrInvalidNumberOfPoints = errors.New("number of digests should be equal to the number of points")
-	ErrVerifyOpeningProof    = errors.New("can't verify batch opening proof")
+	ErrInvalidNumberOfPoints  = errors.New("number of digests should be equal to the number of points")
+	ErrVerifyOpeningProof     = errors.New("can't verify batch opening proof")
+	ErrInvalidNumberOfDigests = errors.New("number of digests should be equal to the number of polynomials")
 )
 
 // OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
@@ -58,6 +59,9 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	if len(polynomials) != len(points) {
 		return res, ErrInvalidNumberOfPoints
 	}
+	if len(polynomials) != len(digests) {
+		return res, ErrInvalidNumberOfDigests
+	}
 
 	// transcript
 	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
diff --git a/ecc/bw6-633/shplonk/shplonk.go b/ecc/bw6-633/shplonk/shplonk.go
index a3d6bd1999..a078923710 100644
--- a/ecc/bw6-633/shplonk/shplonk.go
+++ b/ecc/bw6-633/shplonk/shplonk.go
@@ -29,8 +29,9 @@ import (
 )
 
 var (
-	ErrInvalidNumberOfPoints = errors.New("number of digests should be equal to the number of points")
-	ErrVerifyOpeningProof    = errors.New("can't verify batch opening proof")
+	ErrInvalidNumberOfPoints  = errors.New("number of digests should be equal to the number of points")
+	ErrVerifyOpeningProof     = errors.New("can't verify batch opening proof")
+	ErrInvalidNumberOfDigests = errors.New("number of digests should be equal to the number of polynomials")
 )
 
 // OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
@@ -58,6 +59,9 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	if len(polynomials) != len(points) {
 		return res, ErrInvalidNumberOfPoints
 	}
+	if len(polynomials) != len(digests) {
+		return res, ErrInvalidNumberOfDigests
+	}
 
 	// transcript
 	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
diff --git a/ecc/bw6-756/shplonk/shplonk.go b/ecc/bw6-756/shplonk/shplonk.go
index d8353e303b..252c034fca 100644
--- a/ecc/bw6-756/shplonk/shplonk.go
+++ b/ecc/bw6-756/shplonk/shplonk.go
@@ -29,8 +29,9 @@ import (
 )
 
 var (
-	ErrInvalidNumberOfPoints = errors.New("number of digests should be equal to the number of points")
-	ErrVerifyOpeningProof    = errors.New("can't verify batch opening proof")
+	ErrInvalidNumberOfPoints  = errors.New("number of digests should be equal to the number of points")
+	ErrVerifyOpeningProof     = errors.New("can't verify batch opening proof")
+	ErrInvalidNumberOfDigests = errors.New("number of digests should be equal to the number of polynomials")
 )
 
 // OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
@@ -58,6 +59,9 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	if len(polynomials) != len(points) {
 		return res, ErrInvalidNumberOfPoints
 	}
+	if len(polynomials) != len(digests) {
+		return res, ErrInvalidNumberOfDigests
+	}
 
 	// transcript
 	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
diff --git a/ecc/bw6-761/shplonk/shplonk.go b/ecc/bw6-761/shplonk/shplonk.go
index a4d81d6def..9e6e90b00e 100644
--- a/ecc/bw6-761/shplonk/shplonk.go
+++ b/ecc/bw6-761/shplonk/shplonk.go
@@ -29,8 +29,9 @@ import (
 )
 
 var (
-	ErrInvalidNumberOfPoints = errors.New("number of digests should be equal to the number of points")
-	ErrVerifyOpeningProof    = errors.New("can't verify batch opening proof")
+	ErrInvalidNumberOfPoints  = errors.New("number of digests should be equal to the number of points")
+	ErrVerifyOpeningProof     = errors.New("can't verify batch opening proof")
+	ErrInvalidNumberOfDigests = errors.New("number of digests should be equal to the number of polynomials")
 )
 
 // OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
@@ -58,6 +59,9 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	if len(polynomials) != len(points) {
 		return res, ErrInvalidNumberOfPoints
 	}
+	if len(polynomials) != len(digests) {
+		return res, ErrInvalidNumberOfDigests
+	}
 
 	// transcript
 	fs := fiatshamir.NewTranscript(hf, "gamma", "z")
diff --git a/internal/generator/shplonk/template/shplonk.go.tmpl b/internal/generator/shplonk/template/shplonk.go.tmpl
index c5f8fcbee4..9d6a153c2d 100644
--- a/internal/generator/shplonk/template/shplonk.go.tmpl
+++ b/internal/generator/shplonk/template/shplonk.go.tmpl
@@ -13,6 +13,7 @@ import (
 var (
 	ErrInvalidNumberOfPoints = errors.New("number of digests should be equal to the number of points")
 	ErrVerifyOpeningProof    = errors.New("can't verify batch opening proof")
+	ErrInvalidNumberOfDigests = errors.New("number of digests should be equal to the number of polynomials")
 )
 
 // OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
@@ -40,6 +41,9 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	if len(polynomials) != len(points) {
 		return res, ErrInvalidNumberOfPoints
 	}
+	if len(polynomials) != len(digests) {
+		return res, ErrInvalidNumberOfDigests
+	}
 
 	// transcript
 	fs := fiatshamir.NewTranscript(hf, "gamma", "z")

From 5a5f678981f60f6d056bb36f3f0c0d04dbc6e4b5 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Wed, 18 Sep 2024 19:07:09 +0200
Subject: [PATCH 050/114] style: nbInstances -> nbPolynomials

---
 ecc/bls12-377/shplonk/shplonk.go                   | 14 +++++++-------
 ecc/bls12-378/shplonk/shplonk.go                   | 14 +++++++-------
 ecc/bls12-381/shplonk/shplonk.go                   | 14 +++++++-------
 ecc/bls24-315/shplonk/shplonk.go                   | 14 +++++++-------
 ecc/bls24-317/shplonk/shplonk.go                   | 14 +++++++-------
 ecc/bn254/shplonk/shplonk.go                       | 14 +++++++-------
 ecc/bw6-633/shplonk/shplonk.go                     | 14 +++++++-------
 ecc/bw6-756/shplonk/shplonk.go                     | 14 +++++++-------
 ecc/bw6-761/shplonk/shplonk.go                     | 14 +++++++-------
 .../generator/shplonk/template/shplonk.go.tmpl     | 14 +++++++-------
 10 files changed, 70 insertions(+), 70 deletions(-)

diff --git a/ecc/bls12-377/shplonk/shplonk.go b/ecc/bls12-377/shplonk/shplonk.go
index fb17486b45..25ab085deb 100644
--- a/ecc/bls12-377/shplonk/shplonk.go
+++ b/ecc/bls12-377/shplonk/shplonk.go
@@ -55,7 +55,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 
 	var res OpeningProof
 
-	nbInstances := len(polynomials)
+	nbPolynomials := len(polynomials)
 	if len(polynomials) != len(points) {
 		return res, ErrInvalidNumberOfPoints
 	}
@@ -81,7 +81,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	}
 	nbPoints := 0
 	sizeSi := make([]int, len(points))
-	for i := 0; i < nbInstances; i++ {
+	for i := 0; i < nbPolynomials; i++ {
 		nbPoints += len(points[i])
 		sizeSi[i] = len(points[i])
 	}
@@ -90,16 +90,16 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
 	bufTotalSize := make([]fr.Element, totalSize)
 	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
-	res.ClaimedValues = make([][]fr.Element, nbInstances)
-	for i := 0; i < nbInstances; i++ {
+	res.ClaimedValues = make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
 		res.ClaimedValues[i] = make([]fr.Element, len(points[i]))
 	}
 	var accGamma fr.Element
 	accGamma.SetOne()
 
-	ztMinusSi := make([][]fr.Element, nbInstances)
-	ri := make([][]fr.Element, nbInstances)
-	for i := 0; i < nbInstances; i++ {
+	ztMinusSi := make([][]fr.Element, nbPolynomials)
+	ri := make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
 
 		for j := 0; j < len(points[i]); j++ {
 			res.ClaimedValues[i][j] = eval(polynomials[i], points[i][j])
diff --git a/ecc/bls12-378/shplonk/shplonk.go b/ecc/bls12-378/shplonk/shplonk.go
index 6f464422c3..8ee2ed9fba 100644
--- a/ecc/bls12-378/shplonk/shplonk.go
+++ b/ecc/bls12-378/shplonk/shplonk.go
@@ -55,7 +55,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 
 	var res OpeningProof
 
-	nbInstances := len(polynomials)
+	nbPolynomials := len(polynomials)
 	if len(polynomials) != len(points) {
 		return res, ErrInvalidNumberOfPoints
 	}
@@ -81,7 +81,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	}
 	nbPoints := 0
 	sizeSi := make([]int, len(points))
-	for i := 0; i < nbInstances; i++ {
+	for i := 0; i < nbPolynomials; i++ {
 		nbPoints += len(points[i])
 		sizeSi[i] = len(points[i])
 	}
@@ -90,16 +90,16 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
 	bufTotalSize := make([]fr.Element, totalSize)
 	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
-	res.ClaimedValues = make([][]fr.Element, nbInstances)
-	for i := 0; i < nbInstances; i++ {
+	res.ClaimedValues = make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
 		res.ClaimedValues[i] = make([]fr.Element, len(points[i]))
 	}
 	var accGamma fr.Element
 	accGamma.SetOne()
 
-	ztMinusSi := make([][]fr.Element, nbInstances)
-	ri := make([][]fr.Element, nbInstances)
-	for i := 0; i < nbInstances; i++ {
+	ztMinusSi := make([][]fr.Element, nbPolynomials)
+	ri := make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
 
 		for j := 0; j < len(points[i]); j++ {
 			res.ClaimedValues[i][j] = eval(polynomials[i], points[i][j])
diff --git a/ecc/bls12-381/shplonk/shplonk.go b/ecc/bls12-381/shplonk/shplonk.go
index 09fc264dd9..835efaa8fc 100644
--- a/ecc/bls12-381/shplonk/shplonk.go
+++ b/ecc/bls12-381/shplonk/shplonk.go
@@ -55,7 +55,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 
 	var res OpeningProof
 
-	nbInstances := len(polynomials)
+	nbPolynomials := len(polynomials)
 	if len(polynomials) != len(points) {
 		return res, ErrInvalidNumberOfPoints
 	}
@@ -81,7 +81,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	}
 	nbPoints := 0
 	sizeSi := make([]int, len(points))
-	for i := 0; i < nbInstances; i++ {
+	for i := 0; i < nbPolynomials; i++ {
 		nbPoints += len(points[i])
 		sizeSi[i] = len(points[i])
 	}
@@ -90,16 +90,16 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
 	bufTotalSize := make([]fr.Element, totalSize)
 	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
-	res.ClaimedValues = make([][]fr.Element, nbInstances)
-	for i := 0; i < nbInstances; i++ {
+	res.ClaimedValues = make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
 		res.ClaimedValues[i] = make([]fr.Element, len(points[i]))
 	}
 	var accGamma fr.Element
 	accGamma.SetOne()
 
-	ztMinusSi := make([][]fr.Element, nbInstances)
-	ri := make([][]fr.Element, nbInstances)
-	for i := 0; i < nbInstances; i++ {
+	ztMinusSi := make([][]fr.Element, nbPolynomials)
+	ri := make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
 
 		for j := 0; j < len(points[i]); j++ {
 			res.ClaimedValues[i][j] = eval(polynomials[i], points[i][j])
diff --git a/ecc/bls24-315/shplonk/shplonk.go b/ecc/bls24-315/shplonk/shplonk.go
index e0733e5d1c..2629d18d3d 100644
--- a/ecc/bls24-315/shplonk/shplonk.go
+++ b/ecc/bls24-315/shplonk/shplonk.go
@@ -55,7 +55,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 
 	var res OpeningProof
 
-	nbInstances := len(polynomials)
+	nbPolynomials := len(polynomials)
 	if len(polynomials) != len(points) {
 		return res, ErrInvalidNumberOfPoints
 	}
@@ -81,7 +81,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	}
 	nbPoints := 0
 	sizeSi := make([]int, len(points))
-	for i := 0; i < nbInstances; i++ {
+	for i := 0; i < nbPolynomials; i++ {
 		nbPoints += len(points[i])
 		sizeSi[i] = len(points[i])
 	}
@@ -90,16 +90,16 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
 	bufTotalSize := make([]fr.Element, totalSize)
 	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
-	res.ClaimedValues = make([][]fr.Element, nbInstances)
-	for i := 0; i < nbInstances; i++ {
+	res.ClaimedValues = make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
 		res.ClaimedValues[i] = make([]fr.Element, len(points[i]))
 	}
 	var accGamma fr.Element
 	accGamma.SetOne()
 
-	ztMinusSi := make([][]fr.Element, nbInstances)
-	ri := make([][]fr.Element, nbInstances)
-	for i := 0; i < nbInstances; i++ {
+	ztMinusSi := make([][]fr.Element, nbPolynomials)
+	ri := make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
 
 		for j := 0; j < len(points[i]); j++ {
 			res.ClaimedValues[i][j] = eval(polynomials[i], points[i][j])
diff --git a/ecc/bls24-317/shplonk/shplonk.go b/ecc/bls24-317/shplonk/shplonk.go
index 722ca208cd..ff8f07e185 100644
--- a/ecc/bls24-317/shplonk/shplonk.go
+++ b/ecc/bls24-317/shplonk/shplonk.go
@@ -55,7 +55,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 
 	var res OpeningProof
 
-	nbInstances := len(polynomials)
+	nbPolynomials := len(polynomials)
 	if len(polynomials) != len(points) {
 		return res, ErrInvalidNumberOfPoints
 	}
@@ -81,7 +81,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	}
 	nbPoints := 0
 	sizeSi := make([]int, len(points))
-	for i := 0; i < nbInstances; i++ {
+	for i := 0; i < nbPolynomials; i++ {
 		nbPoints += len(points[i])
 		sizeSi[i] = len(points[i])
 	}
@@ -90,16 +90,16 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
 	bufTotalSize := make([]fr.Element, totalSize)
 	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
-	res.ClaimedValues = make([][]fr.Element, nbInstances)
-	for i := 0; i < nbInstances; i++ {
+	res.ClaimedValues = make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
 		res.ClaimedValues[i] = make([]fr.Element, len(points[i]))
 	}
 	var accGamma fr.Element
 	accGamma.SetOne()
 
-	ztMinusSi := make([][]fr.Element, nbInstances)
-	ri := make([][]fr.Element, nbInstances)
-	for i := 0; i < nbInstances; i++ {
+	ztMinusSi := make([][]fr.Element, nbPolynomials)
+	ri := make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
 
 		for j := 0; j < len(points[i]); j++ {
 			res.ClaimedValues[i][j] = eval(polynomials[i], points[i][j])
diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
index c33fa05c4c..7a86ed72e6 100644
--- a/ecc/bn254/shplonk/shplonk.go
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -55,7 +55,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 
 	var res OpeningProof
 
-	nbInstances := len(polynomials)
+	nbPolynomials := len(polynomials)
 	if len(polynomials) != len(points) {
 		return res, ErrInvalidNumberOfPoints
 	}
@@ -81,7 +81,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	}
 	nbPoints := 0
 	sizeSi := make([]int, len(points))
-	for i := 0; i < nbInstances; i++ {
+	for i := 0; i < nbPolynomials; i++ {
 		nbPoints += len(points[i])
 		sizeSi[i] = len(points[i])
 	}
@@ -90,16 +90,16 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
 	bufTotalSize := make([]fr.Element, totalSize)
 	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
-	res.ClaimedValues = make([][]fr.Element, nbInstances)
-	for i := 0; i < nbInstances; i++ {
+	res.ClaimedValues = make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
 		res.ClaimedValues[i] = make([]fr.Element, len(points[i]))
 	}
 	var accGamma fr.Element
 	accGamma.SetOne()
 
-	ztMinusSi := make([][]fr.Element, nbInstances)
-	ri := make([][]fr.Element, nbInstances)
-	for i := 0; i < nbInstances; i++ {
+	ztMinusSi := make([][]fr.Element, nbPolynomials)
+	ri := make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
 
 		for j := 0; j < len(points[i]); j++ {
 			res.ClaimedValues[i][j] = eval(polynomials[i], points[i][j])
diff --git a/ecc/bw6-633/shplonk/shplonk.go b/ecc/bw6-633/shplonk/shplonk.go
index a078923710..91b953d4d7 100644
--- a/ecc/bw6-633/shplonk/shplonk.go
+++ b/ecc/bw6-633/shplonk/shplonk.go
@@ -55,7 +55,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 
 	var res OpeningProof
 
-	nbInstances := len(polynomials)
+	nbPolynomials := len(polynomials)
 	if len(polynomials) != len(points) {
 		return res, ErrInvalidNumberOfPoints
 	}
@@ -81,7 +81,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	}
 	nbPoints := 0
 	sizeSi := make([]int, len(points))
-	for i := 0; i < nbInstances; i++ {
+	for i := 0; i < nbPolynomials; i++ {
 		nbPoints += len(points[i])
 		sizeSi[i] = len(points[i])
 	}
@@ -90,16 +90,16 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
 	bufTotalSize := make([]fr.Element, totalSize)
 	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
-	res.ClaimedValues = make([][]fr.Element, nbInstances)
-	for i := 0; i < nbInstances; i++ {
+	res.ClaimedValues = make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
 		res.ClaimedValues[i] = make([]fr.Element, len(points[i]))
 	}
 	var accGamma fr.Element
 	accGamma.SetOne()
 
-	ztMinusSi := make([][]fr.Element, nbInstances)
-	ri := make([][]fr.Element, nbInstances)
-	for i := 0; i < nbInstances; i++ {
+	ztMinusSi := make([][]fr.Element, nbPolynomials)
+	ri := make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
 
 		for j := 0; j < len(points[i]); j++ {
 			res.ClaimedValues[i][j] = eval(polynomials[i], points[i][j])
diff --git a/ecc/bw6-756/shplonk/shplonk.go b/ecc/bw6-756/shplonk/shplonk.go
index 252c034fca..dffbf7f409 100644
--- a/ecc/bw6-756/shplonk/shplonk.go
+++ b/ecc/bw6-756/shplonk/shplonk.go
@@ -55,7 +55,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 
 	var res OpeningProof
 
-	nbInstances := len(polynomials)
+	nbPolynomials := len(polynomials)
 	if len(polynomials) != len(points) {
 		return res, ErrInvalidNumberOfPoints
 	}
@@ -81,7 +81,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	}
 	nbPoints := 0
 	sizeSi := make([]int, len(points))
-	for i := 0; i < nbInstances; i++ {
+	for i := 0; i < nbPolynomials; i++ {
 		nbPoints += len(points[i])
 		sizeSi[i] = len(points[i])
 	}
@@ -90,16 +90,16 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
 	bufTotalSize := make([]fr.Element, totalSize)
 	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
-	res.ClaimedValues = make([][]fr.Element, nbInstances)
-	for i := 0; i < nbInstances; i++ {
+	res.ClaimedValues = make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
 		res.ClaimedValues[i] = make([]fr.Element, len(points[i]))
 	}
 	var accGamma fr.Element
 	accGamma.SetOne()
 
-	ztMinusSi := make([][]fr.Element, nbInstances)
-	ri := make([][]fr.Element, nbInstances)
-	for i := 0; i < nbInstances; i++ {
+	ztMinusSi := make([][]fr.Element, nbPolynomials)
+	ri := make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
 
 		for j := 0; j < len(points[i]); j++ {
 			res.ClaimedValues[i][j] = eval(polynomials[i], points[i][j])
diff --git a/ecc/bw6-761/shplonk/shplonk.go b/ecc/bw6-761/shplonk/shplonk.go
index 9e6e90b00e..49c4e2015e 100644
--- a/ecc/bw6-761/shplonk/shplonk.go
+++ b/ecc/bw6-761/shplonk/shplonk.go
@@ -55,7 +55,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 
 	var res OpeningProof
 
-	nbInstances := len(polynomials)
+	nbPolynomials := len(polynomials)
 	if len(polynomials) != len(points) {
 		return res, ErrInvalidNumberOfPoints
 	}
@@ -81,7 +81,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	}
 	nbPoints := 0
 	sizeSi := make([]int, len(points))
-	for i := 0; i < nbInstances; i++ {
+	for i := 0; i < nbPolynomials; i++ {
 		nbPoints += len(points[i])
 		sizeSi[i] = len(points[i])
 	}
@@ -90,16 +90,16 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
 	bufTotalSize := make([]fr.Element, totalSize)
 	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
-	res.ClaimedValues = make([][]fr.Element, nbInstances)
-	for i := 0; i < nbInstances; i++ {
+	res.ClaimedValues = make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
 		res.ClaimedValues[i] = make([]fr.Element, len(points[i]))
 	}
 	var accGamma fr.Element
 	accGamma.SetOne()
 
-	ztMinusSi := make([][]fr.Element, nbInstances)
-	ri := make([][]fr.Element, nbInstances)
-	for i := 0; i < nbInstances; i++ {
+	ztMinusSi := make([][]fr.Element, nbPolynomials)
+	ri := make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
 
 		for j := 0; j < len(points[i]); j++ {
 			res.ClaimedValues[i][j] = eval(polynomials[i], points[i][j])
diff --git a/internal/generator/shplonk/template/shplonk.go.tmpl b/internal/generator/shplonk/template/shplonk.go.tmpl
index 9d6a153c2d..76689457d6 100644
--- a/internal/generator/shplonk/template/shplonk.go.tmpl
+++ b/internal/generator/shplonk/template/shplonk.go.tmpl
@@ -37,7 +37,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 
 	var res OpeningProof
 
-	nbInstances := len(polynomials)
+	nbPolynomials := len(polynomials)
 	if len(polynomials) != len(points) {
 		return res, ErrInvalidNumberOfPoints
 	}
@@ -63,7 +63,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	}
 	nbPoints := 0
 	sizeSi := make([]int, len(points))
-	for i := 0; i < nbInstances; i++ {
+	for i := 0; i < nbPolynomials; i++ {
 		nbPoints += len(points[i])
 		sizeSi[i] = len(points[i])
 	}
@@ -72,16 +72,16 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 	bufMaxSizePolynomials := make([]fr.Element, maxSizePolys)
 	bufTotalSize := make([]fr.Element, totalSize)
 	f := make([]fr.Element, totalSize) // cf https://eprint.iacr.org/2020/081.pdf page 11 for notation
-	res.ClaimedValues = make([][]fr.Element, nbInstances)
-	for i := 0; i < nbInstances; i++ {
+	res.ClaimedValues = make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
 		res.ClaimedValues[i] = make([]fr.Element, len(points[i]))
 	}
 	var accGamma fr.Element
 	accGamma.SetOne()
 
-	ztMinusSi := make([][]fr.Element, nbInstances)
-	ri := make([][]fr.Element, nbInstances)
-	for i := 0; i < nbInstances; i++ {
+	ztMinusSi := make([][]fr.Element, nbPolynomials)
+	ri := make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
 
 		for j := 0; j < len(points[i]); j++ {
 			res.ClaimedValues[i][j] = eval(polynomials[i], points[i][j])

From 3d938b71b89ae053cfb300d213da1528c2137dbc Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Wed, 18 Sep 2024 19:18:19 +0200
Subject: [PATCH 051/114] fix: randomised size poly

---
 ecc/bls12-377/shplonk/shplonk_test.go                    | 4 +++-
 ecc/bls12-378/shplonk/shplonk_test.go                    | 4 +++-
 ecc/bls12-381/shplonk/shplonk_test.go                    | 4 +++-
 ecc/bls24-315/shplonk/shplonk_test.go                    | 4 +++-
 ecc/bls24-317/shplonk/shplonk_test.go                    | 4 +++-
 ecc/bn254/shplonk/shplonk_test.go                        | 4 +++-
 ecc/bw6-633/shplonk/shplonk_test.go                      | 4 +++-
 ecc/bw6-756/shplonk/shplonk_test.go                      | 4 +++-
 ecc/bw6-761/shplonk/shplonk_test.go                      | 4 +++-
 internal/generator/shplonk/template/shplonk.test.go.tmpl | 4 +++-
 10 files changed, 30 insertions(+), 10 deletions(-)

diff --git a/ecc/bls12-377/shplonk/shplonk_test.go b/ecc/bls12-377/shplonk/shplonk_test.go
index b956361f86..602ee3f9d0 100644
--- a/ecc/bls12-377/shplonk/shplonk_test.go
+++ b/ecc/bls12-377/shplonk/shplonk_test.go
@@ -19,6 +19,7 @@ package shplonk
 import (
 	"crypto/sha256"
 	"math/big"
+	"math/rand"
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
@@ -35,6 +36,7 @@ func init() {
 	const srsSize = 230
 	var frAlpha fr.Element
 	frAlpha.SetRandom()
+	bAlpha = big.NewInt(0)
 	frAlpha.BigInt(bAlpha)
 	var err error
 	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
@@ -50,7 +52,7 @@ func TestOpening(t *testing.T) {
 	nbPolys := 2
 	sizePoly := make([]int, nbPolys)
 	for i := 0; i < nbPolys; i++ {
-		sizePoly[i] = 10 + i
+		sizePoly[i] = rand.Intn(10) + 2
 	}
 	polys := make([][]fr.Element, nbPolys)
 	for i := 0; i < nbPolys; i++ {
diff --git a/ecc/bls12-378/shplonk/shplonk_test.go b/ecc/bls12-378/shplonk/shplonk_test.go
index 5bbb9fc122..34e4127cc0 100644
--- a/ecc/bls12-378/shplonk/shplonk_test.go
+++ b/ecc/bls12-378/shplonk/shplonk_test.go
@@ -19,6 +19,7 @@ package shplonk
 import (
 	"crypto/sha256"
 	"math/big"
+	"math/rand"
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
@@ -35,6 +36,7 @@ func init() {
 	const srsSize = 230
 	var frAlpha fr.Element
 	frAlpha.SetRandom()
+	bAlpha = big.NewInt(0)
 	frAlpha.BigInt(bAlpha)
 	var err error
 	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
@@ -50,7 +52,7 @@ func TestOpening(t *testing.T) {
 	nbPolys := 2
 	sizePoly := make([]int, nbPolys)
 	for i := 0; i < nbPolys; i++ {
-		sizePoly[i] = 10 + i
+		sizePoly[i] = rand.Intn(10) + 2
 	}
 	polys := make([][]fr.Element, nbPolys)
 	for i := 0; i < nbPolys; i++ {
diff --git a/ecc/bls12-381/shplonk/shplonk_test.go b/ecc/bls12-381/shplonk/shplonk_test.go
index 67eba49ba3..05fb93a3f6 100644
--- a/ecc/bls12-381/shplonk/shplonk_test.go
+++ b/ecc/bls12-381/shplonk/shplonk_test.go
@@ -19,6 +19,7 @@ package shplonk
 import (
 	"crypto/sha256"
 	"math/big"
+	"math/rand"
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
@@ -35,6 +36,7 @@ func init() {
 	const srsSize = 230
 	var frAlpha fr.Element
 	frAlpha.SetRandom()
+	bAlpha = big.NewInt(0)
 	frAlpha.BigInt(bAlpha)
 	var err error
 	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
@@ -50,7 +52,7 @@ func TestOpening(t *testing.T) {
 	nbPolys := 2
 	sizePoly := make([]int, nbPolys)
 	for i := 0; i < nbPolys; i++ {
-		sizePoly[i] = 10 + i
+		sizePoly[i] = rand.Intn(10) + 2
 	}
 	polys := make([][]fr.Element, nbPolys)
 	for i := 0; i < nbPolys; i++ {
diff --git a/ecc/bls24-315/shplonk/shplonk_test.go b/ecc/bls24-315/shplonk/shplonk_test.go
index 93b6636857..a8d35f5c00 100644
--- a/ecc/bls24-315/shplonk/shplonk_test.go
+++ b/ecc/bls24-315/shplonk/shplonk_test.go
@@ -19,6 +19,7 @@ package shplonk
 import (
 	"crypto/sha256"
 	"math/big"
+	"math/rand"
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
@@ -35,6 +36,7 @@ func init() {
 	const srsSize = 230
 	var frAlpha fr.Element
 	frAlpha.SetRandom()
+	bAlpha = big.NewInt(0)
 	frAlpha.BigInt(bAlpha)
 	var err error
 	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
@@ -50,7 +52,7 @@ func TestOpening(t *testing.T) {
 	nbPolys := 2
 	sizePoly := make([]int, nbPolys)
 	for i := 0; i < nbPolys; i++ {
-		sizePoly[i] = 10 + i
+		sizePoly[i] = rand.Intn(10) + 2
 	}
 	polys := make([][]fr.Element, nbPolys)
 	for i := 0; i < nbPolys; i++ {
diff --git a/ecc/bls24-317/shplonk/shplonk_test.go b/ecc/bls24-317/shplonk/shplonk_test.go
index 7afffeb886..9e6d76ded0 100644
--- a/ecc/bls24-317/shplonk/shplonk_test.go
+++ b/ecc/bls24-317/shplonk/shplonk_test.go
@@ -19,6 +19,7 @@ package shplonk
 import (
 	"crypto/sha256"
 	"math/big"
+	"math/rand"
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
@@ -35,6 +36,7 @@ func init() {
 	const srsSize = 230
 	var frAlpha fr.Element
 	frAlpha.SetRandom()
+	bAlpha = big.NewInt(0)
 	frAlpha.BigInt(bAlpha)
 	var err error
 	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
@@ -50,7 +52,7 @@ func TestOpening(t *testing.T) {
 	nbPolys := 2
 	sizePoly := make([]int, nbPolys)
 	for i := 0; i < nbPolys; i++ {
-		sizePoly[i] = 10 + i
+		sizePoly[i] = rand.Intn(10) + 2
 	}
 	polys := make([][]fr.Element, nbPolys)
 	for i := 0; i < nbPolys; i++ {
diff --git a/ecc/bn254/shplonk/shplonk_test.go b/ecc/bn254/shplonk/shplonk_test.go
index 7b14e5544f..d0e4ce0695 100644
--- a/ecc/bn254/shplonk/shplonk_test.go
+++ b/ecc/bn254/shplonk/shplonk_test.go
@@ -19,6 +19,7 @@ package shplonk
 import (
 	"crypto/sha256"
 	"math/big"
+	"math/rand"
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
@@ -35,6 +36,7 @@ func init() {
 	const srsSize = 230
 	var frAlpha fr.Element
 	frAlpha.SetRandom()
+	bAlpha = big.NewInt(0)
 	frAlpha.BigInt(bAlpha)
 	var err error
 	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
@@ -50,7 +52,7 @@ func TestOpening(t *testing.T) {
 	nbPolys := 2
 	sizePoly := make([]int, nbPolys)
 	for i := 0; i < nbPolys; i++ {
-		sizePoly[i] = 10 + i
+		sizePoly[i] = rand.Intn(10) + 2
 	}
 	polys := make([][]fr.Element, nbPolys)
 	for i := 0; i < nbPolys; i++ {
diff --git a/ecc/bw6-633/shplonk/shplonk_test.go b/ecc/bw6-633/shplonk/shplonk_test.go
index c813a1bf53..ea171cbefb 100644
--- a/ecc/bw6-633/shplonk/shplonk_test.go
+++ b/ecc/bw6-633/shplonk/shplonk_test.go
@@ -19,6 +19,7 @@ package shplonk
 import (
 	"crypto/sha256"
 	"math/big"
+	"math/rand"
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
@@ -35,6 +36,7 @@ func init() {
 	const srsSize = 230
 	var frAlpha fr.Element
 	frAlpha.SetRandom()
+	bAlpha = big.NewInt(0)
 	frAlpha.BigInt(bAlpha)
 	var err error
 	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
@@ -50,7 +52,7 @@ func TestOpening(t *testing.T) {
 	nbPolys := 2
 	sizePoly := make([]int, nbPolys)
 	for i := 0; i < nbPolys; i++ {
-		sizePoly[i] = 10 + i
+		sizePoly[i] = rand.Intn(10) + 2
 	}
 	polys := make([][]fr.Element, nbPolys)
 	for i := 0; i < nbPolys; i++ {
diff --git a/ecc/bw6-756/shplonk/shplonk_test.go b/ecc/bw6-756/shplonk/shplonk_test.go
index c72b57d7ec..4643d87606 100644
--- a/ecc/bw6-756/shplonk/shplonk_test.go
+++ b/ecc/bw6-756/shplonk/shplonk_test.go
@@ -19,6 +19,7 @@ package shplonk
 import (
 	"crypto/sha256"
 	"math/big"
+	"math/rand"
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
@@ -35,6 +36,7 @@ func init() {
 	const srsSize = 230
 	var frAlpha fr.Element
 	frAlpha.SetRandom()
+	bAlpha = big.NewInt(0)
 	frAlpha.BigInt(bAlpha)
 	var err error
 	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
@@ -50,7 +52,7 @@ func TestOpening(t *testing.T) {
 	nbPolys := 2
 	sizePoly := make([]int, nbPolys)
 	for i := 0; i < nbPolys; i++ {
-		sizePoly[i] = 10 + i
+		sizePoly[i] = rand.Intn(10) + 2
 	}
 	polys := make([][]fr.Element, nbPolys)
 	for i := 0; i < nbPolys; i++ {
diff --git a/ecc/bw6-761/shplonk/shplonk_test.go b/ecc/bw6-761/shplonk/shplonk_test.go
index 95702777e1..ca08b62e53 100644
--- a/ecc/bw6-761/shplonk/shplonk_test.go
+++ b/ecc/bw6-761/shplonk/shplonk_test.go
@@ -19,6 +19,7 @@ package shplonk
 import (
 	"crypto/sha256"
 	"math/big"
+	"math/rand"
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
@@ -35,6 +36,7 @@ func init() {
 	const srsSize = 230
 	var frAlpha fr.Element
 	frAlpha.SetRandom()
+	bAlpha = big.NewInt(0)
 	frAlpha.BigInt(bAlpha)
 	var err error
 	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
@@ -50,7 +52,7 @@ func TestOpening(t *testing.T) {
 	nbPolys := 2
 	sizePoly := make([]int, nbPolys)
 	for i := 0; i < nbPolys; i++ {
-		sizePoly[i] = 10 + i
+		sizePoly[i] = rand.Intn(10) + 2
 	}
 	polys := make([][]fr.Element, nbPolys)
 	for i := 0; i < nbPolys; i++ {
diff --git a/internal/generator/shplonk/template/shplonk.test.go.tmpl b/internal/generator/shplonk/template/shplonk.test.go.tmpl
index d6e8302b93..7d642ed8fa 100644
--- a/internal/generator/shplonk/template/shplonk.test.go.tmpl
+++ b/internal/generator/shplonk/template/shplonk.test.go.tmpl
@@ -2,6 +2,7 @@ import (
 	"crypto/sha256"
 	"math/big"
 	"testing"
+	"math/rand"
 
 	"github.com/consensys/gnark-crypto/ecc"
 	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/fr"
@@ -18,6 +19,7 @@ func init() {
 	const srsSize = 230
 	var frAlpha fr.Element
 	frAlpha.SetRandom()
+	bAlpha = big.NewInt(0)
 	frAlpha.BigInt(bAlpha)
 	var err error
 	testSrs, err = kzg.NewSRS(ecc.NextPowerOfTwo(srsSize), bAlpha)
@@ -33,7 +35,7 @@ func TestOpening(t *testing.T) {
 	nbPolys := 2
 	sizePoly := make([]int, nbPolys)
 	for i := 0; i < nbPolys; i++ {
-		sizePoly[i] = 10 + i
+		sizePoly[i] = rand.Intn(10) + 2
 	}
 	polys := make([][]fr.Element, nbPolys)
 	for i := 0; i < nbPolys; i++ {

From 86aed27ee6f5c66223a521bb40adb923b4e01a9e Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Wed, 18 Sep 2024 19:28:54 +0200
Subject: [PATCH 052/114] fix: check pairing error

---
 ecc/bls12-377/shplonk/shplonk.go                    | 4 ++++
 ecc/bls12-378/shplonk/shplonk.go                    | 4 ++++
 ecc/bls12-381/shplonk/shplonk.go                    | 4 ++++
 ecc/bls24-315/shplonk/shplonk.go                    | 4 ++++
 ecc/bls24-317/shplonk/shplonk.go                    | 4 ++++
 ecc/bn254/shplonk/shplonk.go                        | 4 ++++
 ecc/bw6-633/shplonk/shplonk.go                      | 4 ++++
 ecc/bw6-756/shplonk/shplonk.go                      | 4 ++++
 ecc/bw6-761/shplonk/shplonk.go                      | 4 ++++
 internal/generator/shplonk/template/shplonk.go.tmpl | 4 ++++
 10 files changed, 40 insertions(+)

diff --git a/ecc/bls12-377/shplonk/shplonk.go b/ecc/bls12-377/shplonk/shplonk.go
index 25ab085deb..55619bac39 100644
--- a/ecc/bls12-377/shplonk/shplonk.go
+++ b/ecc/bls12-377/shplonk/shplonk.go
@@ -32,6 +32,7 @@ var (
 	ErrInvalidNumberOfPoints  = errors.New("number of digests should be equal to the number of points")
 	ErrVerifyOpeningProof     = errors.New("can't verify batch opening proof")
 	ErrInvalidNumberOfDigests = errors.New("number of digests should be equal to the number of polynomials")
+	ErrPairingCheck           = errors.New("pairing product is not 1")
 )
 
 // OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
@@ -267,6 +268,9 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 		[]bls12377.G1Affine{f, proof.WPrime},
 		vk.Lines[:],
 	)
+	if err != nil {
+		return ErrPairingCheck
+	}
 
 	if !check {
 		return ErrVerifyOpeningProof
diff --git a/ecc/bls12-378/shplonk/shplonk.go b/ecc/bls12-378/shplonk/shplonk.go
index 8ee2ed9fba..7eadfcad16 100644
--- a/ecc/bls12-378/shplonk/shplonk.go
+++ b/ecc/bls12-378/shplonk/shplonk.go
@@ -32,6 +32,7 @@ var (
 	ErrInvalidNumberOfPoints  = errors.New("number of digests should be equal to the number of points")
 	ErrVerifyOpeningProof     = errors.New("can't verify batch opening proof")
 	ErrInvalidNumberOfDigests = errors.New("number of digests should be equal to the number of polynomials")
+	ErrPairingCheck           = errors.New("pairing product is not 1")
 )
 
 // OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
@@ -267,6 +268,9 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 		[]bls12378.G1Affine{f, proof.WPrime},
 		vk.Lines[:],
 	)
+	if err != nil {
+		return ErrPairingCheck
+	}
 
 	if !check {
 		return ErrVerifyOpeningProof
diff --git a/ecc/bls12-381/shplonk/shplonk.go b/ecc/bls12-381/shplonk/shplonk.go
index 835efaa8fc..a9c2c44319 100644
--- a/ecc/bls12-381/shplonk/shplonk.go
+++ b/ecc/bls12-381/shplonk/shplonk.go
@@ -32,6 +32,7 @@ var (
 	ErrInvalidNumberOfPoints  = errors.New("number of digests should be equal to the number of points")
 	ErrVerifyOpeningProof     = errors.New("can't verify batch opening proof")
 	ErrInvalidNumberOfDigests = errors.New("number of digests should be equal to the number of polynomials")
+	ErrPairingCheck           = errors.New("pairing product is not 1")
 )
 
 // OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
@@ -267,6 +268,9 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 		[]bls12381.G1Affine{f, proof.WPrime},
 		vk.Lines[:],
 	)
+	if err != nil {
+		return ErrPairingCheck
+	}
 
 	if !check {
 		return ErrVerifyOpeningProof
diff --git a/ecc/bls24-315/shplonk/shplonk.go b/ecc/bls24-315/shplonk/shplonk.go
index 2629d18d3d..038a0800e3 100644
--- a/ecc/bls24-315/shplonk/shplonk.go
+++ b/ecc/bls24-315/shplonk/shplonk.go
@@ -32,6 +32,7 @@ var (
 	ErrInvalidNumberOfPoints  = errors.New("number of digests should be equal to the number of points")
 	ErrVerifyOpeningProof     = errors.New("can't verify batch opening proof")
 	ErrInvalidNumberOfDigests = errors.New("number of digests should be equal to the number of polynomials")
+	ErrPairingCheck           = errors.New("pairing product is not 1")
 )
 
 // OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
@@ -267,6 +268,9 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 		[]bls24315.G1Affine{f, proof.WPrime},
 		vk.Lines[:],
 	)
+	if err != nil {
+		return ErrPairingCheck
+	}
 
 	if !check {
 		return ErrVerifyOpeningProof
diff --git a/ecc/bls24-317/shplonk/shplonk.go b/ecc/bls24-317/shplonk/shplonk.go
index ff8f07e185..2b6c0c553d 100644
--- a/ecc/bls24-317/shplonk/shplonk.go
+++ b/ecc/bls24-317/shplonk/shplonk.go
@@ -32,6 +32,7 @@ var (
 	ErrInvalidNumberOfPoints  = errors.New("number of digests should be equal to the number of points")
 	ErrVerifyOpeningProof     = errors.New("can't verify batch opening proof")
 	ErrInvalidNumberOfDigests = errors.New("number of digests should be equal to the number of polynomials")
+	ErrPairingCheck           = errors.New("pairing product is not 1")
 )
 
 // OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
@@ -267,6 +268,9 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 		[]bls24317.G1Affine{f, proof.WPrime},
 		vk.Lines[:],
 	)
+	if err != nil {
+		return ErrPairingCheck
+	}
 
 	if !check {
 		return ErrVerifyOpeningProof
diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
index 7a86ed72e6..5e9c6d5399 100644
--- a/ecc/bn254/shplonk/shplonk.go
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -32,6 +32,7 @@ var (
 	ErrInvalidNumberOfPoints  = errors.New("number of digests should be equal to the number of points")
 	ErrVerifyOpeningProof     = errors.New("can't verify batch opening proof")
 	ErrInvalidNumberOfDigests = errors.New("number of digests should be equal to the number of polynomials")
+	ErrPairingCheck           = errors.New("pairing product is not 1")
 )
 
 // OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
@@ -267,6 +268,9 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 		[]bn254.G1Affine{f, proof.WPrime},
 		vk.Lines[:],
 	)
+	if err != nil {
+		return ErrPairingCheck
+	}
 
 	if !check {
 		return ErrVerifyOpeningProof
diff --git a/ecc/bw6-633/shplonk/shplonk.go b/ecc/bw6-633/shplonk/shplonk.go
index 91b953d4d7..c901548d01 100644
--- a/ecc/bw6-633/shplonk/shplonk.go
+++ b/ecc/bw6-633/shplonk/shplonk.go
@@ -32,6 +32,7 @@ var (
 	ErrInvalidNumberOfPoints  = errors.New("number of digests should be equal to the number of points")
 	ErrVerifyOpeningProof     = errors.New("can't verify batch opening proof")
 	ErrInvalidNumberOfDigests = errors.New("number of digests should be equal to the number of polynomials")
+	ErrPairingCheck           = errors.New("pairing product is not 1")
 )
 
 // OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
@@ -267,6 +268,9 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 		[]bw6633.G1Affine{f, proof.WPrime},
 		vk.Lines[:],
 	)
+	if err != nil {
+		return ErrPairingCheck
+	}
 
 	if !check {
 		return ErrVerifyOpeningProof
diff --git a/ecc/bw6-756/shplonk/shplonk.go b/ecc/bw6-756/shplonk/shplonk.go
index dffbf7f409..eea8739b03 100644
--- a/ecc/bw6-756/shplonk/shplonk.go
+++ b/ecc/bw6-756/shplonk/shplonk.go
@@ -32,6 +32,7 @@ var (
 	ErrInvalidNumberOfPoints  = errors.New("number of digests should be equal to the number of points")
 	ErrVerifyOpeningProof     = errors.New("can't verify batch opening proof")
 	ErrInvalidNumberOfDigests = errors.New("number of digests should be equal to the number of polynomials")
+	ErrPairingCheck           = errors.New("pairing product is not 1")
 )
 
 // OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
@@ -267,6 +268,9 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 		[]bw6756.G1Affine{f, proof.WPrime},
 		vk.Lines[:],
 	)
+	if err != nil {
+		return ErrPairingCheck
+	}
 
 	if !check {
 		return ErrVerifyOpeningProof
diff --git a/ecc/bw6-761/shplonk/shplonk.go b/ecc/bw6-761/shplonk/shplonk.go
index 49c4e2015e..96806b2e89 100644
--- a/ecc/bw6-761/shplonk/shplonk.go
+++ b/ecc/bw6-761/shplonk/shplonk.go
@@ -32,6 +32,7 @@ var (
 	ErrInvalidNumberOfPoints  = errors.New("number of digests should be equal to the number of points")
 	ErrVerifyOpeningProof     = errors.New("can't verify batch opening proof")
 	ErrInvalidNumberOfDigests = errors.New("number of digests should be equal to the number of polynomials")
+	ErrPairingCheck           = errors.New("pairing product is not 1")
 )
 
 // OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
@@ -267,6 +268,9 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 		[]bw6761.G1Affine{f, proof.WPrime},
 		vk.Lines[:],
 	)
+	if err != nil {
+		return ErrPairingCheck
+	}
 
 	if !check {
 		return ErrVerifyOpeningProof
diff --git a/internal/generator/shplonk/template/shplonk.go.tmpl b/internal/generator/shplonk/template/shplonk.go.tmpl
index 76689457d6..0f510b4f4a 100644
--- a/internal/generator/shplonk/template/shplonk.go.tmpl
+++ b/internal/generator/shplonk/template/shplonk.go.tmpl
@@ -14,6 +14,7 @@ var (
 	ErrInvalidNumberOfPoints = errors.New("number of digests should be equal to the number of points")
 	ErrVerifyOpeningProof    = errors.New("can't verify batch opening proof")
 	ErrInvalidNumberOfDigests = errors.New("number of digests should be equal to the number of polynomials")
+	ErrPairingCheck           = errors.New("pairing product is not 1")
 )
 
 // OpeningProof KZG proof for opening (fᵢ)_{i} at a different points (xᵢ)_{i}.
@@ -249,6 +250,9 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 		[]{{ .CurvePackage }}.G1Affine{f, proof.WPrime},
 		vk.Lines[:],
 	)
+	if err!=nil {
+		return ErrPairingCheck
+	}
 
 	if !check {
 		return ErrVerifyOpeningProof

From c3a70ce287ad2fe9f2f4e5ebb1b6e0fffb5ce466 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Thu, 19 Sep 2024 15:12:27 +0200
Subject: [PATCH 053/114] feat: used
 bufMaxSizePolynomials[:len(polynomials[i])]

---
 ecc/bls12-377/shplonk/shplonk.go                    | 4 ++--
 ecc/bls12-378/shplonk/shplonk.go                    | 4 ++--
 ecc/bls12-381/shplonk/shplonk.go                    | 4 ++--
 ecc/bls24-315/shplonk/shplonk.go                    | 4 ++--
 ecc/bls24-317/shplonk/shplonk.go                    | 4 ++--
 ecc/bn254/shplonk/shplonk.go                        | 4 ++--
 ecc/bw6-633/shplonk/shplonk.go                      | 4 ++--
 ecc/bw6-756/shplonk/shplonk.go                      | 4 ++--
 ecc/bw6-761/shplonk/shplonk.go                      | 4 ++--
 internal/generator/shplonk/template/shplonk.go.tmpl | 2 +-
 10 files changed, 19 insertions(+), 19 deletions(-)

diff --git a/ecc/bls12-377/shplonk/shplonk.go b/ecc/bls12-377/shplonk/shplonk.go
index 55619bac39..197d994c34 100644
--- a/ecc/bls12-377/shplonk/shplonk.go
+++ b/ecc/bls12-377/shplonk/shplonk.go
@@ -146,8 +146,8 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 
 		copy(bufMaxSizePolynomials, polynomials[i])
 		riz := eval(ri[i], z)
-		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz) // (fᵢ-rᵢ(z))
-		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusSiZ)        // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
+		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz)                // (fᵢ-rᵢ(z))
+		mulByConstant(bufMaxSizePolynomials[:len(polynomials[i])], gammaiZtMinusSiZ) // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
 		for j := 0; j < len(bufMaxSizePolynomials); j++ {
 			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
 		}
diff --git a/ecc/bls12-378/shplonk/shplonk.go b/ecc/bls12-378/shplonk/shplonk.go
index 7eadfcad16..afcdbcfe91 100644
--- a/ecc/bls12-378/shplonk/shplonk.go
+++ b/ecc/bls12-378/shplonk/shplonk.go
@@ -146,8 +146,8 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 
 		copy(bufMaxSizePolynomials, polynomials[i])
 		riz := eval(ri[i], z)
-		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz) // (fᵢ-rᵢ(z))
-		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusSiZ)        // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
+		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz)                // (fᵢ-rᵢ(z))
+		mulByConstant(bufMaxSizePolynomials[:len(polynomials[i])], gammaiZtMinusSiZ) // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
 		for j := 0; j < len(bufMaxSizePolynomials); j++ {
 			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
 		}
diff --git a/ecc/bls12-381/shplonk/shplonk.go b/ecc/bls12-381/shplonk/shplonk.go
index a9c2c44319..21f226dafa 100644
--- a/ecc/bls12-381/shplonk/shplonk.go
+++ b/ecc/bls12-381/shplonk/shplonk.go
@@ -146,8 +146,8 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 
 		copy(bufMaxSizePolynomials, polynomials[i])
 		riz := eval(ri[i], z)
-		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz) // (fᵢ-rᵢ(z))
-		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusSiZ)        // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
+		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz)                // (fᵢ-rᵢ(z))
+		mulByConstant(bufMaxSizePolynomials[:len(polynomials[i])], gammaiZtMinusSiZ) // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
 		for j := 0; j < len(bufMaxSizePolynomials); j++ {
 			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
 		}
diff --git a/ecc/bls24-315/shplonk/shplonk.go b/ecc/bls24-315/shplonk/shplonk.go
index 038a0800e3..4c439a8137 100644
--- a/ecc/bls24-315/shplonk/shplonk.go
+++ b/ecc/bls24-315/shplonk/shplonk.go
@@ -146,8 +146,8 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 
 		copy(bufMaxSizePolynomials, polynomials[i])
 		riz := eval(ri[i], z)
-		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz) // (fᵢ-rᵢ(z))
-		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusSiZ)        // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
+		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz)                // (fᵢ-rᵢ(z))
+		mulByConstant(bufMaxSizePolynomials[:len(polynomials[i])], gammaiZtMinusSiZ) // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
 		for j := 0; j < len(bufMaxSizePolynomials); j++ {
 			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
 		}
diff --git a/ecc/bls24-317/shplonk/shplonk.go b/ecc/bls24-317/shplonk/shplonk.go
index 2b6c0c553d..b8a9795369 100644
--- a/ecc/bls24-317/shplonk/shplonk.go
+++ b/ecc/bls24-317/shplonk/shplonk.go
@@ -146,8 +146,8 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 
 		copy(bufMaxSizePolynomials, polynomials[i])
 		riz := eval(ri[i], z)
-		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz) // (fᵢ-rᵢ(z))
-		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusSiZ)        // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
+		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz)                // (fᵢ-rᵢ(z))
+		mulByConstant(bufMaxSizePolynomials[:len(polynomials[i])], gammaiZtMinusSiZ) // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
 		for j := 0; j < len(bufMaxSizePolynomials); j++ {
 			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
 		}
diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
index 5e9c6d5399..98db94c5a9 100644
--- a/ecc/bn254/shplonk/shplonk.go
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -146,8 +146,8 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 
 		copy(bufMaxSizePolynomials, polynomials[i])
 		riz := eval(ri[i], z)
-		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz) // (fᵢ-rᵢ(z))
-		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusSiZ)        // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
+		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz)                // (fᵢ-rᵢ(z))
+		mulByConstant(bufMaxSizePolynomials[:len(polynomials[i])], gammaiZtMinusSiZ) // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
 		for j := 0; j < len(bufMaxSizePolynomials); j++ {
 			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
 		}
diff --git a/ecc/bw6-633/shplonk/shplonk.go b/ecc/bw6-633/shplonk/shplonk.go
index c901548d01..c2962f210a 100644
--- a/ecc/bw6-633/shplonk/shplonk.go
+++ b/ecc/bw6-633/shplonk/shplonk.go
@@ -146,8 +146,8 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 
 		copy(bufMaxSizePolynomials, polynomials[i])
 		riz := eval(ri[i], z)
-		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz) // (fᵢ-rᵢ(z))
-		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusSiZ)        // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
+		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz)                // (fᵢ-rᵢ(z))
+		mulByConstant(bufMaxSizePolynomials[:len(polynomials[i])], gammaiZtMinusSiZ) // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
 		for j := 0; j < len(bufMaxSizePolynomials); j++ {
 			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
 		}
diff --git a/ecc/bw6-756/shplonk/shplonk.go b/ecc/bw6-756/shplonk/shplonk.go
index eea8739b03..5864904a44 100644
--- a/ecc/bw6-756/shplonk/shplonk.go
+++ b/ecc/bw6-756/shplonk/shplonk.go
@@ -146,8 +146,8 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 
 		copy(bufMaxSizePolynomials, polynomials[i])
 		riz := eval(ri[i], z)
-		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz) // (fᵢ-rᵢ(z))
-		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusSiZ)        // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
+		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz)                // (fᵢ-rᵢ(z))
+		mulByConstant(bufMaxSizePolynomials[:len(polynomials[i])], gammaiZtMinusSiZ) // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
 		for j := 0; j < len(bufMaxSizePolynomials); j++ {
 			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
 		}
diff --git a/ecc/bw6-761/shplonk/shplonk.go b/ecc/bw6-761/shplonk/shplonk.go
index 96806b2e89..0880e5be45 100644
--- a/ecc/bw6-761/shplonk/shplonk.go
+++ b/ecc/bw6-761/shplonk/shplonk.go
@@ -146,8 +146,8 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 
 		copy(bufMaxSizePolynomials, polynomials[i])
 		riz := eval(ri[i], z)
-		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz) // (fᵢ-rᵢ(z))
-		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusSiZ)        // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
+		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz)                // (fᵢ-rᵢ(z))
+		mulByConstant(bufMaxSizePolynomials[:len(polynomials[i])], gammaiZtMinusSiZ) // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
 		for j := 0; j < len(bufMaxSizePolynomials); j++ {
 			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
 		}
diff --git a/internal/generator/shplonk/template/shplonk.go.tmpl b/internal/generator/shplonk/template/shplonk.go.tmpl
index 0f510b4f4a..253ed25bb4 100644
--- a/internal/generator/shplonk/template/shplonk.go.tmpl
+++ b/internal/generator/shplonk/template/shplonk.go.tmpl
@@ -129,7 +129,7 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 		copy(bufMaxSizePolynomials, polynomials[i])
 		riz := eval(ri[i], z)
 		bufMaxSizePolynomials[0].Sub(&bufMaxSizePolynomials[0], &riz) // (fᵢ-rᵢ(z))
-		mulByConstant(bufMaxSizePolynomials, gammaiZtMinusSiZ)        // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
+		mulByConstant(bufMaxSizePolynomials[:len(polynomials[i])], gammaiZtMinusSiZ)        // γⁱZ_{T\Sᵢ}(z)(fᵢ-rᵢ(z))
 		for j := 0; j < len(bufMaxSizePolynomials); j++ {
 			l[j].Add(&l[j], &bufMaxSizePolynomials[j])
 		}

From 699c2138f8258591a1fdbadbf6505ec19051497c Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Thu, 19 Sep 2024 15:28:03 +0200
Subject: [PATCH 054/114] feat: renaming gamma -> challenge

---
 ecc/bls12-377/shplonk/shplonk.go                    | 8 ++++----
 ecc/bls12-378/shplonk/shplonk.go                    | 8 ++++----
 ecc/bls12-381/shplonk/shplonk.go                    | 8 ++++----
 ecc/bls24-315/shplonk/shplonk.go                    | 8 ++++----
 ecc/bls24-317/shplonk/shplonk.go                    | 8 ++++----
 ecc/bn254/shplonk/shplonk.go                        | 8 ++++----
 ecc/bw6-633/shplonk/shplonk.go                      | 8 ++++----
 ecc/bw6-756/shplonk/shplonk.go                      | 8 ++++----
 ecc/bw6-761/shplonk/shplonk.go                      | 8 ++++----
 internal/generator/shplonk/template/shplonk.go.tmpl | 8 ++++----
 10 files changed, 40 insertions(+), 40 deletions(-)

diff --git a/ecc/bls12-377/shplonk/shplonk.go b/ecc/bls12-377/shplonk/shplonk.go
index 197d994c34..f2faa6d860 100644
--- a/ecc/bls12-377/shplonk/shplonk.go
+++ b/ecc/bls12-377/shplonk/shplonk.go
@@ -303,14 +303,14 @@ func deriveChallenge(name string, points [][]fr.Element, digests []kzg.Digest, t
 		}
 	}
 
-	gammaByte, err := t.ComputeChallenge(name)
+	challengeByte, err := t.ComputeChallenge(name)
 	if err != nil {
 		return fr.Element{}, err
 	}
-	var gamma fr.Element
-	gamma.SetBytes(gammaByte)
+	var challenge fr.Element
+	challenge.SetBytes(challengeByte)
 
-	return gamma, nil
+	return challenge, nil
 }
 
 // ------------------------------
diff --git a/ecc/bls12-378/shplonk/shplonk.go b/ecc/bls12-378/shplonk/shplonk.go
index afcdbcfe91..7742ad48a2 100644
--- a/ecc/bls12-378/shplonk/shplonk.go
+++ b/ecc/bls12-378/shplonk/shplonk.go
@@ -303,14 +303,14 @@ func deriveChallenge(name string, points [][]fr.Element, digests []kzg.Digest, t
 		}
 	}
 
-	gammaByte, err := t.ComputeChallenge(name)
+	challengeByte, err := t.ComputeChallenge(name)
 	if err != nil {
 		return fr.Element{}, err
 	}
-	var gamma fr.Element
-	gamma.SetBytes(gammaByte)
+	var challenge fr.Element
+	challenge.SetBytes(challengeByte)
 
-	return gamma, nil
+	return challenge, nil
 }
 
 // ------------------------------
diff --git a/ecc/bls12-381/shplonk/shplonk.go b/ecc/bls12-381/shplonk/shplonk.go
index 21f226dafa..d5adfa3f07 100644
--- a/ecc/bls12-381/shplonk/shplonk.go
+++ b/ecc/bls12-381/shplonk/shplonk.go
@@ -303,14 +303,14 @@ func deriveChallenge(name string, points [][]fr.Element, digests []kzg.Digest, t
 		}
 	}
 
-	gammaByte, err := t.ComputeChallenge(name)
+	challengeByte, err := t.ComputeChallenge(name)
 	if err != nil {
 		return fr.Element{}, err
 	}
-	var gamma fr.Element
-	gamma.SetBytes(gammaByte)
+	var challenge fr.Element
+	challenge.SetBytes(challengeByte)
 
-	return gamma, nil
+	return challenge, nil
 }
 
 // ------------------------------
diff --git a/ecc/bls24-315/shplonk/shplonk.go b/ecc/bls24-315/shplonk/shplonk.go
index 4c439a8137..825c756cf3 100644
--- a/ecc/bls24-315/shplonk/shplonk.go
+++ b/ecc/bls24-315/shplonk/shplonk.go
@@ -303,14 +303,14 @@ func deriveChallenge(name string, points [][]fr.Element, digests []kzg.Digest, t
 		}
 	}
 
-	gammaByte, err := t.ComputeChallenge(name)
+	challengeByte, err := t.ComputeChallenge(name)
 	if err != nil {
 		return fr.Element{}, err
 	}
-	var gamma fr.Element
-	gamma.SetBytes(gammaByte)
+	var challenge fr.Element
+	challenge.SetBytes(challengeByte)
 
-	return gamma, nil
+	return challenge, nil
 }
 
 // ------------------------------
diff --git a/ecc/bls24-317/shplonk/shplonk.go b/ecc/bls24-317/shplonk/shplonk.go
index b8a9795369..33640bb695 100644
--- a/ecc/bls24-317/shplonk/shplonk.go
+++ b/ecc/bls24-317/shplonk/shplonk.go
@@ -303,14 +303,14 @@ func deriveChallenge(name string, points [][]fr.Element, digests []kzg.Digest, t
 		}
 	}
 
-	gammaByte, err := t.ComputeChallenge(name)
+	challengeByte, err := t.ComputeChallenge(name)
 	if err != nil {
 		return fr.Element{}, err
 	}
-	var gamma fr.Element
-	gamma.SetBytes(gammaByte)
+	var challenge fr.Element
+	challenge.SetBytes(challengeByte)
 
-	return gamma, nil
+	return challenge, nil
 }
 
 // ------------------------------
diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
index 98db94c5a9..90c7ea5bb1 100644
--- a/ecc/bn254/shplonk/shplonk.go
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -303,14 +303,14 @@ func deriveChallenge(name string, points [][]fr.Element, digests []kzg.Digest, t
 		}
 	}
 
-	gammaByte, err := t.ComputeChallenge(name)
+	challengeByte, err := t.ComputeChallenge(name)
 	if err != nil {
 		return fr.Element{}, err
 	}
-	var gamma fr.Element
-	gamma.SetBytes(gammaByte)
+	var challenge fr.Element
+	challenge.SetBytes(challengeByte)
 
-	return gamma, nil
+	return challenge, nil
 }
 
 // ------------------------------
diff --git a/ecc/bw6-633/shplonk/shplonk.go b/ecc/bw6-633/shplonk/shplonk.go
index c2962f210a..af23c6ec58 100644
--- a/ecc/bw6-633/shplonk/shplonk.go
+++ b/ecc/bw6-633/shplonk/shplonk.go
@@ -303,14 +303,14 @@ func deriveChallenge(name string, points [][]fr.Element, digests []kzg.Digest, t
 		}
 	}
 
-	gammaByte, err := t.ComputeChallenge(name)
+	challengeByte, err := t.ComputeChallenge(name)
 	if err != nil {
 		return fr.Element{}, err
 	}
-	var gamma fr.Element
-	gamma.SetBytes(gammaByte)
+	var challenge fr.Element
+	challenge.SetBytes(challengeByte)
 
-	return gamma, nil
+	return challenge, nil
 }
 
 // ------------------------------
diff --git a/ecc/bw6-756/shplonk/shplonk.go b/ecc/bw6-756/shplonk/shplonk.go
index 5864904a44..c3ac6d7330 100644
--- a/ecc/bw6-756/shplonk/shplonk.go
+++ b/ecc/bw6-756/shplonk/shplonk.go
@@ -303,14 +303,14 @@ func deriveChallenge(name string, points [][]fr.Element, digests []kzg.Digest, t
 		}
 	}
 
-	gammaByte, err := t.ComputeChallenge(name)
+	challengeByte, err := t.ComputeChallenge(name)
 	if err != nil {
 		return fr.Element{}, err
 	}
-	var gamma fr.Element
-	gamma.SetBytes(gammaByte)
+	var challenge fr.Element
+	challenge.SetBytes(challengeByte)
 
-	return gamma, nil
+	return challenge, nil
 }
 
 // ------------------------------
diff --git a/ecc/bw6-761/shplonk/shplonk.go b/ecc/bw6-761/shplonk/shplonk.go
index 0880e5be45..b02bcd5451 100644
--- a/ecc/bw6-761/shplonk/shplonk.go
+++ b/ecc/bw6-761/shplonk/shplonk.go
@@ -303,14 +303,14 @@ func deriveChallenge(name string, points [][]fr.Element, digests []kzg.Digest, t
 		}
 	}
 
-	gammaByte, err := t.ComputeChallenge(name)
+	challengeByte, err := t.ComputeChallenge(name)
 	if err != nil {
 		return fr.Element{}, err
 	}
-	var gamma fr.Element
-	gamma.SetBytes(gammaByte)
+	var challenge fr.Element
+	challenge.SetBytes(challengeByte)
 
-	return gamma, nil
+	return challenge, nil
 }
 
 // ------------------------------
diff --git a/internal/generator/shplonk/template/shplonk.go.tmpl b/internal/generator/shplonk/template/shplonk.go.tmpl
index 253ed25bb4..94f83cc92f 100644
--- a/internal/generator/shplonk/template/shplonk.go.tmpl
+++ b/internal/generator/shplonk/template/shplonk.go.tmpl
@@ -285,14 +285,14 @@ func deriveChallenge(name string, points [][]fr.Element, digests []kzg.Digest, t
 		}
 	}
 
-	gammaByte, err := t.ComputeChallenge(name)
+	challengeByte, err := t.ComputeChallenge(name)
 	if err != nil {
 		return fr.Element{}, err
 	}
-	var gamma fr.Element
-	gamma.SetBytes(gammaByte)
+	var challenge fr.Element
+	challenge.SetBytes(challengeByte)
 
-	return gamma, nil
+	return challenge, nil
 }
 
 // ------------------------------

From 803e9ce9028c61b94a3adf43b369275a6307ab4f Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 20 Sep 2024 10:17:27 +0200
Subject: [PATCH 055/114] feat: add round trip serialisation test

---
 ecc/bls12-377/shplonk/marshal.go              |  2 +-
 ecc/bls12-377/shplonk/shplonk_test.go         | 20 +++++++++++++++++++
 ecc/bls12-378/shplonk/marshal.go              |  2 +-
 ecc/bls12-378/shplonk/shplonk_test.go         | 20 +++++++++++++++++++
 ecc/bls12-381/shplonk/marshal.go              |  2 +-
 ecc/bls12-381/shplonk/shplonk_test.go         | 20 +++++++++++++++++++
 ecc/bls24-315/shplonk/marshal.go              |  2 +-
 ecc/bls24-315/shplonk/shplonk_test.go         | 20 +++++++++++++++++++
 ecc/bls24-317/shplonk/marshal.go              |  2 +-
 ecc/bls24-317/shplonk/shplonk_test.go         | 20 +++++++++++++++++++
 ecc/bn254/shplonk/marshal.go                  |  2 +-
 ecc/bn254/shplonk/shplonk_test.go             | 20 +++++++++++++++++++
 ecc/bw6-633/shplonk/marshal.go                |  2 +-
 ecc/bw6-633/shplonk/shplonk_test.go           | 20 +++++++++++++++++++
 ecc/bw6-756/shplonk/marshal.go                |  2 +-
 ecc/bw6-756/shplonk/shplonk_test.go           | 20 +++++++++++++++++++
 ecc/bw6-761/shplonk/marshal.go                |  2 +-
 ecc/bw6-761/shplonk/shplonk_test.go           | 20 +++++++++++++++++++
 .../shplonk/template/marshal.go.tmpl          |  2 +-
 .../shplonk/template/shplonk.test.go.tmpl     | 20 +++++++++++++++++++
 20 files changed, 210 insertions(+), 10 deletions(-)

diff --git a/ecc/bls12-377/shplonk/marshal.go b/ecc/bls12-377/shplonk/marshal.go
index 9e03a86d06..c2b805a8b5 100644
--- a/ecc/bls12-377/shplonk/marshal.go
+++ b/ecc/bls12-377/shplonk/marshal.go
@@ -29,7 +29,7 @@ func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
 	toDecode := []interface{}{
 		&proof.W,
 		&proof.WPrime,
-		proof.ClaimedValues,
+		&proof.ClaimedValues,
 	}
 
 	for _, v := range toDecode {
diff --git a/ecc/bls12-377/shplonk/shplonk_test.go b/ecc/bls12-377/shplonk/shplonk_test.go
index 602ee3f9d0..9333499557 100644
--- a/ecc/bls12-377/shplonk/shplonk_test.go
+++ b/ecc/bls12-377/shplonk/shplonk_test.go
@@ -23,8 +23,10 @@ import (
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bls12-377"
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/kzg"
+	"github.com/consensys/gnark-crypto/utils/testutils"
 	"github.com/stretchr/testify/require"
 )
 
@@ -45,6 +47,24 @@ func init() {
 	}
 }
 
+func TestSerialization(t *testing.T) {
+
+	_, _, g, _ := bls12377.Generators()
+	var proof OpeningProof
+	proof.W.Set(&g)
+	proof.WPrime.Set(&g)
+	nbClaimedValues := 10
+	proof.ClaimedValues = make([][]fr.Element, nbClaimedValues)
+	for i := 0; i < nbClaimedValues; i++ {
+		proof.ClaimedValues[i] = make([]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			proof.ClaimedValues[i][j].SetRandom()
+		}
+	}
+
+	t.Run("opening proof round trip", testutils.SerializationRoundTrip(&proof))
+}
+
 func TestOpening(t *testing.T) {
 
 	assert := require.New(t)
diff --git a/ecc/bls12-378/shplonk/marshal.go b/ecc/bls12-378/shplonk/marshal.go
index 6774448de5..bbe0b8d9e1 100644
--- a/ecc/bls12-378/shplonk/marshal.go
+++ b/ecc/bls12-378/shplonk/marshal.go
@@ -29,7 +29,7 @@ func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
 	toDecode := []interface{}{
 		&proof.W,
 		&proof.WPrime,
-		proof.ClaimedValues,
+		&proof.ClaimedValues,
 	}
 
 	for _, v := range toDecode {
diff --git a/ecc/bls12-378/shplonk/shplonk_test.go b/ecc/bls12-378/shplonk/shplonk_test.go
index 34e4127cc0..4b73e50e4c 100644
--- a/ecc/bls12-378/shplonk/shplonk_test.go
+++ b/ecc/bls12-378/shplonk/shplonk_test.go
@@ -23,8 +23,10 @@ import (
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bls12-378"
 	"github.com/consensys/gnark-crypto/ecc/bls12-378/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls12-378/kzg"
+	"github.com/consensys/gnark-crypto/utils/testutils"
 	"github.com/stretchr/testify/require"
 )
 
@@ -45,6 +47,24 @@ func init() {
 	}
 }
 
+func TestSerialization(t *testing.T) {
+
+	_, _, g, _ := bls12378.Generators()
+	var proof OpeningProof
+	proof.W.Set(&g)
+	proof.WPrime.Set(&g)
+	nbClaimedValues := 10
+	proof.ClaimedValues = make([][]fr.Element, nbClaimedValues)
+	for i := 0; i < nbClaimedValues; i++ {
+		proof.ClaimedValues[i] = make([]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			proof.ClaimedValues[i][j].SetRandom()
+		}
+	}
+
+	t.Run("opening proof round trip", testutils.SerializationRoundTrip(&proof))
+}
+
 func TestOpening(t *testing.T) {
 
 	assert := require.New(t)
diff --git a/ecc/bls12-381/shplonk/marshal.go b/ecc/bls12-381/shplonk/marshal.go
index b609b73266..e013c2d3ef 100644
--- a/ecc/bls12-381/shplonk/marshal.go
+++ b/ecc/bls12-381/shplonk/marshal.go
@@ -29,7 +29,7 @@ func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
 	toDecode := []interface{}{
 		&proof.W,
 		&proof.WPrime,
-		proof.ClaimedValues,
+		&proof.ClaimedValues,
 	}
 
 	for _, v := range toDecode {
diff --git a/ecc/bls12-381/shplonk/shplonk_test.go b/ecc/bls12-381/shplonk/shplonk_test.go
index 05fb93a3f6..b007b75590 100644
--- a/ecc/bls12-381/shplonk/shplonk_test.go
+++ b/ecc/bls12-381/shplonk/shplonk_test.go
@@ -23,8 +23,10 @@ import (
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bls12-381"
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/kzg"
+	"github.com/consensys/gnark-crypto/utils/testutils"
 	"github.com/stretchr/testify/require"
 )
 
@@ -45,6 +47,24 @@ func init() {
 	}
 }
 
+func TestSerialization(t *testing.T) {
+
+	_, _, g, _ := bls12381.Generators()
+	var proof OpeningProof
+	proof.W.Set(&g)
+	proof.WPrime.Set(&g)
+	nbClaimedValues := 10
+	proof.ClaimedValues = make([][]fr.Element, nbClaimedValues)
+	for i := 0; i < nbClaimedValues; i++ {
+		proof.ClaimedValues[i] = make([]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			proof.ClaimedValues[i][j].SetRandom()
+		}
+	}
+
+	t.Run("opening proof round trip", testutils.SerializationRoundTrip(&proof))
+}
+
 func TestOpening(t *testing.T) {
 
 	assert := require.New(t)
diff --git a/ecc/bls24-315/shplonk/marshal.go b/ecc/bls24-315/shplonk/marshal.go
index a57a90679f..a936f40bbe 100644
--- a/ecc/bls24-315/shplonk/marshal.go
+++ b/ecc/bls24-315/shplonk/marshal.go
@@ -29,7 +29,7 @@ func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
 	toDecode := []interface{}{
 		&proof.W,
 		&proof.WPrime,
-		proof.ClaimedValues,
+		&proof.ClaimedValues,
 	}
 
 	for _, v := range toDecode {
diff --git a/ecc/bls24-315/shplonk/shplonk_test.go b/ecc/bls24-315/shplonk/shplonk_test.go
index a8d35f5c00..c97b6dda88 100644
--- a/ecc/bls24-315/shplonk/shplonk_test.go
+++ b/ecc/bls24-315/shplonk/shplonk_test.go
@@ -23,8 +23,10 @@ import (
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bls24-315"
 	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls24-315/kzg"
+	"github.com/consensys/gnark-crypto/utils/testutils"
 	"github.com/stretchr/testify/require"
 )
 
@@ -45,6 +47,24 @@ func init() {
 	}
 }
 
+func TestSerialization(t *testing.T) {
+
+	_, _, g, _ := bls24315.Generators()
+	var proof OpeningProof
+	proof.W.Set(&g)
+	proof.WPrime.Set(&g)
+	nbClaimedValues := 10
+	proof.ClaimedValues = make([][]fr.Element, nbClaimedValues)
+	for i := 0; i < nbClaimedValues; i++ {
+		proof.ClaimedValues[i] = make([]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			proof.ClaimedValues[i][j].SetRandom()
+		}
+	}
+
+	t.Run("opening proof round trip", testutils.SerializationRoundTrip(&proof))
+}
+
 func TestOpening(t *testing.T) {
 
 	assert := require.New(t)
diff --git a/ecc/bls24-317/shplonk/marshal.go b/ecc/bls24-317/shplonk/marshal.go
index b69c0946ca..f3f4520ac2 100644
--- a/ecc/bls24-317/shplonk/marshal.go
+++ b/ecc/bls24-317/shplonk/marshal.go
@@ -29,7 +29,7 @@ func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
 	toDecode := []interface{}{
 		&proof.W,
 		&proof.WPrime,
-		proof.ClaimedValues,
+		&proof.ClaimedValues,
 	}
 
 	for _, v := range toDecode {
diff --git a/ecc/bls24-317/shplonk/shplonk_test.go b/ecc/bls24-317/shplonk/shplonk_test.go
index 9e6d76ded0..bd89089b78 100644
--- a/ecc/bls24-317/shplonk/shplonk_test.go
+++ b/ecc/bls24-317/shplonk/shplonk_test.go
@@ -23,8 +23,10 @@ import (
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bls24-317"
 	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls24-317/kzg"
+	"github.com/consensys/gnark-crypto/utils/testutils"
 	"github.com/stretchr/testify/require"
 )
 
@@ -45,6 +47,24 @@ func init() {
 	}
 }
 
+func TestSerialization(t *testing.T) {
+
+	_, _, g, _ := bls24317.Generators()
+	var proof OpeningProof
+	proof.W.Set(&g)
+	proof.WPrime.Set(&g)
+	nbClaimedValues := 10
+	proof.ClaimedValues = make([][]fr.Element, nbClaimedValues)
+	for i := 0; i < nbClaimedValues; i++ {
+		proof.ClaimedValues[i] = make([]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			proof.ClaimedValues[i][j].SetRandom()
+		}
+	}
+
+	t.Run("opening proof round trip", testutils.SerializationRoundTrip(&proof))
+}
+
 func TestOpening(t *testing.T) {
 
 	assert := require.New(t)
diff --git a/ecc/bn254/shplonk/marshal.go b/ecc/bn254/shplonk/marshal.go
index 050e1d6fdf..5da8c732a5 100644
--- a/ecc/bn254/shplonk/marshal.go
+++ b/ecc/bn254/shplonk/marshal.go
@@ -29,7 +29,7 @@ func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
 	toDecode := []interface{}{
 		&proof.W,
 		&proof.WPrime,
-		proof.ClaimedValues,
+		&proof.ClaimedValues,
 	}
 
 	for _, v := range toDecode {
diff --git a/ecc/bn254/shplonk/shplonk_test.go b/ecc/bn254/shplonk/shplonk_test.go
index d0e4ce0695..88fa11fc0a 100644
--- a/ecc/bn254/shplonk/shplonk_test.go
+++ b/ecc/bn254/shplonk/shplonk_test.go
@@ -23,8 +23,10 @@ import (
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bn254"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
 	"github.com/consensys/gnark-crypto/ecc/bn254/kzg"
+	"github.com/consensys/gnark-crypto/utils/testutils"
 	"github.com/stretchr/testify/require"
 )
 
@@ -45,6 +47,24 @@ func init() {
 	}
 }
 
+func TestSerialization(t *testing.T) {
+
+	_, _, g, _ := bn254.Generators()
+	var proof OpeningProof
+	proof.W.Set(&g)
+	proof.WPrime.Set(&g)
+	nbClaimedValues := 10
+	proof.ClaimedValues = make([][]fr.Element, nbClaimedValues)
+	for i := 0; i < nbClaimedValues; i++ {
+		proof.ClaimedValues[i] = make([]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			proof.ClaimedValues[i][j].SetRandom()
+		}
+	}
+
+	t.Run("opening proof round trip", testutils.SerializationRoundTrip(&proof))
+}
+
 func TestOpening(t *testing.T) {
 
 	assert := require.New(t)
diff --git a/ecc/bw6-633/shplonk/marshal.go b/ecc/bw6-633/shplonk/marshal.go
index 2c44c28a65..80661c53db 100644
--- a/ecc/bw6-633/shplonk/marshal.go
+++ b/ecc/bw6-633/shplonk/marshal.go
@@ -29,7 +29,7 @@ func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
 	toDecode := []interface{}{
 		&proof.W,
 		&proof.WPrime,
-		proof.ClaimedValues,
+		&proof.ClaimedValues,
 	}
 
 	for _, v := range toDecode {
diff --git a/ecc/bw6-633/shplonk/shplonk_test.go b/ecc/bw6-633/shplonk/shplonk_test.go
index ea171cbefb..dcb46ffeea 100644
--- a/ecc/bw6-633/shplonk/shplonk_test.go
+++ b/ecc/bw6-633/shplonk/shplonk_test.go
@@ -23,8 +23,10 @@ import (
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bw6-633"
 	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
 	"github.com/consensys/gnark-crypto/ecc/bw6-633/kzg"
+	"github.com/consensys/gnark-crypto/utils/testutils"
 	"github.com/stretchr/testify/require"
 )
 
@@ -45,6 +47,24 @@ func init() {
 	}
 }
 
+func TestSerialization(t *testing.T) {
+
+	_, _, g, _ := bw6633.Generators()
+	var proof OpeningProof
+	proof.W.Set(&g)
+	proof.WPrime.Set(&g)
+	nbClaimedValues := 10
+	proof.ClaimedValues = make([][]fr.Element, nbClaimedValues)
+	for i := 0; i < nbClaimedValues; i++ {
+		proof.ClaimedValues[i] = make([]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			proof.ClaimedValues[i][j].SetRandom()
+		}
+	}
+
+	t.Run("opening proof round trip", testutils.SerializationRoundTrip(&proof))
+}
+
 func TestOpening(t *testing.T) {
 
 	assert := require.New(t)
diff --git a/ecc/bw6-756/shplonk/marshal.go b/ecc/bw6-756/shplonk/marshal.go
index e7b0bf4ed8..8977a57254 100644
--- a/ecc/bw6-756/shplonk/marshal.go
+++ b/ecc/bw6-756/shplonk/marshal.go
@@ -29,7 +29,7 @@ func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
 	toDecode := []interface{}{
 		&proof.W,
 		&proof.WPrime,
-		proof.ClaimedValues,
+		&proof.ClaimedValues,
 	}
 
 	for _, v := range toDecode {
diff --git a/ecc/bw6-756/shplonk/shplonk_test.go b/ecc/bw6-756/shplonk/shplonk_test.go
index 4643d87606..ce1c480464 100644
--- a/ecc/bw6-756/shplonk/shplonk_test.go
+++ b/ecc/bw6-756/shplonk/shplonk_test.go
@@ -23,8 +23,10 @@ import (
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bw6-756"
 	"github.com/consensys/gnark-crypto/ecc/bw6-756/fr"
 	"github.com/consensys/gnark-crypto/ecc/bw6-756/kzg"
+	"github.com/consensys/gnark-crypto/utils/testutils"
 	"github.com/stretchr/testify/require"
 )
 
@@ -45,6 +47,24 @@ func init() {
 	}
 }
 
+func TestSerialization(t *testing.T) {
+
+	_, _, g, _ := bw6756.Generators()
+	var proof OpeningProof
+	proof.W.Set(&g)
+	proof.WPrime.Set(&g)
+	nbClaimedValues := 10
+	proof.ClaimedValues = make([][]fr.Element, nbClaimedValues)
+	for i := 0; i < nbClaimedValues; i++ {
+		proof.ClaimedValues[i] = make([]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			proof.ClaimedValues[i][j].SetRandom()
+		}
+	}
+
+	t.Run("opening proof round trip", testutils.SerializationRoundTrip(&proof))
+}
+
 func TestOpening(t *testing.T) {
 
 	assert := require.New(t)
diff --git a/ecc/bw6-761/shplonk/marshal.go b/ecc/bw6-761/shplonk/marshal.go
index f931b1dd51..6e03808eeb 100644
--- a/ecc/bw6-761/shplonk/marshal.go
+++ b/ecc/bw6-761/shplonk/marshal.go
@@ -29,7 +29,7 @@ func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
 	toDecode := []interface{}{
 		&proof.W,
 		&proof.WPrime,
-		proof.ClaimedValues,
+		&proof.ClaimedValues,
 	}
 
 	for _, v := range toDecode {
diff --git a/ecc/bw6-761/shplonk/shplonk_test.go b/ecc/bw6-761/shplonk/shplonk_test.go
index ca08b62e53..1e4ecc2d81 100644
--- a/ecc/bw6-761/shplonk/shplonk_test.go
+++ b/ecc/bw6-761/shplonk/shplonk_test.go
@@ -23,8 +23,10 @@ import (
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bw6-761"
 	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
 	"github.com/consensys/gnark-crypto/ecc/bw6-761/kzg"
+	"github.com/consensys/gnark-crypto/utils/testutils"
 	"github.com/stretchr/testify/require"
 )
 
@@ -45,6 +47,24 @@ func init() {
 	}
 }
 
+func TestSerialization(t *testing.T) {
+
+	_, _, g, _ := bw6761.Generators()
+	var proof OpeningProof
+	proof.W.Set(&g)
+	proof.WPrime.Set(&g)
+	nbClaimedValues := 10
+	proof.ClaimedValues = make([][]fr.Element, nbClaimedValues)
+	for i := 0; i < nbClaimedValues; i++ {
+		proof.ClaimedValues[i] = make([]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			proof.ClaimedValues[i][j].SetRandom()
+		}
+	}
+
+	t.Run("opening proof round trip", testutils.SerializationRoundTrip(&proof))
+}
+
 func TestOpening(t *testing.T) {
 
 	assert := require.New(t)
diff --git a/internal/generator/shplonk/template/marshal.go.tmpl b/internal/generator/shplonk/template/marshal.go.tmpl
index 316f852ef5..98f11f61a6 100644
--- a/internal/generator/shplonk/template/marshal.go.tmpl
+++ b/internal/generator/shplonk/template/marshal.go.tmpl
@@ -11,7 +11,7 @@ func (proof *OpeningProof) ReadFrom(r io.Reader) (int64, error) {
 	toDecode := []interface{}{
 		&proof.W,
 		&proof.WPrime,
-		proof.ClaimedValues,
+		&proof.ClaimedValues,
 	}
 
 	for _, v := range toDecode {
diff --git a/internal/generator/shplonk/template/shplonk.test.go.tmpl b/internal/generator/shplonk/template/shplonk.test.go.tmpl
index 7d642ed8fa..775995c032 100644
--- a/internal/generator/shplonk/template/shplonk.test.go.tmpl
+++ b/internal/generator/shplonk/template/shplonk.test.go.tmpl
@@ -5,8 +5,10 @@ import (
 	"math/rand"
 
 	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}"
 	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/fr"
 	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/kzg"
+	"github.com/consensys/gnark-crypto/utils/testutils"
 	"github.com/stretchr/testify/require"
 )
 
@@ -28,6 +30,24 @@ func init() {
 	}
 }
 
+func TestSerialization(t *testing.T) {
+
+	_, _, g, _ := {{ .CurvePackage }}.Generators()
+	var proof OpeningProof
+	proof.W.Set(&g)
+	proof.WPrime.Set(&g)
+	nbClaimedValues := 10
+	proof.ClaimedValues = make([][]fr.Element, nbClaimedValues)
+	for i := 0; i < nbClaimedValues; i++ {
+		proof.ClaimedValues[i] = make([]fr.Element, i+2)
+		for j := 0; j < i+2; j++ {
+			proof.ClaimedValues[i][j].SetRandom()
+		}
+	}
+
+	t.Run("opening proof round trip", testutils.SerializationRoundTrip(&proof))
+}
+
 func TestOpening(t *testing.T) {
 
 	assert := require.New(t)

From 4072df91e46e26b561a663afe548b494658f55c9 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 20 Sep 2024 10:43:48 +0200
Subject: [PATCH 056/114] feat: use GeneratorFullMultiplicativeGroup

---
 ecc/bls12-377/fflonk/fflonk.go                | 14 ++-------
 ecc/bls12-378/fflonk/fflonk.go                | 14 ++-------
 ecc/bls12-381/fflonk/fflonk.go                | 14 ++-------
 ecc/bls24-315/fflonk/fflonk.go                | 14 ++-------
 ecc/bls24-317/fflonk/fflonk.go                | 14 ++-------
 ecc/bn254/fflonk/fflonk.go                    | 14 ++-------
 ecc/bw6-633/fflonk/fflonk.go                  | 14 ++-------
 ecc/bw6-756/fflonk/fflonk.go                  | 14 ++-------
 ecc/bw6-761/fflonk/fflonk.go                  | 14 ++-------
 .../generator/fflonk/template/fflonk.go.tmpl  | 30 ++-----------------
 10 files changed, 30 insertions(+), 126 deletions(-)

diff --git a/ecc/bls12-377/fflonk/fflonk.go b/ecc/bls12-377/fflonk/fflonk.go
index 6acd7bc79f..18c0ba6e63 100644
--- a/ecc/bls12-377/fflonk/fflonk.go
+++ b/ecc/bls12-377/fflonk/fflonk.go
@@ -22,12 +22,13 @@ import (
 	"math/big"
 
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr/fft"
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/kzg"
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/shplonk"
 )
 
 var (
-	ErrRootsOne                       = errors.New("Fr does not contain all the t-th roots of 1")
+	ErrRootsOne                       = errors.New("fr does not contain all the t-th roots of 1")
 	ErrNbPolynomialsNbPoints          = errors.New("the number of packs of polynomials should be the same as the number of pack of points")
 	ErrInonsistentFolding             = errors.New("the outer claimed values are not consistent with the shplonk proof")
 	ErrInconsistentNumberFoldedPoints = errors.New("the number of outer claimed values is inconsistent with the number of claimed values in the shplonk proof")
@@ -230,7 +231,7 @@ func getIthRootOne(i int) (fr.Element, error) {
 	if tmpBigInt.Cmp(&zeroBigInt) != 0 {
 		return omega, ErrRootsOne
 	}
-	genFrStar := getGenFrStar()
+	genFrStar := fft.GeneratorFullMultiplicativeGroup()
 	tmpBigInt.SetUint64(uint64(i))
 	tmpBigInt.Div(rMinusOneBigInt, &tmpBigInt)
 	omega.Exp(genFrStar, &tmpBigInt)
@@ -280,12 +281,3 @@ func eval(f []fr.Element, x fr.Element) fr.Element {
 	}
 	return y
 }
-
-// getGenFrStar returns a generator of Fr^{*}
-func getGenFrStar() fr.Element {
-	var res fr.Element
-
-	res.SetUint64(22)
-
-	return res
-}
diff --git a/ecc/bls12-378/fflonk/fflonk.go b/ecc/bls12-378/fflonk/fflonk.go
index 2397f3fc77..bea7e4876a 100644
--- a/ecc/bls12-378/fflonk/fflonk.go
+++ b/ecc/bls12-378/fflonk/fflonk.go
@@ -22,12 +22,13 @@ import (
 	"math/big"
 
 	"github.com/consensys/gnark-crypto/ecc/bls12-378/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls12-378/fr/fft"
 	"github.com/consensys/gnark-crypto/ecc/bls12-378/kzg"
 	"github.com/consensys/gnark-crypto/ecc/bls12-378/shplonk"
 )
 
 var (
-	ErrRootsOne                       = errors.New("Fr does not contain all the t-th roots of 1")
+	ErrRootsOne                       = errors.New("fr does not contain all the t-th roots of 1")
 	ErrNbPolynomialsNbPoints          = errors.New("the number of packs of polynomials should be the same as the number of pack of points")
 	ErrInonsistentFolding             = errors.New("the outer claimed values are not consistent with the shplonk proof")
 	ErrInconsistentNumberFoldedPoints = errors.New("the number of outer claimed values is inconsistent with the number of claimed values in the shplonk proof")
@@ -230,7 +231,7 @@ func getIthRootOne(i int) (fr.Element, error) {
 	if tmpBigInt.Cmp(&zeroBigInt) != 0 {
 		return omega, ErrRootsOne
 	}
-	genFrStar := getGenFrStar()
+	genFrStar := fft.GeneratorFullMultiplicativeGroup()
 	tmpBigInt.SetUint64(uint64(i))
 	tmpBigInt.Div(rMinusOneBigInt, &tmpBigInt)
 	omega.Exp(genFrStar, &tmpBigInt)
@@ -280,12 +281,3 @@ func eval(f []fr.Element, x fr.Element) fr.Element {
 	}
 	return y
 }
-
-// getGenFrStar returns a generator of Fr^{*}
-func getGenFrStar() fr.Element {
-	var res fr.Element
-
-	res.SetUint64(22)
-
-	return res
-}
diff --git a/ecc/bls12-381/fflonk/fflonk.go b/ecc/bls12-381/fflonk/fflonk.go
index 037d45885f..239a4037a6 100644
--- a/ecc/bls12-381/fflonk/fflonk.go
+++ b/ecc/bls12-381/fflonk/fflonk.go
@@ -22,12 +22,13 @@ import (
 	"math/big"
 
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr/fft"
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/kzg"
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/shplonk"
 )
 
 var (
-	ErrRootsOne                       = errors.New("Fr does not contain all the t-th roots of 1")
+	ErrRootsOne                       = errors.New("fr does not contain all the t-th roots of 1")
 	ErrNbPolynomialsNbPoints          = errors.New("the number of packs of polynomials should be the same as the number of pack of points")
 	ErrInonsistentFolding             = errors.New("the outer claimed values are not consistent with the shplonk proof")
 	ErrInconsistentNumberFoldedPoints = errors.New("the number of outer claimed values is inconsistent with the number of claimed values in the shplonk proof")
@@ -230,7 +231,7 @@ func getIthRootOne(i int) (fr.Element, error) {
 	if tmpBigInt.Cmp(&zeroBigInt) != 0 {
 		return omega, ErrRootsOne
 	}
-	genFrStar := getGenFrStar()
+	genFrStar := fft.GeneratorFullMultiplicativeGroup()
 	tmpBigInt.SetUint64(uint64(i))
 	tmpBigInt.Div(rMinusOneBigInt, &tmpBigInt)
 	omega.Exp(genFrStar, &tmpBigInt)
@@ -280,12 +281,3 @@ func eval(f []fr.Element, x fr.Element) fr.Element {
 	}
 	return y
 }
-
-// getGenFrStar returns a generator of Fr^{*}
-func getGenFrStar() fr.Element {
-	var res fr.Element
-
-	res.SetUint64(7)
-
-	return res
-}
diff --git a/ecc/bls24-315/fflonk/fflonk.go b/ecc/bls24-315/fflonk/fflonk.go
index dd7ce2d560..d7be125897 100644
--- a/ecc/bls24-315/fflonk/fflonk.go
+++ b/ecc/bls24-315/fflonk/fflonk.go
@@ -22,12 +22,13 @@ import (
 	"math/big"
 
 	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr/fft"
 	"github.com/consensys/gnark-crypto/ecc/bls24-315/kzg"
 	"github.com/consensys/gnark-crypto/ecc/bls24-315/shplonk"
 )
 
 var (
-	ErrRootsOne                       = errors.New("Fr does not contain all the t-th roots of 1")
+	ErrRootsOne                       = errors.New("fr does not contain all the t-th roots of 1")
 	ErrNbPolynomialsNbPoints          = errors.New("the number of packs of polynomials should be the same as the number of pack of points")
 	ErrInonsistentFolding             = errors.New("the outer claimed values are not consistent with the shplonk proof")
 	ErrInconsistentNumberFoldedPoints = errors.New("the number of outer claimed values is inconsistent with the number of claimed values in the shplonk proof")
@@ -230,7 +231,7 @@ func getIthRootOne(i int) (fr.Element, error) {
 	if tmpBigInt.Cmp(&zeroBigInt) != 0 {
 		return omega, ErrRootsOne
 	}
-	genFrStar := getGenFrStar()
+	genFrStar := fft.GeneratorFullMultiplicativeGroup()
 	tmpBigInt.SetUint64(uint64(i))
 	tmpBigInt.Div(rMinusOneBigInt, &tmpBigInt)
 	omega.Exp(genFrStar, &tmpBigInt)
@@ -280,12 +281,3 @@ func eval(f []fr.Element, x fr.Element) fr.Element {
 	}
 	return y
 }
-
-// getGenFrStar returns a generator of Fr^{*}
-func getGenFrStar() fr.Element {
-	var res fr.Element
-
-	res.SetUint64(7)
-
-	return res
-}
diff --git a/ecc/bls24-317/fflonk/fflonk.go b/ecc/bls24-317/fflonk/fflonk.go
index c88257f32c..6a805b805e 100644
--- a/ecc/bls24-317/fflonk/fflonk.go
+++ b/ecc/bls24-317/fflonk/fflonk.go
@@ -22,12 +22,13 @@ import (
 	"math/big"
 
 	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr/fft"
 	"github.com/consensys/gnark-crypto/ecc/bls24-317/kzg"
 	"github.com/consensys/gnark-crypto/ecc/bls24-317/shplonk"
 )
 
 var (
-	ErrRootsOne                       = errors.New("Fr does not contain all the t-th roots of 1")
+	ErrRootsOne                       = errors.New("fr does not contain all the t-th roots of 1")
 	ErrNbPolynomialsNbPoints          = errors.New("the number of packs of polynomials should be the same as the number of pack of points")
 	ErrInonsistentFolding             = errors.New("the outer claimed values are not consistent with the shplonk proof")
 	ErrInconsistentNumberFoldedPoints = errors.New("the number of outer claimed values is inconsistent with the number of claimed values in the shplonk proof")
@@ -230,7 +231,7 @@ func getIthRootOne(i int) (fr.Element, error) {
 	if tmpBigInt.Cmp(&zeroBigInt) != 0 {
 		return omega, ErrRootsOne
 	}
-	genFrStar := getGenFrStar()
+	genFrStar := fft.GeneratorFullMultiplicativeGroup()
 	tmpBigInt.SetUint64(uint64(i))
 	tmpBigInt.Div(rMinusOneBigInt, &tmpBigInt)
 	omega.Exp(genFrStar, &tmpBigInt)
@@ -280,12 +281,3 @@ func eval(f []fr.Element, x fr.Element) fr.Element {
 	}
 	return y
 }
-
-// getGenFrStar returns a generator of Fr^{*}
-func getGenFrStar() fr.Element {
-	var res fr.Element
-
-	res.SetUint64(7)
-
-	return res
-}
diff --git a/ecc/bn254/fflonk/fflonk.go b/ecc/bn254/fflonk/fflonk.go
index 77b37730ba..0c87f49288 100644
--- a/ecc/bn254/fflonk/fflonk.go
+++ b/ecc/bn254/fflonk/fflonk.go
@@ -22,12 +22,13 @@ import (
 	"math/big"
 
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
+	"github.com/consensys/gnark-crypto/ecc/bn254/fr/fft"
 	"github.com/consensys/gnark-crypto/ecc/bn254/kzg"
 	"github.com/consensys/gnark-crypto/ecc/bn254/shplonk"
 )
 
 var (
-	ErrRootsOne                       = errors.New("Fr does not contain all the t-th roots of 1")
+	ErrRootsOne                       = errors.New("fr does not contain all the t-th roots of 1")
 	ErrNbPolynomialsNbPoints          = errors.New("the number of packs of polynomials should be the same as the number of pack of points")
 	ErrInonsistentFolding             = errors.New("the outer claimed values are not consistent with the shplonk proof")
 	ErrInconsistentNumberFoldedPoints = errors.New("the number of outer claimed values is inconsistent with the number of claimed values in the shplonk proof")
@@ -230,7 +231,7 @@ func getIthRootOne(i int) (fr.Element, error) {
 	if tmpBigInt.Cmp(&zeroBigInt) != 0 {
 		return omega, ErrRootsOne
 	}
-	genFrStar := getGenFrStar()
+	genFrStar := fft.GeneratorFullMultiplicativeGroup()
 	tmpBigInt.SetUint64(uint64(i))
 	tmpBigInt.Div(rMinusOneBigInt, &tmpBigInt)
 	omega.Exp(genFrStar, &tmpBigInt)
@@ -280,12 +281,3 @@ func eval(f []fr.Element, x fr.Element) fr.Element {
 	}
 	return y
 }
-
-// getGenFrStar returns a generator of Fr^{*}
-func getGenFrStar() fr.Element {
-	var res fr.Element
-
-	res.SetUint64(5)
-
-	return res
-}
diff --git a/ecc/bw6-633/fflonk/fflonk.go b/ecc/bw6-633/fflonk/fflonk.go
index c009315e66..e1e69779c2 100644
--- a/ecc/bw6-633/fflonk/fflonk.go
+++ b/ecc/bw6-633/fflonk/fflonk.go
@@ -22,12 +22,13 @@ import (
 	"math/big"
 
 	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
+	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr/fft"
 	"github.com/consensys/gnark-crypto/ecc/bw6-633/kzg"
 	"github.com/consensys/gnark-crypto/ecc/bw6-633/shplonk"
 )
 
 var (
-	ErrRootsOne                       = errors.New("Fr does not contain all the t-th roots of 1")
+	ErrRootsOne                       = errors.New("fr does not contain all the t-th roots of 1")
 	ErrNbPolynomialsNbPoints          = errors.New("the number of packs of polynomials should be the same as the number of pack of points")
 	ErrInonsistentFolding             = errors.New("the outer claimed values are not consistent with the shplonk proof")
 	ErrInconsistentNumberFoldedPoints = errors.New("the number of outer claimed values is inconsistent with the number of claimed values in the shplonk proof")
@@ -230,7 +231,7 @@ func getIthRootOne(i int) (fr.Element, error) {
 	if tmpBigInt.Cmp(&zeroBigInt) != 0 {
 		return omega, ErrRootsOne
 	}
-	genFrStar := getGenFrStar()
+	genFrStar := fft.GeneratorFullMultiplicativeGroup()
 	tmpBigInt.SetUint64(uint64(i))
 	tmpBigInt.Div(rMinusOneBigInt, &tmpBigInt)
 	omega.Exp(genFrStar, &tmpBigInt)
@@ -280,12 +281,3 @@ func eval(f []fr.Element, x fr.Element) fr.Element {
 	}
 	return y
 }
-
-// getGenFrStar returns a generator of Fr^{*}
-func getGenFrStar() fr.Element {
-	var res fr.Element
-
-	res.SetUint64(13)
-
-	return res
-}
diff --git a/ecc/bw6-756/fflonk/fflonk.go b/ecc/bw6-756/fflonk/fflonk.go
index 6c687b4aef..bf2604a11d 100644
--- a/ecc/bw6-756/fflonk/fflonk.go
+++ b/ecc/bw6-756/fflonk/fflonk.go
@@ -22,12 +22,13 @@ import (
 	"math/big"
 
 	"github.com/consensys/gnark-crypto/ecc/bw6-756/fr"
+	"github.com/consensys/gnark-crypto/ecc/bw6-756/fr/fft"
 	"github.com/consensys/gnark-crypto/ecc/bw6-756/kzg"
 	"github.com/consensys/gnark-crypto/ecc/bw6-756/shplonk"
 )
 
 var (
-	ErrRootsOne                       = errors.New("Fr does not contain all the t-th roots of 1")
+	ErrRootsOne                       = errors.New("fr does not contain all the t-th roots of 1")
 	ErrNbPolynomialsNbPoints          = errors.New("the number of packs of polynomials should be the same as the number of pack of points")
 	ErrInonsistentFolding             = errors.New("the outer claimed values are not consistent with the shplonk proof")
 	ErrInconsistentNumberFoldedPoints = errors.New("the number of outer claimed values is inconsistent with the number of claimed values in the shplonk proof")
@@ -230,7 +231,7 @@ func getIthRootOne(i int) (fr.Element, error) {
 	if tmpBigInt.Cmp(&zeroBigInt) != 0 {
 		return omega, ErrRootsOne
 	}
-	genFrStar := getGenFrStar()
+	genFrStar := fft.GeneratorFullMultiplicativeGroup()
 	tmpBigInt.SetUint64(uint64(i))
 	tmpBigInt.Div(rMinusOneBigInt, &tmpBigInt)
 	omega.Exp(genFrStar, &tmpBigInt)
@@ -280,12 +281,3 @@ func eval(f []fr.Element, x fr.Element) fr.Element {
 	}
 	return y
 }
-
-// getGenFrStar returns a generator of Fr^{*}
-func getGenFrStar() fr.Element {
-	var res fr.Element
-
-	res.SetUint64(5)
-
-	return res
-}
diff --git a/ecc/bw6-761/fflonk/fflonk.go b/ecc/bw6-761/fflonk/fflonk.go
index fe58acc678..c5878dc8e5 100644
--- a/ecc/bw6-761/fflonk/fflonk.go
+++ b/ecc/bw6-761/fflonk/fflonk.go
@@ -22,12 +22,13 @@ import (
 	"math/big"
 
 	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
+	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr/fft"
 	"github.com/consensys/gnark-crypto/ecc/bw6-761/kzg"
 	"github.com/consensys/gnark-crypto/ecc/bw6-761/shplonk"
 )
 
 var (
-	ErrRootsOne                       = errors.New("Fr does not contain all the t-th roots of 1")
+	ErrRootsOne                       = errors.New("fr does not contain all the t-th roots of 1")
 	ErrNbPolynomialsNbPoints          = errors.New("the number of packs of polynomials should be the same as the number of pack of points")
 	ErrInonsistentFolding             = errors.New("the outer claimed values are not consistent with the shplonk proof")
 	ErrInconsistentNumberFoldedPoints = errors.New("the number of outer claimed values is inconsistent with the number of claimed values in the shplonk proof")
@@ -230,7 +231,7 @@ func getIthRootOne(i int) (fr.Element, error) {
 	if tmpBigInt.Cmp(&zeroBigInt) != 0 {
 		return omega, ErrRootsOne
 	}
-	genFrStar := getGenFrStar()
+	genFrStar := fft.GeneratorFullMultiplicativeGroup()
 	tmpBigInt.SetUint64(uint64(i))
 	tmpBigInt.Div(rMinusOneBigInt, &tmpBigInt)
 	omega.Exp(genFrStar, &tmpBigInt)
@@ -280,12 +281,3 @@ func eval(f []fr.Element, x fr.Element) fr.Element {
 	}
 	return y
 }
-
-// getGenFrStar returns a generator of Fr^{*}
-func getGenFrStar() fr.Element {
-	var res fr.Element
-
-	res.SetUint64(15)
-
-	return res
-}
diff --git a/internal/generator/fflonk/template/fflonk.go.tmpl b/internal/generator/fflonk/template/fflonk.go.tmpl
index e20df4a656..512febb956 100644
--- a/internal/generator/fflonk/template/fflonk.go.tmpl
+++ b/internal/generator/fflonk/template/fflonk.go.tmpl
@@ -4,12 +4,13 @@ import (
 	"math/big"
 
 	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/fr"
+	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/fr/fft"
 	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/kzg"
 	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/shplonk"
 )
 
 var (
-	ErrRootsOne                       = errors.New("Fr does not contain all the t-th roots of 1")
+	ErrRootsOne                       = errors.New("fr does not contain all the t-th roots of 1")
 	ErrNbPolynomialsNbPoints          = errors.New("the number of packs of polynomials should be the same as the number of pack of points")
 	ErrInonsistentFolding             = errors.New("the outer claimed values are not consistent with the shplonk proof")
 	ErrInconsistentNumberFoldedPoints = errors.New("the number of outer claimed values is inconsistent with the number of claimed values in the shplonk proof")
@@ -212,7 +213,7 @@ func getIthRootOne(i int) (fr.Element, error) {
 	if tmpBigInt.Cmp(&zeroBigInt) != 0 {
 		return omega, ErrRootsOne
 	}
-	genFrStar := getGenFrStar()
+	genFrStar := fft.GeneratorFullMultiplicativeGroup()
 	tmpBigInt.SetUint64(uint64(i))
 	tmpBigInt.Div(rMinusOneBigInt, &tmpBigInt)
 	omega.Exp(genFrStar, &tmpBigInt)
@@ -261,29 +262,4 @@ func eval(f []fr.Element, x fr.Element) fr.Element {
 		y.Mul(&y, &x).Add(&y, &f[i])
 	}
 	return y
-}
-
-// getGenFrStar returns a generator of Fr^{*}
-func getGenFrStar() fr.Element {
-	var res fr.Element
-    {{if eq .Name "bls12-378"}}
-        res.SetUint64(22)
-	{{else if eq .Name "bls12-377"}}
-        res.SetUint64(22)
-	{{else if eq .Name "bls12-381"}}
-        res.SetUint64(7)
-	{{else if eq .Name "bn254"}}
-        res.SetUint64(5)
-	{{else if eq .Name "bw6-761"}}
-        res.SetUint64(15)
-	{{else if eq .Name "bw6-756"}}
-        res.SetUint64(5)
-    {{else if eq .Name "bw6-633"}}
-        res.SetUint64(13)
-	{{else if eq .Name "bls24-315"}}
-        res.SetUint64(7)
-	{{else if eq .Name "bls24-317"}}
-        res.SetUint64(7)
-	{{end}}
-	return res
 }
\ No newline at end of file

From 486f8c5c74792b9ff21f4210970fab7f57d9ffbc Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 20 Sep 2024 11:17:52 +0200
Subject: [PATCH 057/114] fix: check error

---
 ecc/bls12-377/fflonk/fflonk.go                    | 2 +-
 ecc/bls12-378/fflonk/fflonk.go                    | 2 +-
 ecc/bls12-381/fflonk/fflonk.go                    | 2 +-
 ecc/bls24-315/fflonk/fflonk.go                    | 2 +-
 ecc/bls24-317/fflonk/fflonk.go                    | 2 +-
 ecc/bn254/fflonk/fflonk.go                        | 2 +-
 ecc/bw6-633/fflonk/fflonk.go                      | 2 +-
 ecc/bw6-756/fflonk/fflonk.go                      | 2 +-
 ecc/bw6-761/fflonk/fflonk.go                      | 2 +-
 internal/generator/fflonk/template/fflonk.go.tmpl | 2 +-
 10 files changed, 10 insertions(+), 10 deletions(-)

diff --git a/ecc/bls12-377/fflonk/fflonk.go b/ecc/bls12-377/fflonk/fflonk.go
index 18c0ba6e63..35668a4c14 100644
--- a/ecc/bls12-377/fflonk/fflonk.go
+++ b/ecc/bls12-377/fflonk/fflonk.go
@@ -213,7 +213,7 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 	}
 	err = shplonk.BatchVerify(proof.SOpeningProof, digests, extendedPoints, hf, vk, dataTranscript...)
 
-	return nil
+	return err
 }
 
 // utils
diff --git a/ecc/bls12-378/fflonk/fflonk.go b/ecc/bls12-378/fflonk/fflonk.go
index bea7e4876a..917f25186e 100644
--- a/ecc/bls12-378/fflonk/fflonk.go
+++ b/ecc/bls12-378/fflonk/fflonk.go
@@ -213,7 +213,7 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 	}
 	err = shplonk.BatchVerify(proof.SOpeningProof, digests, extendedPoints, hf, vk, dataTranscript...)
 
-	return nil
+	return err
 }
 
 // utils
diff --git a/ecc/bls12-381/fflonk/fflonk.go b/ecc/bls12-381/fflonk/fflonk.go
index 239a4037a6..56b0fa1c04 100644
--- a/ecc/bls12-381/fflonk/fflonk.go
+++ b/ecc/bls12-381/fflonk/fflonk.go
@@ -213,7 +213,7 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 	}
 	err = shplonk.BatchVerify(proof.SOpeningProof, digests, extendedPoints, hf, vk, dataTranscript...)
 
-	return nil
+	return err
 }
 
 // utils
diff --git a/ecc/bls24-315/fflonk/fflonk.go b/ecc/bls24-315/fflonk/fflonk.go
index d7be125897..88e8f4c143 100644
--- a/ecc/bls24-315/fflonk/fflonk.go
+++ b/ecc/bls24-315/fflonk/fflonk.go
@@ -213,7 +213,7 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 	}
 	err = shplonk.BatchVerify(proof.SOpeningProof, digests, extendedPoints, hf, vk, dataTranscript...)
 
-	return nil
+	return err
 }
 
 // utils
diff --git a/ecc/bls24-317/fflonk/fflonk.go b/ecc/bls24-317/fflonk/fflonk.go
index 6a805b805e..e867d801cf 100644
--- a/ecc/bls24-317/fflonk/fflonk.go
+++ b/ecc/bls24-317/fflonk/fflonk.go
@@ -213,7 +213,7 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 	}
 	err = shplonk.BatchVerify(proof.SOpeningProof, digests, extendedPoints, hf, vk, dataTranscript...)
 
-	return nil
+	return err
 }
 
 // utils
diff --git a/ecc/bn254/fflonk/fflonk.go b/ecc/bn254/fflonk/fflonk.go
index 0c87f49288..5e4a78fa03 100644
--- a/ecc/bn254/fflonk/fflonk.go
+++ b/ecc/bn254/fflonk/fflonk.go
@@ -213,7 +213,7 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 	}
 	err = shplonk.BatchVerify(proof.SOpeningProof, digests, extendedPoints, hf, vk, dataTranscript...)
 
-	return nil
+	return err
 }
 
 // utils
diff --git a/ecc/bw6-633/fflonk/fflonk.go b/ecc/bw6-633/fflonk/fflonk.go
index e1e69779c2..043ed4d2aa 100644
--- a/ecc/bw6-633/fflonk/fflonk.go
+++ b/ecc/bw6-633/fflonk/fflonk.go
@@ -213,7 +213,7 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 	}
 	err = shplonk.BatchVerify(proof.SOpeningProof, digests, extendedPoints, hf, vk, dataTranscript...)
 
-	return nil
+	return err
 }
 
 // utils
diff --git a/ecc/bw6-756/fflonk/fflonk.go b/ecc/bw6-756/fflonk/fflonk.go
index bf2604a11d..b08a2f7f39 100644
--- a/ecc/bw6-756/fflonk/fflonk.go
+++ b/ecc/bw6-756/fflonk/fflonk.go
@@ -213,7 +213,7 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 	}
 	err = shplonk.BatchVerify(proof.SOpeningProof, digests, extendedPoints, hf, vk, dataTranscript...)
 
-	return nil
+	return err
 }
 
 // utils
diff --git a/ecc/bw6-761/fflonk/fflonk.go b/ecc/bw6-761/fflonk/fflonk.go
index c5878dc8e5..500f788e35 100644
--- a/ecc/bw6-761/fflonk/fflonk.go
+++ b/ecc/bw6-761/fflonk/fflonk.go
@@ -213,7 +213,7 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 	}
 	err = shplonk.BatchVerify(proof.SOpeningProof, digests, extendedPoints, hf, vk, dataTranscript...)
 
-	return nil
+	return err
 }
 
 // utils
diff --git a/internal/generator/fflonk/template/fflonk.go.tmpl b/internal/generator/fflonk/template/fflonk.go.tmpl
index 512febb956..a919355840 100644
--- a/internal/generator/fflonk/template/fflonk.go.tmpl
+++ b/internal/generator/fflonk/template/fflonk.go.tmpl
@@ -195,7 +195,7 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 	}
 	err = shplonk.BatchVerify(proof.SOpeningProof, digests, extendedPoints, hf, vk, dataTranscript...)
 
-	return nil
+	return err
 }
 
 // utils

From 8acaa9cf9b0f5821f5f615eac7a4f22b0ee2ed1f Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 20 Sep 2024 11:50:04 +0200
Subject: [PATCH 058/114] feat: renaming

---
 ecc/bls12-377/fflonk/fflonk.go                    | 6 +++---
 ecc/bls12-378/fflonk/fflonk.go                    | 6 +++---
 ecc/bls12-381/fflonk/fflonk.go                    | 6 +++---
 ecc/bls24-315/fflonk/fflonk.go                    | 6 +++---
 ecc/bls24-317/fflonk/fflonk.go                    | 6 +++---
 ecc/bn254/fflonk/fflonk.go                        | 6 +++---
 ecc/bw6-633/fflonk/fflonk.go                      | 6 +++---
 ecc/bw6-756/fflonk/fflonk.go                      | 6 +++---
 ecc/bw6-761/fflonk/fflonk.go                      | 6 +++---
 internal/generator/fflonk/template/fflonk.go.tmpl | 6 +++---
 10 files changed, 30 insertions(+), 30 deletions(-)

diff --git a/ecc/bls12-377/fflonk/fflonk.go b/ecc/bls12-377/fflonk/fflonk.go
index 35668a4c14..df4872da0f 100644
--- a/ecc/bls12-377/fflonk/fflonk.go
+++ b/ecc/bls12-377/fflonk/fflonk.go
@@ -49,9 +49,9 @@ type OpeningProof struct {
 	ClaimedValues [][][]fr.Element
 }
 
-// CommitAndFold commits to a list of polynomial by intertwinning them like in the FFT, that is
+// FoldAndCommit commits to a list of polynomial by intertwinning them like in the FFT, that is
 // returns ∑_{i<t}Pᵢ(Xᵗ)Xⁱ for t polynomials
-func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
+func FoldAndCommit(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
 	buf := Fold(p)
 	com, err := kzg.Commit(buf, pk, nbTasks...)
 	return com, err
@@ -81,7 +81,7 @@ func Fold(p [][]fr.Element) []fr.Element {
 
 // BatchOpen computes a batch opening proof of p (the (fʲᵢ)ᵢ ) on powers of points (the ((Sʲᵢ)ᵢ)ⱼ).
 // The j-th pack of polynomials is opened on the power |(fʲᵢ)ᵢ| of (Sʲᵢ)ᵢ.
-// digests is the list (CommitAndFold(p[i]))ᵢ. It is assumed that the list has been computed beforehand
+// digests is the list (FoldAndCommit(p[i]))ᵢ. It is assumed that the list has been computed beforehand
 // and provided as an input to not duplicate computations.
 func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
 
diff --git a/ecc/bls12-378/fflonk/fflonk.go b/ecc/bls12-378/fflonk/fflonk.go
index 917f25186e..f27f7c4945 100644
--- a/ecc/bls12-378/fflonk/fflonk.go
+++ b/ecc/bls12-378/fflonk/fflonk.go
@@ -49,9 +49,9 @@ type OpeningProof struct {
 	ClaimedValues [][][]fr.Element
 }
 
-// CommitAndFold commits to a list of polynomial by intertwinning them like in the FFT, that is
+// FoldAndCommit commits to a list of polynomial by intertwinning them like in the FFT, that is
 // returns ∑_{i<t}Pᵢ(Xᵗ)Xⁱ for t polynomials
-func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
+func FoldAndCommit(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
 	buf := Fold(p)
 	com, err := kzg.Commit(buf, pk, nbTasks...)
 	return com, err
@@ -81,7 +81,7 @@ func Fold(p [][]fr.Element) []fr.Element {
 
 // BatchOpen computes a batch opening proof of p (the (fʲᵢ)ᵢ ) on powers of points (the ((Sʲᵢ)ᵢ)ⱼ).
 // The j-th pack of polynomials is opened on the power |(fʲᵢ)ᵢ| of (Sʲᵢ)ᵢ.
-// digests is the list (CommitAndFold(p[i]))ᵢ. It is assumed that the list has been computed beforehand
+// digests is the list (FoldAndCommit(p[i]))ᵢ. It is assumed that the list has been computed beforehand
 // and provided as an input to not duplicate computations.
 func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
 
diff --git a/ecc/bls12-381/fflonk/fflonk.go b/ecc/bls12-381/fflonk/fflonk.go
index 56b0fa1c04..3460fe5d7a 100644
--- a/ecc/bls12-381/fflonk/fflonk.go
+++ b/ecc/bls12-381/fflonk/fflonk.go
@@ -49,9 +49,9 @@ type OpeningProof struct {
 	ClaimedValues [][][]fr.Element
 }
 
-// CommitAndFold commits to a list of polynomial by intertwinning them like in the FFT, that is
+// FoldAndCommit commits to a list of polynomial by intertwinning them like in the FFT, that is
 // returns ∑_{i<t}Pᵢ(Xᵗ)Xⁱ for t polynomials
-func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
+func FoldAndCommit(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
 	buf := Fold(p)
 	com, err := kzg.Commit(buf, pk, nbTasks...)
 	return com, err
@@ -81,7 +81,7 @@ func Fold(p [][]fr.Element) []fr.Element {
 
 // BatchOpen computes a batch opening proof of p (the (fʲᵢ)ᵢ ) on powers of points (the ((Sʲᵢ)ᵢ)ⱼ).
 // The j-th pack of polynomials is opened on the power |(fʲᵢ)ᵢ| of (Sʲᵢ)ᵢ.
-// digests is the list (CommitAndFold(p[i]))ᵢ. It is assumed that the list has been computed beforehand
+// digests is the list (FoldAndCommit(p[i]))ᵢ. It is assumed that the list has been computed beforehand
 // and provided as an input to not duplicate computations.
 func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
 
diff --git a/ecc/bls24-315/fflonk/fflonk.go b/ecc/bls24-315/fflonk/fflonk.go
index 88e8f4c143..edd7bfe4d9 100644
--- a/ecc/bls24-315/fflonk/fflonk.go
+++ b/ecc/bls24-315/fflonk/fflonk.go
@@ -49,9 +49,9 @@ type OpeningProof struct {
 	ClaimedValues [][][]fr.Element
 }
 
-// CommitAndFold commits to a list of polynomial by intertwinning them like in the FFT, that is
+// FoldAndCommit commits to a list of polynomial by intertwinning them like in the FFT, that is
 // returns ∑_{i<t}Pᵢ(Xᵗ)Xⁱ for t polynomials
-func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
+func FoldAndCommit(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
 	buf := Fold(p)
 	com, err := kzg.Commit(buf, pk, nbTasks...)
 	return com, err
@@ -81,7 +81,7 @@ func Fold(p [][]fr.Element) []fr.Element {
 
 // BatchOpen computes a batch opening proof of p (the (fʲᵢ)ᵢ ) on powers of points (the ((Sʲᵢ)ᵢ)ⱼ).
 // The j-th pack of polynomials is opened on the power |(fʲᵢ)ᵢ| of (Sʲᵢ)ᵢ.
-// digests is the list (CommitAndFold(p[i]))ᵢ. It is assumed that the list has been computed beforehand
+// digests is the list (FoldAndCommit(p[i]))ᵢ. It is assumed that the list has been computed beforehand
 // and provided as an input to not duplicate computations.
 func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
 
diff --git a/ecc/bls24-317/fflonk/fflonk.go b/ecc/bls24-317/fflonk/fflonk.go
index e867d801cf..af1536fc36 100644
--- a/ecc/bls24-317/fflonk/fflonk.go
+++ b/ecc/bls24-317/fflonk/fflonk.go
@@ -49,9 +49,9 @@ type OpeningProof struct {
 	ClaimedValues [][][]fr.Element
 }
 
-// CommitAndFold commits to a list of polynomial by intertwinning them like in the FFT, that is
+// FoldAndCommit commits to a list of polynomial by intertwinning them like in the FFT, that is
 // returns ∑_{i<t}Pᵢ(Xᵗ)Xⁱ for t polynomials
-func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
+func FoldAndCommit(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
 	buf := Fold(p)
 	com, err := kzg.Commit(buf, pk, nbTasks...)
 	return com, err
@@ -81,7 +81,7 @@ func Fold(p [][]fr.Element) []fr.Element {
 
 // BatchOpen computes a batch opening proof of p (the (fʲᵢ)ᵢ ) on powers of points (the ((Sʲᵢ)ᵢ)ⱼ).
 // The j-th pack of polynomials is opened on the power |(fʲᵢ)ᵢ| of (Sʲᵢ)ᵢ.
-// digests is the list (CommitAndFold(p[i]))ᵢ. It is assumed that the list has been computed beforehand
+// digests is the list (FoldAndCommit(p[i]))ᵢ. It is assumed that the list has been computed beforehand
 // and provided as an input to not duplicate computations.
 func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
 
diff --git a/ecc/bn254/fflonk/fflonk.go b/ecc/bn254/fflonk/fflonk.go
index 5e4a78fa03..99f09b7fe5 100644
--- a/ecc/bn254/fflonk/fflonk.go
+++ b/ecc/bn254/fflonk/fflonk.go
@@ -49,9 +49,9 @@ type OpeningProof struct {
 	ClaimedValues [][][]fr.Element
 }
 
-// CommitAndFold commits to a list of polynomial by intertwinning them like in the FFT, that is
+// FoldAndCommit commits to a list of polynomial by intertwinning them like in the FFT, that is
 // returns ∑_{i<t}Pᵢ(Xᵗ)Xⁱ for t polynomials
-func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
+func FoldAndCommit(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
 	buf := Fold(p)
 	com, err := kzg.Commit(buf, pk, nbTasks...)
 	return com, err
@@ -81,7 +81,7 @@ func Fold(p [][]fr.Element) []fr.Element {
 
 // BatchOpen computes a batch opening proof of p (the (fʲᵢ)ᵢ ) on powers of points (the ((Sʲᵢ)ᵢ)ⱼ).
 // The j-th pack of polynomials is opened on the power |(fʲᵢ)ᵢ| of (Sʲᵢ)ᵢ.
-// digests is the list (CommitAndFold(p[i]))ᵢ. It is assumed that the list has been computed beforehand
+// digests is the list (FoldAndCommit(p[i]))ᵢ. It is assumed that the list has been computed beforehand
 // and provided as an input to not duplicate computations.
 func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
 
diff --git a/ecc/bw6-633/fflonk/fflonk.go b/ecc/bw6-633/fflonk/fflonk.go
index 043ed4d2aa..c0aa739062 100644
--- a/ecc/bw6-633/fflonk/fflonk.go
+++ b/ecc/bw6-633/fflonk/fflonk.go
@@ -49,9 +49,9 @@ type OpeningProof struct {
 	ClaimedValues [][][]fr.Element
 }
 
-// CommitAndFold commits to a list of polynomial by intertwinning them like in the FFT, that is
+// FoldAndCommit commits to a list of polynomial by intertwinning them like in the FFT, that is
 // returns ∑_{i<t}Pᵢ(Xᵗ)Xⁱ for t polynomials
-func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
+func FoldAndCommit(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
 	buf := Fold(p)
 	com, err := kzg.Commit(buf, pk, nbTasks...)
 	return com, err
@@ -81,7 +81,7 @@ func Fold(p [][]fr.Element) []fr.Element {
 
 // BatchOpen computes a batch opening proof of p (the (fʲᵢ)ᵢ ) on powers of points (the ((Sʲᵢ)ᵢ)ⱼ).
 // The j-th pack of polynomials is opened on the power |(fʲᵢ)ᵢ| of (Sʲᵢ)ᵢ.
-// digests is the list (CommitAndFold(p[i]))ᵢ. It is assumed that the list has been computed beforehand
+// digests is the list (FoldAndCommit(p[i]))ᵢ. It is assumed that the list has been computed beforehand
 // and provided as an input to not duplicate computations.
 func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
 
diff --git a/ecc/bw6-756/fflonk/fflonk.go b/ecc/bw6-756/fflonk/fflonk.go
index b08a2f7f39..292635328f 100644
--- a/ecc/bw6-756/fflonk/fflonk.go
+++ b/ecc/bw6-756/fflonk/fflonk.go
@@ -49,9 +49,9 @@ type OpeningProof struct {
 	ClaimedValues [][][]fr.Element
 }
 
-// CommitAndFold commits to a list of polynomial by intertwinning them like in the FFT, that is
+// FoldAndCommit commits to a list of polynomial by intertwinning them like in the FFT, that is
 // returns ∑_{i<t}Pᵢ(Xᵗ)Xⁱ for t polynomials
-func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
+func FoldAndCommit(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
 	buf := Fold(p)
 	com, err := kzg.Commit(buf, pk, nbTasks...)
 	return com, err
@@ -81,7 +81,7 @@ func Fold(p [][]fr.Element) []fr.Element {
 
 // BatchOpen computes a batch opening proof of p (the (fʲᵢ)ᵢ ) on powers of points (the ((Sʲᵢ)ᵢ)ⱼ).
 // The j-th pack of polynomials is opened on the power |(fʲᵢ)ᵢ| of (Sʲᵢ)ᵢ.
-// digests is the list (CommitAndFold(p[i]))ᵢ. It is assumed that the list has been computed beforehand
+// digests is the list (FoldAndCommit(p[i]))ᵢ. It is assumed that the list has been computed beforehand
 // and provided as an input to not duplicate computations.
 func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
 
diff --git a/ecc/bw6-761/fflonk/fflonk.go b/ecc/bw6-761/fflonk/fflonk.go
index 500f788e35..7891c2479f 100644
--- a/ecc/bw6-761/fflonk/fflonk.go
+++ b/ecc/bw6-761/fflonk/fflonk.go
@@ -49,9 +49,9 @@ type OpeningProof struct {
 	ClaimedValues [][][]fr.Element
 }
 
-// CommitAndFold commits to a list of polynomial by intertwinning them like in the FFT, that is
+// FoldAndCommit commits to a list of polynomial by intertwinning them like in the FFT, that is
 // returns ∑_{i<t}Pᵢ(Xᵗ)Xⁱ for t polynomials
-func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
+func FoldAndCommit(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
 	buf := Fold(p)
 	com, err := kzg.Commit(buf, pk, nbTasks...)
 	return com, err
@@ -81,7 +81,7 @@ func Fold(p [][]fr.Element) []fr.Element {
 
 // BatchOpen computes a batch opening proof of p (the (fʲᵢ)ᵢ ) on powers of points (the ((Sʲᵢ)ᵢ)ⱼ).
 // The j-th pack of polynomials is opened on the power |(fʲᵢ)ᵢ| of (Sʲᵢ)ᵢ.
-// digests is the list (CommitAndFold(p[i]))ᵢ. It is assumed that the list has been computed beforehand
+// digests is the list (FoldAndCommit(p[i]))ᵢ. It is assumed that the list has been computed beforehand
 // and provided as an input to not duplicate computations.
 func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
 
diff --git a/internal/generator/fflonk/template/fflonk.go.tmpl b/internal/generator/fflonk/template/fflonk.go.tmpl
index a919355840..027a90af8a 100644
--- a/internal/generator/fflonk/template/fflonk.go.tmpl
+++ b/internal/generator/fflonk/template/fflonk.go.tmpl
@@ -31,9 +31,9 @@ type OpeningProof struct {
 	ClaimedValues [][][]fr.Element
 }
 
-// CommitAndFold commits to a list of polynomial by intertwinning them like in the FFT, that is
+// FoldAndCommit commits to a list of polynomial by intertwinning them like in the FFT, that is
 // returns ∑_{i<t}Pᵢ(Xᵗ)Xⁱ for t polynomials
-func CommitAndFold(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
+func FoldAndCommit(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Digest, error) {
 	buf := Fold(p)
 	com, err := kzg.Commit(buf, pk, nbTasks...)
 	return com, err
@@ -63,7 +63,7 @@ func Fold(p [][]fr.Element) []fr.Element {
 
 // BatchOpen computes a batch opening proof of p (the (fʲᵢ)ᵢ ) on powers of points (the ((Sʲᵢ)ᵢ)ⱼ).
 // The j-th pack of polynomials is opened on the power |(fʲᵢ)ᵢ| of (Sʲᵢ)ᵢ.
-// digests is the list (CommitAndFold(p[i]))ᵢ. It is assumed that the list has been computed beforehand
+// digests is the list (FoldAndCommit(p[i]))ᵢ. It is assumed that the list has been computed beforehand
 // and provided as an input to not duplicate computations.
 func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element, hf hash.Hash, pk kzg.ProvingKey, dataTranscript ...[]byte) (OpeningProof, error) {
 

From 847d5bfe8d49310af65de38e582358fbf77ee957 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 20 Sep 2024 14:59:31 +0200
Subject: [PATCH 059/114] feat: fixed size folded polynomials

---
 ecc/bls12-377/fflonk/fflonk.go                         | 6 ++++--
 ecc/bls12-377/fflonk/fflonk_test.go                    | 2 +-
 ecc/bls12-378/fflonk/fflonk.go                         | 6 ++++--
 ecc/bls12-378/fflonk/fflonk_test.go                    | 2 +-
 ecc/bls12-381/fflonk/fflonk.go                         | 6 ++++--
 ecc/bls12-381/fflonk/fflonk_test.go                    | 2 +-
 ecc/bls24-315/fflonk/fflonk.go                         | 6 ++++--
 ecc/bls24-315/fflonk/fflonk_test.go                    | 2 +-
 ecc/bls24-317/fflonk/fflonk.go                         | 6 ++++--
 ecc/bls24-317/fflonk/fflonk_test.go                    | 2 +-
 ecc/bn254/fflonk/fflonk.go                             | 6 ++++--
 ecc/bn254/fflonk/fflonk_test.go                        | 2 +-
 ecc/bw6-633/fflonk/fflonk.go                           | 6 ++++--
 ecc/bw6-633/fflonk/fflonk_test.go                      | 2 +-
 ecc/bw6-756/fflonk/fflonk.go                           | 6 ++++--
 ecc/bw6-756/fflonk/fflonk_test.go                      | 2 +-
 ecc/bw6-761/fflonk/fflonk.go                           | 6 ++++--
 ecc/bw6-761/fflonk/fflonk_test.go                      | 2 +-
 internal/generator/fflonk/template/fflonk.go.tmpl      | 6 ++++--
 internal/generator/fflonk/template/fflonk.test.go.tmpl | 2 +-
 20 files changed, 50 insertions(+), 30 deletions(-)

diff --git a/ecc/bls12-377/fflonk/fflonk.go b/ecc/bls12-377/fflonk/fflonk.go
index df4872da0f..376d414800 100644
--- a/ecc/bls12-377/fflonk/fflonk.go
+++ b/ecc/bls12-377/fflonk/fflonk.go
@@ -57,7 +57,9 @@ func FoldAndCommit(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Dig
 	return com, err
 }
 
-// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ. The
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ.
+// Say max{degree(P_{i})}=n-1. The total degree of the folded polynomial
+// is t(n-1)+(t-1). The total size is therefore t(n-1)+(t-1)+1 = tn.
 func Fold(p [][]fr.Element) []fr.Element {
 
 	// we first pick the smallest divisor of r-1 bounding above len(p)
@@ -69,7 +71,7 @@ func Fold(p [][]fr.Element) []fr.Element {
 			sizeResult = len(p[i])
 		}
 	}
-	sizeResult = sizeResult*t + t - 1
+	sizeResult = sizeResult * t
 	buf := make([]fr.Element, sizeResult)
 	for i := range p {
 		for j := range p[i] {
diff --git a/ecc/bls12-377/fflonk/fflonk_test.go b/ecc/bls12-377/fflonk/fflonk_test.go
index 143f7c552a..55e2dcc78b 100644
--- a/ecc/bls12-377/fflonk/fflonk_test.go
+++ b/ecc/bls12-377/fflonk/fflonk_test.go
@@ -70,7 +70,7 @@ func TestFflonk(t *testing.T) {
 	digests := make([]kzg.Digest, nbSets)
 	var err error
 	for i := 0; i < nbSets; i++ {
-		digests[i], err = CommitAndFold(p[i], testSrs.Pk)
+		digests[i], err = FoldAndCommit(p[i], testSrs.Pk)
 		assert.NoError(err)
 	}
 
diff --git a/ecc/bls12-378/fflonk/fflonk.go b/ecc/bls12-378/fflonk/fflonk.go
index f27f7c4945..500870dbbe 100644
--- a/ecc/bls12-378/fflonk/fflonk.go
+++ b/ecc/bls12-378/fflonk/fflonk.go
@@ -57,7 +57,9 @@ func FoldAndCommit(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Dig
 	return com, err
 }
 
-// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ. The
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ.
+// Say max{degree(P_{i})}=n-1. The total degree of the folded polynomial
+// is t(n-1)+(t-1). The total size is therefore t(n-1)+(t-1)+1 = tn.
 func Fold(p [][]fr.Element) []fr.Element {
 
 	// we first pick the smallest divisor of r-1 bounding above len(p)
@@ -69,7 +71,7 @@ func Fold(p [][]fr.Element) []fr.Element {
 			sizeResult = len(p[i])
 		}
 	}
-	sizeResult = sizeResult*t + t - 1
+	sizeResult = sizeResult * t
 	buf := make([]fr.Element, sizeResult)
 	for i := range p {
 		for j := range p[i] {
diff --git a/ecc/bls12-378/fflonk/fflonk_test.go b/ecc/bls12-378/fflonk/fflonk_test.go
index f27ea33482..7958a6af6b 100644
--- a/ecc/bls12-378/fflonk/fflonk_test.go
+++ b/ecc/bls12-378/fflonk/fflonk_test.go
@@ -70,7 +70,7 @@ func TestFflonk(t *testing.T) {
 	digests := make([]kzg.Digest, nbSets)
 	var err error
 	for i := 0; i < nbSets; i++ {
-		digests[i], err = CommitAndFold(p[i], testSrs.Pk)
+		digests[i], err = FoldAndCommit(p[i], testSrs.Pk)
 		assert.NoError(err)
 	}
 
diff --git a/ecc/bls12-381/fflonk/fflonk.go b/ecc/bls12-381/fflonk/fflonk.go
index 3460fe5d7a..16455c1b86 100644
--- a/ecc/bls12-381/fflonk/fflonk.go
+++ b/ecc/bls12-381/fflonk/fflonk.go
@@ -57,7 +57,9 @@ func FoldAndCommit(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Dig
 	return com, err
 }
 
-// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ. The
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ.
+// Say max{degree(P_{i})}=n-1. The total degree of the folded polynomial
+// is t(n-1)+(t-1). The total size is therefore t(n-1)+(t-1)+1 = tn.
 func Fold(p [][]fr.Element) []fr.Element {
 
 	// we first pick the smallest divisor of r-1 bounding above len(p)
@@ -69,7 +71,7 @@ func Fold(p [][]fr.Element) []fr.Element {
 			sizeResult = len(p[i])
 		}
 	}
-	sizeResult = sizeResult*t + t - 1
+	sizeResult = sizeResult * t
 	buf := make([]fr.Element, sizeResult)
 	for i := range p {
 		for j := range p[i] {
diff --git a/ecc/bls12-381/fflonk/fflonk_test.go b/ecc/bls12-381/fflonk/fflonk_test.go
index 77ff8b54f0..ad8519fedc 100644
--- a/ecc/bls12-381/fflonk/fflonk_test.go
+++ b/ecc/bls12-381/fflonk/fflonk_test.go
@@ -70,7 +70,7 @@ func TestFflonk(t *testing.T) {
 	digests := make([]kzg.Digest, nbSets)
 	var err error
 	for i := 0; i < nbSets; i++ {
-		digests[i], err = CommitAndFold(p[i], testSrs.Pk)
+		digests[i], err = FoldAndCommit(p[i], testSrs.Pk)
 		assert.NoError(err)
 	}
 
diff --git a/ecc/bls24-315/fflonk/fflonk.go b/ecc/bls24-315/fflonk/fflonk.go
index edd7bfe4d9..678bbd86c9 100644
--- a/ecc/bls24-315/fflonk/fflonk.go
+++ b/ecc/bls24-315/fflonk/fflonk.go
@@ -57,7 +57,9 @@ func FoldAndCommit(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Dig
 	return com, err
 }
 
-// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ. The
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ.
+// Say max{degree(P_{i})}=n-1. The total degree of the folded polynomial
+// is t(n-1)+(t-1). The total size is therefore t(n-1)+(t-1)+1 = tn.
 func Fold(p [][]fr.Element) []fr.Element {
 
 	// we first pick the smallest divisor of r-1 bounding above len(p)
@@ -69,7 +71,7 @@ func Fold(p [][]fr.Element) []fr.Element {
 			sizeResult = len(p[i])
 		}
 	}
-	sizeResult = sizeResult*t + t - 1
+	sizeResult = sizeResult * t
 	buf := make([]fr.Element, sizeResult)
 	for i := range p {
 		for j := range p[i] {
diff --git a/ecc/bls24-315/fflonk/fflonk_test.go b/ecc/bls24-315/fflonk/fflonk_test.go
index 0084bf3a55..aed1030914 100644
--- a/ecc/bls24-315/fflonk/fflonk_test.go
+++ b/ecc/bls24-315/fflonk/fflonk_test.go
@@ -70,7 +70,7 @@ func TestFflonk(t *testing.T) {
 	digests := make([]kzg.Digest, nbSets)
 	var err error
 	for i := 0; i < nbSets; i++ {
-		digests[i], err = CommitAndFold(p[i], testSrs.Pk)
+		digests[i], err = FoldAndCommit(p[i], testSrs.Pk)
 		assert.NoError(err)
 	}
 
diff --git a/ecc/bls24-317/fflonk/fflonk.go b/ecc/bls24-317/fflonk/fflonk.go
index af1536fc36..820e90e430 100644
--- a/ecc/bls24-317/fflonk/fflonk.go
+++ b/ecc/bls24-317/fflonk/fflonk.go
@@ -57,7 +57,9 @@ func FoldAndCommit(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Dig
 	return com, err
 }
 
-// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ. The
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ.
+// Say max{degree(P_{i})}=n-1. The total degree of the folded polynomial
+// is t(n-1)+(t-1). The total size is therefore t(n-1)+(t-1)+1 = tn.
 func Fold(p [][]fr.Element) []fr.Element {
 
 	// we first pick the smallest divisor of r-1 bounding above len(p)
@@ -69,7 +71,7 @@ func Fold(p [][]fr.Element) []fr.Element {
 			sizeResult = len(p[i])
 		}
 	}
-	sizeResult = sizeResult*t + t - 1
+	sizeResult = sizeResult * t
 	buf := make([]fr.Element, sizeResult)
 	for i := range p {
 		for j := range p[i] {
diff --git a/ecc/bls24-317/fflonk/fflonk_test.go b/ecc/bls24-317/fflonk/fflonk_test.go
index 6385ff35ca..f6d8213874 100644
--- a/ecc/bls24-317/fflonk/fflonk_test.go
+++ b/ecc/bls24-317/fflonk/fflonk_test.go
@@ -70,7 +70,7 @@ func TestFflonk(t *testing.T) {
 	digests := make([]kzg.Digest, nbSets)
 	var err error
 	for i := 0; i < nbSets; i++ {
-		digests[i], err = CommitAndFold(p[i], testSrs.Pk)
+		digests[i], err = FoldAndCommit(p[i], testSrs.Pk)
 		assert.NoError(err)
 	}
 
diff --git a/ecc/bn254/fflonk/fflonk.go b/ecc/bn254/fflonk/fflonk.go
index 99f09b7fe5..b64faf95fd 100644
--- a/ecc/bn254/fflonk/fflonk.go
+++ b/ecc/bn254/fflonk/fflonk.go
@@ -57,7 +57,9 @@ func FoldAndCommit(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Dig
 	return com, err
 }
 
-// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ. The
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ.
+// Say max{degree(P_{i})}=n-1. The total degree of the folded polynomial
+// is t(n-1)+(t-1). The total size is therefore t(n-1)+(t-1)+1 = tn.
 func Fold(p [][]fr.Element) []fr.Element {
 
 	// we first pick the smallest divisor of r-1 bounding above len(p)
@@ -69,7 +71,7 @@ func Fold(p [][]fr.Element) []fr.Element {
 			sizeResult = len(p[i])
 		}
 	}
-	sizeResult = sizeResult*t + t - 1
+	sizeResult = sizeResult * t
 	buf := make([]fr.Element, sizeResult)
 	for i := range p {
 		for j := range p[i] {
diff --git a/ecc/bn254/fflonk/fflonk_test.go b/ecc/bn254/fflonk/fflonk_test.go
index 28a02458f8..7f9441f4fb 100644
--- a/ecc/bn254/fflonk/fflonk_test.go
+++ b/ecc/bn254/fflonk/fflonk_test.go
@@ -70,7 +70,7 @@ func TestFflonk(t *testing.T) {
 	digests := make([]kzg.Digest, nbSets)
 	var err error
 	for i := 0; i < nbSets; i++ {
-		digests[i], err = CommitAndFold(p[i], testSrs.Pk)
+		digests[i], err = FoldAndCommit(p[i], testSrs.Pk)
 		assert.NoError(err)
 	}
 
diff --git a/ecc/bw6-633/fflonk/fflonk.go b/ecc/bw6-633/fflonk/fflonk.go
index c0aa739062..04e11fb49d 100644
--- a/ecc/bw6-633/fflonk/fflonk.go
+++ b/ecc/bw6-633/fflonk/fflonk.go
@@ -57,7 +57,9 @@ func FoldAndCommit(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Dig
 	return com, err
 }
 
-// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ. The
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ.
+// Say max{degree(P_{i})}=n-1. The total degree of the folded polynomial
+// is t(n-1)+(t-1). The total size is therefore t(n-1)+(t-1)+1 = tn.
 func Fold(p [][]fr.Element) []fr.Element {
 
 	// we first pick the smallest divisor of r-1 bounding above len(p)
@@ -69,7 +71,7 @@ func Fold(p [][]fr.Element) []fr.Element {
 			sizeResult = len(p[i])
 		}
 	}
-	sizeResult = sizeResult*t + t - 1
+	sizeResult = sizeResult * t
 	buf := make([]fr.Element, sizeResult)
 	for i := range p {
 		for j := range p[i] {
diff --git a/ecc/bw6-633/fflonk/fflonk_test.go b/ecc/bw6-633/fflonk/fflonk_test.go
index 7615629666..ae1755145c 100644
--- a/ecc/bw6-633/fflonk/fflonk_test.go
+++ b/ecc/bw6-633/fflonk/fflonk_test.go
@@ -70,7 +70,7 @@ func TestFflonk(t *testing.T) {
 	digests := make([]kzg.Digest, nbSets)
 	var err error
 	for i := 0; i < nbSets; i++ {
-		digests[i], err = CommitAndFold(p[i], testSrs.Pk)
+		digests[i], err = FoldAndCommit(p[i], testSrs.Pk)
 		assert.NoError(err)
 	}
 
diff --git a/ecc/bw6-756/fflonk/fflonk.go b/ecc/bw6-756/fflonk/fflonk.go
index 292635328f..91e8026789 100644
--- a/ecc/bw6-756/fflonk/fflonk.go
+++ b/ecc/bw6-756/fflonk/fflonk.go
@@ -57,7 +57,9 @@ func FoldAndCommit(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Dig
 	return com, err
 }
 
-// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ. The
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ.
+// Say max{degree(P_{i})}=n-1. The total degree of the folded polynomial
+// is t(n-1)+(t-1). The total size is therefore t(n-1)+(t-1)+1 = tn.
 func Fold(p [][]fr.Element) []fr.Element {
 
 	// we first pick the smallest divisor of r-1 bounding above len(p)
@@ -69,7 +71,7 @@ func Fold(p [][]fr.Element) []fr.Element {
 			sizeResult = len(p[i])
 		}
 	}
-	sizeResult = sizeResult*t + t - 1
+	sizeResult = sizeResult * t
 	buf := make([]fr.Element, sizeResult)
 	for i := range p {
 		for j := range p[i] {
diff --git a/ecc/bw6-756/fflonk/fflonk_test.go b/ecc/bw6-756/fflonk/fflonk_test.go
index 2bacfcdcc0..4d743800e5 100644
--- a/ecc/bw6-756/fflonk/fflonk_test.go
+++ b/ecc/bw6-756/fflonk/fflonk_test.go
@@ -70,7 +70,7 @@ func TestFflonk(t *testing.T) {
 	digests := make([]kzg.Digest, nbSets)
 	var err error
 	for i := 0; i < nbSets; i++ {
-		digests[i], err = CommitAndFold(p[i], testSrs.Pk)
+		digests[i], err = FoldAndCommit(p[i], testSrs.Pk)
 		assert.NoError(err)
 	}
 
diff --git a/ecc/bw6-761/fflonk/fflonk.go b/ecc/bw6-761/fflonk/fflonk.go
index 7891c2479f..3ad69a3a60 100644
--- a/ecc/bw6-761/fflonk/fflonk.go
+++ b/ecc/bw6-761/fflonk/fflonk.go
@@ -57,7 +57,9 @@ func FoldAndCommit(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Dig
 	return com, err
 }
 
-// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ. The
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ.
+// Say max{degree(P_{i})}=n-1. The total degree of the folded polynomial
+// is t(n-1)+(t-1). The total size is therefore t(n-1)+(t-1)+1 = tn.
 func Fold(p [][]fr.Element) []fr.Element {
 
 	// we first pick the smallest divisor of r-1 bounding above len(p)
@@ -69,7 +71,7 @@ func Fold(p [][]fr.Element) []fr.Element {
 			sizeResult = len(p[i])
 		}
 	}
-	sizeResult = sizeResult*t + t - 1
+	sizeResult = sizeResult * t
 	buf := make([]fr.Element, sizeResult)
 	for i := range p {
 		for j := range p[i] {
diff --git a/ecc/bw6-761/fflonk/fflonk_test.go b/ecc/bw6-761/fflonk/fflonk_test.go
index c1f726fc68..0802648d0e 100644
--- a/ecc/bw6-761/fflonk/fflonk_test.go
+++ b/ecc/bw6-761/fflonk/fflonk_test.go
@@ -70,7 +70,7 @@ func TestFflonk(t *testing.T) {
 	digests := make([]kzg.Digest, nbSets)
 	var err error
 	for i := 0; i < nbSets; i++ {
-		digests[i], err = CommitAndFold(p[i], testSrs.Pk)
+		digests[i], err = FoldAndCommit(p[i], testSrs.Pk)
 		assert.NoError(err)
 	}
 
diff --git a/internal/generator/fflonk/template/fflonk.go.tmpl b/internal/generator/fflonk/template/fflonk.go.tmpl
index 027a90af8a..60232b46fb 100644
--- a/internal/generator/fflonk/template/fflonk.go.tmpl
+++ b/internal/generator/fflonk/template/fflonk.go.tmpl
@@ -39,7 +39,9 @@ func FoldAndCommit(p [][]fr.Element, pk kzg.ProvingKey, nbTasks ...int) (kzg.Dig
 	return com, err
 }
 
-// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ. The
+// Fold returns p folded as in the fft, that is ∑_{i<t}Pᵢ(Xᵗ)Xⁱ.
+// Say max{degree(P_{i})}=n-1. The total degree of the folded polynomial
+// is t(n-1)+(t-1). The total size is therefore t(n-1)+(t-1)+1 = tn.
 func Fold(p [][]fr.Element) []fr.Element {
 
 	// we first pick the smallest divisor of r-1 bounding above len(p)
@@ -51,7 +53,7 @@ func Fold(p [][]fr.Element) []fr.Element {
 			sizeResult = len(p[i])
 		}
 	}
-	sizeResult = sizeResult*t + t - 1
+	sizeResult = sizeResult*t
 	buf := make([]fr.Element, sizeResult)
 	for i := range p {
 		for j := range p[i] {
diff --git a/internal/generator/fflonk/template/fflonk.test.go.tmpl b/internal/generator/fflonk/template/fflonk.test.go.tmpl
index 316b720572..b35a532301 100644
--- a/internal/generator/fflonk/template/fflonk.test.go.tmpl
+++ b/internal/generator/fflonk/template/fflonk.test.go.tmpl
@@ -52,7 +52,7 @@ func TestFflonk(t *testing.T) {
 	digests := make([]kzg.Digest, nbSets)
 	var err error
 	for i := 0; i < nbSets; i++ {
-		digests[i], err = CommitAndFold(p[i], testSrs.Pk)
+		digests[i], err = FoldAndCommit(p[i], testSrs.Pk)
 		assert.NoError(err)
 	}
 

From bcdf6c9fab76d0c1bcf4db1f59fa2580eda77dd1 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 20 Sep 2024 15:11:03 +0200
Subject: [PATCH 060/114] feat: renaming

---
 ecc/bls12-377/fflonk/fflonk.go                    | 12 ++++++------
 ecc/bls12-378/fflonk/fflonk.go                    | 12 ++++++------
 ecc/bls12-381/fflonk/fflonk.go                    | 12 ++++++------
 ecc/bls24-315/fflonk/fflonk.go                    | 12 ++++++------
 ecc/bls24-317/fflonk/fflonk.go                    | 12 ++++++------
 ecc/bn254/fflonk/fflonk.go                        | 12 ++++++------
 ecc/bw6-633/fflonk/fflonk.go                      | 12 ++++++------
 ecc/bw6-756/fflonk/fflonk.go                      | 12 ++++++------
 ecc/bw6-761/fflonk/fflonk.go                      | 12 ++++++------
 internal/generator/fflonk/template/fflonk.go.tmpl | 12 ++++++------
 10 files changed, 60 insertions(+), 60 deletions(-)

diff --git a/ecc/bls12-377/fflonk/fflonk.go b/ecc/bls12-377/fflonk/fflonk.go
index 376d414800..773f9a00a1 100644
--- a/ecc/bls12-377/fflonk/fflonk.go
+++ b/ecc/bls12-377/fflonk/fflonk.go
@@ -95,15 +95,15 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 
 	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
 	nbPolysPerPack := make([]int, len(p))
-	nextPowerOfTwoPerPack := make([]int, len(p))
+	nextDivisorRminusOnePerPack := make([]int, len(p))
 	for i := 0; i < len(p); i++ {
 		nbPolysPerPack[i] = len(p[i])
-		nextPowerOfTwoPerPack[i] = getNextDivisorRMinusOne(len(p[i]))
+		nextDivisorRminusOnePerPack[i] = getNextDivisorRMinusOne(len(p[i]))
 	}
 	pointsPowerM := make([][]fr.Element, len(points))
 	var tmpBigInt big.Int
 	for i := 0; i < len(p); i++ {
-		tmpBigInt.SetUint64(uint64(nextPowerOfTwoPerPack[i]))
+		tmpBigInt.SetUint64(uint64(nextDivisorRminusOnePerPack[i]))
 		pointsPowerM[i] = make([]fr.Element, len(points[i]))
 		for j := 0; j < len(points[i]); j++ {
 			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
@@ -114,14 +114,14 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	// on the relevant powers of the sets
 	res.ClaimedValues = make([][][]fr.Element, len(p))
 	for i := 0; i < len(p); i++ {
-		res.ClaimedValues[i] = make([][]fr.Element, nextPowerOfTwoPerPack[i])
+		res.ClaimedValues[i] = make([][]fr.Element, nextDivisorRminusOnePerPack[i])
 		for j := 0; j < len(p[i]); j++ {
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 			for k := 0; k < len(points[i]); k++ {
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
-		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaining polynomials are zero
+		for j := len(p[i]); j < nextDivisorRminusOnePerPack[i]; j++ { // -> the remaining polynomials are zero
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 		}
 	}
@@ -138,7 +138,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	newPoints := make([][]fr.Element, len(points))
 	var err error
 	for i := 0; i < len(p); i++ {
-		newPoints[i], err = extendSet(points[i], nextPowerOfTwoPerPack[i])
+		newPoints[i], err = extendSet(points[i], nextDivisorRminusOnePerPack[i])
 		if err != nil {
 			return res, err
 		}
diff --git a/ecc/bls12-378/fflonk/fflonk.go b/ecc/bls12-378/fflonk/fflonk.go
index 500870dbbe..ae9834c61a 100644
--- a/ecc/bls12-378/fflonk/fflonk.go
+++ b/ecc/bls12-378/fflonk/fflonk.go
@@ -95,15 +95,15 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 
 	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
 	nbPolysPerPack := make([]int, len(p))
-	nextPowerOfTwoPerPack := make([]int, len(p))
+	nextDivisorRminusOnePerPack := make([]int, len(p))
 	for i := 0; i < len(p); i++ {
 		nbPolysPerPack[i] = len(p[i])
-		nextPowerOfTwoPerPack[i] = getNextDivisorRMinusOne(len(p[i]))
+		nextDivisorRminusOnePerPack[i] = getNextDivisorRMinusOne(len(p[i]))
 	}
 	pointsPowerM := make([][]fr.Element, len(points))
 	var tmpBigInt big.Int
 	for i := 0; i < len(p); i++ {
-		tmpBigInt.SetUint64(uint64(nextPowerOfTwoPerPack[i]))
+		tmpBigInt.SetUint64(uint64(nextDivisorRminusOnePerPack[i]))
 		pointsPowerM[i] = make([]fr.Element, len(points[i]))
 		for j := 0; j < len(points[i]); j++ {
 			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
@@ -114,14 +114,14 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	// on the relevant powers of the sets
 	res.ClaimedValues = make([][][]fr.Element, len(p))
 	for i := 0; i < len(p); i++ {
-		res.ClaimedValues[i] = make([][]fr.Element, nextPowerOfTwoPerPack[i])
+		res.ClaimedValues[i] = make([][]fr.Element, nextDivisorRminusOnePerPack[i])
 		for j := 0; j < len(p[i]); j++ {
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 			for k := 0; k < len(points[i]); k++ {
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
-		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaining polynomials are zero
+		for j := len(p[i]); j < nextDivisorRminusOnePerPack[i]; j++ { // -> the remaining polynomials are zero
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 		}
 	}
@@ -138,7 +138,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	newPoints := make([][]fr.Element, len(points))
 	var err error
 	for i := 0; i < len(p); i++ {
-		newPoints[i], err = extendSet(points[i], nextPowerOfTwoPerPack[i])
+		newPoints[i], err = extendSet(points[i], nextDivisorRminusOnePerPack[i])
 		if err != nil {
 			return res, err
 		}
diff --git a/ecc/bls12-381/fflonk/fflonk.go b/ecc/bls12-381/fflonk/fflonk.go
index 16455c1b86..7a8c1f94fd 100644
--- a/ecc/bls12-381/fflonk/fflonk.go
+++ b/ecc/bls12-381/fflonk/fflonk.go
@@ -95,15 +95,15 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 
 	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
 	nbPolysPerPack := make([]int, len(p))
-	nextPowerOfTwoPerPack := make([]int, len(p))
+	nextDivisorRminusOnePerPack := make([]int, len(p))
 	for i := 0; i < len(p); i++ {
 		nbPolysPerPack[i] = len(p[i])
-		nextPowerOfTwoPerPack[i] = getNextDivisorRMinusOne(len(p[i]))
+		nextDivisorRminusOnePerPack[i] = getNextDivisorRMinusOne(len(p[i]))
 	}
 	pointsPowerM := make([][]fr.Element, len(points))
 	var tmpBigInt big.Int
 	for i := 0; i < len(p); i++ {
-		tmpBigInt.SetUint64(uint64(nextPowerOfTwoPerPack[i]))
+		tmpBigInt.SetUint64(uint64(nextDivisorRminusOnePerPack[i]))
 		pointsPowerM[i] = make([]fr.Element, len(points[i]))
 		for j := 0; j < len(points[i]); j++ {
 			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
@@ -114,14 +114,14 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	// on the relevant powers of the sets
 	res.ClaimedValues = make([][][]fr.Element, len(p))
 	for i := 0; i < len(p); i++ {
-		res.ClaimedValues[i] = make([][]fr.Element, nextPowerOfTwoPerPack[i])
+		res.ClaimedValues[i] = make([][]fr.Element, nextDivisorRminusOnePerPack[i])
 		for j := 0; j < len(p[i]); j++ {
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 			for k := 0; k < len(points[i]); k++ {
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
-		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaining polynomials are zero
+		for j := len(p[i]); j < nextDivisorRminusOnePerPack[i]; j++ { // -> the remaining polynomials are zero
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 		}
 	}
@@ -138,7 +138,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	newPoints := make([][]fr.Element, len(points))
 	var err error
 	for i := 0; i < len(p); i++ {
-		newPoints[i], err = extendSet(points[i], nextPowerOfTwoPerPack[i])
+		newPoints[i], err = extendSet(points[i], nextDivisorRminusOnePerPack[i])
 		if err != nil {
 			return res, err
 		}
diff --git a/ecc/bls24-315/fflonk/fflonk.go b/ecc/bls24-315/fflonk/fflonk.go
index 678bbd86c9..a8e808680c 100644
--- a/ecc/bls24-315/fflonk/fflonk.go
+++ b/ecc/bls24-315/fflonk/fflonk.go
@@ -95,15 +95,15 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 
 	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
 	nbPolysPerPack := make([]int, len(p))
-	nextPowerOfTwoPerPack := make([]int, len(p))
+	nextDivisorRminusOnePerPack := make([]int, len(p))
 	for i := 0; i < len(p); i++ {
 		nbPolysPerPack[i] = len(p[i])
-		nextPowerOfTwoPerPack[i] = getNextDivisorRMinusOne(len(p[i]))
+		nextDivisorRminusOnePerPack[i] = getNextDivisorRMinusOne(len(p[i]))
 	}
 	pointsPowerM := make([][]fr.Element, len(points))
 	var tmpBigInt big.Int
 	for i := 0; i < len(p); i++ {
-		tmpBigInt.SetUint64(uint64(nextPowerOfTwoPerPack[i]))
+		tmpBigInt.SetUint64(uint64(nextDivisorRminusOnePerPack[i]))
 		pointsPowerM[i] = make([]fr.Element, len(points[i]))
 		for j := 0; j < len(points[i]); j++ {
 			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
@@ -114,14 +114,14 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	// on the relevant powers of the sets
 	res.ClaimedValues = make([][][]fr.Element, len(p))
 	for i := 0; i < len(p); i++ {
-		res.ClaimedValues[i] = make([][]fr.Element, nextPowerOfTwoPerPack[i])
+		res.ClaimedValues[i] = make([][]fr.Element, nextDivisorRminusOnePerPack[i])
 		for j := 0; j < len(p[i]); j++ {
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 			for k := 0; k < len(points[i]); k++ {
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
-		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaining polynomials are zero
+		for j := len(p[i]); j < nextDivisorRminusOnePerPack[i]; j++ { // -> the remaining polynomials are zero
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 		}
 	}
@@ -138,7 +138,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	newPoints := make([][]fr.Element, len(points))
 	var err error
 	for i := 0; i < len(p); i++ {
-		newPoints[i], err = extendSet(points[i], nextPowerOfTwoPerPack[i])
+		newPoints[i], err = extendSet(points[i], nextDivisorRminusOnePerPack[i])
 		if err != nil {
 			return res, err
 		}
diff --git a/ecc/bls24-317/fflonk/fflonk.go b/ecc/bls24-317/fflonk/fflonk.go
index 820e90e430..3c736cb1a0 100644
--- a/ecc/bls24-317/fflonk/fflonk.go
+++ b/ecc/bls24-317/fflonk/fflonk.go
@@ -95,15 +95,15 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 
 	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
 	nbPolysPerPack := make([]int, len(p))
-	nextPowerOfTwoPerPack := make([]int, len(p))
+	nextDivisorRminusOnePerPack := make([]int, len(p))
 	for i := 0; i < len(p); i++ {
 		nbPolysPerPack[i] = len(p[i])
-		nextPowerOfTwoPerPack[i] = getNextDivisorRMinusOne(len(p[i]))
+		nextDivisorRminusOnePerPack[i] = getNextDivisorRMinusOne(len(p[i]))
 	}
 	pointsPowerM := make([][]fr.Element, len(points))
 	var tmpBigInt big.Int
 	for i := 0; i < len(p); i++ {
-		tmpBigInt.SetUint64(uint64(nextPowerOfTwoPerPack[i]))
+		tmpBigInt.SetUint64(uint64(nextDivisorRminusOnePerPack[i]))
 		pointsPowerM[i] = make([]fr.Element, len(points[i]))
 		for j := 0; j < len(points[i]); j++ {
 			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
@@ -114,14 +114,14 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	// on the relevant powers of the sets
 	res.ClaimedValues = make([][][]fr.Element, len(p))
 	for i := 0; i < len(p); i++ {
-		res.ClaimedValues[i] = make([][]fr.Element, nextPowerOfTwoPerPack[i])
+		res.ClaimedValues[i] = make([][]fr.Element, nextDivisorRminusOnePerPack[i])
 		for j := 0; j < len(p[i]); j++ {
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 			for k := 0; k < len(points[i]); k++ {
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
-		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaining polynomials are zero
+		for j := len(p[i]); j < nextDivisorRminusOnePerPack[i]; j++ { // -> the remaining polynomials are zero
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 		}
 	}
@@ -138,7 +138,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	newPoints := make([][]fr.Element, len(points))
 	var err error
 	for i := 0; i < len(p); i++ {
-		newPoints[i], err = extendSet(points[i], nextPowerOfTwoPerPack[i])
+		newPoints[i], err = extendSet(points[i], nextDivisorRminusOnePerPack[i])
 		if err != nil {
 			return res, err
 		}
diff --git a/ecc/bn254/fflonk/fflonk.go b/ecc/bn254/fflonk/fflonk.go
index b64faf95fd..f2995d3b6e 100644
--- a/ecc/bn254/fflonk/fflonk.go
+++ b/ecc/bn254/fflonk/fflonk.go
@@ -95,15 +95,15 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 
 	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
 	nbPolysPerPack := make([]int, len(p))
-	nextPowerOfTwoPerPack := make([]int, len(p))
+	nextDivisorRminusOnePerPack := make([]int, len(p))
 	for i := 0; i < len(p); i++ {
 		nbPolysPerPack[i] = len(p[i])
-		nextPowerOfTwoPerPack[i] = getNextDivisorRMinusOne(len(p[i]))
+		nextDivisorRminusOnePerPack[i] = getNextDivisorRMinusOne(len(p[i]))
 	}
 	pointsPowerM := make([][]fr.Element, len(points))
 	var tmpBigInt big.Int
 	for i := 0; i < len(p); i++ {
-		tmpBigInt.SetUint64(uint64(nextPowerOfTwoPerPack[i]))
+		tmpBigInt.SetUint64(uint64(nextDivisorRminusOnePerPack[i]))
 		pointsPowerM[i] = make([]fr.Element, len(points[i]))
 		for j := 0; j < len(points[i]); j++ {
 			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
@@ -114,14 +114,14 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	// on the relevant powers of the sets
 	res.ClaimedValues = make([][][]fr.Element, len(p))
 	for i := 0; i < len(p); i++ {
-		res.ClaimedValues[i] = make([][]fr.Element, nextPowerOfTwoPerPack[i])
+		res.ClaimedValues[i] = make([][]fr.Element, nextDivisorRminusOnePerPack[i])
 		for j := 0; j < len(p[i]); j++ {
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 			for k := 0; k < len(points[i]); k++ {
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
-		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaining polynomials are zero
+		for j := len(p[i]); j < nextDivisorRminusOnePerPack[i]; j++ { // -> the remaining polynomials are zero
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 		}
 	}
@@ -138,7 +138,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	newPoints := make([][]fr.Element, len(points))
 	var err error
 	for i := 0; i < len(p); i++ {
-		newPoints[i], err = extendSet(points[i], nextPowerOfTwoPerPack[i])
+		newPoints[i], err = extendSet(points[i], nextDivisorRminusOnePerPack[i])
 		if err != nil {
 			return res, err
 		}
diff --git a/ecc/bw6-633/fflonk/fflonk.go b/ecc/bw6-633/fflonk/fflonk.go
index 04e11fb49d..2c1a34f0b4 100644
--- a/ecc/bw6-633/fflonk/fflonk.go
+++ b/ecc/bw6-633/fflonk/fflonk.go
@@ -95,15 +95,15 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 
 	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
 	nbPolysPerPack := make([]int, len(p))
-	nextPowerOfTwoPerPack := make([]int, len(p))
+	nextDivisorRminusOnePerPack := make([]int, len(p))
 	for i := 0; i < len(p); i++ {
 		nbPolysPerPack[i] = len(p[i])
-		nextPowerOfTwoPerPack[i] = getNextDivisorRMinusOne(len(p[i]))
+		nextDivisorRminusOnePerPack[i] = getNextDivisorRMinusOne(len(p[i]))
 	}
 	pointsPowerM := make([][]fr.Element, len(points))
 	var tmpBigInt big.Int
 	for i := 0; i < len(p); i++ {
-		tmpBigInt.SetUint64(uint64(nextPowerOfTwoPerPack[i]))
+		tmpBigInt.SetUint64(uint64(nextDivisorRminusOnePerPack[i]))
 		pointsPowerM[i] = make([]fr.Element, len(points[i]))
 		for j := 0; j < len(points[i]); j++ {
 			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
@@ -114,14 +114,14 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	// on the relevant powers of the sets
 	res.ClaimedValues = make([][][]fr.Element, len(p))
 	for i := 0; i < len(p); i++ {
-		res.ClaimedValues[i] = make([][]fr.Element, nextPowerOfTwoPerPack[i])
+		res.ClaimedValues[i] = make([][]fr.Element, nextDivisorRminusOnePerPack[i])
 		for j := 0; j < len(p[i]); j++ {
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 			for k := 0; k < len(points[i]); k++ {
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
-		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaining polynomials are zero
+		for j := len(p[i]); j < nextDivisorRminusOnePerPack[i]; j++ { // -> the remaining polynomials are zero
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 		}
 	}
@@ -138,7 +138,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	newPoints := make([][]fr.Element, len(points))
 	var err error
 	for i := 0; i < len(p); i++ {
-		newPoints[i], err = extendSet(points[i], nextPowerOfTwoPerPack[i])
+		newPoints[i], err = extendSet(points[i], nextDivisorRminusOnePerPack[i])
 		if err != nil {
 			return res, err
 		}
diff --git a/ecc/bw6-756/fflonk/fflonk.go b/ecc/bw6-756/fflonk/fflonk.go
index 91e8026789..5bcafe8217 100644
--- a/ecc/bw6-756/fflonk/fflonk.go
+++ b/ecc/bw6-756/fflonk/fflonk.go
@@ -95,15 +95,15 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 
 	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
 	nbPolysPerPack := make([]int, len(p))
-	nextPowerOfTwoPerPack := make([]int, len(p))
+	nextDivisorRminusOnePerPack := make([]int, len(p))
 	for i := 0; i < len(p); i++ {
 		nbPolysPerPack[i] = len(p[i])
-		nextPowerOfTwoPerPack[i] = getNextDivisorRMinusOne(len(p[i]))
+		nextDivisorRminusOnePerPack[i] = getNextDivisorRMinusOne(len(p[i]))
 	}
 	pointsPowerM := make([][]fr.Element, len(points))
 	var tmpBigInt big.Int
 	for i := 0; i < len(p); i++ {
-		tmpBigInt.SetUint64(uint64(nextPowerOfTwoPerPack[i]))
+		tmpBigInt.SetUint64(uint64(nextDivisorRminusOnePerPack[i]))
 		pointsPowerM[i] = make([]fr.Element, len(points[i]))
 		for j := 0; j < len(points[i]); j++ {
 			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
@@ -114,14 +114,14 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	// on the relevant powers of the sets
 	res.ClaimedValues = make([][][]fr.Element, len(p))
 	for i := 0; i < len(p); i++ {
-		res.ClaimedValues[i] = make([][]fr.Element, nextPowerOfTwoPerPack[i])
+		res.ClaimedValues[i] = make([][]fr.Element, nextDivisorRminusOnePerPack[i])
 		for j := 0; j < len(p[i]); j++ {
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 			for k := 0; k < len(points[i]); k++ {
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
-		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaining polynomials are zero
+		for j := len(p[i]); j < nextDivisorRminusOnePerPack[i]; j++ { // -> the remaining polynomials are zero
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 		}
 	}
@@ -138,7 +138,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	newPoints := make([][]fr.Element, len(points))
 	var err error
 	for i := 0; i < len(p); i++ {
-		newPoints[i], err = extendSet(points[i], nextPowerOfTwoPerPack[i])
+		newPoints[i], err = extendSet(points[i], nextDivisorRminusOnePerPack[i])
 		if err != nil {
 			return res, err
 		}
diff --git a/ecc/bw6-761/fflonk/fflonk.go b/ecc/bw6-761/fflonk/fflonk.go
index 3ad69a3a60..d03c9a3ebb 100644
--- a/ecc/bw6-761/fflonk/fflonk.go
+++ b/ecc/bw6-761/fflonk/fflonk.go
@@ -95,15 +95,15 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 
 	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
 	nbPolysPerPack := make([]int, len(p))
-	nextPowerOfTwoPerPack := make([]int, len(p))
+	nextDivisorRminusOnePerPack := make([]int, len(p))
 	for i := 0; i < len(p); i++ {
 		nbPolysPerPack[i] = len(p[i])
-		nextPowerOfTwoPerPack[i] = getNextDivisorRMinusOne(len(p[i]))
+		nextDivisorRminusOnePerPack[i] = getNextDivisorRMinusOne(len(p[i]))
 	}
 	pointsPowerM := make([][]fr.Element, len(points))
 	var tmpBigInt big.Int
 	for i := 0; i < len(p); i++ {
-		tmpBigInt.SetUint64(uint64(nextPowerOfTwoPerPack[i]))
+		tmpBigInt.SetUint64(uint64(nextDivisorRminusOnePerPack[i]))
 		pointsPowerM[i] = make([]fr.Element, len(points[i]))
 		for j := 0; j < len(points[i]); j++ {
 			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
@@ -114,14 +114,14 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	// on the relevant powers of the sets
 	res.ClaimedValues = make([][][]fr.Element, len(p))
 	for i := 0; i < len(p); i++ {
-		res.ClaimedValues[i] = make([][]fr.Element, nextPowerOfTwoPerPack[i])
+		res.ClaimedValues[i] = make([][]fr.Element, nextDivisorRminusOnePerPack[i])
 		for j := 0; j < len(p[i]); j++ {
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 			for k := 0; k < len(points[i]); k++ {
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
-		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaining polynomials are zero
+		for j := len(p[i]); j < nextDivisorRminusOnePerPack[i]; j++ { // -> the remaining polynomials are zero
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 		}
 	}
@@ -138,7 +138,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	newPoints := make([][]fr.Element, len(points))
 	var err error
 	for i := 0; i < len(p); i++ {
-		newPoints[i], err = extendSet(points[i], nextPowerOfTwoPerPack[i])
+		newPoints[i], err = extendSet(points[i], nextDivisorRminusOnePerPack[i])
 		if err != nil {
 			return res, err
 		}
diff --git a/internal/generator/fflonk/template/fflonk.go.tmpl b/internal/generator/fflonk/template/fflonk.go.tmpl
index 60232b46fb..b7cfcc6c3d 100644
--- a/internal/generator/fflonk/template/fflonk.go.tmpl
+++ b/internal/generator/fflonk/template/fflonk.go.tmpl
@@ -77,15 +77,15 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 
 	// step 0: compute the relevant powers of the ((Sʲᵢ)ᵢ)ⱼ)
 	nbPolysPerPack := make([]int, len(p))
-	nextPowerOfTwoPerPack := make([]int, len(p))
+	nextDivisorRminusOnePerPack := make([]int, len(p))
 	for i := 0; i < len(p); i++ {
 		nbPolysPerPack[i] = len(p[i])
-		nextPowerOfTwoPerPack[i] = getNextDivisorRMinusOne(len(p[i]))
+		nextDivisorRminusOnePerPack[i] = getNextDivisorRMinusOne(len(p[i]))
 	}
 	pointsPowerM := make([][]fr.Element, len(points))
 	var tmpBigInt big.Int
 	for i := 0; i < len(p); i++ {
-		tmpBigInt.SetUint64(uint64(nextPowerOfTwoPerPack[i]))
+		tmpBigInt.SetUint64(uint64(nextDivisorRminusOnePerPack[i]))
 		pointsPowerM[i] = make([]fr.Element, len(points[i]))
 		for j := 0; j < len(points[i]); j++ {
 			pointsPowerM[i][j].Exp(points[i][j], &tmpBigInt)
@@ -96,14 +96,14 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	// on the relevant powers of the sets
 	res.ClaimedValues = make([][][]fr.Element, len(p))
 	for i := 0; i < len(p); i++ {
-		res.ClaimedValues[i] = make([][]fr.Element, nextPowerOfTwoPerPack[i])
+		res.ClaimedValues[i] = make([][]fr.Element, nextDivisorRminusOnePerPack[i])
 		for j := 0; j < len(p[i]); j++ {
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 			for k := 0; k < len(points[i]); k++ {
 				res.ClaimedValues[i][j][k] = eval(p[i][j], pointsPowerM[i][k])
 			}
 		}
-		for j := len(p[i]); j < nextPowerOfTwoPerPack[i]; j++ { // -> the remaining polynomials are zero
+		for j := len(p[i]); j < nextDivisorRminusOnePerPack[i]; j++ { // -> the remaining polynomials are zero
 			res.ClaimedValues[i][j] = make([]fr.Element, len(points[i]))
 		}
 	}
@@ -120,7 +120,7 @@ func BatchOpen(p [][][]fr.Element, digests []kzg.Digest, points [][]fr.Element,
 	newPoints := make([][]fr.Element, len(points))
 	var err error
 	for i := 0; i < len(p); i++ {
-		newPoints[i], err = extendSet(points[i], nextPowerOfTwoPerPack[i])
+		newPoints[i], err = extendSet(points[i], nextDivisorRminusOnePerPack[i])
 		if err != nil {
 			return res, err
 		}

From 83eac47ca06ea4a3a310f6c3abe997d43b34b6c0 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Fri, 20 Sep 2024 15:39:47 +0200
Subject: [PATCH 061/114] feat: number of trials for finding the next divisor
 of r-1 is now limited

---
 ecc/bls12-377/fflonk/fflonk.go                    | 7 ++++++-
 ecc/bls12-378/fflonk/fflonk.go                    | 7 ++++++-
 ecc/bls12-381/fflonk/fflonk.go                    | 7 ++++++-
 ecc/bls24-315/fflonk/fflonk.go                    | 7 ++++++-
 ecc/bls24-317/fflonk/fflonk.go                    | 7 ++++++-
 ecc/bn254/fflonk/fflonk.go                        | 7 ++++++-
 ecc/bw6-633/fflonk/fflonk.go                      | 7 ++++++-
 ecc/bw6-756/fflonk/fflonk.go                      | 7 ++++++-
 ecc/bw6-761/fflonk/fflonk.go                      | 7 ++++++-
 internal/generator/fflonk/template/fflonk.go.tmpl | 7 ++++++-
 10 files changed, 60 insertions(+), 10 deletions(-)

diff --git a/ecc/bls12-377/fflonk/fflonk.go b/ecc/bls12-377/fflonk/fflonk.go
index 773f9a00a1..65c19b0516 100644
--- a/ecc/bls12-377/fflonk/fflonk.go
+++ b/ecc/bls12-377/fflonk/fflonk.go
@@ -249,10 +249,15 @@ func getNextDivisorRMinusOne(i int) int {
 	r.Sub(r, &one)
 	tmp.SetUint64(uint64(i))
 	tmp.Mod(r, &tmp)
-	for tmp.Cmp(&zero) != 0 {
+	nbTrials := 100 // prevent DOS attack if the prime is not smooth
+	for tmp.Cmp(&zero) != 0 && nbTrials > 0 {
 		i += 1
 		tmp.SetUint64(uint64(i))
 		tmp.Mod(r, &tmp)
+		nbTrials--
+	}
+	if nbTrials == 0 {
+		panic("did not find any divisor of r-1")
 	}
 	return i
 }
diff --git a/ecc/bls12-378/fflonk/fflonk.go b/ecc/bls12-378/fflonk/fflonk.go
index ae9834c61a..ed9539acdd 100644
--- a/ecc/bls12-378/fflonk/fflonk.go
+++ b/ecc/bls12-378/fflonk/fflonk.go
@@ -249,10 +249,15 @@ func getNextDivisorRMinusOne(i int) int {
 	r.Sub(r, &one)
 	tmp.SetUint64(uint64(i))
 	tmp.Mod(r, &tmp)
-	for tmp.Cmp(&zero) != 0 {
+	nbTrials := 100 // prevent DOS attack if the prime is not smooth
+	for tmp.Cmp(&zero) != 0 && nbTrials > 0 {
 		i += 1
 		tmp.SetUint64(uint64(i))
 		tmp.Mod(r, &tmp)
+		nbTrials--
+	}
+	if nbTrials == 0 {
+		panic("did not find any divisor of r-1")
 	}
 	return i
 }
diff --git a/ecc/bls12-381/fflonk/fflonk.go b/ecc/bls12-381/fflonk/fflonk.go
index 7a8c1f94fd..293d58f181 100644
--- a/ecc/bls12-381/fflonk/fflonk.go
+++ b/ecc/bls12-381/fflonk/fflonk.go
@@ -249,10 +249,15 @@ func getNextDivisorRMinusOne(i int) int {
 	r.Sub(r, &one)
 	tmp.SetUint64(uint64(i))
 	tmp.Mod(r, &tmp)
-	for tmp.Cmp(&zero) != 0 {
+	nbTrials := 100 // prevent DOS attack if the prime is not smooth
+	for tmp.Cmp(&zero) != 0 && nbTrials > 0 {
 		i += 1
 		tmp.SetUint64(uint64(i))
 		tmp.Mod(r, &tmp)
+		nbTrials--
+	}
+	if nbTrials == 0 {
+		panic("did not find any divisor of r-1")
 	}
 	return i
 }
diff --git a/ecc/bls24-315/fflonk/fflonk.go b/ecc/bls24-315/fflonk/fflonk.go
index a8e808680c..d33a0cac62 100644
--- a/ecc/bls24-315/fflonk/fflonk.go
+++ b/ecc/bls24-315/fflonk/fflonk.go
@@ -249,10 +249,15 @@ func getNextDivisorRMinusOne(i int) int {
 	r.Sub(r, &one)
 	tmp.SetUint64(uint64(i))
 	tmp.Mod(r, &tmp)
-	for tmp.Cmp(&zero) != 0 {
+	nbTrials := 100 // prevent DOS attack if the prime is not smooth
+	for tmp.Cmp(&zero) != 0 && nbTrials > 0 {
 		i += 1
 		tmp.SetUint64(uint64(i))
 		tmp.Mod(r, &tmp)
+		nbTrials--
+	}
+	if nbTrials == 0 {
+		panic("did not find any divisor of r-1")
 	}
 	return i
 }
diff --git a/ecc/bls24-317/fflonk/fflonk.go b/ecc/bls24-317/fflonk/fflonk.go
index 3c736cb1a0..79bca3973b 100644
--- a/ecc/bls24-317/fflonk/fflonk.go
+++ b/ecc/bls24-317/fflonk/fflonk.go
@@ -249,10 +249,15 @@ func getNextDivisorRMinusOne(i int) int {
 	r.Sub(r, &one)
 	tmp.SetUint64(uint64(i))
 	tmp.Mod(r, &tmp)
-	for tmp.Cmp(&zero) != 0 {
+	nbTrials := 100 // prevent DOS attack if the prime is not smooth
+	for tmp.Cmp(&zero) != 0 && nbTrials > 0 {
 		i += 1
 		tmp.SetUint64(uint64(i))
 		tmp.Mod(r, &tmp)
+		nbTrials--
+	}
+	if nbTrials == 0 {
+		panic("did not find any divisor of r-1")
 	}
 	return i
 }
diff --git a/ecc/bn254/fflonk/fflonk.go b/ecc/bn254/fflonk/fflonk.go
index f2995d3b6e..dc7b99e70b 100644
--- a/ecc/bn254/fflonk/fflonk.go
+++ b/ecc/bn254/fflonk/fflonk.go
@@ -249,10 +249,15 @@ func getNextDivisorRMinusOne(i int) int {
 	r.Sub(r, &one)
 	tmp.SetUint64(uint64(i))
 	tmp.Mod(r, &tmp)
-	for tmp.Cmp(&zero) != 0 {
+	nbTrials := 100 // prevent DOS attack if the prime is not smooth
+	for tmp.Cmp(&zero) != 0 && nbTrials > 0 {
 		i += 1
 		tmp.SetUint64(uint64(i))
 		tmp.Mod(r, &tmp)
+		nbTrials--
+	}
+	if nbTrials == 0 {
+		panic("did not find any divisor of r-1")
 	}
 	return i
 }
diff --git a/ecc/bw6-633/fflonk/fflonk.go b/ecc/bw6-633/fflonk/fflonk.go
index 2c1a34f0b4..a66233e78d 100644
--- a/ecc/bw6-633/fflonk/fflonk.go
+++ b/ecc/bw6-633/fflonk/fflonk.go
@@ -249,10 +249,15 @@ func getNextDivisorRMinusOne(i int) int {
 	r.Sub(r, &one)
 	tmp.SetUint64(uint64(i))
 	tmp.Mod(r, &tmp)
-	for tmp.Cmp(&zero) != 0 {
+	nbTrials := 100 // prevent DOS attack if the prime is not smooth
+	for tmp.Cmp(&zero) != 0 && nbTrials > 0 {
 		i += 1
 		tmp.SetUint64(uint64(i))
 		tmp.Mod(r, &tmp)
+		nbTrials--
+	}
+	if nbTrials == 0 {
+		panic("did not find any divisor of r-1")
 	}
 	return i
 }
diff --git a/ecc/bw6-756/fflonk/fflonk.go b/ecc/bw6-756/fflonk/fflonk.go
index 5bcafe8217..672d78337c 100644
--- a/ecc/bw6-756/fflonk/fflonk.go
+++ b/ecc/bw6-756/fflonk/fflonk.go
@@ -249,10 +249,15 @@ func getNextDivisorRMinusOne(i int) int {
 	r.Sub(r, &one)
 	tmp.SetUint64(uint64(i))
 	tmp.Mod(r, &tmp)
-	for tmp.Cmp(&zero) != 0 {
+	nbTrials := 100 // prevent DOS attack if the prime is not smooth
+	for tmp.Cmp(&zero) != 0 && nbTrials > 0 {
 		i += 1
 		tmp.SetUint64(uint64(i))
 		tmp.Mod(r, &tmp)
+		nbTrials--
+	}
+	if nbTrials == 0 {
+		panic("did not find any divisor of r-1")
 	}
 	return i
 }
diff --git a/ecc/bw6-761/fflonk/fflonk.go b/ecc/bw6-761/fflonk/fflonk.go
index d03c9a3ebb..3a18d58b65 100644
--- a/ecc/bw6-761/fflonk/fflonk.go
+++ b/ecc/bw6-761/fflonk/fflonk.go
@@ -249,10 +249,15 @@ func getNextDivisorRMinusOne(i int) int {
 	r.Sub(r, &one)
 	tmp.SetUint64(uint64(i))
 	tmp.Mod(r, &tmp)
-	for tmp.Cmp(&zero) != 0 {
+	nbTrials := 100 // prevent DOS attack if the prime is not smooth
+	for tmp.Cmp(&zero) != 0 && nbTrials > 0 {
 		i += 1
 		tmp.SetUint64(uint64(i))
 		tmp.Mod(r, &tmp)
+		nbTrials--
+	}
+	if nbTrials == 0 {
+		panic("did not find any divisor of r-1")
 	}
 	return i
 }
diff --git a/internal/generator/fflonk/template/fflonk.go.tmpl b/internal/generator/fflonk/template/fflonk.go.tmpl
index b7cfcc6c3d..f3baa753f3 100644
--- a/internal/generator/fflonk/template/fflonk.go.tmpl
+++ b/internal/generator/fflonk/template/fflonk.go.tmpl
@@ -231,10 +231,15 @@ func getNextDivisorRMinusOne(i int) int {
 	r.Sub(r, &one)
 	tmp.SetUint64(uint64(i))
 	tmp.Mod(r, &tmp)
-	for tmp.Cmp(&zero) != 0 {
+	nbTrials := 100 // prevent DOS attack if the prime is not smooth
+	for tmp.Cmp(&zero) != 0 && nbTrials>0{
 		i += 1
 		tmp.SetUint64(uint64(i))
 		tmp.Mod(r, &tmp)
+		nbTrials--
+	}
+	if nbTrials==0 {
+		panic("did not find any divisor of r-1")
 	}
 	return i
 }

From 2a834f5d2839e2213fce4e0a8dc20c2bcd26614f Mon Sep 17 00:00:00 2001
From: Youssef El Housni <youssef.housni21@gmail.com>
Date: Fri, 20 Sep 2024 16:58:49 -0400
Subject: [PATCH 062/114] feat: implement Eisenstein integers arithmetic

---
 ecc/eisenstein.go      | 103 ++++++++++++++++++
 ecc/eisenstein_test.go | 232 +++++++++++++++++++++++++++++++++++++++++
 2 files changed, 335 insertions(+)
 create mode 100644 ecc/eisenstein.go
 create mode 100644 ecc/eisenstein_test.go

diff --git a/ecc/eisenstein.go b/ecc/eisenstein.go
new file mode 100644
index 0000000000..7d6d223b07
--- /dev/null
+++ b/ecc/eisenstein.go
@@ -0,0 +1,103 @@
+// The Eisenstein integers form a commutative ring of algebraic integers in the
+// algebraic number field Q(ω) – the third cyclotomic field.  These are of the
+// form z = a + bω, where a and b are integers and ω is a primitive third root
+// of unity i.e. ω²+ω+1 = 0.
+package ecc
+
+import (
+	"math/big"
+)
+
+// A ComplexNumber represents an arbitrary-precision Eisenstein integer.
+type ComplexNumber struct {
+	A0, A1 big.Int
+}
+
+// Equal returns true if z equals x, false otherwise
+func (z *ComplexNumber) Equal(x *ComplexNumber) bool {
+	return z.A0.Cmp(&x.A0) == 0 && z.A1.Cmp(&x.A1) == 0
+}
+
+// Set sets z equal to x, and returns z.
+func (z *ComplexNumber) Set(x *ComplexNumber) *ComplexNumber {
+	z.A0.Set(&x.A0)
+	z.A1.Set(&x.A1)
+	return z
+}
+
+// Neg sets z to the negative of x, and returns z.
+func (z *ComplexNumber) Neg(x *ComplexNumber) *ComplexNumber {
+	z.A0.Neg(&x.A0)
+	z.A1.Neg(&x.A1)
+	return z
+}
+
+// Conjugate sets z to the conjugate of x, and returns z.
+func (z *ComplexNumber) Conjugate(x *ComplexNumber) *ComplexNumber {
+	z.A0.Sub(&x.A0, &x.A1)
+	z.A1.Neg(&x.A1)
+	return z
+}
+
+// Add sets z to the sum of x and y, and returns z.
+func (z *ComplexNumber) Add(x, y *ComplexNumber) *ComplexNumber {
+	z.A0.Add(&x.A0, &y.A0)
+	z.A1.Add(&x.A1, &y.A1)
+	return z
+}
+
+// Sub sets z to the difference of x and y, and returns z.
+func (z *ComplexNumber) Sub(x, y *ComplexNumber) *ComplexNumber {
+	z.A0.Sub(&x.A0, &y.A0)
+	z.A1.Sub(&x.A1, &y.A1)
+	return z
+}
+
+// Mul sets z to the product of x and y, and returns z.
+//
+// Given that ω²+ω+1=0, the explicit formula is:
+//
+//	(x0+x1ω)(y0+y1ω) = (x0y0-x1y1) + (x0y1+x1y0-x1y1)ω
+func (z *ComplexNumber) Mul(x, y *ComplexNumber) *ComplexNumber {
+	var t [3]big.Int
+	var z0, z1 big.Int
+	t[0].Mul(&x.A0, &y.A0)
+	t[1].Mul(&x.A1, &y.A1)
+	z0.Sub(&t[0], &t[1])
+	t[0].Mul(&x.A0, &y.A1)
+	t[2].Mul(&x.A1, &y.A0)
+	t[0].Add(&t[0], &t[2])
+	z1.Sub(&t[0], &t[1])
+	z.A0.Set(&z0)
+	z.A1.Set(&z1)
+	return z
+}
+
+// Norm returns the norm of z.
+//
+// The explicit formula is:
+//
+//	N(x0+x1ω) = x0² + x1² - x0*x1
+func (z *ComplexNumber) Norm() *big.Int {
+	norm := new(big.Int)
+	temp := new(big.Int)
+	norm.Add(
+		norm.Mul(&z.A0, &z.A0),
+		temp.Mul(&z.A1, &z.A1),
+	)
+	norm.Sub(
+		norm,
+		temp.Mul(&z.A0, &z.A1),
+	)
+	return norm
+}
+
+// Quo sets z to the quotient of x and y, and returns z.
+func (z *ComplexNumber) Quo(x, y *ComplexNumber) *ComplexNumber {
+	norm := y.Norm()
+	z.Conjugate(y)
+	z.Mul(x, z)
+	z.A0.Quo(&z.A0, norm)
+	z.A1.Quo(&z.A1, norm)
+	return z
+}
diff --git a/ecc/eisenstein_test.go b/ecc/eisenstein_test.go
new file mode 100644
index 0000000000..bfe8381ed1
--- /dev/null
+++ b/ecc/eisenstein_test.go
@@ -0,0 +1,232 @@
+package ecc
+
+import (
+	"math/big"
+	"math/rand"
+	"testing"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/prop"
+)
+
+const (
+	nbFuzzShort = 10
+	nbFuzz      = 50
+)
+
+func TestEisensteinReceiverIsOperand(t *testing.T) {
+
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genE := GenComplexNumber()
+
+	properties.Property("Having the receiver as operand (addition) should output the same result", prop.ForAll(
+		func(a, b *ComplexNumber) bool {
+			var c, d ComplexNumber
+			d.Set(a)
+			c.Add(a, b)
+			a.Add(a, b)
+			b.Add(&d, b)
+			return a.Equal(b) && a.Equal(&c) && b.Equal(&c)
+		},
+		genE,
+		genE,
+	))
+
+	properties.Property("Having the receiver as operand (sub) should output the same result", prop.ForAll(
+		func(a, b *ComplexNumber) bool {
+			var c, d ComplexNumber
+			d.Set(a)
+			c.Sub(a, b)
+			a.Sub(a, b)
+			b.Sub(&d, b)
+			return a.Equal(b) && a.Equal(&c) && b.Equal(&c)
+		},
+		genE,
+		genE,
+	))
+
+	properties.Property("Having the receiver as operand (mul) should output the same result", prop.ForAll(
+		func(a, b *ComplexNumber) bool {
+			var c, d ComplexNumber
+			d.Set(a)
+			c.Mul(a, b)
+			a.Mul(a, b)
+			b.Mul(&d, b)
+			return a.Equal(b) && a.Equal(&c) && b.Equal(&c)
+		},
+		genE,
+		genE,
+	))
+
+	properties.Property("Having the receiver as operand (neg) should output the same result", prop.ForAll(
+		func(a *ComplexNumber) bool {
+			var b ComplexNumber
+			b.Neg(a)
+			a.Neg(a)
+			return a.Equal(&b)
+		},
+		genE,
+	))
+
+	properties.Property("Having the receiver as operand (conjugate) should output the same result", prop.ForAll(
+		func(a *ComplexNumber) bool {
+			var b ComplexNumber
+			b.Conjugate(a)
+			a.Conjugate(a)
+			return a.Equal(&b)
+		},
+		genE,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+}
+
+func TestEisensteinArithmetic(t *testing.T) {
+
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genE := GenComplexNumber()
+
+	properties.Property("sub & add should leave an element invariant", prop.ForAll(
+		func(a, b *ComplexNumber) bool {
+			var c ComplexNumber
+			c.Set(a)
+			c.Add(&c, b).Sub(&c, b)
+			return c.Equal(a)
+		},
+		genE,
+		genE,
+	))
+
+	properties.Property("neg twice should leave an element invariant", prop.ForAll(
+		func(a *ComplexNumber) bool {
+			var b ComplexNumber
+			b.Neg(a).Neg(&b)
+			return a.Equal(&b)
+		},
+		genE,
+	))
+
+	properties.Property("conj twice should leave an element invariant", prop.ForAll(
+		func(a *ComplexNumber) bool {
+			var b ComplexNumber
+			b.Conjugate(a).Conjugate(&b)
+			return a.Equal(&b)
+		},
+		genE,
+	))
+
+	properties.Property("add zero should leave element invariant", prop.ForAll(
+		func(a *ComplexNumber) bool {
+			var b ComplexNumber
+			zero := new(ComplexNumber)
+			b.Add(a, zero)
+			return a.Equal(&b)
+		},
+		genE,
+	))
+
+	properties.Property("mul by one should leave element invariant", prop.ForAll(
+		func(a *ComplexNumber) bool {
+			var b ComplexNumber
+			one := &ComplexNumber{
+				*big.NewInt(1),
+				*big.NewInt(0),
+			}
+			b.Mul(a, one)
+			return a.Equal(&b)
+		},
+		genE,
+	))
+
+	properties.Property("add should be commutative", prop.ForAll(
+		func(a, b *ComplexNumber) bool {
+			var c, d ComplexNumber
+			c.Add(a, b)
+			d.Add(b, a)
+			return c.Equal(&d)
+		},
+		genE,
+		genE,
+	))
+
+	properties.Property("add should be assiocative", prop.ForAll(
+		func(a, b, c *ComplexNumber) bool {
+			var d, e ComplexNumber
+			d.Add(a, b).Add(&d, c)
+			e.Add(c, b).Add(&e, a)
+			return e.Equal(&d)
+		},
+		genE,
+		genE,
+		genE,
+	))
+
+	properties.Property("mul should be commutative", prop.ForAll(
+		func(a, b *ComplexNumber) bool {
+			var c, d ComplexNumber
+			c.Mul(a, b)
+			d.Mul(b, a)
+			return c.Equal(&d)
+		},
+		genE,
+		genE,
+	))
+
+	properties.Property("mul should be assiocative", prop.ForAll(
+		func(a, b, c *ComplexNumber) bool {
+			var d, e ComplexNumber
+			d.Mul(a, b).Mul(&d, c)
+			e.Mul(c, b).Mul(&e, a)
+			return e.Equal(&d)
+		},
+		genE,
+		genE,
+		genE,
+	))
+
+	properties.Property("norm should always be positive", prop.ForAll(
+		func(a *ComplexNumber) bool {
+			return a.Norm().Sign() > 0
+		},
+		genE,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+}
+
+// GenNumber generates a random integer
+func GenNumber() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		elmt := *big.NewInt(rand.Int63())
+		genResult := gopter.NewGenResult(elmt, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+// GenComplexNumber generates a random integer
+func GenComplexNumber() gopter.Gen {
+	return gopter.CombineGens(
+		GenNumber(),
+		GenNumber(),
+	).Map(func(values []interface{}) *ComplexNumber {
+		return &ComplexNumber{A0: values[0].(big.Int), A1: values[1].(big.Int)}
+	})
+}

From dda7a27023eb77d3e00e2a0ab54ea194617115f6 Mon Sep 17 00:00:00 2001
From: Youssef El Housni <youssef.housni21@gmail.com>
Date: Sat, 21 Sep 2024 00:44:57 -0400
Subject: [PATCH 063/114] feat: half-GCD for Eisenstein integers

---
 ecc/eisenstein.go      | 58 +++++++++++++++++++++++++++++++++++++++---
 ecc/eisenstein_test.go | 30 ++++++++++++++++++++++
 2 files changed, 85 insertions(+), 3 deletions(-)

diff --git a/ecc/eisenstein.go b/ecc/eisenstein.go
index 7d6d223b07..a950a51fc2 100644
--- a/ecc/eisenstein.go
+++ b/ecc/eisenstein.go
@@ -13,18 +13,37 @@ type ComplexNumber struct {
 	A0, A1 big.Int
 }
 
+// String implements Stringer interface for fancy printing
+func (z *ComplexNumber) String() string {
+	return z.A0.String() + "+(" + z.A1.String() + "*ω)"
+}
+
 // Equal returns true if z equals x, false otherwise
 func (z *ComplexNumber) Equal(x *ComplexNumber) bool {
 	return z.A0.Cmp(&x.A0) == 0 && z.A1.Cmp(&x.A1) == 0
 }
 
-// Set sets z equal to x, and returns z.
+// Set sets z to x, and returns z.
 func (z *ComplexNumber) Set(x *ComplexNumber) *ComplexNumber {
 	z.A0.Set(&x.A0)
 	z.A1.Set(&x.A1)
 	return z
 }
 
+// Set sets z to 0, and returns z.
+func (z *ComplexNumber) SetZero() *ComplexNumber {
+	z.A0 = *big.NewInt(0)
+	z.A1 = *big.NewInt(0)
+	return z
+}
+
+// Set sets z to 1, and returns z.
+func (z *ComplexNumber) SetOne() *ComplexNumber {
+	z.A0 = *big.NewInt(1)
+	z.A1 = *big.NewInt(0)
+	return z
+}
+
 // Neg sets z to the negative of x, and returns z.
 func (z *ComplexNumber) Neg(x *ComplexNumber) *ComplexNumber {
 	z.A0.Neg(&x.A0)
@@ -97,7 +116,40 @@ func (z *ComplexNumber) Quo(x, y *ComplexNumber) *ComplexNumber {
 	norm := y.Norm()
 	z.Conjugate(y)
 	z.Mul(x, z)
-	z.A0.Quo(&z.A0, norm)
-	z.A1.Quo(&z.A1, norm)
+	z.A0.Div(&z.A0, norm)
+	z.A1.Div(&z.A1, norm)
 	return z
 }
+
+// HalfGCD returns the rational reconstruction of l mod r.
+// This outputs u, v s.t. l = u/v mod r
+func HalfGCD(a, b *ComplexNumber) [3]*ComplexNumber {
+
+	var aRun, bRun, u, v, u_, v_, quotient, remainder, t, t1, t2 ComplexNumber
+
+	aRun.Set(a)
+	bRun.Set(b)
+	u.SetOne()
+	v.SetZero()
+	u_.SetZero()
+	v_.SetOne()
+	nbits := a.Norm().BitLen() / 2
+
+	for aRun.Norm().BitLen() > nbits {
+		quotient.Quo(&aRun, &bRun)
+		t.Mul(&bRun, &quotient)
+		remainder.Sub(&aRun, &t)
+		t.Mul(&u_, &quotient)
+		t1.Sub(&u, &t)
+		t.Mul(&v_, &quotient)
+		t2.Sub(&v, &t)
+		aRun.Set(&bRun)
+		u.Set(&u_)
+		v.Set(&v_)
+		bRun.Set(&remainder)
+		u_.Set(&t1)
+		v_.Set(&t2)
+	}
+
+	return [3]*ComplexNumber{&aRun, &v, &u}
+}
diff --git a/ecc/eisenstein_test.go b/ecc/eisenstein_test.go
index bfe8381ed1..794b2caeb6 100644
--- a/ecc/eisenstein_test.go
+++ b/ecc/eisenstein_test.go
@@ -212,6 +212,36 @@ func TestEisensteinArithmetic(t *testing.T) {
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
 }
 
+func TestEisensteinHalfGCD(t *testing.T) {
+
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genE := GenComplexNumber()
+
+	properties.Property("half-GCD", prop.ForAll(
+		func(a, b *ComplexNumber) bool {
+			res := HalfGCD(a, b)
+			var c, d ComplexNumber
+			c.Mul(b, res[1])
+			d.Mul(a, res[2])
+			d.Add(&c, &d)
+			return d.Equal(res[0])
+		},
+		genE,
+		genE,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+}
+
 // GenNumber generates a random integer
 func GenNumber() gopter.Gen {
 	return func(genParams *gopter.GenParameters) *gopter.GenResult {

From 6f69c7e12ed97fdeebd625f86410cee1ede88abf Mon Sep 17 00:00:00 2001
From: Youssef El Housni <youssef.housni21@gmail.com>
Date: Sat, 21 Sep 2024 00:56:16 -0400
Subject: [PATCH 064/114] test: half-GCD test with bigger integers

---
 ecc/eisenstein_test.go | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/ecc/eisenstein_test.go b/ecc/eisenstein_test.go
index 794b2caeb6..40374cdbf0 100644
--- a/ecc/eisenstein_test.go
+++ b/ecc/eisenstein_test.go
@@ -1,8 +1,8 @@
 package ecc
 
 import (
+	"crypto/rand"
 	"math/big"
-	"math/rand"
 	"testing"
 
 	"github.com/leanovate/gopter"
@@ -245,8 +245,9 @@ func TestEisensteinHalfGCD(t *testing.T) {
 // GenNumber generates a random integer
 func GenNumber() gopter.Gen {
 	return func(genParams *gopter.GenParameters) *gopter.GenResult {
-		elmt := *big.NewInt(rand.Int63())
-		genResult := gopter.NewGenResult(elmt, gopter.NoShrinker)
+		var prime, _ = new(big.Int).SetString("7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed", 16) // 2^255 - 19
+		elmt, _ := rand.Int(rand.Reader, prime)
+		genResult := gopter.NewGenResult(*elmt, gopter.NoShrinker)
 		return genResult
 	}
 }

From 9b3186918b44a860918374a2c91665df3cb924d7 Mon Sep 17 00:00:00 2001
From: Youssef El Housni <youssef.housni21@gmail.com>
Date: Sat, 21 Sep 2024 01:13:54 -0400
Subject: [PATCH 065/114] style: clean comments

---
 ecc/eisenstein.go      |  8 ++++----
 ecc/eisenstein_test.go | 15 +++++++++++++++
 2 files changed, 19 insertions(+), 4 deletions(-)

diff --git a/ecc/eisenstein.go b/ecc/eisenstein.go
index a950a51fc2..e24dbc1657 100644
--- a/ecc/eisenstein.go
+++ b/ecc/eisenstein.go
@@ -30,14 +30,14 @@ func (z *ComplexNumber) Set(x *ComplexNumber) *ComplexNumber {
 	return z
 }
 
-// Set sets z to 0, and returns z.
+// SetZero sets z to 0, and returns z.
 func (z *ComplexNumber) SetZero() *ComplexNumber {
 	z.A0 = *big.NewInt(0)
 	z.A1 = *big.NewInt(0)
 	return z
 }
 
-// Set sets z to 1, and returns z.
+// SetOne sets z to 1, and returns z.
 func (z *ComplexNumber) SetOne() *ComplexNumber {
 	z.A0 = *big.NewInt(1)
 	z.A1 = *big.NewInt(0)
@@ -121,8 +121,8 @@ func (z *ComplexNumber) Quo(x, y *ComplexNumber) *ComplexNumber {
 	return z
 }
 
-// HalfGCD returns the rational reconstruction of l mod r.
-// This outputs u, v s.t. l = u/v mod r
+// HalfGCD returns the rational reconstruction of a, b.
+// This outputs w, v, u s.t. w = a*u + b*v.
 func HalfGCD(a, b *ComplexNumber) [3]*ComplexNumber {
 
 	var aRun, bRun, u, v, u_, v_, quotient, remainder, t, t1, t2 ComplexNumber
diff --git a/ecc/eisenstein_test.go b/ecc/eisenstein_test.go
index 40374cdbf0..fdd9f25435 100644
--- a/ecc/eisenstein_test.go
+++ b/ecc/eisenstein_test.go
@@ -261,3 +261,18 @@ func GenComplexNumber() gopter.Gen {
 		return &ComplexNumber{A0: values[0].(big.Int), A1: values[1].(big.Int)}
 	})
 }
+
+// bench
+func BenchmarkHalfGCD(b *testing.B) {
+	var prime, _ = new(big.Int).SetString("7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed", 16) // 2^255 - 19
+	a0, _ := rand.Int(rand.Reader, prime)
+	a1, _ := rand.Int(rand.Reader, prime)
+	c0, _ := rand.Int(rand.Reader, prime)
+	c1, _ := rand.Int(rand.Reader, prime)
+	a := ComplexNumber{A0: *a0, A1: *a1}
+	c := ComplexNumber{A0: *c0, A1: *c1}
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		HalfGCD(&a, &c)
+	}
+}

From 705a31ade028608759d7198becd54ed943c2f565 Mon Sep 17 00:00:00 2001
From: Youssef El Housni <youssef.housni21@gmail.com>
Date: Tue, 24 Sep 2024 15:11:22 -0400
Subject: [PATCH 066/114] refactor: move eisenstein under field/

---
 {ecc => field/eisenstein}/eisenstein.go      | 2 +-
 {ecc => field/eisenstein}/eisenstein_test.go | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)
 rename {ecc => field/eisenstein}/eisenstein.go (99%)
 rename {ecc => field/eisenstein}/eisenstein_test.go (99%)

diff --git a/ecc/eisenstein.go b/field/eisenstein/eisenstein.go
similarity index 99%
rename from ecc/eisenstein.go
rename to field/eisenstein/eisenstein.go
index e24dbc1657..8276a416bd 100644
--- a/ecc/eisenstein.go
+++ b/field/eisenstein/eisenstein.go
@@ -2,7 +2,7 @@
 // algebraic number field Q(ω) – the third cyclotomic field.  These are of the
 // form z = a + bω, where a and b are integers and ω is a primitive third root
 // of unity i.e. ω²+ω+1 = 0.
-package ecc
+package eisenstein
 
 import (
 	"math/big"
diff --git a/ecc/eisenstein_test.go b/field/eisenstein/eisenstein_test.go
similarity index 99%
rename from ecc/eisenstein_test.go
rename to field/eisenstein/eisenstein_test.go
index fdd9f25435..197036f1e5 100644
--- a/ecc/eisenstein_test.go
+++ b/field/eisenstein/eisenstein_test.go
@@ -1,4 +1,4 @@
-package ecc
+package eisenstein
 
 import (
 	"crypto/rand"

From 7febb567664cdbb5d4214d3cb3b7e47120be10e4 Mon Sep 17 00:00:00 2001
From: Youssef El Housni <youssef.housni21@gmail.com>
Date: Wed, 25 Sep 2024 14:24:14 -0400
Subject: [PATCH 067/114] fix: apply review suggestions

---
 field/eisenstein/doc.go             |  7 +++++
 field/eisenstein/eisenstein.go      | 44 ++++++++++++++++++++++-------
 field/eisenstein/eisenstein_test.go | 39 +++++++++++++------------
 3 files changed, 60 insertions(+), 30 deletions(-)
 create mode 100644 field/eisenstein/doc.go

diff --git a/field/eisenstein/doc.go b/field/eisenstein/doc.go
new file mode 100644
index 0000000000..3d353e2ab3
--- /dev/null
+++ b/field/eisenstein/doc.go
@@ -0,0 +1,7 @@
+// Package Eisenstein provides Eisenstein integer arithmetic.
+//
+// The Eisenstein integers form a commutative ring of algebraic integers in the
+// algebraic number field Q(ω) – the third cyclotomic field.  These are of the
+// form z = a + bω, where a and b are integers and ω is a primitive third root
+// of unity i.e. ω²+ω+1 = 0.
+package eisenstein
diff --git a/field/eisenstein/eisenstein.go b/field/eisenstein/eisenstein.go
index 8276a416bd..eddb54994a 100644
--- a/field/eisenstein/eisenstein.go
+++ b/field/eisenstein/eisenstein.go
@@ -1,7 +1,3 @@
-// The Eisenstein integers form a commutative ring of algebraic integers in the
-// algebraic number field Q(ω) – the third cyclotomic field.  These are of the
-// form z = a + bω, where a and b are integers and ω is a primitive third root
-// of unity i.e. ω²+ω+1 = 0.
 package eisenstein
 
 import (
@@ -114,6 +110,9 @@ func (z *ComplexNumber) Norm() *big.Int {
 // Quo sets z to the quotient of x and y, and returns z.
 func (z *ComplexNumber) Quo(x, y *ComplexNumber) *ComplexNumber {
 	norm := y.Norm()
+	if norm.Cmp(big.NewInt(0)) == 0 {
+		panic("division by zero")
+	}
 	z.Conjugate(y)
 	z.Mul(x, z)
 	z.A0.Div(&z.A0, norm)
@@ -121,11 +120,37 @@ func (z *ComplexNumber) Quo(x, y *ComplexNumber) *ComplexNumber {
 	return z
 }
 
+// QuoRem sets z to the quotient of x and y, r to the remaind, and returns z and r.
+func (z *ComplexNumber) QuoRem(x, y, r *ComplexNumber) (*ComplexNumber, *ComplexNumber) {
+	norm := y.Norm()
+	if norm.Cmp(big.NewInt(0)) == 0 {
+		panic("division by zero")
+	}
+	z.Conjugate(y)
+	z.Mul(x, z)
+	z.A0.Div(&z.A0, norm)
+	z.A1.Div(&z.A1, norm)
+	var t ComplexNumber
+	r.Sub(x, t.Mul(y, z))
+	return z, r
+}
+
+// Min returns the minimum of z... with respect to the norm.
+func Min(z ...*ComplexNumber) *ComplexNumber {
+	min := z[0]
+	for _, v := range z {
+		if v.Norm().Cmp(min.Norm()) == -1 {
+			min = v
+		}
+	}
+	return min
+}
+
 // HalfGCD returns the rational reconstruction of a, b.
 // This outputs w, v, u s.t. w = a*u + b*v.
 func HalfGCD(a, b *ComplexNumber) [3]*ComplexNumber {
 
-	var aRun, bRun, u, v, u_, v_, quotient, remainder, t, t1, t2 ComplexNumber
+	var check, aRun, bRun, u, v, u_, v_, quotient, remainder, t, t1, t2 ComplexNumber
 
 	aRun.Set(a)
 	bRun.Set(b)
@@ -133,12 +158,11 @@ func HalfGCD(a, b *ComplexNumber) [3]*ComplexNumber {
 	v.SetZero()
 	u_.SetZero()
 	v_.SetOne()
-	nbits := a.Norm().BitLen() / 2
 
-	for aRun.Norm().BitLen() > nbits {
-		quotient.Quo(&aRun, &bRun)
-		t.Mul(&bRun, &quotient)
-		remainder.Sub(&aRun, &t)
+	// Eisenstein integers form an Euclidean domain for the norm
+	aNorm := a.Norm()
+	for check.Mul(&aRun, &aRun).Norm().Cmp(aNorm) == 1 {
+		quotient.QuoRem(&aRun, &bRun, &remainder)
 		t.Mul(&u_, &quotient)
 		t1.Sub(&u, &t)
 		t.Mul(&v_, &quotient)
diff --git a/field/eisenstein/eisenstein_test.go b/field/eisenstein/eisenstein_test.go
index 197036f1e5..2244972010 100644
--- a/field/eisenstein/eisenstein_test.go
+++ b/field/eisenstein/eisenstein_test.go
@@ -12,6 +12,7 @@ import (
 const (
 	nbFuzzShort = 10
 	nbFuzz      = 50
+	boundSize   = 256
 )
 
 func TestEisensteinReceiverIsOperand(t *testing.T) {
@@ -26,7 +27,7 @@ func TestEisensteinReceiverIsOperand(t *testing.T) {
 
 	properties := gopter.NewProperties(parameters)
 
-	genE := GenComplexNumber()
+	genE := GenComplexNumber(boundSize)
 
 	properties.Property("Having the receiver as operand (addition) should output the same result", prop.ForAll(
 		func(a, b *ComplexNumber) bool {
@@ -102,7 +103,7 @@ func TestEisensteinArithmetic(t *testing.T) {
 
 	properties := gopter.NewProperties(parameters)
 
-	genE := GenComplexNumber()
+	genE := GenComplexNumber(boundSize)
 
 	properties.Property("sub & add should leave an element invariant", prop.ForAll(
 		func(a, b *ComplexNumber) bool {
@@ -135,9 +136,9 @@ func TestEisensteinArithmetic(t *testing.T) {
 
 	properties.Property("add zero should leave element invariant", prop.ForAll(
 		func(a *ComplexNumber) bool {
-			var b ComplexNumber
-			zero := new(ComplexNumber)
-			b.Add(a, zero)
+			var b, zero ComplexNumber
+			zero.SetZero()
+			b.Add(a, &zero)
 			return a.Equal(&b)
 		},
 		genE,
@@ -145,12 +146,9 @@ func TestEisensteinArithmetic(t *testing.T) {
 
 	properties.Property("mul by one should leave element invariant", prop.ForAll(
 		func(a *ComplexNumber) bool {
-			var b ComplexNumber
-			one := &ComplexNumber{
-				*big.NewInt(1),
-				*big.NewInt(0),
-			}
-			b.Mul(a, one)
+			var b, one ComplexNumber
+			one.SetOne()
+			b.Mul(a, &one)
 			return a.Equal(&b)
 		},
 		genE,
@@ -204,7 +202,7 @@ func TestEisensteinArithmetic(t *testing.T) {
 
 	properties.Property("norm should always be positive", prop.ForAll(
 		func(a *ComplexNumber) bool {
-			return a.Norm().Sign() > 0
+			return a.Norm().Sign() >= 0
 		},
 		genE,
 	))
@@ -224,7 +222,7 @@ func TestEisensteinHalfGCD(t *testing.T) {
 
 	properties := gopter.NewProperties(parameters)
 
-	genE := GenComplexNumber()
+	genE := GenComplexNumber(boundSize)
 
 	properties.Property("half-GCD", prop.ForAll(
 		func(a, b *ComplexNumber) bool {
@@ -243,20 +241,21 @@ func TestEisensteinHalfGCD(t *testing.T) {
 }
 
 // GenNumber generates a random integer
-func GenNumber() gopter.Gen {
+func GenNumber(boundSize int64) gopter.Gen {
 	return func(genParams *gopter.GenParameters) *gopter.GenResult {
-		var prime, _ = new(big.Int).SetString("7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed", 16) // 2^255 - 19
-		elmt, _ := rand.Int(rand.Reader, prime)
+		var bound big.Int
+		bound.Exp(big.NewInt(2), big.NewInt(boundSize), nil)
+		elmt, _ := rand.Int(genParams.Rng, &bound)
 		genResult := gopter.NewGenResult(*elmt, gopter.NoShrinker)
 		return genResult
 	}
 }
 
 // GenComplexNumber generates a random integer
-func GenComplexNumber() gopter.Gen {
+func GenComplexNumber(boundSize int64) gopter.Gen {
 	return gopter.CombineGens(
-		GenNumber(),
-		GenNumber(),
+		GenNumber(boundSize),
+		GenNumber(boundSize),
 	).Map(func(values []interface{}) *ComplexNumber {
 		return &ComplexNumber{A0: values[0].(big.Int), A1: values[1].(big.Int)}
 	})
@@ -273,6 +272,6 @@ func BenchmarkHalfGCD(b *testing.B) {
 	c := ComplexNumber{A0: *c0, A1: *c1}
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		HalfGCD(&a, &c)
+		_ = HalfGCD(&a, &c)
 	}
 }

From 12d53bfaad6f1706d8f940137f2512fb27a29d25 Mon Sep 17 00:00:00 2001
From: Youssef El Housni <youssef.housni21@gmail.com>
Date: Wed, 25 Sep 2024 14:30:30 -0400
Subject: [PATCH 068/114] fix: makes linter happy

---
 field/eisenstein/eisenstein.go | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/field/eisenstein/eisenstein.go b/field/eisenstein/eisenstein.go
index eddb54994a..54bfde8af2 100644
--- a/field/eisenstein/eisenstein.go
+++ b/field/eisenstein/eisenstein.go
@@ -120,7 +120,7 @@ func (z *ComplexNumber) Quo(x, y *ComplexNumber) *ComplexNumber {
 	return z
 }
 
-// QuoRem sets z to the quotient of x and y, r to the remaind, and returns z and r.
+// QuoRem sets z to the quotient of x and y, r to the remainder, and returns z and r.
 func (z *ComplexNumber) QuoRem(x, y, r *ComplexNumber) (*ComplexNumber, *ComplexNumber) {
 	norm := y.Norm()
 	if norm.Cmp(big.NewInt(0)) == 0 {

From fa1b905322a14c23c71718bf4a361ea53490ab75 Mon Sep 17 00:00:00 2001
From: Youssef El Housni <youssef.housni21@gmail.com>
Date: Thu, 26 Sep 2024 16:01:43 -0400
Subject: [PATCH 069/114] fix: consider all possible remainders

---
 field/eisenstein/eisenstein.go      | 35 ++++++++++++++++++++++-------
 field/eisenstein/eisenstein_test.go |  2 +-
 2 files changed, 28 insertions(+), 9 deletions(-)

diff --git a/field/eisenstein/eisenstein.go b/field/eisenstein/eisenstein.go
index 54bfde8af2..b77aa9a392 100644
--- a/field/eisenstein/eisenstein.go
+++ b/field/eisenstein/eisenstein.go
@@ -120,6 +120,23 @@ func (z *ComplexNumber) Quo(x, y *ComplexNumber) *ComplexNumber {
 	return z
 }
 
+func (z *ComplexNumber) Rem(x, y, q *ComplexNumber) *ComplexNumber {
+	var t ComplexNumber
+	z.Sub(x, t.Mul(y, q))
+	var r1, r2, r3, r4, r5, r6, w, wy, w2y ComplexNumber
+	w.A1.SetUint64(1)
+	wy.Mul(&w, y)
+	w2y.Mul(&w, &wy)
+	r1.Sub(z, y)
+	r2.Add(z, y)
+	r3.Sub(z, &wy)
+	r4.Add(z, &wy)
+	r5.Sub(z, &w2y)
+	r6.Add(z, &w2y)
+	z = Min(z, &r1, &r2, &r3, &r4, &r5, &r6)
+	return z
+}
+
 // QuoRem sets z to the quotient of x and y, r to the remainder, and returns z and r.
 func (z *ComplexNumber) QuoRem(x, y, r *ComplexNumber) (*ComplexNumber, *ComplexNumber) {
 	norm := y.Norm()
@@ -130,8 +147,8 @@ func (z *ComplexNumber) QuoRem(x, y, r *ComplexNumber) (*ComplexNumber, *Complex
 	z.Mul(x, z)
 	z.A0.Div(&z.A0, norm)
 	z.A1.Div(&z.A1, norm)
-	var t ComplexNumber
-	r.Sub(x, t.Mul(y, z))
+	r.Rem(x, y, z)
+
 	return z, r
 }
 
@@ -150,7 +167,7 @@ func Min(z ...*ComplexNumber) *ComplexNumber {
 // This outputs w, v, u s.t. w = a*u + b*v.
 func HalfGCD(a, b *ComplexNumber) [3]*ComplexNumber {
 
-	var check, aRun, bRun, u, v, u_, v_, quotient, remainder, t, t1, t2 ComplexNumber
+	var check, aRun, bRun, u, v, u_, v_, quotient, remainder, t1, t2 ComplexNumber
 
 	aRun.Set(a)
 	bRun.Set(b)
@@ -161,12 +178,10 @@ func HalfGCD(a, b *ComplexNumber) [3]*ComplexNumber {
 
 	// Eisenstein integers form an Euclidean domain for the norm
 	aNorm := a.Norm()
-	for check.Mul(&aRun, &aRun).Norm().Cmp(aNorm) == 1 {
+	for check.Mul(&aRun, &aRun).Norm().Cmp(aNorm) >= 0 {
 		quotient.QuoRem(&aRun, &bRun, &remainder)
-		t.Mul(&u_, &quotient)
-		t1.Sub(&u, &t)
-		t.Mul(&v_, &quotient)
-		t2.Sub(&v, &t)
+		t1.Rem(&u, &u_, &quotient)
+		t2.Rem(&v, &v_, &quotient)
 		aRun.Set(&bRun)
 		u.Set(&u_)
 		v.Set(&v_)
@@ -175,5 +190,9 @@ func HalfGCD(a, b *ComplexNumber) [3]*ComplexNumber {
 		v_.Set(&t2)
 	}
 
+	if v_.Norm().Cmp(v.Norm()) == -1 {
+		return [3]*ComplexNumber{&bRun, &v_, &u_}
+	}
+
 	return [3]*ComplexNumber{&aRun, &v, &u}
 }
diff --git a/field/eisenstein/eisenstein_test.go b/field/eisenstein/eisenstein_test.go
index 2244972010..89c7dc5d44 100644
--- a/field/eisenstein/eisenstein_test.go
+++ b/field/eisenstein/eisenstein_test.go
@@ -12,7 +12,7 @@ import (
 const (
 	nbFuzzShort = 10
 	nbFuzz      = 50
-	boundSize   = 256
+	boundSize   = 128
 )
 
 func TestEisensteinReceiverIsOperand(t *testing.T) {

From 13fa612255da2bcf57b77a24510c69a17b5476e6 Mon Sep 17 00:00:00 2001
From: Youssef El Housni <youssef.housni21@gmail.com>
Date: Fri, 27 Sep 2024 17:21:45 -0400
Subject: [PATCH 070/114] fix: use sqrt in eisenstein halfgcd condition

---
 field/eisenstein/eisenstein.go | 13 +++++--------
 1 file changed, 5 insertions(+), 8 deletions(-)

diff --git a/field/eisenstein/eisenstein.go b/field/eisenstein/eisenstein.go
index b77aa9a392..9fe12ad832 100644
--- a/field/eisenstein/eisenstein.go
+++ b/field/eisenstein/eisenstein.go
@@ -167,7 +167,8 @@ func Min(z ...*ComplexNumber) *ComplexNumber {
 // This outputs w, v, u s.t. w = a*u + b*v.
 func HalfGCD(a, b *ComplexNumber) [3]*ComplexNumber {
 
-	var check, aRun, bRun, u, v, u_, v_, quotient, remainder, t1, t2 ComplexNumber
+	var aRun, bRun, u, v, u_, v_, quotient, remainder, t1, t2 ComplexNumber
+	var sqrt big.Int
 
 	aRun.Set(a)
 	bRun.Set(b)
@@ -177,8 +178,8 @@ func HalfGCD(a, b *ComplexNumber) [3]*ComplexNumber {
 	v_.SetOne()
 
 	// Eisenstein integers form an Euclidean domain for the norm
-	aNorm := a.Norm()
-	for check.Mul(&aRun, &aRun).Norm().Cmp(aNorm) >= 0 {
+	sqrt.Sqrt(a.Norm())
+	for bRun.Norm().Cmp(&sqrt) == 1 {
 		quotient.QuoRem(&aRun, &bRun, &remainder)
 		t1.Rem(&u, &u_, &quotient)
 		t2.Rem(&v, &v_, &quotient)
@@ -190,9 +191,5 @@ func HalfGCD(a, b *ComplexNumber) [3]*ComplexNumber {
 		v_.Set(&t2)
 	}
 
-	if v_.Norm().Cmp(v.Norm()) == -1 {
-		return [3]*ComplexNumber{&bRun, &v_, &u_}
-	}
-
-	return [3]*ComplexNumber{&aRun, &v, &u}
+	return [3]*ComplexNumber{&bRun, &v_, &u_}
 }

From 5a736a2a8405e86b2ff41d73a5dd2b5f80a88d1a Mon Sep 17 00:00:00 2001
From: Arya Tabaie <15056835+Tabaie@users.noreply.github.com>
Date: Wed, 2 Oct 2024 16:34:40 -0500
Subject: [PATCH 071/114] docs: GSigma -> GSigmaNeg bn254

---
 ecc/bn254/fr/pedersen/pedersen.go      | 14 +++++++-------
 ecc/bn254/fr/pedersen/pedersen_test.go |  2 +-
 2 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/ecc/bn254/fr/pedersen/pedersen.go b/ecc/bn254/fr/pedersen/pedersen.go
index 81e55ebb48..1d0969fadf 100644
--- a/ecc/bn254/fr/pedersen/pedersen.go
+++ b/ecc/bn254/fr/pedersen/pedersen.go
@@ -33,8 +33,8 @@ type ProvingKey struct {
 }
 
 type VerifyingKey struct {
-	G      curve.G2Affine
-	GSigma curve.G2Affine // GRootSigmaNeg = G^{-σ}
+	G         curve.G2Affine
+	GSigmaNeg curve.G2Affine // GSigmaNeg = G^{-σ}
 }
 
 func randomFrSizedBytes() ([]byte, error) {
@@ -94,7 +94,7 @@ func Setup(bases [][]curve.G1Affine, options ...SetupOption) (pk []ProvingKey, v
 	sigma.Add(sigma, big.NewInt(1))
 
 	sigmaNeg := new(big.Int).Neg(sigma)
-	vk.GSigma.ScalarMultiplication(&vk.G, sigmaNeg)
+	vk.GSigmaNeg.ScalarMultiplication(&vk.G, sigmaNeg)
 
 	pk = make([]ProvingKey, len(bases))
 	for i := range bases {
@@ -211,7 +211,7 @@ func (vk *VerifyingKey) Verify(commitment curve.G1Affine, knowledgeProof curve.G
 		return errors.New("subgroup check failed")
 	}
 
-	if isOne, err := curve.PairingCheck([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.GSigma, vk.G}); err != nil {
+	if isOne, err := curve.PairingCheck([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.GSigmaNeg, vk.G}); err != nil {
 		return err
 	} else if !isOne {
 		return errors.New("proof rejected")
@@ -262,7 +262,7 @@ func BatchVerifyMultiVk(vk []VerifyingKey, commitments []curve.G1Affine, pok []c
 	pairingG1[0] = commitments[0]
 	var rI big.Int
 	for i := range vk {
-		pairingG2[i] = vk[i].GSigma
+		pairingG2[i] = vk[i].GSigmaNeg
 		if i != 0 {
 			r.BigInt(&rI)
 			pairingG1[i].ScalarMultiplication(&commitments[i], &rI)
@@ -337,7 +337,7 @@ func (vk *VerifyingKey) writeTo(enc *curve.Encoder) (int64, error) {
 	if err = enc.Encode(&vk.G); err != nil {
 		return enc.BytesWritten(), err
 	}
-	err = enc.Encode(&vk.GSigma)
+	err = enc.Encode(&vk.GSigmaNeg)
 	return enc.BytesWritten(), err
 }
 
@@ -356,6 +356,6 @@ func (vk *VerifyingKey) readFrom(r io.Reader, decOptions ...func(*curve.Decoder)
 	if err = dec.Decode(&vk.G); err != nil {
 		return dec.BytesRead(), err
 	}
-	err = dec.Decode(&vk.GSigma)
+	err = dec.Decode(&vk.GSigmaNeg)
 	return dec.BytesRead(), err
 }
diff --git a/ecc/bn254/fr/pedersen/pedersen_test.go b/ecc/bn254/fr/pedersen/pedersen_test.go
index 0aafe1a623..1dc736cddd 100644
--- a/ecc/bn254/fr/pedersen/pedersen_test.go
+++ b/ecc/bn254/fr/pedersen/pedersen_test.go
@@ -180,7 +180,7 @@ func TestMarshal(t *testing.T) {
 	)
 	vk.G, err = curve.RandomOnG2()
 	assert.NoError(t, err)
-	vk.GSigma, err = curve.RandomOnG2()
+	vk.GSigmaNeg, err = curve.RandomOnG2()
 	assert.NoError(t, err)
 
 	t.Run("ProvingKey -> Bytes -> ProvingKey must remain identical.", testutils.SerializationRoundTrip(&pk))

From 485db50997ef88794ac1b569becb391b343c6186 Mon Sep 17 00:00:00 2001
From: Arya Tabaie <15056835+Tabaie@users.noreply.github.com>
Date: Wed, 2 Oct 2024 16:40:24 -0500
Subject: [PATCH 072/114] build: generify

---
 ecc/bls12-377/fr/pedersen/pedersen.go              | 14 +++++++-------
 ecc/bls12-377/fr/pedersen/pedersen_test.go         |  2 +-
 ecc/bls12-381/fr/pedersen/pedersen.go              | 14 +++++++-------
 ecc/bls12-381/fr/pedersen/pedersen_test.go         |  2 +-
 ecc/bls24-315/fr/pedersen/pedersen.go              | 14 +++++++-------
 ecc/bls24-315/fr/pedersen/pedersen_test.go         |  2 +-
 ecc/bls24-317/fr/pedersen/pedersen.go              | 14 +++++++-------
 ecc/bls24-317/fr/pedersen/pedersen_test.go         |  2 +-
 ecc/bw6-633/fr/pedersen/pedersen.go                | 14 +++++++-------
 ecc/bw6-633/fr/pedersen/pedersen_test.go           |  2 +-
 ecc/bw6-761/fr/pedersen/pedersen.go                | 14 +++++++-------
 ecc/bw6-761/fr/pedersen/pedersen_test.go           |  2 +-
 .../generator/pedersen/template/pedersen.go.tmpl   | 12 ++++++------
 .../pedersen/template/pedersen.test.go.tmpl        |  2 +-
 14 files changed, 55 insertions(+), 55 deletions(-)

diff --git a/ecc/bls12-377/fr/pedersen/pedersen.go b/ecc/bls12-377/fr/pedersen/pedersen.go
index 9670e85c57..1ff3fda8d9 100644
--- a/ecc/bls12-377/fr/pedersen/pedersen.go
+++ b/ecc/bls12-377/fr/pedersen/pedersen.go
@@ -33,8 +33,8 @@ type ProvingKey struct {
 }
 
 type VerifyingKey struct {
-	G      curve.G2Affine
-	GSigma curve.G2Affine // GRootSigmaNeg = G^{-σ}
+	G         curve.G2Affine
+	GSigmaNeg curve.G2Affine // GSigmaNeg = G^{-σ}
 }
 
 func randomFrSizedBytes() ([]byte, error) {
@@ -94,7 +94,7 @@ func Setup(bases [][]curve.G1Affine, options ...SetupOption) (pk []ProvingKey, v
 	sigma.Add(sigma, big.NewInt(1))
 
 	sigmaNeg := new(big.Int).Neg(sigma)
-	vk.GSigma.ScalarMultiplication(&vk.G, sigmaNeg)
+	vk.GSigmaNeg.ScalarMultiplication(&vk.G, sigmaNeg)
 
 	pk = make([]ProvingKey, len(bases))
 	for i := range bases {
@@ -211,7 +211,7 @@ func (vk *VerifyingKey) Verify(commitment curve.G1Affine, knowledgeProof curve.G
 		return errors.New("subgroup check failed")
 	}
 
-	if isOne, err := curve.PairingCheck([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.GSigma, vk.G}); err != nil {
+	if isOne, err := curve.PairingCheck([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.GSigmaNeg, vk.G}); err != nil {
 		return err
 	} else if !isOne {
 		return errors.New("proof rejected")
@@ -262,7 +262,7 @@ func BatchVerifyMultiVk(vk []VerifyingKey, commitments []curve.G1Affine, pok []c
 	pairingG1[0] = commitments[0]
 	var rI big.Int
 	for i := range vk {
-		pairingG2[i] = vk[i].GSigma
+		pairingG2[i] = vk[i].GSigmaNeg
 		if i != 0 {
 			r.BigInt(&rI)
 			pairingG1[i].ScalarMultiplication(&commitments[i], &rI)
@@ -337,7 +337,7 @@ func (vk *VerifyingKey) writeTo(enc *curve.Encoder) (int64, error) {
 	if err = enc.Encode(&vk.G); err != nil {
 		return enc.BytesWritten(), err
 	}
-	err = enc.Encode(&vk.GSigma)
+	err = enc.Encode(&vk.GSigmaNeg)
 	return enc.BytesWritten(), err
 }
 
@@ -356,6 +356,6 @@ func (vk *VerifyingKey) readFrom(r io.Reader, decOptions ...func(*curve.Decoder)
 	if err = dec.Decode(&vk.G); err != nil {
 		return dec.BytesRead(), err
 	}
-	err = dec.Decode(&vk.GSigma)
+	err = dec.Decode(&vk.GSigmaNeg)
 	return dec.BytesRead(), err
 }
diff --git a/ecc/bls12-377/fr/pedersen/pedersen_test.go b/ecc/bls12-377/fr/pedersen/pedersen_test.go
index 227579ca9c..80718aa750 100644
--- a/ecc/bls12-377/fr/pedersen/pedersen_test.go
+++ b/ecc/bls12-377/fr/pedersen/pedersen_test.go
@@ -180,7 +180,7 @@ func TestMarshal(t *testing.T) {
 	)
 	vk.G, err = curve.RandomOnG2()
 	assert.NoError(t, err)
-	vk.GSigma, err = curve.RandomOnG2()
+	vk.GSigmaNeg, err = curve.RandomOnG2()
 	assert.NoError(t, err)
 
 	t.Run("ProvingKey -> Bytes -> ProvingKey must remain identical.", testutils.SerializationRoundTrip(&pk))
diff --git a/ecc/bls12-381/fr/pedersen/pedersen.go b/ecc/bls12-381/fr/pedersen/pedersen.go
index e49828fc72..09830a7759 100644
--- a/ecc/bls12-381/fr/pedersen/pedersen.go
+++ b/ecc/bls12-381/fr/pedersen/pedersen.go
@@ -33,8 +33,8 @@ type ProvingKey struct {
 }
 
 type VerifyingKey struct {
-	G      curve.G2Affine
-	GSigma curve.G2Affine // GRootSigmaNeg = G^{-σ}
+	G         curve.G2Affine
+	GSigmaNeg curve.G2Affine // GSigmaNeg = G^{-σ}
 }
 
 func randomFrSizedBytes() ([]byte, error) {
@@ -94,7 +94,7 @@ func Setup(bases [][]curve.G1Affine, options ...SetupOption) (pk []ProvingKey, v
 	sigma.Add(sigma, big.NewInt(1))
 
 	sigmaNeg := new(big.Int).Neg(sigma)
-	vk.GSigma.ScalarMultiplication(&vk.G, sigmaNeg)
+	vk.GSigmaNeg.ScalarMultiplication(&vk.G, sigmaNeg)
 
 	pk = make([]ProvingKey, len(bases))
 	for i := range bases {
@@ -211,7 +211,7 @@ func (vk *VerifyingKey) Verify(commitment curve.G1Affine, knowledgeProof curve.G
 		return errors.New("subgroup check failed")
 	}
 
-	if isOne, err := curve.PairingCheck([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.GSigma, vk.G}); err != nil {
+	if isOne, err := curve.PairingCheck([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.GSigmaNeg, vk.G}); err != nil {
 		return err
 	} else if !isOne {
 		return errors.New("proof rejected")
@@ -262,7 +262,7 @@ func BatchVerifyMultiVk(vk []VerifyingKey, commitments []curve.G1Affine, pok []c
 	pairingG1[0] = commitments[0]
 	var rI big.Int
 	for i := range vk {
-		pairingG2[i] = vk[i].GSigma
+		pairingG2[i] = vk[i].GSigmaNeg
 		if i != 0 {
 			r.BigInt(&rI)
 			pairingG1[i].ScalarMultiplication(&commitments[i], &rI)
@@ -337,7 +337,7 @@ func (vk *VerifyingKey) writeTo(enc *curve.Encoder) (int64, error) {
 	if err = enc.Encode(&vk.G); err != nil {
 		return enc.BytesWritten(), err
 	}
-	err = enc.Encode(&vk.GSigma)
+	err = enc.Encode(&vk.GSigmaNeg)
 	return enc.BytesWritten(), err
 }
 
@@ -356,6 +356,6 @@ func (vk *VerifyingKey) readFrom(r io.Reader, decOptions ...func(*curve.Decoder)
 	if err = dec.Decode(&vk.G); err != nil {
 		return dec.BytesRead(), err
 	}
-	err = dec.Decode(&vk.GSigma)
+	err = dec.Decode(&vk.GSigmaNeg)
 	return dec.BytesRead(), err
 }
diff --git a/ecc/bls12-381/fr/pedersen/pedersen_test.go b/ecc/bls12-381/fr/pedersen/pedersen_test.go
index ab04d7813a..833f0c66a1 100644
--- a/ecc/bls12-381/fr/pedersen/pedersen_test.go
+++ b/ecc/bls12-381/fr/pedersen/pedersen_test.go
@@ -180,7 +180,7 @@ func TestMarshal(t *testing.T) {
 	)
 	vk.G, err = curve.RandomOnG2()
 	assert.NoError(t, err)
-	vk.GSigma, err = curve.RandomOnG2()
+	vk.GSigmaNeg, err = curve.RandomOnG2()
 	assert.NoError(t, err)
 
 	t.Run("ProvingKey -> Bytes -> ProvingKey must remain identical.", testutils.SerializationRoundTrip(&pk))
diff --git a/ecc/bls24-315/fr/pedersen/pedersen.go b/ecc/bls24-315/fr/pedersen/pedersen.go
index 65375a022d..8bc6fef455 100644
--- a/ecc/bls24-315/fr/pedersen/pedersen.go
+++ b/ecc/bls24-315/fr/pedersen/pedersen.go
@@ -33,8 +33,8 @@ type ProvingKey struct {
 }
 
 type VerifyingKey struct {
-	G      curve.G2Affine
-	GSigma curve.G2Affine // GRootSigmaNeg = G^{-σ}
+	G         curve.G2Affine
+	GSigmaNeg curve.G2Affine // GSigmaNeg = G^{-σ}
 }
 
 func randomFrSizedBytes() ([]byte, error) {
@@ -94,7 +94,7 @@ func Setup(bases [][]curve.G1Affine, options ...SetupOption) (pk []ProvingKey, v
 	sigma.Add(sigma, big.NewInt(1))
 
 	sigmaNeg := new(big.Int).Neg(sigma)
-	vk.GSigma.ScalarMultiplication(&vk.G, sigmaNeg)
+	vk.GSigmaNeg.ScalarMultiplication(&vk.G, sigmaNeg)
 
 	pk = make([]ProvingKey, len(bases))
 	for i := range bases {
@@ -211,7 +211,7 @@ func (vk *VerifyingKey) Verify(commitment curve.G1Affine, knowledgeProof curve.G
 		return errors.New("subgroup check failed")
 	}
 
-	if isOne, err := curve.PairingCheck([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.GSigma, vk.G}); err != nil {
+	if isOne, err := curve.PairingCheck([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.GSigmaNeg, vk.G}); err != nil {
 		return err
 	} else if !isOne {
 		return errors.New("proof rejected")
@@ -262,7 +262,7 @@ func BatchVerifyMultiVk(vk []VerifyingKey, commitments []curve.G1Affine, pok []c
 	pairingG1[0] = commitments[0]
 	var rI big.Int
 	for i := range vk {
-		pairingG2[i] = vk[i].GSigma
+		pairingG2[i] = vk[i].GSigmaNeg
 		if i != 0 {
 			r.BigInt(&rI)
 			pairingG1[i].ScalarMultiplication(&commitments[i], &rI)
@@ -337,7 +337,7 @@ func (vk *VerifyingKey) writeTo(enc *curve.Encoder) (int64, error) {
 	if err = enc.Encode(&vk.G); err != nil {
 		return enc.BytesWritten(), err
 	}
-	err = enc.Encode(&vk.GSigma)
+	err = enc.Encode(&vk.GSigmaNeg)
 	return enc.BytesWritten(), err
 }
 
@@ -356,6 +356,6 @@ func (vk *VerifyingKey) readFrom(r io.Reader, decOptions ...func(*curve.Decoder)
 	if err = dec.Decode(&vk.G); err != nil {
 		return dec.BytesRead(), err
 	}
-	err = dec.Decode(&vk.GSigma)
+	err = dec.Decode(&vk.GSigmaNeg)
 	return dec.BytesRead(), err
 }
diff --git a/ecc/bls24-315/fr/pedersen/pedersen_test.go b/ecc/bls24-315/fr/pedersen/pedersen_test.go
index 78fbae5230..5c162db58d 100644
--- a/ecc/bls24-315/fr/pedersen/pedersen_test.go
+++ b/ecc/bls24-315/fr/pedersen/pedersen_test.go
@@ -180,7 +180,7 @@ func TestMarshal(t *testing.T) {
 	)
 	vk.G, err = curve.RandomOnG2()
 	assert.NoError(t, err)
-	vk.GSigma, err = curve.RandomOnG2()
+	vk.GSigmaNeg, err = curve.RandomOnG2()
 	assert.NoError(t, err)
 
 	t.Run("ProvingKey -> Bytes -> ProvingKey must remain identical.", testutils.SerializationRoundTrip(&pk))
diff --git a/ecc/bls24-317/fr/pedersen/pedersen.go b/ecc/bls24-317/fr/pedersen/pedersen.go
index bbf2b51d5d..9fca8b9fce 100644
--- a/ecc/bls24-317/fr/pedersen/pedersen.go
+++ b/ecc/bls24-317/fr/pedersen/pedersen.go
@@ -33,8 +33,8 @@ type ProvingKey struct {
 }
 
 type VerifyingKey struct {
-	G      curve.G2Affine
-	GSigma curve.G2Affine // GRootSigmaNeg = G^{-σ}
+	G         curve.G2Affine
+	GSigmaNeg curve.G2Affine // GSigmaNeg = G^{-σ}
 }
 
 func randomFrSizedBytes() ([]byte, error) {
@@ -94,7 +94,7 @@ func Setup(bases [][]curve.G1Affine, options ...SetupOption) (pk []ProvingKey, v
 	sigma.Add(sigma, big.NewInt(1))
 
 	sigmaNeg := new(big.Int).Neg(sigma)
-	vk.GSigma.ScalarMultiplication(&vk.G, sigmaNeg)
+	vk.GSigmaNeg.ScalarMultiplication(&vk.G, sigmaNeg)
 
 	pk = make([]ProvingKey, len(bases))
 	for i := range bases {
@@ -211,7 +211,7 @@ func (vk *VerifyingKey) Verify(commitment curve.G1Affine, knowledgeProof curve.G
 		return errors.New("subgroup check failed")
 	}
 
-	if isOne, err := curve.PairingCheck([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.GSigma, vk.G}); err != nil {
+	if isOne, err := curve.PairingCheck([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.GSigmaNeg, vk.G}); err != nil {
 		return err
 	} else if !isOne {
 		return errors.New("proof rejected")
@@ -262,7 +262,7 @@ func BatchVerifyMultiVk(vk []VerifyingKey, commitments []curve.G1Affine, pok []c
 	pairingG1[0] = commitments[0]
 	var rI big.Int
 	for i := range vk {
-		pairingG2[i] = vk[i].GSigma
+		pairingG2[i] = vk[i].GSigmaNeg
 		if i != 0 {
 			r.BigInt(&rI)
 			pairingG1[i].ScalarMultiplication(&commitments[i], &rI)
@@ -337,7 +337,7 @@ func (vk *VerifyingKey) writeTo(enc *curve.Encoder) (int64, error) {
 	if err = enc.Encode(&vk.G); err != nil {
 		return enc.BytesWritten(), err
 	}
-	err = enc.Encode(&vk.GSigma)
+	err = enc.Encode(&vk.GSigmaNeg)
 	return enc.BytesWritten(), err
 }
 
@@ -356,6 +356,6 @@ func (vk *VerifyingKey) readFrom(r io.Reader, decOptions ...func(*curve.Decoder)
 	if err = dec.Decode(&vk.G); err != nil {
 		return dec.BytesRead(), err
 	}
-	err = dec.Decode(&vk.GSigma)
+	err = dec.Decode(&vk.GSigmaNeg)
 	return dec.BytesRead(), err
 }
diff --git a/ecc/bls24-317/fr/pedersen/pedersen_test.go b/ecc/bls24-317/fr/pedersen/pedersen_test.go
index 9d3d359159..b732b3e025 100644
--- a/ecc/bls24-317/fr/pedersen/pedersen_test.go
+++ b/ecc/bls24-317/fr/pedersen/pedersen_test.go
@@ -180,7 +180,7 @@ func TestMarshal(t *testing.T) {
 	)
 	vk.G, err = curve.RandomOnG2()
 	assert.NoError(t, err)
-	vk.GSigma, err = curve.RandomOnG2()
+	vk.GSigmaNeg, err = curve.RandomOnG2()
 	assert.NoError(t, err)
 
 	t.Run("ProvingKey -> Bytes -> ProvingKey must remain identical.", testutils.SerializationRoundTrip(&pk))
diff --git a/ecc/bw6-633/fr/pedersen/pedersen.go b/ecc/bw6-633/fr/pedersen/pedersen.go
index 832088a1c2..be584fdcd3 100644
--- a/ecc/bw6-633/fr/pedersen/pedersen.go
+++ b/ecc/bw6-633/fr/pedersen/pedersen.go
@@ -33,8 +33,8 @@ type ProvingKey struct {
 }
 
 type VerifyingKey struct {
-	G      curve.G2Affine
-	GSigma curve.G2Affine // GRootSigmaNeg = G^{-σ}
+	G         curve.G2Affine
+	GSigmaNeg curve.G2Affine // GSigmaNeg = G^{-σ}
 }
 
 func randomFrSizedBytes() ([]byte, error) {
@@ -94,7 +94,7 @@ func Setup(bases [][]curve.G1Affine, options ...SetupOption) (pk []ProvingKey, v
 	sigma.Add(sigma, big.NewInt(1))
 
 	sigmaNeg := new(big.Int).Neg(sigma)
-	vk.GSigma.ScalarMultiplication(&vk.G, sigmaNeg)
+	vk.GSigmaNeg.ScalarMultiplication(&vk.G, sigmaNeg)
 
 	pk = make([]ProvingKey, len(bases))
 	for i := range bases {
@@ -211,7 +211,7 @@ func (vk *VerifyingKey) Verify(commitment curve.G1Affine, knowledgeProof curve.G
 		return errors.New("subgroup check failed")
 	}
 
-	if isOne, err := curve.PairingCheck([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.GSigma, vk.G}); err != nil {
+	if isOne, err := curve.PairingCheck([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.GSigmaNeg, vk.G}); err != nil {
 		return err
 	} else if !isOne {
 		return errors.New("proof rejected")
@@ -262,7 +262,7 @@ func BatchVerifyMultiVk(vk []VerifyingKey, commitments []curve.G1Affine, pok []c
 	pairingG1[0] = commitments[0]
 	var rI big.Int
 	for i := range vk {
-		pairingG2[i] = vk[i].GSigma
+		pairingG2[i] = vk[i].GSigmaNeg
 		if i != 0 {
 			r.BigInt(&rI)
 			pairingG1[i].ScalarMultiplication(&commitments[i], &rI)
@@ -337,7 +337,7 @@ func (vk *VerifyingKey) writeTo(enc *curve.Encoder) (int64, error) {
 	if err = enc.Encode(&vk.G); err != nil {
 		return enc.BytesWritten(), err
 	}
-	err = enc.Encode(&vk.GSigma)
+	err = enc.Encode(&vk.GSigmaNeg)
 	return enc.BytesWritten(), err
 }
 
@@ -356,6 +356,6 @@ func (vk *VerifyingKey) readFrom(r io.Reader, decOptions ...func(*curve.Decoder)
 	if err = dec.Decode(&vk.G); err != nil {
 		return dec.BytesRead(), err
 	}
-	err = dec.Decode(&vk.GSigma)
+	err = dec.Decode(&vk.GSigmaNeg)
 	return dec.BytesRead(), err
 }
diff --git a/ecc/bw6-633/fr/pedersen/pedersen_test.go b/ecc/bw6-633/fr/pedersen/pedersen_test.go
index f8389334d6..24e4e60948 100644
--- a/ecc/bw6-633/fr/pedersen/pedersen_test.go
+++ b/ecc/bw6-633/fr/pedersen/pedersen_test.go
@@ -180,7 +180,7 @@ func TestMarshal(t *testing.T) {
 	)
 	vk.G, err = curve.RandomOnG2()
 	assert.NoError(t, err)
-	vk.GSigma, err = curve.RandomOnG2()
+	vk.GSigmaNeg, err = curve.RandomOnG2()
 	assert.NoError(t, err)
 
 	t.Run("ProvingKey -> Bytes -> ProvingKey must remain identical.", testutils.SerializationRoundTrip(&pk))
diff --git a/ecc/bw6-761/fr/pedersen/pedersen.go b/ecc/bw6-761/fr/pedersen/pedersen.go
index 35860442d9..8b761fe4ac 100644
--- a/ecc/bw6-761/fr/pedersen/pedersen.go
+++ b/ecc/bw6-761/fr/pedersen/pedersen.go
@@ -33,8 +33,8 @@ type ProvingKey struct {
 }
 
 type VerifyingKey struct {
-	G      curve.G2Affine
-	GSigma curve.G2Affine // GRootSigmaNeg = G^{-σ}
+	G         curve.G2Affine
+	GSigmaNeg curve.G2Affine // GSigmaNeg = G^{-σ}
 }
 
 func randomFrSizedBytes() ([]byte, error) {
@@ -94,7 +94,7 @@ func Setup(bases [][]curve.G1Affine, options ...SetupOption) (pk []ProvingKey, v
 	sigma.Add(sigma, big.NewInt(1))
 
 	sigmaNeg := new(big.Int).Neg(sigma)
-	vk.GSigma.ScalarMultiplication(&vk.G, sigmaNeg)
+	vk.GSigmaNeg.ScalarMultiplication(&vk.G, sigmaNeg)
 
 	pk = make([]ProvingKey, len(bases))
 	for i := range bases {
@@ -211,7 +211,7 @@ func (vk *VerifyingKey) Verify(commitment curve.G1Affine, knowledgeProof curve.G
 		return errors.New("subgroup check failed")
 	}
 
-	if isOne, err := curve.PairingCheck([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.GSigma, vk.G}); err != nil {
+	if isOne, err := curve.PairingCheck([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.GSigmaNeg, vk.G}); err != nil {
 		return err
 	} else if !isOne {
 		return errors.New("proof rejected")
@@ -262,7 +262,7 @@ func BatchVerifyMultiVk(vk []VerifyingKey, commitments []curve.G1Affine, pok []c
 	pairingG1[0] = commitments[0]
 	var rI big.Int
 	for i := range vk {
-		pairingG2[i] = vk[i].GSigma
+		pairingG2[i] = vk[i].GSigmaNeg
 		if i != 0 {
 			r.BigInt(&rI)
 			pairingG1[i].ScalarMultiplication(&commitments[i], &rI)
@@ -337,7 +337,7 @@ func (vk *VerifyingKey) writeTo(enc *curve.Encoder) (int64, error) {
 	if err = enc.Encode(&vk.G); err != nil {
 		return enc.BytesWritten(), err
 	}
-	err = enc.Encode(&vk.GSigma)
+	err = enc.Encode(&vk.GSigmaNeg)
 	return enc.BytesWritten(), err
 }
 
@@ -356,6 +356,6 @@ func (vk *VerifyingKey) readFrom(r io.Reader, decOptions ...func(*curve.Decoder)
 	if err = dec.Decode(&vk.G); err != nil {
 		return dec.BytesRead(), err
 	}
-	err = dec.Decode(&vk.GSigma)
+	err = dec.Decode(&vk.GSigmaNeg)
 	return dec.BytesRead(), err
 }
diff --git a/ecc/bw6-761/fr/pedersen/pedersen_test.go b/ecc/bw6-761/fr/pedersen/pedersen_test.go
index 5a0bb96038..d8ba4a1f16 100644
--- a/ecc/bw6-761/fr/pedersen/pedersen_test.go
+++ b/ecc/bw6-761/fr/pedersen/pedersen_test.go
@@ -180,7 +180,7 @@ func TestMarshal(t *testing.T) {
 	)
 	vk.G, err = curve.RandomOnG2()
 	assert.NoError(t, err)
-	vk.GSigma, err = curve.RandomOnG2()
+	vk.GSigmaNeg, err = curve.RandomOnG2()
 	assert.NoError(t, err)
 
 	t.Run("ProvingKey -> Bytes -> ProvingKey must remain identical.", testutils.SerializationRoundTrip(&pk))
diff --git a/internal/generator/pedersen/template/pedersen.go.tmpl b/internal/generator/pedersen/template/pedersen.go.tmpl
index 496b9c253d..3497987dc0 100644
--- a/internal/generator/pedersen/template/pedersen.go.tmpl
+++ b/internal/generator/pedersen/template/pedersen.go.tmpl
@@ -16,7 +16,7 @@ type ProvingKey struct {
 
 type VerifyingKey struct {
 	G             curve.G2Affine
-	GSigma        curve.G2Affine // GRootSigmaNeg = G^{-σ}
+	GSigmaNeg     curve.G2Affine // GSigmaNeg = G^{-σ}
 }
 
 func randomFrSizedBytes() ([]byte, error) {
@@ -76,7 +76,7 @@ func Setup(bases [][]curve.G1Affine, options ...SetupOption) (pk []ProvingKey, v
 	sigma.Add(sigma, big.NewInt(1))
 
 	sigmaNeg := new(big.Int).Neg(sigma)
-	vk.GSigma.ScalarMultiplication(&vk.G, sigmaNeg)
+	vk.GSigmaNeg.ScalarMultiplication(&vk.G, sigmaNeg)
 
 	pk = make([]ProvingKey, len(bases))
 	for i := range bases {
@@ -193,7 +193,7 @@ func (vk *VerifyingKey) Verify(commitment curve.G1Affine, knowledgeProof curve.G
 		return errors.New("subgroup check failed")
 	}
 
-	if isOne, err := curve.PairingCheck([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.GSigma, vk.G}); err != nil {
+	if isOne, err := curve.PairingCheck([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.GSigmaNeg, vk.G}); err != nil {
 		return err
 	} else if !isOne {
 		return errors.New("proof rejected")
@@ -244,7 +244,7 @@ func BatchVerifyMultiVk(vk []VerifyingKey, commitments []curve.G1Affine, pok []c
 	pairingG1[0] = commitments[0]
 	var rI big.Int
 	for i := range vk {
-		pairingG2[i] = vk[i].GSigma
+		pairingG2[i] = vk[i].GSigmaNeg
 		if i != 0 {
 			r.BigInt(&rI)
 			pairingG1[i].ScalarMultiplication(&commitments[i], &rI)
@@ -319,7 +319,7 @@ func (vk *VerifyingKey) writeTo(enc *curve.Encoder) (int64, error) {
 	if err = enc.Encode(&vk.G); err != nil {
 		return enc.BytesWritten(), err
 	}
-	err = enc.Encode(&vk.GSigma)
+	err = enc.Encode(&vk.GSigmaNeg)
 	return enc.BytesWritten(), err
 }
 
@@ -338,6 +338,6 @@ func (vk *VerifyingKey) readFrom(r io.Reader, decOptions ...func(*curve.Decoder)
 	if err = dec.Decode(&vk.G); err != nil {
 		return dec.BytesRead(), err
 	}
-	err = dec.Decode(&vk.GSigma)
+	err = dec.Decode(&vk.GSigmaNeg)
 	return dec.BytesRead(), err
 }
\ No newline at end of file
diff --git a/internal/generator/pedersen/template/pedersen.test.go.tmpl b/internal/generator/pedersen/template/pedersen.test.go.tmpl
index fdfa2f4fde..571e6ece6e 100644
--- a/internal/generator/pedersen/template/pedersen.test.go.tmpl
+++ b/internal/generator/pedersen/template/pedersen.test.go.tmpl
@@ -162,7 +162,7 @@ func TestMarshal(t *testing.T) {
 	)
 	vk.G, err = curve.RandomOnG2()
 	assert.NoError(t, err)
-	vk.GSigma, err = curve.RandomOnG2()
+	vk.GSigmaNeg, err = curve.RandomOnG2()
 	assert.NoError(t, err)
 
 	t.Run("ProvingKey -> Bytes -> ProvingKey must remain identical.", testutils.SerializationRoundTrip(&pk))

From 507de623a0cd11ebe1fd3e858e12612090e38670 Mon Sep 17 00:00:00 2001
From: Youssef El Housni <youssef.housni21@gmail.com>
Date: Thu, 3 Oct 2024 15:30:25 -0400
Subject: [PATCH 073/114] perf(eisentein/half-GCD): only 1 remainder option

---
 field/eisenstein/eisenstein.go | 14 +++++++++-----
 1 file changed, 9 insertions(+), 5 deletions(-)

diff --git a/field/eisenstein/eisenstein.go b/field/eisenstein/eisenstein.go
index 9fe12ad832..1b1f2a0666 100644
--- a/field/eisenstein/eisenstein.go
+++ b/field/eisenstein/eisenstein.go
@@ -120,6 +120,7 @@ func (z *ComplexNumber) Quo(x, y *ComplexNumber) *ComplexNumber {
 	return z
 }
 
+// Rem sets z to the minimum of all possible remainders of x by y, and returns z.
 func (z *ComplexNumber) Rem(x, y, q *ComplexNumber) *ComplexNumber {
 	var t ComplexNumber
 	z.Sub(x, t.Mul(y, q))
@@ -147,7 +148,8 @@ func (z *ComplexNumber) QuoRem(x, y, r *ComplexNumber) (*ComplexNumber, *Complex
 	z.Mul(x, z)
 	z.A0.Div(&z.A0, norm)
 	z.A1.Div(&z.A1, norm)
-	r.Rem(x, y, z)
+	r.Mul(y, z)
+	r.Sub(x, r)
 
 	return z, r
 }
@@ -167,7 +169,7 @@ func Min(z ...*ComplexNumber) *ComplexNumber {
 // This outputs w, v, u s.t. w = a*u + b*v.
 func HalfGCD(a, b *ComplexNumber) [3]*ComplexNumber {
 
-	var aRun, bRun, u, v, u_, v_, quotient, remainder, t1, t2 ComplexNumber
+	var aRun, bRun, u, v, u_, v_, quotient, remainder, t, t1, t2 ComplexNumber
 	var sqrt big.Int
 
 	aRun.Set(a)
@@ -179,10 +181,12 @@ func HalfGCD(a, b *ComplexNumber) [3]*ComplexNumber {
 
 	// Eisenstein integers form an Euclidean domain for the norm
 	sqrt.Sqrt(a.Norm())
-	for bRun.Norm().Cmp(&sqrt) == 1 {
+	for bRun.Norm().Cmp(&sqrt) >= 0 {
 		quotient.QuoRem(&aRun, &bRun, &remainder)
-		t1.Rem(&u, &u_, &quotient)
-		t2.Rem(&v, &v_, &quotient)
+		t.Mul(&u_, &quotient)
+		t1.Sub(&u, &t)
+		t.Mul(&v_, &quotient)
+		t2.Sub(&v, &t)
 		aRun.Set(&bRun)
 		u.Set(&u_)
 		v.Set(&v_)

From 2e01a9f52a522c3630fec533ec5db066751ccd08 Mon Sep 17 00:00:00 2001
From: Youssef El Housni <youssef.housni21@gmail.com>
Date: Thu, 3 Oct 2024 15:53:16 -0400
Subject: [PATCH 074/114] refactor: apply review suggestions

---
 field/eisenstein/eisenstein.go      | 109 +++++++++++-----------------
 field/eisenstein/eisenstein_test.go |  22 +++---
 2 files changed, 54 insertions(+), 77 deletions(-)

diff --git a/field/eisenstein/eisenstein.go b/field/eisenstein/eisenstein.go
index 1b1f2a0666..e809154133 100644
--- a/field/eisenstein/eisenstein.go
+++ b/field/eisenstein/eisenstein.go
@@ -6,7 +6,18 @@ import (
 
 // A ComplexNumber represents an arbitrary-precision Eisenstein integer.
 type ComplexNumber struct {
-	A0, A1 big.Int
+	A0, A1 *big.Int
+}
+
+func (z *ComplexNumber) init() {
+	if z.A0 == nil {
+		z.A0 = new(big.Int)
+
+	}
+	if z.A1 == nil {
+		z.A1 = new(big.Int)
+
+	}
 }
 
 // String implements Stringer interface for fancy printing
@@ -16,55 +27,60 @@ func (z *ComplexNumber) String() string {
 
 // Equal returns true if z equals x, false otherwise
 func (z *ComplexNumber) Equal(x *ComplexNumber) bool {
-	return z.A0.Cmp(&x.A0) == 0 && z.A1.Cmp(&x.A1) == 0
+	return z.A0.Cmp(x.A0) == 0 && z.A1.Cmp(x.A1) == 0
 }
 
 // Set sets z to x, and returns z.
 func (z *ComplexNumber) Set(x *ComplexNumber) *ComplexNumber {
-	z.A0.Set(&x.A0)
-	z.A1.Set(&x.A1)
+	z.init()
+	z.A0.Set(x.A0)
+	z.A1.Set(x.A1)
 	return z
 }
 
 // SetZero sets z to 0, and returns z.
 func (z *ComplexNumber) SetZero() *ComplexNumber {
-	z.A0 = *big.NewInt(0)
-	z.A1 = *big.NewInt(0)
+	z.A0 = big.NewInt(0)
+	z.A1 = big.NewInt(0)
 	return z
 }
 
 // SetOne sets z to 1, and returns z.
 func (z *ComplexNumber) SetOne() *ComplexNumber {
-	z.A0 = *big.NewInt(1)
-	z.A1 = *big.NewInt(0)
+	z.A0 = big.NewInt(1)
+	z.A1 = big.NewInt(0)
 	return z
 }
 
 // Neg sets z to the negative of x, and returns z.
 func (z *ComplexNumber) Neg(x *ComplexNumber) *ComplexNumber {
-	z.A0.Neg(&x.A0)
-	z.A1.Neg(&x.A1)
+	z.init()
+	z.A0.Neg(x.A0)
+	z.A1.Neg(x.A1)
 	return z
 }
 
 // Conjugate sets z to the conjugate of x, and returns z.
 func (z *ComplexNumber) Conjugate(x *ComplexNumber) *ComplexNumber {
-	z.A0.Sub(&x.A0, &x.A1)
-	z.A1.Neg(&x.A1)
+	z.init()
+	z.A0.Sub(x.A0, x.A1)
+	z.A1.Neg(x.A1)
 	return z
 }
 
 // Add sets z to the sum of x and y, and returns z.
 func (z *ComplexNumber) Add(x, y *ComplexNumber) *ComplexNumber {
-	z.A0.Add(&x.A0, &y.A0)
-	z.A1.Add(&x.A1, &y.A1)
+	z.init()
+	z.A0.Add(x.A0, y.A0)
+	z.A1.Add(x.A1, y.A1)
 	return z
 }
 
 // Sub sets z to the difference of x and y, and returns z.
 func (z *ComplexNumber) Sub(x, y *ComplexNumber) *ComplexNumber {
-	z.A0.Sub(&x.A0, &y.A0)
-	z.A1.Sub(&x.A1, &y.A1)
+	z.init()
+	z.A0.Sub(x.A0, y.A0)
+	z.A1.Sub(x.A1, y.A1)
 	return z
 }
 
@@ -74,13 +90,14 @@ func (z *ComplexNumber) Sub(x, y *ComplexNumber) *ComplexNumber {
 //
 //	(x0+x1ω)(y0+y1ω) = (x0y0-x1y1) + (x0y1+x1y0-x1y1)ω
 func (z *ComplexNumber) Mul(x, y *ComplexNumber) *ComplexNumber {
+	z.init()
 	var t [3]big.Int
 	var z0, z1 big.Int
-	t[0].Mul(&x.A0, &y.A0)
-	t[1].Mul(&x.A1, &y.A1)
+	t[0].Mul(x.A0, y.A0)
+	t[1].Mul(x.A1, y.A1)
 	z0.Sub(&t[0], &t[1])
-	t[0].Mul(&x.A0, &y.A1)
-	t[2].Mul(&x.A1, &y.A0)
+	t[0].Mul(x.A0, y.A1)
+	t[2].Mul(x.A1, y.A0)
 	t[0].Add(&t[0], &t[2])
 	z1.Sub(&t[0], &t[1])
 	z.A0.Set(&z0)
@@ -97,47 +114,16 @@ func (z *ComplexNumber) Norm() *big.Int {
 	norm := new(big.Int)
 	temp := new(big.Int)
 	norm.Add(
-		norm.Mul(&z.A0, &z.A0),
-		temp.Mul(&z.A1, &z.A1),
+		norm.Mul(z.A0, z.A0),
+		temp.Mul(z.A1, z.A1),
 	)
 	norm.Sub(
 		norm,
-		temp.Mul(&z.A0, &z.A1),
+		temp.Mul(z.A0, z.A1),
 	)
 	return norm
 }
 
-// Quo sets z to the quotient of x and y, and returns z.
-func (z *ComplexNumber) Quo(x, y *ComplexNumber) *ComplexNumber {
-	norm := y.Norm()
-	if norm.Cmp(big.NewInt(0)) == 0 {
-		panic("division by zero")
-	}
-	z.Conjugate(y)
-	z.Mul(x, z)
-	z.A0.Div(&z.A0, norm)
-	z.A1.Div(&z.A1, norm)
-	return z
-}
-
-// Rem sets z to the minimum of all possible remainders of x by y, and returns z.
-func (z *ComplexNumber) Rem(x, y, q *ComplexNumber) *ComplexNumber {
-	var t ComplexNumber
-	z.Sub(x, t.Mul(y, q))
-	var r1, r2, r3, r4, r5, r6, w, wy, w2y ComplexNumber
-	w.A1.SetUint64(1)
-	wy.Mul(&w, y)
-	w2y.Mul(&w, &wy)
-	r1.Sub(z, y)
-	r2.Add(z, y)
-	r3.Sub(z, &wy)
-	r4.Add(z, &wy)
-	r5.Sub(z, &w2y)
-	r6.Add(z, &w2y)
-	z = Min(z, &r1, &r2, &r3, &r4, &r5, &r6)
-	return z
-}
-
 // QuoRem sets z to the quotient of x and y, r to the remainder, and returns z and r.
 func (z *ComplexNumber) QuoRem(x, y, r *ComplexNumber) (*ComplexNumber, *ComplexNumber) {
 	norm := y.Norm()
@@ -146,25 +132,14 @@ func (z *ComplexNumber) QuoRem(x, y, r *ComplexNumber) (*ComplexNumber, *Complex
 	}
 	z.Conjugate(y)
 	z.Mul(x, z)
-	z.A0.Div(&z.A0, norm)
-	z.A1.Div(&z.A1, norm)
+	z.A0.Div(z.A0, norm)
+	z.A1.Div(z.A1, norm)
 	r.Mul(y, z)
 	r.Sub(x, r)
 
 	return z, r
 }
 
-// Min returns the minimum of z... with respect to the norm.
-func Min(z ...*ComplexNumber) *ComplexNumber {
-	min := z[0]
-	for _, v := range z {
-		if v.Norm().Cmp(min.Norm()) == -1 {
-			min = v
-		}
-	}
-	return min
-}
-
 // HalfGCD returns the rational reconstruction of a, b.
 // This outputs w, v, u s.t. w = a*u + b*v.
 func HalfGCD(a, b *ComplexNumber) [3]*ComplexNumber {
diff --git a/field/eisenstein/eisenstein_test.go b/field/eisenstein/eisenstein_test.go
index 89c7dc5d44..6aff795f92 100644
--- a/field/eisenstein/eisenstein_test.go
+++ b/field/eisenstein/eisenstein_test.go
@@ -246,7 +246,7 @@ func GenNumber(boundSize int64) gopter.Gen {
 		var bound big.Int
 		bound.Exp(big.NewInt(2), big.NewInt(boundSize), nil)
 		elmt, _ := rand.Int(genParams.Rng, &bound)
-		genResult := gopter.NewGenResult(*elmt, gopter.NoShrinker)
+		genResult := gopter.NewGenResult(elmt, gopter.NoShrinker)
 		return genResult
 	}
 }
@@ -257,21 +257,23 @@ func GenComplexNumber(boundSize int64) gopter.Gen {
 		GenNumber(boundSize),
 		GenNumber(boundSize),
 	).Map(func(values []interface{}) *ComplexNumber {
-		return &ComplexNumber{A0: values[0].(big.Int), A1: values[1].(big.Int)}
+		return &ComplexNumber{A0: values[0].(*big.Int), A1: values[1].(*big.Int)}
 	})
 }
 
 // bench
+var benchRes [3]*ComplexNumber
+
 func BenchmarkHalfGCD(b *testing.B) {
-	var prime, _ = new(big.Int).SetString("7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed", 16) // 2^255 - 19
-	a0, _ := rand.Int(rand.Reader, prime)
-	a1, _ := rand.Int(rand.Reader, prime)
-	c0, _ := rand.Int(rand.Reader, prime)
-	c1, _ := rand.Int(rand.Reader, prime)
-	a := ComplexNumber{A0: *a0, A1: *a1}
-	c := ComplexNumber{A0: *c0, A1: *c1}
+	var n, _ = new(big.Int).SetString("100000000000000000000000000000000", 16) // 2^128
+	a0, _ := rand.Int(rand.Reader, n)
+	a1, _ := rand.Int(rand.Reader, n)
+	c0, _ := rand.Int(rand.Reader, n)
+	c1, _ := rand.Int(rand.Reader, n)
+	a := ComplexNumber{A0: a0, A1: a1}
+	c := ComplexNumber{A0: c0, A1: c1}
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		_ = HalfGCD(&a, &c)
+		benchRes = HalfGCD(&a, &c)
 	}
 }

From a357b132953e9adad67ac6625b19dc281479ea95 Mon Sep 17 00:00:00 2001
From: Ivo Kubjas <ivo.kubjas@consensys.net>
Date: Fri, 4 Oct 2024 15:14:10 +0200
Subject: [PATCH 075/114] chore: use golint option to include generated files
 (#549)

---
 .github/workflows/pr.yml   | 5 -----
 .github/workflows/push.yml | 5 -----
 .golangci.yml              | 2 ++
 3 files changed, 2 insertions(+), 10 deletions(-)

diff --git a/.github/workflows/pr.yml b/.github/workflows/pr.yml
index b702fcdd5c..6da517779b 100644
--- a/.github/workflows/pr.yml
+++ b/.github/workflows/pr.yml
@@ -24,11 +24,6 @@ jobs:
         git update-index --assume-unchanged go.sum
         if [[ -n $(git status --porcelain) ]]; then echo "git repo is dirty after running go generate -- please don't modify generated files"; echo $(git diff);echo $(git status --porcelain); exit 1; fi
 
-     # hack to ensure golanglint process generated files
-    - name: remove "generated by" comments from generated files 
-      run: |
-        find . -type f -name '*.go' -exec sed -i 's/Code generated by .* DO NOT EDIT/FOO/g' {} \;
-      # on macos: find . -type f -name '*.go' -exec sed -i '' -E 's/Code generated by .* DO NOT EDIT/FOO/g' {} \;
     - name: golangci-lint
       uses: golangci/golangci-lint-action@v6
       with:
diff --git a/.github/workflows/push.yml b/.github/workflows/push.yml
index 64f340fea7..1ed9bfa9bc 100644
--- a/.github/workflows/push.yml
+++ b/.github/workflows/push.yml
@@ -27,11 +27,6 @@ jobs:
         git update-index --assume-unchanged go.sum
         if [[ -n $(git status --porcelain) ]]; then echo "git repo is dirty after running go generate -- please don't modify generated files"; echo $(git diff);echo $(git status --porcelain); exit 1; fi
 
-     # hack to ensure golanglint process generated files
-    - name: remove "generated by" comments from generated files 
-      run: |
-        find . -type f -name '*.go' -exec sed -i 's/Code generated by .* DO NOT EDIT/FOO/g' {} \;
-      # on macos: find . -type f -name '*.go' -exec sed -i '' -E 's/Code generated by .* DO NOT EDIT/FOO/g' {} \;
     - name: golangci-lint
       uses: golangci/golangci-lint-action@v6
       with:
diff --git a/.golangci.yml b/.golangci.yml
index e30a16a61e..414732bfef 100644
--- a/.golangci.yml
+++ b/.golangci.yml
@@ -12,5 +12,7 @@ linters-settings:
   gosec:
     excludes:
       - G115 # Conversions from int -> uint etc.
+issues:
+  exclude-generated: disable
 run:
   issues-exit-code: 1
\ No newline at end of file

From 7fa434fd77cd447e837a4584b0d82089b74f45d4 Mon Sep 17 00:00:00 2001
From: Ivo Kubjas <ivo.kubjas@consensys.net>
Date: Fri, 4 Oct 2024 13:20:09 +0000
Subject: [PATCH 076/114] chore: ignore gosec false positive

---
 ecc/bls12-377/shplonk/shplonk_test.go                    | 2 +-
 ecc/bls12-381/shplonk/shplonk_test.go                    | 2 +-
 ecc/bls24-315/shplonk/shplonk_test.go                    | 2 +-
 ecc/bls24-317/shplonk/shplonk_test.go                    | 2 +-
 ecc/bn254/shplonk/shplonk_test.go                        | 2 +-
 ecc/bw6-633/shplonk/shplonk_test.go                      | 2 +-
 ecc/bw6-761/shplonk/shplonk_test.go                      | 2 +-
 internal/generator/shplonk/template/shplonk.test.go.tmpl | 2 +-
 8 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/ecc/bls12-377/shplonk/shplonk_test.go b/ecc/bls12-377/shplonk/shplonk_test.go
index 9333499557..9b321fa4ef 100644
--- a/ecc/bls12-377/shplonk/shplonk_test.go
+++ b/ecc/bls12-377/shplonk/shplonk_test.go
@@ -72,7 +72,7 @@ func TestOpening(t *testing.T) {
 	nbPolys := 2
 	sizePoly := make([]int, nbPolys)
 	for i := 0; i < nbPolys; i++ {
-		sizePoly[i] = rand.Intn(10) + 2
+		sizePoly[i] = rand.Intn(10) + 2 //nolint: gosec // G404, no strong PRNG needed here
 	}
 	polys := make([][]fr.Element, nbPolys)
 	for i := 0; i < nbPolys; i++ {
diff --git a/ecc/bls12-381/shplonk/shplonk_test.go b/ecc/bls12-381/shplonk/shplonk_test.go
index b007b75590..e2295bbe36 100644
--- a/ecc/bls12-381/shplonk/shplonk_test.go
+++ b/ecc/bls12-381/shplonk/shplonk_test.go
@@ -72,7 +72,7 @@ func TestOpening(t *testing.T) {
 	nbPolys := 2
 	sizePoly := make([]int, nbPolys)
 	for i := 0; i < nbPolys; i++ {
-		sizePoly[i] = rand.Intn(10) + 2
+		sizePoly[i] = rand.Intn(10) + 2 //nolint: gosec // G404, no strong PRNG needed here
 	}
 	polys := make([][]fr.Element, nbPolys)
 	for i := 0; i < nbPolys; i++ {
diff --git a/ecc/bls24-315/shplonk/shplonk_test.go b/ecc/bls24-315/shplonk/shplonk_test.go
index c97b6dda88..4f7f41f122 100644
--- a/ecc/bls24-315/shplonk/shplonk_test.go
+++ b/ecc/bls24-315/shplonk/shplonk_test.go
@@ -72,7 +72,7 @@ func TestOpening(t *testing.T) {
 	nbPolys := 2
 	sizePoly := make([]int, nbPolys)
 	for i := 0; i < nbPolys; i++ {
-		sizePoly[i] = rand.Intn(10) + 2
+		sizePoly[i] = rand.Intn(10) + 2 //nolint: gosec // G404, no strong PRNG needed here
 	}
 	polys := make([][]fr.Element, nbPolys)
 	for i := 0; i < nbPolys; i++ {
diff --git a/ecc/bls24-317/shplonk/shplonk_test.go b/ecc/bls24-317/shplonk/shplonk_test.go
index bd89089b78..33d055815e 100644
--- a/ecc/bls24-317/shplonk/shplonk_test.go
+++ b/ecc/bls24-317/shplonk/shplonk_test.go
@@ -72,7 +72,7 @@ func TestOpening(t *testing.T) {
 	nbPolys := 2
 	sizePoly := make([]int, nbPolys)
 	for i := 0; i < nbPolys; i++ {
-		sizePoly[i] = rand.Intn(10) + 2
+		sizePoly[i] = rand.Intn(10) + 2 //nolint: gosec // G404, no strong PRNG needed here
 	}
 	polys := make([][]fr.Element, nbPolys)
 	for i := 0; i < nbPolys; i++ {
diff --git a/ecc/bn254/shplonk/shplonk_test.go b/ecc/bn254/shplonk/shplonk_test.go
index 88fa11fc0a..d0558c4725 100644
--- a/ecc/bn254/shplonk/shplonk_test.go
+++ b/ecc/bn254/shplonk/shplonk_test.go
@@ -72,7 +72,7 @@ func TestOpening(t *testing.T) {
 	nbPolys := 2
 	sizePoly := make([]int, nbPolys)
 	for i := 0; i < nbPolys; i++ {
-		sizePoly[i] = rand.Intn(10) + 2
+		sizePoly[i] = rand.Intn(10) + 2 //nolint: gosec // G404, no strong PRNG needed here
 	}
 	polys := make([][]fr.Element, nbPolys)
 	for i := 0; i < nbPolys; i++ {
diff --git a/ecc/bw6-633/shplonk/shplonk_test.go b/ecc/bw6-633/shplonk/shplonk_test.go
index dcb46ffeea..2cc4d27f57 100644
--- a/ecc/bw6-633/shplonk/shplonk_test.go
+++ b/ecc/bw6-633/shplonk/shplonk_test.go
@@ -72,7 +72,7 @@ func TestOpening(t *testing.T) {
 	nbPolys := 2
 	sizePoly := make([]int, nbPolys)
 	for i := 0; i < nbPolys; i++ {
-		sizePoly[i] = rand.Intn(10) + 2
+		sizePoly[i] = rand.Intn(10) + 2 //nolint: gosec // G404, no strong PRNG needed here
 	}
 	polys := make([][]fr.Element, nbPolys)
 	for i := 0; i < nbPolys; i++ {
diff --git a/ecc/bw6-761/shplonk/shplonk_test.go b/ecc/bw6-761/shplonk/shplonk_test.go
index 1e4ecc2d81..bcdbccea65 100644
--- a/ecc/bw6-761/shplonk/shplonk_test.go
+++ b/ecc/bw6-761/shplonk/shplonk_test.go
@@ -72,7 +72,7 @@ func TestOpening(t *testing.T) {
 	nbPolys := 2
 	sizePoly := make([]int, nbPolys)
 	for i := 0; i < nbPolys; i++ {
-		sizePoly[i] = rand.Intn(10) + 2
+		sizePoly[i] = rand.Intn(10) + 2 //nolint: gosec // G404, no strong PRNG needed here
 	}
 	polys := make([][]fr.Element, nbPolys)
 	for i := 0; i < nbPolys; i++ {
diff --git a/internal/generator/shplonk/template/shplonk.test.go.tmpl b/internal/generator/shplonk/template/shplonk.test.go.tmpl
index 775995c032..d8ff5b8adb 100644
--- a/internal/generator/shplonk/template/shplonk.test.go.tmpl
+++ b/internal/generator/shplonk/template/shplonk.test.go.tmpl
@@ -55,7 +55,7 @@ func TestOpening(t *testing.T) {
 	nbPolys := 2
 	sizePoly := make([]int, nbPolys)
 	for i := 0; i < nbPolys; i++ {
-		sizePoly[i] = rand.Intn(10) + 2
+		sizePoly[i] = rand.Intn(10) + 2 //nolint: gosec // G404, no strong PRNG needed here
 	}
 	polys := make([][]fr.Element, nbPolys)
 	for i := 0; i < nbPolys; i++ {

From e26bbdf97a4ae5edce421ca693a1464e20a3bec1 Mon Sep 17 00:00:00 2001
From: Gautam Botrel <gautam.botrel@gmail.com>
Date: Mon, 7 Oct 2024 09:56:20 -0500
Subject: [PATCH 077/114] perf: adds AVX512 implementations of vector.Sum,
 vector.InnerProduct + assembly refactor (#547)

* feat: asm Vector sum slower, no avx

* checkpoint

* checkpoint

* checkpoint

* feat: add vec.Sum AVX512

* test: make odd bound for better test case

* build: make linter happy

* fix: update bound for vec sum to match parameter choices

* perf: loop 8 by 8, cosmetics

* style: cosmetics

* test: better sum test

* test: more test

* refactor: move common assembly routine in subfolder (#545)

* refactor: move common assembly routines in root

* build: make linter happier

* style: cosmetics

* test: start fixing integration test

* style: factorize mul documentation

* feat: add .ASMVector and fix integartion test

* test: fix 32bit test

* test: fix previous commit

* doc: add reference for reduction algorithm

* feat: use latest bavard for avx512 instructions

* feat: added purego InnerProduct

* checkpoint wip

* checkpoint

* refactor: checkpoint

* test: better tests for vec ops

* checkpoint

* test: add more tests for vector ops

* feat: update bavard and use better syntax in asm

* test: make benchmarks on varying sizes

* test: bench on larger vector

* test: bench on larger vector

* checkpoint

* checkpoint

* checkpoint

* checkpoint

* checkpoint

* checkpoint

* checkpoint

* checkpoint

* checkpoint

* checkpoint

* checkpoint

* checkpoint

* checkpoint

* checkpoint

* checkpoint

* refactor: use defines for mul

* feat: make use of defines in assembly

* checkpoint

* style: code cleaning

* perf: prefetches in vec ops

* perf: minor adjustements

* style: costmetics

* feat: handle case where len(vec)==0

* fix: address PR review comments
---
 ecc/bls12-377/fp/{asm.go => asm_adx.go}       |    0
 ecc/bls12-377/fp/element.go                   |   28 +-
 ecc/bls12-377/fp/element_mul_amd64.s          |  857 -----
 ecc/bls12-377/fp/element_ops_amd64.go         |   44 +-
 ecc/bls12-377/fp/element_ops_amd64.s          |  306 +-
 ecc/bls12-377/fp/element_ops_purego.go        |   44 +-
 ecc/bls12-377/fp/element_test.go              |  142 +-
 ecc/bls12-377/fp/vector.go                    |   45 +
 ecc/bls12-377/fp/vector_test.go               |  285 ++
 ecc/bls12-377/fr/{asm.go => asm_adx.go}       |    0
 ecc/bls12-377/fr/asm_avx.go                   |   27 +
 ecc/bls12-377/fr/asm_noavx.go                 |   22 +
 ecc/bls12-377/fr/element.go                   |   31 +-
 ecc/bls12-377/fr/element_mul_amd64.s          |  487 ---
 ecc/bls12-377/fr/element_ops_amd64.go         |  155 +-
 ecc/bls12-377/fr/element_ops_amd64.s          |  627 +---
 ecc/bls12-377/fr/element_ops_purego.go        |   63 +-
 ecc/bls12-377/fr/element_test.go              |  134 +-
 ecc/bls12-377/fr/vector.go                    |   26 +
 ecc/bls12-377/fr/vector_test.go               |  281 ++
 ecc/bls12-377/internal/fptower/e2_amd64.go    |   27 +
 ecc/bls12-377/internal/fptower/e2_amd64.s     |   50 +-
 ecc/bls12-381/fp/{asm.go => asm_adx.go}       |    0
 ecc/bls12-381/fp/element.go                   |   28 +-
 ecc/bls12-381/fp/element_mul_amd64.s          |  857 -----
 ecc/bls12-381/fp/element_ops_amd64.go         |   44 +-
 ecc/bls12-381/fp/element_ops_amd64.s          |  306 +-
 ecc/bls12-381/fp/element_ops_purego.go        |   44 +-
 ecc/bls12-381/fp/element_test.go              |  142 +-
 ecc/bls12-381/fp/vector.go                    |   45 +
 ecc/bls12-381/fp/vector_test.go               |  285 ++
 ecc/bls12-381/fr/{asm.go => asm_adx.go}       |    0
 ecc/bls12-381/fr/asm_avx.go                   |   27 +
 ecc/bls12-381/fr/asm_noavx.go                 |   22 +
 ecc/bls12-381/fr/element.go                   |   31 +-
 ecc/bls12-381/fr/element_mul_amd64.s          |  487 ---
 ecc/bls12-381/fr/element_ops_amd64.go         |  155 +-
 ecc/bls12-381/fr/element_ops_amd64.s          |  627 +---
 ecc/bls12-381/fr/element_ops_purego.go        |   63 +-
 ecc/bls12-381/fr/element_test.go              |  134 +-
 ecc/bls12-381/fr/vector.go                    |   26 +
 ecc/bls12-381/fr/vector_test.go               |  281 ++
 ecc/bls12-381/internal/fptower/e2_amd64.go    |   27 +
 ecc/bls12-381/internal/fptower/e2_amd64.s     | 2745 ++--------------
 ecc/bls24-315/fp/{asm.go => asm_adx.go}       |    0
 ecc/bls24-315/fp/element.go                   |   28 +-
 ecc/bls24-315/fp/element_mul_amd64.s          |  656 ----
 ecc/bls24-315/fp/element_ops_amd64.go         |   44 +-
 ecc/bls24-315/fp/element_ops_amd64.s          |  272 +-
 ecc/bls24-315/fp/element_ops_purego.go        |   44 +-
 ecc/bls24-315/fp/element_test.go              |  138 +-
 ecc/bls24-315/fp/vector.go                    |   45 +
 ecc/bls24-315/fp/vector_test.go               |  283 ++
 ecc/bls24-315/fr/{asm.go => asm_adx.go}       |    0
 ecc/bls24-315/fr/asm_avx.go                   |   27 +
 ecc/bls24-315/fr/asm_noavx.go                 |   22 +
 ecc/bls24-315/fr/element.go                   |   31 +-
 ecc/bls24-315/fr/element_mul_amd64.s          |  487 ---
 ecc/bls24-315/fr/element_ops_amd64.go         |  155 +-
 ecc/bls24-315/fr/element_ops_amd64.s          |  627 +---
 ecc/bls24-315/fr/element_ops_purego.go        |   63 +-
 ecc/bls24-315/fr/element_test.go              |  134 +-
 ecc/bls24-315/fr/vector.go                    |   26 +
 ecc/bls24-315/fr/vector_test.go               |  281 ++
 ecc/bls24-317/fp/{asm.go => asm_adx.go}       |    0
 ecc/bls24-317/fp/element.go                   |   28 +-
 ecc/bls24-317/fp/element_mul_amd64.s          |  656 ----
 ecc/bls24-317/fp/element_ops_amd64.go         |   44 +-
 ecc/bls24-317/fp/element_ops_amd64.s          |  272 +-
 ecc/bls24-317/fp/element_ops_purego.go        |   44 +-
 ecc/bls24-317/fp/element_test.go              |  138 +-
 ecc/bls24-317/fp/vector.go                    |   45 +
 ecc/bls24-317/fp/vector_test.go               |  283 ++
 ecc/bls24-317/fr/{asm.go => asm_adx.go}       |    0
 ecc/bls24-317/fr/asm_avx.go                   |   27 +
 ecc/bls24-317/fr/asm_noavx.go                 |   22 +
 ecc/bls24-317/fr/element.go                   |   31 +-
 ecc/bls24-317/fr/element_mul_amd64.s          |  487 ---
 ecc/bls24-317/fr/element_ops_amd64.go         |  155 +-
 ecc/bls24-317/fr/element_ops_amd64.s          |  627 +---
 ecc/bls24-317/fr/element_ops_purego.go        |   63 +-
 ecc/bls24-317/fr/element_test.go              |  134 +-
 ecc/bls24-317/fr/vector.go                    |   26 +
 ecc/bls24-317/fr/vector_test.go               |  281 ++
 ecc/bn254/fp/{asm.go => asm_adx.go}           |    0
 ecc/bn254/fp/asm_avx.go                       |   27 +
 ecc/bn254/fp/asm_noavx.go                     |   22 +
 ecc/bn254/fp/element.go                       |   31 +-
 ecc/bn254/fp/element_mul_amd64.s              |  487 ---
 ecc/bn254/fp/element_ops_amd64.go             |  155 +-
 ecc/bn254/fp/element_ops_amd64.s              |  627 +---
 ecc/bn254/fp/element_ops_purego.go            |   63 +-
 ecc/bn254/fp/element_test.go                  |  134 +-
 ecc/bn254/fp/vector.go                        |   26 +
 ecc/bn254/fp/vector_test.go                   |  281 ++
 ecc/bn254/fr/{asm.go => asm_adx.go}           |    0
 ecc/bn254/fr/asm_avx.go                       |   27 +
 ecc/bn254/fr/asm_noavx.go                     |   22 +
 ecc/bn254/fr/element.go                       |   31 +-
 ecc/bn254/fr/element_mul_amd64.s              |  487 ---
 ecc/bn254/fr/element_ops_amd64.go             |  155 +-
 ecc/bn254/fr/element_ops_amd64.s              |  627 +---
 ecc/bn254/fr/element_ops_purego.go            |   63 +-
 ecc/bn254/fr/element_test.go                  |  134 +-
 ecc/bn254/fr/vector.go                        |   26 +
 ecc/bn254/fr/vector_test.go                   |  281 ++
 ecc/bn254/internal/fptower/e2_amd64.go        |   23 +
 ecc/bn254/internal/fptower/e2_amd64.s         |  234 +-
 ecc/bw6-633/fp/{asm.go => asm_adx.go}         |    0
 ecc/bw6-633/fp/element.go                     |   28 +-
 ecc/bw6-633/fp/element_mul_amd64.s            | 1974 ------------
 ecc/bw6-633/fp/element_ops_amd64.go           |   44 +-
 ecc/bw6-633/fp/element_ops_amd64.s            |  436 +--
 ecc/bw6-633/fp/element_ops_purego.go          |   44 +-
 ecc/bw6-633/fp/element_test.go                |  158 +-
 ecc/bw6-633/fp/vector.go                      |   45 +
 ecc/bw6-633/fp/vector_test.go                 |  293 ++
 ecc/bw6-633/fr/{asm.go => asm_adx.go}         |    0
 ecc/bw6-633/fr/element.go                     |   28 +-
 ecc/bw6-633/fr/element_mul_amd64.s            |  656 ----
 ecc/bw6-633/fr/element_ops_amd64.go           |   44 +-
 ecc/bw6-633/fr/element_ops_amd64.s            |  272 +-
 ecc/bw6-633/fr/element_ops_purego.go          |   44 +-
 ecc/bw6-633/fr/element_test.go                |  138 +-
 ecc/bw6-633/fr/vector.go                      |   45 +
 ecc/bw6-633/fr/vector_test.go                 |  283 ++
 ecc/bw6-761/fp/{asm.go => asm_adx.go}         |    0
 ecc/bw6-761/fp/element.go                     |   28 +-
 ecc/bw6-761/fp/element_mul_amd64.s            | 2758 -----------------
 ecc/bw6-761/fp/element_ops_amd64.go           |   44 +-
 ecc/bw6-761/fp/element_ops_amd64.s            |  502 +--
 ecc/bw6-761/fp/element_ops_purego.go          |   44 +-
 ecc/bw6-761/fp/element_test.go                |  166 +-
 ecc/bw6-761/fp/vector.go                      |   45 +
 ecc/bw6-761/fp/vector_test.go                 |  297 ++
 ecc/bw6-761/fr/{asm.go => asm_adx.go}         |    0
 ecc/bw6-761/fr/element.go                     |   28 +-
 ecc/bw6-761/fr/element_mul_amd64.s            |  857 -----
 ecc/bw6-761/fr/element_ops_amd64.go           |   44 +-
 ecc/bw6-761/fr/element_ops_amd64.s            |  306 +-
 ecc/bw6-761/fr/element_ops_purego.go          |   44 +-
 ecc/bw6-761/fr/element_test.go                |  142 +-
 ecc/bw6-761/fr/vector.go                      |   45 +
 ecc/bw6-761/fr/vector_test.go                 |  285 ++
 ecc/secp256k1/fp/element.go                   |   31 +-
 ecc/secp256k1/fp/element_ops_purego.go        |   46 +-
 ecc/secp256k1/fp/element_test.go              |  134 +-
 ecc/secp256k1/fp/vector.go                    |   63 +
 ecc/secp256k1/fp/vector_test.go               |  281 ++
 ecc/secp256k1/fr/element.go                   |   31 +-
 ecc/secp256k1/fr/element_ops_purego.go        |   46 +-
 ecc/secp256k1/fr/element_test.go              |  134 +-
 ecc/secp256k1/fr/vector.go                    |   63 +
 ecc/secp256k1/fr/vector_test.go               |  281 ++
 ecc/stark-curve/fp/{asm.go => asm_adx.go}     |    0
 ecc/stark-curve/fp/asm_avx.go                 |   27 +
 ecc/stark-curve/fp/asm_noavx.go               |   22 +
 ecc/stark-curve/fp/element.go                 |   31 +-
 ecc/stark-curve/fp/element_mul_amd64.s        |  487 ---
 ecc/stark-curve/fp/element_ops_amd64.go       |  155 +-
 ecc/stark-curve/fp/element_ops_amd64.s        |  627 +---
 ecc/stark-curve/fp/element_ops_purego.go      |   63 +-
 ecc/stark-curve/fp/element_test.go            |  134 +-
 ecc/stark-curve/fp/vector.go                  |   26 +
 ecc/stark-curve/fp/vector_test.go             |  281 ++
 ecc/stark-curve/fr/{asm.go => asm_adx.go}     |    0
 ecc/stark-curve/fr/asm_avx.go                 |   27 +
 ecc/stark-curve/fr/asm_noavx.go               |   22 +
 ecc/stark-curve/fr/element.go                 |   31 +-
 ecc/stark-curve/fr/element_mul_amd64.s        |  487 ---
 ecc/stark-curve/fr/element_ops_amd64.go       |  155 +-
 ecc/stark-curve/fr/element_ops_amd64.s        |  627 +---
 ecc/stark-curve/fr/element_ops_purego.go      |   63 +-
 ecc/stark-curve/fr/element_test.go            |  134 +-
 ecc/stark-curve/fr/vector.go                  |   26 +
 ecc/stark-curve/fr/vector_test.go             |  281 ++
 field/asm/.gitignore                          |    6 +
 field/asm/element_10w_amd64.s                 | 1187 +++++++
 field/asm/element_12w_amd64.s                 | 1557 ++++++++++
 field/asm/element_4w_amd64.s                  | 2438 +++++++++++++++
 field/asm/element_5w_amd64.s                  |  563 ++++
 field/asm/element_6w_amd64.s                  |  670 ++++
 field/generator/asm/amd64/asm_macros.go       |   22 +-
 field/generator/asm/amd64/build.go            |  206 +-
 .../generator/asm/amd64/element_butterfly.go  |   15 +-
 field/generator/asm/amd64/element_frommont.go |    4 +-
 field/generator/asm/amd64/element_mul.go      |  163 +-
 field/generator/asm/amd64/element_vec.go      | 1387 ++++++++-
 field/generator/config/field_config.go        |   12 +
 field/generator/generator.go                  |   90 +-
 field/generator/generator_test.go             |   63 +-
 .../internal/templates/element/asm.go         |   13 +
 .../internal/templates/element/base.go        |    8 +-
 .../internal/templates/element/mul_cios.go    |   49 +-
 .../internal/templates/element/mul_nocarry.go |    4 +-
 .../internal/templates/element/ops_asm.go     |  114 +-
 .../internal/templates/element/ops_purego.go  |   22 +-
 .../internal/templates/element/tests.go       |  151 +-
 .../templates/element/tests_vector.go         |  285 +-
 .../internal/templates/element/vector.go      |   49 +-
 field/goff/cmd/root.go                        |    9 +-
 field/goldilocks/element.go                   |   28 +-
 field/goldilocks/element_test.go              |  122 +-
 field/goldilocks/internal/main.go             |    2 +-
 field/goldilocks/vector.go                    |   45 +
 field/goldilocks/vector_test.go               |  275 ++
 go.mod                                        |    3 +-
 go.sum                                        |    5 +-
 internal/generator/main.go                    |   49 +-
 internal/generator/tower/asm/amd64/e2.go      |   11 +-
 .../generator/tower/asm/amd64/e2_bn254.go     |   22 +-
 .../template/fq12over6over2/amd64.fq2.go.tmpl |   22 +
 212 files changed, 17671 insertions(+), 27729 deletions(-)
 rename ecc/bls12-377/fp/{asm.go => asm_adx.go} (100%)
 delete mode 100644 ecc/bls12-377/fp/element_mul_amd64.s
 rename ecc/bls12-377/fr/{asm.go => asm_adx.go} (100%)
 create mode 100644 ecc/bls12-377/fr/asm_avx.go
 create mode 100644 ecc/bls12-377/fr/asm_noavx.go
 delete mode 100644 ecc/bls12-377/fr/element_mul_amd64.s
 rename ecc/bls12-381/fp/{asm.go => asm_adx.go} (100%)
 delete mode 100644 ecc/bls12-381/fp/element_mul_amd64.s
 rename ecc/bls12-381/fr/{asm.go => asm_adx.go} (100%)
 create mode 100644 ecc/bls12-381/fr/asm_avx.go
 create mode 100644 ecc/bls12-381/fr/asm_noavx.go
 delete mode 100644 ecc/bls12-381/fr/element_mul_amd64.s
 rename ecc/bls24-315/fp/{asm.go => asm_adx.go} (100%)
 delete mode 100644 ecc/bls24-315/fp/element_mul_amd64.s
 rename ecc/bls24-315/fr/{asm.go => asm_adx.go} (100%)
 create mode 100644 ecc/bls24-315/fr/asm_avx.go
 create mode 100644 ecc/bls24-315/fr/asm_noavx.go
 delete mode 100644 ecc/bls24-315/fr/element_mul_amd64.s
 rename ecc/bls24-317/fp/{asm.go => asm_adx.go} (100%)
 delete mode 100644 ecc/bls24-317/fp/element_mul_amd64.s
 rename ecc/bls24-317/fr/{asm.go => asm_adx.go} (100%)
 create mode 100644 ecc/bls24-317/fr/asm_avx.go
 create mode 100644 ecc/bls24-317/fr/asm_noavx.go
 delete mode 100644 ecc/bls24-317/fr/element_mul_amd64.s
 rename ecc/bn254/fp/{asm.go => asm_adx.go} (100%)
 create mode 100644 ecc/bn254/fp/asm_avx.go
 create mode 100644 ecc/bn254/fp/asm_noavx.go
 delete mode 100644 ecc/bn254/fp/element_mul_amd64.s
 rename ecc/bn254/fr/{asm.go => asm_adx.go} (100%)
 create mode 100644 ecc/bn254/fr/asm_avx.go
 create mode 100644 ecc/bn254/fr/asm_noavx.go
 delete mode 100644 ecc/bn254/fr/element_mul_amd64.s
 rename ecc/bw6-633/fp/{asm.go => asm_adx.go} (100%)
 delete mode 100644 ecc/bw6-633/fp/element_mul_amd64.s
 rename ecc/bw6-633/fr/{asm.go => asm_adx.go} (100%)
 delete mode 100644 ecc/bw6-633/fr/element_mul_amd64.s
 rename ecc/bw6-761/fp/{asm.go => asm_adx.go} (100%)
 delete mode 100644 ecc/bw6-761/fp/element_mul_amd64.s
 rename ecc/bw6-761/fr/{asm.go => asm_adx.go} (100%)
 delete mode 100644 ecc/bw6-761/fr/element_mul_amd64.s
 rename ecc/stark-curve/fp/{asm.go => asm_adx.go} (100%)
 create mode 100644 ecc/stark-curve/fp/asm_avx.go
 create mode 100644 ecc/stark-curve/fp/asm_noavx.go
 delete mode 100644 ecc/stark-curve/fp/element_mul_amd64.s
 rename ecc/stark-curve/fr/{asm.go => asm_adx.go} (100%)
 create mode 100644 ecc/stark-curve/fr/asm_avx.go
 create mode 100644 ecc/stark-curve/fr/asm_noavx.go
 delete mode 100644 ecc/stark-curve/fr/element_mul_amd64.s
 create mode 100644 field/asm/.gitignore
 create mode 100644 field/asm/element_10w_amd64.s
 create mode 100644 field/asm/element_12w_amd64.s
 create mode 100644 field/asm/element_4w_amd64.s
 create mode 100644 field/asm/element_5w_amd64.s
 create mode 100644 field/asm/element_6w_amd64.s

diff --git a/ecc/bls12-377/fp/asm.go b/ecc/bls12-377/fp/asm_adx.go
similarity index 100%
rename from ecc/bls12-377/fp/asm.go
rename to ecc/bls12-377/fp/asm_adx.go
diff --git a/ecc/bls12-377/fp/element.go b/ecc/bls12-377/fp/element.go
index 81a730fbd4..393f45744d 100644
--- a/ecc/bls12-377/fp/element.go
+++ b/ecc/bls12-377/fp/element.go
@@ -521,32 +521,8 @@ func (z *Element) Select(c int, x0 *Element, x1 *Element) *Element {
 // and is used for testing purposes.
 func _mulGeneric(z, x, y *Element) {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t [7]uint64
 	var D uint64
diff --git a/ecc/bls12-377/fp/element_mul_amd64.s b/ecc/bls12-377/fp/element_mul_amd64.s
deleted file mode 100644
index 1e19c4d3fd..0000000000
--- a/ecc/bls12-377/fp/element_mul_amd64.s
+++ /dev/null
@@ -1,857 +0,0 @@
-// +build !purego
-
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0x8508c00000000001
-DATA q<>+8(SB)/8, $0x170b5d4430000000
-DATA q<>+16(SB)/8, $0x1ef3622fba094800
-DATA q<>+24(SB)/8, $0x1a22d9f300f5138f
-DATA q<>+32(SB)/8, $0xc63b05c06ca1493b
-DATA q<>+40(SB)/8, $0x01ae3a4617c510ea
-GLOBL q<>(SB), (RODATA+NOPTR), $48
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0x8508bfffffffffff
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, ra4, ra5, rb0, rb1, rb2, rb3, rb4, rb5) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	MOVQ    ra4, rb4;        \
-	SBBQ    q<>+32(SB), ra4; \
-	MOVQ    ra5, rb5;        \
-	SBBQ    q<>+40(SB), ra5; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-	CMOVQCS rb4, ra4;        \
-	CMOVQCS rb5, ra5;        \
-
-// mul(res, x, y *Element)
-TEXT ·mul(SB), $24-24
-
-	// the algorithm is described in the Element.Mul declaration (.go)
-	// however, to benefit from the ADCX and ADOX carry chains
-	// we split the inner loops in 2:
-	// for i=0 to N-1
-	// 		for j=0 to N-1
-	// 		    (A,t[j])  := t[j] + x[j]*y[i] + A
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C + A
-
-	NO_LOCAL_POINTERS
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_1
-	MOVQ x+8(FP), R8
-
-	// x[0] -> R10
-	// x[1] -> R11
-	// x[2] -> R12
-	MOVQ 0(R8), R10
-	MOVQ 8(R8), R11
-	MOVQ 16(R8), R12
-	MOVQ y+16(FP), R13
-
-	// A -> BP
-	// t[0] -> R14
-	// t[1] -> R15
-	// t[2] -> CX
-	// t[3] -> BX
-	// t[4] -> SI
-	// t[5] -> DI
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 0(R13), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ R10, R14, R15
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ R11, AX, CX
-	ADOXQ AX, R15
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ R12, AX, BX
-	ADOXQ AX, CX
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ 24(R8), AX, SI
-	ADOXQ AX, BX
-
-	// (A,t[4])  := x[4]*y[0] + A
-	MULXQ 32(R8), AX, DI
-	ADOXQ AX, SI
-
-	// (A,t[5])  := x[5]*y[0] + A
-	MULXQ 40(R8), AX, BP
-	ADOXQ AX, DI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R9
-	ADCXQ R14, AX
-	MOVQ  R9, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ BP, DI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 8(R13), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ R10, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R15
-	MULXQ R11, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, CX
-	MULXQ R12, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, BX
-	MULXQ 24(R8), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[1] + A
-	ADCXQ BP, SI
-	MULXQ 32(R8), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[1] + A
-	ADCXQ BP, DI
-	MULXQ 40(R8), AX, BP
-	ADOXQ AX, DI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R9
-	ADCXQ R14, AX
-	MOVQ  R9, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ BP, DI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 16(R13), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ R10, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R15
-	MULXQ R11, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, CX
-	MULXQ R12, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, BX
-	MULXQ 24(R8), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[2] + A
-	ADCXQ BP, SI
-	MULXQ 32(R8), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[2] + A
-	ADCXQ BP, DI
-	MULXQ 40(R8), AX, BP
-	ADOXQ AX, DI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R9
-	ADCXQ R14, AX
-	MOVQ  R9, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ BP, DI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 24(R13), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ R10, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R15
-	MULXQ R11, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, CX
-	MULXQ R12, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, BX
-	MULXQ 24(R8), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[3] + A
-	ADCXQ BP, SI
-	MULXQ 32(R8), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[3] + A
-	ADCXQ BP, DI
-	MULXQ 40(R8), AX, BP
-	ADOXQ AX, DI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R9
-	ADCXQ R14, AX
-	MOVQ  R9, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ BP, DI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 32(R13), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[4] + A
-	MULXQ R10, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[4] + A
-	ADCXQ BP, R15
-	MULXQ R11, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[4] + A
-	ADCXQ BP, CX
-	MULXQ R12, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[4] + A
-	ADCXQ BP, BX
-	MULXQ 24(R8), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[4] + A
-	ADCXQ BP, SI
-	MULXQ 32(R8), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[4] + A
-	ADCXQ BP, DI
-	MULXQ 40(R8), AX, BP
-	ADOXQ AX, DI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R9
-	ADCXQ R14, AX
-	MOVQ  R9, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ BP, DI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 40(R13), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[5] + A
-	MULXQ R10, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[5] + A
-	ADCXQ BP, R15
-	MULXQ R11, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[5] + A
-	ADCXQ BP, CX
-	MULXQ R12, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[5] + A
-	ADCXQ BP, BX
-	MULXQ 24(R8), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[5] + A
-	ADCXQ BP, SI
-	MULXQ 32(R8), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[5] + A
-	ADCXQ BP, DI
-	MULXQ 40(R8), AX, BP
-	ADOXQ AX, DI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R9
-	ADCXQ R14, AX
-	MOVQ  R9, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ BP, DI
-
-	// reduce element(R14,R15,CX,BX,SI,DI) using temp registers (R9,R8,R13,R10,R11,R12)
-	REDUCE(R14,R15,CX,BX,SI,DI,R9,R8,R13,R10,R11,R12)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R15, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	MOVQ SI, 32(AX)
-	MOVQ DI, 40(AX)
-	RET
-
-noAdx_1:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	MOVQ x+8(FP), AX
-	MOVQ AX, 8(SP)
-	MOVQ y+16(FP), AX
-	MOVQ AX, 16(SP)
-	CALL ·_mulGeneric(SB)
-	RET
-
-TEXT ·fromMont(SB), $8-8
-	NO_LOCAL_POINTERS
-
-	// the algorithm is described here
-	// https://hackmd.io/@gnark/modular_multiplication
-	// when y = 1 we have:
-	// for i=0 to N-1
-	// 		t[i] = x[i]
-	// for i=0 to N-1
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_2
-	MOVQ res+0(FP), DX
-	MOVQ 0(DX), R14
-	MOVQ 8(DX), R15
-	MOVQ 16(DX), CX
-	MOVQ 24(DX), BX
-	MOVQ 32(DX), SI
-	MOVQ 40(DX), DI
-	XORQ DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ AX, DI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ AX, DI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ AX, DI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ AX, DI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ AX, DI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ AX, DI
-
-	// reduce element(R14,R15,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12,R13)
-	REDUCE(R14,R15,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R15, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	MOVQ SI, 32(AX)
-	MOVQ DI, 40(AX)
-	RET
-
-noAdx_2:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	CALL ·_fromMontGeneric(SB)
-	RET
diff --git a/ecc/bls12-377/fp/element_ops_amd64.go b/ecc/bls12-377/fp/element_ops_amd64.go
index 83bba45aed..ed2803d717 100644
--- a/ecc/bls12-377/fp/element_ops_amd64.go
+++ b/ecc/bls12-377/fp/element_ops_amd64.go
@@ -50,48 +50,8 @@ func Butterfly(a, b *Element)
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	mul(z, x, y)
 	return z
diff --git a/ecc/bls12-377/fp/element_ops_amd64.s b/ecc/bls12-377/fp/element_ops_amd64.s
index 7242622a4a..cabff26f70 100644
--- a/ecc/bls12-377/fp/element_ops_amd64.s
+++ b/ecc/bls12-377/fp/element_ops_amd64.s
@@ -1,306 +1,6 @@
 // +build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+// We include the hash to force the Go compiler to recompile: 11124594824487954849
+#include "../../../field/asm/element_6w_amd64.s"
 
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0x8508c00000000001
-DATA q<>+8(SB)/8, $0x170b5d4430000000
-DATA q<>+16(SB)/8, $0x1ef3622fba094800
-DATA q<>+24(SB)/8, $0x1a22d9f300f5138f
-DATA q<>+32(SB)/8, $0xc63b05c06ca1493b
-DATA q<>+40(SB)/8, $0x01ae3a4617c510ea
-GLOBL q<>(SB), (RODATA+NOPTR), $48
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0x8508bfffffffffff
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, ra4, ra5, rb0, rb1, rb2, rb3, rb4, rb5) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	MOVQ    ra4, rb4;        \
-	SBBQ    q<>+32(SB), ra4; \
-	MOVQ    ra5, rb5;        \
-	SBBQ    q<>+40(SB), ra5; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-	CMOVQCS rb4, ra4;        \
-	CMOVQCS rb5, ra5;        \
-
-TEXT ·reduce(SB), NOSPLIT, $0-8
-	MOVQ res+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	MOVQ 40(AX), R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	MOVQ R8, 40(AX)
-	RET
-
-// MulBy3(x *Element)
-TEXT ·MulBy3(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	MOVQ 40(AX), R8
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-	ADCQ 40(AX), R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R15,R9,R10,R11,R12,R13)
-	REDUCE(DX,CX,BX,SI,DI,R8,R15,R9,R10,R11,R12,R13)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	MOVQ R8, 40(AX)
-	RET
-
-// MulBy5(x *Element)
-TEXT ·MulBy5(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	MOVQ 40(AX), R8
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R15,R9,R10,R11,R12,R13)
-	REDUCE(DX,CX,BX,SI,DI,R8,R15,R9,R10,R11,R12,R13)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-	ADCQ 40(AX), R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R14,R15,R9,R10,R11,R12)
-	REDUCE(DX,CX,BX,SI,DI,R8,R14,R15,R9,R10,R11,R12)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	MOVQ R8, 40(AX)
-	RET
-
-// MulBy13(x *Element)
-TEXT ·MulBy13(SB), $40-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	MOVQ 40(AX), R8
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP))
-
-	MOVQ DX, R15
-	MOVQ CX, s0-8(SP)
-	MOVQ BX, s1-16(SP)
-	MOVQ SI, s2-24(SP)
-	MOVQ DI, s3-32(SP)
-	MOVQ R8, s4-40(SP)
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
-
-	ADDQ R15, DX
-	ADCQ s0-8(SP), CX
-	ADCQ s1-16(SP), BX
-	ADCQ s2-24(SP), SI
-	ADCQ s3-32(SP), DI
-	ADCQ s4-40(SP), R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-	ADCQ 40(AX), R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	MOVQ R8, 40(AX)
-	RET
-
-// Butterfly(a, b *Element) sets a = a + b; b = a - b
-TEXT ·Butterfly(SB), $48-16
-	MOVQ    a+0(FP), AX
-	MOVQ    0(AX), CX
-	MOVQ    8(AX), BX
-	MOVQ    16(AX), SI
-	MOVQ    24(AX), DI
-	MOVQ    32(AX), R8
-	MOVQ    40(AX), R9
-	MOVQ    CX, R10
-	MOVQ    BX, R11
-	MOVQ    SI, R12
-	MOVQ    DI, R13
-	MOVQ    R8, R14
-	MOVQ    R9, R15
-	XORQ    AX, AX
-	MOVQ    b+8(FP), DX
-	ADDQ    0(DX), CX
-	ADCQ    8(DX), BX
-	ADCQ    16(DX), SI
-	ADCQ    24(DX), DI
-	ADCQ    32(DX), R8
-	ADCQ    40(DX), R9
-	SUBQ    0(DX), R10
-	SBBQ    8(DX), R11
-	SBBQ    16(DX), R12
-	SBBQ    24(DX), R13
-	SBBQ    32(DX), R14
-	SBBQ    40(DX), R15
-	MOVQ    CX, s0-8(SP)
-	MOVQ    BX, s1-16(SP)
-	MOVQ    SI, s2-24(SP)
-	MOVQ    DI, s3-32(SP)
-	MOVQ    R8, s4-40(SP)
-	MOVQ    R9, s5-48(SP)
-	MOVQ    $0x8508c00000000001, CX
-	MOVQ    $0x170b5d4430000000, BX
-	MOVQ    $0x1ef3622fba094800, SI
-	MOVQ    $0x1a22d9f300f5138f, DI
-	MOVQ    $0xc63b05c06ca1493b, R8
-	MOVQ    $0x01ae3a4617c510ea, R9
-	CMOVQCC AX, CX
-	CMOVQCC AX, BX
-	CMOVQCC AX, SI
-	CMOVQCC AX, DI
-	CMOVQCC AX, R8
-	CMOVQCC AX, R9
-	ADDQ    CX, R10
-	ADCQ    BX, R11
-	ADCQ    SI, R12
-	ADCQ    DI, R13
-	ADCQ    R8, R14
-	ADCQ    R9, R15
-	MOVQ    s0-8(SP), CX
-	MOVQ    s1-16(SP), BX
-	MOVQ    s2-24(SP), SI
-	MOVQ    s3-32(SP), DI
-	MOVQ    s4-40(SP), R8
-	MOVQ    s5-48(SP), R9
-	MOVQ    R10, 0(DX)
-	MOVQ    R11, 8(DX)
-	MOVQ    R12, 16(DX)
-	MOVQ    R13, 24(DX)
-	MOVQ    R14, 32(DX)
-	MOVQ    R15, 40(DX)
-
-	// reduce element(CX,BX,SI,DI,R8,R9) using temp registers (R10,R11,R12,R13,R14,R15)
-	REDUCE(CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15)
-
-	MOVQ a+0(FP), AX
-	MOVQ CX, 0(AX)
-	MOVQ BX, 8(AX)
-	MOVQ SI, 16(AX)
-	MOVQ DI, 24(AX)
-	MOVQ R8, 32(AX)
-	MOVQ R9, 40(AX)
-	RET
diff --git a/ecc/bls12-377/fp/element_ops_purego.go b/ecc/bls12-377/fp/element_ops_purego.go
index a4c3796b96..072fb87c01 100644
--- a/ecc/bls12-377/fp/element_ops_purego.go
+++ b/ecc/bls12-377/fp/element_ops_purego.go
@@ -67,48 +67,8 @@ func reduce(z *Element) {
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t0, t1, t2, t3, t4, t5 uint64
 	var u0, u1, u2, u3, u4, u5 uint64
diff --git a/ecc/bls12-377/fp/element_test.go b/ecc/bls12-377/fp/element_test.go
index 582d8b4aff..a060095a0a 100644
--- a/ecc/bls12-377/fp/element_test.go
+++ b/ecc/bls12-377/fp/element_test.go
@@ -641,7 +641,6 @@ func TestElementBitLen(t *testing.T) {
 	))
 
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
-
 }
 
 func TestElementButterflies(t *testing.T) {
@@ -711,77 +710,6 @@ func TestElementLexicographicallyLargest(t *testing.T) {
 
 }
 
-func TestElementVecOps(t *testing.T) {
-	assert := require.New(t)
-
-	const N = 7
-	a := make(Vector, N)
-	b := make(Vector, N)
-	c := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a[i].SetRandom()
-		b[i].SetRandom()
-	}
-
-	// Vector addition
-	c.Add(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Add(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector addition failed")
-	}
-
-	// Vector subtraction
-	c.Sub(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Sub(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector subtraction failed")
-	}
-
-	// Vector scaling
-	c.ScalarMul(a, &b[0])
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Mul(&a[i], &b[0])
-		assert.True(c[i].Equal(&expected), "Vector scaling failed")
-	}
-}
-
-func BenchmarkElementVecOps(b *testing.B) {
-	// note; to benchmark against "no asm" version, use the following
-	// build tag: -tags purego
-	const N = 1024
-	a1 := make(Vector, N)
-	b1 := make(Vector, N)
-	c1 := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a1[i].SetRandom()
-		b1[i].SetRandom()
-	}
-
-	b.Run("Add", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Add(a1, b1)
-		}
-	})
-
-	b.Run("Sub", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Sub(a1, b1)
-		}
-	})
-
-	b.Run("ScalarMul", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.ScalarMul(a1, &b1[0])
-		}
-	})
-}
-
 func TestElementAdd(t *testing.T) {
 	t.Parallel()
 	parameters := gopter.DefaultTestParameters()
@@ -2353,42 +2281,42 @@ func gen() gopter.Gen {
 	}
 }
 
-func genFull() gopter.Gen {
-	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+func genRandomFq(genParams *gopter.GenParameters) Element {
+	var g Element
 
-		genRandomFq := func() Element {
-			var g Element
+	g = Element{
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+	}
 
-			g = Element{
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-			}
+	if qElement[5] != ^uint64(0) {
+		g[5] %= (qElement[5] + 1)
+	}
 
-			if qElement[5] != ^uint64(0) {
-				g[5] %= (qElement[5] + 1)
-			}
+	for !g.smallerThanModulus() {
+		g = Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[5] != ^uint64(0) {
+			g[5] %= (qElement[5] + 1)
+		}
+	}
 
-			for !g.smallerThanModulus() {
-				g = Element{
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-				}
-				if qElement[5] != ^uint64(0) {
-					g[5] %= (qElement[5] + 1)
-				}
-			}
+	return g
+}
 
-			return g
-		}
-		a := genRandomFq()
+func genFull() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
 
 		var carry uint64
 		a[0], carry = bits.Add64(a[0], qElement[0], carry)
@@ -2403,6 +2331,14 @@ func genFull() gopter.Gen {
 	}
 }
 
+func genElement() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
+		genResult := gopter.NewGenResult(a, gopter.NoShrinker)
+		return genResult
+	}
+}
+
 func (z *Element) matchVeryBigInt(aHi uint64, aInt *big.Int) error {
 	var modulus big.Int
 	var aIntMod big.Int
diff --git a/ecc/bls12-377/fp/vector.go b/ecc/bls12-377/fp/vector.go
index 0df05e3373..f1d659e767 100644
--- a/ecc/bls12-377/fp/vector.go
+++ b/ecc/bls12-377/fp/vector.go
@@ -219,6 +219,25 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	scalarMulVecGeneric(*vector, a, b)
 }
 
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
+
 func addVecGeneric(res, a, b Vector) {
 	if len(a) != len(b) || len(a) != len(res) {
 		panic("vector.Add: vectors don't have the same length")
@@ -246,6 +265,32 @@ func scalarMulVecGeneric(res, a Vector, b *Element) {
 	}
 }
 
+func sumVecGeneric(res *Element, a Vector) {
+	for i := 0; i < len(a); i++ {
+		res.Add(res, &a[i])
+	}
+}
+
+func innerProductVecGeneric(res *Element, a, b Vector) {
+	if len(a) != len(b) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	var tmp Element
+	for i := 0; i < len(a); i++ {
+		tmp.Mul(&a[i], &b[i])
+		res.Add(res, &tmp)
+	}
+}
+
+func mulVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Mul(&a[i], &b[i])
+	}
+}
+
 // TODO @gbotrel make a public package out of that.
 // execute executes the work function in parallel.
 // this is copy paste from internal/parallel/parallel.go
diff --git a/ecc/bls12-377/fp/vector_test.go b/ecc/bls12-377/fp/vector_test.go
index 5d88af91c0..a8deef9451 100644
--- a/ecc/bls12-377/fp/vector_test.go
+++ b/ecc/bls12-377/fp/vector_test.go
@@ -18,10 +18,15 @@ package fp
 
 import (
 	"bytes"
+	"fmt"
 	"github.com/stretchr/testify/require"
+	"os"
 	"reflect"
 	"sort"
 	"testing"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/prop"
 )
 
 func TestVectorSort(t *testing.T) {
@@ -88,3 +93,283 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 	}
 	return <-chErr
 }
+
+func TestVectorOps(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = 2
+	} else {
+		parameters.MinSuccessfulTests = 10
+	}
+	properties := gopter.NewProperties(parameters)
+
+	addVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Add(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Add(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	subVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Sub(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Sub(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	scalarMulVector := func(a Vector, b Element) bool {
+		c := make(Vector, len(a))
+		c.ScalarMul(a, &b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b)
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sumVector := func(a Vector) bool {
+		var sum Element
+		computed := a.Sum()
+		for i := 0; i < len(a); i++ {
+			sum.Add(&sum, &a[i])
+		}
+
+		return sum.Equal(&computed)
+	}
+
+	innerProductVector := func(a, b Vector) bool {
+		computed := a.InnerProduct(b)
+		var innerProduct Element
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			innerProduct.Add(&innerProduct, &tmp)
+		}
+
+		return innerProduct.Equal(&computed)
+	}
+
+	mulVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		a[0].SetUint64(0x24)
+		b[0].SetUint64(0x42)
+		c.Mul(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sizes := []int{1, 2, 3, 4, 8, 9, 15, 16, 509, 510, 511, 512, 513, 514}
+	type genPair struct {
+		g1, g2 gopter.Gen
+		label  string
+	}
+
+	for _, size := range sizes {
+		generators := []genPair{
+			{genZeroVector(size), genZeroVector(size), "zero vectors"},
+			{genMaxVector(size), genMaxVector(size), "max vectors"},
+			{genVector(size), genVector(size), "random vectors"},
+			{genVector(size), genZeroVector(size), "random and zero vectors"},
+		}
+		for _, gp := range generators {
+			properties.Property(fmt.Sprintf("vector addition %d - %s", size, gp.label), prop.ForAll(
+				addVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector subtraction %d - %s", size, gp.label), prop.ForAll(
+				subVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector scalar multiplication %d - %s", size, gp.label), prop.ForAll(
+				scalarMulVector,
+				gp.g1,
+				genElement(),
+			))
+
+			properties.Property(fmt.Sprintf("vector sum %d - %s", size, gp.label), prop.ForAll(
+				sumVector,
+				gp.g1,
+			))
+
+			properties.Property(fmt.Sprintf("vector inner product %d - %s", size, gp.label), prop.ForAll(
+				innerProductVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector multiplication %d - %s", size, gp.label), prop.ForAll(
+				mulVector,
+				gp.g1,
+				gp.g2,
+			))
+		}
+	}
+
+	properties.TestingRun(t, gopter.NewFormatedReporter(false, 260, os.Stdout))
+}
+
+func BenchmarkVectorOps(b *testing.B) {
+	// note; to benchmark against "no asm" version, use the following
+	// build tag: -tags purego
+	const N = 1 << 24
+	a1 := make(Vector, N)
+	b1 := make(Vector, N)
+	c1 := make(Vector, N)
+	var mixer Element
+	mixer.SetRandom()
+	for i := 1; i < N; i++ {
+		a1[i-1].SetUint64(uint64(i)).
+			Mul(&a1[i-1], &mixer)
+		b1[i-1].SetUint64(^uint64(i)).
+			Mul(&b1[i-1], &mixer)
+	}
+
+	for n := 1 << 4; n <= N; n <<= 1 {
+		b.Run(fmt.Sprintf("add %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Add(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sub %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Sub(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("scalarMul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.ScalarMul(_a, &mixer)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sum %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.Sum()
+			}
+		})
+
+		b.Run(fmt.Sprintf("innerProduct %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.InnerProduct(_b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("mul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Mul(_a, _b)
+			}
+		})
+	}
+}
+
+func genZeroVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genMaxVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+
+		qMinusOne := qElement
+		qMinusOne[0]--
+
+		for i := 0; i < size; i++ {
+			g[i] = qMinusOne
+		}
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		mixer := Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[5] != ^uint64(0) {
+			mixer[5] %= (qElement[5] + 1)
+		}
+
+		for !mixer.smallerThanModulus() {
+			mixer = Element{
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+			}
+			if qElement[5] != ^uint64(0) {
+				mixer[5] %= (qElement[5] + 1)
+			}
+		}
+
+		for i := 1; i <= size; i++ {
+			g[i-1].SetUint64(uint64(i)).
+				Mul(&g[i-1], &mixer)
+		}
+
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/ecc/bls12-377/fr/asm.go b/ecc/bls12-377/fr/asm_adx.go
similarity index 100%
rename from ecc/bls12-377/fr/asm.go
rename to ecc/bls12-377/fr/asm_adx.go
diff --git a/ecc/bls12-377/fr/asm_avx.go b/ecc/bls12-377/fr/asm_avx.go
new file mode 100644
index 0000000000..955f559799
--- /dev/null
+++ b/ecc/bls12-377/fr/asm_avx.go
@@ -0,0 +1,27 @@
+//go:build !noavx
+// +build !noavx
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+import "golang.org/x/sys/cpu"
+
+var (
+	supportAvx512 = supportAdx && cpu.X86.HasAVX512 && cpu.X86.HasAVX512DQ
+	_             = supportAvx512
+)
diff --git a/ecc/bls12-377/fr/asm_noavx.go b/ecc/bls12-377/fr/asm_noavx.go
new file mode 100644
index 0000000000..e5a5b1f2cc
--- /dev/null
+++ b/ecc/bls12-377/fr/asm_noavx.go
@@ -0,0 +1,22 @@
+//go:build noavx
+// +build noavx
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+const supportAvx512 = false
diff --git a/ecc/bls12-377/fr/element.go b/ecc/bls12-377/fr/element.go
index 07be74489e..af277e8bb1 100644
--- a/ecc/bls12-377/fr/element.go
+++ b/ecc/bls12-377/fr/element.go
@@ -81,6 +81,9 @@ func Modulus() *big.Int {
 // used for Montgomery reduction
 const qInvNeg uint64 = 725501752471715839
 
+// mu = 2^288 / q needed for partial Barrett reduction
+const mu uint64 = 58893420465
+
 func init() {
 	_modulus.SetString("12ab655e9a2ca55660b44d1e5c37b00159aa76fed00000010a11800000000001", 16)
 }
@@ -477,32 +480,8 @@ func (z *Element) Select(c int, x0 *Element, x1 *Element) *Element {
 // and is used for testing purposes.
 func _mulGeneric(z, x, y *Element) {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t [5]uint64
 	var D uint64
diff --git a/ecc/bls12-377/fr/element_mul_amd64.s b/ecc/bls12-377/fr/element_mul_amd64.s
deleted file mode 100644
index ab18162458..0000000000
--- a/ecc/bls12-377/fr/element_mul_amd64.s
+++ /dev/null
@@ -1,487 +0,0 @@
-// +build !purego
-
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0x0a11800000000001
-DATA q<>+8(SB)/8, $0x59aa76fed0000001
-DATA q<>+16(SB)/8, $0x60b44d1e5c37b001
-DATA q<>+24(SB)/8, $0x12ab655e9a2ca556
-GLOBL q<>(SB), (RODATA+NOPTR), $32
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0x0a117fffffffffff
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, rb0, rb1, rb2, rb3) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-
-// mul(res, x, y *Element)
-TEXT ·mul(SB), $24-24
-
-	// the algorithm is described in the Element.Mul declaration (.go)
-	// however, to benefit from the ADCX and ADOX carry chains
-	// we split the inner loops in 2:
-	// for i=0 to N-1
-	// 		for j=0 to N-1
-	// 		    (A,t[j])  := t[j] + x[j]*y[i] + A
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C + A
-
-	NO_LOCAL_POINTERS
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_1
-	MOVQ x+8(FP), SI
-
-	// x[0] -> DI
-	// x[1] -> R8
-	// x[2] -> R9
-	// x[3] -> R10
-	MOVQ 0(SI), DI
-	MOVQ 8(SI), R8
-	MOVQ 16(SI), R9
-	MOVQ 24(SI), R10
-	MOVQ y+16(FP), R11
-
-	// A -> BP
-	// t[0] -> R14
-	// t[1] -> R13
-	// t[2] -> CX
-	// t[3] -> BX
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 0(R11), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ DI, R14, R13
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ R8, AX, CX
-	ADOXQ AX, R13
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ R9, AX, BX
-	ADOXQ AX, CX
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 8(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R13
-	MULXQ R8, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, CX
-	MULXQ R9, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, BX
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 16(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R13
-	MULXQ R8, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, CX
-	MULXQ R9, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, BX
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 24(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R13
-	MULXQ R8, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, CX
-	MULXQ R9, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, BX
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// reduce element(R14,R13,CX,BX) using temp registers (SI,R12,R11,DI)
-	REDUCE(R14,R13,CX,BX,SI,R12,R11,DI)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R13, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	RET
-
-noAdx_1:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	MOVQ x+8(FP), AX
-	MOVQ AX, 8(SP)
-	MOVQ y+16(FP), AX
-	MOVQ AX, 16(SP)
-	CALL ·_mulGeneric(SB)
-	RET
-
-TEXT ·fromMont(SB), $8-8
-	NO_LOCAL_POINTERS
-
-	// the algorithm is described here
-	// https://hackmd.io/@gnark/modular_multiplication
-	// when y = 1 we have:
-	// for i=0 to N-1
-	// 		t[i] = x[i]
-	// for i=0 to N-1
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_2
-	MOVQ res+0(FP), DX
-	MOVQ 0(DX), R14
-	MOVQ 8(DX), R13
-	MOVQ 16(DX), CX
-	MOVQ 24(DX), BX
-	XORQ DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-
-	// reduce element(R14,R13,CX,BX) using temp registers (SI,DI,R8,R9)
-	REDUCE(R14,R13,CX,BX,SI,DI,R8,R9)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R13, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	RET
-
-noAdx_2:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	CALL ·_fromMontGeneric(SB)
-	RET
diff --git a/ecc/bls12-377/fr/element_ops_amd64.go b/ecc/bls12-377/fr/element_ops_amd64.go
index 21568255de..b653e80069 100644
--- a/ecc/bls12-377/fr/element_ops_amd64.go
+++ b/ecc/bls12-377/fr/element_ops_amd64.go
@@ -51,7 +51,8 @@ func (vector *Vector) Add(a, b Vector) {
 	if len(a) != len(b) || len(a) != len(*vector) {
 		panic("vector.Add: vectors don't have the same length")
 	}
-	addVec(&(*vector)[0], &a[0], &b[0], uint64(len(a)))
+	n := uint64(len(a))
+	addVec(&(*vector)[0], &a[0], &b[0], n)
 }
 
 //go:noescape
@@ -75,59 +76,123 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	if len(a) != len(*vector) {
 		panic("vector.ScalarMul: vectors don't have the same length")
 	}
-	scalarMulVec(&(*vector)[0], &a[0], b, uint64(len(a)))
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || uint64(len(a)) >= maxN {
+		// call scalarMulVecGeneric
+		scalarMulVecGeneric(*vector, a, b)
+		return
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	// the code for scalarMul is identical to mulVec; and it expects at least
+	// 2 elements in the vector to fill the Z registers
+	var bb [2]Element
+	bb[0] = *b
+	bb[1] = *b
+	const blockSize = 16
+	scalarMulVec(&(*vector)[0], &a[0], &bb[0], n/blockSize, qInvNeg)
+	if n%blockSize != 0 {
+		// call scalarMulVecGeneric on the rest
+		start := n - n%blockSize
+		scalarMulVecGeneric((*vector)[start:], a[start:], b)
+	}
+}
+
+//go:noescape
+func scalarMulVec(res, a, b *Element, n uint64, qInvNeg uint64)
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	const minN = 16 * 7 // AVX512 slower than generic for small n
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n <= minN || n >= maxN {
+		// call sumVecGeneric
+		sumVecGeneric(&res, *vector)
+		return
+	}
+	sumVec(&res, &(*vector)[0], uint64(len(*vector)))
+	return
 }
 
 //go:noescape
-func scalarMulVec(res, a, b *Element, n uint64)
+func sumVec(res *Element, a *Element, n uint64)
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	if n != uint64(len(other)) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n >= maxN {
+		// call innerProductVecGeneric
+		// note; we could split the vector into smaller chunks and call innerProductVec
+		innerProductVecGeneric(&res, *vector, other)
+		return
+	}
+	innerProdVec(&res[0], &(*vector)[0], &other[0], uint64(len(*vector)))
+
+	return
+}
+
+//go:noescape
+func innerProdVec(res *uint64, a, b *Element, n uint64)
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n >= maxN {
+		// call mulVecGeneric
+		mulVecGeneric(*vector, a, b)
+		return
+	}
+
+	const blockSize = 16
+	mulVec(&(*vector)[0], &a[0], &b[0], n/blockSize, qInvNeg)
+	if n%blockSize != 0 {
+		// call mulVecGeneric on the rest
+		start := n - n%blockSize
+		mulVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+
+}
+
+// Patterns use for transposing the vectors in mulVec
+var (
+	pattern1 = [8]uint64{0, 8, 1, 9, 2, 10, 3, 11}
+	pattern2 = [8]uint64{12, 4, 13, 5, 14, 6, 15, 7}
+	pattern3 = [8]uint64{0, 1, 8, 9, 2, 3, 10, 11}
+	pattern4 = [8]uint64{12, 13, 4, 5, 14, 15, 6, 7}
+)
+
+//go:noescape
+func mulVec(res, a, b *Element, n uint64, qInvNeg uint64)
 
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	mul(z, x, y)
 	return z
diff --git a/ecc/bls12-377/fr/element_ops_amd64.s b/ecc/bls12-377/fr/element_ops_amd64.s
index ffa3b7bcae..6c42136a7a 100644
--- a/ecc/bls12-377/fr/element_ops_amd64.s
+++ b/ecc/bls12-377/fr/element_ops_amd64.s
@@ -1,627 +1,6 @@
 // +build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+// We include the hash to force the Go compiler to recompile: 9425145785761608449
+#include "../../../field/asm/element_4w_amd64.s"
 
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0x0a11800000000001
-DATA q<>+8(SB)/8, $0x59aa76fed0000001
-DATA q<>+16(SB)/8, $0x60b44d1e5c37b001
-DATA q<>+24(SB)/8, $0x12ab655e9a2ca556
-GLOBL q<>(SB), (RODATA+NOPTR), $32
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0x0a117fffffffffff
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, rb0, rb1, rb2, rb3) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-
-TEXT ·reduce(SB), NOSPLIT, $0-8
-	MOVQ res+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// MulBy3(x *Element)
-TEXT ·MulBy3(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// MulBy5(x *Element)
-TEXT ·MulBy5(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R15,DI,R8,R9)
-	REDUCE(DX,CX,BX,SI,R15,DI,R8,R9)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// MulBy13(x *Element)
-TEXT ·MulBy13(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
-
-	MOVQ DX, R11
-	MOVQ CX, R12
-	MOVQ BX, R13
-	MOVQ SI, R14
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ R11, DX
-	ADCQ R12, CX
-	ADCQ R13, BX
-	ADCQ R14, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// Butterfly(a, b *Element) sets a = a + b; b = a - b
-TEXT ·Butterfly(SB), NOSPLIT, $0-16
-	MOVQ    a+0(FP), AX
-	MOVQ    0(AX), CX
-	MOVQ    8(AX), BX
-	MOVQ    16(AX), SI
-	MOVQ    24(AX), DI
-	MOVQ    CX, R8
-	MOVQ    BX, R9
-	MOVQ    SI, R10
-	MOVQ    DI, R11
-	XORQ    AX, AX
-	MOVQ    b+8(FP), DX
-	ADDQ    0(DX), CX
-	ADCQ    8(DX), BX
-	ADCQ    16(DX), SI
-	ADCQ    24(DX), DI
-	SUBQ    0(DX), R8
-	SBBQ    8(DX), R9
-	SBBQ    16(DX), R10
-	SBBQ    24(DX), R11
-	MOVQ    $0x0a11800000000001, R12
-	MOVQ    $0x59aa76fed0000001, R13
-	MOVQ    $0x60b44d1e5c37b001, R14
-	MOVQ    $0x12ab655e9a2ca556, R15
-	CMOVQCC AX, R12
-	CMOVQCC AX, R13
-	CMOVQCC AX, R14
-	CMOVQCC AX, R15
-	ADDQ    R12, R8
-	ADCQ    R13, R9
-	ADCQ    R14, R10
-	ADCQ    R15, R11
-	MOVQ    R8, 0(DX)
-	MOVQ    R9, 8(DX)
-	MOVQ    R10, 16(DX)
-	MOVQ    R11, 24(DX)
-
-	// reduce element(CX,BX,SI,DI) using temp registers (R8,R9,R10,R11)
-	REDUCE(CX,BX,SI,DI,R8,R9,R10,R11)
-
-	MOVQ a+0(FP), AX
-	MOVQ CX, 0(AX)
-	MOVQ BX, 8(AX)
-	MOVQ SI, 16(AX)
-	MOVQ DI, 24(AX)
-	RET
-
-// addVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] + b[0...n]
-TEXT ·addVec(SB), NOSPLIT, $0-32
-	MOVQ res+0(FP), CX
-	MOVQ a+8(FP), AX
-	MOVQ b+16(FP), DX
-	MOVQ n+24(FP), BX
-
-loop_1:
-	TESTQ BX, BX
-	JEQ   done_2 // n == 0, we are done
-
-	// a[0] -> SI
-	// a[1] -> DI
-	// a[2] -> R8
-	// a[3] -> R9
-	MOVQ 0(AX), SI
-	MOVQ 8(AX), DI
-	MOVQ 16(AX), R8
-	MOVQ 24(AX), R9
-	ADDQ 0(DX), SI
-	ADCQ 8(DX), DI
-	ADCQ 16(DX), R8
-	ADCQ 24(DX), R9
-
-	// reduce element(SI,DI,R8,R9) using temp registers (R10,R11,R12,R13)
-	REDUCE(SI,DI,R8,R9,R10,R11,R12,R13)
-
-	MOVQ SI, 0(CX)
-	MOVQ DI, 8(CX)
-	MOVQ R8, 16(CX)
-	MOVQ R9, 24(CX)
-
-	// increment pointers to visit next element
-	ADDQ $32, AX
-	ADDQ $32, DX
-	ADDQ $32, CX
-	DECQ BX      // decrement n
-	JMP  loop_1
-
-done_2:
-	RET
-
-// subVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] - b[0...n]
-TEXT ·subVec(SB), NOSPLIT, $0-32
-	MOVQ res+0(FP), CX
-	MOVQ a+8(FP), AX
-	MOVQ b+16(FP), DX
-	MOVQ n+24(FP), BX
-	XORQ SI, SI
-
-loop_3:
-	TESTQ BX, BX
-	JEQ   done_4 // n == 0, we are done
-
-	// a[0] -> DI
-	// a[1] -> R8
-	// a[2] -> R9
-	// a[3] -> R10
-	MOVQ 0(AX), DI
-	MOVQ 8(AX), R8
-	MOVQ 16(AX), R9
-	MOVQ 24(AX), R10
-	SUBQ 0(DX), DI
-	SBBQ 8(DX), R8
-	SBBQ 16(DX), R9
-	SBBQ 24(DX), R10
-
-	// reduce (a-b) mod q
-	// q[0] -> R11
-	// q[1] -> R12
-	// q[2] -> R13
-	// q[3] -> R14
-	MOVQ    $0x0a11800000000001, R11
-	MOVQ    $0x59aa76fed0000001, R12
-	MOVQ    $0x60b44d1e5c37b001, R13
-	MOVQ    $0x12ab655e9a2ca556, R14
-	CMOVQCC SI, R11
-	CMOVQCC SI, R12
-	CMOVQCC SI, R13
-	CMOVQCC SI, R14
-
-	// add registers (q or 0) to a, and set to result
-	ADDQ R11, DI
-	ADCQ R12, R8
-	ADCQ R13, R9
-	ADCQ R14, R10
-	MOVQ DI, 0(CX)
-	MOVQ R8, 8(CX)
-	MOVQ R9, 16(CX)
-	MOVQ R10, 24(CX)
-
-	// increment pointers to visit next element
-	ADDQ $32, AX
-	ADDQ $32, DX
-	ADDQ $32, CX
-	DECQ BX      // decrement n
-	JMP  loop_3
-
-done_4:
-	RET
-
-// scalarMulVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] * b
-TEXT ·scalarMulVec(SB), $56-32
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_5
-	MOVQ a+8(FP), R11
-	MOVQ b+16(FP), R10
-	MOVQ n+24(FP), R12
-
-	// scalar[0] -> SI
-	// scalar[1] -> DI
-	// scalar[2] -> R8
-	// scalar[3] -> R9
-	MOVQ 0(R10), SI
-	MOVQ 8(R10), DI
-	MOVQ 16(R10), R8
-	MOVQ 24(R10), R9
-	MOVQ res+0(FP), R10
-
-loop_6:
-	TESTQ R12, R12
-	JEQ   done_7   // n == 0, we are done
-
-	// TODO @gbotrel this is generated from the same macro as the unit mul, we should refactor this in a single asm function
-	// A -> BP
-	// t[0] -> R14
-	// t[1] -> R15
-	// t[2] -> CX
-	// t[3] -> BX
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 0(R11), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ SI, R14, R15
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ DI, AX, CX
-	ADOXQ AX, R15
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ R8, AX, BX
-	ADOXQ AX, CX
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 8(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ SI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R15
-	MULXQ DI, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, CX
-	MULXQ R8, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, BX
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 16(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ SI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R15
-	MULXQ DI, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, CX
-	MULXQ R8, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, BX
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 24(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ SI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R15
-	MULXQ DI, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, CX
-	MULXQ R8, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, BX
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// reduce t mod q
-	// reduce element(R14,R15,CX,BX) using temp registers (R13,AX,DX,s0-8(SP))
-	REDUCE(R14,R15,CX,BX,R13,AX,DX,s0-8(SP))
-
-	MOVQ R14, 0(R10)
-	MOVQ R15, 8(R10)
-	MOVQ CX, 16(R10)
-	MOVQ BX, 24(R10)
-
-	// increment pointers to visit next element
-	ADDQ $32, R11
-	ADDQ $32, R10
-	DECQ R12      // decrement n
-	JMP  loop_6
-
-done_7:
-	RET
-
-noAdx_5:
-	MOVQ n+24(FP), DX
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	MOVQ DX, 8(SP)
-	MOVQ DX, 16(SP)
-	MOVQ a+8(FP), AX
-	MOVQ AX, 24(SP)
-	MOVQ DX, 32(SP)
-	MOVQ DX, 40(SP)
-	MOVQ b+16(FP), AX
-	MOVQ AX, 48(SP)
-	CALL ·scalarMulVecGeneric(SB)
-	RET
diff --git a/ecc/bls12-377/fr/element_ops_purego.go b/ecc/bls12-377/fr/element_ops_purego.go
index 9c34ebecce..f107066c79 100644
--- a/ecc/bls12-377/fr/element_ops_purego.go
+++ b/ecc/bls12-377/fr/element_ops_purego.go
@@ -78,53 +78,32 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	scalarMulVecGeneric(*vector, a, b)
 }
 
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
+
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t0, t1, t2, t3 uint64
 	var u0, u1, u2, u3 uint64
diff --git a/ecc/bls12-377/fr/element_test.go b/ecc/bls12-377/fr/element_test.go
index 9b41902857..27f878c17f 100644
--- a/ecc/bls12-377/fr/element_test.go
+++ b/ecc/bls12-377/fr/element_test.go
@@ -637,7 +637,6 @@ func TestElementBitLen(t *testing.T) {
 	))
 
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
-
 }
 
 func TestElementButterflies(t *testing.T) {
@@ -707,77 +706,6 @@ func TestElementLexicographicallyLargest(t *testing.T) {
 
 }
 
-func TestElementVecOps(t *testing.T) {
-	assert := require.New(t)
-
-	const N = 7
-	a := make(Vector, N)
-	b := make(Vector, N)
-	c := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a[i].SetRandom()
-		b[i].SetRandom()
-	}
-
-	// Vector addition
-	c.Add(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Add(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector addition failed")
-	}
-
-	// Vector subtraction
-	c.Sub(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Sub(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector subtraction failed")
-	}
-
-	// Vector scaling
-	c.ScalarMul(a, &b[0])
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Mul(&a[i], &b[0])
-		assert.True(c[i].Equal(&expected), "Vector scaling failed")
-	}
-}
-
-func BenchmarkElementVecOps(b *testing.B) {
-	// note; to benchmark against "no asm" version, use the following
-	// build tag: -tags purego
-	const N = 1024
-	a1 := make(Vector, N)
-	b1 := make(Vector, N)
-	c1 := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a1[i].SetRandom()
-		b1[i].SetRandom()
-	}
-
-	b.Run("Add", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Add(a1, b1)
-		}
-	})
-
-	b.Run("Sub", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Sub(a1, b1)
-		}
-	})
-
-	b.Run("ScalarMul", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.ScalarMul(a1, &b1[0])
-		}
-	})
-}
-
 func TestElementAdd(t *testing.T) {
 	t.Parallel()
 	parameters := gopter.DefaultTestParameters()
@@ -2345,38 +2273,38 @@ func gen() gopter.Gen {
 	}
 }
 
-func genFull() gopter.Gen {
-	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+func genRandomFq(genParams *gopter.GenParameters) Element {
+	var g Element
 
-		genRandomFq := func() Element {
-			var g Element
+	g = Element{
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+	}
 
-			g = Element{
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-			}
+	if qElement[3] != ^uint64(0) {
+		g[3] %= (qElement[3] + 1)
+	}
 
-			if qElement[3] != ^uint64(0) {
-				g[3] %= (qElement[3] + 1)
-			}
+	for !g.smallerThanModulus() {
+		g = Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[3] != ^uint64(0) {
+			g[3] %= (qElement[3] + 1)
+		}
+	}
 
-			for !g.smallerThanModulus() {
-				g = Element{
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-				}
-				if qElement[3] != ^uint64(0) {
-					g[3] %= (qElement[3] + 1)
-				}
-			}
+	return g
+}
 
-			return g
-		}
-		a := genRandomFq()
+func genFull() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
 
 		var carry uint64
 		a[0], carry = bits.Add64(a[0], qElement[0], carry)
@@ -2389,6 +2317,14 @@ func genFull() gopter.Gen {
 	}
 }
 
+func genElement() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
+		genResult := gopter.NewGenResult(a, gopter.NoShrinker)
+		return genResult
+	}
+}
+
 func (z *Element) matchVeryBigInt(aHi uint64, aInt *big.Int) error {
 	var modulus big.Int
 	var aIntMod big.Int
diff --git a/ecc/bls12-377/fr/vector.go b/ecc/bls12-377/fr/vector.go
index f39828547f..867cabbc3d 100644
--- a/ecc/bls12-377/fr/vector.go
+++ b/ecc/bls12-377/fr/vector.go
@@ -226,6 +226,32 @@ func scalarMulVecGeneric(res, a Vector, b *Element) {
 	}
 }
 
+func sumVecGeneric(res *Element, a Vector) {
+	for i := 0; i < len(a); i++ {
+		res.Add(res, &a[i])
+	}
+}
+
+func innerProductVecGeneric(res *Element, a, b Vector) {
+	if len(a) != len(b) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	var tmp Element
+	for i := 0; i < len(a); i++ {
+		tmp.Mul(&a[i], &b[i])
+		res.Add(res, &tmp)
+	}
+}
+
+func mulVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Mul(&a[i], &b[i])
+	}
+}
+
 // TODO @gbotrel make a public package out of that.
 // execute executes the work function in parallel.
 // this is copy paste from internal/parallel/parallel.go
diff --git a/ecc/bls12-377/fr/vector_test.go b/ecc/bls12-377/fr/vector_test.go
index e58f2d9a38..b6344c18b7 100644
--- a/ecc/bls12-377/fr/vector_test.go
+++ b/ecc/bls12-377/fr/vector_test.go
@@ -18,10 +18,15 @@ package fr
 
 import (
 	"bytes"
+	"fmt"
 	"github.com/stretchr/testify/require"
+	"os"
 	"reflect"
 	"sort"
 	"testing"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/prop"
 )
 
 func TestVectorSort(t *testing.T) {
@@ -88,3 +93,279 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 	}
 	return <-chErr
 }
+
+func TestVectorOps(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = 2
+	} else {
+		parameters.MinSuccessfulTests = 10
+	}
+	properties := gopter.NewProperties(parameters)
+
+	addVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Add(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Add(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	subVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Sub(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Sub(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	scalarMulVector := func(a Vector, b Element) bool {
+		c := make(Vector, len(a))
+		c.ScalarMul(a, &b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b)
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sumVector := func(a Vector) bool {
+		var sum Element
+		computed := a.Sum()
+		for i := 0; i < len(a); i++ {
+			sum.Add(&sum, &a[i])
+		}
+
+		return sum.Equal(&computed)
+	}
+
+	innerProductVector := func(a, b Vector) bool {
+		computed := a.InnerProduct(b)
+		var innerProduct Element
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			innerProduct.Add(&innerProduct, &tmp)
+		}
+
+		return innerProduct.Equal(&computed)
+	}
+
+	mulVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		a[0].SetUint64(0x24)
+		b[0].SetUint64(0x42)
+		c.Mul(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sizes := []int{1, 2, 3, 4, 8, 9, 15, 16, 509, 510, 511, 512, 513, 514}
+	type genPair struct {
+		g1, g2 gopter.Gen
+		label  string
+	}
+
+	for _, size := range sizes {
+		generators := []genPair{
+			{genZeroVector(size), genZeroVector(size), "zero vectors"},
+			{genMaxVector(size), genMaxVector(size), "max vectors"},
+			{genVector(size), genVector(size), "random vectors"},
+			{genVector(size), genZeroVector(size), "random and zero vectors"},
+		}
+		for _, gp := range generators {
+			properties.Property(fmt.Sprintf("vector addition %d - %s", size, gp.label), prop.ForAll(
+				addVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector subtraction %d - %s", size, gp.label), prop.ForAll(
+				subVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector scalar multiplication %d - %s", size, gp.label), prop.ForAll(
+				scalarMulVector,
+				gp.g1,
+				genElement(),
+			))
+
+			properties.Property(fmt.Sprintf("vector sum %d - %s", size, gp.label), prop.ForAll(
+				sumVector,
+				gp.g1,
+			))
+
+			properties.Property(fmt.Sprintf("vector inner product %d - %s", size, gp.label), prop.ForAll(
+				innerProductVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector multiplication %d - %s", size, gp.label), prop.ForAll(
+				mulVector,
+				gp.g1,
+				gp.g2,
+			))
+		}
+	}
+
+	properties.TestingRun(t, gopter.NewFormatedReporter(false, 260, os.Stdout))
+}
+
+func BenchmarkVectorOps(b *testing.B) {
+	// note; to benchmark against "no asm" version, use the following
+	// build tag: -tags purego
+	const N = 1 << 24
+	a1 := make(Vector, N)
+	b1 := make(Vector, N)
+	c1 := make(Vector, N)
+	var mixer Element
+	mixer.SetRandom()
+	for i := 1; i < N; i++ {
+		a1[i-1].SetUint64(uint64(i)).
+			Mul(&a1[i-1], &mixer)
+		b1[i-1].SetUint64(^uint64(i)).
+			Mul(&b1[i-1], &mixer)
+	}
+
+	for n := 1 << 4; n <= N; n <<= 1 {
+		b.Run(fmt.Sprintf("add %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Add(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sub %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Sub(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("scalarMul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.ScalarMul(_a, &mixer)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sum %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.Sum()
+			}
+		})
+
+		b.Run(fmt.Sprintf("innerProduct %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.InnerProduct(_b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("mul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Mul(_a, _b)
+			}
+		})
+	}
+}
+
+func genZeroVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genMaxVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+
+		qMinusOne := qElement
+		qMinusOne[0]--
+
+		for i := 0; i < size; i++ {
+			g[i] = qMinusOne
+		}
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		mixer := Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[3] != ^uint64(0) {
+			mixer[3] %= (qElement[3] + 1)
+		}
+
+		for !mixer.smallerThanModulus() {
+			mixer = Element{
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+			}
+			if qElement[3] != ^uint64(0) {
+				mixer[3] %= (qElement[3] + 1)
+			}
+		}
+
+		for i := 1; i <= size; i++ {
+			g[i-1].SetUint64(uint64(i)).
+				Mul(&g[i-1], &mixer)
+		}
+
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/ecc/bls12-377/internal/fptower/e2_amd64.go b/ecc/bls12-377/internal/fptower/e2_amd64.go
index ac68ffa578..7df0c375f5 100644
--- a/ecc/bls12-377/internal/fptower/e2_amd64.go
+++ b/ecc/bls12-377/internal/fptower/e2_amd64.go
@@ -16,6 +16,33 @@
 
 package fptower
 
+import (
+	"github.com/consensys/gnark-crypto/ecc/bls12-377/fp"
+)
+
+// q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
+// used for Montgomery reduction
+const qInvNeg uint64 = 9586122913090633727
+
+// Field modulus q (Fp)
+const (
+	q0 uint64 = 9586122913090633729
+	q1 uint64 = 1660523435060625408
+	q2 uint64 = 2230234197602682880
+	q3 uint64 = 1883307231910630287
+	q4 uint64 = 14284016967150029115
+	q5 uint64 = 121098312706494698
+)
+
+var qElement = fp.Element{
+	q0,
+	q1,
+	q2,
+	q3,
+	q4,
+	q5,
+}
+
 //go:noescape
 func addE2(res, x, y *E2)
 
diff --git a/ecc/bls12-377/internal/fptower/e2_amd64.s b/ecc/bls12-377/internal/fptower/e2_amd64.s
index 053bd8ded1..b52a56a856 100644
--- a/ecc/bls12-377/internal/fptower/e2_amd64.s
+++ b/ecc/bls12-377/internal/fptower/e2_amd64.s
@@ -14,39 +14,27 @@
 
 #include "textflag.h"
 #include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0x8508c00000000001
-DATA q<>+8(SB)/8, $0x170b5d4430000000
-DATA q<>+16(SB)/8, $0x1ef3622fba094800
-DATA q<>+24(SB)/8, $0x1a22d9f300f5138f
-DATA q<>+32(SB)/8, $0xc63b05c06ca1493b
-DATA q<>+40(SB)/8, $0x01ae3a4617c510ea
-GLOBL q<>(SB), (RODATA+NOPTR), $48
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0x8508bfffffffffff
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
+#include "go_asm.h"
 
 #define REDUCE(ra0, ra1, ra2, ra3, ra4, ra5, rb0, rb1, rb2, rb3, rb4, rb5) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	MOVQ    ra4, rb4;        \
-	SBBQ    q<>+32(SB), ra4; \
-	MOVQ    ra5, rb5;        \
-	SBBQ    q<>+40(SB), ra5; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-	CMOVQCS rb4, ra4;        \
-	CMOVQCS rb5, ra5;        \
+	MOVQ    ra0, rb0;              \
+	SUBQ    ·qElement(SB), ra0;    \
+	MOVQ    ra1, rb1;              \
+	SBBQ    ·qElement+8(SB), ra1;  \
+	MOVQ    ra2, rb2;              \
+	SBBQ    ·qElement+16(SB), ra2; \
+	MOVQ    ra3, rb3;              \
+	SBBQ    ·qElement+24(SB), ra3; \
+	MOVQ    ra4, rb4;              \
+	SBBQ    ·qElement+32(SB), ra4; \
+	MOVQ    ra5, rb5;              \
+	SBBQ    ·qElement+40(SB), ra5; \
+	CMOVQCS rb0, ra0;              \
+	CMOVQCS rb1, ra1;              \
+	CMOVQCS rb2, ra2;              \
+	CMOVQCS rb3, ra3;              \
+	CMOVQCS rb4, ra4;              \
+	CMOVQCS rb5, ra5;              \
 
 TEXT ·addE2(SB), NOSPLIT, $0-24
 	MOVQ x+8(FP), AX
diff --git a/ecc/bls12-381/fp/asm.go b/ecc/bls12-381/fp/asm_adx.go
similarity index 100%
rename from ecc/bls12-381/fp/asm.go
rename to ecc/bls12-381/fp/asm_adx.go
diff --git a/ecc/bls12-381/fp/element.go b/ecc/bls12-381/fp/element.go
index f5c2df0c28..f0bcfe51bc 100644
--- a/ecc/bls12-381/fp/element.go
+++ b/ecc/bls12-381/fp/element.go
@@ -521,32 +521,8 @@ func (z *Element) Select(c int, x0 *Element, x1 *Element) *Element {
 // and is used for testing purposes.
 func _mulGeneric(z, x, y *Element) {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t [7]uint64
 	var D uint64
diff --git a/ecc/bls12-381/fp/element_mul_amd64.s b/ecc/bls12-381/fp/element_mul_amd64.s
deleted file mode 100644
index e95c984037..0000000000
--- a/ecc/bls12-381/fp/element_mul_amd64.s
+++ /dev/null
@@ -1,857 +0,0 @@
-// +build !purego
-
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0xb9feffffffffaaab
-DATA q<>+8(SB)/8, $0x1eabfffeb153ffff
-DATA q<>+16(SB)/8, $0x6730d2a0f6b0f624
-DATA q<>+24(SB)/8, $0x64774b84f38512bf
-DATA q<>+32(SB)/8, $0x4b1ba7b6434bacd7
-DATA q<>+40(SB)/8, $0x1a0111ea397fe69a
-GLOBL q<>(SB), (RODATA+NOPTR), $48
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0x89f3fffcfffcfffd
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, ra4, ra5, rb0, rb1, rb2, rb3, rb4, rb5) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	MOVQ    ra4, rb4;        \
-	SBBQ    q<>+32(SB), ra4; \
-	MOVQ    ra5, rb5;        \
-	SBBQ    q<>+40(SB), ra5; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-	CMOVQCS rb4, ra4;        \
-	CMOVQCS rb5, ra5;        \
-
-// mul(res, x, y *Element)
-TEXT ·mul(SB), $24-24
-
-	// the algorithm is described in the Element.Mul declaration (.go)
-	// however, to benefit from the ADCX and ADOX carry chains
-	// we split the inner loops in 2:
-	// for i=0 to N-1
-	// 		for j=0 to N-1
-	// 		    (A,t[j])  := t[j] + x[j]*y[i] + A
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C + A
-
-	NO_LOCAL_POINTERS
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_1
-	MOVQ x+8(FP), R8
-
-	// x[0] -> R10
-	// x[1] -> R11
-	// x[2] -> R12
-	MOVQ 0(R8), R10
-	MOVQ 8(R8), R11
-	MOVQ 16(R8), R12
-	MOVQ y+16(FP), R13
-
-	// A -> BP
-	// t[0] -> R14
-	// t[1] -> R15
-	// t[2] -> CX
-	// t[3] -> BX
-	// t[4] -> SI
-	// t[5] -> DI
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 0(R13), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ R10, R14, R15
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ R11, AX, CX
-	ADOXQ AX, R15
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ R12, AX, BX
-	ADOXQ AX, CX
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ 24(R8), AX, SI
-	ADOXQ AX, BX
-
-	// (A,t[4])  := x[4]*y[0] + A
-	MULXQ 32(R8), AX, DI
-	ADOXQ AX, SI
-
-	// (A,t[5])  := x[5]*y[0] + A
-	MULXQ 40(R8), AX, BP
-	ADOXQ AX, DI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R9
-	ADCXQ R14, AX
-	MOVQ  R9, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ BP, DI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 8(R13), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ R10, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R15
-	MULXQ R11, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, CX
-	MULXQ R12, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, BX
-	MULXQ 24(R8), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[1] + A
-	ADCXQ BP, SI
-	MULXQ 32(R8), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[1] + A
-	ADCXQ BP, DI
-	MULXQ 40(R8), AX, BP
-	ADOXQ AX, DI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R9
-	ADCXQ R14, AX
-	MOVQ  R9, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ BP, DI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 16(R13), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ R10, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R15
-	MULXQ R11, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, CX
-	MULXQ R12, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, BX
-	MULXQ 24(R8), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[2] + A
-	ADCXQ BP, SI
-	MULXQ 32(R8), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[2] + A
-	ADCXQ BP, DI
-	MULXQ 40(R8), AX, BP
-	ADOXQ AX, DI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R9
-	ADCXQ R14, AX
-	MOVQ  R9, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ BP, DI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 24(R13), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ R10, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R15
-	MULXQ R11, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, CX
-	MULXQ R12, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, BX
-	MULXQ 24(R8), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[3] + A
-	ADCXQ BP, SI
-	MULXQ 32(R8), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[3] + A
-	ADCXQ BP, DI
-	MULXQ 40(R8), AX, BP
-	ADOXQ AX, DI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R9
-	ADCXQ R14, AX
-	MOVQ  R9, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ BP, DI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 32(R13), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[4] + A
-	MULXQ R10, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[4] + A
-	ADCXQ BP, R15
-	MULXQ R11, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[4] + A
-	ADCXQ BP, CX
-	MULXQ R12, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[4] + A
-	ADCXQ BP, BX
-	MULXQ 24(R8), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[4] + A
-	ADCXQ BP, SI
-	MULXQ 32(R8), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[4] + A
-	ADCXQ BP, DI
-	MULXQ 40(R8), AX, BP
-	ADOXQ AX, DI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R9
-	ADCXQ R14, AX
-	MOVQ  R9, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ BP, DI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 40(R13), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[5] + A
-	MULXQ R10, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[5] + A
-	ADCXQ BP, R15
-	MULXQ R11, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[5] + A
-	ADCXQ BP, CX
-	MULXQ R12, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[5] + A
-	ADCXQ BP, BX
-	MULXQ 24(R8), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[5] + A
-	ADCXQ BP, SI
-	MULXQ 32(R8), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[5] + A
-	ADCXQ BP, DI
-	MULXQ 40(R8), AX, BP
-	ADOXQ AX, DI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R9
-	ADCXQ R14, AX
-	MOVQ  R9, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ BP, DI
-
-	// reduce element(R14,R15,CX,BX,SI,DI) using temp registers (R9,R8,R13,R10,R11,R12)
-	REDUCE(R14,R15,CX,BX,SI,DI,R9,R8,R13,R10,R11,R12)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R15, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	MOVQ SI, 32(AX)
-	MOVQ DI, 40(AX)
-	RET
-
-noAdx_1:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	MOVQ x+8(FP), AX
-	MOVQ AX, 8(SP)
-	MOVQ y+16(FP), AX
-	MOVQ AX, 16(SP)
-	CALL ·_mulGeneric(SB)
-	RET
-
-TEXT ·fromMont(SB), $8-8
-	NO_LOCAL_POINTERS
-
-	// the algorithm is described here
-	// https://hackmd.io/@gnark/modular_multiplication
-	// when y = 1 we have:
-	// for i=0 to N-1
-	// 		t[i] = x[i]
-	// for i=0 to N-1
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_2
-	MOVQ res+0(FP), DX
-	MOVQ 0(DX), R14
-	MOVQ 8(DX), R15
-	MOVQ 16(DX), CX
-	MOVQ 24(DX), BX
-	MOVQ 32(DX), SI
-	MOVQ 40(DX), DI
-	XORQ DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ AX, DI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ AX, DI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ AX, DI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ AX, DI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ AX, DI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ AX, DI
-
-	// reduce element(R14,R15,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12,R13)
-	REDUCE(R14,R15,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R15, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	MOVQ SI, 32(AX)
-	MOVQ DI, 40(AX)
-	RET
-
-noAdx_2:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	CALL ·_fromMontGeneric(SB)
-	RET
diff --git a/ecc/bls12-381/fp/element_ops_amd64.go b/ecc/bls12-381/fp/element_ops_amd64.go
index 83bba45aed..ed2803d717 100644
--- a/ecc/bls12-381/fp/element_ops_amd64.go
+++ b/ecc/bls12-381/fp/element_ops_amd64.go
@@ -50,48 +50,8 @@ func Butterfly(a, b *Element)
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	mul(z, x, y)
 	return z
diff --git a/ecc/bls12-381/fp/element_ops_amd64.s b/ecc/bls12-381/fp/element_ops_amd64.s
index 830b2dd63f..cabff26f70 100644
--- a/ecc/bls12-381/fp/element_ops_amd64.s
+++ b/ecc/bls12-381/fp/element_ops_amd64.s
@@ -1,306 +1,6 @@
 // +build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+// We include the hash to force the Go compiler to recompile: 11124594824487954849
+#include "../../../field/asm/element_6w_amd64.s"
 
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0xb9feffffffffaaab
-DATA q<>+8(SB)/8, $0x1eabfffeb153ffff
-DATA q<>+16(SB)/8, $0x6730d2a0f6b0f624
-DATA q<>+24(SB)/8, $0x64774b84f38512bf
-DATA q<>+32(SB)/8, $0x4b1ba7b6434bacd7
-DATA q<>+40(SB)/8, $0x1a0111ea397fe69a
-GLOBL q<>(SB), (RODATA+NOPTR), $48
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0x89f3fffcfffcfffd
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, ra4, ra5, rb0, rb1, rb2, rb3, rb4, rb5) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	MOVQ    ra4, rb4;        \
-	SBBQ    q<>+32(SB), ra4; \
-	MOVQ    ra5, rb5;        \
-	SBBQ    q<>+40(SB), ra5; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-	CMOVQCS rb4, ra4;        \
-	CMOVQCS rb5, ra5;        \
-
-TEXT ·reduce(SB), NOSPLIT, $0-8
-	MOVQ res+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	MOVQ 40(AX), R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	MOVQ R8, 40(AX)
-	RET
-
-// MulBy3(x *Element)
-TEXT ·MulBy3(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	MOVQ 40(AX), R8
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-	ADCQ 40(AX), R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R15,R9,R10,R11,R12,R13)
-	REDUCE(DX,CX,BX,SI,DI,R8,R15,R9,R10,R11,R12,R13)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	MOVQ R8, 40(AX)
-	RET
-
-// MulBy5(x *Element)
-TEXT ·MulBy5(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	MOVQ 40(AX), R8
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R15,R9,R10,R11,R12,R13)
-	REDUCE(DX,CX,BX,SI,DI,R8,R15,R9,R10,R11,R12,R13)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-	ADCQ 40(AX), R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R14,R15,R9,R10,R11,R12)
-	REDUCE(DX,CX,BX,SI,DI,R8,R14,R15,R9,R10,R11,R12)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	MOVQ R8, 40(AX)
-	RET
-
-// MulBy13(x *Element)
-TEXT ·MulBy13(SB), $40-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	MOVQ 40(AX), R8
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP))
-
-	MOVQ DX, R15
-	MOVQ CX, s0-8(SP)
-	MOVQ BX, s1-16(SP)
-	MOVQ SI, s2-24(SP)
-	MOVQ DI, s3-32(SP)
-	MOVQ R8, s4-40(SP)
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
-
-	ADDQ R15, DX
-	ADCQ s0-8(SP), CX
-	ADCQ s1-16(SP), BX
-	ADCQ s2-24(SP), SI
-	ADCQ s3-32(SP), DI
-	ADCQ s4-40(SP), R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-	ADCQ 40(AX), R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	MOVQ R8, 40(AX)
-	RET
-
-// Butterfly(a, b *Element) sets a = a + b; b = a - b
-TEXT ·Butterfly(SB), $48-16
-	MOVQ    a+0(FP), AX
-	MOVQ    0(AX), CX
-	MOVQ    8(AX), BX
-	MOVQ    16(AX), SI
-	MOVQ    24(AX), DI
-	MOVQ    32(AX), R8
-	MOVQ    40(AX), R9
-	MOVQ    CX, R10
-	MOVQ    BX, R11
-	MOVQ    SI, R12
-	MOVQ    DI, R13
-	MOVQ    R8, R14
-	MOVQ    R9, R15
-	XORQ    AX, AX
-	MOVQ    b+8(FP), DX
-	ADDQ    0(DX), CX
-	ADCQ    8(DX), BX
-	ADCQ    16(DX), SI
-	ADCQ    24(DX), DI
-	ADCQ    32(DX), R8
-	ADCQ    40(DX), R9
-	SUBQ    0(DX), R10
-	SBBQ    8(DX), R11
-	SBBQ    16(DX), R12
-	SBBQ    24(DX), R13
-	SBBQ    32(DX), R14
-	SBBQ    40(DX), R15
-	MOVQ    CX, s0-8(SP)
-	MOVQ    BX, s1-16(SP)
-	MOVQ    SI, s2-24(SP)
-	MOVQ    DI, s3-32(SP)
-	MOVQ    R8, s4-40(SP)
-	MOVQ    R9, s5-48(SP)
-	MOVQ    $0xb9feffffffffaaab, CX
-	MOVQ    $0x1eabfffeb153ffff, BX
-	MOVQ    $0x6730d2a0f6b0f624, SI
-	MOVQ    $0x64774b84f38512bf, DI
-	MOVQ    $0x4b1ba7b6434bacd7, R8
-	MOVQ    $0x1a0111ea397fe69a, R9
-	CMOVQCC AX, CX
-	CMOVQCC AX, BX
-	CMOVQCC AX, SI
-	CMOVQCC AX, DI
-	CMOVQCC AX, R8
-	CMOVQCC AX, R9
-	ADDQ    CX, R10
-	ADCQ    BX, R11
-	ADCQ    SI, R12
-	ADCQ    DI, R13
-	ADCQ    R8, R14
-	ADCQ    R9, R15
-	MOVQ    s0-8(SP), CX
-	MOVQ    s1-16(SP), BX
-	MOVQ    s2-24(SP), SI
-	MOVQ    s3-32(SP), DI
-	MOVQ    s4-40(SP), R8
-	MOVQ    s5-48(SP), R9
-	MOVQ    R10, 0(DX)
-	MOVQ    R11, 8(DX)
-	MOVQ    R12, 16(DX)
-	MOVQ    R13, 24(DX)
-	MOVQ    R14, 32(DX)
-	MOVQ    R15, 40(DX)
-
-	// reduce element(CX,BX,SI,DI,R8,R9) using temp registers (R10,R11,R12,R13,R14,R15)
-	REDUCE(CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15)
-
-	MOVQ a+0(FP), AX
-	MOVQ CX, 0(AX)
-	MOVQ BX, 8(AX)
-	MOVQ SI, 16(AX)
-	MOVQ DI, 24(AX)
-	MOVQ R8, 32(AX)
-	MOVQ R9, 40(AX)
-	RET
diff --git a/ecc/bls12-381/fp/element_ops_purego.go b/ecc/bls12-381/fp/element_ops_purego.go
index fc10b3df30..ee3f7e7408 100644
--- a/ecc/bls12-381/fp/element_ops_purego.go
+++ b/ecc/bls12-381/fp/element_ops_purego.go
@@ -67,48 +67,8 @@ func reduce(z *Element) {
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t0, t1, t2, t3, t4, t5 uint64
 	var u0, u1, u2, u3, u4, u5 uint64
diff --git a/ecc/bls12-381/fp/element_test.go b/ecc/bls12-381/fp/element_test.go
index d070a1814a..af57409dab 100644
--- a/ecc/bls12-381/fp/element_test.go
+++ b/ecc/bls12-381/fp/element_test.go
@@ -641,7 +641,6 @@ func TestElementBitLen(t *testing.T) {
 	))
 
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
-
 }
 
 func TestElementButterflies(t *testing.T) {
@@ -711,77 +710,6 @@ func TestElementLexicographicallyLargest(t *testing.T) {
 
 }
 
-func TestElementVecOps(t *testing.T) {
-	assert := require.New(t)
-
-	const N = 7
-	a := make(Vector, N)
-	b := make(Vector, N)
-	c := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a[i].SetRandom()
-		b[i].SetRandom()
-	}
-
-	// Vector addition
-	c.Add(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Add(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector addition failed")
-	}
-
-	// Vector subtraction
-	c.Sub(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Sub(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector subtraction failed")
-	}
-
-	// Vector scaling
-	c.ScalarMul(a, &b[0])
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Mul(&a[i], &b[0])
-		assert.True(c[i].Equal(&expected), "Vector scaling failed")
-	}
-}
-
-func BenchmarkElementVecOps(b *testing.B) {
-	// note; to benchmark against "no asm" version, use the following
-	// build tag: -tags purego
-	const N = 1024
-	a1 := make(Vector, N)
-	b1 := make(Vector, N)
-	c1 := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a1[i].SetRandom()
-		b1[i].SetRandom()
-	}
-
-	b.Run("Add", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Add(a1, b1)
-		}
-	})
-
-	b.Run("Sub", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Sub(a1, b1)
-		}
-	})
-
-	b.Run("ScalarMul", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.ScalarMul(a1, &b1[0])
-		}
-	})
-}
-
 func TestElementAdd(t *testing.T) {
 	t.Parallel()
 	parameters := gopter.DefaultTestParameters()
@@ -2353,42 +2281,42 @@ func gen() gopter.Gen {
 	}
 }
 
-func genFull() gopter.Gen {
-	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+func genRandomFq(genParams *gopter.GenParameters) Element {
+	var g Element
 
-		genRandomFq := func() Element {
-			var g Element
+	g = Element{
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+	}
 
-			g = Element{
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-			}
+	if qElement[5] != ^uint64(0) {
+		g[5] %= (qElement[5] + 1)
+	}
 
-			if qElement[5] != ^uint64(0) {
-				g[5] %= (qElement[5] + 1)
-			}
+	for !g.smallerThanModulus() {
+		g = Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[5] != ^uint64(0) {
+			g[5] %= (qElement[5] + 1)
+		}
+	}
 
-			for !g.smallerThanModulus() {
-				g = Element{
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-				}
-				if qElement[5] != ^uint64(0) {
-					g[5] %= (qElement[5] + 1)
-				}
-			}
+	return g
+}
 
-			return g
-		}
-		a := genRandomFq()
+func genFull() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
 
 		var carry uint64
 		a[0], carry = bits.Add64(a[0], qElement[0], carry)
@@ -2403,6 +2331,14 @@ func genFull() gopter.Gen {
 	}
 }
 
+func genElement() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
+		genResult := gopter.NewGenResult(a, gopter.NoShrinker)
+		return genResult
+	}
+}
+
 func (z *Element) matchVeryBigInt(aHi uint64, aInt *big.Int) error {
 	var modulus big.Int
 	var aIntMod big.Int
diff --git a/ecc/bls12-381/fp/vector.go b/ecc/bls12-381/fp/vector.go
index 0df05e3373..f1d659e767 100644
--- a/ecc/bls12-381/fp/vector.go
+++ b/ecc/bls12-381/fp/vector.go
@@ -219,6 +219,25 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	scalarMulVecGeneric(*vector, a, b)
 }
 
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
+
 func addVecGeneric(res, a, b Vector) {
 	if len(a) != len(b) || len(a) != len(res) {
 		panic("vector.Add: vectors don't have the same length")
@@ -246,6 +265,32 @@ func scalarMulVecGeneric(res, a Vector, b *Element) {
 	}
 }
 
+func sumVecGeneric(res *Element, a Vector) {
+	for i := 0; i < len(a); i++ {
+		res.Add(res, &a[i])
+	}
+}
+
+func innerProductVecGeneric(res *Element, a, b Vector) {
+	if len(a) != len(b) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	var tmp Element
+	for i := 0; i < len(a); i++ {
+		tmp.Mul(&a[i], &b[i])
+		res.Add(res, &tmp)
+	}
+}
+
+func mulVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Mul(&a[i], &b[i])
+	}
+}
+
 // TODO @gbotrel make a public package out of that.
 // execute executes the work function in parallel.
 // this is copy paste from internal/parallel/parallel.go
diff --git a/ecc/bls12-381/fp/vector_test.go b/ecc/bls12-381/fp/vector_test.go
index 5d88af91c0..a8deef9451 100644
--- a/ecc/bls12-381/fp/vector_test.go
+++ b/ecc/bls12-381/fp/vector_test.go
@@ -18,10 +18,15 @@ package fp
 
 import (
 	"bytes"
+	"fmt"
 	"github.com/stretchr/testify/require"
+	"os"
 	"reflect"
 	"sort"
 	"testing"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/prop"
 )
 
 func TestVectorSort(t *testing.T) {
@@ -88,3 +93,283 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 	}
 	return <-chErr
 }
+
+func TestVectorOps(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = 2
+	} else {
+		parameters.MinSuccessfulTests = 10
+	}
+	properties := gopter.NewProperties(parameters)
+
+	addVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Add(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Add(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	subVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Sub(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Sub(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	scalarMulVector := func(a Vector, b Element) bool {
+		c := make(Vector, len(a))
+		c.ScalarMul(a, &b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b)
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sumVector := func(a Vector) bool {
+		var sum Element
+		computed := a.Sum()
+		for i := 0; i < len(a); i++ {
+			sum.Add(&sum, &a[i])
+		}
+
+		return sum.Equal(&computed)
+	}
+
+	innerProductVector := func(a, b Vector) bool {
+		computed := a.InnerProduct(b)
+		var innerProduct Element
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			innerProduct.Add(&innerProduct, &tmp)
+		}
+
+		return innerProduct.Equal(&computed)
+	}
+
+	mulVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		a[0].SetUint64(0x24)
+		b[0].SetUint64(0x42)
+		c.Mul(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sizes := []int{1, 2, 3, 4, 8, 9, 15, 16, 509, 510, 511, 512, 513, 514}
+	type genPair struct {
+		g1, g2 gopter.Gen
+		label  string
+	}
+
+	for _, size := range sizes {
+		generators := []genPair{
+			{genZeroVector(size), genZeroVector(size), "zero vectors"},
+			{genMaxVector(size), genMaxVector(size), "max vectors"},
+			{genVector(size), genVector(size), "random vectors"},
+			{genVector(size), genZeroVector(size), "random and zero vectors"},
+		}
+		for _, gp := range generators {
+			properties.Property(fmt.Sprintf("vector addition %d - %s", size, gp.label), prop.ForAll(
+				addVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector subtraction %d - %s", size, gp.label), prop.ForAll(
+				subVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector scalar multiplication %d - %s", size, gp.label), prop.ForAll(
+				scalarMulVector,
+				gp.g1,
+				genElement(),
+			))
+
+			properties.Property(fmt.Sprintf("vector sum %d - %s", size, gp.label), prop.ForAll(
+				sumVector,
+				gp.g1,
+			))
+
+			properties.Property(fmt.Sprintf("vector inner product %d - %s", size, gp.label), prop.ForAll(
+				innerProductVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector multiplication %d - %s", size, gp.label), prop.ForAll(
+				mulVector,
+				gp.g1,
+				gp.g2,
+			))
+		}
+	}
+
+	properties.TestingRun(t, gopter.NewFormatedReporter(false, 260, os.Stdout))
+}
+
+func BenchmarkVectorOps(b *testing.B) {
+	// note; to benchmark against "no asm" version, use the following
+	// build tag: -tags purego
+	const N = 1 << 24
+	a1 := make(Vector, N)
+	b1 := make(Vector, N)
+	c1 := make(Vector, N)
+	var mixer Element
+	mixer.SetRandom()
+	for i := 1; i < N; i++ {
+		a1[i-1].SetUint64(uint64(i)).
+			Mul(&a1[i-1], &mixer)
+		b1[i-1].SetUint64(^uint64(i)).
+			Mul(&b1[i-1], &mixer)
+	}
+
+	for n := 1 << 4; n <= N; n <<= 1 {
+		b.Run(fmt.Sprintf("add %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Add(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sub %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Sub(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("scalarMul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.ScalarMul(_a, &mixer)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sum %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.Sum()
+			}
+		})
+
+		b.Run(fmt.Sprintf("innerProduct %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.InnerProduct(_b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("mul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Mul(_a, _b)
+			}
+		})
+	}
+}
+
+func genZeroVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genMaxVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+
+		qMinusOne := qElement
+		qMinusOne[0]--
+
+		for i := 0; i < size; i++ {
+			g[i] = qMinusOne
+		}
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		mixer := Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[5] != ^uint64(0) {
+			mixer[5] %= (qElement[5] + 1)
+		}
+
+		for !mixer.smallerThanModulus() {
+			mixer = Element{
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+			}
+			if qElement[5] != ^uint64(0) {
+				mixer[5] %= (qElement[5] + 1)
+			}
+		}
+
+		for i := 1; i <= size; i++ {
+			g[i-1].SetUint64(uint64(i)).
+				Mul(&g[i-1], &mixer)
+		}
+
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/ecc/bls12-381/fr/asm.go b/ecc/bls12-381/fr/asm_adx.go
similarity index 100%
rename from ecc/bls12-381/fr/asm.go
rename to ecc/bls12-381/fr/asm_adx.go
diff --git a/ecc/bls12-381/fr/asm_avx.go b/ecc/bls12-381/fr/asm_avx.go
new file mode 100644
index 0000000000..955f559799
--- /dev/null
+++ b/ecc/bls12-381/fr/asm_avx.go
@@ -0,0 +1,27 @@
+//go:build !noavx
+// +build !noavx
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+import "golang.org/x/sys/cpu"
+
+var (
+	supportAvx512 = supportAdx && cpu.X86.HasAVX512 && cpu.X86.HasAVX512DQ
+	_             = supportAvx512
+)
diff --git a/ecc/bls12-381/fr/asm_noavx.go b/ecc/bls12-381/fr/asm_noavx.go
new file mode 100644
index 0000000000..e5a5b1f2cc
--- /dev/null
+++ b/ecc/bls12-381/fr/asm_noavx.go
@@ -0,0 +1,22 @@
+//go:build noavx
+// +build noavx
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+const supportAvx512 = false
diff --git a/ecc/bls12-381/fr/element.go b/ecc/bls12-381/fr/element.go
index aa6c47cdd1..dc38f08cd3 100644
--- a/ecc/bls12-381/fr/element.go
+++ b/ecc/bls12-381/fr/element.go
@@ -81,6 +81,9 @@ func Modulus() *big.Int {
 // used for Montgomery reduction
 const qInvNeg uint64 = 18446744069414584319
 
+// mu = 2^288 / q needed for partial Barrett reduction
+const mu uint64 = 9484408045
+
 func init() {
 	_modulus.SetString("73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001", 16)
 }
@@ -477,32 +480,8 @@ func (z *Element) Select(c int, x0 *Element, x1 *Element) *Element {
 // and is used for testing purposes.
 func _mulGeneric(z, x, y *Element) {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t [5]uint64
 	var D uint64
diff --git a/ecc/bls12-381/fr/element_mul_amd64.s b/ecc/bls12-381/fr/element_mul_amd64.s
deleted file mode 100644
index 396d990b75..0000000000
--- a/ecc/bls12-381/fr/element_mul_amd64.s
+++ /dev/null
@@ -1,487 +0,0 @@
-// +build !purego
-
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0xffffffff00000001
-DATA q<>+8(SB)/8, $0x53bda402fffe5bfe
-DATA q<>+16(SB)/8, $0x3339d80809a1d805
-DATA q<>+24(SB)/8, $0x73eda753299d7d48
-GLOBL q<>(SB), (RODATA+NOPTR), $32
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0xfffffffeffffffff
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, rb0, rb1, rb2, rb3) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-
-// mul(res, x, y *Element)
-TEXT ·mul(SB), $24-24
-
-	// the algorithm is described in the Element.Mul declaration (.go)
-	// however, to benefit from the ADCX and ADOX carry chains
-	// we split the inner loops in 2:
-	// for i=0 to N-1
-	// 		for j=0 to N-1
-	// 		    (A,t[j])  := t[j] + x[j]*y[i] + A
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C + A
-
-	NO_LOCAL_POINTERS
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_1
-	MOVQ x+8(FP), SI
-
-	// x[0] -> DI
-	// x[1] -> R8
-	// x[2] -> R9
-	// x[3] -> R10
-	MOVQ 0(SI), DI
-	MOVQ 8(SI), R8
-	MOVQ 16(SI), R9
-	MOVQ 24(SI), R10
-	MOVQ y+16(FP), R11
-
-	// A -> BP
-	// t[0] -> R14
-	// t[1] -> R13
-	// t[2] -> CX
-	// t[3] -> BX
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 0(R11), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ DI, R14, R13
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ R8, AX, CX
-	ADOXQ AX, R13
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ R9, AX, BX
-	ADOXQ AX, CX
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 8(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R13
-	MULXQ R8, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, CX
-	MULXQ R9, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, BX
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 16(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R13
-	MULXQ R8, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, CX
-	MULXQ R9, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, BX
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 24(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R13
-	MULXQ R8, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, CX
-	MULXQ R9, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, BX
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// reduce element(R14,R13,CX,BX) using temp registers (SI,R12,R11,DI)
-	REDUCE(R14,R13,CX,BX,SI,R12,R11,DI)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R13, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	RET
-
-noAdx_1:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	MOVQ x+8(FP), AX
-	MOVQ AX, 8(SP)
-	MOVQ y+16(FP), AX
-	MOVQ AX, 16(SP)
-	CALL ·_mulGeneric(SB)
-	RET
-
-TEXT ·fromMont(SB), $8-8
-	NO_LOCAL_POINTERS
-
-	// the algorithm is described here
-	// https://hackmd.io/@gnark/modular_multiplication
-	// when y = 1 we have:
-	// for i=0 to N-1
-	// 		t[i] = x[i]
-	// for i=0 to N-1
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_2
-	MOVQ res+0(FP), DX
-	MOVQ 0(DX), R14
-	MOVQ 8(DX), R13
-	MOVQ 16(DX), CX
-	MOVQ 24(DX), BX
-	XORQ DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-
-	// reduce element(R14,R13,CX,BX) using temp registers (SI,DI,R8,R9)
-	REDUCE(R14,R13,CX,BX,SI,DI,R8,R9)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R13, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	RET
-
-noAdx_2:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	CALL ·_fromMontGeneric(SB)
-	RET
diff --git a/ecc/bls12-381/fr/element_ops_amd64.go b/ecc/bls12-381/fr/element_ops_amd64.go
index 21568255de..b653e80069 100644
--- a/ecc/bls12-381/fr/element_ops_amd64.go
+++ b/ecc/bls12-381/fr/element_ops_amd64.go
@@ -51,7 +51,8 @@ func (vector *Vector) Add(a, b Vector) {
 	if len(a) != len(b) || len(a) != len(*vector) {
 		panic("vector.Add: vectors don't have the same length")
 	}
-	addVec(&(*vector)[0], &a[0], &b[0], uint64(len(a)))
+	n := uint64(len(a))
+	addVec(&(*vector)[0], &a[0], &b[0], n)
 }
 
 //go:noescape
@@ -75,59 +76,123 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	if len(a) != len(*vector) {
 		panic("vector.ScalarMul: vectors don't have the same length")
 	}
-	scalarMulVec(&(*vector)[0], &a[0], b, uint64(len(a)))
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || uint64(len(a)) >= maxN {
+		// call scalarMulVecGeneric
+		scalarMulVecGeneric(*vector, a, b)
+		return
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	// the code for scalarMul is identical to mulVec; and it expects at least
+	// 2 elements in the vector to fill the Z registers
+	var bb [2]Element
+	bb[0] = *b
+	bb[1] = *b
+	const blockSize = 16
+	scalarMulVec(&(*vector)[0], &a[0], &bb[0], n/blockSize, qInvNeg)
+	if n%blockSize != 0 {
+		// call scalarMulVecGeneric on the rest
+		start := n - n%blockSize
+		scalarMulVecGeneric((*vector)[start:], a[start:], b)
+	}
+}
+
+//go:noescape
+func scalarMulVec(res, a, b *Element, n uint64, qInvNeg uint64)
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	const minN = 16 * 7 // AVX512 slower than generic for small n
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n <= minN || n >= maxN {
+		// call sumVecGeneric
+		sumVecGeneric(&res, *vector)
+		return
+	}
+	sumVec(&res, &(*vector)[0], uint64(len(*vector)))
+	return
 }
 
 //go:noescape
-func scalarMulVec(res, a, b *Element, n uint64)
+func sumVec(res *Element, a *Element, n uint64)
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	if n != uint64(len(other)) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n >= maxN {
+		// call innerProductVecGeneric
+		// note; we could split the vector into smaller chunks and call innerProductVec
+		innerProductVecGeneric(&res, *vector, other)
+		return
+	}
+	innerProdVec(&res[0], &(*vector)[0], &other[0], uint64(len(*vector)))
+
+	return
+}
+
+//go:noescape
+func innerProdVec(res *uint64, a, b *Element, n uint64)
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n >= maxN {
+		// call mulVecGeneric
+		mulVecGeneric(*vector, a, b)
+		return
+	}
+
+	const blockSize = 16
+	mulVec(&(*vector)[0], &a[0], &b[0], n/blockSize, qInvNeg)
+	if n%blockSize != 0 {
+		// call mulVecGeneric on the rest
+		start := n - n%blockSize
+		mulVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+
+}
+
+// Patterns use for transposing the vectors in mulVec
+var (
+	pattern1 = [8]uint64{0, 8, 1, 9, 2, 10, 3, 11}
+	pattern2 = [8]uint64{12, 4, 13, 5, 14, 6, 15, 7}
+	pattern3 = [8]uint64{0, 1, 8, 9, 2, 3, 10, 11}
+	pattern4 = [8]uint64{12, 13, 4, 5, 14, 15, 6, 7}
+)
+
+//go:noescape
+func mulVec(res, a, b *Element, n uint64, qInvNeg uint64)
 
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	mul(z, x, y)
 	return z
diff --git a/ecc/bls12-381/fr/element_ops_amd64.s b/ecc/bls12-381/fr/element_ops_amd64.s
index caffb72b1f..6c42136a7a 100644
--- a/ecc/bls12-381/fr/element_ops_amd64.s
+++ b/ecc/bls12-381/fr/element_ops_amd64.s
@@ -1,627 +1,6 @@
 // +build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+// We include the hash to force the Go compiler to recompile: 9425145785761608449
+#include "../../../field/asm/element_4w_amd64.s"
 
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0xffffffff00000001
-DATA q<>+8(SB)/8, $0x53bda402fffe5bfe
-DATA q<>+16(SB)/8, $0x3339d80809a1d805
-DATA q<>+24(SB)/8, $0x73eda753299d7d48
-GLOBL q<>(SB), (RODATA+NOPTR), $32
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0xfffffffeffffffff
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, rb0, rb1, rb2, rb3) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-
-TEXT ·reduce(SB), NOSPLIT, $0-8
-	MOVQ res+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// MulBy3(x *Element)
-TEXT ·MulBy3(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// MulBy5(x *Element)
-TEXT ·MulBy5(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R15,DI,R8,R9)
-	REDUCE(DX,CX,BX,SI,R15,DI,R8,R9)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// MulBy13(x *Element)
-TEXT ·MulBy13(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
-
-	MOVQ DX, R11
-	MOVQ CX, R12
-	MOVQ BX, R13
-	MOVQ SI, R14
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ R11, DX
-	ADCQ R12, CX
-	ADCQ R13, BX
-	ADCQ R14, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// Butterfly(a, b *Element) sets a = a + b; b = a - b
-TEXT ·Butterfly(SB), NOSPLIT, $0-16
-	MOVQ    a+0(FP), AX
-	MOVQ    0(AX), CX
-	MOVQ    8(AX), BX
-	MOVQ    16(AX), SI
-	MOVQ    24(AX), DI
-	MOVQ    CX, R8
-	MOVQ    BX, R9
-	MOVQ    SI, R10
-	MOVQ    DI, R11
-	XORQ    AX, AX
-	MOVQ    b+8(FP), DX
-	ADDQ    0(DX), CX
-	ADCQ    8(DX), BX
-	ADCQ    16(DX), SI
-	ADCQ    24(DX), DI
-	SUBQ    0(DX), R8
-	SBBQ    8(DX), R9
-	SBBQ    16(DX), R10
-	SBBQ    24(DX), R11
-	MOVQ    $0xffffffff00000001, R12
-	MOVQ    $0x53bda402fffe5bfe, R13
-	MOVQ    $0x3339d80809a1d805, R14
-	MOVQ    $0x73eda753299d7d48, R15
-	CMOVQCC AX, R12
-	CMOVQCC AX, R13
-	CMOVQCC AX, R14
-	CMOVQCC AX, R15
-	ADDQ    R12, R8
-	ADCQ    R13, R9
-	ADCQ    R14, R10
-	ADCQ    R15, R11
-	MOVQ    R8, 0(DX)
-	MOVQ    R9, 8(DX)
-	MOVQ    R10, 16(DX)
-	MOVQ    R11, 24(DX)
-
-	// reduce element(CX,BX,SI,DI) using temp registers (R8,R9,R10,R11)
-	REDUCE(CX,BX,SI,DI,R8,R9,R10,R11)
-
-	MOVQ a+0(FP), AX
-	MOVQ CX, 0(AX)
-	MOVQ BX, 8(AX)
-	MOVQ SI, 16(AX)
-	MOVQ DI, 24(AX)
-	RET
-
-// addVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] + b[0...n]
-TEXT ·addVec(SB), NOSPLIT, $0-32
-	MOVQ res+0(FP), CX
-	MOVQ a+8(FP), AX
-	MOVQ b+16(FP), DX
-	MOVQ n+24(FP), BX
-
-loop_1:
-	TESTQ BX, BX
-	JEQ   done_2 // n == 0, we are done
-
-	// a[0] -> SI
-	// a[1] -> DI
-	// a[2] -> R8
-	// a[3] -> R9
-	MOVQ 0(AX), SI
-	MOVQ 8(AX), DI
-	MOVQ 16(AX), R8
-	MOVQ 24(AX), R9
-	ADDQ 0(DX), SI
-	ADCQ 8(DX), DI
-	ADCQ 16(DX), R8
-	ADCQ 24(DX), R9
-
-	// reduce element(SI,DI,R8,R9) using temp registers (R10,R11,R12,R13)
-	REDUCE(SI,DI,R8,R9,R10,R11,R12,R13)
-
-	MOVQ SI, 0(CX)
-	MOVQ DI, 8(CX)
-	MOVQ R8, 16(CX)
-	MOVQ R9, 24(CX)
-
-	// increment pointers to visit next element
-	ADDQ $32, AX
-	ADDQ $32, DX
-	ADDQ $32, CX
-	DECQ BX      // decrement n
-	JMP  loop_1
-
-done_2:
-	RET
-
-// subVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] - b[0...n]
-TEXT ·subVec(SB), NOSPLIT, $0-32
-	MOVQ res+0(FP), CX
-	MOVQ a+8(FP), AX
-	MOVQ b+16(FP), DX
-	MOVQ n+24(FP), BX
-	XORQ SI, SI
-
-loop_3:
-	TESTQ BX, BX
-	JEQ   done_4 // n == 0, we are done
-
-	// a[0] -> DI
-	// a[1] -> R8
-	// a[2] -> R9
-	// a[3] -> R10
-	MOVQ 0(AX), DI
-	MOVQ 8(AX), R8
-	MOVQ 16(AX), R9
-	MOVQ 24(AX), R10
-	SUBQ 0(DX), DI
-	SBBQ 8(DX), R8
-	SBBQ 16(DX), R9
-	SBBQ 24(DX), R10
-
-	// reduce (a-b) mod q
-	// q[0] -> R11
-	// q[1] -> R12
-	// q[2] -> R13
-	// q[3] -> R14
-	MOVQ    $0xffffffff00000001, R11
-	MOVQ    $0x53bda402fffe5bfe, R12
-	MOVQ    $0x3339d80809a1d805, R13
-	MOVQ    $0x73eda753299d7d48, R14
-	CMOVQCC SI, R11
-	CMOVQCC SI, R12
-	CMOVQCC SI, R13
-	CMOVQCC SI, R14
-
-	// add registers (q or 0) to a, and set to result
-	ADDQ R11, DI
-	ADCQ R12, R8
-	ADCQ R13, R9
-	ADCQ R14, R10
-	MOVQ DI, 0(CX)
-	MOVQ R8, 8(CX)
-	MOVQ R9, 16(CX)
-	MOVQ R10, 24(CX)
-
-	// increment pointers to visit next element
-	ADDQ $32, AX
-	ADDQ $32, DX
-	ADDQ $32, CX
-	DECQ BX      // decrement n
-	JMP  loop_3
-
-done_4:
-	RET
-
-// scalarMulVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] * b
-TEXT ·scalarMulVec(SB), $56-32
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_5
-	MOVQ a+8(FP), R11
-	MOVQ b+16(FP), R10
-	MOVQ n+24(FP), R12
-
-	// scalar[0] -> SI
-	// scalar[1] -> DI
-	// scalar[2] -> R8
-	// scalar[3] -> R9
-	MOVQ 0(R10), SI
-	MOVQ 8(R10), DI
-	MOVQ 16(R10), R8
-	MOVQ 24(R10), R9
-	MOVQ res+0(FP), R10
-
-loop_6:
-	TESTQ R12, R12
-	JEQ   done_7   // n == 0, we are done
-
-	// TODO @gbotrel this is generated from the same macro as the unit mul, we should refactor this in a single asm function
-	// A -> BP
-	// t[0] -> R14
-	// t[1] -> R15
-	// t[2] -> CX
-	// t[3] -> BX
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 0(R11), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ SI, R14, R15
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ DI, AX, CX
-	ADOXQ AX, R15
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ R8, AX, BX
-	ADOXQ AX, CX
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 8(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ SI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R15
-	MULXQ DI, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, CX
-	MULXQ R8, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, BX
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 16(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ SI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R15
-	MULXQ DI, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, CX
-	MULXQ R8, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, BX
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 24(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ SI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R15
-	MULXQ DI, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, CX
-	MULXQ R8, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, BX
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// reduce t mod q
-	// reduce element(R14,R15,CX,BX) using temp registers (R13,AX,DX,s0-8(SP))
-	REDUCE(R14,R15,CX,BX,R13,AX,DX,s0-8(SP))
-
-	MOVQ R14, 0(R10)
-	MOVQ R15, 8(R10)
-	MOVQ CX, 16(R10)
-	MOVQ BX, 24(R10)
-
-	// increment pointers to visit next element
-	ADDQ $32, R11
-	ADDQ $32, R10
-	DECQ R12      // decrement n
-	JMP  loop_6
-
-done_7:
-	RET
-
-noAdx_5:
-	MOVQ n+24(FP), DX
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	MOVQ DX, 8(SP)
-	MOVQ DX, 16(SP)
-	MOVQ a+8(FP), AX
-	MOVQ AX, 24(SP)
-	MOVQ DX, 32(SP)
-	MOVQ DX, 40(SP)
-	MOVQ b+16(FP), AX
-	MOVQ AX, 48(SP)
-	CALL ·scalarMulVecGeneric(SB)
-	RET
diff --git a/ecc/bls12-381/fr/element_ops_purego.go b/ecc/bls12-381/fr/element_ops_purego.go
index 50e839865c..8c10496433 100644
--- a/ecc/bls12-381/fr/element_ops_purego.go
+++ b/ecc/bls12-381/fr/element_ops_purego.go
@@ -78,53 +78,32 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	scalarMulVecGeneric(*vector, a, b)
 }
 
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
+
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t0, t1, t2, t3 uint64
 	var u0, u1, u2, u3 uint64
diff --git a/ecc/bls12-381/fr/element_test.go b/ecc/bls12-381/fr/element_test.go
index 684ea15253..b9bc1e3979 100644
--- a/ecc/bls12-381/fr/element_test.go
+++ b/ecc/bls12-381/fr/element_test.go
@@ -637,7 +637,6 @@ func TestElementBitLen(t *testing.T) {
 	))
 
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
-
 }
 
 func TestElementButterflies(t *testing.T) {
@@ -707,77 +706,6 @@ func TestElementLexicographicallyLargest(t *testing.T) {
 
 }
 
-func TestElementVecOps(t *testing.T) {
-	assert := require.New(t)
-
-	const N = 7
-	a := make(Vector, N)
-	b := make(Vector, N)
-	c := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a[i].SetRandom()
-		b[i].SetRandom()
-	}
-
-	// Vector addition
-	c.Add(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Add(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector addition failed")
-	}
-
-	// Vector subtraction
-	c.Sub(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Sub(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector subtraction failed")
-	}
-
-	// Vector scaling
-	c.ScalarMul(a, &b[0])
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Mul(&a[i], &b[0])
-		assert.True(c[i].Equal(&expected), "Vector scaling failed")
-	}
-}
-
-func BenchmarkElementVecOps(b *testing.B) {
-	// note; to benchmark against "no asm" version, use the following
-	// build tag: -tags purego
-	const N = 1024
-	a1 := make(Vector, N)
-	b1 := make(Vector, N)
-	c1 := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a1[i].SetRandom()
-		b1[i].SetRandom()
-	}
-
-	b.Run("Add", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Add(a1, b1)
-		}
-	})
-
-	b.Run("Sub", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Sub(a1, b1)
-		}
-	})
-
-	b.Run("ScalarMul", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.ScalarMul(a1, &b1[0])
-		}
-	})
-}
-
 func TestElementAdd(t *testing.T) {
 	t.Parallel()
 	parameters := gopter.DefaultTestParameters()
@@ -2345,38 +2273,38 @@ func gen() gopter.Gen {
 	}
 }
 
-func genFull() gopter.Gen {
-	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+func genRandomFq(genParams *gopter.GenParameters) Element {
+	var g Element
 
-		genRandomFq := func() Element {
-			var g Element
+	g = Element{
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+	}
 
-			g = Element{
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-			}
+	if qElement[3] != ^uint64(0) {
+		g[3] %= (qElement[3] + 1)
+	}
 
-			if qElement[3] != ^uint64(0) {
-				g[3] %= (qElement[3] + 1)
-			}
+	for !g.smallerThanModulus() {
+		g = Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[3] != ^uint64(0) {
+			g[3] %= (qElement[3] + 1)
+		}
+	}
 
-			for !g.smallerThanModulus() {
-				g = Element{
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-				}
-				if qElement[3] != ^uint64(0) {
-					g[3] %= (qElement[3] + 1)
-				}
-			}
+	return g
+}
 
-			return g
-		}
-		a := genRandomFq()
+func genFull() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
 
 		var carry uint64
 		a[0], carry = bits.Add64(a[0], qElement[0], carry)
@@ -2389,6 +2317,14 @@ func genFull() gopter.Gen {
 	}
 }
 
+func genElement() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
+		genResult := gopter.NewGenResult(a, gopter.NoShrinker)
+		return genResult
+	}
+}
+
 func (z *Element) matchVeryBigInt(aHi uint64, aInt *big.Int) error {
 	var modulus big.Int
 	var aIntMod big.Int
diff --git a/ecc/bls12-381/fr/vector.go b/ecc/bls12-381/fr/vector.go
index f39828547f..867cabbc3d 100644
--- a/ecc/bls12-381/fr/vector.go
+++ b/ecc/bls12-381/fr/vector.go
@@ -226,6 +226,32 @@ func scalarMulVecGeneric(res, a Vector, b *Element) {
 	}
 }
 
+func sumVecGeneric(res *Element, a Vector) {
+	for i := 0; i < len(a); i++ {
+		res.Add(res, &a[i])
+	}
+}
+
+func innerProductVecGeneric(res *Element, a, b Vector) {
+	if len(a) != len(b) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	var tmp Element
+	for i := 0; i < len(a); i++ {
+		tmp.Mul(&a[i], &b[i])
+		res.Add(res, &tmp)
+	}
+}
+
+func mulVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Mul(&a[i], &b[i])
+	}
+}
+
 // TODO @gbotrel make a public package out of that.
 // execute executes the work function in parallel.
 // this is copy paste from internal/parallel/parallel.go
diff --git a/ecc/bls12-381/fr/vector_test.go b/ecc/bls12-381/fr/vector_test.go
index e58f2d9a38..b6344c18b7 100644
--- a/ecc/bls12-381/fr/vector_test.go
+++ b/ecc/bls12-381/fr/vector_test.go
@@ -18,10 +18,15 @@ package fr
 
 import (
 	"bytes"
+	"fmt"
 	"github.com/stretchr/testify/require"
+	"os"
 	"reflect"
 	"sort"
 	"testing"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/prop"
 )
 
 func TestVectorSort(t *testing.T) {
@@ -88,3 +93,279 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 	}
 	return <-chErr
 }
+
+func TestVectorOps(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = 2
+	} else {
+		parameters.MinSuccessfulTests = 10
+	}
+	properties := gopter.NewProperties(parameters)
+
+	addVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Add(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Add(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	subVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Sub(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Sub(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	scalarMulVector := func(a Vector, b Element) bool {
+		c := make(Vector, len(a))
+		c.ScalarMul(a, &b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b)
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sumVector := func(a Vector) bool {
+		var sum Element
+		computed := a.Sum()
+		for i := 0; i < len(a); i++ {
+			sum.Add(&sum, &a[i])
+		}
+
+		return sum.Equal(&computed)
+	}
+
+	innerProductVector := func(a, b Vector) bool {
+		computed := a.InnerProduct(b)
+		var innerProduct Element
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			innerProduct.Add(&innerProduct, &tmp)
+		}
+
+		return innerProduct.Equal(&computed)
+	}
+
+	mulVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		a[0].SetUint64(0x24)
+		b[0].SetUint64(0x42)
+		c.Mul(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sizes := []int{1, 2, 3, 4, 8, 9, 15, 16, 509, 510, 511, 512, 513, 514}
+	type genPair struct {
+		g1, g2 gopter.Gen
+		label  string
+	}
+
+	for _, size := range sizes {
+		generators := []genPair{
+			{genZeroVector(size), genZeroVector(size), "zero vectors"},
+			{genMaxVector(size), genMaxVector(size), "max vectors"},
+			{genVector(size), genVector(size), "random vectors"},
+			{genVector(size), genZeroVector(size), "random and zero vectors"},
+		}
+		for _, gp := range generators {
+			properties.Property(fmt.Sprintf("vector addition %d - %s", size, gp.label), prop.ForAll(
+				addVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector subtraction %d - %s", size, gp.label), prop.ForAll(
+				subVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector scalar multiplication %d - %s", size, gp.label), prop.ForAll(
+				scalarMulVector,
+				gp.g1,
+				genElement(),
+			))
+
+			properties.Property(fmt.Sprintf("vector sum %d - %s", size, gp.label), prop.ForAll(
+				sumVector,
+				gp.g1,
+			))
+
+			properties.Property(fmt.Sprintf("vector inner product %d - %s", size, gp.label), prop.ForAll(
+				innerProductVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector multiplication %d - %s", size, gp.label), prop.ForAll(
+				mulVector,
+				gp.g1,
+				gp.g2,
+			))
+		}
+	}
+
+	properties.TestingRun(t, gopter.NewFormatedReporter(false, 260, os.Stdout))
+}
+
+func BenchmarkVectorOps(b *testing.B) {
+	// note; to benchmark against "no asm" version, use the following
+	// build tag: -tags purego
+	const N = 1 << 24
+	a1 := make(Vector, N)
+	b1 := make(Vector, N)
+	c1 := make(Vector, N)
+	var mixer Element
+	mixer.SetRandom()
+	for i := 1; i < N; i++ {
+		a1[i-1].SetUint64(uint64(i)).
+			Mul(&a1[i-1], &mixer)
+		b1[i-1].SetUint64(^uint64(i)).
+			Mul(&b1[i-1], &mixer)
+	}
+
+	for n := 1 << 4; n <= N; n <<= 1 {
+		b.Run(fmt.Sprintf("add %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Add(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sub %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Sub(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("scalarMul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.ScalarMul(_a, &mixer)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sum %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.Sum()
+			}
+		})
+
+		b.Run(fmt.Sprintf("innerProduct %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.InnerProduct(_b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("mul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Mul(_a, _b)
+			}
+		})
+	}
+}
+
+func genZeroVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genMaxVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+
+		qMinusOne := qElement
+		qMinusOne[0]--
+
+		for i := 0; i < size; i++ {
+			g[i] = qMinusOne
+		}
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		mixer := Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[3] != ^uint64(0) {
+			mixer[3] %= (qElement[3] + 1)
+		}
+
+		for !mixer.smallerThanModulus() {
+			mixer = Element{
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+			}
+			if qElement[3] != ^uint64(0) {
+				mixer[3] %= (qElement[3] + 1)
+			}
+		}
+
+		for i := 1; i <= size; i++ {
+			g[i-1].SetUint64(uint64(i)).
+				Mul(&g[i-1], &mixer)
+		}
+
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/ecc/bls12-381/internal/fptower/e2_amd64.go b/ecc/bls12-381/internal/fptower/e2_amd64.go
index 5121f7cca2..469d319277 100644
--- a/ecc/bls12-381/internal/fptower/e2_amd64.go
+++ b/ecc/bls12-381/internal/fptower/e2_amd64.go
@@ -16,6 +16,33 @@
 
 package fptower
 
+import (
+	"github.com/consensys/gnark-crypto/ecc/bls12-381/fp"
+)
+
+// q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
+// used for Montgomery reduction
+const qInvNeg uint64 = 9940570264628428797
+
+// Field modulus q (Fp)
+const (
+	q0 uint64 = 13402431016077863595
+	q1 uint64 = 2210141511517208575
+	q2 uint64 = 7435674573564081700
+	q3 uint64 = 7239337960414712511
+	q4 uint64 = 5412103778470702295
+	q5 uint64 = 1873798617647539866
+)
+
+var qElement = fp.Element{
+	q0,
+	q1,
+	q2,
+	q3,
+	q4,
+	q5,
+}
+
 //go:noescape
 func addE2(res, x, y *E2)
 
diff --git a/ecc/bls12-381/internal/fptower/e2_amd64.s b/ecc/bls12-381/internal/fptower/e2_amd64.s
index 7fc53f4633..e90e3ed545 100644
--- a/ecc/bls12-381/internal/fptower/e2_amd64.s
+++ b/ecc/bls12-381/internal/fptower/e2_amd64.s
@@ -14,39 +14,27 @@
 
 #include "textflag.h"
 #include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0xb9feffffffffaaab
-DATA q<>+8(SB)/8, $0x1eabfffeb153ffff
-DATA q<>+16(SB)/8, $0x6730d2a0f6b0f624
-DATA q<>+24(SB)/8, $0x64774b84f38512bf
-DATA q<>+32(SB)/8, $0x4b1ba7b6434bacd7
-DATA q<>+40(SB)/8, $0x1a0111ea397fe69a
-GLOBL q<>(SB), (RODATA+NOPTR), $48
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0x89f3fffcfffcfffd
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
+#include "go_asm.h"
 
 #define REDUCE(ra0, ra1, ra2, ra3, ra4, ra5, rb0, rb1, rb2, rb3, rb4, rb5) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	MOVQ    ra4, rb4;        \
-	SBBQ    q<>+32(SB), ra4; \
-	MOVQ    ra5, rb5;        \
-	SBBQ    q<>+40(SB), ra5; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-	CMOVQCS rb4, ra4;        \
-	CMOVQCS rb5, ra5;        \
+	MOVQ    ra0, rb0;              \
+	SUBQ    ·qElement(SB), ra0;    \
+	MOVQ    ra1, rb1;              \
+	SBBQ    ·qElement+8(SB), ra1;  \
+	MOVQ    ra2, rb2;              \
+	SBBQ    ·qElement+16(SB), ra2; \
+	MOVQ    ra3, rb3;              \
+	SBBQ    ·qElement+24(SB), ra3; \
+	MOVQ    ra4, rb4;              \
+	SBBQ    ·qElement+32(SB), ra4; \
+	MOVQ    ra5, rb5;              \
+	SBBQ    ·qElement+40(SB), ra5; \
+	CMOVQCS rb0, ra0;              \
+	CMOVQCS rb1, ra1;              \
+	CMOVQCS rb2, ra2;              \
+	CMOVQCS rb3, ra3;              \
+	CMOVQCS rb4, ra4;              \
+	CMOVQCS rb5, ra5;              \
 
 TEXT ·addE2(SB), NOSPLIT, $0-24
 	MOVQ x+8(FP), AX
@@ -421,496 +409,79 @@ TEXT ·squareAdxE2(SB), $48-16
 	// t[3] -> R11
 	// t[4] -> R12
 	// t[5] -> R13
-	// clear the flags
-	XORQ AX, AX
+#define MACC(in0, in1, in2) \
+	ADCXQ in0, in1     \
+	MULXQ in2, AX, in0 \
+	ADOXQ AX, in1      \
+
+#define DIV_SHIFT() \
+	PUSHQ BP                         \
+	MOVQ  $const_qInvNeg, DX         \
+	IMULQ R8, DX                     \
+	XORQ  AX, AX                     \
+	MULXQ ·qElement+0(SB), AX, BP    \
+	ADCXQ R8, AX                     \
+	MOVQ  BP, R8                     \
+	POPQ  BP                         \
+	MACC(R9, R8, ·qElement+8(SB))    \
+	MACC(R10, R9, ·qElement+16(SB))  \
+	MACC(R11, R10, ·qElement+24(SB)) \
+	MACC(R12, R11, ·qElement+32(SB)) \
+	MACC(R13, R12, ·qElement+40(SB)) \
+	MOVQ  $0, AX                     \
+	ADCXQ AX, R13                    \
+	ADOXQ BP, R13                    \
+
+#define MUL_WORD_0() \
+	XORQ  AX, AX       \
+	MULXQ R14, R8, R9  \
+	MULXQ R15, AX, R10 \
+	ADOXQ AX, R9       \
+	MULXQ CX, AX, R11  \
+	ADOXQ AX, R10      \
+	MULXQ BX, AX, R12  \
+	ADOXQ AX, R11      \
+	MULXQ SI, AX, R13  \
+	ADOXQ AX, R12      \
+	MULXQ DI, AX, BP   \
+	ADOXQ AX, R13      \
+	MOVQ  $0, AX       \
+	ADOXQ AX, BP       \
+	DIV_SHIFT()        \
+
+#define MUL_WORD_N() \
+	XORQ  AX, AX      \
+	MULXQ R14, AX, BP \
+	ADOXQ AX, R8      \
+	MACC(BP, R9, R15) \
+	MACC(BP, R10, CX) \
+	MACC(BP, R11, BX) \
+	MACC(BP, R12, SI) \
+	MACC(BP, R13, DI) \
+	MOVQ  $0, AX      \
+	ADCXQ AX, BP      \
+	ADOXQ AX, BP      \
+	DIV_SHIFT()       \
+
+	// mul body
 	MOVQ x+8(FP), DX
 	MOVQ 0(DX), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ R14, R8, R9
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ R15, AX, R10
-	ADOXQ AX, R9
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ CX, AX, R11
-	ADOXQ AX, R10
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ BX, AX, R12
-	ADOXQ AX, R11
-
-	// (A,t[4])  := x[4]*y[0] + A
-	MULXQ SI, AX, R13
-	ADOXQ AX, R12
-
-	// (A,t[5])  := x[5]*y[0] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_0()
 	MOVQ x+8(FP), DX
 	MOVQ 8(DX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[1] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[1] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_N()
 	MOVQ x+8(FP), DX
 	MOVQ 16(DX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[2] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[2] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_N()
 	MOVQ x+8(FP), DX
 	MOVQ 24(DX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[3] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[3] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_N()
 	MOVQ x+8(FP), DX
 	MOVQ 32(DX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[4] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[4] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[4] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[4] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[4] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[4] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_N()
 	MOVQ x+8(FP), DX
 	MOVQ 40(DX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[5] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[5] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[5] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[5] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[5] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[5] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
+	MUL_WORD_N()
 
 	// reduce element(R8,R9,R10,R11,R12,R13) using temp registers (R14,R15,CX,BX,SI,DI)
 	REDUCE(R8,R9,R10,R11,R12,R13,R14,R15,CX,BX,SI,DI)
@@ -997,490 +568,73 @@ TEXT ·squareAdxE2(SB), $48-16
 	// t[3] -> R11
 	// t[4] -> R12
 	// t[5] -> R13
-	// clear the flags
-	XORQ AX, AX
+#define MACC_0(in0, in1, in2) \
+	ADCXQ in0, in1     \
+	MULXQ in2, AX, in0 \
+	ADOXQ AX, in1      \
+
+#define DIV_SHIFT_0() \
+	PUSHQ BP                           \
+	MOVQ  $const_qInvNeg, DX           \
+	IMULQ R8, DX                       \
+	XORQ  AX, AX                       \
+	MULXQ ·qElement+0(SB), AX, BP      \
+	ADCXQ R8, AX                       \
+	MOVQ  BP, R8                       \
+	POPQ  BP                           \
+	MACC_0(R9, R8, ·qElement+8(SB))    \
+	MACC_0(R10, R9, ·qElement+16(SB))  \
+	MACC_0(R11, R10, ·qElement+24(SB)) \
+	MACC_0(R12, R11, ·qElement+32(SB)) \
+	MACC_0(R13, R12, ·qElement+40(SB)) \
+	MOVQ  $0, AX                       \
+	ADCXQ AX, R13                      \
+	ADOXQ BP, R13                      \
+
+#define MUL_WORD_0_0() \
+	XORQ  AX, AX       \
+	MULXQ R14, R8, R9  \
+	MULXQ R15, AX, R10 \
+	ADOXQ AX, R9       \
+	MULXQ CX, AX, R11  \
+	ADOXQ AX, R10      \
+	MULXQ BX, AX, R12  \
+	ADOXQ AX, R11      \
+	MULXQ SI, AX, R13  \
+	ADOXQ AX, R12      \
+	MULXQ DI, AX, BP   \
+	ADOXQ AX, R13      \
+	MOVQ  $0, AX       \
+	ADOXQ AX, BP       \
+	DIV_SHIFT_0()      \
+
+#define MUL_WORD_N_0() \
+	XORQ  AX, AX        \
+	MULXQ R14, AX, BP   \
+	ADOXQ AX, R8        \
+	MACC_0(BP, R9, R15) \
+	MACC_0(BP, R10, CX) \
+	MACC_0(BP, R11, BX) \
+	MACC_0(BP, R12, SI) \
+	MACC_0(BP, R13, DI) \
+	MOVQ  $0, AX        \
+	ADCXQ AX, BP        \
+	ADOXQ AX, BP        \
+	DIV_SHIFT_0()       \
+
+	// mul body
 	MOVQ s0-8(SP), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ R14, R8, R9
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ R15, AX, R10
-	ADOXQ AX, R9
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ CX, AX, R11
-	ADOXQ AX, R10
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ BX, AX, R12
-	ADOXQ AX, R11
-
-	// (A,t[4])  := x[4]*y[0] + A
-	MULXQ SI, AX, R13
-	ADOXQ AX, R12
-
-	// (A,t[5])  := x[5]*y[0] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_0_0()
 	MOVQ s1-16(SP), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[1] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[1] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_N_0()
 	MOVQ s2-24(SP), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[2] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[2] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_N_0()
 	MOVQ s3-32(SP), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[3] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[3] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_N_0()
 	MOVQ s4-40(SP), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[4] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[4] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[4] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[4] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[4] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[4] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_N_0()
 	MOVQ s5-48(SP), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[5] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[5] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[5] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[5] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[5] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[5] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
+	MUL_WORD_N_0()
 
 	// reduce element(R8,R9,R10,R11,R12,R13) using temp registers (R14,R15,CX,BX,SI,DI)
 	REDUCE(R8,R9,R10,R11,R12,R13,R14,R15,CX,BX,SI,DI)
@@ -1531,496 +685,79 @@ TEXT ·mulAdxE2(SB), $96-24
 	// t[3] -> R11
 	// t[4] -> R12
 	// t[5] -> R13
-	// clear the flags
-	XORQ AX, AX
+#define MACC_1(in0, in1, in2) \
+	ADCXQ in0, in1     \
+	MULXQ in2, AX, in0 \
+	ADOXQ AX, in1      \
+
+#define DIV_SHIFT_1() \
+	PUSHQ BP                           \
+	MOVQ  $const_qInvNeg, DX           \
+	IMULQ R8, DX                       \
+	XORQ  AX, AX                       \
+	MULXQ ·qElement+0(SB), AX, BP      \
+	ADCXQ R8, AX                       \
+	MOVQ  BP, R8                       \
+	POPQ  BP                           \
+	MACC_1(R9, R8, ·qElement+8(SB))    \
+	MACC_1(R10, R9, ·qElement+16(SB))  \
+	MACC_1(R11, R10, ·qElement+24(SB)) \
+	MACC_1(R12, R11, ·qElement+32(SB)) \
+	MACC_1(R13, R12, ·qElement+40(SB)) \
+	MOVQ  $0, AX                       \
+	ADCXQ AX, R13                      \
+	ADOXQ BP, R13                      \
+
+#define MUL_WORD_0_1() \
+	XORQ  AX, AX       \
+	MULXQ R14, R8, R9  \
+	MULXQ R15, AX, R10 \
+	ADOXQ AX, R9       \
+	MULXQ CX, AX, R11  \
+	ADOXQ AX, R10      \
+	MULXQ BX, AX, R12  \
+	ADOXQ AX, R11      \
+	MULXQ SI, AX, R13  \
+	ADOXQ AX, R12      \
+	MULXQ DI, AX, BP   \
+	ADOXQ AX, R13      \
+	MOVQ  $0, AX       \
+	ADOXQ AX, BP       \
+	DIV_SHIFT_1()      \
+
+#define MUL_WORD_N_1() \
+	XORQ  AX, AX        \
+	MULXQ R14, AX, BP   \
+	ADOXQ AX, R8        \
+	MACC_1(BP, R9, R15) \
+	MACC_1(BP, R10, CX) \
+	MACC_1(BP, R11, BX) \
+	MACC_1(BP, R12, SI) \
+	MACC_1(BP, R13, DI) \
+	MOVQ  $0, AX        \
+	ADCXQ AX, BP        \
+	ADOXQ AX, BP        \
+	DIV_SHIFT_1()       \
+
+	// mul body
 	MOVQ y+16(FP), DX
 	MOVQ 48(DX), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ R14, R8, R9
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ R15, AX, R10
-	ADOXQ AX, R9
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ CX, AX, R11
-	ADOXQ AX, R10
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ BX, AX, R12
-	ADOXQ AX, R11
-
-	// (A,t[4])  := x[4]*y[0] + A
-	MULXQ SI, AX, R13
-	ADOXQ AX, R12
-
-	// (A,t[5])  := x[5]*y[0] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_0_1()
 	MOVQ y+16(FP), DX
 	MOVQ 56(DX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[1] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[1] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_N_1()
 	MOVQ y+16(FP), DX
 	MOVQ 64(DX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[2] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[2] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_N_1()
 	MOVQ y+16(FP), DX
 	MOVQ 72(DX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[3] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[3] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_N_1()
 	MOVQ y+16(FP), DX
 	MOVQ 80(DX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[4] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[4] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[4] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[4] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[4] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[4] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_N_1()
 	MOVQ y+16(FP), DX
 	MOVQ 88(DX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[5] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[5] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[5] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[5] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[5] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[5] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
+	MUL_WORD_N_1()
 
 	// reduce element(R8,R9,R10,R11,R12,R13) using temp registers (R14,R15,CX,BX,SI,DI)
 	REDUCE(R8,R9,R10,R11,R12,R13,R14,R15,CX,BX,SI,DI)
@@ -2071,490 +808,73 @@ TEXT ·mulAdxE2(SB), $96-24
 	// t[3] -> R11
 	// t[4] -> R12
 	// t[5] -> R13
-	// clear the flags
-	XORQ AX, AX
+#define MACC_2(in0, in1, in2) \
+	ADCXQ in0, in1     \
+	MULXQ in2, AX, in0 \
+	ADOXQ AX, in1      \
+
+#define DIV_SHIFT_2() \
+	PUSHQ BP                           \
+	MOVQ  $const_qInvNeg, DX           \
+	IMULQ R8, DX                       \
+	XORQ  AX, AX                       \
+	MULXQ ·qElement+0(SB), AX, BP      \
+	ADCXQ R8, AX                       \
+	MOVQ  BP, R8                       \
+	POPQ  BP                           \
+	MACC_2(R9, R8, ·qElement+8(SB))    \
+	MACC_2(R10, R9, ·qElement+16(SB))  \
+	MACC_2(R11, R10, ·qElement+24(SB)) \
+	MACC_2(R12, R11, ·qElement+32(SB)) \
+	MACC_2(R13, R12, ·qElement+40(SB)) \
+	MOVQ  $0, AX                       \
+	ADCXQ AX, R13                      \
+	ADOXQ BP, R13                      \
+
+#define MUL_WORD_0_2() \
+	XORQ  AX, AX       \
+	MULXQ R14, R8, R9  \
+	MULXQ R15, AX, R10 \
+	ADOXQ AX, R9       \
+	MULXQ CX, AX, R11  \
+	ADOXQ AX, R10      \
+	MULXQ BX, AX, R12  \
+	ADOXQ AX, R11      \
+	MULXQ SI, AX, R13  \
+	ADOXQ AX, R12      \
+	MULXQ DI, AX, BP   \
+	ADOXQ AX, R13      \
+	MOVQ  $0, AX       \
+	ADOXQ AX, BP       \
+	DIV_SHIFT_2()      \
+
+#define MUL_WORD_N_2() \
+	XORQ  AX, AX        \
+	MULXQ R14, AX, BP   \
+	ADOXQ AX, R8        \
+	MACC_2(BP, R9, R15) \
+	MACC_2(BP, R10, CX) \
+	MACC_2(BP, R11, BX) \
+	MACC_2(BP, R12, SI) \
+	MACC_2(BP, R13, DI) \
+	MOVQ  $0, AX        \
+	ADCXQ AX, BP        \
+	ADOXQ AX, BP        \
+	DIV_SHIFT_2()       \
+
+	// mul body
 	MOVQ s0-8(SP), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ R14, R8, R9
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ R15, AX, R10
-	ADOXQ AX, R9
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ CX, AX, R11
-	ADOXQ AX, R10
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ BX, AX, R12
-	ADOXQ AX, R11
-
-	// (A,t[4])  := x[4]*y[0] + A
-	MULXQ SI, AX, R13
-	ADOXQ AX, R12
-
-	// (A,t[5])  := x[5]*y[0] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_0_2()
 	MOVQ s1-16(SP), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[1] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[1] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_N_2()
 	MOVQ s2-24(SP), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[2] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[2] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_N_2()
 	MOVQ s3-32(SP), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[3] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[3] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_N_2()
 	MOVQ s4-40(SP), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[4] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[4] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[4] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[4] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[4] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[4] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_N_2()
 	MOVQ s5-48(SP), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[5] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[5] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[5] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[5] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[5] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[5] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
+	MUL_WORD_N_2()
 
 	// reduce element(R8,R9,R10,R11,R12,R13) using temp registers (R14,R15,CX,BX,SI,DI)
 	REDUCE(R8,R9,R10,R11,R12,R13,R14,R15,CX,BX,SI,DI)
@@ -2580,496 +900,79 @@ TEXT ·mulAdxE2(SB), $96-24
 	// t[3] -> R11
 	// t[4] -> R12
 	// t[5] -> R13
-	// clear the flags
-	XORQ AX, AX
+#define MACC_3(in0, in1, in2) \
+	ADCXQ in0, in1     \
+	MULXQ in2, AX, in0 \
+	ADOXQ AX, in1      \
+
+#define DIV_SHIFT_3() \
+	PUSHQ BP                           \
+	MOVQ  $const_qInvNeg, DX           \
+	IMULQ R8, DX                       \
+	XORQ  AX, AX                       \
+	MULXQ ·qElement+0(SB), AX, BP      \
+	ADCXQ R8, AX                       \
+	MOVQ  BP, R8                       \
+	POPQ  BP                           \
+	MACC_3(R9, R8, ·qElement+8(SB))    \
+	MACC_3(R10, R9, ·qElement+16(SB))  \
+	MACC_3(R11, R10, ·qElement+24(SB)) \
+	MACC_3(R12, R11, ·qElement+32(SB)) \
+	MACC_3(R13, R12, ·qElement+40(SB)) \
+	MOVQ  $0, AX                       \
+	ADCXQ AX, R13                      \
+	ADOXQ BP, R13                      \
+
+#define MUL_WORD_0_3() \
+	XORQ  AX, AX       \
+	MULXQ R14, R8, R9  \
+	MULXQ R15, AX, R10 \
+	ADOXQ AX, R9       \
+	MULXQ CX, AX, R11  \
+	ADOXQ AX, R10      \
+	MULXQ BX, AX, R12  \
+	ADOXQ AX, R11      \
+	MULXQ SI, AX, R13  \
+	ADOXQ AX, R12      \
+	MULXQ DI, AX, BP   \
+	ADOXQ AX, R13      \
+	MOVQ  $0, AX       \
+	ADOXQ AX, BP       \
+	DIV_SHIFT_3()      \
+
+#define MUL_WORD_N_3() \
+	XORQ  AX, AX        \
+	MULXQ R14, AX, BP   \
+	ADOXQ AX, R8        \
+	MACC_3(BP, R9, R15) \
+	MACC_3(BP, R10, CX) \
+	MACC_3(BP, R11, BX) \
+	MACC_3(BP, R12, SI) \
+	MACC_3(BP, R13, DI) \
+	MOVQ  $0, AX        \
+	ADCXQ AX, BP        \
+	ADOXQ AX, BP        \
+	DIV_SHIFT_3()       \
+
+	// mul body
 	MOVQ y+16(FP), DX
 	MOVQ 0(DX), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ R14, R8, R9
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ R15, AX, R10
-	ADOXQ AX, R9
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ CX, AX, R11
-	ADOXQ AX, R10
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ BX, AX, R12
-	ADOXQ AX, R11
-
-	// (A,t[4])  := x[4]*y[0] + A
-	MULXQ SI, AX, R13
-	ADOXQ AX, R12
-
-	// (A,t[5])  := x[5]*y[0] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_0_3()
 	MOVQ y+16(FP), DX
 	MOVQ 8(DX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[1] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[1] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_N_3()
 	MOVQ y+16(FP), DX
 	MOVQ 16(DX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[2] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[2] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_N_3()
 	MOVQ y+16(FP), DX
 	MOVQ 24(DX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[3] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[3] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_N_3()
 	MOVQ y+16(FP), DX
 	MOVQ 32(DX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[4] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[4] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[4] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[4] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[4] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[4] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
+	MUL_WORD_N_3()
 	MOVQ y+16(FP), DX
 	MOVQ 40(DX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[5] + A
-	MULXQ R14, AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[1])  := t[1] + x[1]*y[5] + A
-	ADCXQ BP, R9
-	MULXQ R15, AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[2])  := t[2] + x[2]*y[5] + A
-	ADCXQ BP, R10
-	MULXQ CX, AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[3])  := t[3] + x[3]*y[5] + A
-	ADCXQ BP, R11
-	MULXQ BX, AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[4])  := t[4] + x[4]*y[5] + A
-	ADCXQ BP, R12
-	MULXQ SI, AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[5])  := t[5] + x[5]*y[5] + A
-	ADCXQ BP, R13
-	MULXQ DI, AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R8, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R8, AX
-	MOVQ  BP, R8
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R9, R8
-	MULXQ q<>+8(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ R10, R9
-	MULXQ q<>+16(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ R11, R10
-	MULXQ q<>+24(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ R12, R11
-	MULXQ q<>+32(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ R13, R12
-	MULXQ q<>+40(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
+	MUL_WORD_N_3()
 
 	// reduce element(R8,R9,R10,R11,R12,R13) using temp registers (R14,R15,CX,BX,SI,DI)
 	REDUCE(R8,R9,R10,R11,R12,R13,R14,R15,CX,BX,SI,DI)
diff --git a/ecc/bls24-315/fp/asm.go b/ecc/bls24-315/fp/asm_adx.go
similarity index 100%
rename from ecc/bls24-315/fp/asm.go
rename to ecc/bls24-315/fp/asm_adx.go
diff --git a/ecc/bls24-315/fp/element.go b/ecc/bls24-315/fp/element.go
index 4d61386863..4ab67695e3 100644
--- a/ecc/bls24-315/fp/element.go
+++ b/ecc/bls24-315/fp/element.go
@@ -499,32 +499,8 @@ func (z *Element) Select(c int, x0 *Element, x1 *Element) *Element {
 // and is used for testing purposes.
 func _mulGeneric(z, x, y *Element) {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t [6]uint64
 	var D uint64
diff --git a/ecc/bls24-315/fp/element_mul_amd64.s b/ecc/bls24-315/fp/element_mul_amd64.s
deleted file mode 100644
index 92bba4f58a..0000000000
--- a/ecc/bls24-315/fp/element_mul_amd64.s
+++ /dev/null
@@ -1,656 +0,0 @@
-// +build !purego
-
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0x6fe802ff40300001
-DATA q<>+8(SB)/8, $0x421ee5da52bde502
-DATA q<>+16(SB)/8, $0xdec1d01aa27a1ae0
-DATA q<>+24(SB)/8, $0xd3f7498be97c5eaf
-DATA q<>+32(SB)/8, $0x04c23a02b586d650
-GLOBL q<>(SB), (RODATA+NOPTR), $40
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0x702ff9ff402fffff
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, ra4, rb0, rb1, rb2, rb3, rb4) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	MOVQ    ra4, rb4;        \
-	SBBQ    q<>+32(SB), ra4; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-	CMOVQCS rb4, ra4;        \
-
-// mul(res, x, y *Element)
-TEXT ·mul(SB), $24-24
-
-	// the algorithm is described in the Element.Mul declaration (.go)
-	// however, to benefit from the ADCX and ADOX carry chains
-	// we split the inner loops in 2:
-	// for i=0 to N-1
-	// 		for j=0 to N-1
-	// 		    (A,t[j])  := t[j] + x[j]*y[i] + A
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C + A
-
-	NO_LOCAL_POINTERS
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_1
-	MOVQ x+8(FP), DI
-
-	// x[0] -> R9
-	// x[1] -> R10
-	// x[2] -> R11
-	MOVQ 0(DI), R9
-	MOVQ 8(DI), R10
-	MOVQ 16(DI), R11
-	MOVQ y+16(FP), R12
-
-	// A -> BP
-	// t[0] -> R14
-	// t[1] -> R13
-	// t[2] -> CX
-	// t[3] -> BX
-	// t[4] -> SI
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 0(R12), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ R9, R14, R13
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ R10, AX, CX
-	ADOXQ AX, R13
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ R11, AX, BX
-	ADOXQ AX, CX
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ 24(DI), AX, SI
-	ADOXQ AX, BX
-
-	// (A,t[4])  := x[4]*y[0] + A
-	MULXQ 32(DI), AX, BP
-	ADOXQ AX, SI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R8
-	ADCXQ R14, AX
-	MOVQ  R8, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// t[4] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ BP, SI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 8(R12), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ R9, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R13
-	MULXQ R10, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, CX
-	MULXQ R11, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, BX
-	MULXQ 24(DI), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[1] + A
-	ADCXQ BP, SI
-	MULXQ 32(DI), AX, BP
-	ADOXQ AX, SI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R8
-	ADCXQ R14, AX
-	MOVQ  R8, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// t[4] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ BP, SI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 16(R12), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ R9, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R13
-	MULXQ R10, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, CX
-	MULXQ R11, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, BX
-	MULXQ 24(DI), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[2] + A
-	ADCXQ BP, SI
-	MULXQ 32(DI), AX, BP
-	ADOXQ AX, SI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R8
-	ADCXQ R14, AX
-	MOVQ  R8, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// t[4] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ BP, SI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 24(R12), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ R9, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R13
-	MULXQ R10, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, CX
-	MULXQ R11, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, BX
-	MULXQ 24(DI), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[3] + A
-	ADCXQ BP, SI
-	MULXQ 32(DI), AX, BP
-	ADOXQ AX, SI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R8
-	ADCXQ R14, AX
-	MOVQ  R8, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// t[4] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ BP, SI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 32(R12), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[4] + A
-	MULXQ R9, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[4] + A
-	ADCXQ BP, R13
-	MULXQ R10, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[4] + A
-	ADCXQ BP, CX
-	MULXQ R11, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[4] + A
-	ADCXQ BP, BX
-	MULXQ 24(DI), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[4] + A
-	ADCXQ BP, SI
-	MULXQ 32(DI), AX, BP
-	ADOXQ AX, SI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R8
-	ADCXQ R14, AX
-	MOVQ  R8, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// t[4] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ BP, SI
-
-	// reduce element(R14,R13,CX,BX,SI) using temp registers (R8,DI,R12,R9,R10)
-	REDUCE(R14,R13,CX,BX,SI,R8,DI,R12,R9,R10)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R13, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	MOVQ SI, 32(AX)
-	RET
-
-noAdx_1:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	MOVQ x+8(FP), AX
-	MOVQ AX, 8(SP)
-	MOVQ y+16(FP), AX
-	MOVQ AX, 16(SP)
-	CALL ·_mulGeneric(SB)
-	RET
-
-TEXT ·fromMont(SB), $8-8
-	NO_LOCAL_POINTERS
-
-	// the algorithm is described here
-	// https://hackmd.io/@gnark/modular_multiplication
-	// when y = 1 we have:
-	// for i=0 to N-1
-	// 		t[i] = x[i]
-	// for i=0 to N-1
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_2
-	MOVQ res+0(FP), DX
-	MOVQ 0(DX), R14
-	MOVQ 8(DX), R13
-	MOVQ 16(DX), CX
-	MOVQ 24(DX), BX
-	MOVQ 32(DX), SI
-	XORQ DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ AX, SI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ AX, SI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ AX, SI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ AX, SI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ AX, SI
-
-	// reduce element(R14,R13,CX,BX,SI) using temp registers (DI,R8,R9,R10,R11)
-	REDUCE(R14,R13,CX,BX,SI,DI,R8,R9,R10,R11)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R13, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	MOVQ SI, 32(AX)
-	RET
-
-noAdx_2:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	CALL ·_fromMontGeneric(SB)
-	RET
diff --git a/ecc/bls24-315/fp/element_ops_amd64.go b/ecc/bls24-315/fp/element_ops_amd64.go
index 83bba45aed..ed2803d717 100644
--- a/ecc/bls24-315/fp/element_ops_amd64.go
+++ b/ecc/bls24-315/fp/element_ops_amd64.go
@@ -50,48 +50,8 @@ func Butterfly(a, b *Element)
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	mul(z, x, y)
 	return z
diff --git a/ecc/bls24-315/fp/element_ops_amd64.s b/ecc/bls24-315/fp/element_ops_amd64.s
index 9528ab595c..29314843d7 100644
--- a/ecc/bls24-315/fp/element_ops_amd64.s
+++ b/ecc/bls24-315/fp/element_ops_amd64.s
@@ -1,272 +1,6 @@
 // +build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+// We include the hash to force the Go compiler to recompile: 18184981773209750009
+#include "../../../field/asm/element_5w_amd64.s"
 
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0x6fe802ff40300001
-DATA q<>+8(SB)/8, $0x421ee5da52bde502
-DATA q<>+16(SB)/8, $0xdec1d01aa27a1ae0
-DATA q<>+24(SB)/8, $0xd3f7498be97c5eaf
-DATA q<>+32(SB)/8, $0x04c23a02b586d650
-GLOBL q<>(SB), (RODATA+NOPTR), $40
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0x702ff9ff402fffff
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, ra4, rb0, rb1, rb2, rb3, rb4) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	MOVQ    ra4, rb4;        \
-	SBBQ    q<>+32(SB), ra4; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-	CMOVQCS rb4, ra4;        \
-
-TEXT ·reduce(SB), NOSPLIT, $0-8
-	MOVQ res+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	RET
-
-// MulBy3(x *Element)
-TEXT ·MulBy3(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R13,R14,R15,R8,R9)
-	REDUCE(DX,CX,BX,SI,DI,R13,R14,R15,R8,R9)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	RET
-
-// MulBy5(x *Element)
-TEXT ·MulBy5(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R13,R14,R15,R8,R9)
-	REDUCE(DX,CX,BX,SI,DI,R13,R14,R15,R8,R9)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R10,R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,DI,R10,R11,R12,R13,R14)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	RET
-
-// MulBy13(x *Element)
-TEXT ·MulBy13(SB), $16-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP))
-	REDUCE(DX,CX,BX,SI,DI,R13,R14,R15,s0-8(SP),s1-16(SP))
-
-	MOVQ DX, R13
-	MOVQ CX, R14
-	MOVQ BX, R15
-	MOVQ SI, s0-8(SP)
-	MOVQ DI, s1-16(SP)
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
-
-	ADDQ R13, DX
-	ADCQ R14, CX
-	ADCQ R15, BX
-	ADCQ s0-8(SP), SI
-	ADCQ s1-16(SP), DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	RET
-
-// Butterfly(a, b *Element) sets a = a + b; b = a - b
-TEXT ·Butterfly(SB), $24-16
-	MOVQ    a+0(FP), AX
-	MOVQ    0(AX), CX
-	MOVQ    8(AX), BX
-	MOVQ    16(AX), SI
-	MOVQ    24(AX), DI
-	MOVQ    32(AX), R8
-	MOVQ    CX, R9
-	MOVQ    BX, R10
-	MOVQ    SI, R11
-	MOVQ    DI, R12
-	MOVQ    R8, R13
-	XORQ    AX, AX
-	MOVQ    b+8(FP), DX
-	ADDQ    0(DX), CX
-	ADCQ    8(DX), BX
-	ADCQ    16(DX), SI
-	ADCQ    24(DX), DI
-	ADCQ    32(DX), R8
-	SUBQ    0(DX), R9
-	SBBQ    8(DX), R10
-	SBBQ    16(DX), R11
-	SBBQ    24(DX), R12
-	SBBQ    32(DX), R13
-	MOVQ    CX, R14
-	MOVQ    BX, R15
-	MOVQ    SI, s0-8(SP)
-	MOVQ    DI, s1-16(SP)
-	MOVQ    R8, s2-24(SP)
-	MOVQ    $0x6fe802ff40300001, CX
-	MOVQ    $0x421ee5da52bde502, BX
-	MOVQ    $0xdec1d01aa27a1ae0, SI
-	MOVQ    $0xd3f7498be97c5eaf, DI
-	MOVQ    $0x04c23a02b586d650, R8
-	CMOVQCC AX, CX
-	CMOVQCC AX, BX
-	CMOVQCC AX, SI
-	CMOVQCC AX, DI
-	CMOVQCC AX, R8
-	ADDQ    CX, R9
-	ADCQ    BX, R10
-	ADCQ    SI, R11
-	ADCQ    DI, R12
-	ADCQ    R8, R13
-	MOVQ    R14, CX
-	MOVQ    R15, BX
-	MOVQ    s0-8(SP), SI
-	MOVQ    s1-16(SP), DI
-	MOVQ    s2-24(SP), R8
-	MOVQ    R9, 0(DX)
-	MOVQ    R10, 8(DX)
-	MOVQ    R11, 16(DX)
-	MOVQ    R12, 24(DX)
-	MOVQ    R13, 32(DX)
-
-	// reduce element(CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13)
-	REDUCE(CX,BX,SI,DI,R8,R9,R10,R11,R12,R13)
-
-	MOVQ a+0(FP), AX
-	MOVQ CX, 0(AX)
-	MOVQ BX, 8(AX)
-	MOVQ SI, 16(AX)
-	MOVQ DI, 24(AX)
-	MOVQ R8, 32(AX)
-	RET
diff --git a/ecc/bls24-315/fp/element_ops_purego.go b/ecc/bls24-315/fp/element_ops_purego.go
index 9a557a3588..4796fc3c5b 100644
--- a/ecc/bls24-315/fp/element_ops_purego.go
+++ b/ecc/bls24-315/fp/element_ops_purego.go
@@ -66,48 +66,8 @@ func reduce(z *Element) {
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t0, t1, t2, t3, t4 uint64
 	var u0, u1, u2, u3, u4 uint64
diff --git a/ecc/bls24-315/fp/element_test.go b/ecc/bls24-315/fp/element_test.go
index 665ffce6a4..d4656a26d3 100644
--- a/ecc/bls24-315/fp/element_test.go
+++ b/ecc/bls24-315/fp/element_test.go
@@ -639,7 +639,6 @@ func TestElementBitLen(t *testing.T) {
 	))
 
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
-
 }
 
 func TestElementButterflies(t *testing.T) {
@@ -709,77 +708,6 @@ func TestElementLexicographicallyLargest(t *testing.T) {
 
 }
 
-func TestElementVecOps(t *testing.T) {
-	assert := require.New(t)
-
-	const N = 7
-	a := make(Vector, N)
-	b := make(Vector, N)
-	c := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a[i].SetRandom()
-		b[i].SetRandom()
-	}
-
-	// Vector addition
-	c.Add(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Add(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector addition failed")
-	}
-
-	// Vector subtraction
-	c.Sub(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Sub(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector subtraction failed")
-	}
-
-	// Vector scaling
-	c.ScalarMul(a, &b[0])
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Mul(&a[i], &b[0])
-		assert.True(c[i].Equal(&expected), "Vector scaling failed")
-	}
-}
-
-func BenchmarkElementVecOps(b *testing.B) {
-	// note; to benchmark against "no asm" version, use the following
-	// build tag: -tags purego
-	const N = 1024
-	a1 := make(Vector, N)
-	b1 := make(Vector, N)
-	c1 := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a1[i].SetRandom()
-		b1[i].SetRandom()
-	}
-
-	b.Run("Add", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Add(a1, b1)
-		}
-	})
-
-	b.Run("Sub", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Sub(a1, b1)
-		}
-	})
-
-	b.Run("ScalarMul", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.ScalarMul(a1, &b1[0])
-		}
-	})
-}
-
 func TestElementAdd(t *testing.T) {
 	t.Parallel()
 	parameters := gopter.DefaultTestParameters()
@@ -2349,40 +2277,40 @@ func gen() gopter.Gen {
 	}
 }
 
-func genFull() gopter.Gen {
-	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+func genRandomFq(genParams *gopter.GenParameters) Element {
+	var g Element
 
-		genRandomFq := func() Element {
-			var g Element
+	g = Element{
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+	}
 
-			g = Element{
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-			}
+	if qElement[4] != ^uint64(0) {
+		g[4] %= (qElement[4] + 1)
+	}
 
-			if qElement[4] != ^uint64(0) {
-				g[4] %= (qElement[4] + 1)
-			}
+	for !g.smallerThanModulus() {
+		g = Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[4] != ^uint64(0) {
+			g[4] %= (qElement[4] + 1)
+		}
+	}
 
-			for !g.smallerThanModulus() {
-				g = Element{
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-				}
-				if qElement[4] != ^uint64(0) {
-					g[4] %= (qElement[4] + 1)
-				}
-			}
+	return g
+}
 
-			return g
-		}
-		a := genRandomFq()
+func genFull() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
 
 		var carry uint64
 		a[0], carry = bits.Add64(a[0], qElement[0], carry)
@@ -2396,6 +2324,14 @@ func genFull() gopter.Gen {
 	}
 }
 
+func genElement() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
+		genResult := gopter.NewGenResult(a, gopter.NoShrinker)
+		return genResult
+	}
+}
+
 func (z *Element) matchVeryBigInt(aHi uint64, aInt *big.Int) error {
 	var modulus big.Int
 	var aIntMod big.Int
diff --git a/ecc/bls24-315/fp/vector.go b/ecc/bls24-315/fp/vector.go
index 01b326d498..ce61e70ea0 100644
--- a/ecc/bls24-315/fp/vector.go
+++ b/ecc/bls24-315/fp/vector.go
@@ -218,6 +218,25 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	scalarMulVecGeneric(*vector, a, b)
 }
 
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
+
 func addVecGeneric(res, a, b Vector) {
 	if len(a) != len(b) || len(a) != len(res) {
 		panic("vector.Add: vectors don't have the same length")
@@ -245,6 +264,32 @@ func scalarMulVecGeneric(res, a Vector, b *Element) {
 	}
 }
 
+func sumVecGeneric(res *Element, a Vector) {
+	for i := 0; i < len(a); i++ {
+		res.Add(res, &a[i])
+	}
+}
+
+func innerProductVecGeneric(res *Element, a, b Vector) {
+	if len(a) != len(b) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	var tmp Element
+	for i := 0; i < len(a); i++ {
+		tmp.Mul(&a[i], &b[i])
+		res.Add(res, &tmp)
+	}
+}
+
+func mulVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Mul(&a[i], &b[i])
+	}
+}
+
 // TODO @gbotrel make a public package out of that.
 // execute executes the work function in parallel.
 // this is copy paste from internal/parallel/parallel.go
diff --git a/ecc/bls24-315/fp/vector_test.go b/ecc/bls24-315/fp/vector_test.go
index 5d88af91c0..c60ee08440 100644
--- a/ecc/bls24-315/fp/vector_test.go
+++ b/ecc/bls24-315/fp/vector_test.go
@@ -18,10 +18,15 @@ package fp
 
 import (
 	"bytes"
+	"fmt"
 	"github.com/stretchr/testify/require"
+	"os"
 	"reflect"
 	"sort"
 	"testing"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/prop"
 )
 
 func TestVectorSort(t *testing.T) {
@@ -88,3 +93,281 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 	}
 	return <-chErr
 }
+
+func TestVectorOps(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = 2
+	} else {
+		parameters.MinSuccessfulTests = 10
+	}
+	properties := gopter.NewProperties(parameters)
+
+	addVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Add(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Add(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	subVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Sub(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Sub(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	scalarMulVector := func(a Vector, b Element) bool {
+		c := make(Vector, len(a))
+		c.ScalarMul(a, &b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b)
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sumVector := func(a Vector) bool {
+		var sum Element
+		computed := a.Sum()
+		for i := 0; i < len(a); i++ {
+			sum.Add(&sum, &a[i])
+		}
+
+		return sum.Equal(&computed)
+	}
+
+	innerProductVector := func(a, b Vector) bool {
+		computed := a.InnerProduct(b)
+		var innerProduct Element
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			innerProduct.Add(&innerProduct, &tmp)
+		}
+
+		return innerProduct.Equal(&computed)
+	}
+
+	mulVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		a[0].SetUint64(0x24)
+		b[0].SetUint64(0x42)
+		c.Mul(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sizes := []int{1, 2, 3, 4, 8, 9, 15, 16, 509, 510, 511, 512, 513, 514}
+	type genPair struct {
+		g1, g2 gopter.Gen
+		label  string
+	}
+
+	for _, size := range sizes {
+		generators := []genPair{
+			{genZeroVector(size), genZeroVector(size), "zero vectors"},
+			{genMaxVector(size), genMaxVector(size), "max vectors"},
+			{genVector(size), genVector(size), "random vectors"},
+			{genVector(size), genZeroVector(size), "random and zero vectors"},
+		}
+		for _, gp := range generators {
+			properties.Property(fmt.Sprintf("vector addition %d - %s", size, gp.label), prop.ForAll(
+				addVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector subtraction %d - %s", size, gp.label), prop.ForAll(
+				subVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector scalar multiplication %d - %s", size, gp.label), prop.ForAll(
+				scalarMulVector,
+				gp.g1,
+				genElement(),
+			))
+
+			properties.Property(fmt.Sprintf("vector sum %d - %s", size, gp.label), prop.ForAll(
+				sumVector,
+				gp.g1,
+			))
+
+			properties.Property(fmt.Sprintf("vector inner product %d - %s", size, gp.label), prop.ForAll(
+				innerProductVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector multiplication %d - %s", size, gp.label), prop.ForAll(
+				mulVector,
+				gp.g1,
+				gp.g2,
+			))
+		}
+	}
+
+	properties.TestingRun(t, gopter.NewFormatedReporter(false, 260, os.Stdout))
+}
+
+func BenchmarkVectorOps(b *testing.B) {
+	// note; to benchmark against "no asm" version, use the following
+	// build tag: -tags purego
+	const N = 1 << 24
+	a1 := make(Vector, N)
+	b1 := make(Vector, N)
+	c1 := make(Vector, N)
+	var mixer Element
+	mixer.SetRandom()
+	for i := 1; i < N; i++ {
+		a1[i-1].SetUint64(uint64(i)).
+			Mul(&a1[i-1], &mixer)
+		b1[i-1].SetUint64(^uint64(i)).
+			Mul(&b1[i-1], &mixer)
+	}
+
+	for n := 1 << 4; n <= N; n <<= 1 {
+		b.Run(fmt.Sprintf("add %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Add(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sub %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Sub(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("scalarMul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.ScalarMul(_a, &mixer)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sum %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.Sum()
+			}
+		})
+
+		b.Run(fmt.Sprintf("innerProduct %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.InnerProduct(_b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("mul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Mul(_a, _b)
+			}
+		})
+	}
+}
+
+func genZeroVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genMaxVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+
+		qMinusOne := qElement
+		qMinusOne[0]--
+
+		for i := 0; i < size; i++ {
+			g[i] = qMinusOne
+		}
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		mixer := Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[4] != ^uint64(0) {
+			mixer[4] %= (qElement[4] + 1)
+		}
+
+		for !mixer.smallerThanModulus() {
+			mixer = Element{
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+			}
+			if qElement[4] != ^uint64(0) {
+				mixer[4] %= (qElement[4] + 1)
+			}
+		}
+
+		for i := 1; i <= size; i++ {
+			g[i-1].SetUint64(uint64(i)).
+				Mul(&g[i-1], &mixer)
+		}
+
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/ecc/bls24-315/fr/asm.go b/ecc/bls24-315/fr/asm_adx.go
similarity index 100%
rename from ecc/bls24-315/fr/asm.go
rename to ecc/bls24-315/fr/asm_adx.go
diff --git a/ecc/bls24-315/fr/asm_avx.go b/ecc/bls24-315/fr/asm_avx.go
new file mode 100644
index 0000000000..955f559799
--- /dev/null
+++ b/ecc/bls24-315/fr/asm_avx.go
@@ -0,0 +1,27 @@
+//go:build !noavx
+// +build !noavx
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+import "golang.org/x/sys/cpu"
+
+var (
+	supportAvx512 = supportAdx && cpu.X86.HasAVX512 && cpu.X86.HasAVX512DQ
+	_             = supportAvx512
+)
diff --git a/ecc/bls24-315/fr/asm_noavx.go b/ecc/bls24-315/fr/asm_noavx.go
new file mode 100644
index 0000000000..e5a5b1f2cc
--- /dev/null
+++ b/ecc/bls24-315/fr/asm_noavx.go
@@ -0,0 +1,22 @@
+//go:build noavx
+// +build noavx
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+const supportAvx512 = false
diff --git a/ecc/bls24-315/fr/element.go b/ecc/bls24-315/fr/element.go
index c24a104a66..abdb822acf 100644
--- a/ecc/bls24-315/fr/element.go
+++ b/ecc/bls24-315/fr/element.go
@@ -81,6 +81,9 @@ func Modulus() *big.Int {
 // used for Montgomery reduction
 const qInvNeg uint64 = 2184305180030271487
 
+// mu = 2^288 / q needed for partial Barrett reduction
+const mu uint64 = 43237874697
+
 func init() {
 	_modulus.SetString("196deac24a9da12b25fc7ec9cf927a98c8c480ece644e36419d0c5fd00c00001", 16)
 }
@@ -477,32 +480,8 @@ func (z *Element) Select(c int, x0 *Element, x1 *Element) *Element {
 // and is used for testing purposes.
 func _mulGeneric(z, x, y *Element) {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t [5]uint64
 	var D uint64
diff --git a/ecc/bls24-315/fr/element_mul_amd64.s b/ecc/bls24-315/fr/element_mul_amd64.s
deleted file mode 100644
index d028fed20a..0000000000
--- a/ecc/bls24-315/fr/element_mul_amd64.s
+++ /dev/null
@@ -1,487 +0,0 @@
-// +build !purego
-
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0x19d0c5fd00c00001
-DATA q<>+8(SB)/8, $0xc8c480ece644e364
-DATA q<>+16(SB)/8, $0x25fc7ec9cf927a98
-DATA q<>+24(SB)/8, $0x196deac24a9da12b
-GLOBL q<>(SB), (RODATA+NOPTR), $32
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0x1e5035fd00bfffff
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, rb0, rb1, rb2, rb3) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-
-// mul(res, x, y *Element)
-TEXT ·mul(SB), $24-24
-
-	// the algorithm is described in the Element.Mul declaration (.go)
-	// however, to benefit from the ADCX and ADOX carry chains
-	// we split the inner loops in 2:
-	// for i=0 to N-1
-	// 		for j=0 to N-1
-	// 		    (A,t[j])  := t[j] + x[j]*y[i] + A
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C + A
-
-	NO_LOCAL_POINTERS
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_1
-	MOVQ x+8(FP), SI
-
-	// x[0] -> DI
-	// x[1] -> R8
-	// x[2] -> R9
-	// x[3] -> R10
-	MOVQ 0(SI), DI
-	MOVQ 8(SI), R8
-	MOVQ 16(SI), R9
-	MOVQ 24(SI), R10
-	MOVQ y+16(FP), R11
-
-	// A -> BP
-	// t[0] -> R14
-	// t[1] -> R13
-	// t[2] -> CX
-	// t[3] -> BX
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 0(R11), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ DI, R14, R13
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ R8, AX, CX
-	ADOXQ AX, R13
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ R9, AX, BX
-	ADOXQ AX, CX
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 8(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R13
-	MULXQ R8, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, CX
-	MULXQ R9, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, BX
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 16(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R13
-	MULXQ R8, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, CX
-	MULXQ R9, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, BX
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 24(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R13
-	MULXQ R8, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, CX
-	MULXQ R9, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, BX
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// reduce element(R14,R13,CX,BX) using temp registers (SI,R12,R11,DI)
-	REDUCE(R14,R13,CX,BX,SI,R12,R11,DI)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R13, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	RET
-
-noAdx_1:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	MOVQ x+8(FP), AX
-	MOVQ AX, 8(SP)
-	MOVQ y+16(FP), AX
-	MOVQ AX, 16(SP)
-	CALL ·_mulGeneric(SB)
-	RET
-
-TEXT ·fromMont(SB), $8-8
-	NO_LOCAL_POINTERS
-
-	// the algorithm is described here
-	// https://hackmd.io/@gnark/modular_multiplication
-	// when y = 1 we have:
-	// for i=0 to N-1
-	// 		t[i] = x[i]
-	// for i=0 to N-1
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_2
-	MOVQ res+0(FP), DX
-	MOVQ 0(DX), R14
-	MOVQ 8(DX), R13
-	MOVQ 16(DX), CX
-	MOVQ 24(DX), BX
-	XORQ DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-
-	// reduce element(R14,R13,CX,BX) using temp registers (SI,DI,R8,R9)
-	REDUCE(R14,R13,CX,BX,SI,DI,R8,R9)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R13, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	RET
-
-noAdx_2:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	CALL ·_fromMontGeneric(SB)
-	RET
diff --git a/ecc/bls24-315/fr/element_ops_amd64.go b/ecc/bls24-315/fr/element_ops_amd64.go
index 21568255de..b653e80069 100644
--- a/ecc/bls24-315/fr/element_ops_amd64.go
+++ b/ecc/bls24-315/fr/element_ops_amd64.go
@@ -51,7 +51,8 @@ func (vector *Vector) Add(a, b Vector) {
 	if len(a) != len(b) || len(a) != len(*vector) {
 		panic("vector.Add: vectors don't have the same length")
 	}
-	addVec(&(*vector)[0], &a[0], &b[0], uint64(len(a)))
+	n := uint64(len(a))
+	addVec(&(*vector)[0], &a[0], &b[0], n)
 }
 
 //go:noescape
@@ -75,59 +76,123 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	if len(a) != len(*vector) {
 		panic("vector.ScalarMul: vectors don't have the same length")
 	}
-	scalarMulVec(&(*vector)[0], &a[0], b, uint64(len(a)))
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || uint64(len(a)) >= maxN {
+		// call scalarMulVecGeneric
+		scalarMulVecGeneric(*vector, a, b)
+		return
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	// the code for scalarMul is identical to mulVec; and it expects at least
+	// 2 elements in the vector to fill the Z registers
+	var bb [2]Element
+	bb[0] = *b
+	bb[1] = *b
+	const blockSize = 16
+	scalarMulVec(&(*vector)[0], &a[0], &bb[0], n/blockSize, qInvNeg)
+	if n%blockSize != 0 {
+		// call scalarMulVecGeneric on the rest
+		start := n - n%blockSize
+		scalarMulVecGeneric((*vector)[start:], a[start:], b)
+	}
+}
+
+//go:noescape
+func scalarMulVec(res, a, b *Element, n uint64, qInvNeg uint64)
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	const minN = 16 * 7 // AVX512 slower than generic for small n
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n <= minN || n >= maxN {
+		// call sumVecGeneric
+		sumVecGeneric(&res, *vector)
+		return
+	}
+	sumVec(&res, &(*vector)[0], uint64(len(*vector)))
+	return
 }
 
 //go:noescape
-func scalarMulVec(res, a, b *Element, n uint64)
+func sumVec(res *Element, a *Element, n uint64)
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	if n != uint64(len(other)) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n >= maxN {
+		// call innerProductVecGeneric
+		// note; we could split the vector into smaller chunks and call innerProductVec
+		innerProductVecGeneric(&res, *vector, other)
+		return
+	}
+	innerProdVec(&res[0], &(*vector)[0], &other[0], uint64(len(*vector)))
+
+	return
+}
+
+//go:noescape
+func innerProdVec(res *uint64, a, b *Element, n uint64)
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n >= maxN {
+		// call mulVecGeneric
+		mulVecGeneric(*vector, a, b)
+		return
+	}
+
+	const blockSize = 16
+	mulVec(&(*vector)[0], &a[0], &b[0], n/blockSize, qInvNeg)
+	if n%blockSize != 0 {
+		// call mulVecGeneric on the rest
+		start := n - n%blockSize
+		mulVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+
+}
+
+// Patterns use for transposing the vectors in mulVec
+var (
+	pattern1 = [8]uint64{0, 8, 1, 9, 2, 10, 3, 11}
+	pattern2 = [8]uint64{12, 4, 13, 5, 14, 6, 15, 7}
+	pattern3 = [8]uint64{0, 1, 8, 9, 2, 3, 10, 11}
+	pattern4 = [8]uint64{12, 13, 4, 5, 14, 15, 6, 7}
+)
+
+//go:noescape
+func mulVec(res, a, b *Element, n uint64, qInvNeg uint64)
 
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	mul(z, x, y)
 	return z
diff --git a/ecc/bls24-315/fr/element_ops_amd64.s b/ecc/bls24-315/fr/element_ops_amd64.s
index 2e52c653bf..6c42136a7a 100644
--- a/ecc/bls24-315/fr/element_ops_amd64.s
+++ b/ecc/bls24-315/fr/element_ops_amd64.s
@@ -1,627 +1,6 @@
 // +build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+// We include the hash to force the Go compiler to recompile: 9425145785761608449
+#include "../../../field/asm/element_4w_amd64.s"
 
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0x19d0c5fd00c00001
-DATA q<>+8(SB)/8, $0xc8c480ece644e364
-DATA q<>+16(SB)/8, $0x25fc7ec9cf927a98
-DATA q<>+24(SB)/8, $0x196deac24a9da12b
-GLOBL q<>(SB), (RODATA+NOPTR), $32
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0x1e5035fd00bfffff
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, rb0, rb1, rb2, rb3) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-
-TEXT ·reduce(SB), NOSPLIT, $0-8
-	MOVQ res+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// MulBy3(x *Element)
-TEXT ·MulBy3(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// MulBy5(x *Element)
-TEXT ·MulBy5(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R15,DI,R8,R9)
-	REDUCE(DX,CX,BX,SI,R15,DI,R8,R9)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// MulBy13(x *Element)
-TEXT ·MulBy13(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
-
-	MOVQ DX, R11
-	MOVQ CX, R12
-	MOVQ BX, R13
-	MOVQ SI, R14
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ R11, DX
-	ADCQ R12, CX
-	ADCQ R13, BX
-	ADCQ R14, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// Butterfly(a, b *Element) sets a = a + b; b = a - b
-TEXT ·Butterfly(SB), NOSPLIT, $0-16
-	MOVQ    a+0(FP), AX
-	MOVQ    0(AX), CX
-	MOVQ    8(AX), BX
-	MOVQ    16(AX), SI
-	MOVQ    24(AX), DI
-	MOVQ    CX, R8
-	MOVQ    BX, R9
-	MOVQ    SI, R10
-	MOVQ    DI, R11
-	XORQ    AX, AX
-	MOVQ    b+8(FP), DX
-	ADDQ    0(DX), CX
-	ADCQ    8(DX), BX
-	ADCQ    16(DX), SI
-	ADCQ    24(DX), DI
-	SUBQ    0(DX), R8
-	SBBQ    8(DX), R9
-	SBBQ    16(DX), R10
-	SBBQ    24(DX), R11
-	MOVQ    $0x19d0c5fd00c00001, R12
-	MOVQ    $0xc8c480ece644e364, R13
-	MOVQ    $0x25fc7ec9cf927a98, R14
-	MOVQ    $0x196deac24a9da12b, R15
-	CMOVQCC AX, R12
-	CMOVQCC AX, R13
-	CMOVQCC AX, R14
-	CMOVQCC AX, R15
-	ADDQ    R12, R8
-	ADCQ    R13, R9
-	ADCQ    R14, R10
-	ADCQ    R15, R11
-	MOVQ    R8, 0(DX)
-	MOVQ    R9, 8(DX)
-	MOVQ    R10, 16(DX)
-	MOVQ    R11, 24(DX)
-
-	// reduce element(CX,BX,SI,DI) using temp registers (R8,R9,R10,R11)
-	REDUCE(CX,BX,SI,DI,R8,R9,R10,R11)
-
-	MOVQ a+0(FP), AX
-	MOVQ CX, 0(AX)
-	MOVQ BX, 8(AX)
-	MOVQ SI, 16(AX)
-	MOVQ DI, 24(AX)
-	RET
-
-// addVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] + b[0...n]
-TEXT ·addVec(SB), NOSPLIT, $0-32
-	MOVQ res+0(FP), CX
-	MOVQ a+8(FP), AX
-	MOVQ b+16(FP), DX
-	MOVQ n+24(FP), BX
-
-loop_1:
-	TESTQ BX, BX
-	JEQ   done_2 // n == 0, we are done
-
-	// a[0] -> SI
-	// a[1] -> DI
-	// a[2] -> R8
-	// a[3] -> R9
-	MOVQ 0(AX), SI
-	MOVQ 8(AX), DI
-	MOVQ 16(AX), R8
-	MOVQ 24(AX), R9
-	ADDQ 0(DX), SI
-	ADCQ 8(DX), DI
-	ADCQ 16(DX), R8
-	ADCQ 24(DX), R9
-
-	// reduce element(SI,DI,R8,R9) using temp registers (R10,R11,R12,R13)
-	REDUCE(SI,DI,R8,R9,R10,R11,R12,R13)
-
-	MOVQ SI, 0(CX)
-	MOVQ DI, 8(CX)
-	MOVQ R8, 16(CX)
-	MOVQ R9, 24(CX)
-
-	// increment pointers to visit next element
-	ADDQ $32, AX
-	ADDQ $32, DX
-	ADDQ $32, CX
-	DECQ BX      // decrement n
-	JMP  loop_1
-
-done_2:
-	RET
-
-// subVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] - b[0...n]
-TEXT ·subVec(SB), NOSPLIT, $0-32
-	MOVQ res+0(FP), CX
-	MOVQ a+8(FP), AX
-	MOVQ b+16(FP), DX
-	MOVQ n+24(FP), BX
-	XORQ SI, SI
-
-loop_3:
-	TESTQ BX, BX
-	JEQ   done_4 // n == 0, we are done
-
-	// a[0] -> DI
-	// a[1] -> R8
-	// a[2] -> R9
-	// a[3] -> R10
-	MOVQ 0(AX), DI
-	MOVQ 8(AX), R8
-	MOVQ 16(AX), R9
-	MOVQ 24(AX), R10
-	SUBQ 0(DX), DI
-	SBBQ 8(DX), R8
-	SBBQ 16(DX), R9
-	SBBQ 24(DX), R10
-
-	// reduce (a-b) mod q
-	// q[0] -> R11
-	// q[1] -> R12
-	// q[2] -> R13
-	// q[3] -> R14
-	MOVQ    $0x19d0c5fd00c00001, R11
-	MOVQ    $0xc8c480ece644e364, R12
-	MOVQ    $0x25fc7ec9cf927a98, R13
-	MOVQ    $0x196deac24a9da12b, R14
-	CMOVQCC SI, R11
-	CMOVQCC SI, R12
-	CMOVQCC SI, R13
-	CMOVQCC SI, R14
-
-	// add registers (q or 0) to a, and set to result
-	ADDQ R11, DI
-	ADCQ R12, R8
-	ADCQ R13, R9
-	ADCQ R14, R10
-	MOVQ DI, 0(CX)
-	MOVQ R8, 8(CX)
-	MOVQ R9, 16(CX)
-	MOVQ R10, 24(CX)
-
-	// increment pointers to visit next element
-	ADDQ $32, AX
-	ADDQ $32, DX
-	ADDQ $32, CX
-	DECQ BX      // decrement n
-	JMP  loop_3
-
-done_4:
-	RET
-
-// scalarMulVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] * b
-TEXT ·scalarMulVec(SB), $56-32
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_5
-	MOVQ a+8(FP), R11
-	MOVQ b+16(FP), R10
-	MOVQ n+24(FP), R12
-
-	// scalar[0] -> SI
-	// scalar[1] -> DI
-	// scalar[2] -> R8
-	// scalar[3] -> R9
-	MOVQ 0(R10), SI
-	MOVQ 8(R10), DI
-	MOVQ 16(R10), R8
-	MOVQ 24(R10), R9
-	MOVQ res+0(FP), R10
-
-loop_6:
-	TESTQ R12, R12
-	JEQ   done_7   // n == 0, we are done
-
-	// TODO @gbotrel this is generated from the same macro as the unit mul, we should refactor this in a single asm function
-	// A -> BP
-	// t[0] -> R14
-	// t[1] -> R15
-	// t[2] -> CX
-	// t[3] -> BX
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 0(R11), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ SI, R14, R15
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ DI, AX, CX
-	ADOXQ AX, R15
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ R8, AX, BX
-	ADOXQ AX, CX
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 8(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ SI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R15
-	MULXQ DI, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, CX
-	MULXQ R8, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, BX
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 16(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ SI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R15
-	MULXQ DI, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, CX
-	MULXQ R8, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, BX
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 24(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ SI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R15
-	MULXQ DI, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, CX
-	MULXQ R8, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, BX
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// reduce t mod q
-	// reduce element(R14,R15,CX,BX) using temp registers (R13,AX,DX,s0-8(SP))
-	REDUCE(R14,R15,CX,BX,R13,AX,DX,s0-8(SP))
-
-	MOVQ R14, 0(R10)
-	MOVQ R15, 8(R10)
-	MOVQ CX, 16(R10)
-	MOVQ BX, 24(R10)
-
-	// increment pointers to visit next element
-	ADDQ $32, R11
-	ADDQ $32, R10
-	DECQ R12      // decrement n
-	JMP  loop_6
-
-done_7:
-	RET
-
-noAdx_5:
-	MOVQ n+24(FP), DX
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	MOVQ DX, 8(SP)
-	MOVQ DX, 16(SP)
-	MOVQ a+8(FP), AX
-	MOVQ AX, 24(SP)
-	MOVQ DX, 32(SP)
-	MOVQ DX, 40(SP)
-	MOVQ b+16(FP), AX
-	MOVQ AX, 48(SP)
-	CALL ·scalarMulVecGeneric(SB)
-	RET
diff --git a/ecc/bls24-315/fr/element_ops_purego.go b/ecc/bls24-315/fr/element_ops_purego.go
index 7b6cfd87b4..e7a8817f01 100644
--- a/ecc/bls24-315/fr/element_ops_purego.go
+++ b/ecc/bls24-315/fr/element_ops_purego.go
@@ -78,53 +78,32 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	scalarMulVecGeneric(*vector, a, b)
 }
 
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
+
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t0, t1, t2, t3 uint64
 	var u0, u1, u2, u3 uint64
diff --git a/ecc/bls24-315/fr/element_test.go b/ecc/bls24-315/fr/element_test.go
index ac030b6d05..7933f3aa3c 100644
--- a/ecc/bls24-315/fr/element_test.go
+++ b/ecc/bls24-315/fr/element_test.go
@@ -637,7 +637,6 @@ func TestElementBitLen(t *testing.T) {
 	))
 
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
-
 }
 
 func TestElementButterflies(t *testing.T) {
@@ -707,77 +706,6 @@ func TestElementLexicographicallyLargest(t *testing.T) {
 
 }
 
-func TestElementVecOps(t *testing.T) {
-	assert := require.New(t)
-
-	const N = 7
-	a := make(Vector, N)
-	b := make(Vector, N)
-	c := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a[i].SetRandom()
-		b[i].SetRandom()
-	}
-
-	// Vector addition
-	c.Add(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Add(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector addition failed")
-	}
-
-	// Vector subtraction
-	c.Sub(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Sub(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector subtraction failed")
-	}
-
-	// Vector scaling
-	c.ScalarMul(a, &b[0])
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Mul(&a[i], &b[0])
-		assert.True(c[i].Equal(&expected), "Vector scaling failed")
-	}
-}
-
-func BenchmarkElementVecOps(b *testing.B) {
-	// note; to benchmark against "no asm" version, use the following
-	// build tag: -tags purego
-	const N = 1024
-	a1 := make(Vector, N)
-	b1 := make(Vector, N)
-	c1 := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a1[i].SetRandom()
-		b1[i].SetRandom()
-	}
-
-	b.Run("Add", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Add(a1, b1)
-		}
-	})
-
-	b.Run("Sub", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Sub(a1, b1)
-		}
-	})
-
-	b.Run("ScalarMul", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.ScalarMul(a1, &b1[0])
-		}
-	})
-}
-
 func TestElementAdd(t *testing.T) {
 	t.Parallel()
 	parameters := gopter.DefaultTestParameters()
@@ -2345,38 +2273,38 @@ func gen() gopter.Gen {
 	}
 }
 
-func genFull() gopter.Gen {
-	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+func genRandomFq(genParams *gopter.GenParameters) Element {
+	var g Element
 
-		genRandomFq := func() Element {
-			var g Element
+	g = Element{
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+	}
 
-			g = Element{
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-			}
+	if qElement[3] != ^uint64(0) {
+		g[3] %= (qElement[3] + 1)
+	}
 
-			if qElement[3] != ^uint64(0) {
-				g[3] %= (qElement[3] + 1)
-			}
+	for !g.smallerThanModulus() {
+		g = Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[3] != ^uint64(0) {
+			g[3] %= (qElement[3] + 1)
+		}
+	}
 
-			for !g.smallerThanModulus() {
-				g = Element{
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-				}
-				if qElement[3] != ^uint64(0) {
-					g[3] %= (qElement[3] + 1)
-				}
-			}
+	return g
+}
 
-			return g
-		}
-		a := genRandomFq()
+func genFull() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
 
 		var carry uint64
 		a[0], carry = bits.Add64(a[0], qElement[0], carry)
@@ -2389,6 +2317,14 @@ func genFull() gopter.Gen {
 	}
 }
 
+func genElement() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
+		genResult := gopter.NewGenResult(a, gopter.NoShrinker)
+		return genResult
+	}
+}
+
 func (z *Element) matchVeryBigInt(aHi uint64, aInt *big.Int) error {
 	var modulus big.Int
 	var aIntMod big.Int
diff --git a/ecc/bls24-315/fr/vector.go b/ecc/bls24-315/fr/vector.go
index f39828547f..867cabbc3d 100644
--- a/ecc/bls24-315/fr/vector.go
+++ b/ecc/bls24-315/fr/vector.go
@@ -226,6 +226,32 @@ func scalarMulVecGeneric(res, a Vector, b *Element) {
 	}
 }
 
+func sumVecGeneric(res *Element, a Vector) {
+	for i := 0; i < len(a); i++ {
+		res.Add(res, &a[i])
+	}
+}
+
+func innerProductVecGeneric(res *Element, a, b Vector) {
+	if len(a) != len(b) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	var tmp Element
+	for i := 0; i < len(a); i++ {
+		tmp.Mul(&a[i], &b[i])
+		res.Add(res, &tmp)
+	}
+}
+
+func mulVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Mul(&a[i], &b[i])
+	}
+}
+
 // TODO @gbotrel make a public package out of that.
 // execute executes the work function in parallel.
 // this is copy paste from internal/parallel/parallel.go
diff --git a/ecc/bls24-315/fr/vector_test.go b/ecc/bls24-315/fr/vector_test.go
index e58f2d9a38..b6344c18b7 100644
--- a/ecc/bls24-315/fr/vector_test.go
+++ b/ecc/bls24-315/fr/vector_test.go
@@ -18,10 +18,15 @@ package fr
 
 import (
 	"bytes"
+	"fmt"
 	"github.com/stretchr/testify/require"
+	"os"
 	"reflect"
 	"sort"
 	"testing"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/prop"
 )
 
 func TestVectorSort(t *testing.T) {
@@ -88,3 +93,279 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 	}
 	return <-chErr
 }
+
+func TestVectorOps(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = 2
+	} else {
+		parameters.MinSuccessfulTests = 10
+	}
+	properties := gopter.NewProperties(parameters)
+
+	addVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Add(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Add(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	subVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Sub(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Sub(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	scalarMulVector := func(a Vector, b Element) bool {
+		c := make(Vector, len(a))
+		c.ScalarMul(a, &b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b)
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sumVector := func(a Vector) bool {
+		var sum Element
+		computed := a.Sum()
+		for i := 0; i < len(a); i++ {
+			sum.Add(&sum, &a[i])
+		}
+
+		return sum.Equal(&computed)
+	}
+
+	innerProductVector := func(a, b Vector) bool {
+		computed := a.InnerProduct(b)
+		var innerProduct Element
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			innerProduct.Add(&innerProduct, &tmp)
+		}
+
+		return innerProduct.Equal(&computed)
+	}
+
+	mulVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		a[0].SetUint64(0x24)
+		b[0].SetUint64(0x42)
+		c.Mul(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sizes := []int{1, 2, 3, 4, 8, 9, 15, 16, 509, 510, 511, 512, 513, 514}
+	type genPair struct {
+		g1, g2 gopter.Gen
+		label  string
+	}
+
+	for _, size := range sizes {
+		generators := []genPair{
+			{genZeroVector(size), genZeroVector(size), "zero vectors"},
+			{genMaxVector(size), genMaxVector(size), "max vectors"},
+			{genVector(size), genVector(size), "random vectors"},
+			{genVector(size), genZeroVector(size), "random and zero vectors"},
+		}
+		for _, gp := range generators {
+			properties.Property(fmt.Sprintf("vector addition %d - %s", size, gp.label), prop.ForAll(
+				addVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector subtraction %d - %s", size, gp.label), prop.ForAll(
+				subVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector scalar multiplication %d - %s", size, gp.label), prop.ForAll(
+				scalarMulVector,
+				gp.g1,
+				genElement(),
+			))
+
+			properties.Property(fmt.Sprintf("vector sum %d - %s", size, gp.label), prop.ForAll(
+				sumVector,
+				gp.g1,
+			))
+
+			properties.Property(fmt.Sprintf("vector inner product %d - %s", size, gp.label), prop.ForAll(
+				innerProductVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector multiplication %d - %s", size, gp.label), prop.ForAll(
+				mulVector,
+				gp.g1,
+				gp.g2,
+			))
+		}
+	}
+
+	properties.TestingRun(t, gopter.NewFormatedReporter(false, 260, os.Stdout))
+}
+
+func BenchmarkVectorOps(b *testing.B) {
+	// note; to benchmark against "no asm" version, use the following
+	// build tag: -tags purego
+	const N = 1 << 24
+	a1 := make(Vector, N)
+	b1 := make(Vector, N)
+	c1 := make(Vector, N)
+	var mixer Element
+	mixer.SetRandom()
+	for i := 1; i < N; i++ {
+		a1[i-1].SetUint64(uint64(i)).
+			Mul(&a1[i-1], &mixer)
+		b1[i-1].SetUint64(^uint64(i)).
+			Mul(&b1[i-1], &mixer)
+	}
+
+	for n := 1 << 4; n <= N; n <<= 1 {
+		b.Run(fmt.Sprintf("add %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Add(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sub %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Sub(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("scalarMul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.ScalarMul(_a, &mixer)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sum %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.Sum()
+			}
+		})
+
+		b.Run(fmt.Sprintf("innerProduct %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.InnerProduct(_b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("mul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Mul(_a, _b)
+			}
+		})
+	}
+}
+
+func genZeroVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genMaxVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+
+		qMinusOne := qElement
+		qMinusOne[0]--
+
+		for i := 0; i < size; i++ {
+			g[i] = qMinusOne
+		}
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		mixer := Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[3] != ^uint64(0) {
+			mixer[3] %= (qElement[3] + 1)
+		}
+
+		for !mixer.smallerThanModulus() {
+			mixer = Element{
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+			}
+			if qElement[3] != ^uint64(0) {
+				mixer[3] %= (qElement[3] + 1)
+			}
+		}
+
+		for i := 1; i <= size; i++ {
+			g[i-1].SetUint64(uint64(i)).
+				Mul(&g[i-1], &mixer)
+		}
+
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/ecc/bls24-317/fp/asm.go b/ecc/bls24-317/fp/asm_adx.go
similarity index 100%
rename from ecc/bls24-317/fp/asm.go
rename to ecc/bls24-317/fp/asm_adx.go
diff --git a/ecc/bls24-317/fp/element.go b/ecc/bls24-317/fp/element.go
index 652a4a78e2..77818de479 100644
--- a/ecc/bls24-317/fp/element.go
+++ b/ecc/bls24-317/fp/element.go
@@ -499,32 +499,8 @@ func (z *Element) Select(c int, x0 *Element, x1 *Element) *Element {
 // and is used for testing purposes.
 func _mulGeneric(z, x, y *Element) {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t [6]uint64
 	var D uint64
diff --git a/ecc/bls24-317/fp/element_mul_amd64.s b/ecc/bls24-317/fp/element_mul_amd64.s
deleted file mode 100644
index bfc863eeba..0000000000
--- a/ecc/bls24-317/fp/element_mul_amd64.s
+++ /dev/null
@@ -1,656 +0,0 @@
-// +build !purego
-
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0x8d512e565dab2aab
-DATA q<>+8(SB)/8, $0xd6f339e43424bf7e
-DATA q<>+16(SB)/8, $0x169a61e684c73446
-DATA q<>+24(SB)/8, $0xf28fc5a0b7f9d039
-DATA q<>+32(SB)/8, $0x1058ca226f60892c
-GLOBL q<>(SB), (RODATA+NOPTR), $40
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0x55b5e0028b047ffd
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, ra4, rb0, rb1, rb2, rb3, rb4) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	MOVQ    ra4, rb4;        \
-	SBBQ    q<>+32(SB), ra4; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-	CMOVQCS rb4, ra4;        \
-
-// mul(res, x, y *Element)
-TEXT ·mul(SB), $24-24
-
-	// the algorithm is described in the Element.Mul declaration (.go)
-	// however, to benefit from the ADCX and ADOX carry chains
-	// we split the inner loops in 2:
-	// for i=0 to N-1
-	// 		for j=0 to N-1
-	// 		    (A,t[j])  := t[j] + x[j]*y[i] + A
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C + A
-
-	NO_LOCAL_POINTERS
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_1
-	MOVQ x+8(FP), DI
-
-	// x[0] -> R9
-	// x[1] -> R10
-	// x[2] -> R11
-	MOVQ 0(DI), R9
-	MOVQ 8(DI), R10
-	MOVQ 16(DI), R11
-	MOVQ y+16(FP), R12
-
-	// A -> BP
-	// t[0] -> R14
-	// t[1] -> R13
-	// t[2] -> CX
-	// t[3] -> BX
-	// t[4] -> SI
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 0(R12), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ R9, R14, R13
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ R10, AX, CX
-	ADOXQ AX, R13
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ R11, AX, BX
-	ADOXQ AX, CX
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ 24(DI), AX, SI
-	ADOXQ AX, BX
-
-	// (A,t[4])  := x[4]*y[0] + A
-	MULXQ 32(DI), AX, BP
-	ADOXQ AX, SI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R8
-	ADCXQ R14, AX
-	MOVQ  R8, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// t[4] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ BP, SI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 8(R12), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ R9, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R13
-	MULXQ R10, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, CX
-	MULXQ R11, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, BX
-	MULXQ 24(DI), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[1] + A
-	ADCXQ BP, SI
-	MULXQ 32(DI), AX, BP
-	ADOXQ AX, SI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R8
-	ADCXQ R14, AX
-	MOVQ  R8, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// t[4] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ BP, SI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 16(R12), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ R9, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R13
-	MULXQ R10, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, CX
-	MULXQ R11, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, BX
-	MULXQ 24(DI), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[2] + A
-	ADCXQ BP, SI
-	MULXQ 32(DI), AX, BP
-	ADOXQ AX, SI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R8
-	ADCXQ R14, AX
-	MOVQ  R8, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// t[4] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ BP, SI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 24(R12), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ R9, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R13
-	MULXQ R10, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, CX
-	MULXQ R11, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, BX
-	MULXQ 24(DI), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[3] + A
-	ADCXQ BP, SI
-	MULXQ 32(DI), AX, BP
-	ADOXQ AX, SI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R8
-	ADCXQ R14, AX
-	MOVQ  R8, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// t[4] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ BP, SI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 32(R12), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[4] + A
-	MULXQ R9, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[4] + A
-	ADCXQ BP, R13
-	MULXQ R10, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[4] + A
-	ADCXQ BP, CX
-	MULXQ R11, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[4] + A
-	ADCXQ BP, BX
-	MULXQ 24(DI), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[4] + A
-	ADCXQ BP, SI
-	MULXQ 32(DI), AX, BP
-	ADOXQ AX, SI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R8
-	ADCXQ R14, AX
-	MOVQ  R8, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// t[4] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ BP, SI
-
-	// reduce element(R14,R13,CX,BX,SI) using temp registers (R8,DI,R12,R9,R10)
-	REDUCE(R14,R13,CX,BX,SI,R8,DI,R12,R9,R10)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R13, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	MOVQ SI, 32(AX)
-	RET
-
-noAdx_1:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	MOVQ x+8(FP), AX
-	MOVQ AX, 8(SP)
-	MOVQ y+16(FP), AX
-	MOVQ AX, 16(SP)
-	CALL ·_mulGeneric(SB)
-	RET
-
-TEXT ·fromMont(SB), $8-8
-	NO_LOCAL_POINTERS
-
-	// the algorithm is described here
-	// https://hackmd.io/@gnark/modular_multiplication
-	// when y = 1 we have:
-	// for i=0 to N-1
-	// 		t[i] = x[i]
-	// for i=0 to N-1
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_2
-	MOVQ res+0(FP), DX
-	MOVQ 0(DX), R14
-	MOVQ 8(DX), R13
-	MOVQ 16(DX), CX
-	MOVQ 24(DX), BX
-	MOVQ 32(DX), SI
-	XORQ DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ AX, SI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ AX, SI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ AX, SI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ AX, SI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ AX, SI
-
-	// reduce element(R14,R13,CX,BX,SI) using temp registers (DI,R8,R9,R10,R11)
-	REDUCE(R14,R13,CX,BX,SI,DI,R8,R9,R10,R11)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R13, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	MOVQ SI, 32(AX)
-	RET
-
-noAdx_2:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	CALL ·_fromMontGeneric(SB)
-	RET
diff --git a/ecc/bls24-317/fp/element_ops_amd64.go b/ecc/bls24-317/fp/element_ops_amd64.go
index 83bba45aed..ed2803d717 100644
--- a/ecc/bls24-317/fp/element_ops_amd64.go
+++ b/ecc/bls24-317/fp/element_ops_amd64.go
@@ -50,48 +50,8 @@ func Butterfly(a, b *Element)
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	mul(z, x, y)
 	return z
diff --git a/ecc/bls24-317/fp/element_ops_amd64.s b/ecc/bls24-317/fp/element_ops_amd64.s
index cb68645b3b..29314843d7 100644
--- a/ecc/bls24-317/fp/element_ops_amd64.s
+++ b/ecc/bls24-317/fp/element_ops_amd64.s
@@ -1,272 +1,6 @@
 // +build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+// We include the hash to force the Go compiler to recompile: 18184981773209750009
+#include "../../../field/asm/element_5w_amd64.s"
 
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0x8d512e565dab2aab
-DATA q<>+8(SB)/8, $0xd6f339e43424bf7e
-DATA q<>+16(SB)/8, $0x169a61e684c73446
-DATA q<>+24(SB)/8, $0xf28fc5a0b7f9d039
-DATA q<>+32(SB)/8, $0x1058ca226f60892c
-GLOBL q<>(SB), (RODATA+NOPTR), $40
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0x55b5e0028b047ffd
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, ra4, rb0, rb1, rb2, rb3, rb4) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	MOVQ    ra4, rb4;        \
-	SBBQ    q<>+32(SB), ra4; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-	CMOVQCS rb4, ra4;        \
-
-TEXT ·reduce(SB), NOSPLIT, $0-8
-	MOVQ res+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	RET
-
-// MulBy3(x *Element)
-TEXT ·MulBy3(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R13,R14,R15,R8,R9)
-	REDUCE(DX,CX,BX,SI,DI,R13,R14,R15,R8,R9)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	RET
-
-// MulBy5(x *Element)
-TEXT ·MulBy5(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R13,R14,R15,R8,R9)
-	REDUCE(DX,CX,BX,SI,DI,R13,R14,R15,R8,R9)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R10,R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,DI,R10,R11,R12,R13,R14)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	RET
-
-// MulBy13(x *Element)
-TEXT ·MulBy13(SB), $16-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP))
-	REDUCE(DX,CX,BX,SI,DI,R13,R14,R15,s0-8(SP),s1-16(SP))
-
-	MOVQ DX, R13
-	MOVQ CX, R14
-	MOVQ BX, R15
-	MOVQ SI, s0-8(SP)
-	MOVQ DI, s1-16(SP)
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
-
-	ADDQ R13, DX
-	ADCQ R14, CX
-	ADCQ R15, BX
-	ADCQ s0-8(SP), SI
-	ADCQ s1-16(SP), DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	RET
-
-// Butterfly(a, b *Element) sets a = a + b; b = a - b
-TEXT ·Butterfly(SB), $24-16
-	MOVQ    a+0(FP), AX
-	MOVQ    0(AX), CX
-	MOVQ    8(AX), BX
-	MOVQ    16(AX), SI
-	MOVQ    24(AX), DI
-	MOVQ    32(AX), R8
-	MOVQ    CX, R9
-	MOVQ    BX, R10
-	MOVQ    SI, R11
-	MOVQ    DI, R12
-	MOVQ    R8, R13
-	XORQ    AX, AX
-	MOVQ    b+8(FP), DX
-	ADDQ    0(DX), CX
-	ADCQ    8(DX), BX
-	ADCQ    16(DX), SI
-	ADCQ    24(DX), DI
-	ADCQ    32(DX), R8
-	SUBQ    0(DX), R9
-	SBBQ    8(DX), R10
-	SBBQ    16(DX), R11
-	SBBQ    24(DX), R12
-	SBBQ    32(DX), R13
-	MOVQ    CX, R14
-	MOVQ    BX, R15
-	MOVQ    SI, s0-8(SP)
-	MOVQ    DI, s1-16(SP)
-	MOVQ    R8, s2-24(SP)
-	MOVQ    $0x8d512e565dab2aab, CX
-	MOVQ    $0xd6f339e43424bf7e, BX
-	MOVQ    $0x169a61e684c73446, SI
-	MOVQ    $0xf28fc5a0b7f9d039, DI
-	MOVQ    $0x1058ca226f60892c, R8
-	CMOVQCC AX, CX
-	CMOVQCC AX, BX
-	CMOVQCC AX, SI
-	CMOVQCC AX, DI
-	CMOVQCC AX, R8
-	ADDQ    CX, R9
-	ADCQ    BX, R10
-	ADCQ    SI, R11
-	ADCQ    DI, R12
-	ADCQ    R8, R13
-	MOVQ    R14, CX
-	MOVQ    R15, BX
-	MOVQ    s0-8(SP), SI
-	MOVQ    s1-16(SP), DI
-	MOVQ    s2-24(SP), R8
-	MOVQ    R9, 0(DX)
-	MOVQ    R10, 8(DX)
-	MOVQ    R11, 16(DX)
-	MOVQ    R12, 24(DX)
-	MOVQ    R13, 32(DX)
-
-	// reduce element(CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13)
-	REDUCE(CX,BX,SI,DI,R8,R9,R10,R11,R12,R13)
-
-	MOVQ a+0(FP), AX
-	MOVQ CX, 0(AX)
-	MOVQ BX, 8(AX)
-	MOVQ SI, 16(AX)
-	MOVQ DI, 24(AX)
-	MOVQ R8, 32(AX)
-	RET
diff --git a/ecc/bls24-317/fp/element_ops_purego.go b/ecc/bls24-317/fp/element_ops_purego.go
index aed04e01f3..9f72e6f84b 100644
--- a/ecc/bls24-317/fp/element_ops_purego.go
+++ b/ecc/bls24-317/fp/element_ops_purego.go
@@ -66,48 +66,8 @@ func reduce(z *Element) {
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t0, t1, t2, t3, t4 uint64
 	var u0, u1, u2, u3, u4 uint64
diff --git a/ecc/bls24-317/fp/element_test.go b/ecc/bls24-317/fp/element_test.go
index 7bbabe2599..7d179efec4 100644
--- a/ecc/bls24-317/fp/element_test.go
+++ b/ecc/bls24-317/fp/element_test.go
@@ -639,7 +639,6 @@ func TestElementBitLen(t *testing.T) {
 	))
 
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
-
 }
 
 func TestElementButterflies(t *testing.T) {
@@ -709,77 +708,6 @@ func TestElementLexicographicallyLargest(t *testing.T) {
 
 }
 
-func TestElementVecOps(t *testing.T) {
-	assert := require.New(t)
-
-	const N = 7
-	a := make(Vector, N)
-	b := make(Vector, N)
-	c := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a[i].SetRandom()
-		b[i].SetRandom()
-	}
-
-	// Vector addition
-	c.Add(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Add(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector addition failed")
-	}
-
-	// Vector subtraction
-	c.Sub(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Sub(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector subtraction failed")
-	}
-
-	// Vector scaling
-	c.ScalarMul(a, &b[0])
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Mul(&a[i], &b[0])
-		assert.True(c[i].Equal(&expected), "Vector scaling failed")
-	}
-}
-
-func BenchmarkElementVecOps(b *testing.B) {
-	// note; to benchmark against "no asm" version, use the following
-	// build tag: -tags purego
-	const N = 1024
-	a1 := make(Vector, N)
-	b1 := make(Vector, N)
-	c1 := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a1[i].SetRandom()
-		b1[i].SetRandom()
-	}
-
-	b.Run("Add", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Add(a1, b1)
-		}
-	})
-
-	b.Run("Sub", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Sub(a1, b1)
-		}
-	})
-
-	b.Run("ScalarMul", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.ScalarMul(a1, &b1[0])
-		}
-	})
-}
-
 func TestElementAdd(t *testing.T) {
 	t.Parallel()
 	parameters := gopter.DefaultTestParameters()
@@ -2349,40 +2277,40 @@ func gen() gopter.Gen {
 	}
 }
 
-func genFull() gopter.Gen {
-	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+func genRandomFq(genParams *gopter.GenParameters) Element {
+	var g Element
 
-		genRandomFq := func() Element {
-			var g Element
+	g = Element{
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+	}
 
-			g = Element{
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-			}
+	if qElement[4] != ^uint64(0) {
+		g[4] %= (qElement[4] + 1)
+	}
 
-			if qElement[4] != ^uint64(0) {
-				g[4] %= (qElement[4] + 1)
-			}
+	for !g.smallerThanModulus() {
+		g = Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[4] != ^uint64(0) {
+			g[4] %= (qElement[4] + 1)
+		}
+	}
 
-			for !g.smallerThanModulus() {
-				g = Element{
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-				}
-				if qElement[4] != ^uint64(0) {
-					g[4] %= (qElement[4] + 1)
-				}
-			}
+	return g
+}
 
-			return g
-		}
-		a := genRandomFq()
+func genFull() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
 
 		var carry uint64
 		a[0], carry = bits.Add64(a[0], qElement[0], carry)
@@ -2396,6 +2324,14 @@ func genFull() gopter.Gen {
 	}
 }
 
+func genElement() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
+		genResult := gopter.NewGenResult(a, gopter.NoShrinker)
+		return genResult
+	}
+}
+
 func (z *Element) matchVeryBigInt(aHi uint64, aInt *big.Int) error {
 	var modulus big.Int
 	var aIntMod big.Int
diff --git a/ecc/bls24-317/fp/vector.go b/ecc/bls24-317/fp/vector.go
index 01b326d498..ce61e70ea0 100644
--- a/ecc/bls24-317/fp/vector.go
+++ b/ecc/bls24-317/fp/vector.go
@@ -218,6 +218,25 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	scalarMulVecGeneric(*vector, a, b)
 }
 
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
+
 func addVecGeneric(res, a, b Vector) {
 	if len(a) != len(b) || len(a) != len(res) {
 		panic("vector.Add: vectors don't have the same length")
@@ -245,6 +264,32 @@ func scalarMulVecGeneric(res, a Vector, b *Element) {
 	}
 }
 
+func sumVecGeneric(res *Element, a Vector) {
+	for i := 0; i < len(a); i++ {
+		res.Add(res, &a[i])
+	}
+}
+
+func innerProductVecGeneric(res *Element, a, b Vector) {
+	if len(a) != len(b) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	var tmp Element
+	for i := 0; i < len(a); i++ {
+		tmp.Mul(&a[i], &b[i])
+		res.Add(res, &tmp)
+	}
+}
+
+func mulVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Mul(&a[i], &b[i])
+	}
+}
+
 // TODO @gbotrel make a public package out of that.
 // execute executes the work function in parallel.
 // this is copy paste from internal/parallel/parallel.go
diff --git a/ecc/bls24-317/fp/vector_test.go b/ecc/bls24-317/fp/vector_test.go
index 5d88af91c0..c60ee08440 100644
--- a/ecc/bls24-317/fp/vector_test.go
+++ b/ecc/bls24-317/fp/vector_test.go
@@ -18,10 +18,15 @@ package fp
 
 import (
 	"bytes"
+	"fmt"
 	"github.com/stretchr/testify/require"
+	"os"
 	"reflect"
 	"sort"
 	"testing"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/prop"
 )
 
 func TestVectorSort(t *testing.T) {
@@ -88,3 +93,281 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 	}
 	return <-chErr
 }
+
+func TestVectorOps(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = 2
+	} else {
+		parameters.MinSuccessfulTests = 10
+	}
+	properties := gopter.NewProperties(parameters)
+
+	addVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Add(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Add(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	subVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Sub(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Sub(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	scalarMulVector := func(a Vector, b Element) bool {
+		c := make(Vector, len(a))
+		c.ScalarMul(a, &b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b)
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sumVector := func(a Vector) bool {
+		var sum Element
+		computed := a.Sum()
+		for i := 0; i < len(a); i++ {
+			sum.Add(&sum, &a[i])
+		}
+
+		return sum.Equal(&computed)
+	}
+
+	innerProductVector := func(a, b Vector) bool {
+		computed := a.InnerProduct(b)
+		var innerProduct Element
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			innerProduct.Add(&innerProduct, &tmp)
+		}
+
+		return innerProduct.Equal(&computed)
+	}
+
+	mulVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		a[0].SetUint64(0x24)
+		b[0].SetUint64(0x42)
+		c.Mul(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sizes := []int{1, 2, 3, 4, 8, 9, 15, 16, 509, 510, 511, 512, 513, 514}
+	type genPair struct {
+		g1, g2 gopter.Gen
+		label  string
+	}
+
+	for _, size := range sizes {
+		generators := []genPair{
+			{genZeroVector(size), genZeroVector(size), "zero vectors"},
+			{genMaxVector(size), genMaxVector(size), "max vectors"},
+			{genVector(size), genVector(size), "random vectors"},
+			{genVector(size), genZeroVector(size), "random and zero vectors"},
+		}
+		for _, gp := range generators {
+			properties.Property(fmt.Sprintf("vector addition %d - %s", size, gp.label), prop.ForAll(
+				addVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector subtraction %d - %s", size, gp.label), prop.ForAll(
+				subVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector scalar multiplication %d - %s", size, gp.label), prop.ForAll(
+				scalarMulVector,
+				gp.g1,
+				genElement(),
+			))
+
+			properties.Property(fmt.Sprintf("vector sum %d - %s", size, gp.label), prop.ForAll(
+				sumVector,
+				gp.g1,
+			))
+
+			properties.Property(fmt.Sprintf("vector inner product %d - %s", size, gp.label), prop.ForAll(
+				innerProductVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector multiplication %d - %s", size, gp.label), prop.ForAll(
+				mulVector,
+				gp.g1,
+				gp.g2,
+			))
+		}
+	}
+
+	properties.TestingRun(t, gopter.NewFormatedReporter(false, 260, os.Stdout))
+}
+
+func BenchmarkVectorOps(b *testing.B) {
+	// note; to benchmark against "no asm" version, use the following
+	// build tag: -tags purego
+	const N = 1 << 24
+	a1 := make(Vector, N)
+	b1 := make(Vector, N)
+	c1 := make(Vector, N)
+	var mixer Element
+	mixer.SetRandom()
+	for i := 1; i < N; i++ {
+		a1[i-1].SetUint64(uint64(i)).
+			Mul(&a1[i-1], &mixer)
+		b1[i-1].SetUint64(^uint64(i)).
+			Mul(&b1[i-1], &mixer)
+	}
+
+	for n := 1 << 4; n <= N; n <<= 1 {
+		b.Run(fmt.Sprintf("add %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Add(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sub %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Sub(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("scalarMul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.ScalarMul(_a, &mixer)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sum %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.Sum()
+			}
+		})
+
+		b.Run(fmt.Sprintf("innerProduct %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.InnerProduct(_b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("mul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Mul(_a, _b)
+			}
+		})
+	}
+}
+
+func genZeroVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genMaxVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+
+		qMinusOne := qElement
+		qMinusOne[0]--
+
+		for i := 0; i < size; i++ {
+			g[i] = qMinusOne
+		}
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		mixer := Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[4] != ^uint64(0) {
+			mixer[4] %= (qElement[4] + 1)
+		}
+
+		for !mixer.smallerThanModulus() {
+			mixer = Element{
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+			}
+			if qElement[4] != ^uint64(0) {
+				mixer[4] %= (qElement[4] + 1)
+			}
+		}
+
+		for i := 1; i <= size; i++ {
+			g[i-1].SetUint64(uint64(i)).
+				Mul(&g[i-1], &mixer)
+		}
+
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/ecc/bls24-317/fr/asm.go b/ecc/bls24-317/fr/asm_adx.go
similarity index 100%
rename from ecc/bls24-317/fr/asm.go
rename to ecc/bls24-317/fr/asm_adx.go
diff --git a/ecc/bls24-317/fr/asm_avx.go b/ecc/bls24-317/fr/asm_avx.go
new file mode 100644
index 0000000000..955f559799
--- /dev/null
+++ b/ecc/bls24-317/fr/asm_avx.go
@@ -0,0 +1,27 @@
+//go:build !noavx
+// +build !noavx
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+import "golang.org/x/sys/cpu"
+
+var (
+	supportAvx512 = supportAdx && cpu.X86.HasAVX512 && cpu.X86.HasAVX512DQ
+	_             = supportAvx512
+)
diff --git a/ecc/bls24-317/fr/asm_noavx.go b/ecc/bls24-317/fr/asm_noavx.go
new file mode 100644
index 0000000000..e5a5b1f2cc
--- /dev/null
+++ b/ecc/bls24-317/fr/asm_noavx.go
@@ -0,0 +1,22 @@
+//go:build noavx
+// +build noavx
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+const supportAvx512 = false
diff --git a/ecc/bls24-317/fr/element.go b/ecc/bls24-317/fr/element.go
index bf3215dadd..3aefaebe62 100644
--- a/ecc/bls24-317/fr/element.go
+++ b/ecc/bls24-317/fr/element.go
@@ -81,6 +81,9 @@ func Modulus() *big.Int {
 // used for Montgomery reduction
 const qInvNeg uint64 = 17293822569102704639
 
+// mu = 2^288 / q needed for partial Barrett reduction
+const mu uint64 = 16110458503
+
 func init() {
 	_modulus.SetString("443f917ea68dafc2d0b097f28d83cd491cd1e79196bf0e7af000000000000001", 16)
 }
@@ -477,32 +480,8 @@ func (z *Element) Select(c int, x0 *Element, x1 *Element) *Element {
 // and is used for testing purposes.
 func _mulGeneric(z, x, y *Element) {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t [5]uint64
 	var D uint64
diff --git a/ecc/bls24-317/fr/element_mul_amd64.s b/ecc/bls24-317/fr/element_mul_amd64.s
deleted file mode 100644
index 6e58b40d60..0000000000
--- a/ecc/bls24-317/fr/element_mul_amd64.s
+++ /dev/null
@@ -1,487 +0,0 @@
-// +build !purego
-
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0xf000000000000001
-DATA q<>+8(SB)/8, $0x1cd1e79196bf0e7a
-DATA q<>+16(SB)/8, $0xd0b097f28d83cd49
-DATA q<>+24(SB)/8, $0x443f917ea68dafc2
-GLOBL q<>(SB), (RODATA+NOPTR), $32
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0xefffffffffffffff
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, rb0, rb1, rb2, rb3) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-
-// mul(res, x, y *Element)
-TEXT ·mul(SB), $24-24
-
-	// the algorithm is described in the Element.Mul declaration (.go)
-	// however, to benefit from the ADCX and ADOX carry chains
-	// we split the inner loops in 2:
-	// for i=0 to N-1
-	// 		for j=0 to N-1
-	// 		    (A,t[j])  := t[j] + x[j]*y[i] + A
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C + A
-
-	NO_LOCAL_POINTERS
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_1
-	MOVQ x+8(FP), SI
-
-	// x[0] -> DI
-	// x[1] -> R8
-	// x[2] -> R9
-	// x[3] -> R10
-	MOVQ 0(SI), DI
-	MOVQ 8(SI), R8
-	MOVQ 16(SI), R9
-	MOVQ 24(SI), R10
-	MOVQ y+16(FP), R11
-
-	// A -> BP
-	// t[0] -> R14
-	// t[1] -> R13
-	// t[2] -> CX
-	// t[3] -> BX
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 0(R11), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ DI, R14, R13
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ R8, AX, CX
-	ADOXQ AX, R13
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ R9, AX, BX
-	ADOXQ AX, CX
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 8(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R13
-	MULXQ R8, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, CX
-	MULXQ R9, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, BX
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 16(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R13
-	MULXQ R8, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, CX
-	MULXQ R9, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, BX
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 24(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R13
-	MULXQ R8, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, CX
-	MULXQ R9, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, BX
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// reduce element(R14,R13,CX,BX) using temp registers (SI,R12,R11,DI)
-	REDUCE(R14,R13,CX,BX,SI,R12,R11,DI)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R13, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	RET
-
-noAdx_1:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	MOVQ x+8(FP), AX
-	MOVQ AX, 8(SP)
-	MOVQ y+16(FP), AX
-	MOVQ AX, 16(SP)
-	CALL ·_mulGeneric(SB)
-	RET
-
-TEXT ·fromMont(SB), $8-8
-	NO_LOCAL_POINTERS
-
-	// the algorithm is described here
-	// https://hackmd.io/@gnark/modular_multiplication
-	// when y = 1 we have:
-	// for i=0 to N-1
-	// 		t[i] = x[i]
-	// for i=0 to N-1
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_2
-	MOVQ res+0(FP), DX
-	MOVQ 0(DX), R14
-	MOVQ 8(DX), R13
-	MOVQ 16(DX), CX
-	MOVQ 24(DX), BX
-	XORQ DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-
-	// reduce element(R14,R13,CX,BX) using temp registers (SI,DI,R8,R9)
-	REDUCE(R14,R13,CX,BX,SI,DI,R8,R9)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R13, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	RET
-
-noAdx_2:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	CALL ·_fromMontGeneric(SB)
-	RET
diff --git a/ecc/bls24-317/fr/element_ops_amd64.go b/ecc/bls24-317/fr/element_ops_amd64.go
index 21568255de..b653e80069 100644
--- a/ecc/bls24-317/fr/element_ops_amd64.go
+++ b/ecc/bls24-317/fr/element_ops_amd64.go
@@ -51,7 +51,8 @@ func (vector *Vector) Add(a, b Vector) {
 	if len(a) != len(b) || len(a) != len(*vector) {
 		panic("vector.Add: vectors don't have the same length")
 	}
-	addVec(&(*vector)[0], &a[0], &b[0], uint64(len(a)))
+	n := uint64(len(a))
+	addVec(&(*vector)[0], &a[0], &b[0], n)
 }
 
 //go:noescape
@@ -75,59 +76,123 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	if len(a) != len(*vector) {
 		panic("vector.ScalarMul: vectors don't have the same length")
 	}
-	scalarMulVec(&(*vector)[0], &a[0], b, uint64(len(a)))
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || uint64(len(a)) >= maxN {
+		// call scalarMulVecGeneric
+		scalarMulVecGeneric(*vector, a, b)
+		return
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	// the code for scalarMul is identical to mulVec; and it expects at least
+	// 2 elements in the vector to fill the Z registers
+	var bb [2]Element
+	bb[0] = *b
+	bb[1] = *b
+	const blockSize = 16
+	scalarMulVec(&(*vector)[0], &a[0], &bb[0], n/blockSize, qInvNeg)
+	if n%blockSize != 0 {
+		// call scalarMulVecGeneric on the rest
+		start := n - n%blockSize
+		scalarMulVecGeneric((*vector)[start:], a[start:], b)
+	}
+}
+
+//go:noescape
+func scalarMulVec(res, a, b *Element, n uint64, qInvNeg uint64)
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	const minN = 16 * 7 // AVX512 slower than generic for small n
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n <= minN || n >= maxN {
+		// call sumVecGeneric
+		sumVecGeneric(&res, *vector)
+		return
+	}
+	sumVec(&res, &(*vector)[0], uint64(len(*vector)))
+	return
 }
 
 //go:noescape
-func scalarMulVec(res, a, b *Element, n uint64)
+func sumVec(res *Element, a *Element, n uint64)
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	if n != uint64(len(other)) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n >= maxN {
+		// call innerProductVecGeneric
+		// note; we could split the vector into smaller chunks and call innerProductVec
+		innerProductVecGeneric(&res, *vector, other)
+		return
+	}
+	innerProdVec(&res[0], &(*vector)[0], &other[0], uint64(len(*vector)))
+
+	return
+}
+
+//go:noescape
+func innerProdVec(res *uint64, a, b *Element, n uint64)
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n >= maxN {
+		// call mulVecGeneric
+		mulVecGeneric(*vector, a, b)
+		return
+	}
+
+	const blockSize = 16
+	mulVec(&(*vector)[0], &a[0], &b[0], n/blockSize, qInvNeg)
+	if n%blockSize != 0 {
+		// call mulVecGeneric on the rest
+		start := n - n%blockSize
+		mulVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+
+}
+
+// Patterns use for transposing the vectors in mulVec
+var (
+	pattern1 = [8]uint64{0, 8, 1, 9, 2, 10, 3, 11}
+	pattern2 = [8]uint64{12, 4, 13, 5, 14, 6, 15, 7}
+	pattern3 = [8]uint64{0, 1, 8, 9, 2, 3, 10, 11}
+	pattern4 = [8]uint64{12, 13, 4, 5, 14, 15, 6, 7}
+)
+
+//go:noescape
+func mulVec(res, a, b *Element, n uint64, qInvNeg uint64)
 
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	mul(z, x, y)
 	return z
diff --git a/ecc/bls24-317/fr/element_ops_amd64.s b/ecc/bls24-317/fr/element_ops_amd64.s
index fd237dad9f..6c42136a7a 100644
--- a/ecc/bls24-317/fr/element_ops_amd64.s
+++ b/ecc/bls24-317/fr/element_ops_amd64.s
@@ -1,627 +1,6 @@
 // +build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+// We include the hash to force the Go compiler to recompile: 9425145785761608449
+#include "../../../field/asm/element_4w_amd64.s"
 
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0xf000000000000001
-DATA q<>+8(SB)/8, $0x1cd1e79196bf0e7a
-DATA q<>+16(SB)/8, $0xd0b097f28d83cd49
-DATA q<>+24(SB)/8, $0x443f917ea68dafc2
-GLOBL q<>(SB), (RODATA+NOPTR), $32
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0xefffffffffffffff
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, rb0, rb1, rb2, rb3) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-
-TEXT ·reduce(SB), NOSPLIT, $0-8
-	MOVQ res+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// MulBy3(x *Element)
-TEXT ·MulBy3(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// MulBy5(x *Element)
-TEXT ·MulBy5(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R15,DI,R8,R9)
-	REDUCE(DX,CX,BX,SI,R15,DI,R8,R9)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// MulBy13(x *Element)
-TEXT ·MulBy13(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
-
-	MOVQ DX, R11
-	MOVQ CX, R12
-	MOVQ BX, R13
-	MOVQ SI, R14
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ R11, DX
-	ADCQ R12, CX
-	ADCQ R13, BX
-	ADCQ R14, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// Butterfly(a, b *Element) sets a = a + b; b = a - b
-TEXT ·Butterfly(SB), NOSPLIT, $0-16
-	MOVQ    a+0(FP), AX
-	MOVQ    0(AX), CX
-	MOVQ    8(AX), BX
-	MOVQ    16(AX), SI
-	MOVQ    24(AX), DI
-	MOVQ    CX, R8
-	MOVQ    BX, R9
-	MOVQ    SI, R10
-	MOVQ    DI, R11
-	XORQ    AX, AX
-	MOVQ    b+8(FP), DX
-	ADDQ    0(DX), CX
-	ADCQ    8(DX), BX
-	ADCQ    16(DX), SI
-	ADCQ    24(DX), DI
-	SUBQ    0(DX), R8
-	SBBQ    8(DX), R9
-	SBBQ    16(DX), R10
-	SBBQ    24(DX), R11
-	MOVQ    $0xf000000000000001, R12
-	MOVQ    $0x1cd1e79196bf0e7a, R13
-	MOVQ    $0xd0b097f28d83cd49, R14
-	MOVQ    $0x443f917ea68dafc2, R15
-	CMOVQCC AX, R12
-	CMOVQCC AX, R13
-	CMOVQCC AX, R14
-	CMOVQCC AX, R15
-	ADDQ    R12, R8
-	ADCQ    R13, R9
-	ADCQ    R14, R10
-	ADCQ    R15, R11
-	MOVQ    R8, 0(DX)
-	MOVQ    R9, 8(DX)
-	MOVQ    R10, 16(DX)
-	MOVQ    R11, 24(DX)
-
-	// reduce element(CX,BX,SI,DI) using temp registers (R8,R9,R10,R11)
-	REDUCE(CX,BX,SI,DI,R8,R9,R10,R11)
-
-	MOVQ a+0(FP), AX
-	MOVQ CX, 0(AX)
-	MOVQ BX, 8(AX)
-	MOVQ SI, 16(AX)
-	MOVQ DI, 24(AX)
-	RET
-
-// addVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] + b[0...n]
-TEXT ·addVec(SB), NOSPLIT, $0-32
-	MOVQ res+0(FP), CX
-	MOVQ a+8(FP), AX
-	MOVQ b+16(FP), DX
-	MOVQ n+24(FP), BX
-
-loop_1:
-	TESTQ BX, BX
-	JEQ   done_2 // n == 0, we are done
-
-	// a[0] -> SI
-	// a[1] -> DI
-	// a[2] -> R8
-	// a[3] -> R9
-	MOVQ 0(AX), SI
-	MOVQ 8(AX), DI
-	MOVQ 16(AX), R8
-	MOVQ 24(AX), R9
-	ADDQ 0(DX), SI
-	ADCQ 8(DX), DI
-	ADCQ 16(DX), R8
-	ADCQ 24(DX), R9
-
-	// reduce element(SI,DI,R8,R9) using temp registers (R10,R11,R12,R13)
-	REDUCE(SI,DI,R8,R9,R10,R11,R12,R13)
-
-	MOVQ SI, 0(CX)
-	MOVQ DI, 8(CX)
-	MOVQ R8, 16(CX)
-	MOVQ R9, 24(CX)
-
-	// increment pointers to visit next element
-	ADDQ $32, AX
-	ADDQ $32, DX
-	ADDQ $32, CX
-	DECQ BX      // decrement n
-	JMP  loop_1
-
-done_2:
-	RET
-
-// subVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] - b[0...n]
-TEXT ·subVec(SB), NOSPLIT, $0-32
-	MOVQ res+0(FP), CX
-	MOVQ a+8(FP), AX
-	MOVQ b+16(FP), DX
-	MOVQ n+24(FP), BX
-	XORQ SI, SI
-
-loop_3:
-	TESTQ BX, BX
-	JEQ   done_4 // n == 0, we are done
-
-	// a[0] -> DI
-	// a[1] -> R8
-	// a[2] -> R9
-	// a[3] -> R10
-	MOVQ 0(AX), DI
-	MOVQ 8(AX), R8
-	MOVQ 16(AX), R9
-	MOVQ 24(AX), R10
-	SUBQ 0(DX), DI
-	SBBQ 8(DX), R8
-	SBBQ 16(DX), R9
-	SBBQ 24(DX), R10
-
-	// reduce (a-b) mod q
-	// q[0] -> R11
-	// q[1] -> R12
-	// q[2] -> R13
-	// q[3] -> R14
-	MOVQ    $0xf000000000000001, R11
-	MOVQ    $0x1cd1e79196bf0e7a, R12
-	MOVQ    $0xd0b097f28d83cd49, R13
-	MOVQ    $0x443f917ea68dafc2, R14
-	CMOVQCC SI, R11
-	CMOVQCC SI, R12
-	CMOVQCC SI, R13
-	CMOVQCC SI, R14
-
-	// add registers (q or 0) to a, and set to result
-	ADDQ R11, DI
-	ADCQ R12, R8
-	ADCQ R13, R9
-	ADCQ R14, R10
-	MOVQ DI, 0(CX)
-	MOVQ R8, 8(CX)
-	MOVQ R9, 16(CX)
-	MOVQ R10, 24(CX)
-
-	// increment pointers to visit next element
-	ADDQ $32, AX
-	ADDQ $32, DX
-	ADDQ $32, CX
-	DECQ BX      // decrement n
-	JMP  loop_3
-
-done_4:
-	RET
-
-// scalarMulVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] * b
-TEXT ·scalarMulVec(SB), $56-32
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_5
-	MOVQ a+8(FP), R11
-	MOVQ b+16(FP), R10
-	MOVQ n+24(FP), R12
-
-	// scalar[0] -> SI
-	// scalar[1] -> DI
-	// scalar[2] -> R8
-	// scalar[3] -> R9
-	MOVQ 0(R10), SI
-	MOVQ 8(R10), DI
-	MOVQ 16(R10), R8
-	MOVQ 24(R10), R9
-	MOVQ res+0(FP), R10
-
-loop_6:
-	TESTQ R12, R12
-	JEQ   done_7   // n == 0, we are done
-
-	// TODO @gbotrel this is generated from the same macro as the unit mul, we should refactor this in a single asm function
-	// A -> BP
-	// t[0] -> R14
-	// t[1] -> R15
-	// t[2] -> CX
-	// t[3] -> BX
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 0(R11), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ SI, R14, R15
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ DI, AX, CX
-	ADOXQ AX, R15
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ R8, AX, BX
-	ADOXQ AX, CX
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 8(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ SI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R15
-	MULXQ DI, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, CX
-	MULXQ R8, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, BX
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 16(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ SI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R15
-	MULXQ DI, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, CX
-	MULXQ R8, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, BX
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 24(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ SI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R15
-	MULXQ DI, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, CX
-	MULXQ R8, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, BX
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// reduce t mod q
-	// reduce element(R14,R15,CX,BX) using temp registers (R13,AX,DX,s0-8(SP))
-	REDUCE(R14,R15,CX,BX,R13,AX,DX,s0-8(SP))
-
-	MOVQ R14, 0(R10)
-	MOVQ R15, 8(R10)
-	MOVQ CX, 16(R10)
-	MOVQ BX, 24(R10)
-
-	// increment pointers to visit next element
-	ADDQ $32, R11
-	ADDQ $32, R10
-	DECQ R12      // decrement n
-	JMP  loop_6
-
-done_7:
-	RET
-
-noAdx_5:
-	MOVQ n+24(FP), DX
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	MOVQ DX, 8(SP)
-	MOVQ DX, 16(SP)
-	MOVQ a+8(FP), AX
-	MOVQ AX, 24(SP)
-	MOVQ DX, 32(SP)
-	MOVQ DX, 40(SP)
-	MOVQ b+16(FP), AX
-	MOVQ AX, 48(SP)
-	CALL ·scalarMulVecGeneric(SB)
-	RET
diff --git a/ecc/bls24-317/fr/element_ops_purego.go b/ecc/bls24-317/fr/element_ops_purego.go
index 14505483c7..7afd9cc8df 100644
--- a/ecc/bls24-317/fr/element_ops_purego.go
+++ b/ecc/bls24-317/fr/element_ops_purego.go
@@ -78,53 +78,32 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	scalarMulVecGeneric(*vector, a, b)
 }
 
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
+
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t0, t1, t2, t3 uint64
 	var u0, u1, u2, u3 uint64
diff --git a/ecc/bls24-317/fr/element_test.go b/ecc/bls24-317/fr/element_test.go
index c533cc1c92..b5db750d64 100644
--- a/ecc/bls24-317/fr/element_test.go
+++ b/ecc/bls24-317/fr/element_test.go
@@ -637,7 +637,6 @@ func TestElementBitLen(t *testing.T) {
 	))
 
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
-
 }
 
 func TestElementButterflies(t *testing.T) {
@@ -707,77 +706,6 @@ func TestElementLexicographicallyLargest(t *testing.T) {
 
 }
 
-func TestElementVecOps(t *testing.T) {
-	assert := require.New(t)
-
-	const N = 7
-	a := make(Vector, N)
-	b := make(Vector, N)
-	c := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a[i].SetRandom()
-		b[i].SetRandom()
-	}
-
-	// Vector addition
-	c.Add(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Add(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector addition failed")
-	}
-
-	// Vector subtraction
-	c.Sub(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Sub(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector subtraction failed")
-	}
-
-	// Vector scaling
-	c.ScalarMul(a, &b[0])
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Mul(&a[i], &b[0])
-		assert.True(c[i].Equal(&expected), "Vector scaling failed")
-	}
-}
-
-func BenchmarkElementVecOps(b *testing.B) {
-	// note; to benchmark against "no asm" version, use the following
-	// build tag: -tags purego
-	const N = 1024
-	a1 := make(Vector, N)
-	b1 := make(Vector, N)
-	c1 := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a1[i].SetRandom()
-		b1[i].SetRandom()
-	}
-
-	b.Run("Add", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Add(a1, b1)
-		}
-	})
-
-	b.Run("Sub", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Sub(a1, b1)
-		}
-	})
-
-	b.Run("ScalarMul", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.ScalarMul(a1, &b1[0])
-		}
-	})
-}
-
 func TestElementAdd(t *testing.T) {
 	t.Parallel()
 	parameters := gopter.DefaultTestParameters()
@@ -2345,38 +2273,38 @@ func gen() gopter.Gen {
 	}
 }
 
-func genFull() gopter.Gen {
-	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+func genRandomFq(genParams *gopter.GenParameters) Element {
+	var g Element
 
-		genRandomFq := func() Element {
-			var g Element
+	g = Element{
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+	}
 
-			g = Element{
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-			}
+	if qElement[3] != ^uint64(0) {
+		g[3] %= (qElement[3] + 1)
+	}
 
-			if qElement[3] != ^uint64(0) {
-				g[3] %= (qElement[3] + 1)
-			}
+	for !g.smallerThanModulus() {
+		g = Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[3] != ^uint64(0) {
+			g[3] %= (qElement[3] + 1)
+		}
+	}
 
-			for !g.smallerThanModulus() {
-				g = Element{
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-				}
-				if qElement[3] != ^uint64(0) {
-					g[3] %= (qElement[3] + 1)
-				}
-			}
+	return g
+}
 
-			return g
-		}
-		a := genRandomFq()
+func genFull() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
 
 		var carry uint64
 		a[0], carry = bits.Add64(a[0], qElement[0], carry)
@@ -2389,6 +2317,14 @@ func genFull() gopter.Gen {
 	}
 }
 
+func genElement() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
+		genResult := gopter.NewGenResult(a, gopter.NoShrinker)
+		return genResult
+	}
+}
+
 func (z *Element) matchVeryBigInt(aHi uint64, aInt *big.Int) error {
 	var modulus big.Int
 	var aIntMod big.Int
diff --git a/ecc/bls24-317/fr/vector.go b/ecc/bls24-317/fr/vector.go
index f39828547f..867cabbc3d 100644
--- a/ecc/bls24-317/fr/vector.go
+++ b/ecc/bls24-317/fr/vector.go
@@ -226,6 +226,32 @@ func scalarMulVecGeneric(res, a Vector, b *Element) {
 	}
 }
 
+func sumVecGeneric(res *Element, a Vector) {
+	for i := 0; i < len(a); i++ {
+		res.Add(res, &a[i])
+	}
+}
+
+func innerProductVecGeneric(res *Element, a, b Vector) {
+	if len(a) != len(b) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	var tmp Element
+	for i := 0; i < len(a); i++ {
+		tmp.Mul(&a[i], &b[i])
+		res.Add(res, &tmp)
+	}
+}
+
+func mulVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Mul(&a[i], &b[i])
+	}
+}
+
 // TODO @gbotrel make a public package out of that.
 // execute executes the work function in parallel.
 // this is copy paste from internal/parallel/parallel.go
diff --git a/ecc/bls24-317/fr/vector_test.go b/ecc/bls24-317/fr/vector_test.go
index e58f2d9a38..b6344c18b7 100644
--- a/ecc/bls24-317/fr/vector_test.go
+++ b/ecc/bls24-317/fr/vector_test.go
@@ -18,10 +18,15 @@ package fr
 
 import (
 	"bytes"
+	"fmt"
 	"github.com/stretchr/testify/require"
+	"os"
 	"reflect"
 	"sort"
 	"testing"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/prop"
 )
 
 func TestVectorSort(t *testing.T) {
@@ -88,3 +93,279 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 	}
 	return <-chErr
 }
+
+func TestVectorOps(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = 2
+	} else {
+		parameters.MinSuccessfulTests = 10
+	}
+	properties := gopter.NewProperties(parameters)
+
+	addVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Add(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Add(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	subVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Sub(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Sub(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	scalarMulVector := func(a Vector, b Element) bool {
+		c := make(Vector, len(a))
+		c.ScalarMul(a, &b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b)
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sumVector := func(a Vector) bool {
+		var sum Element
+		computed := a.Sum()
+		for i := 0; i < len(a); i++ {
+			sum.Add(&sum, &a[i])
+		}
+
+		return sum.Equal(&computed)
+	}
+
+	innerProductVector := func(a, b Vector) bool {
+		computed := a.InnerProduct(b)
+		var innerProduct Element
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			innerProduct.Add(&innerProduct, &tmp)
+		}
+
+		return innerProduct.Equal(&computed)
+	}
+
+	mulVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		a[0].SetUint64(0x24)
+		b[0].SetUint64(0x42)
+		c.Mul(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sizes := []int{1, 2, 3, 4, 8, 9, 15, 16, 509, 510, 511, 512, 513, 514}
+	type genPair struct {
+		g1, g2 gopter.Gen
+		label  string
+	}
+
+	for _, size := range sizes {
+		generators := []genPair{
+			{genZeroVector(size), genZeroVector(size), "zero vectors"},
+			{genMaxVector(size), genMaxVector(size), "max vectors"},
+			{genVector(size), genVector(size), "random vectors"},
+			{genVector(size), genZeroVector(size), "random and zero vectors"},
+		}
+		for _, gp := range generators {
+			properties.Property(fmt.Sprintf("vector addition %d - %s", size, gp.label), prop.ForAll(
+				addVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector subtraction %d - %s", size, gp.label), prop.ForAll(
+				subVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector scalar multiplication %d - %s", size, gp.label), prop.ForAll(
+				scalarMulVector,
+				gp.g1,
+				genElement(),
+			))
+
+			properties.Property(fmt.Sprintf("vector sum %d - %s", size, gp.label), prop.ForAll(
+				sumVector,
+				gp.g1,
+			))
+
+			properties.Property(fmt.Sprintf("vector inner product %d - %s", size, gp.label), prop.ForAll(
+				innerProductVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector multiplication %d - %s", size, gp.label), prop.ForAll(
+				mulVector,
+				gp.g1,
+				gp.g2,
+			))
+		}
+	}
+
+	properties.TestingRun(t, gopter.NewFormatedReporter(false, 260, os.Stdout))
+}
+
+func BenchmarkVectorOps(b *testing.B) {
+	// note; to benchmark against "no asm" version, use the following
+	// build tag: -tags purego
+	const N = 1 << 24
+	a1 := make(Vector, N)
+	b1 := make(Vector, N)
+	c1 := make(Vector, N)
+	var mixer Element
+	mixer.SetRandom()
+	for i := 1; i < N; i++ {
+		a1[i-1].SetUint64(uint64(i)).
+			Mul(&a1[i-1], &mixer)
+		b1[i-1].SetUint64(^uint64(i)).
+			Mul(&b1[i-1], &mixer)
+	}
+
+	for n := 1 << 4; n <= N; n <<= 1 {
+		b.Run(fmt.Sprintf("add %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Add(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sub %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Sub(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("scalarMul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.ScalarMul(_a, &mixer)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sum %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.Sum()
+			}
+		})
+
+		b.Run(fmt.Sprintf("innerProduct %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.InnerProduct(_b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("mul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Mul(_a, _b)
+			}
+		})
+	}
+}
+
+func genZeroVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genMaxVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+
+		qMinusOne := qElement
+		qMinusOne[0]--
+
+		for i := 0; i < size; i++ {
+			g[i] = qMinusOne
+		}
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		mixer := Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[3] != ^uint64(0) {
+			mixer[3] %= (qElement[3] + 1)
+		}
+
+		for !mixer.smallerThanModulus() {
+			mixer = Element{
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+			}
+			if qElement[3] != ^uint64(0) {
+				mixer[3] %= (qElement[3] + 1)
+			}
+		}
+
+		for i := 1; i <= size; i++ {
+			g[i-1].SetUint64(uint64(i)).
+				Mul(&g[i-1], &mixer)
+		}
+
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/ecc/bn254/fp/asm.go b/ecc/bn254/fp/asm_adx.go
similarity index 100%
rename from ecc/bn254/fp/asm.go
rename to ecc/bn254/fp/asm_adx.go
diff --git a/ecc/bn254/fp/asm_avx.go b/ecc/bn254/fp/asm_avx.go
new file mode 100644
index 0000000000..cea035ee84
--- /dev/null
+++ b/ecc/bn254/fp/asm_avx.go
@@ -0,0 +1,27 @@
+//go:build !noavx
+// +build !noavx
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fp
+
+import "golang.org/x/sys/cpu"
+
+var (
+	supportAvx512 = supportAdx && cpu.X86.HasAVX512 && cpu.X86.HasAVX512DQ
+	_             = supportAvx512
+)
diff --git a/ecc/bn254/fp/asm_noavx.go b/ecc/bn254/fp/asm_noavx.go
new file mode 100644
index 0000000000..9ca08a375a
--- /dev/null
+++ b/ecc/bn254/fp/asm_noavx.go
@@ -0,0 +1,22 @@
+//go:build noavx
+// +build noavx
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fp
+
+const supportAvx512 = false
diff --git a/ecc/bn254/fp/element.go b/ecc/bn254/fp/element.go
index 5ba388e737..25fcdb67cc 100644
--- a/ecc/bn254/fp/element.go
+++ b/ecc/bn254/fp/element.go
@@ -81,6 +81,9 @@ func Modulus() *big.Int {
 // used for Montgomery reduction
 const qInvNeg uint64 = 9786893198990664585
 
+// mu = 2^288 / q needed for partial Barrett reduction
+const mu uint64 = 22721021478
+
 func init() {
 	_modulus.SetString("30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47", 16)
 }
@@ -477,32 +480,8 @@ func (z *Element) Select(c int, x0 *Element, x1 *Element) *Element {
 // and is used for testing purposes.
 func _mulGeneric(z, x, y *Element) {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t [5]uint64
 	var D uint64
diff --git a/ecc/bn254/fp/element_mul_amd64.s b/ecc/bn254/fp/element_mul_amd64.s
deleted file mode 100644
index 9357a21d75..0000000000
--- a/ecc/bn254/fp/element_mul_amd64.s
+++ /dev/null
@@ -1,487 +0,0 @@
-// +build !purego
-
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0x3c208c16d87cfd47
-DATA q<>+8(SB)/8, $0x97816a916871ca8d
-DATA q<>+16(SB)/8, $0xb85045b68181585d
-DATA q<>+24(SB)/8, $0x30644e72e131a029
-GLOBL q<>(SB), (RODATA+NOPTR), $32
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0x87d20782e4866389
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, rb0, rb1, rb2, rb3) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-
-// mul(res, x, y *Element)
-TEXT ·mul(SB), $24-24
-
-	// the algorithm is described in the Element.Mul declaration (.go)
-	// however, to benefit from the ADCX and ADOX carry chains
-	// we split the inner loops in 2:
-	// for i=0 to N-1
-	// 		for j=0 to N-1
-	// 		    (A,t[j])  := t[j] + x[j]*y[i] + A
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C + A
-
-	NO_LOCAL_POINTERS
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_1
-	MOVQ x+8(FP), SI
-
-	// x[0] -> DI
-	// x[1] -> R8
-	// x[2] -> R9
-	// x[3] -> R10
-	MOVQ 0(SI), DI
-	MOVQ 8(SI), R8
-	MOVQ 16(SI), R9
-	MOVQ 24(SI), R10
-	MOVQ y+16(FP), R11
-
-	// A -> BP
-	// t[0] -> R14
-	// t[1] -> R13
-	// t[2] -> CX
-	// t[3] -> BX
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 0(R11), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ DI, R14, R13
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ R8, AX, CX
-	ADOXQ AX, R13
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ R9, AX, BX
-	ADOXQ AX, CX
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 8(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R13
-	MULXQ R8, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, CX
-	MULXQ R9, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, BX
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 16(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R13
-	MULXQ R8, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, CX
-	MULXQ R9, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, BX
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 24(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R13
-	MULXQ R8, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, CX
-	MULXQ R9, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, BX
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// reduce element(R14,R13,CX,BX) using temp registers (SI,R12,R11,DI)
-	REDUCE(R14,R13,CX,BX,SI,R12,R11,DI)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R13, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	RET
-
-noAdx_1:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	MOVQ x+8(FP), AX
-	MOVQ AX, 8(SP)
-	MOVQ y+16(FP), AX
-	MOVQ AX, 16(SP)
-	CALL ·_mulGeneric(SB)
-	RET
-
-TEXT ·fromMont(SB), $8-8
-	NO_LOCAL_POINTERS
-
-	// the algorithm is described here
-	// https://hackmd.io/@gnark/modular_multiplication
-	// when y = 1 we have:
-	// for i=0 to N-1
-	// 		t[i] = x[i]
-	// for i=0 to N-1
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_2
-	MOVQ res+0(FP), DX
-	MOVQ 0(DX), R14
-	MOVQ 8(DX), R13
-	MOVQ 16(DX), CX
-	MOVQ 24(DX), BX
-	XORQ DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-
-	// reduce element(R14,R13,CX,BX) using temp registers (SI,DI,R8,R9)
-	REDUCE(R14,R13,CX,BX,SI,DI,R8,R9)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R13, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	RET
-
-noAdx_2:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	CALL ·_fromMontGeneric(SB)
-	RET
diff --git a/ecc/bn254/fp/element_ops_amd64.go b/ecc/bn254/fp/element_ops_amd64.go
index 6f16baf686..2ab1a98399 100644
--- a/ecc/bn254/fp/element_ops_amd64.go
+++ b/ecc/bn254/fp/element_ops_amd64.go
@@ -51,7 +51,8 @@ func (vector *Vector) Add(a, b Vector) {
 	if len(a) != len(b) || len(a) != len(*vector) {
 		panic("vector.Add: vectors don't have the same length")
 	}
-	addVec(&(*vector)[0], &a[0], &b[0], uint64(len(a)))
+	n := uint64(len(a))
+	addVec(&(*vector)[0], &a[0], &b[0], n)
 }
 
 //go:noescape
@@ -75,59 +76,123 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	if len(a) != len(*vector) {
 		panic("vector.ScalarMul: vectors don't have the same length")
 	}
-	scalarMulVec(&(*vector)[0], &a[0], b, uint64(len(a)))
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || uint64(len(a)) >= maxN {
+		// call scalarMulVecGeneric
+		scalarMulVecGeneric(*vector, a, b)
+		return
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	// the code for scalarMul is identical to mulVec; and it expects at least
+	// 2 elements in the vector to fill the Z registers
+	var bb [2]Element
+	bb[0] = *b
+	bb[1] = *b
+	const blockSize = 16
+	scalarMulVec(&(*vector)[0], &a[0], &bb[0], n/blockSize, qInvNeg)
+	if n%blockSize != 0 {
+		// call scalarMulVecGeneric on the rest
+		start := n - n%blockSize
+		scalarMulVecGeneric((*vector)[start:], a[start:], b)
+	}
+}
+
+//go:noescape
+func scalarMulVec(res, a, b *Element, n uint64, qInvNeg uint64)
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	const minN = 16 * 7 // AVX512 slower than generic for small n
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n <= minN || n >= maxN {
+		// call sumVecGeneric
+		sumVecGeneric(&res, *vector)
+		return
+	}
+	sumVec(&res, &(*vector)[0], uint64(len(*vector)))
+	return
 }
 
 //go:noescape
-func scalarMulVec(res, a, b *Element, n uint64)
+func sumVec(res *Element, a *Element, n uint64)
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	if n != uint64(len(other)) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n >= maxN {
+		// call innerProductVecGeneric
+		// note; we could split the vector into smaller chunks and call innerProductVec
+		innerProductVecGeneric(&res, *vector, other)
+		return
+	}
+	innerProdVec(&res[0], &(*vector)[0], &other[0], uint64(len(*vector)))
+
+	return
+}
+
+//go:noescape
+func innerProdVec(res *uint64, a, b *Element, n uint64)
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n >= maxN {
+		// call mulVecGeneric
+		mulVecGeneric(*vector, a, b)
+		return
+	}
+
+	const blockSize = 16
+	mulVec(&(*vector)[0], &a[0], &b[0], n/blockSize, qInvNeg)
+	if n%blockSize != 0 {
+		// call mulVecGeneric on the rest
+		start := n - n%blockSize
+		mulVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+
+}
+
+// Patterns use for transposing the vectors in mulVec
+var (
+	pattern1 = [8]uint64{0, 8, 1, 9, 2, 10, 3, 11}
+	pattern2 = [8]uint64{12, 4, 13, 5, 14, 6, 15, 7}
+	pattern3 = [8]uint64{0, 1, 8, 9, 2, 3, 10, 11}
+	pattern4 = [8]uint64{12, 13, 4, 5, 14, 15, 6, 7}
+)
+
+//go:noescape
+func mulVec(res, a, b *Element, n uint64, qInvNeg uint64)
 
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	mul(z, x, y)
 	return z
diff --git a/ecc/bn254/fp/element_ops_amd64.s b/ecc/bn254/fp/element_ops_amd64.s
index cbfba4ee59..6c42136a7a 100644
--- a/ecc/bn254/fp/element_ops_amd64.s
+++ b/ecc/bn254/fp/element_ops_amd64.s
@@ -1,627 +1,6 @@
 // +build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+// We include the hash to force the Go compiler to recompile: 9425145785761608449
+#include "../../../field/asm/element_4w_amd64.s"
 
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0x3c208c16d87cfd47
-DATA q<>+8(SB)/8, $0x97816a916871ca8d
-DATA q<>+16(SB)/8, $0xb85045b68181585d
-DATA q<>+24(SB)/8, $0x30644e72e131a029
-GLOBL q<>(SB), (RODATA+NOPTR), $32
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0x87d20782e4866389
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, rb0, rb1, rb2, rb3) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-
-TEXT ·reduce(SB), NOSPLIT, $0-8
-	MOVQ res+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// MulBy3(x *Element)
-TEXT ·MulBy3(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// MulBy5(x *Element)
-TEXT ·MulBy5(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R15,DI,R8,R9)
-	REDUCE(DX,CX,BX,SI,R15,DI,R8,R9)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// MulBy13(x *Element)
-TEXT ·MulBy13(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
-
-	MOVQ DX, R11
-	MOVQ CX, R12
-	MOVQ BX, R13
-	MOVQ SI, R14
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ R11, DX
-	ADCQ R12, CX
-	ADCQ R13, BX
-	ADCQ R14, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// Butterfly(a, b *Element) sets a = a + b; b = a - b
-TEXT ·Butterfly(SB), NOSPLIT, $0-16
-	MOVQ    a+0(FP), AX
-	MOVQ    0(AX), CX
-	MOVQ    8(AX), BX
-	MOVQ    16(AX), SI
-	MOVQ    24(AX), DI
-	MOVQ    CX, R8
-	MOVQ    BX, R9
-	MOVQ    SI, R10
-	MOVQ    DI, R11
-	XORQ    AX, AX
-	MOVQ    b+8(FP), DX
-	ADDQ    0(DX), CX
-	ADCQ    8(DX), BX
-	ADCQ    16(DX), SI
-	ADCQ    24(DX), DI
-	SUBQ    0(DX), R8
-	SBBQ    8(DX), R9
-	SBBQ    16(DX), R10
-	SBBQ    24(DX), R11
-	MOVQ    $0x3c208c16d87cfd47, R12
-	MOVQ    $0x97816a916871ca8d, R13
-	MOVQ    $0xb85045b68181585d, R14
-	MOVQ    $0x30644e72e131a029, R15
-	CMOVQCC AX, R12
-	CMOVQCC AX, R13
-	CMOVQCC AX, R14
-	CMOVQCC AX, R15
-	ADDQ    R12, R8
-	ADCQ    R13, R9
-	ADCQ    R14, R10
-	ADCQ    R15, R11
-	MOVQ    R8, 0(DX)
-	MOVQ    R9, 8(DX)
-	MOVQ    R10, 16(DX)
-	MOVQ    R11, 24(DX)
-
-	// reduce element(CX,BX,SI,DI) using temp registers (R8,R9,R10,R11)
-	REDUCE(CX,BX,SI,DI,R8,R9,R10,R11)
-
-	MOVQ a+0(FP), AX
-	MOVQ CX, 0(AX)
-	MOVQ BX, 8(AX)
-	MOVQ SI, 16(AX)
-	MOVQ DI, 24(AX)
-	RET
-
-// addVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] + b[0...n]
-TEXT ·addVec(SB), NOSPLIT, $0-32
-	MOVQ res+0(FP), CX
-	MOVQ a+8(FP), AX
-	MOVQ b+16(FP), DX
-	MOVQ n+24(FP), BX
-
-loop_1:
-	TESTQ BX, BX
-	JEQ   done_2 // n == 0, we are done
-
-	// a[0] -> SI
-	// a[1] -> DI
-	// a[2] -> R8
-	// a[3] -> R9
-	MOVQ 0(AX), SI
-	MOVQ 8(AX), DI
-	MOVQ 16(AX), R8
-	MOVQ 24(AX), R9
-	ADDQ 0(DX), SI
-	ADCQ 8(DX), DI
-	ADCQ 16(DX), R8
-	ADCQ 24(DX), R9
-
-	// reduce element(SI,DI,R8,R9) using temp registers (R10,R11,R12,R13)
-	REDUCE(SI,DI,R8,R9,R10,R11,R12,R13)
-
-	MOVQ SI, 0(CX)
-	MOVQ DI, 8(CX)
-	MOVQ R8, 16(CX)
-	MOVQ R9, 24(CX)
-
-	// increment pointers to visit next element
-	ADDQ $32, AX
-	ADDQ $32, DX
-	ADDQ $32, CX
-	DECQ BX      // decrement n
-	JMP  loop_1
-
-done_2:
-	RET
-
-// subVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] - b[0...n]
-TEXT ·subVec(SB), NOSPLIT, $0-32
-	MOVQ res+0(FP), CX
-	MOVQ a+8(FP), AX
-	MOVQ b+16(FP), DX
-	MOVQ n+24(FP), BX
-	XORQ SI, SI
-
-loop_3:
-	TESTQ BX, BX
-	JEQ   done_4 // n == 0, we are done
-
-	// a[0] -> DI
-	// a[1] -> R8
-	// a[2] -> R9
-	// a[3] -> R10
-	MOVQ 0(AX), DI
-	MOVQ 8(AX), R8
-	MOVQ 16(AX), R9
-	MOVQ 24(AX), R10
-	SUBQ 0(DX), DI
-	SBBQ 8(DX), R8
-	SBBQ 16(DX), R9
-	SBBQ 24(DX), R10
-
-	// reduce (a-b) mod q
-	// q[0] -> R11
-	// q[1] -> R12
-	// q[2] -> R13
-	// q[3] -> R14
-	MOVQ    $0x3c208c16d87cfd47, R11
-	MOVQ    $0x97816a916871ca8d, R12
-	MOVQ    $0xb85045b68181585d, R13
-	MOVQ    $0x30644e72e131a029, R14
-	CMOVQCC SI, R11
-	CMOVQCC SI, R12
-	CMOVQCC SI, R13
-	CMOVQCC SI, R14
-
-	// add registers (q or 0) to a, and set to result
-	ADDQ R11, DI
-	ADCQ R12, R8
-	ADCQ R13, R9
-	ADCQ R14, R10
-	MOVQ DI, 0(CX)
-	MOVQ R8, 8(CX)
-	MOVQ R9, 16(CX)
-	MOVQ R10, 24(CX)
-
-	// increment pointers to visit next element
-	ADDQ $32, AX
-	ADDQ $32, DX
-	ADDQ $32, CX
-	DECQ BX      // decrement n
-	JMP  loop_3
-
-done_4:
-	RET
-
-// scalarMulVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] * b
-TEXT ·scalarMulVec(SB), $56-32
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_5
-	MOVQ a+8(FP), R11
-	MOVQ b+16(FP), R10
-	MOVQ n+24(FP), R12
-
-	// scalar[0] -> SI
-	// scalar[1] -> DI
-	// scalar[2] -> R8
-	// scalar[3] -> R9
-	MOVQ 0(R10), SI
-	MOVQ 8(R10), DI
-	MOVQ 16(R10), R8
-	MOVQ 24(R10), R9
-	MOVQ res+0(FP), R10
-
-loop_6:
-	TESTQ R12, R12
-	JEQ   done_7   // n == 0, we are done
-
-	// TODO @gbotrel this is generated from the same macro as the unit mul, we should refactor this in a single asm function
-	// A -> BP
-	// t[0] -> R14
-	// t[1] -> R15
-	// t[2] -> CX
-	// t[3] -> BX
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 0(R11), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ SI, R14, R15
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ DI, AX, CX
-	ADOXQ AX, R15
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ R8, AX, BX
-	ADOXQ AX, CX
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 8(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ SI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R15
-	MULXQ DI, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, CX
-	MULXQ R8, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, BX
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 16(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ SI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R15
-	MULXQ DI, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, CX
-	MULXQ R8, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, BX
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 24(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ SI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R15
-	MULXQ DI, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, CX
-	MULXQ R8, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, BX
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// reduce t mod q
-	// reduce element(R14,R15,CX,BX) using temp registers (R13,AX,DX,s0-8(SP))
-	REDUCE(R14,R15,CX,BX,R13,AX,DX,s0-8(SP))
-
-	MOVQ R14, 0(R10)
-	MOVQ R15, 8(R10)
-	MOVQ CX, 16(R10)
-	MOVQ BX, 24(R10)
-
-	// increment pointers to visit next element
-	ADDQ $32, R11
-	ADDQ $32, R10
-	DECQ R12      // decrement n
-	JMP  loop_6
-
-done_7:
-	RET
-
-noAdx_5:
-	MOVQ n+24(FP), DX
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	MOVQ DX, 8(SP)
-	MOVQ DX, 16(SP)
-	MOVQ a+8(FP), AX
-	MOVQ AX, 24(SP)
-	MOVQ DX, 32(SP)
-	MOVQ DX, 40(SP)
-	MOVQ b+16(FP), AX
-	MOVQ AX, 48(SP)
-	CALL ·scalarMulVecGeneric(SB)
-	RET
diff --git a/ecc/bn254/fp/element_ops_purego.go b/ecc/bn254/fp/element_ops_purego.go
index 250ac5bce0..454376da57 100644
--- a/ecc/bn254/fp/element_ops_purego.go
+++ b/ecc/bn254/fp/element_ops_purego.go
@@ -78,53 +78,32 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	scalarMulVecGeneric(*vector, a, b)
 }
 
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
+
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t0, t1, t2, t3 uint64
 	var u0, u1, u2, u3 uint64
diff --git a/ecc/bn254/fp/element_test.go b/ecc/bn254/fp/element_test.go
index a923ef657d..22d11d4acc 100644
--- a/ecc/bn254/fp/element_test.go
+++ b/ecc/bn254/fp/element_test.go
@@ -637,7 +637,6 @@ func TestElementBitLen(t *testing.T) {
 	))
 
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
-
 }
 
 func TestElementButterflies(t *testing.T) {
@@ -707,77 +706,6 @@ func TestElementLexicographicallyLargest(t *testing.T) {
 
 }
 
-func TestElementVecOps(t *testing.T) {
-	assert := require.New(t)
-
-	const N = 7
-	a := make(Vector, N)
-	b := make(Vector, N)
-	c := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a[i].SetRandom()
-		b[i].SetRandom()
-	}
-
-	// Vector addition
-	c.Add(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Add(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector addition failed")
-	}
-
-	// Vector subtraction
-	c.Sub(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Sub(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector subtraction failed")
-	}
-
-	// Vector scaling
-	c.ScalarMul(a, &b[0])
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Mul(&a[i], &b[0])
-		assert.True(c[i].Equal(&expected), "Vector scaling failed")
-	}
-}
-
-func BenchmarkElementVecOps(b *testing.B) {
-	// note; to benchmark against "no asm" version, use the following
-	// build tag: -tags purego
-	const N = 1024
-	a1 := make(Vector, N)
-	b1 := make(Vector, N)
-	c1 := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a1[i].SetRandom()
-		b1[i].SetRandom()
-	}
-
-	b.Run("Add", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Add(a1, b1)
-		}
-	})
-
-	b.Run("Sub", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Sub(a1, b1)
-		}
-	})
-
-	b.Run("ScalarMul", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.ScalarMul(a1, &b1[0])
-		}
-	})
-}
-
 func TestElementAdd(t *testing.T) {
 	t.Parallel()
 	parameters := gopter.DefaultTestParameters()
@@ -2345,38 +2273,38 @@ func gen() gopter.Gen {
 	}
 }
 
-func genFull() gopter.Gen {
-	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+func genRandomFq(genParams *gopter.GenParameters) Element {
+	var g Element
 
-		genRandomFq := func() Element {
-			var g Element
+	g = Element{
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+	}
 
-			g = Element{
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-			}
+	if qElement[3] != ^uint64(0) {
+		g[3] %= (qElement[3] + 1)
+	}
 
-			if qElement[3] != ^uint64(0) {
-				g[3] %= (qElement[3] + 1)
-			}
+	for !g.smallerThanModulus() {
+		g = Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[3] != ^uint64(0) {
+			g[3] %= (qElement[3] + 1)
+		}
+	}
 
-			for !g.smallerThanModulus() {
-				g = Element{
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-				}
-				if qElement[3] != ^uint64(0) {
-					g[3] %= (qElement[3] + 1)
-				}
-			}
+	return g
+}
 
-			return g
-		}
-		a := genRandomFq()
+func genFull() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
 
 		var carry uint64
 		a[0], carry = bits.Add64(a[0], qElement[0], carry)
@@ -2389,6 +2317,14 @@ func genFull() gopter.Gen {
 	}
 }
 
+func genElement() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
+		genResult := gopter.NewGenResult(a, gopter.NoShrinker)
+		return genResult
+	}
+}
+
 func (z *Element) matchVeryBigInt(aHi uint64, aInt *big.Int) error {
 	var modulus big.Int
 	var aIntMod big.Int
diff --git a/ecc/bn254/fp/vector.go b/ecc/bn254/fp/vector.go
index 850b3603d8..c97b4283ce 100644
--- a/ecc/bn254/fp/vector.go
+++ b/ecc/bn254/fp/vector.go
@@ -226,6 +226,32 @@ func scalarMulVecGeneric(res, a Vector, b *Element) {
 	}
 }
 
+func sumVecGeneric(res *Element, a Vector) {
+	for i := 0; i < len(a); i++ {
+		res.Add(res, &a[i])
+	}
+}
+
+func innerProductVecGeneric(res *Element, a, b Vector) {
+	if len(a) != len(b) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	var tmp Element
+	for i := 0; i < len(a); i++ {
+		tmp.Mul(&a[i], &b[i])
+		res.Add(res, &tmp)
+	}
+}
+
+func mulVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Mul(&a[i], &b[i])
+	}
+}
+
 // TODO @gbotrel make a public package out of that.
 // execute executes the work function in parallel.
 // this is copy paste from internal/parallel/parallel.go
diff --git a/ecc/bn254/fp/vector_test.go b/ecc/bn254/fp/vector_test.go
index 5d88af91c0..12f17e21fb 100644
--- a/ecc/bn254/fp/vector_test.go
+++ b/ecc/bn254/fp/vector_test.go
@@ -18,10 +18,15 @@ package fp
 
 import (
 	"bytes"
+	"fmt"
 	"github.com/stretchr/testify/require"
+	"os"
 	"reflect"
 	"sort"
 	"testing"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/prop"
 )
 
 func TestVectorSort(t *testing.T) {
@@ -88,3 +93,279 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 	}
 	return <-chErr
 }
+
+func TestVectorOps(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = 2
+	} else {
+		parameters.MinSuccessfulTests = 10
+	}
+	properties := gopter.NewProperties(parameters)
+
+	addVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Add(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Add(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	subVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Sub(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Sub(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	scalarMulVector := func(a Vector, b Element) bool {
+		c := make(Vector, len(a))
+		c.ScalarMul(a, &b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b)
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sumVector := func(a Vector) bool {
+		var sum Element
+		computed := a.Sum()
+		for i := 0; i < len(a); i++ {
+			sum.Add(&sum, &a[i])
+		}
+
+		return sum.Equal(&computed)
+	}
+
+	innerProductVector := func(a, b Vector) bool {
+		computed := a.InnerProduct(b)
+		var innerProduct Element
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			innerProduct.Add(&innerProduct, &tmp)
+		}
+
+		return innerProduct.Equal(&computed)
+	}
+
+	mulVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		a[0].SetUint64(0x24)
+		b[0].SetUint64(0x42)
+		c.Mul(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sizes := []int{1, 2, 3, 4, 8, 9, 15, 16, 509, 510, 511, 512, 513, 514}
+	type genPair struct {
+		g1, g2 gopter.Gen
+		label  string
+	}
+
+	for _, size := range sizes {
+		generators := []genPair{
+			{genZeroVector(size), genZeroVector(size), "zero vectors"},
+			{genMaxVector(size), genMaxVector(size), "max vectors"},
+			{genVector(size), genVector(size), "random vectors"},
+			{genVector(size), genZeroVector(size), "random and zero vectors"},
+		}
+		for _, gp := range generators {
+			properties.Property(fmt.Sprintf("vector addition %d - %s", size, gp.label), prop.ForAll(
+				addVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector subtraction %d - %s", size, gp.label), prop.ForAll(
+				subVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector scalar multiplication %d - %s", size, gp.label), prop.ForAll(
+				scalarMulVector,
+				gp.g1,
+				genElement(),
+			))
+
+			properties.Property(fmt.Sprintf("vector sum %d - %s", size, gp.label), prop.ForAll(
+				sumVector,
+				gp.g1,
+			))
+
+			properties.Property(fmt.Sprintf("vector inner product %d - %s", size, gp.label), prop.ForAll(
+				innerProductVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector multiplication %d - %s", size, gp.label), prop.ForAll(
+				mulVector,
+				gp.g1,
+				gp.g2,
+			))
+		}
+	}
+
+	properties.TestingRun(t, gopter.NewFormatedReporter(false, 260, os.Stdout))
+}
+
+func BenchmarkVectorOps(b *testing.B) {
+	// note; to benchmark against "no asm" version, use the following
+	// build tag: -tags purego
+	const N = 1 << 24
+	a1 := make(Vector, N)
+	b1 := make(Vector, N)
+	c1 := make(Vector, N)
+	var mixer Element
+	mixer.SetRandom()
+	for i := 1; i < N; i++ {
+		a1[i-1].SetUint64(uint64(i)).
+			Mul(&a1[i-1], &mixer)
+		b1[i-1].SetUint64(^uint64(i)).
+			Mul(&b1[i-1], &mixer)
+	}
+
+	for n := 1 << 4; n <= N; n <<= 1 {
+		b.Run(fmt.Sprintf("add %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Add(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sub %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Sub(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("scalarMul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.ScalarMul(_a, &mixer)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sum %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.Sum()
+			}
+		})
+
+		b.Run(fmt.Sprintf("innerProduct %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.InnerProduct(_b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("mul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Mul(_a, _b)
+			}
+		})
+	}
+}
+
+func genZeroVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genMaxVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+
+		qMinusOne := qElement
+		qMinusOne[0]--
+
+		for i := 0; i < size; i++ {
+			g[i] = qMinusOne
+		}
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		mixer := Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[3] != ^uint64(0) {
+			mixer[3] %= (qElement[3] + 1)
+		}
+
+		for !mixer.smallerThanModulus() {
+			mixer = Element{
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+			}
+			if qElement[3] != ^uint64(0) {
+				mixer[3] %= (qElement[3] + 1)
+			}
+		}
+
+		for i := 1; i <= size; i++ {
+			g[i-1].SetUint64(uint64(i)).
+				Mul(&g[i-1], &mixer)
+		}
+
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/ecc/bn254/fr/asm.go b/ecc/bn254/fr/asm_adx.go
similarity index 100%
rename from ecc/bn254/fr/asm.go
rename to ecc/bn254/fr/asm_adx.go
diff --git a/ecc/bn254/fr/asm_avx.go b/ecc/bn254/fr/asm_avx.go
new file mode 100644
index 0000000000..955f559799
--- /dev/null
+++ b/ecc/bn254/fr/asm_avx.go
@@ -0,0 +1,27 @@
+//go:build !noavx
+// +build !noavx
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+import "golang.org/x/sys/cpu"
+
+var (
+	supportAvx512 = supportAdx && cpu.X86.HasAVX512 && cpu.X86.HasAVX512DQ
+	_             = supportAvx512
+)
diff --git a/ecc/bn254/fr/asm_noavx.go b/ecc/bn254/fr/asm_noavx.go
new file mode 100644
index 0000000000..e5a5b1f2cc
--- /dev/null
+++ b/ecc/bn254/fr/asm_noavx.go
@@ -0,0 +1,22 @@
+//go:build noavx
+// +build noavx
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+const supportAvx512 = false
diff --git a/ecc/bn254/fr/element.go b/ecc/bn254/fr/element.go
index cda0b2c288..3650c954c5 100644
--- a/ecc/bn254/fr/element.go
+++ b/ecc/bn254/fr/element.go
@@ -81,6 +81,9 @@ func Modulus() *big.Int {
 // used for Montgomery reduction
 const qInvNeg uint64 = 14042775128853446655
 
+// mu = 2^288 / q needed for partial Barrett reduction
+const mu uint64 = 22721021478
+
 func init() {
 	_modulus.SetString("30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001", 16)
 }
@@ -477,32 +480,8 @@ func (z *Element) Select(c int, x0 *Element, x1 *Element) *Element {
 // and is used for testing purposes.
 func _mulGeneric(z, x, y *Element) {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t [5]uint64
 	var D uint64
diff --git a/ecc/bn254/fr/element_mul_amd64.s b/ecc/bn254/fr/element_mul_amd64.s
deleted file mode 100644
index 4a9321837d..0000000000
--- a/ecc/bn254/fr/element_mul_amd64.s
+++ /dev/null
@@ -1,487 +0,0 @@
-// +build !purego
-
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0x43e1f593f0000001
-DATA q<>+8(SB)/8, $0x2833e84879b97091
-DATA q<>+16(SB)/8, $0xb85045b68181585d
-DATA q<>+24(SB)/8, $0x30644e72e131a029
-GLOBL q<>(SB), (RODATA+NOPTR), $32
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0xc2e1f593efffffff
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, rb0, rb1, rb2, rb3) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-
-// mul(res, x, y *Element)
-TEXT ·mul(SB), $24-24
-
-	// the algorithm is described in the Element.Mul declaration (.go)
-	// however, to benefit from the ADCX and ADOX carry chains
-	// we split the inner loops in 2:
-	// for i=0 to N-1
-	// 		for j=0 to N-1
-	// 		    (A,t[j])  := t[j] + x[j]*y[i] + A
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C + A
-
-	NO_LOCAL_POINTERS
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_1
-	MOVQ x+8(FP), SI
-
-	// x[0] -> DI
-	// x[1] -> R8
-	// x[2] -> R9
-	// x[3] -> R10
-	MOVQ 0(SI), DI
-	MOVQ 8(SI), R8
-	MOVQ 16(SI), R9
-	MOVQ 24(SI), R10
-	MOVQ y+16(FP), R11
-
-	// A -> BP
-	// t[0] -> R14
-	// t[1] -> R13
-	// t[2] -> CX
-	// t[3] -> BX
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 0(R11), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ DI, R14, R13
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ R8, AX, CX
-	ADOXQ AX, R13
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ R9, AX, BX
-	ADOXQ AX, CX
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 8(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R13
-	MULXQ R8, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, CX
-	MULXQ R9, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, BX
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 16(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R13
-	MULXQ R8, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, CX
-	MULXQ R9, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, BX
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 24(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R13
-	MULXQ R8, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, CX
-	MULXQ R9, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, BX
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// reduce element(R14,R13,CX,BX) using temp registers (SI,R12,R11,DI)
-	REDUCE(R14,R13,CX,BX,SI,R12,R11,DI)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R13, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	RET
-
-noAdx_1:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	MOVQ x+8(FP), AX
-	MOVQ AX, 8(SP)
-	MOVQ y+16(FP), AX
-	MOVQ AX, 16(SP)
-	CALL ·_mulGeneric(SB)
-	RET
-
-TEXT ·fromMont(SB), $8-8
-	NO_LOCAL_POINTERS
-
-	// the algorithm is described here
-	// https://hackmd.io/@gnark/modular_multiplication
-	// when y = 1 we have:
-	// for i=0 to N-1
-	// 		t[i] = x[i]
-	// for i=0 to N-1
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_2
-	MOVQ res+0(FP), DX
-	MOVQ 0(DX), R14
-	MOVQ 8(DX), R13
-	MOVQ 16(DX), CX
-	MOVQ 24(DX), BX
-	XORQ DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-
-	// reduce element(R14,R13,CX,BX) using temp registers (SI,DI,R8,R9)
-	REDUCE(R14,R13,CX,BX,SI,DI,R8,R9)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R13, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	RET
-
-noAdx_2:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	CALL ·_fromMontGeneric(SB)
-	RET
diff --git a/ecc/bn254/fr/element_ops_amd64.go b/ecc/bn254/fr/element_ops_amd64.go
index 21568255de..b653e80069 100644
--- a/ecc/bn254/fr/element_ops_amd64.go
+++ b/ecc/bn254/fr/element_ops_amd64.go
@@ -51,7 +51,8 @@ func (vector *Vector) Add(a, b Vector) {
 	if len(a) != len(b) || len(a) != len(*vector) {
 		panic("vector.Add: vectors don't have the same length")
 	}
-	addVec(&(*vector)[0], &a[0], &b[0], uint64(len(a)))
+	n := uint64(len(a))
+	addVec(&(*vector)[0], &a[0], &b[0], n)
 }
 
 //go:noescape
@@ -75,59 +76,123 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	if len(a) != len(*vector) {
 		panic("vector.ScalarMul: vectors don't have the same length")
 	}
-	scalarMulVec(&(*vector)[0], &a[0], b, uint64(len(a)))
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || uint64(len(a)) >= maxN {
+		// call scalarMulVecGeneric
+		scalarMulVecGeneric(*vector, a, b)
+		return
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	// the code for scalarMul is identical to mulVec; and it expects at least
+	// 2 elements in the vector to fill the Z registers
+	var bb [2]Element
+	bb[0] = *b
+	bb[1] = *b
+	const blockSize = 16
+	scalarMulVec(&(*vector)[0], &a[0], &bb[0], n/blockSize, qInvNeg)
+	if n%blockSize != 0 {
+		// call scalarMulVecGeneric on the rest
+		start := n - n%blockSize
+		scalarMulVecGeneric((*vector)[start:], a[start:], b)
+	}
+}
+
+//go:noescape
+func scalarMulVec(res, a, b *Element, n uint64, qInvNeg uint64)
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	const minN = 16 * 7 // AVX512 slower than generic for small n
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n <= minN || n >= maxN {
+		// call sumVecGeneric
+		sumVecGeneric(&res, *vector)
+		return
+	}
+	sumVec(&res, &(*vector)[0], uint64(len(*vector)))
+	return
 }
 
 //go:noescape
-func scalarMulVec(res, a, b *Element, n uint64)
+func sumVec(res *Element, a *Element, n uint64)
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	if n != uint64(len(other)) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n >= maxN {
+		// call innerProductVecGeneric
+		// note; we could split the vector into smaller chunks and call innerProductVec
+		innerProductVecGeneric(&res, *vector, other)
+		return
+	}
+	innerProdVec(&res[0], &(*vector)[0], &other[0], uint64(len(*vector)))
+
+	return
+}
+
+//go:noescape
+func innerProdVec(res *uint64, a, b *Element, n uint64)
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n >= maxN {
+		// call mulVecGeneric
+		mulVecGeneric(*vector, a, b)
+		return
+	}
+
+	const blockSize = 16
+	mulVec(&(*vector)[0], &a[0], &b[0], n/blockSize, qInvNeg)
+	if n%blockSize != 0 {
+		// call mulVecGeneric on the rest
+		start := n - n%blockSize
+		mulVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+
+}
+
+// Patterns use for transposing the vectors in mulVec
+var (
+	pattern1 = [8]uint64{0, 8, 1, 9, 2, 10, 3, 11}
+	pattern2 = [8]uint64{12, 4, 13, 5, 14, 6, 15, 7}
+	pattern3 = [8]uint64{0, 1, 8, 9, 2, 3, 10, 11}
+	pattern4 = [8]uint64{12, 13, 4, 5, 14, 15, 6, 7}
+)
+
+//go:noescape
+func mulVec(res, a, b *Element, n uint64, qInvNeg uint64)
 
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	mul(z, x, y)
 	return z
diff --git a/ecc/bn254/fr/element_ops_amd64.s b/ecc/bn254/fr/element_ops_amd64.s
index d077b11246..6c42136a7a 100644
--- a/ecc/bn254/fr/element_ops_amd64.s
+++ b/ecc/bn254/fr/element_ops_amd64.s
@@ -1,627 +1,6 @@
 // +build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+// We include the hash to force the Go compiler to recompile: 9425145785761608449
+#include "../../../field/asm/element_4w_amd64.s"
 
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0x43e1f593f0000001
-DATA q<>+8(SB)/8, $0x2833e84879b97091
-DATA q<>+16(SB)/8, $0xb85045b68181585d
-DATA q<>+24(SB)/8, $0x30644e72e131a029
-GLOBL q<>(SB), (RODATA+NOPTR), $32
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0xc2e1f593efffffff
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, rb0, rb1, rb2, rb3) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-
-TEXT ·reduce(SB), NOSPLIT, $0-8
-	MOVQ res+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// MulBy3(x *Element)
-TEXT ·MulBy3(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// MulBy5(x *Element)
-TEXT ·MulBy5(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R15,DI,R8,R9)
-	REDUCE(DX,CX,BX,SI,R15,DI,R8,R9)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// MulBy13(x *Element)
-TEXT ·MulBy13(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
-
-	MOVQ DX, R11
-	MOVQ CX, R12
-	MOVQ BX, R13
-	MOVQ SI, R14
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ R11, DX
-	ADCQ R12, CX
-	ADCQ R13, BX
-	ADCQ R14, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// Butterfly(a, b *Element) sets a = a + b; b = a - b
-TEXT ·Butterfly(SB), NOSPLIT, $0-16
-	MOVQ    a+0(FP), AX
-	MOVQ    0(AX), CX
-	MOVQ    8(AX), BX
-	MOVQ    16(AX), SI
-	MOVQ    24(AX), DI
-	MOVQ    CX, R8
-	MOVQ    BX, R9
-	MOVQ    SI, R10
-	MOVQ    DI, R11
-	XORQ    AX, AX
-	MOVQ    b+8(FP), DX
-	ADDQ    0(DX), CX
-	ADCQ    8(DX), BX
-	ADCQ    16(DX), SI
-	ADCQ    24(DX), DI
-	SUBQ    0(DX), R8
-	SBBQ    8(DX), R9
-	SBBQ    16(DX), R10
-	SBBQ    24(DX), R11
-	MOVQ    $0x43e1f593f0000001, R12
-	MOVQ    $0x2833e84879b97091, R13
-	MOVQ    $0xb85045b68181585d, R14
-	MOVQ    $0x30644e72e131a029, R15
-	CMOVQCC AX, R12
-	CMOVQCC AX, R13
-	CMOVQCC AX, R14
-	CMOVQCC AX, R15
-	ADDQ    R12, R8
-	ADCQ    R13, R9
-	ADCQ    R14, R10
-	ADCQ    R15, R11
-	MOVQ    R8, 0(DX)
-	MOVQ    R9, 8(DX)
-	MOVQ    R10, 16(DX)
-	MOVQ    R11, 24(DX)
-
-	// reduce element(CX,BX,SI,DI) using temp registers (R8,R9,R10,R11)
-	REDUCE(CX,BX,SI,DI,R8,R9,R10,R11)
-
-	MOVQ a+0(FP), AX
-	MOVQ CX, 0(AX)
-	MOVQ BX, 8(AX)
-	MOVQ SI, 16(AX)
-	MOVQ DI, 24(AX)
-	RET
-
-// addVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] + b[0...n]
-TEXT ·addVec(SB), NOSPLIT, $0-32
-	MOVQ res+0(FP), CX
-	MOVQ a+8(FP), AX
-	MOVQ b+16(FP), DX
-	MOVQ n+24(FP), BX
-
-loop_1:
-	TESTQ BX, BX
-	JEQ   done_2 // n == 0, we are done
-
-	// a[0] -> SI
-	// a[1] -> DI
-	// a[2] -> R8
-	// a[3] -> R9
-	MOVQ 0(AX), SI
-	MOVQ 8(AX), DI
-	MOVQ 16(AX), R8
-	MOVQ 24(AX), R9
-	ADDQ 0(DX), SI
-	ADCQ 8(DX), DI
-	ADCQ 16(DX), R8
-	ADCQ 24(DX), R9
-
-	// reduce element(SI,DI,R8,R9) using temp registers (R10,R11,R12,R13)
-	REDUCE(SI,DI,R8,R9,R10,R11,R12,R13)
-
-	MOVQ SI, 0(CX)
-	MOVQ DI, 8(CX)
-	MOVQ R8, 16(CX)
-	MOVQ R9, 24(CX)
-
-	// increment pointers to visit next element
-	ADDQ $32, AX
-	ADDQ $32, DX
-	ADDQ $32, CX
-	DECQ BX      // decrement n
-	JMP  loop_1
-
-done_2:
-	RET
-
-// subVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] - b[0...n]
-TEXT ·subVec(SB), NOSPLIT, $0-32
-	MOVQ res+0(FP), CX
-	MOVQ a+8(FP), AX
-	MOVQ b+16(FP), DX
-	MOVQ n+24(FP), BX
-	XORQ SI, SI
-
-loop_3:
-	TESTQ BX, BX
-	JEQ   done_4 // n == 0, we are done
-
-	// a[0] -> DI
-	// a[1] -> R8
-	// a[2] -> R9
-	// a[3] -> R10
-	MOVQ 0(AX), DI
-	MOVQ 8(AX), R8
-	MOVQ 16(AX), R9
-	MOVQ 24(AX), R10
-	SUBQ 0(DX), DI
-	SBBQ 8(DX), R8
-	SBBQ 16(DX), R9
-	SBBQ 24(DX), R10
-
-	// reduce (a-b) mod q
-	// q[0] -> R11
-	// q[1] -> R12
-	// q[2] -> R13
-	// q[3] -> R14
-	MOVQ    $0x43e1f593f0000001, R11
-	MOVQ    $0x2833e84879b97091, R12
-	MOVQ    $0xb85045b68181585d, R13
-	MOVQ    $0x30644e72e131a029, R14
-	CMOVQCC SI, R11
-	CMOVQCC SI, R12
-	CMOVQCC SI, R13
-	CMOVQCC SI, R14
-
-	// add registers (q or 0) to a, and set to result
-	ADDQ R11, DI
-	ADCQ R12, R8
-	ADCQ R13, R9
-	ADCQ R14, R10
-	MOVQ DI, 0(CX)
-	MOVQ R8, 8(CX)
-	MOVQ R9, 16(CX)
-	MOVQ R10, 24(CX)
-
-	// increment pointers to visit next element
-	ADDQ $32, AX
-	ADDQ $32, DX
-	ADDQ $32, CX
-	DECQ BX      // decrement n
-	JMP  loop_3
-
-done_4:
-	RET
-
-// scalarMulVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] * b
-TEXT ·scalarMulVec(SB), $56-32
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_5
-	MOVQ a+8(FP), R11
-	MOVQ b+16(FP), R10
-	MOVQ n+24(FP), R12
-
-	// scalar[0] -> SI
-	// scalar[1] -> DI
-	// scalar[2] -> R8
-	// scalar[3] -> R9
-	MOVQ 0(R10), SI
-	MOVQ 8(R10), DI
-	MOVQ 16(R10), R8
-	MOVQ 24(R10), R9
-	MOVQ res+0(FP), R10
-
-loop_6:
-	TESTQ R12, R12
-	JEQ   done_7   // n == 0, we are done
-
-	// TODO @gbotrel this is generated from the same macro as the unit mul, we should refactor this in a single asm function
-	// A -> BP
-	// t[0] -> R14
-	// t[1] -> R15
-	// t[2] -> CX
-	// t[3] -> BX
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 0(R11), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ SI, R14, R15
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ DI, AX, CX
-	ADOXQ AX, R15
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ R8, AX, BX
-	ADOXQ AX, CX
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 8(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ SI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R15
-	MULXQ DI, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, CX
-	MULXQ R8, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, BX
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 16(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ SI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R15
-	MULXQ DI, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, CX
-	MULXQ R8, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, BX
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 24(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ SI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R15
-	MULXQ DI, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, CX
-	MULXQ R8, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, BX
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// reduce t mod q
-	// reduce element(R14,R15,CX,BX) using temp registers (R13,AX,DX,s0-8(SP))
-	REDUCE(R14,R15,CX,BX,R13,AX,DX,s0-8(SP))
-
-	MOVQ R14, 0(R10)
-	MOVQ R15, 8(R10)
-	MOVQ CX, 16(R10)
-	MOVQ BX, 24(R10)
-
-	// increment pointers to visit next element
-	ADDQ $32, R11
-	ADDQ $32, R10
-	DECQ R12      // decrement n
-	JMP  loop_6
-
-done_7:
-	RET
-
-noAdx_5:
-	MOVQ n+24(FP), DX
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	MOVQ DX, 8(SP)
-	MOVQ DX, 16(SP)
-	MOVQ a+8(FP), AX
-	MOVQ AX, 24(SP)
-	MOVQ DX, 32(SP)
-	MOVQ DX, 40(SP)
-	MOVQ b+16(FP), AX
-	MOVQ AX, 48(SP)
-	CALL ·scalarMulVecGeneric(SB)
-	RET
diff --git a/ecc/bn254/fr/element_ops_purego.go b/ecc/bn254/fr/element_ops_purego.go
index cd5c53d8fc..4ea220c185 100644
--- a/ecc/bn254/fr/element_ops_purego.go
+++ b/ecc/bn254/fr/element_ops_purego.go
@@ -78,53 +78,32 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	scalarMulVecGeneric(*vector, a, b)
 }
 
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
+
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t0, t1, t2, t3 uint64
 	var u0, u1, u2, u3 uint64
diff --git a/ecc/bn254/fr/element_test.go b/ecc/bn254/fr/element_test.go
index 3be23d96a4..5bac70c4b4 100644
--- a/ecc/bn254/fr/element_test.go
+++ b/ecc/bn254/fr/element_test.go
@@ -637,7 +637,6 @@ func TestElementBitLen(t *testing.T) {
 	))
 
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
-
 }
 
 func TestElementButterflies(t *testing.T) {
@@ -707,77 +706,6 @@ func TestElementLexicographicallyLargest(t *testing.T) {
 
 }
 
-func TestElementVecOps(t *testing.T) {
-	assert := require.New(t)
-
-	const N = 7
-	a := make(Vector, N)
-	b := make(Vector, N)
-	c := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a[i].SetRandom()
-		b[i].SetRandom()
-	}
-
-	// Vector addition
-	c.Add(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Add(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector addition failed")
-	}
-
-	// Vector subtraction
-	c.Sub(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Sub(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector subtraction failed")
-	}
-
-	// Vector scaling
-	c.ScalarMul(a, &b[0])
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Mul(&a[i], &b[0])
-		assert.True(c[i].Equal(&expected), "Vector scaling failed")
-	}
-}
-
-func BenchmarkElementVecOps(b *testing.B) {
-	// note; to benchmark against "no asm" version, use the following
-	// build tag: -tags purego
-	const N = 1024
-	a1 := make(Vector, N)
-	b1 := make(Vector, N)
-	c1 := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a1[i].SetRandom()
-		b1[i].SetRandom()
-	}
-
-	b.Run("Add", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Add(a1, b1)
-		}
-	})
-
-	b.Run("Sub", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Sub(a1, b1)
-		}
-	})
-
-	b.Run("ScalarMul", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.ScalarMul(a1, &b1[0])
-		}
-	})
-}
-
 func TestElementAdd(t *testing.T) {
 	t.Parallel()
 	parameters := gopter.DefaultTestParameters()
@@ -2345,38 +2273,38 @@ func gen() gopter.Gen {
 	}
 }
 
-func genFull() gopter.Gen {
-	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+func genRandomFq(genParams *gopter.GenParameters) Element {
+	var g Element
 
-		genRandomFq := func() Element {
-			var g Element
+	g = Element{
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+	}
 
-			g = Element{
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-			}
+	if qElement[3] != ^uint64(0) {
+		g[3] %= (qElement[3] + 1)
+	}
 
-			if qElement[3] != ^uint64(0) {
-				g[3] %= (qElement[3] + 1)
-			}
+	for !g.smallerThanModulus() {
+		g = Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[3] != ^uint64(0) {
+			g[3] %= (qElement[3] + 1)
+		}
+	}
 
-			for !g.smallerThanModulus() {
-				g = Element{
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-				}
-				if qElement[3] != ^uint64(0) {
-					g[3] %= (qElement[3] + 1)
-				}
-			}
+	return g
+}
 
-			return g
-		}
-		a := genRandomFq()
+func genFull() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
 
 		var carry uint64
 		a[0], carry = bits.Add64(a[0], qElement[0], carry)
@@ -2389,6 +2317,14 @@ func genFull() gopter.Gen {
 	}
 }
 
+func genElement() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
+		genResult := gopter.NewGenResult(a, gopter.NoShrinker)
+		return genResult
+	}
+}
+
 func (z *Element) matchVeryBigInt(aHi uint64, aInt *big.Int) error {
 	var modulus big.Int
 	var aIntMod big.Int
diff --git a/ecc/bn254/fr/vector.go b/ecc/bn254/fr/vector.go
index f39828547f..867cabbc3d 100644
--- a/ecc/bn254/fr/vector.go
+++ b/ecc/bn254/fr/vector.go
@@ -226,6 +226,32 @@ func scalarMulVecGeneric(res, a Vector, b *Element) {
 	}
 }
 
+func sumVecGeneric(res *Element, a Vector) {
+	for i := 0; i < len(a); i++ {
+		res.Add(res, &a[i])
+	}
+}
+
+func innerProductVecGeneric(res *Element, a, b Vector) {
+	if len(a) != len(b) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	var tmp Element
+	for i := 0; i < len(a); i++ {
+		tmp.Mul(&a[i], &b[i])
+		res.Add(res, &tmp)
+	}
+}
+
+func mulVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Mul(&a[i], &b[i])
+	}
+}
+
 // TODO @gbotrel make a public package out of that.
 // execute executes the work function in parallel.
 // this is copy paste from internal/parallel/parallel.go
diff --git a/ecc/bn254/fr/vector_test.go b/ecc/bn254/fr/vector_test.go
index e58f2d9a38..b6344c18b7 100644
--- a/ecc/bn254/fr/vector_test.go
+++ b/ecc/bn254/fr/vector_test.go
@@ -18,10 +18,15 @@ package fr
 
 import (
 	"bytes"
+	"fmt"
 	"github.com/stretchr/testify/require"
+	"os"
 	"reflect"
 	"sort"
 	"testing"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/prop"
 )
 
 func TestVectorSort(t *testing.T) {
@@ -88,3 +93,279 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 	}
 	return <-chErr
 }
+
+func TestVectorOps(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = 2
+	} else {
+		parameters.MinSuccessfulTests = 10
+	}
+	properties := gopter.NewProperties(parameters)
+
+	addVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Add(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Add(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	subVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Sub(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Sub(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	scalarMulVector := func(a Vector, b Element) bool {
+		c := make(Vector, len(a))
+		c.ScalarMul(a, &b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b)
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sumVector := func(a Vector) bool {
+		var sum Element
+		computed := a.Sum()
+		for i := 0; i < len(a); i++ {
+			sum.Add(&sum, &a[i])
+		}
+
+		return sum.Equal(&computed)
+	}
+
+	innerProductVector := func(a, b Vector) bool {
+		computed := a.InnerProduct(b)
+		var innerProduct Element
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			innerProduct.Add(&innerProduct, &tmp)
+		}
+
+		return innerProduct.Equal(&computed)
+	}
+
+	mulVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		a[0].SetUint64(0x24)
+		b[0].SetUint64(0x42)
+		c.Mul(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sizes := []int{1, 2, 3, 4, 8, 9, 15, 16, 509, 510, 511, 512, 513, 514}
+	type genPair struct {
+		g1, g2 gopter.Gen
+		label  string
+	}
+
+	for _, size := range sizes {
+		generators := []genPair{
+			{genZeroVector(size), genZeroVector(size), "zero vectors"},
+			{genMaxVector(size), genMaxVector(size), "max vectors"},
+			{genVector(size), genVector(size), "random vectors"},
+			{genVector(size), genZeroVector(size), "random and zero vectors"},
+		}
+		for _, gp := range generators {
+			properties.Property(fmt.Sprintf("vector addition %d - %s", size, gp.label), prop.ForAll(
+				addVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector subtraction %d - %s", size, gp.label), prop.ForAll(
+				subVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector scalar multiplication %d - %s", size, gp.label), prop.ForAll(
+				scalarMulVector,
+				gp.g1,
+				genElement(),
+			))
+
+			properties.Property(fmt.Sprintf("vector sum %d - %s", size, gp.label), prop.ForAll(
+				sumVector,
+				gp.g1,
+			))
+
+			properties.Property(fmt.Sprintf("vector inner product %d - %s", size, gp.label), prop.ForAll(
+				innerProductVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector multiplication %d - %s", size, gp.label), prop.ForAll(
+				mulVector,
+				gp.g1,
+				gp.g2,
+			))
+		}
+	}
+
+	properties.TestingRun(t, gopter.NewFormatedReporter(false, 260, os.Stdout))
+}
+
+func BenchmarkVectorOps(b *testing.B) {
+	// note; to benchmark against "no asm" version, use the following
+	// build tag: -tags purego
+	const N = 1 << 24
+	a1 := make(Vector, N)
+	b1 := make(Vector, N)
+	c1 := make(Vector, N)
+	var mixer Element
+	mixer.SetRandom()
+	for i := 1; i < N; i++ {
+		a1[i-1].SetUint64(uint64(i)).
+			Mul(&a1[i-1], &mixer)
+		b1[i-1].SetUint64(^uint64(i)).
+			Mul(&b1[i-1], &mixer)
+	}
+
+	for n := 1 << 4; n <= N; n <<= 1 {
+		b.Run(fmt.Sprintf("add %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Add(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sub %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Sub(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("scalarMul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.ScalarMul(_a, &mixer)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sum %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.Sum()
+			}
+		})
+
+		b.Run(fmt.Sprintf("innerProduct %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.InnerProduct(_b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("mul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Mul(_a, _b)
+			}
+		})
+	}
+}
+
+func genZeroVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genMaxVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+
+		qMinusOne := qElement
+		qMinusOne[0]--
+
+		for i := 0; i < size; i++ {
+			g[i] = qMinusOne
+		}
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		mixer := Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[3] != ^uint64(0) {
+			mixer[3] %= (qElement[3] + 1)
+		}
+
+		for !mixer.smallerThanModulus() {
+			mixer = Element{
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+			}
+			if qElement[3] != ^uint64(0) {
+				mixer[3] %= (qElement[3] + 1)
+			}
+		}
+
+		for i := 1; i <= size; i++ {
+			g[i-1].SetUint64(uint64(i)).
+				Mul(&g[i-1], &mixer)
+		}
+
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/ecc/bn254/internal/fptower/e2_amd64.go b/ecc/bn254/internal/fptower/e2_amd64.go
index 259609bd81..b6db5715a3 100644
--- a/ecc/bn254/internal/fptower/e2_amd64.go
+++ b/ecc/bn254/internal/fptower/e2_amd64.go
@@ -16,6 +16,29 @@
 
 package fptower
 
+import (
+	"github.com/consensys/gnark-crypto/ecc/bn254/fp"
+)
+
+// q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
+// used for Montgomery reduction
+const qInvNeg uint64 = 9786893198990664585
+
+// Field modulus q (Fp)
+const (
+	q0 uint64 = 4332616871279656263
+	q1 uint64 = 10917124144477883021
+	q2 uint64 = 13281191951274694749
+	q3 uint64 = 3486998266802970665
+)
+
+var qElement = fp.Element{
+	q0,
+	q1,
+	q2,
+	q3,
+}
+
 //go:noescape
 func addE2(res, x, y *E2)
 
diff --git a/ecc/bn254/internal/fptower/e2_amd64.s b/ecc/bn254/internal/fptower/e2_amd64.s
index 43ffb7f16c..172cd67e82 100644
--- a/ecc/bn254/internal/fptower/e2_amd64.s
+++ b/ecc/bn254/internal/fptower/e2_amd64.s
@@ -14,173 +14,83 @@
 
 #include "textflag.h"
 #include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0x3c208c16d87cfd47
-DATA q<>+8(SB)/8, $0x97816a916871ca8d
-DATA q<>+16(SB)/8, $0xb85045b68181585d
-DATA q<>+24(SB)/8, $0x30644e72e131a029
-GLOBL q<>(SB), (RODATA+NOPTR), $32
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0x87d20782e4866389
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
+#include "go_asm.h"
 
 #define REDUCE(ra0, ra1, ra2, ra3, rb0, rb1, rb2, rb3) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
+	MOVQ    ra0, rb0;              \
+	SUBQ    ·qElement(SB), ra0;    \
+	MOVQ    ra1, rb1;              \
+	SBBQ    ·qElement+8(SB), ra1;  \
+	MOVQ    ra2, rb2;              \
+	SBBQ    ·qElement+16(SB), ra2; \
+	MOVQ    ra3, rb3;              \
+	SBBQ    ·qElement+24(SB), ra3; \
+	CMOVQCS rb0, ra0;              \
+	CMOVQCS rb1, ra1;              \
+	CMOVQCS rb2, ra2;              \
+	CMOVQCS rb3, ra3;              \
 
 // this code is generated and identical to fp.Mul(...)
+// A -> BP
+// t[0] -> R10
+// t[1] -> R11
+// t[2] -> R12
+// t[3] -> R13
+#define MACC(in0, in1, in2) \
+	ADCXQ in0, in1     \
+	MULXQ in2, AX, in0 \
+	ADOXQ AX, in1      \
+
+#define DIV_SHIFT() \
+	PUSHQ BP                         \
+	MOVQ  $const_qInvNeg, DX         \
+	IMULQ R10, DX                    \
+	XORQ  AX, AX                     \
+	MULXQ ·qElement+0(SB), AX, BP    \
+	ADCXQ R10, AX                    \
+	MOVQ  BP, R10                    \
+	POPQ  BP                         \
+	MACC(R11, R10, ·qElement+8(SB))  \
+	MACC(R12, R11, ·qElement+16(SB)) \
+	MACC(R13, R12, ·qElement+24(SB)) \
+	MOVQ  $0, AX                     \
+	ADCXQ AX, R13                    \
+	ADOXQ BP, R13                    \
+
+#define MUL_WORD_0() \
+	XORQ  AX, AX        \
+	MULXQ R14, R10, R11 \
+	MULXQ R15, AX, R12  \
+	ADOXQ AX, R11       \
+	MULXQ CX, AX, R13   \
+	ADOXQ AX, R12       \
+	MULXQ BX, AX, BP    \
+	ADOXQ AX, R13       \
+	MOVQ  $0, AX        \
+	ADOXQ AX, BP        \
+	DIV_SHIFT()         \
+
+#define MUL_WORD_N() \
+	XORQ  AX, AX       \
+	MULXQ R14, AX, BP  \
+	ADOXQ AX, R10      \
+	MACC(BP, R11, R15) \
+	MACC(BP, R12, CX)  \
+	MACC(BP, R13, BX)  \
+	MOVQ  $0, AX       \
+	ADCXQ AX, BP       \
+	ADOXQ AX, BP       \
+	DIV_SHIFT()        \
+
 #define MUL() \
-	XORQ  AX, AX;              \
-	MOVQ  SI, DX;              \
-	MULXQ R14, R10, R11;       \
-	MULXQ R15, AX, R12;        \
-	ADOXQ AX, R11;             \
-	MULXQ CX, AX, R13;         \
-	ADOXQ AX, R12;             \
-	MULXQ BX, AX, BP;          \
-	ADOXQ AX, R13;             \
-	MOVQ  $0, AX;              \
-	ADOXQ AX, BP;              \
-	PUSHQ BP;                  \
-	MOVQ  qInv0<>(SB), DX;     \
-	IMULQ R10, DX;             \
-	XORQ  AX, AX;              \
-	MULXQ q<>+0(SB), AX, BP;   \
-	ADCXQ R10, AX;             \
-	MOVQ  BP, R10;             \
-	POPQ  BP;                  \
-	ADCXQ R11, R10;            \
-	MULXQ q<>+8(SB), AX, R11;  \
-	ADOXQ AX, R10;             \
-	ADCXQ R12, R11;            \
-	MULXQ q<>+16(SB), AX, R12; \
-	ADOXQ AX, R11;             \
-	ADCXQ R13, R12;            \
-	MULXQ q<>+24(SB), AX, R13; \
-	ADOXQ AX, R12;             \
-	MOVQ  $0, AX;              \
-	ADCXQ AX, R13;             \
-	ADOXQ BP, R13;             \
-	XORQ  AX, AX;              \
-	MOVQ  DI, DX;              \
-	MULXQ R14, AX, BP;         \
-	ADOXQ AX, R10;             \
-	ADCXQ BP, R11;             \
-	MULXQ R15, AX, BP;         \
-	ADOXQ AX, R11;             \
-	ADCXQ BP, R12;             \
-	MULXQ CX, AX, BP;          \
-	ADOXQ AX, R12;             \
-	ADCXQ BP, R13;             \
-	MULXQ BX, AX, BP;          \
-	ADOXQ AX, R13;             \
-	MOVQ  $0, AX;              \
-	ADCXQ AX, BP;              \
-	ADOXQ AX, BP;              \
-	PUSHQ BP;                  \
-	MOVQ  qInv0<>(SB), DX;     \
-	IMULQ R10, DX;             \
-	XORQ  AX, AX;              \
-	MULXQ q<>+0(SB), AX, BP;   \
-	ADCXQ R10, AX;             \
-	MOVQ  BP, R10;             \
-	POPQ  BP;                  \
-	ADCXQ R11, R10;            \
-	MULXQ q<>+8(SB), AX, R11;  \
-	ADOXQ AX, R10;             \
-	ADCXQ R12, R11;            \
-	MULXQ q<>+16(SB), AX, R12; \
-	ADOXQ AX, R11;             \
-	ADCXQ R13, R12;            \
-	MULXQ q<>+24(SB), AX, R13; \
-	ADOXQ AX, R12;             \
-	MOVQ  $0, AX;              \
-	ADCXQ AX, R13;             \
-	ADOXQ BP, R13;             \
-	XORQ  AX, AX;              \
-	MOVQ  R8, DX;              \
-	MULXQ R14, AX, BP;         \
-	ADOXQ AX, R10;             \
-	ADCXQ BP, R11;             \
-	MULXQ R15, AX, BP;         \
-	ADOXQ AX, R11;             \
-	ADCXQ BP, R12;             \
-	MULXQ CX, AX, BP;          \
-	ADOXQ AX, R12;             \
-	ADCXQ BP, R13;             \
-	MULXQ BX, AX, BP;          \
-	ADOXQ AX, R13;             \
-	MOVQ  $0, AX;              \
-	ADCXQ AX, BP;              \
-	ADOXQ AX, BP;              \
-	PUSHQ BP;                  \
-	MOVQ  qInv0<>(SB), DX;     \
-	IMULQ R10, DX;             \
-	XORQ  AX, AX;              \
-	MULXQ q<>+0(SB), AX, BP;   \
-	ADCXQ R10, AX;             \
-	MOVQ  BP, R10;             \
-	POPQ  BP;                  \
-	ADCXQ R11, R10;            \
-	MULXQ q<>+8(SB), AX, R11;  \
-	ADOXQ AX, R10;             \
-	ADCXQ R12, R11;            \
-	MULXQ q<>+16(SB), AX, R12; \
-	ADOXQ AX, R11;             \
-	ADCXQ R13, R12;            \
-	MULXQ q<>+24(SB), AX, R13; \
-	ADOXQ AX, R12;             \
-	MOVQ  $0, AX;              \
-	ADCXQ AX, R13;             \
-	ADOXQ BP, R13;             \
-	XORQ  AX, AX;              \
-	MOVQ  R9, DX;              \
-	MULXQ R14, AX, BP;         \
-	ADOXQ AX, R10;             \
-	ADCXQ BP, R11;             \
-	MULXQ R15, AX, BP;         \
-	ADOXQ AX, R11;             \
-	ADCXQ BP, R12;             \
-	MULXQ CX, AX, BP;          \
-	ADOXQ AX, R12;             \
-	ADCXQ BP, R13;             \
-	MULXQ BX, AX, BP;          \
-	ADOXQ AX, R13;             \
-	MOVQ  $0, AX;              \
-	ADCXQ AX, BP;              \
-	ADOXQ AX, BP;              \
-	PUSHQ BP;                  \
-	MOVQ  qInv0<>(SB), DX;     \
-	IMULQ R10, DX;             \
-	XORQ  AX, AX;              \
-	MULXQ q<>+0(SB), AX, BP;   \
-	ADCXQ R10, AX;             \
-	MOVQ  BP, R10;             \
-	POPQ  BP;                  \
-	ADCXQ R11, R10;            \
-	MULXQ q<>+8(SB), AX, R11;  \
-	ADOXQ AX, R10;             \
-	ADCXQ R12, R11;            \
-	MULXQ q<>+16(SB), AX, R12; \
-	ADOXQ AX, R11;             \
-	ADCXQ R13, R12;            \
-	MULXQ q<>+24(SB), AX, R13; \
-	ADOXQ AX, R12;             \
-	MOVQ  $0, AX;              \
-	ADCXQ AX, R13;             \
-	ADOXQ BP, R13;             \
+	MOVQ SI, DX;  \
+	MUL_WORD_0(); \
+	MOVQ DI, DX;  \
+	MUL_WORD_N(); \
+	MOVQ R8, DX;  \
+	MUL_WORD_N(); \
+	MOVQ R9, DX;  \
+	MUL_WORD_N(); \
 
 TEXT ·addE2(SB), NOSPLIT, $0-24
 	MOVQ x+8(FP), AX
diff --git a/ecc/bw6-633/fp/asm.go b/ecc/bw6-633/fp/asm_adx.go
similarity index 100%
rename from ecc/bw6-633/fp/asm.go
rename to ecc/bw6-633/fp/asm_adx.go
diff --git a/ecc/bw6-633/fp/element.go b/ecc/bw6-633/fp/element.go
index 475abd7e5a..7656002f47 100644
--- a/ecc/bw6-633/fp/element.go
+++ b/ecc/bw6-633/fp/element.go
@@ -609,32 +609,8 @@ func (z *Element) Select(c int, x0 *Element, x1 *Element) *Element {
 // and is used for testing purposes.
 func _mulGeneric(z, x, y *Element) {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t [11]uint64
 	var D uint64
diff --git a/ecc/bw6-633/fp/element_mul_amd64.s b/ecc/bw6-633/fp/element_mul_amd64.s
deleted file mode 100644
index 62a7d4dda2..0000000000
--- a/ecc/bw6-633/fp/element_mul_amd64.s
+++ /dev/null
@@ -1,1974 +0,0 @@
-// +build !purego
-
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0xd74916ea4570000d
-DATA q<>+8(SB)/8, $0x3d369bd31147f73c
-DATA q<>+16(SB)/8, $0xd7b5ce7ab839c225
-DATA q<>+24(SB)/8, $0x7e0e8850edbda407
-DATA q<>+32(SB)/8, $0xb8da9f5e83f57c49
-DATA q<>+40(SB)/8, $0x8152a6c0fadea490
-DATA q<>+48(SB)/8, $0x4e59769ad9bbda2f
-DATA q<>+56(SB)/8, $0xa8fcd8c75d79d2c7
-DATA q<>+64(SB)/8, $0xfc1a174f01d72ab5
-DATA q<>+72(SB)/8, $0x0126633cc0f35f63
-GLOBL q<>(SB), (RODATA+NOPTR), $80
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0xb50f29ab0b03b13b
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, ra4, ra5, ra6, ra7, ra8, ra9, rb0, rb1, rb2, rb3, rb4, rb5, rb6, rb7, rb8, rb9) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	MOVQ    ra4, rb4;        \
-	SBBQ    q<>+32(SB), ra4; \
-	MOVQ    ra5, rb5;        \
-	SBBQ    q<>+40(SB), ra5; \
-	MOVQ    ra6, rb6;        \
-	SBBQ    q<>+48(SB), ra6; \
-	MOVQ    ra7, rb7;        \
-	SBBQ    q<>+56(SB), ra7; \
-	MOVQ    ra8, rb8;        \
-	SBBQ    q<>+64(SB), ra8; \
-	MOVQ    ra9, rb9;        \
-	SBBQ    q<>+72(SB), ra9; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-	CMOVQCS rb4, ra4;        \
-	CMOVQCS rb5, ra5;        \
-	CMOVQCS rb6, ra6;        \
-	CMOVQCS rb7, ra7;        \
-	CMOVQCS rb8, ra8;        \
-	CMOVQCS rb9, ra9;        \
-
-// mul(res, x, y *Element)
-TEXT ·mul(SB), $64-24
-
-	// the algorithm is described in the Element.Mul declaration (.go)
-	// however, to benefit from the ADCX and ADOX carry chains
-	// we split the inner loops in 2:
-	// for i=0 to N-1
-	// 		for j=0 to N-1
-	// 		    (A,t[j])  := t[j] + x[j]*y[i] + A
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C + A
-
-	NO_LOCAL_POINTERS
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_1
-	MOVQ x+8(FP), R12
-	MOVQ y+16(FP), R13
-
-	// A -> BP
-	// t[0] -> R14
-	// t[1] -> R15
-	// t[2] -> CX
-	// t[3] -> BX
-	// t[4] -> SI
-	// t[5] -> DI
-	// t[6] -> R8
-	// t[7] -> R9
-	// t[8] -> R10
-	// t[9] -> R11
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 0(R13), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ 0(R12), R14, R15
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ 8(R12), AX, CX
-	ADOXQ AX, R15
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ 16(R12), AX, BX
-	ADOXQ AX, CX
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ 24(R12), AX, SI
-	ADOXQ AX, BX
-
-	// (A,t[4])  := x[4]*y[0] + A
-	MULXQ 32(R12), AX, DI
-	ADOXQ AX, SI
-
-	// (A,t[5])  := x[5]*y[0] + A
-	MULXQ 40(R12), AX, R8
-	ADOXQ AX, DI
-
-	// (A,t[6])  := x[6]*y[0] + A
-	MULXQ 48(R12), AX, R9
-	ADOXQ AX, R8
-
-	// (A,t[7])  := x[7]*y[0] + A
-	MULXQ 56(R12), AX, R10
-	ADOXQ AX, R9
-
-	// (A,t[8])  := x[8]*y[0] + A
-	MULXQ 64(R12), AX, R11
-	ADOXQ AX, R10
-
-	// (A,t[9])  := x[9]*y[0] + A
-	MULXQ 72(R12), AX, BP
-	ADOXQ AX, R11
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// t[9] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R11
-	ADOXQ BP, R11
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 8(R13), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ 0(R12), AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R15
-	MULXQ 8(R12), AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, CX
-	MULXQ 16(R12), AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, BX
-	MULXQ 24(R12), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[1] + A
-	ADCXQ BP, SI
-	MULXQ 32(R12), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[1] + A
-	ADCXQ BP, DI
-	MULXQ 40(R12), AX, BP
-	ADOXQ AX, DI
-
-	// (A,t[6])  := t[6] + x[6]*y[1] + A
-	ADCXQ BP, R8
-	MULXQ 48(R12), AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[7])  := t[7] + x[7]*y[1] + A
-	ADCXQ BP, R9
-	MULXQ 56(R12), AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[8])  := t[8] + x[8]*y[1] + A
-	ADCXQ BP, R10
-	MULXQ 64(R12), AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[9])  := t[9] + x[9]*y[1] + A
-	ADCXQ BP, R11
-	MULXQ 72(R12), AX, BP
-	ADOXQ AX, R11
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// t[9] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R11
-	ADOXQ BP, R11
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 16(R13), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ 0(R12), AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R15
-	MULXQ 8(R12), AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, CX
-	MULXQ 16(R12), AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, BX
-	MULXQ 24(R12), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[2] + A
-	ADCXQ BP, SI
-	MULXQ 32(R12), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[2] + A
-	ADCXQ BP, DI
-	MULXQ 40(R12), AX, BP
-	ADOXQ AX, DI
-
-	// (A,t[6])  := t[6] + x[6]*y[2] + A
-	ADCXQ BP, R8
-	MULXQ 48(R12), AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[7])  := t[7] + x[7]*y[2] + A
-	ADCXQ BP, R9
-	MULXQ 56(R12), AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[8])  := t[8] + x[8]*y[2] + A
-	ADCXQ BP, R10
-	MULXQ 64(R12), AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[9])  := t[9] + x[9]*y[2] + A
-	ADCXQ BP, R11
-	MULXQ 72(R12), AX, BP
-	ADOXQ AX, R11
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// t[9] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R11
-	ADOXQ BP, R11
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 24(R13), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ 0(R12), AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R15
-	MULXQ 8(R12), AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, CX
-	MULXQ 16(R12), AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, BX
-	MULXQ 24(R12), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[3] + A
-	ADCXQ BP, SI
-	MULXQ 32(R12), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[3] + A
-	ADCXQ BP, DI
-	MULXQ 40(R12), AX, BP
-	ADOXQ AX, DI
-
-	// (A,t[6])  := t[6] + x[6]*y[3] + A
-	ADCXQ BP, R8
-	MULXQ 48(R12), AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[7])  := t[7] + x[7]*y[3] + A
-	ADCXQ BP, R9
-	MULXQ 56(R12), AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[8])  := t[8] + x[8]*y[3] + A
-	ADCXQ BP, R10
-	MULXQ 64(R12), AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[9])  := t[9] + x[9]*y[3] + A
-	ADCXQ BP, R11
-	MULXQ 72(R12), AX, BP
-	ADOXQ AX, R11
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// t[9] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R11
-	ADOXQ BP, R11
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 32(R13), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[4] + A
-	MULXQ 0(R12), AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[4] + A
-	ADCXQ BP, R15
-	MULXQ 8(R12), AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[4] + A
-	ADCXQ BP, CX
-	MULXQ 16(R12), AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[4] + A
-	ADCXQ BP, BX
-	MULXQ 24(R12), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[4] + A
-	ADCXQ BP, SI
-	MULXQ 32(R12), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[4] + A
-	ADCXQ BP, DI
-	MULXQ 40(R12), AX, BP
-	ADOXQ AX, DI
-
-	// (A,t[6])  := t[6] + x[6]*y[4] + A
-	ADCXQ BP, R8
-	MULXQ 48(R12), AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[7])  := t[7] + x[7]*y[4] + A
-	ADCXQ BP, R9
-	MULXQ 56(R12), AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[8])  := t[8] + x[8]*y[4] + A
-	ADCXQ BP, R10
-	MULXQ 64(R12), AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[9])  := t[9] + x[9]*y[4] + A
-	ADCXQ BP, R11
-	MULXQ 72(R12), AX, BP
-	ADOXQ AX, R11
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// t[9] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R11
-	ADOXQ BP, R11
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 40(R13), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[5] + A
-	MULXQ 0(R12), AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[5] + A
-	ADCXQ BP, R15
-	MULXQ 8(R12), AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[5] + A
-	ADCXQ BP, CX
-	MULXQ 16(R12), AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[5] + A
-	ADCXQ BP, BX
-	MULXQ 24(R12), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[5] + A
-	ADCXQ BP, SI
-	MULXQ 32(R12), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[5] + A
-	ADCXQ BP, DI
-	MULXQ 40(R12), AX, BP
-	ADOXQ AX, DI
-
-	// (A,t[6])  := t[6] + x[6]*y[5] + A
-	ADCXQ BP, R8
-	MULXQ 48(R12), AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[7])  := t[7] + x[7]*y[5] + A
-	ADCXQ BP, R9
-	MULXQ 56(R12), AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[8])  := t[8] + x[8]*y[5] + A
-	ADCXQ BP, R10
-	MULXQ 64(R12), AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[9])  := t[9] + x[9]*y[5] + A
-	ADCXQ BP, R11
-	MULXQ 72(R12), AX, BP
-	ADOXQ AX, R11
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// t[9] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R11
-	ADOXQ BP, R11
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 48(R13), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[6] + A
-	MULXQ 0(R12), AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[6] + A
-	ADCXQ BP, R15
-	MULXQ 8(R12), AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[6] + A
-	ADCXQ BP, CX
-	MULXQ 16(R12), AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[6] + A
-	ADCXQ BP, BX
-	MULXQ 24(R12), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[6] + A
-	ADCXQ BP, SI
-	MULXQ 32(R12), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[6] + A
-	ADCXQ BP, DI
-	MULXQ 40(R12), AX, BP
-	ADOXQ AX, DI
-
-	// (A,t[6])  := t[6] + x[6]*y[6] + A
-	ADCXQ BP, R8
-	MULXQ 48(R12), AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[7])  := t[7] + x[7]*y[6] + A
-	ADCXQ BP, R9
-	MULXQ 56(R12), AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[8])  := t[8] + x[8]*y[6] + A
-	ADCXQ BP, R10
-	MULXQ 64(R12), AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[9])  := t[9] + x[9]*y[6] + A
-	ADCXQ BP, R11
-	MULXQ 72(R12), AX, BP
-	ADOXQ AX, R11
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// t[9] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R11
-	ADOXQ BP, R11
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 56(R13), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[7] + A
-	MULXQ 0(R12), AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[7] + A
-	ADCXQ BP, R15
-	MULXQ 8(R12), AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[7] + A
-	ADCXQ BP, CX
-	MULXQ 16(R12), AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[7] + A
-	ADCXQ BP, BX
-	MULXQ 24(R12), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[7] + A
-	ADCXQ BP, SI
-	MULXQ 32(R12), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[7] + A
-	ADCXQ BP, DI
-	MULXQ 40(R12), AX, BP
-	ADOXQ AX, DI
-
-	// (A,t[6])  := t[6] + x[6]*y[7] + A
-	ADCXQ BP, R8
-	MULXQ 48(R12), AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[7])  := t[7] + x[7]*y[7] + A
-	ADCXQ BP, R9
-	MULXQ 56(R12), AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[8])  := t[8] + x[8]*y[7] + A
-	ADCXQ BP, R10
-	MULXQ 64(R12), AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[9])  := t[9] + x[9]*y[7] + A
-	ADCXQ BP, R11
-	MULXQ 72(R12), AX, BP
-	ADOXQ AX, R11
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// t[9] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R11
-	ADOXQ BP, R11
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 64(R13), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[8] + A
-	MULXQ 0(R12), AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[8] + A
-	ADCXQ BP, R15
-	MULXQ 8(R12), AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[8] + A
-	ADCXQ BP, CX
-	MULXQ 16(R12), AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[8] + A
-	ADCXQ BP, BX
-	MULXQ 24(R12), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[8] + A
-	ADCXQ BP, SI
-	MULXQ 32(R12), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[8] + A
-	ADCXQ BP, DI
-	MULXQ 40(R12), AX, BP
-	ADOXQ AX, DI
-
-	// (A,t[6])  := t[6] + x[6]*y[8] + A
-	ADCXQ BP, R8
-	MULXQ 48(R12), AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[7])  := t[7] + x[7]*y[8] + A
-	ADCXQ BP, R9
-	MULXQ 56(R12), AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[8])  := t[8] + x[8]*y[8] + A
-	ADCXQ BP, R10
-	MULXQ 64(R12), AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[9])  := t[9] + x[9]*y[8] + A
-	ADCXQ BP, R11
-	MULXQ 72(R12), AX, BP
-	ADOXQ AX, R11
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// t[9] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R11
-	ADOXQ BP, R11
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 72(R13), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[9] + A
-	MULXQ 0(R12), AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[9] + A
-	ADCXQ BP, R15
-	MULXQ 8(R12), AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[9] + A
-	ADCXQ BP, CX
-	MULXQ 16(R12), AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[9] + A
-	ADCXQ BP, BX
-	MULXQ 24(R12), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[9] + A
-	ADCXQ BP, SI
-	MULXQ 32(R12), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[9] + A
-	ADCXQ BP, DI
-	MULXQ 40(R12), AX, BP
-	ADOXQ AX, DI
-
-	// (A,t[6])  := t[6] + x[6]*y[9] + A
-	ADCXQ BP, R8
-	MULXQ 48(R12), AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[7])  := t[7] + x[7]*y[9] + A
-	ADCXQ BP, R9
-	MULXQ 56(R12), AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[8])  := t[8] + x[8]*y[9] + A
-	ADCXQ BP, R10
-	MULXQ 64(R12), AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[9])  := t[9] + x[9]*y[9] + A
-	ADCXQ BP, R11
-	MULXQ 72(R12), AX, BP
-	ADOXQ AX, R11
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// t[9] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R11
-	ADOXQ BP, R11
-
-	// reduce element(R14,R15,CX,BX,SI,DI,R8,R9,R10,R11) using temp registers (R12,R13,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP))
-	REDUCE(R14,R15,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP))
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R15, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	MOVQ SI, 32(AX)
-	MOVQ DI, 40(AX)
-	MOVQ R8, 48(AX)
-	MOVQ R9, 56(AX)
-	MOVQ R10, 64(AX)
-	MOVQ R11, 72(AX)
-	RET
-
-noAdx_1:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	MOVQ x+8(FP), AX
-	MOVQ AX, 8(SP)
-	MOVQ y+16(FP), AX
-	MOVQ AX, 16(SP)
-	CALL ·_mulGeneric(SB)
-	RET
-
-TEXT ·fromMont(SB), $64-8
-	NO_LOCAL_POINTERS
-
-	// the algorithm is described here
-	// https://hackmd.io/@gnark/modular_multiplication
-	// when y = 1 we have:
-	// for i=0 to N-1
-	// 		t[i] = x[i]
-	// for i=0 to N-1
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_2
-	MOVQ res+0(FP), DX
-	MOVQ 0(DX), R14
-	MOVQ 8(DX), R15
-	MOVQ 16(DX), CX
-	MOVQ 24(DX), BX
-	MOVQ 32(DX), SI
-	MOVQ 40(DX), DI
-	MOVQ 48(DX), R8
-	MOVQ 56(DX), R9
-	MOVQ 64(DX), R10
-	MOVQ 72(DX), R11
-	XORQ DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-	MOVQ  $0, AX
-	ADCXQ AX, R11
-	ADOXQ AX, R11
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-	MOVQ  $0, AX
-	ADCXQ AX, R11
-	ADOXQ AX, R11
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-	MOVQ  $0, AX
-	ADCXQ AX, R11
-	ADOXQ AX, R11
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-	MOVQ  $0, AX
-	ADCXQ AX, R11
-	ADOXQ AX, R11
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-	MOVQ  $0, AX
-	ADCXQ AX, R11
-	ADOXQ AX, R11
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-	MOVQ  $0, AX
-	ADCXQ AX, R11
-	ADOXQ AX, R11
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-	MOVQ  $0, AX
-	ADCXQ AX, R11
-	ADOXQ AX, R11
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-	MOVQ  $0, AX
-	ADCXQ AX, R11
-	ADOXQ AX, R11
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-	MOVQ  $0, AX
-	ADCXQ AX, R11
-	ADOXQ AX, R11
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-	MOVQ  $0, AX
-	ADCXQ AX, R11
-	ADOXQ AX, R11
-
-	// reduce element(R14,R15,CX,BX,SI,DI,R8,R9,R10,R11) using temp registers (R12,R13,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP))
-	REDUCE(R14,R15,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP))
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R15, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	MOVQ SI, 32(AX)
-	MOVQ DI, 40(AX)
-	MOVQ R8, 48(AX)
-	MOVQ R9, 56(AX)
-	MOVQ R10, 64(AX)
-	MOVQ R11, 72(AX)
-	RET
-
-noAdx_2:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	CALL ·_fromMontGeneric(SB)
-	RET
diff --git a/ecc/bw6-633/fp/element_ops_amd64.go b/ecc/bw6-633/fp/element_ops_amd64.go
index 83bba45aed..ed2803d717 100644
--- a/ecc/bw6-633/fp/element_ops_amd64.go
+++ b/ecc/bw6-633/fp/element_ops_amd64.go
@@ -50,48 +50,8 @@ func Butterfly(a, b *Element)
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	mul(z, x, y)
 	return z
diff --git a/ecc/bw6-633/fp/element_ops_amd64.s b/ecc/bw6-633/fp/element_ops_amd64.s
index 12a0789638..db6a61c53a 100644
--- a/ecc/bw6-633/fp/element_ops_amd64.s
+++ b/ecc/bw6-633/fp/element_ops_amd64.s
@@ -1,436 +1,6 @@
 // +build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+// We include the hash to force the Go compiler to recompile: 747913930085520082
+#include "../../../field/asm/element_10w_amd64.s"
 
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0xd74916ea4570000d
-DATA q<>+8(SB)/8, $0x3d369bd31147f73c
-DATA q<>+16(SB)/8, $0xd7b5ce7ab839c225
-DATA q<>+24(SB)/8, $0x7e0e8850edbda407
-DATA q<>+32(SB)/8, $0xb8da9f5e83f57c49
-DATA q<>+40(SB)/8, $0x8152a6c0fadea490
-DATA q<>+48(SB)/8, $0x4e59769ad9bbda2f
-DATA q<>+56(SB)/8, $0xa8fcd8c75d79d2c7
-DATA q<>+64(SB)/8, $0xfc1a174f01d72ab5
-DATA q<>+72(SB)/8, $0x0126633cc0f35f63
-GLOBL q<>(SB), (RODATA+NOPTR), $80
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0xb50f29ab0b03b13b
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, ra4, ra5, ra6, ra7, ra8, ra9, rb0, rb1, rb2, rb3, rb4, rb5, rb6, rb7, rb8, rb9) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	MOVQ    ra4, rb4;        \
-	SBBQ    q<>+32(SB), ra4; \
-	MOVQ    ra5, rb5;        \
-	SBBQ    q<>+40(SB), ra5; \
-	MOVQ    ra6, rb6;        \
-	SBBQ    q<>+48(SB), ra6; \
-	MOVQ    ra7, rb7;        \
-	SBBQ    q<>+56(SB), ra7; \
-	MOVQ    ra8, rb8;        \
-	SBBQ    q<>+64(SB), ra8; \
-	MOVQ    ra9, rb9;        \
-	SBBQ    q<>+72(SB), ra9; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-	CMOVQCS rb4, ra4;        \
-	CMOVQCS rb5, ra5;        \
-	CMOVQCS rb6, ra6;        \
-	CMOVQCS rb7, ra7;        \
-	CMOVQCS rb8, ra8;        \
-	CMOVQCS rb9, ra9;        \
-
-TEXT ·reduce(SB), $56-8
-	MOVQ res+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	MOVQ 40(AX), R8
-	MOVQ 48(AX), R9
-	MOVQ 56(AX), R10
-	MOVQ 64(AX), R11
-	MOVQ 72(AX), R12
-
-	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	MOVQ R8, 40(AX)
-	MOVQ R9, 48(AX)
-	MOVQ R10, 56(AX)
-	MOVQ R11, 64(AX)
-	MOVQ R12, 72(AX)
-	RET
-
-// MulBy3(x *Element)
-TEXT ·MulBy3(SB), $56-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	MOVQ 40(AX), R8
-	MOVQ 48(AX), R9
-	MOVQ 56(AX), R10
-	MOVQ 64(AX), R11
-	MOVQ 72(AX), R12
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-	ADCQ R9, R9
-	ADCQ R10, R10
-	ADCQ R11, R11
-	ADCQ R12, R12
-
-	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-	ADCQ 40(AX), R8
-	ADCQ 48(AX), R9
-	ADCQ 56(AX), R10
-	ADCQ 64(AX), R11
-	ADCQ 72(AX), R12
-
-	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	MOVQ R8, 40(AX)
-	MOVQ R9, 48(AX)
-	MOVQ R10, 56(AX)
-	MOVQ R11, 64(AX)
-	MOVQ R12, 72(AX)
-	RET
-
-// MulBy5(x *Element)
-TEXT ·MulBy5(SB), $56-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	MOVQ 40(AX), R8
-	MOVQ 48(AX), R9
-	MOVQ 56(AX), R10
-	MOVQ 64(AX), R11
-	MOVQ 72(AX), R12
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-	ADCQ R9, R9
-	ADCQ R10, R10
-	ADCQ R11, R11
-	ADCQ R12, R12
-
-	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-	ADCQ R9, R9
-	ADCQ R10, R10
-	ADCQ R11, R11
-	ADCQ R12, R12
-
-	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-	ADCQ 40(AX), R8
-	ADCQ 48(AX), R9
-	ADCQ 56(AX), R10
-	ADCQ 64(AX), R11
-	ADCQ 72(AX), R12
-
-	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	MOVQ R8, 40(AX)
-	MOVQ R9, 48(AX)
-	MOVQ R10, 56(AX)
-	MOVQ R11, 64(AX)
-	MOVQ R12, 72(AX)
-	RET
-
-// MulBy13(x *Element)
-TEXT ·MulBy13(SB), $136-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	MOVQ 40(AX), R8
-	MOVQ 48(AX), R9
-	MOVQ 56(AX), R10
-	MOVQ 64(AX), R11
-	MOVQ 72(AX), R12
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-	ADCQ R9, R9
-	ADCQ R10, R10
-	ADCQ R11, R11
-	ADCQ R12, R12
-
-	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-	ADCQ R9, R9
-	ADCQ R10, R10
-	ADCQ R11, R11
-	ADCQ R12, R12
-
-	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12) using temp registers (s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP),s11-96(SP),s12-104(SP),s13-112(SP),s14-120(SP),s15-128(SP),s16-136(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP),s11-96(SP),s12-104(SP),s13-112(SP),s14-120(SP),s15-128(SP),s16-136(SP))
-
-	MOVQ DX, s7-64(SP)
-	MOVQ CX, s8-72(SP)
-	MOVQ BX, s9-80(SP)
-	MOVQ SI, s10-88(SP)
-	MOVQ DI, s11-96(SP)
-	MOVQ R8, s12-104(SP)
-	MOVQ R9, s13-112(SP)
-	MOVQ R10, s14-120(SP)
-	MOVQ R11, s15-128(SP)
-	MOVQ R12, s16-136(SP)
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-	ADCQ R9, R9
-	ADCQ R10, R10
-	ADCQ R11, R11
-	ADCQ R12, R12
-
-	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
-
-	ADDQ s7-64(SP), DX
-	ADCQ s8-72(SP), CX
-	ADCQ s9-80(SP), BX
-	ADCQ s10-88(SP), SI
-	ADCQ s11-96(SP), DI
-	ADCQ s12-104(SP), R8
-	ADCQ s13-112(SP), R9
-	ADCQ s14-120(SP), R10
-	ADCQ s15-128(SP), R11
-	ADCQ s16-136(SP), R12
-
-	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-	ADCQ 40(AX), R8
-	ADCQ 48(AX), R9
-	ADCQ 56(AX), R10
-	ADCQ 64(AX), R11
-	ADCQ 72(AX), R12
-
-	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	MOVQ R8, 40(AX)
-	MOVQ R9, 48(AX)
-	MOVQ R10, 56(AX)
-	MOVQ R11, 64(AX)
-	MOVQ R12, 72(AX)
-	RET
-
-// Butterfly(a, b *Element) sets a = a + b; b = a - b
-TEXT ·Butterfly(SB), $56-16
-	MOVQ b+8(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	MOVQ 40(AX), R8
-	MOVQ 48(AX), R9
-	MOVQ 56(AX), R10
-	MOVQ 64(AX), R11
-	MOVQ 72(AX), R12
-	MOVQ a+0(FP), AX
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-	ADCQ 40(AX), R8
-	ADCQ 48(AX), R9
-	ADCQ 56(AX), R10
-	ADCQ 64(AX), R11
-	ADCQ 72(AX), R12
-	MOVQ DX, R13
-	MOVQ CX, R14
-	MOVQ BX, R15
-	MOVQ SI, s0-8(SP)
-	MOVQ DI, s1-16(SP)
-	MOVQ R8, s2-24(SP)
-	MOVQ R9, s3-32(SP)
-	MOVQ R10, s4-40(SP)
-	MOVQ R11, s5-48(SP)
-	MOVQ R12, s6-56(SP)
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	MOVQ 40(AX), R8
-	MOVQ 48(AX), R9
-	MOVQ 56(AX), R10
-	MOVQ 64(AX), R11
-	MOVQ 72(AX), R12
-	MOVQ b+8(FP), AX
-	SUBQ 0(AX), DX
-	SBBQ 8(AX), CX
-	SBBQ 16(AX), BX
-	SBBQ 24(AX), SI
-	SBBQ 32(AX), DI
-	SBBQ 40(AX), R8
-	SBBQ 48(AX), R9
-	SBBQ 56(AX), R10
-	SBBQ 64(AX), R11
-	SBBQ 72(AX), R12
-	JCC  noReduce_1
-	MOVQ $0xd74916ea4570000d, AX
-	ADDQ AX, DX
-	MOVQ $0x3d369bd31147f73c, AX
-	ADCQ AX, CX
-	MOVQ $0xd7b5ce7ab839c225, AX
-	ADCQ AX, BX
-	MOVQ $0x7e0e8850edbda407, AX
-	ADCQ AX, SI
-	MOVQ $0xb8da9f5e83f57c49, AX
-	ADCQ AX, DI
-	MOVQ $0x8152a6c0fadea490, AX
-	ADCQ AX, R8
-	MOVQ $0x4e59769ad9bbda2f, AX
-	ADCQ AX, R9
-	MOVQ $0xa8fcd8c75d79d2c7, AX
-	ADCQ AX, R10
-	MOVQ $0xfc1a174f01d72ab5, AX
-	ADCQ AX, R11
-	MOVQ $0x0126633cc0f35f63, AX
-	ADCQ AX, R12
-
-noReduce_1:
-	MOVQ b+8(FP), AX
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	MOVQ R8, 40(AX)
-	MOVQ R9, 48(AX)
-	MOVQ R10, 56(AX)
-	MOVQ R11, 64(AX)
-	MOVQ R12, 72(AX)
-	MOVQ R13, DX
-	MOVQ R14, CX
-	MOVQ R15, BX
-	MOVQ s0-8(SP), SI
-	MOVQ s1-16(SP), DI
-	MOVQ s2-24(SP), R8
-	MOVQ s3-32(SP), R9
-	MOVQ s4-40(SP), R10
-	MOVQ s5-48(SP), R11
-	MOVQ s6-56(SP), R12
-
-	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
-
-	MOVQ a+0(FP), AX
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	MOVQ R8, 40(AX)
-	MOVQ R9, 48(AX)
-	MOVQ R10, 56(AX)
-	MOVQ R11, 64(AX)
-	MOVQ R12, 72(AX)
-	RET
diff --git a/ecc/bw6-633/fp/element_ops_purego.go b/ecc/bw6-633/fp/element_ops_purego.go
index 69c68919e5..3b5d489a30 100644
--- a/ecc/bw6-633/fp/element_ops_purego.go
+++ b/ecc/bw6-633/fp/element_ops_purego.go
@@ -71,48 +71,8 @@ func reduce(z *Element) {
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t0, t1, t2, t3, t4, t5, t6, t7, t8, t9 uint64
 	var u0, u1, u2, u3, u4, u5, u6, u7, u8, u9 uint64
diff --git a/ecc/bw6-633/fp/element_test.go b/ecc/bw6-633/fp/element_test.go
index 169cd6701c..2aaadfa902 100644
--- a/ecc/bw6-633/fp/element_test.go
+++ b/ecc/bw6-633/fp/element_test.go
@@ -649,7 +649,6 @@ func TestElementBitLen(t *testing.T) {
 	))
 
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
-
 }
 
 func TestElementButterflies(t *testing.T) {
@@ -719,77 +718,6 @@ func TestElementLexicographicallyLargest(t *testing.T) {
 
 }
 
-func TestElementVecOps(t *testing.T) {
-	assert := require.New(t)
-
-	const N = 7
-	a := make(Vector, N)
-	b := make(Vector, N)
-	c := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a[i].SetRandom()
-		b[i].SetRandom()
-	}
-
-	// Vector addition
-	c.Add(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Add(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector addition failed")
-	}
-
-	// Vector subtraction
-	c.Sub(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Sub(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector subtraction failed")
-	}
-
-	// Vector scaling
-	c.ScalarMul(a, &b[0])
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Mul(&a[i], &b[0])
-		assert.True(c[i].Equal(&expected), "Vector scaling failed")
-	}
-}
-
-func BenchmarkElementVecOps(b *testing.B) {
-	// note; to benchmark against "no asm" version, use the following
-	// build tag: -tags purego
-	const N = 1024
-	a1 := make(Vector, N)
-	b1 := make(Vector, N)
-	c1 := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a1[i].SetRandom()
-		b1[i].SetRandom()
-	}
-
-	b.Run("Add", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Add(a1, b1)
-		}
-	})
-
-	b.Run("Sub", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Sub(a1, b1)
-		}
-	})
-
-	b.Run("ScalarMul", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.ScalarMul(a1, &b1[0])
-		}
-	})
-}
-
 func TestElementAdd(t *testing.T) {
 	t.Parallel()
 	parameters := gopter.DefaultTestParameters()
@@ -2369,50 +2297,50 @@ func gen() gopter.Gen {
 	}
 }
 
-func genFull() gopter.Gen {
-	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+func genRandomFq(genParams *gopter.GenParameters) Element {
+	var g Element
 
-		genRandomFq := func() Element {
-			var g Element
+	g = Element{
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+	}
 
-			g = Element{
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-			}
+	if qElement[9] != ^uint64(0) {
+		g[9] %= (qElement[9] + 1)
+	}
 
-			if qElement[9] != ^uint64(0) {
-				g[9] %= (qElement[9] + 1)
-			}
+	for !g.smallerThanModulus() {
+		g = Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[9] != ^uint64(0) {
+			g[9] %= (qElement[9] + 1)
+		}
+	}
 
-			for !g.smallerThanModulus() {
-				g = Element{
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-				}
-				if qElement[9] != ^uint64(0) {
-					g[9] %= (qElement[9] + 1)
-				}
-			}
+	return g
+}
 
-			return g
-		}
-		a := genRandomFq()
+func genFull() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
 
 		var carry uint64
 		a[0], carry = bits.Add64(a[0], qElement[0], carry)
@@ -2431,6 +2359,14 @@ func genFull() gopter.Gen {
 	}
 }
 
+func genElement() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
+		genResult := gopter.NewGenResult(a, gopter.NoShrinker)
+		return genResult
+	}
+}
+
 func (z *Element) matchVeryBigInt(aHi uint64, aInt *big.Int) error {
 	var modulus big.Int
 	var aIntMod big.Int
diff --git a/ecc/bw6-633/fp/vector.go b/ecc/bw6-633/fp/vector.go
index 1bd71a36e5..90e2236c7e 100644
--- a/ecc/bw6-633/fp/vector.go
+++ b/ecc/bw6-633/fp/vector.go
@@ -223,6 +223,25 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	scalarMulVecGeneric(*vector, a, b)
 }
 
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
+
 func addVecGeneric(res, a, b Vector) {
 	if len(a) != len(b) || len(a) != len(res) {
 		panic("vector.Add: vectors don't have the same length")
@@ -250,6 +269,32 @@ func scalarMulVecGeneric(res, a Vector, b *Element) {
 	}
 }
 
+func sumVecGeneric(res *Element, a Vector) {
+	for i := 0; i < len(a); i++ {
+		res.Add(res, &a[i])
+	}
+}
+
+func innerProductVecGeneric(res *Element, a, b Vector) {
+	if len(a) != len(b) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	var tmp Element
+	for i := 0; i < len(a); i++ {
+		tmp.Mul(&a[i], &b[i])
+		res.Add(res, &tmp)
+	}
+}
+
+func mulVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Mul(&a[i], &b[i])
+	}
+}
+
 // TODO @gbotrel make a public package out of that.
 // execute executes the work function in parallel.
 // this is copy paste from internal/parallel/parallel.go
diff --git a/ecc/bw6-633/fp/vector_test.go b/ecc/bw6-633/fp/vector_test.go
index 5d88af91c0..94d6557e20 100644
--- a/ecc/bw6-633/fp/vector_test.go
+++ b/ecc/bw6-633/fp/vector_test.go
@@ -18,10 +18,15 @@ package fp
 
 import (
 	"bytes"
+	"fmt"
 	"github.com/stretchr/testify/require"
+	"os"
 	"reflect"
 	"sort"
 	"testing"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/prop"
 )
 
 func TestVectorSort(t *testing.T) {
@@ -88,3 +93,291 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 	}
 	return <-chErr
 }
+
+func TestVectorOps(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = 2
+	} else {
+		parameters.MinSuccessfulTests = 10
+	}
+	properties := gopter.NewProperties(parameters)
+
+	addVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Add(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Add(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	subVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Sub(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Sub(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	scalarMulVector := func(a Vector, b Element) bool {
+		c := make(Vector, len(a))
+		c.ScalarMul(a, &b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b)
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sumVector := func(a Vector) bool {
+		var sum Element
+		computed := a.Sum()
+		for i := 0; i < len(a); i++ {
+			sum.Add(&sum, &a[i])
+		}
+
+		return sum.Equal(&computed)
+	}
+
+	innerProductVector := func(a, b Vector) bool {
+		computed := a.InnerProduct(b)
+		var innerProduct Element
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			innerProduct.Add(&innerProduct, &tmp)
+		}
+
+		return innerProduct.Equal(&computed)
+	}
+
+	mulVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		a[0].SetUint64(0x24)
+		b[0].SetUint64(0x42)
+		c.Mul(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sizes := []int{1, 2, 3, 4, 8, 9, 15, 16, 509, 510, 511, 512, 513, 514}
+	type genPair struct {
+		g1, g2 gopter.Gen
+		label  string
+	}
+
+	for _, size := range sizes {
+		generators := []genPair{
+			{genZeroVector(size), genZeroVector(size), "zero vectors"},
+			{genMaxVector(size), genMaxVector(size), "max vectors"},
+			{genVector(size), genVector(size), "random vectors"},
+			{genVector(size), genZeroVector(size), "random and zero vectors"},
+		}
+		for _, gp := range generators {
+			properties.Property(fmt.Sprintf("vector addition %d - %s", size, gp.label), prop.ForAll(
+				addVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector subtraction %d - %s", size, gp.label), prop.ForAll(
+				subVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector scalar multiplication %d - %s", size, gp.label), prop.ForAll(
+				scalarMulVector,
+				gp.g1,
+				genElement(),
+			))
+
+			properties.Property(fmt.Sprintf("vector sum %d - %s", size, gp.label), prop.ForAll(
+				sumVector,
+				gp.g1,
+			))
+
+			properties.Property(fmt.Sprintf("vector inner product %d - %s", size, gp.label), prop.ForAll(
+				innerProductVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector multiplication %d - %s", size, gp.label), prop.ForAll(
+				mulVector,
+				gp.g1,
+				gp.g2,
+			))
+		}
+	}
+
+	properties.TestingRun(t, gopter.NewFormatedReporter(false, 260, os.Stdout))
+}
+
+func BenchmarkVectorOps(b *testing.B) {
+	// note; to benchmark against "no asm" version, use the following
+	// build tag: -tags purego
+	const N = 1 << 24
+	a1 := make(Vector, N)
+	b1 := make(Vector, N)
+	c1 := make(Vector, N)
+	var mixer Element
+	mixer.SetRandom()
+	for i := 1; i < N; i++ {
+		a1[i-1].SetUint64(uint64(i)).
+			Mul(&a1[i-1], &mixer)
+		b1[i-1].SetUint64(^uint64(i)).
+			Mul(&b1[i-1], &mixer)
+	}
+
+	for n := 1 << 4; n <= N; n <<= 1 {
+		b.Run(fmt.Sprintf("add %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Add(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sub %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Sub(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("scalarMul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.ScalarMul(_a, &mixer)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sum %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.Sum()
+			}
+		})
+
+		b.Run(fmt.Sprintf("innerProduct %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.InnerProduct(_b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("mul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Mul(_a, _b)
+			}
+		})
+	}
+}
+
+func genZeroVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genMaxVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+
+		qMinusOne := qElement
+		qMinusOne[0]--
+
+		for i := 0; i < size; i++ {
+			g[i] = qMinusOne
+		}
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		mixer := Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[9] != ^uint64(0) {
+			mixer[9] %= (qElement[9] + 1)
+		}
+
+		for !mixer.smallerThanModulus() {
+			mixer = Element{
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+			}
+			if qElement[9] != ^uint64(0) {
+				mixer[9] %= (qElement[9] + 1)
+			}
+		}
+
+		for i := 1; i <= size; i++ {
+			g[i-1].SetUint64(uint64(i)).
+				Mul(&g[i-1], &mixer)
+		}
+
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/ecc/bw6-633/fr/asm.go b/ecc/bw6-633/fr/asm_adx.go
similarity index 100%
rename from ecc/bw6-633/fr/asm.go
rename to ecc/bw6-633/fr/asm_adx.go
diff --git a/ecc/bw6-633/fr/element.go b/ecc/bw6-633/fr/element.go
index 208f672b14..8841cd342c 100644
--- a/ecc/bw6-633/fr/element.go
+++ b/ecc/bw6-633/fr/element.go
@@ -499,32 +499,8 @@ func (z *Element) Select(c int, x0 *Element, x1 *Element) *Element {
 // and is used for testing purposes.
 func _mulGeneric(z, x, y *Element) {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t [6]uint64
 	var D uint64
diff --git a/ecc/bw6-633/fr/element_mul_amd64.s b/ecc/bw6-633/fr/element_mul_amd64.s
deleted file mode 100644
index 92bba4f58a..0000000000
--- a/ecc/bw6-633/fr/element_mul_amd64.s
+++ /dev/null
@@ -1,656 +0,0 @@
-// +build !purego
-
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0x6fe802ff40300001
-DATA q<>+8(SB)/8, $0x421ee5da52bde502
-DATA q<>+16(SB)/8, $0xdec1d01aa27a1ae0
-DATA q<>+24(SB)/8, $0xd3f7498be97c5eaf
-DATA q<>+32(SB)/8, $0x04c23a02b586d650
-GLOBL q<>(SB), (RODATA+NOPTR), $40
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0x702ff9ff402fffff
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, ra4, rb0, rb1, rb2, rb3, rb4) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	MOVQ    ra4, rb4;        \
-	SBBQ    q<>+32(SB), ra4; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-	CMOVQCS rb4, ra4;        \
-
-// mul(res, x, y *Element)
-TEXT ·mul(SB), $24-24
-
-	// the algorithm is described in the Element.Mul declaration (.go)
-	// however, to benefit from the ADCX and ADOX carry chains
-	// we split the inner loops in 2:
-	// for i=0 to N-1
-	// 		for j=0 to N-1
-	// 		    (A,t[j])  := t[j] + x[j]*y[i] + A
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C + A
-
-	NO_LOCAL_POINTERS
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_1
-	MOVQ x+8(FP), DI
-
-	// x[0] -> R9
-	// x[1] -> R10
-	// x[2] -> R11
-	MOVQ 0(DI), R9
-	MOVQ 8(DI), R10
-	MOVQ 16(DI), R11
-	MOVQ y+16(FP), R12
-
-	// A -> BP
-	// t[0] -> R14
-	// t[1] -> R13
-	// t[2] -> CX
-	// t[3] -> BX
-	// t[4] -> SI
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 0(R12), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ R9, R14, R13
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ R10, AX, CX
-	ADOXQ AX, R13
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ R11, AX, BX
-	ADOXQ AX, CX
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ 24(DI), AX, SI
-	ADOXQ AX, BX
-
-	// (A,t[4])  := x[4]*y[0] + A
-	MULXQ 32(DI), AX, BP
-	ADOXQ AX, SI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R8
-	ADCXQ R14, AX
-	MOVQ  R8, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// t[4] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ BP, SI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 8(R12), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ R9, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R13
-	MULXQ R10, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, CX
-	MULXQ R11, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, BX
-	MULXQ 24(DI), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[1] + A
-	ADCXQ BP, SI
-	MULXQ 32(DI), AX, BP
-	ADOXQ AX, SI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R8
-	ADCXQ R14, AX
-	MOVQ  R8, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// t[4] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ BP, SI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 16(R12), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ R9, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R13
-	MULXQ R10, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, CX
-	MULXQ R11, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, BX
-	MULXQ 24(DI), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[2] + A
-	ADCXQ BP, SI
-	MULXQ 32(DI), AX, BP
-	ADOXQ AX, SI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R8
-	ADCXQ R14, AX
-	MOVQ  R8, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// t[4] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ BP, SI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 24(R12), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ R9, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R13
-	MULXQ R10, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, CX
-	MULXQ R11, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, BX
-	MULXQ 24(DI), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[3] + A
-	ADCXQ BP, SI
-	MULXQ 32(DI), AX, BP
-	ADOXQ AX, SI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R8
-	ADCXQ R14, AX
-	MOVQ  R8, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// t[4] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ BP, SI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 32(R12), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[4] + A
-	MULXQ R9, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[4] + A
-	ADCXQ BP, R13
-	MULXQ R10, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[4] + A
-	ADCXQ BP, CX
-	MULXQ R11, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[4] + A
-	ADCXQ BP, BX
-	MULXQ 24(DI), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[4] + A
-	ADCXQ BP, SI
-	MULXQ 32(DI), AX, BP
-	ADOXQ AX, SI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R8
-	ADCXQ R14, AX
-	MOVQ  R8, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// t[4] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ BP, SI
-
-	// reduce element(R14,R13,CX,BX,SI) using temp registers (R8,DI,R12,R9,R10)
-	REDUCE(R14,R13,CX,BX,SI,R8,DI,R12,R9,R10)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R13, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	MOVQ SI, 32(AX)
-	RET
-
-noAdx_1:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	MOVQ x+8(FP), AX
-	MOVQ AX, 8(SP)
-	MOVQ y+16(FP), AX
-	MOVQ AX, 16(SP)
-	CALL ·_mulGeneric(SB)
-	RET
-
-TEXT ·fromMont(SB), $8-8
-	NO_LOCAL_POINTERS
-
-	// the algorithm is described here
-	// https://hackmd.io/@gnark/modular_multiplication
-	// when y = 1 we have:
-	// for i=0 to N-1
-	// 		t[i] = x[i]
-	// for i=0 to N-1
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_2
-	MOVQ res+0(FP), DX
-	MOVQ 0(DX), R14
-	MOVQ 8(DX), R13
-	MOVQ 16(DX), CX
-	MOVQ 24(DX), BX
-	MOVQ 32(DX), SI
-	XORQ DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ AX, SI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ AX, SI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ AX, SI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ AX, SI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-	MOVQ  $0, AX
-	ADCXQ AX, SI
-	ADOXQ AX, SI
-
-	// reduce element(R14,R13,CX,BX,SI) using temp registers (DI,R8,R9,R10,R11)
-	REDUCE(R14,R13,CX,BX,SI,DI,R8,R9,R10,R11)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R13, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	MOVQ SI, 32(AX)
-	RET
-
-noAdx_2:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	CALL ·_fromMontGeneric(SB)
-	RET
diff --git a/ecc/bw6-633/fr/element_ops_amd64.go b/ecc/bw6-633/fr/element_ops_amd64.go
index e40a9caed5..83d40c28c1 100644
--- a/ecc/bw6-633/fr/element_ops_amd64.go
+++ b/ecc/bw6-633/fr/element_ops_amd64.go
@@ -50,48 +50,8 @@ func Butterfly(a, b *Element)
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	mul(z, x, y)
 	return z
diff --git a/ecc/bw6-633/fr/element_ops_amd64.s b/ecc/bw6-633/fr/element_ops_amd64.s
index 9528ab595c..29314843d7 100644
--- a/ecc/bw6-633/fr/element_ops_amd64.s
+++ b/ecc/bw6-633/fr/element_ops_amd64.s
@@ -1,272 +1,6 @@
 // +build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+// We include the hash to force the Go compiler to recompile: 18184981773209750009
+#include "../../../field/asm/element_5w_amd64.s"
 
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0x6fe802ff40300001
-DATA q<>+8(SB)/8, $0x421ee5da52bde502
-DATA q<>+16(SB)/8, $0xdec1d01aa27a1ae0
-DATA q<>+24(SB)/8, $0xd3f7498be97c5eaf
-DATA q<>+32(SB)/8, $0x04c23a02b586d650
-GLOBL q<>(SB), (RODATA+NOPTR), $40
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0x702ff9ff402fffff
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, ra4, rb0, rb1, rb2, rb3, rb4) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	MOVQ    ra4, rb4;        \
-	SBBQ    q<>+32(SB), ra4; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-	CMOVQCS rb4, ra4;        \
-
-TEXT ·reduce(SB), NOSPLIT, $0-8
-	MOVQ res+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	RET
-
-// MulBy3(x *Element)
-TEXT ·MulBy3(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R13,R14,R15,R8,R9)
-	REDUCE(DX,CX,BX,SI,DI,R13,R14,R15,R8,R9)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	RET
-
-// MulBy5(x *Element)
-TEXT ·MulBy5(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R13,R14,R15,R8,R9)
-	REDUCE(DX,CX,BX,SI,DI,R13,R14,R15,R8,R9)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R10,R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,DI,R10,R11,R12,R13,R14)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	RET
-
-// MulBy13(x *Element)
-TEXT ·MulBy13(SB), $16-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP))
-	REDUCE(DX,CX,BX,SI,DI,R13,R14,R15,s0-8(SP),s1-16(SP))
-
-	MOVQ DX, R13
-	MOVQ CX, R14
-	MOVQ BX, R15
-	MOVQ SI, s0-8(SP)
-	MOVQ DI, s1-16(SP)
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
-
-	ADDQ R13, DX
-	ADCQ R14, CX
-	ADCQ R15, BX
-	ADCQ s0-8(SP), SI
-	ADCQ s1-16(SP), DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-
-	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	RET
-
-// Butterfly(a, b *Element) sets a = a + b; b = a - b
-TEXT ·Butterfly(SB), $24-16
-	MOVQ    a+0(FP), AX
-	MOVQ    0(AX), CX
-	MOVQ    8(AX), BX
-	MOVQ    16(AX), SI
-	MOVQ    24(AX), DI
-	MOVQ    32(AX), R8
-	MOVQ    CX, R9
-	MOVQ    BX, R10
-	MOVQ    SI, R11
-	MOVQ    DI, R12
-	MOVQ    R8, R13
-	XORQ    AX, AX
-	MOVQ    b+8(FP), DX
-	ADDQ    0(DX), CX
-	ADCQ    8(DX), BX
-	ADCQ    16(DX), SI
-	ADCQ    24(DX), DI
-	ADCQ    32(DX), R8
-	SUBQ    0(DX), R9
-	SBBQ    8(DX), R10
-	SBBQ    16(DX), R11
-	SBBQ    24(DX), R12
-	SBBQ    32(DX), R13
-	MOVQ    CX, R14
-	MOVQ    BX, R15
-	MOVQ    SI, s0-8(SP)
-	MOVQ    DI, s1-16(SP)
-	MOVQ    R8, s2-24(SP)
-	MOVQ    $0x6fe802ff40300001, CX
-	MOVQ    $0x421ee5da52bde502, BX
-	MOVQ    $0xdec1d01aa27a1ae0, SI
-	MOVQ    $0xd3f7498be97c5eaf, DI
-	MOVQ    $0x04c23a02b586d650, R8
-	CMOVQCC AX, CX
-	CMOVQCC AX, BX
-	CMOVQCC AX, SI
-	CMOVQCC AX, DI
-	CMOVQCC AX, R8
-	ADDQ    CX, R9
-	ADCQ    BX, R10
-	ADCQ    SI, R11
-	ADCQ    DI, R12
-	ADCQ    R8, R13
-	MOVQ    R14, CX
-	MOVQ    R15, BX
-	MOVQ    s0-8(SP), SI
-	MOVQ    s1-16(SP), DI
-	MOVQ    s2-24(SP), R8
-	MOVQ    R9, 0(DX)
-	MOVQ    R10, 8(DX)
-	MOVQ    R11, 16(DX)
-	MOVQ    R12, 24(DX)
-	MOVQ    R13, 32(DX)
-
-	// reduce element(CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13)
-	REDUCE(CX,BX,SI,DI,R8,R9,R10,R11,R12,R13)
-
-	MOVQ a+0(FP), AX
-	MOVQ CX, 0(AX)
-	MOVQ BX, 8(AX)
-	MOVQ SI, 16(AX)
-	MOVQ DI, 24(AX)
-	MOVQ R8, 32(AX)
-	RET
diff --git a/ecc/bw6-633/fr/element_ops_purego.go b/ecc/bw6-633/fr/element_ops_purego.go
index 34d6c54fbe..4a7cdbfe46 100644
--- a/ecc/bw6-633/fr/element_ops_purego.go
+++ b/ecc/bw6-633/fr/element_ops_purego.go
@@ -66,48 +66,8 @@ func reduce(z *Element) {
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t0, t1, t2, t3, t4 uint64
 	var u0, u1, u2, u3, u4 uint64
diff --git a/ecc/bw6-633/fr/element_test.go b/ecc/bw6-633/fr/element_test.go
index e232de8c8b..b7acc3840a 100644
--- a/ecc/bw6-633/fr/element_test.go
+++ b/ecc/bw6-633/fr/element_test.go
@@ -639,7 +639,6 @@ func TestElementBitLen(t *testing.T) {
 	))
 
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
-
 }
 
 func TestElementButterflies(t *testing.T) {
@@ -709,77 +708,6 @@ func TestElementLexicographicallyLargest(t *testing.T) {
 
 }
 
-func TestElementVecOps(t *testing.T) {
-	assert := require.New(t)
-
-	const N = 7
-	a := make(Vector, N)
-	b := make(Vector, N)
-	c := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a[i].SetRandom()
-		b[i].SetRandom()
-	}
-
-	// Vector addition
-	c.Add(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Add(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector addition failed")
-	}
-
-	// Vector subtraction
-	c.Sub(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Sub(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector subtraction failed")
-	}
-
-	// Vector scaling
-	c.ScalarMul(a, &b[0])
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Mul(&a[i], &b[0])
-		assert.True(c[i].Equal(&expected), "Vector scaling failed")
-	}
-}
-
-func BenchmarkElementVecOps(b *testing.B) {
-	// note; to benchmark against "no asm" version, use the following
-	// build tag: -tags purego
-	const N = 1024
-	a1 := make(Vector, N)
-	b1 := make(Vector, N)
-	c1 := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a1[i].SetRandom()
-		b1[i].SetRandom()
-	}
-
-	b.Run("Add", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Add(a1, b1)
-		}
-	})
-
-	b.Run("Sub", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Sub(a1, b1)
-		}
-	})
-
-	b.Run("ScalarMul", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.ScalarMul(a1, &b1[0])
-		}
-	})
-}
-
 func TestElementAdd(t *testing.T) {
 	t.Parallel()
 	parameters := gopter.DefaultTestParameters()
@@ -2349,40 +2277,40 @@ func gen() gopter.Gen {
 	}
 }
 
-func genFull() gopter.Gen {
-	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+func genRandomFq(genParams *gopter.GenParameters) Element {
+	var g Element
 
-		genRandomFq := func() Element {
-			var g Element
+	g = Element{
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+	}
 
-			g = Element{
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-			}
+	if qElement[4] != ^uint64(0) {
+		g[4] %= (qElement[4] + 1)
+	}
 
-			if qElement[4] != ^uint64(0) {
-				g[4] %= (qElement[4] + 1)
-			}
+	for !g.smallerThanModulus() {
+		g = Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[4] != ^uint64(0) {
+			g[4] %= (qElement[4] + 1)
+		}
+	}
 
-			for !g.smallerThanModulus() {
-				g = Element{
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-				}
-				if qElement[4] != ^uint64(0) {
-					g[4] %= (qElement[4] + 1)
-				}
-			}
+	return g
+}
 
-			return g
-		}
-		a := genRandomFq()
+func genFull() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
 
 		var carry uint64
 		a[0], carry = bits.Add64(a[0], qElement[0], carry)
@@ -2396,6 +2324,14 @@ func genFull() gopter.Gen {
 	}
 }
 
+func genElement() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
+		genResult := gopter.NewGenResult(a, gopter.NoShrinker)
+		return genResult
+	}
+}
+
 func (z *Element) matchVeryBigInt(aHi uint64, aInt *big.Int) error {
 	var modulus big.Int
 	var aIntMod big.Int
diff --git a/ecc/bw6-633/fr/vector.go b/ecc/bw6-633/fr/vector.go
index 1c9b6b9752..e3bee5fbd3 100644
--- a/ecc/bw6-633/fr/vector.go
+++ b/ecc/bw6-633/fr/vector.go
@@ -218,6 +218,25 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	scalarMulVecGeneric(*vector, a, b)
 }
 
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
+
 func addVecGeneric(res, a, b Vector) {
 	if len(a) != len(b) || len(a) != len(res) {
 		panic("vector.Add: vectors don't have the same length")
@@ -245,6 +264,32 @@ func scalarMulVecGeneric(res, a Vector, b *Element) {
 	}
 }
 
+func sumVecGeneric(res *Element, a Vector) {
+	for i := 0; i < len(a); i++ {
+		res.Add(res, &a[i])
+	}
+}
+
+func innerProductVecGeneric(res *Element, a, b Vector) {
+	if len(a) != len(b) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	var tmp Element
+	for i := 0; i < len(a); i++ {
+		tmp.Mul(&a[i], &b[i])
+		res.Add(res, &tmp)
+	}
+}
+
+func mulVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Mul(&a[i], &b[i])
+	}
+}
+
 // TODO @gbotrel make a public package out of that.
 // execute executes the work function in parallel.
 // this is copy paste from internal/parallel/parallel.go
diff --git a/ecc/bw6-633/fr/vector_test.go b/ecc/bw6-633/fr/vector_test.go
index e58f2d9a38..8245cc9287 100644
--- a/ecc/bw6-633/fr/vector_test.go
+++ b/ecc/bw6-633/fr/vector_test.go
@@ -18,10 +18,15 @@ package fr
 
 import (
 	"bytes"
+	"fmt"
 	"github.com/stretchr/testify/require"
+	"os"
 	"reflect"
 	"sort"
 	"testing"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/prop"
 )
 
 func TestVectorSort(t *testing.T) {
@@ -88,3 +93,281 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 	}
 	return <-chErr
 }
+
+func TestVectorOps(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = 2
+	} else {
+		parameters.MinSuccessfulTests = 10
+	}
+	properties := gopter.NewProperties(parameters)
+
+	addVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Add(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Add(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	subVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Sub(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Sub(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	scalarMulVector := func(a Vector, b Element) bool {
+		c := make(Vector, len(a))
+		c.ScalarMul(a, &b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b)
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sumVector := func(a Vector) bool {
+		var sum Element
+		computed := a.Sum()
+		for i := 0; i < len(a); i++ {
+			sum.Add(&sum, &a[i])
+		}
+
+		return sum.Equal(&computed)
+	}
+
+	innerProductVector := func(a, b Vector) bool {
+		computed := a.InnerProduct(b)
+		var innerProduct Element
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			innerProduct.Add(&innerProduct, &tmp)
+		}
+
+		return innerProduct.Equal(&computed)
+	}
+
+	mulVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		a[0].SetUint64(0x24)
+		b[0].SetUint64(0x42)
+		c.Mul(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sizes := []int{1, 2, 3, 4, 8, 9, 15, 16, 509, 510, 511, 512, 513, 514}
+	type genPair struct {
+		g1, g2 gopter.Gen
+		label  string
+	}
+
+	for _, size := range sizes {
+		generators := []genPair{
+			{genZeroVector(size), genZeroVector(size), "zero vectors"},
+			{genMaxVector(size), genMaxVector(size), "max vectors"},
+			{genVector(size), genVector(size), "random vectors"},
+			{genVector(size), genZeroVector(size), "random and zero vectors"},
+		}
+		for _, gp := range generators {
+			properties.Property(fmt.Sprintf("vector addition %d - %s", size, gp.label), prop.ForAll(
+				addVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector subtraction %d - %s", size, gp.label), prop.ForAll(
+				subVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector scalar multiplication %d - %s", size, gp.label), prop.ForAll(
+				scalarMulVector,
+				gp.g1,
+				genElement(),
+			))
+
+			properties.Property(fmt.Sprintf("vector sum %d - %s", size, gp.label), prop.ForAll(
+				sumVector,
+				gp.g1,
+			))
+
+			properties.Property(fmt.Sprintf("vector inner product %d - %s", size, gp.label), prop.ForAll(
+				innerProductVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector multiplication %d - %s", size, gp.label), prop.ForAll(
+				mulVector,
+				gp.g1,
+				gp.g2,
+			))
+		}
+	}
+
+	properties.TestingRun(t, gopter.NewFormatedReporter(false, 260, os.Stdout))
+}
+
+func BenchmarkVectorOps(b *testing.B) {
+	// note; to benchmark against "no asm" version, use the following
+	// build tag: -tags purego
+	const N = 1 << 24
+	a1 := make(Vector, N)
+	b1 := make(Vector, N)
+	c1 := make(Vector, N)
+	var mixer Element
+	mixer.SetRandom()
+	for i := 1; i < N; i++ {
+		a1[i-1].SetUint64(uint64(i)).
+			Mul(&a1[i-1], &mixer)
+		b1[i-1].SetUint64(^uint64(i)).
+			Mul(&b1[i-1], &mixer)
+	}
+
+	for n := 1 << 4; n <= N; n <<= 1 {
+		b.Run(fmt.Sprintf("add %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Add(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sub %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Sub(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("scalarMul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.ScalarMul(_a, &mixer)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sum %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.Sum()
+			}
+		})
+
+		b.Run(fmt.Sprintf("innerProduct %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.InnerProduct(_b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("mul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Mul(_a, _b)
+			}
+		})
+	}
+}
+
+func genZeroVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genMaxVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+
+		qMinusOne := qElement
+		qMinusOne[0]--
+
+		for i := 0; i < size; i++ {
+			g[i] = qMinusOne
+		}
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		mixer := Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[4] != ^uint64(0) {
+			mixer[4] %= (qElement[4] + 1)
+		}
+
+		for !mixer.smallerThanModulus() {
+			mixer = Element{
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+			}
+			if qElement[4] != ^uint64(0) {
+				mixer[4] %= (qElement[4] + 1)
+			}
+		}
+
+		for i := 1; i <= size; i++ {
+			g[i-1].SetUint64(uint64(i)).
+				Mul(&g[i-1], &mixer)
+		}
+
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/ecc/bw6-761/fp/asm.go b/ecc/bw6-761/fp/asm_adx.go
similarity index 100%
rename from ecc/bw6-761/fp/asm.go
rename to ecc/bw6-761/fp/asm_adx.go
diff --git a/ecc/bw6-761/fp/element.go b/ecc/bw6-761/fp/element.go
index 36232ebff3..8cdd31218e 100644
--- a/ecc/bw6-761/fp/element.go
+++ b/ecc/bw6-761/fp/element.go
@@ -653,32 +653,8 @@ func (z *Element) Select(c int, x0 *Element, x1 *Element) *Element {
 // and is used for testing purposes.
 func _mulGeneric(z, x, y *Element) {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t [13]uint64
 	var D uint64
diff --git a/ecc/bw6-761/fp/element_mul_amd64.s b/ecc/bw6-761/fp/element_mul_amd64.s
deleted file mode 100644
index fd48d8606c..0000000000
--- a/ecc/bw6-761/fp/element_mul_amd64.s
+++ /dev/null
@@ -1,2758 +0,0 @@
-// +build !purego
-
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0xf49d00000000008b
-DATA q<>+8(SB)/8, $0xe6913e6870000082
-DATA q<>+16(SB)/8, $0x160cf8aeeaf0a437
-DATA q<>+24(SB)/8, $0x98a116c25667a8f8
-DATA q<>+32(SB)/8, $0x71dcd3dc73ebff2e
-DATA q<>+40(SB)/8, $0x8689c8ed12f9fd90
-DATA q<>+48(SB)/8, $0x03cebaff25b42304
-DATA q<>+56(SB)/8, $0x707ba638e584e919
-DATA q<>+64(SB)/8, $0x528275ef8087be41
-DATA q<>+72(SB)/8, $0xb926186a81d14688
-DATA q<>+80(SB)/8, $0xd187c94004faff3e
-DATA q<>+88(SB)/8, $0x0122e824fb83ce0a
-GLOBL q<>(SB), (RODATA+NOPTR), $96
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0x0a5593568fa798dd
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, ra4, ra5, ra6, ra7, ra8, ra9, ra10, ra11, rb0, rb1, rb2, rb3, rb4, rb5, rb6, rb7, rb8, rb9, rb10, rb11) \
-	MOVQ    ra0, rb0;         \
-	SUBQ    q<>(SB), ra0;     \
-	MOVQ    ra1, rb1;         \
-	SBBQ    q<>+8(SB), ra1;   \
-	MOVQ    ra2, rb2;         \
-	SBBQ    q<>+16(SB), ra2;  \
-	MOVQ    ra3, rb3;         \
-	SBBQ    q<>+24(SB), ra3;  \
-	MOVQ    ra4, rb4;         \
-	SBBQ    q<>+32(SB), ra4;  \
-	MOVQ    ra5, rb5;         \
-	SBBQ    q<>+40(SB), ra5;  \
-	MOVQ    ra6, rb6;         \
-	SBBQ    q<>+48(SB), ra6;  \
-	MOVQ    ra7, rb7;         \
-	SBBQ    q<>+56(SB), ra7;  \
-	MOVQ    ra8, rb8;         \
-	SBBQ    q<>+64(SB), ra8;  \
-	MOVQ    ra9, rb9;         \
-	SBBQ    q<>+72(SB), ra9;  \
-	MOVQ    ra10, rb10;       \
-	SBBQ    q<>+80(SB), ra10; \
-	MOVQ    ra11, rb11;       \
-	SBBQ    q<>+88(SB), ra11; \
-	CMOVQCS rb0, ra0;         \
-	CMOVQCS rb1, ra1;         \
-	CMOVQCS rb2, ra2;         \
-	CMOVQCS rb3, ra3;         \
-	CMOVQCS rb4, ra4;         \
-	CMOVQCS rb5, ra5;         \
-	CMOVQCS rb6, ra6;         \
-	CMOVQCS rb7, ra7;         \
-	CMOVQCS rb8, ra8;         \
-	CMOVQCS rb9, ra9;         \
-	CMOVQCS rb10, ra10;       \
-	CMOVQCS rb11, ra11;       \
-
-// mul(res, x, y *Element)
-TEXT ·mul(SB), $96-24
-
-	// the algorithm is described in the Element.Mul declaration (.go)
-	// however, to benefit from the ADCX and ADOX carry chains
-	// we split the inner loops in 2:
-	// for i=0 to N-1
-	// 		for j=0 to N-1
-	// 		    (A,t[j])  := t[j] + x[j]*y[i] + A
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C + A
-
-	NO_LOCAL_POINTERS
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_1
-	MOVQ x+8(FP), AX
-
-	// x[0] -> s0-8(SP)
-	// x[1] -> s1-16(SP)
-	// x[2] -> s2-24(SP)
-	// x[3] -> s3-32(SP)
-	// x[4] -> s4-40(SP)
-	// x[5] -> s5-48(SP)
-	// x[6] -> s6-56(SP)
-	// x[7] -> s7-64(SP)
-	// x[8] -> s8-72(SP)
-	// x[9] -> s9-80(SP)
-	// x[10] -> s10-88(SP)
-	// x[11] -> s11-96(SP)
-	MOVQ 0(AX), R14
-	MOVQ 8(AX), R15
-	MOVQ 16(AX), CX
-	MOVQ 24(AX), BX
-	MOVQ 32(AX), SI
-	MOVQ 40(AX), DI
-	MOVQ 48(AX), R8
-	MOVQ 56(AX), R9
-	MOVQ 64(AX), R10
-	MOVQ 72(AX), R11
-	MOVQ 80(AX), R12
-	MOVQ 88(AX), R13
-	MOVQ R14, s0-8(SP)
-	MOVQ R15, s1-16(SP)
-	MOVQ CX, s2-24(SP)
-	MOVQ BX, s3-32(SP)
-	MOVQ SI, s4-40(SP)
-	MOVQ DI, s5-48(SP)
-	MOVQ R8, s6-56(SP)
-	MOVQ R9, s7-64(SP)
-	MOVQ R10, s8-72(SP)
-	MOVQ R11, s9-80(SP)
-	MOVQ R12, s10-88(SP)
-	MOVQ R13, s11-96(SP)
-
-	// A -> BP
-	// t[0] -> R14
-	// t[1] -> R15
-	// t[2] -> CX
-	// t[3] -> BX
-	// t[4] -> SI
-	// t[5] -> DI
-	// t[6] -> R8
-	// t[7] -> R9
-	// t[8] -> R10
-	// t[9] -> R11
-	// t[10] -> R12
-	// t[11] -> R13
-	// clear the flags
-	XORQ AX, AX
-	MOVQ y+16(FP), AX
-	MOVQ 0(AX), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ s0-8(SP), R14, R15
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ s1-16(SP), AX, CX
-	ADOXQ AX, R15
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ s2-24(SP), AX, BX
-	ADOXQ AX, CX
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ s3-32(SP), AX, SI
-	ADOXQ AX, BX
-
-	// (A,t[4])  := x[4]*y[0] + A
-	MULXQ s4-40(SP), AX, DI
-	ADOXQ AX, SI
-
-	// (A,t[5])  := x[5]*y[0] + A
-	MULXQ s5-48(SP), AX, R8
-	ADOXQ AX, DI
-
-	// (A,t[6])  := x[6]*y[0] + A
-	MULXQ s6-56(SP), AX, R9
-	ADOXQ AX, R8
-
-	// (A,t[7])  := x[7]*y[0] + A
-	MULXQ s7-64(SP), AX, R10
-	ADOXQ AX, R9
-
-	// (A,t[8])  := x[8]*y[0] + A
-	MULXQ s8-72(SP), AX, R11
-	ADOXQ AX, R10
-
-	// (A,t[9])  := x[9]*y[0] + A
-	MULXQ s9-80(SP), AX, R12
-	ADOXQ AX, R11
-
-	// (A,t[10])  := x[10]*y[0] + A
-	MULXQ s10-88(SP), AX, R13
-	ADOXQ AX, R12
-
-	// (A,t[11])  := x[11]*y[0] + A
-	MULXQ s11-96(SP), AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[9]) := t[10] + m*q[10] + C
-	ADCXQ R12, R11
-	MULXQ q<>+80(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[10]) := t[11] + m*q[11] + C
-	ADCXQ R13, R12
-	MULXQ q<>+88(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[11] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ y+16(FP), AX
-	MOVQ 8(AX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ s0-8(SP), AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R15
-	MULXQ s1-16(SP), AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, CX
-	MULXQ s2-24(SP), AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, BX
-	MULXQ s3-32(SP), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[1] + A
-	ADCXQ BP, SI
-	MULXQ s4-40(SP), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[1] + A
-	ADCXQ BP, DI
-	MULXQ s5-48(SP), AX, BP
-	ADOXQ AX, DI
-
-	// (A,t[6])  := t[6] + x[6]*y[1] + A
-	ADCXQ BP, R8
-	MULXQ s6-56(SP), AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[7])  := t[7] + x[7]*y[1] + A
-	ADCXQ BP, R9
-	MULXQ s7-64(SP), AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[8])  := t[8] + x[8]*y[1] + A
-	ADCXQ BP, R10
-	MULXQ s8-72(SP), AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[9])  := t[9] + x[9]*y[1] + A
-	ADCXQ BP, R11
-	MULXQ s9-80(SP), AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[10])  := t[10] + x[10]*y[1] + A
-	ADCXQ BP, R12
-	MULXQ s10-88(SP), AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[11])  := t[11] + x[11]*y[1] + A
-	ADCXQ BP, R13
-	MULXQ s11-96(SP), AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[9]) := t[10] + m*q[10] + C
-	ADCXQ R12, R11
-	MULXQ q<>+80(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[10]) := t[11] + m*q[11] + C
-	ADCXQ R13, R12
-	MULXQ q<>+88(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[11] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ y+16(FP), AX
-	MOVQ 16(AX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ s0-8(SP), AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R15
-	MULXQ s1-16(SP), AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, CX
-	MULXQ s2-24(SP), AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, BX
-	MULXQ s3-32(SP), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[2] + A
-	ADCXQ BP, SI
-	MULXQ s4-40(SP), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[2] + A
-	ADCXQ BP, DI
-	MULXQ s5-48(SP), AX, BP
-	ADOXQ AX, DI
-
-	// (A,t[6])  := t[6] + x[6]*y[2] + A
-	ADCXQ BP, R8
-	MULXQ s6-56(SP), AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[7])  := t[7] + x[7]*y[2] + A
-	ADCXQ BP, R9
-	MULXQ s7-64(SP), AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[8])  := t[8] + x[8]*y[2] + A
-	ADCXQ BP, R10
-	MULXQ s8-72(SP), AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[9])  := t[9] + x[9]*y[2] + A
-	ADCXQ BP, R11
-	MULXQ s9-80(SP), AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[10])  := t[10] + x[10]*y[2] + A
-	ADCXQ BP, R12
-	MULXQ s10-88(SP), AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[11])  := t[11] + x[11]*y[2] + A
-	ADCXQ BP, R13
-	MULXQ s11-96(SP), AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[9]) := t[10] + m*q[10] + C
-	ADCXQ R12, R11
-	MULXQ q<>+80(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[10]) := t[11] + m*q[11] + C
-	ADCXQ R13, R12
-	MULXQ q<>+88(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[11] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ y+16(FP), AX
-	MOVQ 24(AX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ s0-8(SP), AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R15
-	MULXQ s1-16(SP), AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, CX
-	MULXQ s2-24(SP), AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, BX
-	MULXQ s3-32(SP), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[3] + A
-	ADCXQ BP, SI
-	MULXQ s4-40(SP), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[3] + A
-	ADCXQ BP, DI
-	MULXQ s5-48(SP), AX, BP
-	ADOXQ AX, DI
-
-	// (A,t[6])  := t[6] + x[6]*y[3] + A
-	ADCXQ BP, R8
-	MULXQ s6-56(SP), AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[7])  := t[7] + x[7]*y[3] + A
-	ADCXQ BP, R9
-	MULXQ s7-64(SP), AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[8])  := t[8] + x[8]*y[3] + A
-	ADCXQ BP, R10
-	MULXQ s8-72(SP), AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[9])  := t[9] + x[9]*y[3] + A
-	ADCXQ BP, R11
-	MULXQ s9-80(SP), AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[10])  := t[10] + x[10]*y[3] + A
-	ADCXQ BP, R12
-	MULXQ s10-88(SP), AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[11])  := t[11] + x[11]*y[3] + A
-	ADCXQ BP, R13
-	MULXQ s11-96(SP), AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[9]) := t[10] + m*q[10] + C
-	ADCXQ R12, R11
-	MULXQ q<>+80(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[10]) := t[11] + m*q[11] + C
-	ADCXQ R13, R12
-	MULXQ q<>+88(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[11] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ y+16(FP), AX
-	MOVQ 32(AX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[4] + A
-	MULXQ s0-8(SP), AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[4] + A
-	ADCXQ BP, R15
-	MULXQ s1-16(SP), AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[4] + A
-	ADCXQ BP, CX
-	MULXQ s2-24(SP), AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[4] + A
-	ADCXQ BP, BX
-	MULXQ s3-32(SP), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[4] + A
-	ADCXQ BP, SI
-	MULXQ s4-40(SP), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[4] + A
-	ADCXQ BP, DI
-	MULXQ s5-48(SP), AX, BP
-	ADOXQ AX, DI
-
-	// (A,t[6])  := t[6] + x[6]*y[4] + A
-	ADCXQ BP, R8
-	MULXQ s6-56(SP), AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[7])  := t[7] + x[7]*y[4] + A
-	ADCXQ BP, R9
-	MULXQ s7-64(SP), AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[8])  := t[8] + x[8]*y[4] + A
-	ADCXQ BP, R10
-	MULXQ s8-72(SP), AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[9])  := t[9] + x[9]*y[4] + A
-	ADCXQ BP, R11
-	MULXQ s9-80(SP), AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[10])  := t[10] + x[10]*y[4] + A
-	ADCXQ BP, R12
-	MULXQ s10-88(SP), AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[11])  := t[11] + x[11]*y[4] + A
-	ADCXQ BP, R13
-	MULXQ s11-96(SP), AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[9]) := t[10] + m*q[10] + C
-	ADCXQ R12, R11
-	MULXQ q<>+80(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[10]) := t[11] + m*q[11] + C
-	ADCXQ R13, R12
-	MULXQ q<>+88(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[11] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ y+16(FP), AX
-	MOVQ 40(AX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[5] + A
-	MULXQ s0-8(SP), AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[5] + A
-	ADCXQ BP, R15
-	MULXQ s1-16(SP), AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[5] + A
-	ADCXQ BP, CX
-	MULXQ s2-24(SP), AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[5] + A
-	ADCXQ BP, BX
-	MULXQ s3-32(SP), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[5] + A
-	ADCXQ BP, SI
-	MULXQ s4-40(SP), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[5] + A
-	ADCXQ BP, DI
-	MULXQ s5-48(SP), AX, BP
-	ADOXQ AX, DI
-
-	// (A,t[6])  := t[6] + x[6]*y[5] + A
-	ADCXQ BP, R8
-	MULXQ s6-56(SP), AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[7])  := t[7] + x[7]*y[5] + A
-	ADCXQ BP, R9
-	MULXQ s7-64(SP), AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[8])  := t[8] + x[8]*y[5] + A
-	ADCXQ BP, R10
-	MULXQ s8-72(SP), AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[9])  := t[9] + x[9]*y[5] + A
-	ADCXQ BP, R11
-	MULXQ s9-80(SP), AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[10])  := t[10] + x[10]*y[5] + A
-	ADCXQ BP, R12
-	MULXQ s10-88(SP), AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[11])  := t[11] + x[11]*y[5] + A
-	ADCXQ BP, R13
-	MULXQ s11-96(SP), AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[9]) := t[10] + m*q[10] + C
-	ADCXQ R12, R11
-	MULXQ q<>+80(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[10]) := t[11] + m*q[11] + C
-	ADCXQ R13, R12
-	MULXQ q<>+88(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[11] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ y+16(FP), AX
-	MOVQ 48(AX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[6] + A
-	MULXQ s0-8(SP), AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[6] + A
-	ADCXQ BP, R15
-	MULXQ s1-16(SP), AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[6] + A
-	ADCXQ BP, CX
-	MULXQ s2-24(SP), AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[6] + A
-	ADCXQ BP, BX
-	MULXQ s3-32(SP), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[6] + A
-	ADCXQ BP, SI
-	MULXQ s4-40(SP), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[6] + A
-	ADCXQ BP, DI
-	MULXQ s5-48(SP), AX, BP
-	ADOXQ AX, DI
-
-	// (A,t[6])  := t[6] + x[6]*y[6] + A
-	ADCXQ BP, R8
-	MULXQ s6-56(SP), AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[7])  := t[7] + x[7]*y[6] + A
-	ADCXQ BP, R9
-	MULXQ s7-64(SP), AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[8])  := t[8] + x[8]*y[6] + A
-	ADCXQ BP, R10
-	MULXQ s8-72(SP), AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[9])  := t[9] + x[9]*y[6] + A
-	ADCXQ BP, R11
-	MULXQ s9-80(SP), AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[10])  := t[10] + x[10]*y[6] + A
-	ADCXQ BP, R12
-	MULXQ s10-88(SP), AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[11])  := t[11] + x[11]*y[6] + A
-	ADCXQ BP, R13
-	MULXQ s11-96(SP), AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[9]) := t[10] + m*q[10] + C
-	ADCXQ R12, R11
-	MULXQ q<>+80(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[10]) := t[11] + m*q[11] + C
-	ADCXQ R13, R12
-	MULXQ q<>+88(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[11] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ y+16(FP), AX
-	MOVQ 56(AX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[7] + A
-	MULXQ s0-8(SP), AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[7] + A
-	ADCXQ BP, R15
-	MULXQ s1-16(SP), AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[7] + A
-	ADCXQ BP, CX
-	MULXQ s2-24(SP), AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[7] + A
-	ADCXQ BP, BX
-	MULXQ s3-32(SP), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[7] + A
-	ADCXQ BP, SI
-	MULXQ s4-40(SP), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[7] + A
-	ADCXQ BP, DI
-	MULXQ s5-48(SP), AX, BP
-	ADOXQ AX, DI
-
-	// (A,t[6])  := t[6] + x[6]*y[7] + A
-	ADCXQ BP, R8
-	MULXQ s6-56(SP), AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[7])  := t[7] + x[7]*y[7] + A
-	ADCXQ BP, R9
-	MULXQ s7-64(SP), AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[8])  := t[8] + x[8]*y[7] + A
-	ADCXQ BP, R10
-	MULXQ s8-72(SP), AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[9])  := t[9] + x[9]*y[7] + A
-	ADCXQ BP, R11
-	MULXQ s9-80(SP), AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[10])  := t[10] + x[10]*y[7] + A
-	ADCXQ BP, R12
-	MULXQ s10-88(SP), AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[11])  := t[11] + x[11]*y[7] + A
-	ADCXQ BP, R13
-	MULXQ s11-96(SP), AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[9]) := t[10] + m*q[10] + C
-	ADCXQ R12, R11
-	MULXQ q<>+80(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[10]) := t[11] + m*q[11] + C
-	ADCXQ R13, R12
-	MULXQ q<>+88(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[11] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ y+16(FP), AX
-	MOVQ 64(AX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[8] + A
-	MULXQ s0-8(SP), AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[8] + A
-	ADCXQ BP, R15
-	MULXQ s1-16(SP), AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[8] + A
-	ADCXQ BP, CX
-	MULXQ s2-24(SP), AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[8] + A
-	ADCXQ BP, BX
-	MULXQ s3-32(SP), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[8] + A
-	ADCXQ BP, SI
-	MULXQ s4-40(SP), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[8] + A
-	ADCXQ BP, DI
-	MULXQ s5-48(SP), AX, BP
-	ADOXQ AX, DI
-
-	// (A,t[6])  := t[6] + x[6]*y[8] + A
-	ADCXQ BP, R8
-	MULXQ s6-56(SP), AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[7])  := t[7] + x[7]*y[8] + A
-	ADCXQ BP, R9
-	MULXQ s7-64(SP), AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[8])  := t[8] + x[8]*y[8] + A
-	ADCXQ BP, R10
-	MULXQ s8-72(SP), AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[9])  := t[9] + x[9]*y[8] + A
-	ADCXQ BP, R11
-	MULXQ s9-80(SP), AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[10])  := t[10] + x[10]*y[8] + A
-	ADCXQ BP, R12
-	MULXQ s10-88(SP), AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[11])  := t[11] + x[11]*y[8] + A
-	ADCXQ BP, R13
-	MULXQ s11-96(SP), AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[9]) := t[10] + m*q[10] + C
-	ADCXQ R12, R11
-	MULXQ q<>+80(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[10]) := t[11] + m*q[11] + C
-	ADCXQ R13, R12
-	MULXQ q<>+88(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[11] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ y+16(FP), AX
-	MOVQ 72(AX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[9] + A
-	MULXQ s0-8(SP), AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[9] + A
-	ADCXQ BP, R15
-	MULXQ s1-16(SP), AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[9] + A
-	ADCXQ BP, CX
-	MULXQ s2-24(SP), AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[9] + A
-	ADCXQ BP, BX
-	MULXQ s3-32(SP), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[9] + A
-	ADCXQ BP, SI
-	MULXQ s4-40(SP), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[9] + A
-	ADCXQ BP, DI
-	MULXQ s5-48(SP), AX, BP
-	ADOXQ AX, DI
-
-	// (A,t[6])  := t[6] + x[6]*y[9] + A
-	ADCXQ BP, R8
-	MULXQ s6-56(SP), AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[7])  := t[7] + x[7]*y[9] + A
-	ADCXQ BP, R9
-	MULXQ s7-64(SP), AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[8])  := t[8] + x[8]*y[9] + A
-	ADCXQ BP, R10
-	MULXQ s8-72(SP), AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[9])  := t[9] + x[9]*y[9] + A
-	ADCXQ BP, R11
-	MULXQ s9-80(SP), AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[10])  := t[10] + x[10]*y[9] + A
-	ADCXQ BP, R12
-	MULXQ s10-88(SP), AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[11])  := t[11] + x[11]*y[9] + A
-	ADCXQ BP, R13
-	MULXQ s11-96(SP), AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[9]) := t[10] + m*q[10] + C
-	ADCXQ R12, R11
-	MULXQ q<>+80(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[10]) := t[11] + m*q[11] + C
-	ADCXQ R13, R12
-	MULXQ q<>+88(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[11] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ y+16(FP), AX
-	MOVQ 80(AX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[10] + A
-	MULXQ s0-8(SP), AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[10] + A
-	ADCXQ BP, R15
-	MULXQ s1-16(SP), AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[10] + A
-	ADCXQ BP, CX
-	MULXQ s2-24(SP), AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[10] + A
-	ADCXQ BP, BX
-	MULXQ s3-32(SP), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[10] + A
-	ADCXQ BP, SI
-	MULXQ s4-40(SP), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[10] + A
-	ADCXQ BP, DI
-	MULXQ s5-48(SP), AX, BP
-	ADOXQ AX, DI
-
-	// (A,t[6])  := t[6] + x[6]*y[10] + A
-	ADCXQ BP, R8
-	MULXQ s6-56(SP), AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[7])  := t[7] + x[7]*y[10] + A
-	ADCXQ BP, R9
-	MULXQ s7-64(SP), AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[8])  := t[8] + x[8]*y[10] + A
-	ADCXQ BP, R10
-	MULXQ s8-72(SP), AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[9])  := t[9] + x[9]*y[10] + A
-	ADCXQ BP, R11
-	MULXQ s9-80(SP), AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[10])  := t[10] + x[10]*y[10] + A
-	ADCXQ BP, R12
-	MULXQ s10-88(SP), AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[11])  := t[11] + x[11]*y[10] + A
-	ADCXQ BP, R13
-	MULXQ s11-96(SP), AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[9]) := t[10] + m*q[10] + C
-	ADCXQ R12, R11
-	MULXQ q<>+80(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[10]) := t[11] + m*q[11] + C
-	ADCXQ R13, R12
-	MULXQ q<>+88(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[11] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ y+16(FP), AX
-	MOVQ 88(AX), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[11] + A
-	MULXQ s0-8(SP), AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[11] + A
-	ADCXQ BP, R15
-	MULXQ s1-16(SP), AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[11] + A
-	ADCXQ BP, CX
-	MULXQ s2-24(SP), AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[11] + A
-	ADCXQ BP, BX
-	MULXQ s3-32(SP), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[11] + A
-	ADCXQ BP, SI
-	MULXQ s4-40(SP), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[11] + A
-	ADCXQ BP, DI
-	MULXQ s5-48(SP), AX, BP
-	ADOXQ AX, DI
-
-	// (A,t[6])  := t[6] + x[6]*y[11] + A
-	ADCXQ BP, R8
-	MULXQ s6-56(SP), AX, BP
-	ADOXQ AX, R8
-
-	// (A,t[7])  := t[7] + x[7]*y[11] + A
-	ADCXQ BP, R9
-	MULXQ s7-64(SP), AX, BP
-	ADOXQ AX, R9
-
-	// (A,t[8])  := t[8] + x[8]*y[11] + A
-	ADCXQ BP, R10
-	MULXQ s8-72(SP), AX, BP
-	ADOXQ AX, R10
-
-	// (A,t[9])  := t[9] + x[9]*y[11] + A
-	ADCXQ BP, R11
-	MULXQ s9-80(SP), AX, BP
-	ADOXQ AX, R11
-
-	// (A,t[10])  := t[10] + x[10]*y[11] + A
-	ADCXQ BP, R12
-	MULXQ s10-88(SP), AX, BP
-	ADOXQ AX, R12
-
-	// (A,t[11])  := t[11] + x[11]*y[11] + A
-	ADCXQ BP, R13
-	MULXQ s11-96(SP), AX, BP
-	ADOXQ AX, R13
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-	PUSHQ BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-	POPQ  BP
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[9]) := t[10] + m*q[10] + C
-	ADCXQ R12, R11
-	MULXQ q<>+80(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[10]) := t[11] + m*q[11] + C
-	ADCXQ R13, R12
-	MULXQ q<>+88(SB), AX, R13
-	ADOXQ AX, R12
-
-	// t[11] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ BP, R13
-
-	// reduce element(R14,R15,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13) using temp registers (s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP),s11-96(SP))
-	REDUCE(R14,R15,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP),s11-96(SP))
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R15, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	MOVQ SI, 32(AX)
-	MOVQ DI, 40(AX)
-	MOVQ R8, 48(AX)
-	MOVQ R9, 56(AX)
-	MOVQ R10, 64(AX)
-	MOVQ R11, 72(AX)
-	MOVQ R12, 80(AX)
-	MOVQ R13, 88(AX)
-	RET
-
-noAdx_1:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	MOVQ x+8(FP), AX
-	MOVQ AX, 8(SP)
-	MOVQ y+16(FP), AX
-	MOVQ AX, 16(SP)
-	CALL ·_mulGeneric(SB)
-	RET
-
-TEXT ·fromMont(SB), $96-8
-	NO_LOCAL_POINTERS
-
-	// the algorithm is described here
-	// https://hackmd.io/@gnark/modular_multiplication
-	// when y = 1 we have:
-	// for i=0 to N-1
-	// 		t[i] = x[i]
-	// for i=0 to N-1
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_2
-	MOVQ res+0(FP), DX
-	MOVQ 0(DX), R14
-	MOVQ 8(DX), R15
-	MOVQ 16(DX), CX
-	MOVQ 24(DX), BX
-	MOVQ 32(DX), SI
-	MOVQ 40(DX), DI
-	MOVQ 48(DX), R8
-	MOVQ 56(DX), R9
-	MOVQ 64(DX), R10
-	MOVQ 72(DX), R11
-	MOVQ 80(DX), R12
-	MOVQ 88(DX), R13
-	XORQ DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[9]) := t[10] + m*q[10] + C
-	ADCXQ R12, R11
-	MULXQ q<>+80(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[10]) := t[11] + m*q[11] + C
-	ADCXQ R13, R12
-	MULXQ q<>+88(SB), AX, R13
-	ADOXQ AX, R12
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ AX, R13
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[9]) := t[10] + m*q[10] + C
-	ADCXQ R12, R11
-	MULXQ q<>+80(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[10]) := t[11] + m*q[11] + C
-	ADCXQ R13, R12
-	MULXQ q<>+88(SB), AX, R13
-	ADOXQ AX, R12
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ AX, R13
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[9]) := t[10] + m*q[10] + C
-	ADCXQ R12, R11
-	MULXQ q<>+80(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[10]) := t[11] + m*q[11] + C
-	ADCXQ R13, R12
-	MULXQ q<>+88(SB), AX, R13
-	ADOXQ AX, R12
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ AX, R13
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[9]) := t[10] + m*q[10] + C
-	ADCXQ R12, R11
-	MULXQ q<>+80(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[10]) := t[11] + m*q[11] + C
-	ADCXQ R13, R12
-	MULXQ q<>+88(SB), AX, R13
-	ADOXQ AX, R12
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ AX, R13
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[9]) := t[10] + m*q[10] + C
-	ADCXQ R12, R11
-	MULXQ q<>+80(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[10]) := t[11] + m*q[11] + C
-	ADCXQ R13, R12
-	MULXQ q<>+88(SB), AX, R13
-	ADOXQ AX, R12
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ AX, R13
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[9]) := t[10] + m*q[10] + C
-	ADCXQ R12, R11
-	MULXQ q<>+80(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[10]) := t[11] + m*q[11] + C
-	ADCXQ R13, R12
-	MULXQ q<>+88(SB), AX, R13
-	ADOXQ AX, R12
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ AX, R13
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[9]) := t[10] + m*q[10] + C
-	ADCXQ R12, R11
-	MULXQ q<>+80(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[10]) := t[11] + m*q[11] + C
-	ADCXQ R13, R12
-	MULXQ q<>+88(SB), AX, R13
-	ADOXQ AX, R12
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ AX, R13
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[9]) := t[10] + m*q[10] + C
-	ADCXQ R12, R11
-	MULXQ q<>+80(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[10]) := t[11] + m*q[11] + C
-	ADCXQ R13, R12
-	MULXQ q<>+88(SB), AX, R13
-	ADOXQ AX, R12
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ AX, R13
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[9]) := t[10] + m*q[10] + C
-	ADCXQ R12, R11
-	MULXQ q<>+80(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[10]) := t[11] + m*q[11] + C
-	ADCXQ R13, R12
-	MULXQ q<>+88(SB), AX, R13
-	ADOXQ AX, R12
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ AX, R13
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[9]) := t[10] + m*q[10] + C
-	ADCXQ R12, R11
-	MULXQ q<>+80(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[10]) := t[11] + m*q[11] + C
-	ADCXQ R13, R12
-	MULXQ q<>+88(SB), AX, R13
-	ADOXQ AX, R12
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ AX, R13
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[9]) := t[10] + m*q[10] + C
-	ADCXQ R12, R11
-	MULXQ q<>+80(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[10]) := t[11] + m*q[11] + C
-	ADCXQ R13, R12
-	MULXQ q<>+88(SB), AX, R13
-	ADOXQ AX, R12
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ AX, R13
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// (C,t[5]) := t[6] + m*q[6] + C
-	ADCXQ R8, DI
-	MULXQ q<>+48(SB), AX, R8
-	ADOXQ AX, DI
-
-	// (C,t[6]) := t[7] + m*q[7] + C
-	ADCXQ R9, R8
-	MULXQ q<>+56(SB), AX, R9
-	ADOXQ AX, R8
-
-	// (C,t[7]) := t[8] + m*q[8] + C
-	ADCXQ R10, R9
-	MULXQ q<>+64(SB), AX, R10
-	ADOXQ AX, R9
-
-	// (C,t[8]) := t[9] + m*q[9] + C
-	ADCXQ R11, R10
-	MULXQ q<>+72(SB), AX, R11
-	ADOXQ AX, R10
-
-	// (C,t[9]) := t[10] + m*q[10] + C
-	ADCXQ R12, R11
-	MULXQ q<>+80(SB), AX, R12
-	ADOXQ AX, R11
-
-	// (C,t[10]) := t[11] + m*q[11] + C
-	ADCXQ R13, R12
-	MULXQ q<>+88(SB), AX, R13
-	ADOXQ AX, R12
-	MOVQ  $0, AX
-	ADCXQ AX, R13
-	ADOXQ AX, R13
-
-	// reduce element(R14,R15,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13) using temp registers (s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP),s11-96(SP))
-	REDUCE(R14,R15,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP),s11-96(SP))
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R15, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	MOVQ SI, 32(AX)
-	MOVQ DI, 40(AX)
-	MOVQ R8, 48(AX)
-	MOVQ R9, 56(AX)
-	MOVQ R10, 64(AX)
-	MOVQ R11, 72(AX)
-	MOVQ R12, 80(AX)
-	MOVQ R13, 88(AX)
-	RET
-
-noAdx_2:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	CALL ·_fromMontGeneric(SB)
-	RET
diff --git a/ecc/bw6-761/fp/element_ops_amd64.go b/ecc/bw6-761/fp/element_ops_amd64.go
index 83bba45aed..ed2803d717 100644
--- a/ecc/bw6-761/fp/element_ops_amd64.go
+++ b/ecc/bw6-761/fp/element_ops_amd64.go
@@ -50,48 +50,8 @@ func Butterfly(a, b *Element)
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	mul(z, x, y)
 	return z
diff --git a/ecc/bw6-761/fp/element_ops_amd64.s b/ecc/bw6-761/fp/element_ops_amd64.s
index 476e9e39ec..3c8e045ed6 100644
--- a/ecc/bw6-761/fp/element_ops_amd64.s
+++ b/ecc/bw6-761/fp/element_ops_amd64.s
@@ -1,502 +1,6 @@
 // +build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+// We include the hash to force the Go compiler to recompile: 13892629867042773109
+#include "../../../field/asm/element_12w_amd64.s"
 
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0xf49d00000000008b
-DATA q<>+8(SB)/8, $0xe6913e6870000082
-DATA q<>+16(SB)/8, $0x160cf8aeeaf0a437
-DATA q<>+24(SB)/8, $0x98a116c25667a8f8
-DATA q<>+32(SB)/8, $0x71dcd3dc73ebff2e
-DATA q<>+40(SB)/8, $0x8689c8ed12f9fd90
-DATA q<>+48(SB)/8, $0x03cebaff25b42304
-DATA q<>+56(SB)/8, $0x707ba638e584e919
-DATA q<>+64(SB)/8, $0x528275ef8087be41
-DATA q<>+72(SB)/8, $0xb926186a81d14688
-DATA q<>+80(SB)/8, $0xd187c94004faff3e
-DATA q<>+88(SB)/8, $0x0122e824fb83ce0a
-GLOBL q<>(SB), (RODATA+NOPTR), $96
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0x0a5593568fa798dd
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, ra4, ra5, ra6, ra7, ra8, ra9, ra10, ra11, rb0, rb1, rb2, rb3, rb4, rb5, rb6, rb7, rb8, rb9, rb10, rb11) \
-	MOVQ    ra0, rb0;         \
-	SUBQ    q<>(SB), ra0;     \
-	MOVQ    ra1, rb1;         \
-	SBBQ    q<>+8(SB), ra1;   \
-	MOVQ    ra2, rb2;         \
-	SBBQ    q<>+16(SB), ra2;  \
-	MOVQ    ra3, rb3;         \
-	SBBQ    q<>+24(SB), ra3;  \
-	MOVQ    ra4, rb4;         \
-	SBBQ    q<>+32(SB), ra4;  \
-	MOVQ    ra5, rb5;         \
-	SBBQ    q<>+40(SB), ra5;  \
-	MOVQ    ra6, rb6;         \
-	SBBQ    q<>+48(SB), ra6;  \
-	MOVQ    ra7, rb7;         \
-	SBBQ    q<>+56(SB), ra7;  \
-	MOVQ    ra8, rb8;         \
-	SBBQ    q<>+64(SB), ra8;  \
-	MOVQ    ra9, rb9;         \
-	SBBQ    q<>+72(SB), ra9;  \
-	MOVQ    ra10, rb10;       \
-	SBBQ    q<>+80(SB), ra10; \
-	MOVQ    ra11, rb11;       \
-	SBBQ    q<>+88(SB), ra11; \
-	CMOVQCS rb0, ra0;         \
-	CMOVQCS rb1, ra1;         \
-	CMOVQCS rb2, ra2;         \
-	CMOVQCS rb3, ra3;         \
-	CMOVQCS rb4, ra4;         \
-	CMOVQCS rb5, ra5;         \
-	CMOVQCS rb6, ra6;         \
-	CMOVQCS rb7, ra7;         \
-	CMOVQCS rb8, ra8;         \
-	CMOVQCS rb9, ra9;         \
-	CMOVQCS rb10, ra10;       \
-	CMOVQCS rb11, ra11;       \
-
-TEXT ·reduce(SB), $88-8
-	MOVQ res+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	MOVQ 40(AX), R8
-	MOVQ 48(AX), R9
-	MOVQ 56(AX), R10
-	MOVQ 64(AX), R11
-	MOVQ 72(AX), R12
-	MOVQ 80(AX), R13
-	MOVQ 88(AX), R14
-
-	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	MOVQ R8, 40(AX)
-	MOVQ R9, 48(AX)
-	MOVQ R10, 56(AX)
-	MOVQ R11, 64(AX)
-	MOVQ R12, 72(AX)
-	MOVQ R13, 80(AX)
-	MOVQ R14, 88(AX)
-	RET
-
-// MulBy3(x *Element)
-TEXT ·MulBy3(SB), $88-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	MOVQ 40(AX), R8
-	MOVQ 48(AX), R9
-	MOVQ 56(AX), R10
-	MOVQ 64(AX), R11
-	MOVQ 72(AX), R12
-	MOVQ 80(AX), R13
-	MOVQ 88(AX), R14
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-	ADCQ R9, R9
-	ADCQ R10, R10
-	ADCQ R11, R11
-	ADCQ R12, R12
-	ADCQ R13, R13
-	ADCQ R14, R14
-
-	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-	ADCQ 40(AX), R8
-	ADCQ 48(AX), R9
-	ADCQ 56(AX), R10
-	ADCQ 64(AX), R11
-	ADCQ 72(AX), R12
-	ADCQ 80(AX), R13
-	ADCQ 88(AX), R14
-
-	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	MOVQ R8, 40(AX)
-	MOVQ R9, 48(AX)
-	MOVQ R10, 56(AX)
-	MOVQ R11, 64(AX)
-	MOVQ R12, 72(AX)
-	MOVQ R13, 80(AX)
-	MOVQ R14, 88(AX)
-	RET
-
-// MulBy5(x *Element)
-TEXT ·MulBy5(SB), $88-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	MOVQ 40(AX), R8
-	MOVQ 48(AX), R9
-	MOVQ 56(AX), R10
-	MOVQ 64(AX), R11
-	MOVQ 72(AX), R12
-	MOVQ 80(AX), R13
-	MOVQ 88(AX), R14
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-	ADCQ R9, R9
-	ADCQ R10, R10
-	ADCQ R11, R11
-	ADCQ R12, R12
-	ADCQ R13, R13
-	ADCQ R14, R14
-
-	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-	ADCQ R9, R9
-	ADCQ R10, R10
-	ADCQ R11, R11
-	ADCQ R12, R12
-	ADCQ R13, R13
-	ADCQ R14, R14
-
-	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-	ADCQ 40(AX), R8
-	ADCQ 48(AX), R9
-	ADCQ 56(AX), R10
-	ADCQ 64(AX), R11
-	ADCQ 72(AX), R12
-	ADCQ 80(AX), R13
-	ADCQ 88(AX), R14
-
-	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	MOVQ R8, 40(AX)
-	MOVQ R9, 48(AX)
-	MOVQ R10, 56(AX)
-	MOVQ R11, 64(AX)
-	MOVQ R12, 72(AX)
-	MOVQ R13, 80(AX)
-	MOVQ R14, 88(AX)
-	RET
-
-// MulBy13(x *Element)
-TEXT ·MulBy13(SB), $184-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	MOVQ 40(AX), R8
-	MOVQ 48(AX), R9
-	MOVQ 56(AX), R10
-	MOVQ 64(AX), R11
-	MOVQ 72(AX), R12
-	MOVQ 80(AX), R13
-	MOVQ 88(AX), R14
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-	ADCQ R9, R9
-	ADCQ R10, R10
-	ADCQ R11, R11
-	ADCQ R12, R12
-	ADCQ R13, R13
-	ADCQ R14, R14
-
-	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-	ADCQ R9, R9
-	ADCQ R10, R10
-	ADCQ R11, R11
-	ADCQ R12, R12
-	ADCQ R13, R13
-	ADCQ R14, R14
-
-	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14) using temp registers (s11-96(SP),s12-104(SP),s13-112(SP),s14-120(SP),s15-128(SP),s16-136(SP),s17-144(SP),s18-152(SP),s19-160(SP),s20-168(SP),s21-176(SP),s22-184(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,s11-96(SP),s12-104(SP),s13-112(SP),s14-120(SP),s15-128(SP),s16-136(SP),s17-144(SP),s18-152(SP),s19-160(SP),s20-168(SP),s21-176(SP),s22-184(SP))
-
-	MOVQ DX, s11-96(SP)
-	MOVQ CX, s12-104(SP)
-	MOVQ BX, s13-112(SP)
-	MOVQ SI, s14-120(SP)
-	MOVQ DI, s15-128(SP)
-	MOVQ R8, s16-136(SP)
-	MOVQ R9, s17-144(SP)
-	MOVQ R10, s18-152(SP)
-	MOVQ R11, s19-160(SP)
-	MOVQ R12, s20-168(SP)
-	MOVQ R13, s21-176(SP)
-	MOVQ R14, s22-184(SP)
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-	ADCQ R9, R9
-	ADCQ R10, R10
-	ADCQ R11, R11
-	ADCQ R12, R12
-	ADCQ R13, R13
-	ADCQ R14, R14
-
-	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
-
-	ADDQ s11-96(SP), DX
-	ADCQ s12-104(SP), CX
-	ADCQ s13-112(SP), BX
-	ADCQ s14-120(SP), SI
-	ADCQ s15-128(SP), DI
-	ADCQ s16-136(SP), R8
-	ADCQ s17-144(SP), R9
-	ADCQ s18-152(SP), R10
-	ADCQ s19-160(SP), R11
-	ADCQ s20-168(SP), R12
-	ADCQ s21-176(SP), R13
-	ADCQ s22-184(SP), R14
-
-	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-	ADCQ 40(AX), R8
-	ADCQ 48(AX), R9
-	ADCQ 56(AX), R10
-	ADCQ 64(AX), R11
-	ADCQ 72(AX), R12
-	ADCQ 80(AX), R13
-	ADCQ 88(AX), R14
-
-	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	MOVQ R8, 40(AX)
-	MOVQ R9, 48(AX)
-	MOVQ R10, 56(AX)
-	MOVQ R11, 64(AX)
-	MOVQ R12, 72(AX)
-	MOVQ R13, 80(AX)
-	MOVQ R14, 88(AX)
-	RET
-
-// Butterfly(a, b *Element) sets a = a + b; b = a - b
-TEXT ·Butterfly(SB), $88-16
-	MOVQ b+8(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	MOVQ 40(AX), R8
-	MOVQ 48(AX), R9
-	MOVQ 56(AX), R10
-	MOVQ 64(AX), R11
-	MOVQ 72(AX), R12
-	MOVQ 80(AX), R13
-	MOVQ 88(AX), R14
-	MOVQ a+0(FP), AX
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-	ADCQ 40(AX), R8
-	ADCQ 48(AX), R9
-	ADCQ 56(AX), R10
-	ADCQ 64(AX), R11
-	ADCQ 72(AX), R12
-	ADCQ 80(AX), R13
-	ADCQ 88(AX), R14
-	MOVQ DX, R15
-	MOVQ CX, s0-8(SP)
-	MOVQ BX, s1-16(SP)
-	MOVQ SI, s2-24(SP)
-	MOVQ DI, s3-32(SP)
-	MOVQ R8, s4-40(SP)
-	MOVQ R9, s5-48(SP)
-	MOVQ R10, s6-56(SP)
-	MOVQ R11, s7-64(SP)
-	MOVQ R12, s8-72(SP)
-	MOVQ R13, s9-80(SP)
-	MOVQ R14, s10-88(SP)
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	MOVQ 40(AX), R8
-	MOVQ 48(AX), R9
-	MOVQ 56(AX), R10
-	MOVQ 64(AX), R11
-	MOVQ 72(AX), R12
-	MOVQ 80(AX), R13
-	MOVQ 88(AX), R14
-	MOVQ b+8(FP), AX
-	SUBQ 0(AX), DX
-	SBBQ 8(AX), CX
-	SBBQ 16(AX), BX
-	SBBQ 24(AX), SI
-	SBBQ 32(AX), DI
-	SBBQ 40(AX), R8
-	SBBQ 48(AX), R9
-	SBBQ 56(AX), R10
-	SBBQ 64(AX), R11
-	SBBQ 72(AX), R12
-	SBBQ 80(AX), R13
-	SBBQ 88(AX), R14
-	JCC  noReduce_1
-	MOVQ $0xf49d00000000008b, AX
-	ADDQ AX, DX
-	MOVQ $0xe6913e6870000082, AX
-	ADCQ AX, CX
-	MOVQ $0x160cf8aeeaf0a437, AX
-	ADCQ AX, BX
-	MOVQ $0x98a116c25667a8f8, AX
-	ADCQ AX, SI
-	MOVQ $0x71dcd3dc73ebff2e, AX
-	ADCQ AX, DI
-	MOVQ $0x8689c8ed12f9fd90, AX
-	ADCQ AX, R8
-	MOVQ $0x03cebaff25b42304, AX
-	ADCQ AX, R9
-	MOVQ $0x707ba638e584e919, AX
-	ADCQ AX, R10
-	MOVQ $0x528275ef8087be41, AX
-	ADCQ AX, R11
-	MOVQ $0xb926186a81d14688, AX
-	ADCQ AX, R12
-	MOVQ $0xd187c94004faff3e, AX
-	ADCQ AX, R13
-	MOVQ $0x0122e824fb83ce0a, AX
-	ADCQ AX, R14
-
-noReduce_1:
-	MOVQ b+8(FP), AX
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	MOVQ R8, 40(AX)
-	MOVQ R9, 48(AX)
-	MOVQ R10, 56(AX)
-	MOVQ R11, 64(AX)
-	MOVQ R12, 72(AX)
-	MOVQ R13, 80(AX)
-	MOVQ R14, 88(AX)
-	MOVQ R15, DX
-	MOVQ s0-8(SP), CX
-	MOVQ s1-16(SP), BX
-	MOVQ s2-24(SP), SI
-	MOVQ s3-32(SP), DI
-	MOVQ s4-40(SP), R8
-	MOVQ s5-48(SP), R9
-	MOVQ s6-56(SP), R10
-	MOVQ s7-64(SP), R11
-	MOVQ s8-72(SP), R12
-	MOVQ s9-80(SP), R13
-	MOVQ s10-88(SP), R14
-
-	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
-
-	MOVQ a+0(FP), AX
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	MOVQ R8, 40(AX)
-	MOVQ R9, 48(AX)
-	MOVQ R10, 56(AX)
-	MOVQ R11, 64(AX)
-	MOVQ R12, 72(AX)
-	MOVQ R13, 80(AX)
-	MOVQ R14, 88(AX)
-	RET
diff --git a/ecc/bw6-761/fp/element_ops_purego.go b/ecc/bw6-761/fp/element_ops_purego.go
index 3c1ffa2456..59d6d1d523 100644
--- a/ecc/bw6-761/fp/element_ops_purego.go
+++ b/ecc/bw6-761/fp/element_ops_purego.go
@@ -73,48 +73,8 @@ func reduce(z *Element) {
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t0, t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11 uint64
 	var u0, u1, u2, u3, u4, u5, u6, u7, u8, u9, u10, u11 uint64
diff --git a/ecc/bw6-761/fp/element_test.go b/ecc/bw6-761/fp/element_test.go
index fbba1f2864..5df3d0de53 100644
--- a/ecc/bw6-761/fp/element_test.go
+++ b/ecc/bw6-761/fp/element_test.go
@@ -653,7 +653,6 @@ func TestElementBitLen(t *testing.T) {
 	))
 
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
-
 }
 
 func TestElementButterflies(t *testing.T) {
@@ -723,77 +722,6 @@ func TestElementLexicographicallyLargest(t *testing.T) {
 
 }
 
-func TestElementVecOps(t *testing.T) {
-	assert := require.New(t)
-
-	const N = 7
-	a := make(Vector, N)
-	b := make(Vector, N)
-	c := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a[i].SetRandom()
-		b[i].SetRandom()
-	}
-
-	// Vector addition
-	c.Add(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Add(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector addition failed")
-	}
-
-	// Vector subtraction
-	c.Sub(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Sub(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector subtraction failed")
-	}
-
-	// Vector scaling
-	c.ScalarMul(a, &b[0])
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Mul(&a[i], &b[0])
-		assert.True(c[i].Equal(&expected), "Vector scaling failed")
-	}
-}
-
-func BenchmarkElementVecOps(b *testing.B) {
-	// note; to benchmark against "no asm" version, use the following
-	// build tag: -tags purego
-	const N = 1024
-	a1 := make(Vector, N)
-	b1 := make(Vector, N)
-	c1 := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a1[i].SetRandom()
-		b1[i].SetRandom()
-	}
-
-	b.Run("Add", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Add(a1, b1)
-		}
-	})
-
-	b.Run("Sub", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Sub(a1, b1)
-		}
-	})
-
-	b.Run("ScalarMul", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.ScalarMul(a1, &b1[0])
-		}
-	})
-}
-
 func TestElementAdd(t *testing.T) {
 	t.Parallel()
 	parameters := gopter.DefaultTestParameters()
@@ -2377,54 +2305,54 @@ func gen() gopter.Gen {
 	}
 }
 
-func genFull() gopter.Gen {
-	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+func genRandomFq(genParams *gopter.GenParameters) Element {
+	var g Element
 
-		genRandomFq := func() Element {
-			var g Element
+	g = Element{
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+	}
 
-			g = Element{
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-			}
+	if qElement[11] != ^uint64(0) {
+		g[11] %= (qElement[11] + 1)
+	}
 
-			if qElement[11] != ^uint64(0) {
-				g[11] %= (qElement[11] + 1)
-			}
+	for !g.smallerThanModulus() {
+		g = Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[11] != ^uint64(0) {
+			g[11] %= (qElement[11] + 1)
+		}
+	}
 
-			for !g.smallerThanModulus() {
-				g = Element{
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-				}
-				if qElement[11] != ^uint64(0) {
-					g[11] %= (qElement[11] + 1)
-				}
-			}
+	return g
+}
 
-			return g
-		}
-		a := genRandomFq()
+func genFull() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
 
 		var carry uint64
 		a[0], carry = bits.Add64(a[0], qElement[0], carry)
@@ -2445,6 +2373,14 @@ func genFull() gopter.Gen {
 	}
 }
 
+func genElement() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
+		genResult := gopter.NewGenResult(a, gopter.NoShrinker)
+		return genResult
+	}
+}
+
 func (z *Element) matchVeryBigInt(aHi uint64, aInt *big.Int) error {
 	var modulus big.Int
 	var aIntMod big.Int
diff --git a/ecc/bw6-761/fp/vector.go b/ecc/bw6-761/fp/vector.go
index 87105028b8..8b91076209 100644
--- a/ecc/bw6-761/fp/vector.go
+++ b/ecc/bw6-761/fp/vector.go
@@ -225,6 +225,25 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	scalarMulVecGeneric(*vector, a, b)
 }
 
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
+
 func addVecGeneric(res, a, b Vector) {
 	if len(a) != len(b) || len(a) != len(res) {
 		panic("vector.Add: vectors don't have the same length")
@@ -252,6 +271,32 @@ func scalarMulVecGeneric(res, a Vector, b *Element) {
 	}
 }
 
+func sumVecGeneric(res *Element, a Vector) {
+	for i := 0; i < len(a); i++ {
+		res.Add(res, &a[i])
+	}
+}
+
+func innerProductVecGeneric(res *Element, a, b Vector) {
+	if len(a) != len(b) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	var tmp Element
+	for i := 0; i < len(a); i++ {
+		tmp.Mul(&a[i], &b[i])
+		res.Add(res, &tmp)
+	}
+}
+
+func mulVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Mul(&a[i], &b[i])
+	}
+}
+
 // TODO @gbotrel make a public package out of that.
 // execute executes the work function in parallel.
 // this is copy paste from internal/parallel/parallel.go
diff --git a/ecc/bw6-761/fp/vector_test.go b/ecc/bw6-761/fp/vector_test.go
index 5d88af91c0..9f59efdd32 100644
--- a/ecc/bw6-761/fp/vector_test.go
+++ b/ecc/bw6-761/fp/vector_test.go
@@ -18,10 +18,15 @@ package fp
 
 import (
 	"bytes"
+	"fmt"
 	"github.com/stretchr/testify/require"
+	"os"
 	"reflect"
 	"sort"
 	"testing"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/prop"
 )
 
 func TestVectorSort(t *testing.T) {
@@ -88,3 +93,295 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 	}
 	return <-chErr
 }
+
+func TestVectorOps(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = 2
+	} else {
+		parameters.MinSuccessfulTests = 10
+	}
+	properties := gopter.NewProperties(parameters)
+
+	addVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Add(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Add(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	subVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Sub(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Sub(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	scalarMulVector := func(a Vector, b Element) bool {
+		c := make(Vector, len(a))
+		c.ScalarMul(a, &b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b)
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sumVector := func(a Vector) bool {
+		var sum Element
+		computed := a.Sum()
+		for i := 0; i < len(a); i++ {
+			sum.Add(&sum, &a[i])
+		}
+
+		return sum.Equal(&computed)
+	}
+
+	innerProductVector := func(a, b Vector) bool {
+		computed := a.InnerProduct(b)
+		var innerProduct Element
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			innerProduct.Add(&innerProduct, &tmp)
+		}
+
+		return innerProduct.Equal(&computed)
+	}
+
+	mulVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		a[0].SetUint64(0x24)
+		b[0].SetUint64(0x42)
+		c.Mul(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sizes := []int{1, 2, 3, 4, 8, 9, 15, 16, 509, 510, 511, 512, 513, 514}
+	type genPair struct {
+		g1, g2 gopter.Gen
+		label  string
+	}
+
+	for _, size := range sizes {
+		generators := []genPair{
+			{genZeroVector(size), genZeroVector(size), "zero vectors"},
+			{genMaxVector(size), genMaxVector(size), "max vectors"},
+			{genVector(size), genVector(size), "random vectors"},
+			{genVector(size), genZeroVector(size), "random and zero vectors"},
+		}
+		for _, gp := range generators {
+			properties.Property(fmt.Sprintf("vector addition %d - %s", size, gp.label), prop.ForAll(
+				addVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector subtraction %d - %s", size, gp.label), prop.ForAll(
+				subVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector scalar multiplication %d - %s", size, gp.label), prop.ForAll(
+				scalarMulVector,
+				gp.g1,
+				genElement(),
+			))
+
+			properties.Property(fmt.Sprintf("vector sum %d - %s", size, gp.label), prop.ForAll(
+				sumVector,
+				gp.g1,
+			))
+
+			properties.Property(fmt.Sprintf("vector inner product %d - %s", size, gp.label), prop.ForAll(
+				innerProductVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector multiplication %d - %s", size, gp.label), prop.ForAll(
+				mulVector,
+				gp.g1,
+				gp.g2,
+			))
+		}
+	}
+
+	properties.TestingRun(t, gopter.NewFormatedReporter(false, 260, os.Stdout))
+}
+
+func BenchmarkVectorOps(b *testing.B) {
+	// note; to benchmark against "no asm" version, use the following
+	// build tag: -tags purego
+	const N = 1 << 24
+	a1 := make(Vector, N)
+	b1 := make(Vector, N)
+	c1 := make(Vector, N)
+	var mixer Element
+	mixer.SetRandom()
+	for i := 1; i < N; i++ {
+		a1[i-1].SetUint64(uint64(i)).
+			Mul(&a1[i-1], &mixer)
+		b1[i-1].SetUint64(^uint64(i)).
+			Mul(&b1[i-1], &mixer)
+	}
+
+	for n := 1 << 4; n <= N; n <<= 1 {
+		b.Run(fmt.Sprintf("add %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Add(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sub %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Sub(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("scalarMul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.ScalarMul(_a, &mixer)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sum %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.Sum()
+			}
+		})
+
+		b.Run(fmt.Sprintf("innerProduct %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.InnerProduct(_b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("mul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Mul(_a, _b)
+			}
+		})
+	}
+}
+
+func genZeroVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genMaxVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+
+		qMinusOne := qElement
+		qMinusOne[0]--
+
+		for i := 0; i < size; i++ {
+			g[i] = qMinusOne
+		}
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		mixer := Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[11] != ^uint64(0) {
+			mixer[11] %= (qElement[11] + 1)
+		}
+
+		for !mixer.smallerThanModulus() {
+			mixer = Element{
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+			}
+			if qElement[11] != ^uint64(0) {
+				mixer[11] %= (qElement[11] + 1)
+			}
+		}
+
+		for i := 1; i <= size; i++ {
+			g[i-1].SetUint64(uint64(i)).
+				Mul(&g[i-1], &mixer)
+		}
+
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/ecc/bw6-761/fr/asm.go b/ecc/bw6-761/fr/asm_adx.go
similarity index 100%
rename from ecc/bw6-761/fr/asm.go
rename to ecc/bw6-761/fr/asm_adx.go
diff --git a/ecc/bw6-761/fr/element.go b/ecc/bw6-761/fr/element.go
index 3e7eacc9e0..6784bc911f 100644
--- a/ecc/bw6-761/fr/element.go
+++ b/ecc/bw6-761/fr/element.go
@@ -521,32 +521,8 @@ func (z *Element) Select(c int, x0 *Element, x1 *Element) *Element {
 // and is used for testing purposes.
 func _mulGeneric(z, x, y *Element) {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t [7]uint64
 	var D uint64
diff --git a/ecc/bw6-761/fr/element_mul_amd64.s b/ecc/bw6-761/fr/element_mul_amd64.s
deleted file mode 100644
index 1e19c4d3fd..0000000000
--- a/ecc/bw6-761/fr/element_mul_amd64.s
+++ /dev/null
@@ -1,857 +0,0 @@
-// +build !purego
-
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0x8508c00000000001
-DATA q<>+8(SB)/8, $0x170b5d4430000000
-DATA q<>+16(SB)/8, $0x1ef3622fba094800
-DATA q<>+24(SB)/8, $0x1a22d9f300f5138f
-DATA q<>+32(SB)/8, $0xc63b05c06ca1493b
-DATA q<>+40(SB)/8, $0x01ae3a4617c510ea
-GLOBL q<>(SB), (RODATA+NOPTR), $48
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0x8508bfffffffffff
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, ra4, ra5, rb0, rb1, rb2, rb3, rb4, rb5) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	MOVQ    ra4, rb4;        \
-	SBBQ    q<>+32(SB), ra4; \
-	MOVQ    ra5, rb5;        \
-	SBBQ    q<>+40(SB), ra5; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-	CMOVQCS rb4, ra4;        \
-	CMOVQCS rb5, ra5;        \
-
-// mul(res, x, y *Element)
-TEXT ·mul(SB), $24-24
-
-	// the algorithm is described in the Element.Mul declaration (.go)
-	// however, to benefit from the ADCX and ADOX carry chains
-	// we split the inner loops in 2:
-	// for i=0 to N-1
-	// 		for j=0 to N-1
-	// 		    (A,t[j])  := t[j] + x[j]*y[i] + A
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C + A
-
-	NO_LOCAL_POINTERS
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_1
-	MOVQ x+8(FP), R8
-
-	// x[0] -> R10
-	// x[1] -> R11
-	// x[2] -> R12
-	MOVQ 0(R8), R10
-	MOVQ 8(R8), R11
-	MOVQ 16(R8), R12
-	MOVQ y+16(FP), R13
-
-	// A -> BP
-	// t[0] -> R14
-	// t[1] -> R15
-	// t[2] -> CX
-	// t[3] -> BX
-	// t[4] -> SI
-	// t[5] -> DI
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 0(R13), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ R10, R14, R15
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ R11, AX, CX
-	ADOXQ AX, R15
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ R12, AX, BX
-	ADOXQ AX, CX
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ 24(R8), AX, SI
-	ADOXQ AX, BX
-
-	// (A,t[4])  := x[4]*y[0] + A
-	MULXQ 32(R8), AX, DI
-	ADOXQ AX, SI
-
-	// (A,t[5])  := x[5]*y[0] + A
-	MULXQ 40(R8), AX, BP
-	ADOXQ AX, DI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R9
-	ADCXQ R14, AX
-	MOVQ  R9, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ BP, DI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 8(R13), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ R10, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R15
-	MULXQ R11, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, CX
-	MULXQ R12, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, BX
-	MULXQ 24(R8), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[1] + A
-	ADCXQ BP, SI
-	MULXQ 32(R8), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[1] + A
-	ADCXQ BP, DI
-	MULXQ 40(R8), AX, BP
-	ADOXQ AX, DI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R9
-	ADCXQ R14, AX
-	MOVQ  R9, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ BP, DI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 16(R13), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ R10, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R15
-	MULXQ R11, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, CX
-	MULXQ R12, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, BX
-	MULXQ 24(R8), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[2] + A
-	ADCXQ BP, SI
-	MULXQ 32(R8), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[2] + A
-	ADCXQ BP, DI
-	MULXQ 40(R8), AX, BP
-	ADOXQ AX, DI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R9
-	ADCXQ R14, AX
-	MOVQ  R9, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ BP, DI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 24(R13), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ R10, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R15
-	MULXQ R11, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, CX
-	MULXQ R12, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, BX
-	MULXQ 24(R8), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[3] + A
-	ADCXQ BP, SI
-	MULXQ 32(R8), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[3] + A
-	ADCXQ BP, DI
-	MULXQ 40(R8), AX, BP
-	ADOXQ AX, DI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R9
-	ADCXQ R14, AX
-	MOVQ  R9, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ BP, DI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 32(R13), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[4] + A
-	MULXQ R10, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[4] + A
-	ADCXQ BP, R15
-	MULXQ R11, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[4] + A
-	ADCXQ BP, CX
-	MULXQ R12, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[4] + A
-	ADCXQ BP, BX
-	MULXQ 24(R8), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[4] + A
-	ADCXQ BP, SI
-	MULXQ 32(R8), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[4] + A
-	ADCXQ BP, DI
-	MULXQ 40(R8), AX, BP
-	ADOXQ AX, DI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R9
-	ADCXQ R14, AX
-	MOVQ  R9, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ BP, DI
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 40(R13), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[5] + A
-	MULXQ R10, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[5] + A
-	ADCXQ BP, R15
-	MULXQ R11, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[5] + A
-	ADCXQ BP, CX
-	MULXQ R12, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[5] + A
-	ADCXQ BP, BX
-	MULXQ 24(R8), AX, BP
-	ADOXQ AX, BX
-
-	// (A,t[4])  := t[4] + x[4]*y[5] + A
-	ADCXQ BP, SI
-	MULXQ 32(R8), AX, BP
-	ADOXQ AX, SI
-
-	// (A,t[5])  := t[5] + x[5]*y[5] + A
-	ADCXQ BP, DI
-	MULXQ 40(R8), AX, BP
-	ADOXQ AX, DI
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R9
-	ADCXQ R14, AX
-	MOVQ  R9, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-
-	// t[5] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ BP, DI
-
-	// reduce element(R14,R15,CX,BX,SI,DI) using temp registers (R9,R8,R13,R10,R11,R12)
-	REDUCE(R14,R15,CX,BX,SI,DI,R9,R8,R13,R10,R11,R12)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R15, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	MOVQ SI, 32(AX)
-	MOVQ DI, 40(AX)
-	RET
-
-noAdx_1:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	MOVQ x+8(FP), AX
-	MOVQ AX, 8(SP)
-	MOVQ y+16(FP), AX
-	MOVQ AX, 16(SP)
-	CALL ·_mulGeneric(SB)
-	RET
-
-TEXT ·fromMont(SB), $8-8
-	NO_LOCAL_POINTERS
-
-	// the algorithm is described here
-	// https://hackmd.io/@gnark/modular_multiplication
-	// when y = 1 we have:
-	// for i=0 to N-1
-	// 		t[i] = x[i]
-	// for i=0 to N-1
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_2
-	MOVQ res+0(FP), DX
-	MOVQ 0(DX), R14
-	MOVQ 8(DX), R15
-	MOVQ 16(DX), CX
-	MOVQ 24(DX), BX
-	MOVQ 32(DX), SI
-	MOVQ 40(DX), DI
-	XORQ DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ AX, DI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ AX, DI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ AX, DI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ AX, DI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ AX, DI
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// (C,t[3]) := t[4] + m*q[4] + C
-	ADCXQ SI, BX
-	MULXQ q<>+32(SB), AX, SI
-	ADOXQ AX, BX
-
-	// (C,t[4]) := t[5] + m*q[5] + C
-	ADCXQ DI, SI
-	MULXQ q<>+40(SB), AX, DI
-	ADOXQ AX, SI
-	MOVQ  $0, AX
-	ADCXQ AX, DI
-	ADOXQ AX, DI
-
-	// reduce element(R14,R15,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12,R13)
-	REDUCE(R14,R15,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R15, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	MOVQ SI, 32(AX)
-	MOVQ DI, 40(AX)
-	RET
-
-noAdx_2:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	CALL ·_fromMontGeneric(SB)
-	RET
diff --git a/ecc/bw6-761/fr/element_ops_amd64.go b/ecc/bw6-761/fr/element_ops_amd64.go
index e40a9caed5..83d40c28c1 100644
--- a/ecc/bw6-761/fr/element_ops_amd64.go
+++ b/ecc/bw6-761/fr/element_ops_amd64.go
@@ -50,48 +50,8 @@ func Butterfly(a, b *Element)
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	mul(z, x, y)
 	return z
diff --git a/ecc/bw6-761/fr/element_ops_amd64.s b/ecc/bw6-761/fr/element_ops_amd64.s
index 7242622a4a..cabff26f70 100644
--- a/ecc/bw6-761/fr/element_ops_amd64.s
+++ b/ecc/bw6-761/fr/element_ops_amd64.s
@@ -1,306 +1,6 @@
 // +build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+// We include the hash to force the Go compiler to recompile: 11124594824487954849
+#include "../../../field/asm/element_6w_amd64.s"
 
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0x8508c00000000001
-DATA q<>+8(SB)/8, $0x170b5d4430000000
-DATA q<>+16(SB)/8, $0x1ef3622fba094800
-DATA q<>+24(SB)/8, $0x1a22d9f300f5138f
-DATA q<>+32(SB)/8, $0xc63b05c06ca1493b
-DATA q<>+40(SB)/8, $0x01ae3a4617c510ea
-GLOBL q<>(SB), (RODATA+NOPTR), $48
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0x8508bfffffffffff
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, ra4, ra5, rb0, rb1, rb2, rb3, rb4, rb5) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	MOVQ    ra4, rb4;        \
-	SBBQ    q<>+32(SB), ra4; \
-	MOVQ    ra5, rb5;        \
-	SBBQ    q<>+40(SB), ra5; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-	CMOVQCS rb4, ra4;        \
-	CMOVQCS rb5, ra5;        \
-
-TEXT ·reduce(SB), NOSPLIT, $0-8
-	MOVQ res+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	MOVQ 40(AX), R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	MOVQ R8, 40(AX)
-	RET
-
-// MulBy3(x *Element)
-TEXT ·MulBy3(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	MOVQ 40(AX), R8
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-	ADCQ 40(AX), R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R15,R9,R10,R11,R12,R13)
-	REDUCE(DX,CX,BX,SI,DI,R8,R15,R9,R10,R11,R12,R13)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	MOVQ R8, 40(AX)
-	RET
-
-// MulBy5(x *Element)
-TEXT ·MulBy5(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	MOVQ 40(AX), R8
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R15,R9,R10,R11,R12,R13)
-	REDUCE(DX,CX,BX,SI,DI,R8,R15,R9,R10,R11,R12,R13)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-	ADCQ 40(AX), R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R14,R15,R9,R10,R11,R12)
-	REDUCE(DX,CX,BX,SI,DI,R8,R14,R15,R9,R10,R11,R12)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	MOVQ R8, 40(AX)
-	RET
-
-// MulBy13(x *Element)
-TEXT ·MulBy13(SB), $40-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	MOVQ 32(AX), DI
-	MOVQ 40(AX), R8
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP))
-	REDUCE(DX,CX,BX,SI,DI,R8,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP))
-
-	MOVQ DX, R15
-	MOVQ CX, s0-8(SP)
-	MOVQ BX, s1-16(SP)
-	MOVQ SI, s2-24(SP)
-	MOVQ DI, s3-32(SP)
-	MOVQ R8, s4-40(SP)
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-	ADCQ DI, DI
-	ADCQ R8, R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
-
-	ADDQ R15, DX
-	ADCQ s0-8(SP), CX
-	ADCQ s1-16(SP), BX
-	ADCQ s2-24(SP), SI
-	ADCQ s3-32(SP), DI
-	ADCQ s4-40(SP), R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-	ADCQ 32(AX), DI
-	ADCQ 40(AX), R8
-
-	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	MOVQ DI, 32(AX)
-	MOVQ R8, 40(AX)
-	RET
-
-// Butterfly(a, b *Element) sets a = a + b; b = a - b
-TEXT ·Butterfly(SB), $48-16
-	MOVQ    a+0(FP), AX
-	MOVQ    0(AX), CX
-	MOVQ    8(AX), BX
-	MOVQ    16(AX), SI
-	MOVQ    24(AX), DI
-	MOVQ    32(AX), R8
-	MOVQ    40(AX), R9
-	MOVQ    CX, R10
-	MOVQ    BX, R11
-	MOVQ    SI, R12
-	MOVQ    DI, R13
-	MOVQ    R8, R14
-	MOVQ    R9, R15
-	XORQ    AX, AX
-	MOVQ    b+8(FP), DX
-	ADDQ    0(DX), CX
-	ADCQ    8(DX), BX
-	ADCQ    16(DX), SI
-	ADCQ    24(DX), DI
-	ADCQ    32(DX), R8
-	ADCQ    40(DX), R9
-	SUBQ    0(DX), R10
-	SBBQ    8(DX), R11
-	SBBQ    16(DX), R12
-	SBBQ    24(DX), R13
-	SBBQ    32(DX), R14
-	SBBQ    40(DX), R15
-	MOVQ    CX, s0-8(SP)
-	MOVQ    BX, s1-16(SP)
-	MOVQ    SI, s2-24(SP)
-	MOVQ    DI, s3-32(SP)
-	MOVQ    R8, s4-40(SP)
-	MOVQ    R9, s5-48(SP)
-	MOVQ    $0x8508c00000000001, CX
-	MOVQ    $0x170b5d4430000000, BX
-	MOVQ    $0x1ef3622fba094800, SI
-	MOVQ    $0x1a22d9f300f5138f, DI
-	MOVQ    $0xc63b05c06ca1493b, R8
-	MOVQ    $0x01ae3a4617c510ea, R9
-	CMOVQCC AX, CX
-	CMOVQCC AX, BX
-	CMOVQCC AX, SI
-	CMOVQCC AX, DI
-	CMOVQCC AX, R8
-	CMOVQCC AX, R9
-	ADDQ    CX, R10
-	ADCQ    BX, R11
-	ADCQ    SI, R12
-	ADCQ    DI, R13
-	ADCQ    R8, R14
-	ADCQ    R9, R15
-	MOVQ    s0-8(SP), CX
-	MOVQ    s1-16(SP), BX
-	MOVQ    s2-24(SP), SI
-	MOVQ    s3-32(SP), DI
-	MOVQ    s4-40(SP), R8
-	MOVQ    s5-48(SP), R9
-	MOVQ    R10, 0(DX)
-	MOVQ    R11, 8(DX)
-	MOVQ    R12, 16(DX)
-	MOVQ    R13, 24(DX)
-	MOVQ    R14, 32(DX)
-	MOVQ    R15, 40(DX)
-
-	// reduce element(CX,BX,SI,DI,R8,R9) using temp registers (R10,R11,R12,R13,R14,R15)
-	REDUCE(CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15)
-
-	MOVQ a+0(FP), AX
-	MOVQ CX, 0(AX)
-	MOVQ BX, 8(AX)
-	MOVQ SI, 16(AX)
-	MOVQ DI, 24(AX)
-	MOVQ R8, 32(AX)
-	MOVQ R9, 40(AX)
-	RET
diff --git a/ecc/bw6-761/fr/element_ops_purego.go b/ecc/bw6-761/fr/element_ops_purego.go
index bd2d332932..bdf76428de 100644
--- a/ecc/bw6-761/fr/element_ops_purego.go
+++ b/ecc/bw6-761/fr/element_ops_purego.go
@@ -67,48 +67,8 @@ func reduce(z *Element) {
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t0, t1, t2, t3, t4, t5 uint64
 	var u0, u1, u2, u3, u4, u5 uint64
diff --git a/ecc/bw6-761/fr/element_test.go b/ecc/bw6-761/fr/element_test.go
index 0596297e8c..bcc35c4841 100644
--- a/ecc/bw6-761/fr/element_test.go
+++ b/ecc/bw6-761/fr/element_test.go
@@ -641,7 +641,6 @@ func TestElementBitLen(t *testing.T) {
 	))
 
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
-
 }
 
 func TestElementButterflies(t *testing.T) {
@@ -711,77 +710,6 @@ func TestElementLexicographicallyLargest(t *testing.T) {
 
 }
 
-func TestElementVecOps(t *testing.T) {
-	assert := require.New(t)
-
-	const N = 7
-	a := make(Vector, N)
-	b := make(Vector, N)
-	c := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a[i].SetRandom()
-		b[i].SetRandom()
-	}
-
-	// Vector addition
-	c.Add(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Add(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector addition failed")
-	}
-
-	// Vector subtraction
-	c.Sub(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Sub(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector subtraction failed")
-	}
-
-	// Vector scaling
-	c.ScalarMul(a, &b[0])
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Mul(&a[i], &b[0])
-		assert.True(c[i].Equal(&expected), "Vector scaling failed")
-	}
-}
-
-func BenchmarkElementVecOps(b *testing.B) {
-	// note; to benchmark against "no asm" version, use the following
-	// build tag: -tags purego
-	const N = 1024
-	a1 := make(Vector, N)
-	b1 := make(Vector, N)
-	c1 := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a1[i].SetRandom()
-		b1[i].SetRandom()
-	}
-
-	b.Run("Add", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Add(a1, b1)
-		}
-	})
-
-	b.Run("Sub", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Sub(a1, b1)
-		}
-	})
-
-	b.Run("ScalarMul", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.ScalarMul(a1, &b1[0])
-		}
-	})
-}
-
 func TestElementAdd(t *testing.T) {
 	t.Parallel()
 	parameters := gopter.DefaultTestParameters()
@@ -2353,42 +2281,42 @@ func gen() gopter.Gen {
 	}
 }
 
-func genFull() gopter.Gen {
-	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+func genRandomFq(genParams *gopter.GenParameters) Element {
+	var g Element
 
-		genRandomFq := func() Element {
-			var g Element
+	g = Element{
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+	}
 
-			g = Element{
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-			}
+	if qElement[5] != ^uint64(0) {
+		g[5] %= (qElement[5] + 1)
+	}
 
-			if qElement[5] != ^uint64(0) {
-				g[5] %= (qElement[5] + 1)
-			}
+	for !g.smallerThanModulus() {
+		g = Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[5] != ^uint64(0) {
+			g[5] %= (qElement[5] + 1)
+		}
+	}
 
-			for !g.smallerThanModulus() {
-				g = Element{
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-				}
-				if qElement[5] != ^uint64(0) {
-					g[5] %= (qElement[5] + 1)
-				}
-			}
+	return g
+}
 
-			return g
-		}
-		a := genRandomFq()
+func genFull() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
 
 		var carry uint64
 		a[0], carry = bits.Add64(a[0], qElement[0], carry)
@@ -2403,6 +2331,14 @@ func genFull() gopter.Gen {
 	}
 }
 
+func genElement() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
+		genResult := gopter.NewGenResult(a, gopter.NoShrinker)
+		return genResult
+	}
+}
+
 func (z *Element) matchVeryBigInt(aHi uint64, aInt *big.Int) error {
 	var modulus big.Int
 	var aIntMod big.Int
diff --git a/ecc/bw6-761/fr/vector.go b/ecc/bw6-761/fr/vector.go
index 8dd4774c5a..af400c4e47 100644
--- a/ecc/bw6-761/fr/vector.go
+++ b/ecc/bw6-761/fr/vector.go
@@ -219,6 +219,25 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	scalarMulVecGeneric(*vector, a, b)
 }
 
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
+
 func addVecGeneric(res, a, b Vector) {
 	if len(a) != len(b) || len(a) != len(res) {
 		panic("vector.Add: vectors don't have the same length")
@@ -246,6 +265,32 @@ func scalarMulVecGeneric(res, a Vector, b *Element) {
 	}
 }
 
+func sumVecGeneric(res *Element, a Vector) {
+	for i := 0; i < len(a); i++ {
+		res.Add(res, &a[i])
+	}
+}
+
+func innerProductVecGeneric(res *Element, a, b Vector) {
+	if len(a) != len(b) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	var tmp Element
+	for i := 0; i < len(a); i++ {
+		tmp.Mul(&a[i], &b[i])
+		res.Add(res, &tmp)
+	}
+}
+
+func mulVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Mul(&a[i], &b[i])
+	}
+}
+
 // TODO @gbotrel make a public package out of that.
 // execute executes the work function in parallel.
 // this is copy paste from internal/parallel/parallel.go
diff --git a/ecc/bw6-761/fr/vector_test.go b/ecc/bw6-761/fr/vector_test.go
index e58f2d9a38..ad574704b1 100644
--- a/ecc/bw6-761/fr/vector_test.go
+++ b/ecc/bw6-761/fr/vector_test.go
@@ -18,10 +18,15 @@ package fr
 
 import (
 	"bytes"
+	"fmt"
 	"github.com/stretchr/testify/require"
+	"os"
 	"reflect"
 	"sort"
 	"testing"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/prop"
 )
 
 func TestVectorSort(t *testing.T) {
@@ -88,3 +93,283 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 	}
 	return <-chErr
 }
+
+func TestVectorOps(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = 2
+	} else {
+		parameters.MinSuccessfulTests = 10
+	}
+	properties := gopter.NewProperties(parameters)
+
+	addVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Add(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Add(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	subVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Sub(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Sub(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	scalarMulVector := func(a Vector, b Element) bool {
+		c := make(Vector, len(a))
+		c.ScalarMul(a, &b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b)
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sumVector := func(a Vector) bool {
+		var sum Element
+		computed := a.Sum()
+		for i := 0; i < len(a); i++ {
+			sum.Add(&sum, &a[i])
+		}
+
+		return sum.Equal(&computed)
+	}
+
+	innerProductVector := func(a, b Vector) bool {
+		computed := a.InnerProduct(b)
+		var innerProduct Element
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			innerProduct.Add(&innerProduct, &tmp)
+		}
+
+		return innerProduct.Equal(&computed)
+	}
+
+	mulVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		a[0].SetUint64(0x24)
+		b[0].SetUint64(0x42)
+		c.Mul(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sizes := []int{1, 2, 3, 4, 8, 9, 15, 16, 509, 510, 511, 512, 513, 514}
+	type genPair struct {
+		g1, g2 gopter.Gen
+		label  string
+	}
+
+	for _, size := range sizes {
+		generators := []genPair{
+			{genZeroVector(size), genZeroVector(size), "zero vectors"},
+			{genMaxVector(size), genMaxVector(size), "max vectors"},
+			{genVector(size), genVector(size), "random vectors"},
+			{genVector(size), genZeroVector(size), "random and zero vectors"},
+		}
+		for _, gp := range generators {
+			properties.Property(fmt.Sprintf("vector addition %d - %s", size, gp.label), prop.ForAll(
+				addVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector subtraction %d - %s", size, gp.label), prop.ForAll(
+				subVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector scalar multiplication %d - %s", size, gp.label), prop.ForAll(
+				scalarMulVector,
+				gp.g1,
+				genElement(),
+			))
+
+			properties.Property(fmt.Sprintf("vector sum %d - %s", size, gp.label), prop.ForAll(
+				sumVector,
+				gp.g1,
+			))
+
+			properties.Property(fmt.Sprintf("vector inner product %d - %s", size, gp.label), prop.ForAll(
+				innerProductVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector multiplication %d - %s", size, gp.label), prop.ForAll(
+				mulVector,
+				gp.g1,
+				gp.g2,
+			))
+		}
+	}
+
+	properties.TestingRun(t, gopter.NewFormatedReporter(false, 260, os.Stdout))
+}
+
+func BenchmarkVectorOps(b *testing.B) {
+	// note; to benchmark against "no asm" version, use the following
+	// build tag: -tags purego
+	const N = 1 << 24
+	a1 := make(Vector, N)
+	b1 := make(Vector, N)
+	c1 := make(Vector, N)
+	var mixer Element
+	mixer.SetRandom()
+	for i := 1; i < N; i++ {
+		a1[i-1].SetUint64(uint64(i)).
+			Mul(&a1[i-1], &mixer)
+		b1[i-1].SetUint64(^uint64(i)).
+			Mul(&b1[i-1], &mixer)
+	}
+
+	for n := 1 << 4; n <= N; n <<= 1 {
+		b.Run(fmt.Sprintf("add %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Add(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sub %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Sub(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("scalarMul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.ScalarMul(_a, &mixer)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sum %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.Sum()
+			}
+		})
+
+		b.Run(fmt.Sprintf("innerProduct %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.InnerProduct(_b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("mul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Mul(_a, _b)
+			}
+		})
+	}
+}
+
+func genZeroVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genMaxVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+
+		qMinusOne := qElement
+		qMinusOne[0]--
+
+		for i := 0; i < size; i++ {
+			g[i] = qMinusOne
+		}
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		mixer := Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[5] != ^uint64(0) {
+			mixer[5] %= (qElement[5] + 1)
+		}
+
+		for !mixer.smallerThanModulus() {
+			mixer = Element{
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+			}
+			if qElement[5] != ^uint64(0) {
+				mixer[5] %= (qElement[5] + 1)
+			}
+		}
+
+		for i := 1; i <= size; i++ {
+			g[i-1].SetUint64(uint64(i)).
+				Mul(&g[i-1], &mixer)
+		}
+
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/ecc/secp256k1/fp/element.go b/ecc/secp256k1/fp/element.go
index 0a242dd371..73045a133c 100644
--- a/ecc/secp256k1/fp/element.go
+++ b/ecc/secp256k1/fp/element.go
@@ -81,6 +81,9 @@ func Modulus() *big.Int {
 // used for Montgomery reduction
 const qInvNeg uint64 = 15580212934572586289
 
+// mu = 2^288 / q needed for partial Barrett reduction
+const mu uint64 = 4294967296
+
 func init() {
 	_modulus.SetString("fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", 16)
 }
@@ -505,32 +508,8 @@ func (z *Element) Select(c int, x0 *Element, x1 *Element) *Element {
 // and is used for testing purposes.
 func _mulGeneric(z, x, y *Element) {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t [5]uint64
 	var D uint64
diff --git a/ecc/secp256k1/fp/element_ops_purego.go b/ecc/secp256k1/fp/element_ops_purego.go
index a8624a511e..f53ffa325b 100644
--- a/ecc/secp256k1/fp/element_ops_purego.go
+++ b/ecc/secp256k1/fp/element_ops_purego.go
@@ -57,53 +57,11 @@ func reduce(z *Element) {
 	_reduceGeneric(z)
 }
 
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	addVecGeneric(*vector, a, b)
-}
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	subVecGeneric(*vector, a, b)
-}
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *Element) {
-	scalarMulVecGeneric(*vector, a, b)
-}
-
 // Mul z = x * y (mod q)
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t [5]uint64
 	var D uint64
diff --git a/ecc/secp256k1/fp/element_test.go b/ecc/secp256k1/fp/element_test.go
index 6f8165b18d..cbe2b50a0c 100644
--- a/ecc/secp256k1/fp/element_test.go
+++ b/ecc/secp256k1/fp/element_test.go
@@ -635,7 +635,6 @@ func TestElementBitLen(t *testing.T) {
 	))
 
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
-
 }
 
 func TestElementButterflies(t *testing.T) {
@@ -705,77 +704,6 @@ func TestElementLexicographicallyLargest(t *testing.T) {
 
 }
 
-func TestElementVecOps(t *testing.T) {
-	assert := require.New(t)
-
-	const N = 7
-	a := make(Vector, N)
-	b := make(Vector, N)
-	c := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a[i].SetRandom()
-		b[i].SetRandom()
-	}
-
-	// Vector addition
-	c.Add(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Add(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector addition failed")
-	}
-
-	// Vector subtraction
-	c.Sub(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Sub(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector subtraction failed")
-	}
-
-	// Vector scaling
-	c.ScalarMul(a, &b[0])
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Mul(&a[i], &b[0])
-		assert.True(c[i].Equal(&expected), "Vector scaling failed")
-	}
-}
-
-func BenchmarkElementVecOps(b *testing.B) {
-	// note; to benchmark against "no asm" version, use the following
-	// build tag: -tags purego
-	const N = 1024
-	a1 := make(Vector, N)
-	b1 := make(Vector, N)
-	c1 := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a1[i].SetRandom()
-		b1[i].SetRandom()
-	}
-
-	b.Run("Add", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Add(a1, b1)
-		}
-	})
-
-	b.Run("Sub", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Sub(a1, b1)
-		}
-	})
-
-	b.Run("ScalarMul", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.ScalarMul(a1, &b1[0])
-		}
-	})
-}
-
 func TestElementAdd(t *testing.T) {
 	t.Parallel()
 	parameters := gopter.DefaultTestParameters()
@@ -2343,38 +2271,38 @@ func gen() gopter.Gen {
 	}
 }
 
-func genFull() gopter.Gen {
-	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+func genRandomFq(genParams *gopter.GenParameters) Element {
+	var g Element
 
-		genRandomFq := func() Element {
-			var g Element
+	g = Element{
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+	}
 
-			g = Element{
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-			}
+	if qElement[3] != ^uint64(0) {
+		g[3] %= (qElement[3] + 1)
+	}
 
-			if qElement[3] != ^uint64(0) {
-				g[3] %= (qElement[3] + 1)
-			}
+	for !g.smallerThanModulus() {
+		g = Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[3] != ^uint64(0) {
+			g[3] %= (qElement[3] + 1)
+		}
+	}
 
-			for !g.smallerThanModulus() {
-				g = Element{
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-				}
-				if qElement[3] != ^uint64(0) {
-					g[3] %= (qElement[3] + 1)
-				}
-			}
+	return g
+}
 
-			return g
-		}
-		a := genRandomFq()
+func genFull() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
 
 		var carry uint64
 		a[0], carry = bits.Add64(a[0], qElement[0], carry)
@@ -2386,3 +2314,11 @@ func genFull() gopter.Gen {
 		return genResult
 	}
 }
+
+func genElement() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
+		genResult := gopter.NewGenResult(a, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/ecc/secp256k1/fp/vector.go b/ecc/secp256k1/fp/vector.go
index 850b3603d8..fa22cb416a 100644
--- a/ecc/secp256k1/fp/vector.go
+++ b/ecc/secp256k1/fp/vector.go
@@ -199,6 +199,43 @@ func (vector Vector) Swap(i, j int) {
 	vector[i], vector[j] = vector[j], vector[i]
 }
 
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	addVecGeneric(*vector, a, b)
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	subVecGeneric(*vector, a, b)
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
+
 func addVecGeneric(res, a, b Vector) {
 	if len(a) != len(b) || len(a) != len(res) {
 		panic("vector.Add: vectors don't have the same length")
@@ -226,6 +263,32 @@ func scalarMulVecGeneric(res, a Vector, b *Element) {
 	}
 }
 
+func sumVecGeneric(res *Element, a Vector) {
+	for i := 0; i < len(a); i++ {
+		res.Add(res, &a[i])
+	}
+}
+
+func innerProductVecGeneric(res *Element, a, b Vector) {
+	if len(a) != len(b) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	var tmp Element
+	for i := 0; i < len(a); i++ {
+		tmp.Mul(&a[i], &b[i])
+		res.Add(res, &tmp)
+	}
+}
+
+func mulVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Mul(&a[i], &b[i])
+	}
+}
+
 // TODO @gbotrel make a public package out of that.
 // execute executes the work function in parallel.
 // this is copy paste from internal/parallel/parallel.go
diff --git a/ecc/secp256k1/fp/vector_test.go b/ecc/secp256k1/fp/vector_test.go
index 5d88af91c0..12f17e21fb 100644
--- a/ecc/secp256k1/fp/vector_test.go
+++ b/ecc/secp256k1/fp/vector_test.go
@@ -18,10 +18,15 @@ package fp
 
 import (
 	"bytes"
+	"fmt"
 	"github.com/stretchr/testify/require"
+	"os"
 	"reflect"
 	"sort"
 	"testing"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/prop"
 )
 
 func TestVectorSort(t *testing.T) {
@@ -88,3 +93,279 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 	}
 	return <-chErr
 }
+
+func TestVectorOps(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = 2
+	} else {
+		parameters.MinSuccessfulTests = 10
+	}
+	properties := gopter.NewProperties(parameters)
+
+	addVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Add(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Add(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	subVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Sub(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Sub(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	scalarMulVector := func(a Vector, b Element) bool {
+		c := make(Vector, len(a))
+		c.ScalarMul(a, &b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b)
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sumVector := func(a Vector) bool {
+		var sum Element
+		computed := a.Sum()
+		for i := 0; i < len(a); i++ {
+			sum.Add(&sum, &a[i])
+		}
+
+		return sum.Equal(&computed)
+	}
+
+	innerProductVector := func(a, b Vector) bool {
+		computed := a.InnerProduct(b)
+		var innerProduct Element
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			innerProduct.Add(&innerProduct, &tmp)
+		}
+
+		return innerProduct.Equal(&computed)
+	}
+
+	mulVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		a[0].SetUint64(0x24)
+		b[0].SetUint64(0x42)
+		c.Mul(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sizes := []int{1, 2, 3, 4, 8, 9, 15, 16, 509, 510, 511, 512, 513, 514}
+	type genPair struct {
+		g1, g2 gopter.Gen
+		label  string
+	}
+
+	for _, size := range sizes {
+		generators := []genPair{
+			{genZeroVector(size), genZeroVector(size), "zero vectors"},
+			{genMaxVector(size), genMaxVector(size), "max vectors"},
+			{genVector(size), genVector(size), "random vectors"},
+			{genVector(size), genZeroVector(size), "random and zero vectors"},
+		}
+		for _, gp := range generators {
+			properties.Property(fmt.Sprintf("vector addition %d - %s", size, gp.label), prop.ForAll(
+				addVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector subtraction %d - %s", size, gp.label), prop.ForAll(
+				subVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector scalar multiplication %d - %s", size, gp.label), prop.ForAll(
+				scalarMulVector,
+				gp.g1,
+				genElement(),
+			))
+
+			properties.Property(fmt.Sprintf("vector sum %d - %s", size, gp.label), prop.ForAll(
+				sumVector,
+				gp.g1,
+			))
+
+			properties.Property(fmt.Sprintf("vector inner product %d - %s", size, gp.label), prop.ForAll(
+				innerProductVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector multiplication %d - %s", size, gp.label), prop.ForAll(
+				mulVector,
+				gp.g1,
+				gp.g2,
+			))
+		}
+	}
+
+	properties.TestingRun(t, gopter.NewFormatedReporter(false, 260, os.Stdout))
+}
+
+func BenchmarkVectorOps(b *testing.B) {
+	// note; to benchmark against "no asm" version, use the following
+	// build tag: -tags purego
+	const N = 1 << 24
+	a1 := make(Vector, N)
+	b1 := make(Vector, N)
+	c1 := make(Vector, N)
+	var mixer Element
+	mixer.SetRandom()
+	for i := 1; i < N; i++ {
+		a1[i-1].SetUint64(uint64(i)).
+			Mul(&a1[i-1], &mixer)
+		b1[i-1].SetUint64(^uint64(i)).
+			Mul(&b1[i-1], &mixer)
+	}
+
+	for n := 1 << 4; n <= N; n <<= 1 {
+		b.Run(fmt.Sprintf("add %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Add(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sub %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Sub(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("scalarMul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.ScalarMul(_a, &mixer)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sum %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.Sum()
+			}
+		})
+
+		b.Run(fmt.Sprintf("innerProduct %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.InnerProduct(_b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("mul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Mul(_a, _b)
+			}
+		})
+	}
+}
+
+func genZeroVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genMaxVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+
+		qMinusOne := qElement
+		qMinusOne[0]--
+
+		for i := 0; i < size; i++ {
+			g[i] = qMinusOne
+		}
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		mixer := Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[3] != ^uint64(0) {
+			mixer[3] %= (qElement[3] + 1)
+		}
+
+		for !mixer.smallerThanModulus() {
+			mixer = Element{
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+			}
+			if qElement[3] != ^uint64(0) {
+				mixer[3] %= (qElement[3] + 1)
+			}
+		}
+
+		for i := 1; i <= size; i++ {
+			g[i-1].SetUint64(uint64(i)).
+				Mul(&g[i-1], &mixer)
+		}
+
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/ecc/secp256k1/fr/element.go b/ecc/secp256k1/fr/element.go
index 6afe3590b6..e2f81b66b3 100644
--- a/ecc/secp256k1/fr/element.go
+++ b/ecc/secp256k1/fr/element.go
@@ -81,6 +81,9 @@ func Modulus() *big.Int {
 // used for Montgomery reduction
 const qInvNeg uint64 = 5408259542528602431
 
+// mu = 2^288 / q needed for partial Barrett reduction
+const mu uint64 = 4294967296
+
 func init() {
 	_modulus.SetString("fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141", 16)
 }
@@ -505,32 +508,8 @@ func (z *Element) Select(c int, x0 *Element, x1 *Element) *Element {
 // and is used for testing purposes.
 func _mulGeneric(z, x, y *Element) {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t [5]uint64
 	var D uint64
diff --git a/ecc/secp256k1/fr/element_ops_purego.go b/ecc/secp256k1/fr/element_ops_purego.go
index 1a46f6d791..ef83ea20a5 100644
--- a/ecc/secp256k1/fr/element_ops_purego.go
+++ b/ecc/secp256k1/fr/element_ops_purego.go
@@ -57,53 +57,11 @@ func reduce(z *Element) {
 	_reduceGeneric(z)
 }
 
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	addVecGeneric(*vector, a, b)
-}
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	subVecGeneric(*vector, a, b)
-}
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *Element) {
-	scalarMulVecGeneric(*vector, a, b)
-}
-
 // Mul z = x * y (mod q)
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t [5]uint64
 	var D uint64
diff --git a/ecc/secp256k1/fr/element_test.go b/ecc/secp256k1/fr/element_test.go
index f554db8e3c..2ab020991b 100644
--- a/ecc/secp256k1/fr/element_test.go
+++ b/ecc/secp256k1/fr/element_test.go
@@ -635,7 +635,6 @@ func TestElementBitLen(t *testing.T) {
 	))
 
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
-
 }
 
 func TestElementButterflies(t *testing.T) {
@@ -705,77 +704,6 @@ func TestElementLexicographicallyLargest(t *testing.T) {
 
 }
 
-func TestElementVecOps(t *testing.T) {
-	assert := require.New(t)
-
-	const N = 7
-	a := make(Vector, N)
-	b := make(Vector, N)
-	c := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a[i].SetRandom()
-		b[i].SetRandom()
-	}
-
-	// Vector addition
-	c.Add(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Add(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector addition failed")
-	}
-
-	// Vector subtraction
-	c.Sub(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Sub(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector subtraction failed")
-	}
-
-	// Vector scaling
-	c.ScalarMul(a, &b[0])
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Mul(&a[i], &b[0])
-		assert.True(c[i].Equal(&expected), "Vector scaling failed")
-	}
-}
-
-func BenchmarkElementVecOps(b *testing.B) {
-	// note; to benchmark against "no asm" version, use the following
-	// build tag: -tags purego
-	const N = 1024
-	a1 := make(Vector, N)
-	b1 := make(Vector, N)
-	c1 := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a1[i].SetRandom()
-		b1[i].SetRandom()
-	}
-
-	b.Run("Add", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Add(a1, b1)
-		}
-	})
-
-	b.Run("Sub", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Sub(a1, b1)
-		}
-	})
-
-	b.Run("ScalarMul", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.ScalarMul(a1, &b1[0])
-		}
-	})
-}
-
 func TestElementAdd(t *testing.T) {
 	t.Parallel()
 	parameters := gopter.DefaultTestParameters()
@@ -2343,38 +2271,38 @@ func gen() gopter.Gen {
 	}
 }
 
-func genFull() gopter.Gen {
-	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+func genRandomFq(genParams *gopter.GenParameters) Element {
+	var g Element
 
-		genRandomFq := func() Element {
-			var g Element
+	g = Element{
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+	}
 
-			g = Element{
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-			}
+	if qElement[3] != ^uint64(0) {
+		g[3] %= (qElement[3] + 1)
+	}
 
-			if qElement[3] != ^uint64(0) {
-				g[3] %= (qElement[3] + 1)
-			}
+	for !g.smallerThanModulus() {
+		g = Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[3] != ^uint64(0) {
+			g[3] %= (qElement[3] + 1)
+		}
+	}
 
-			for !g.smallerThanModulus() {
-				g = Element{
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-				}
-				if qElement[3] != ^uint64(0) {
-					g[3] %= (qElement[3] + 1)
-				}
-			}
+	return g
+}
 
-			return g
-		}
-		a := genRandomFq()
+func genFull() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
 
 		var carry uint64
 		a[0], carry = bits.Add64(a[0], qElement[0], carry)
@@ -2386,3 +2314,11 @@ func genFull() gopter.Gen {
 		return genResult
 	}
 }
+
+func genElement() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
+		genResult := gopter.NewGenResult(a, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/ecc/secp256k1/fr/vector.go b/ecc/secp256k1/fr/vector.go
index f39828547f..bcc71efcd8 100644
--- a/ecc/secp256k1/fr/vector.go
+++ b/ecc/secp256k1/fr/vector.go
@@ -199,6 +199,43 @@ func (vector Vector) Swap(i, j int) {
 	vector[i], vector[j] = vector[j], vector[i]
 }
 
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	addVecGeneric(*vector, a, b)
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	subVecGeneric(*vector, a, b)
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
+
 func addVecGeneric(res, a, b Vector) {
 	if len(a) != len(b) || len(a) != len(res) {
 		panic("vector.Add: vectors don't have the same length")
@@ -226,6 +263,32 @@ func scalarMulVecGeneric(res, a Vector, b *Element) {
 	}
 }
 
+func sumVecGeneric(res *Element, a Vector) {
+	for i := 0; i < len(a); i++ {
+		res.Add(res, &a[i])
+	}
+}
+
+func innerProductVecGeneric(res *Element, a, b Vector) {
+	if len(a) != len(b) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	var tmp Element
+	for i := 0; i < len(a); i++ {
+		tmp.Mul(&a[i], &b[i])
+		res.Add(res, &tmp)
+	}
+}
+
+func mulVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Mul(&a[i], &b[i])
+	}
+}
+
 // TODO @gbotrel make a public package out of that.
 // execute executes the work function in parallel.
 // this is copy paste from internal/parallel/parallel.go
diff --git a/ecc/secp256k1/fr/vector_test.go b/ecc/secp256k1/fr/vector_test.go
index e58f2d9a38..b6344c18b7 100644
--- a/ecc/secp256k1/fr/vector_test.go
+++ b/ecc/secp256k1/fr/vector_test.go
@@ -18,10 +18,15 @@ package fr
 
 import (
 	"bytes"
+	"fmt"
 	"github.com/stretchr/testify/require"
+	"os"
 	"reflect"
 	"sort"
 	"testing"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/prop"
 )
 
 func TestVectorSort(t *testing.T) {
@@ -88,3 +93,279 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 	}
 	return <-chErr
 }
+
+func TestVectorOps(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = 2
+	} else {
+		parameters.MinSuccessfulTests = 10
+	}
+	properties := gopter.NewProperties(parameters)
+
+	addVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Add(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Add(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	subVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Sub(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Sub(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	scalarMulVector := func(a Vector, b Element) bool {
+		c := make(Vector, len(a))
+		c.ScalarMul(a, &b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b)
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sumVector := func(a Vector) bool {
+		var sum Element
+		computed := a.Sum()
+		for i := 0; i < len(a); i++ {
+			sum.Add(&sum, &a[i])
+		}
+
+		return sum.Equal(&computed)
+	}
+
+	innerProductVector := func(a, b Vector) bool {
+		computed := a.InnerProduct(b)
+		var innerProduct Element
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			innerProduct.Add(&innerProduct, &tmp)
+		}
+
+		return innerProduct.Equal(&computed)
+	}
+
+	mulVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		a[0].SetUint64(0x24)
+		b[0].SetUint64(0x42)
+		c.Mul(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sizes := []int{1, 2, 3, 4, 8, 9, 15, 16, 509, 510, 511, 512, 513, 514}
+	type genPair struct {
+		g1, g2 gopter.Gen
+		label  string
+	}
+
+	for _, size := range sizes {
+		generators := []genPair{
+			{genZeroVector(size), genZeroVector(size), "zero vectors"},
+			{genMaxVector(size), genMaxVector(size), "max vectors"},
+			{genVector(size), genVector(size), "random vectors"},
+			{genVector(size), genZeroVector(size), "random and zero vectors"},
+		}
+		for _, gp := range generators {
+			properties.Property(fmt.Sprintf("vector addition %d - %s", size, gp.label), prop.ForAll(
+				addVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector subtraction %d - %s", size, gp.label), prop.ForAll(
+				subVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector scalar multiplication %d - %s", size, gp.label), prop.ForAll(
+				scalarMulVector,
+				gp.g1,
+				genElement(),
+			))
+
+			properties.Property(fmt.Sprintf("vector sum %d - %s", size, gp.label), prop.ForAll(
+				sumVector,
+				gp.g1,
+			))
+
+			properties.Property(fmt.Sprintf("vector inner product %d - %s", size, gp.label), prop.ForAll(
+				innerProductVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector multiplication %d - %s", size, gp.label), prop.ForAll(
+				mulVector,
+				gp.g1,
+				gp.g2,
+			))
+		}
+	}
+
+	properties.TestingRun(t, gopter.NewFormatedReporter(false, 260, os.Stdout))
+}
+
+func BenchmarkVectorOps(b *testing.B) {
+	// note; to benchmark against "no asm" version, use the following
+	// build tag: -tags purego
+	const N = 1 << 24
+	a1 := make(Vector, N)
+	b1 := make(Vector, N)
+	c1 := make(Vector, N)
+	var mixer Element
+	mixer.SetRandom()
+	for i := 1; i < N; i++ {
+		a1[i-1].SetUint64(uint64(i)).
+			Mul(&a1[i-1], &mixer)
+		b1[i-1].SetUint64(^uint64(i)).
+			Mul(&b1[i-1], &mixer)
+	}
+
+	for n := 1 << 4; n <= N; n <<= 1 {
+		b.Run(fmt.Sprintf("add %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Add(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sub %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Sub(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("scalarMul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.ScalarMul(_a, &mixer)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sum %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.Sum()
+			}
+		})
+
+		b.Run(fmt.Sprintf("innerProduct %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.InnerProduct(_b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("mul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Mul(_a, _b)
+			}
+		})
+	}
+}
+
+func genZeroVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genMaxVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+
+		qMinusOne := qElement
+		qMinusOne[0]--
+
+		for i := 0; i < size; i++ {
+			g[i] = qMinusOne
+		}
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		mixer := Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[3] != ^uint64(0) {
+			mixer[3] %= (qElement[3] + 1)
+		}
+
+		for !mixer.smallerThanModulus() {
+			mixer = Element{
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+			}
+			if qElement[3] != ^uint64(0) {
+				mixer[3] %= (qElement[3] + 1)
+			}
+		}
+
+		for i := 1; i <= size; i++ {
+			g[i-1].SetUint64(uint64(i)).
+				Mul(&g[i-1], &mixer)
+		}
+
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/ecc/stark-curve/fp/asm.go b/ecc/stark-curve/fp/asm_adx.go
similarity index 100%
rename from ecc/stark-curve/fp/asm.go
rename to ecc/stark-curve/fp/asm_adx.go
diff --git a/ecc/stark-curve/fp/asm_avx.go b/ecc/stark-curve/fp/asm_avx.go
new file mode 100644
index 0000000000..cea035ee84
--- /dev/null
+++ b/ecc/stark-curve/fp/asm_avx.go
@@ -0,0 +1,27 @@
+//go:build !noavx
+// +build !noavx
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fp
+
+import "golang.org/x/sys/cpu"
+
+var (
+	supportAvx512 = supportAdx && cpu.X86.HasAVX512 && cpu.X86.HasAVX512DQ
+	_             = supportAvx512
+)
diff --git a/ecc/stark-curve/fp/asm_noavx.go b/ecc/stark-curve/fp/asm_noavx.go
new file mode 100644
index 0000000000..9ca08a375a
--- /dev/null
+++ b/ecc/stark-curve/fp/asm_noavx.go
@@ -0,0 +1,22 @@
+//go:build noavx
+// +build noavx
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fp
+
+const supportAvx512 = false
diff --git a/ecc/stark-curve/fp/element.go b/ecc/stark-curve/fp/element.go
index 7a057be069..1c53dcb090 100644
--- a/ecc/stark-curve/fp/element.go
+++ b/ecc/stark-curve/fp/element.go
@@ -81,6 +81,9 @@ func Modulus() *big.Int {
 // used for Montgomery reduction
 const qInvNeg uint64 = 18446744073709551615
 
+// mu = 2^288 / q needed for partial Barrett reduction
+const mu uint64 = 137438953471
+
 func init() {
 	_modulus.SetString("800000000000011000000000000000000000000000000000000000000000001", 16)
 }
@@ -477,32 +480,8 @@ func (z *Element) Select(c int, x0 *Element, x1 *Element) *Element {
 // and is used for testing purposes.
 func _mulGeneric(z, x, y *Element) {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t [5]uint64
 	var D uint64
diff --git a/ecc/stark-curve/fp/element_mul_amd64.s b/ecc/stark-curve/fp/element_mul_amd64.s
deleted file mode 100644
index fab328c861..0000000000
--- a/ecc/stark-curve/fp/element_mul_amd64.s
+++ /dev/null
@@ -1,487 +0,0 @@
-// +build !purego
-
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $1
-DATA q<>+8(SB)/8, $0
-DATA q<>+16(SB)/8, $0
-DATA q<>+24(SB)/8, $0x0800000000000011
-GLOBL q<>(SB), (RODATA+NOPTR), $32
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0xffffffffffffffff
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, rb0, rb1, rb2, rb3) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-
-// mul(res, x, y *Element)
-TEXT ·mul(SB), $24-24
-
-	// the algorithm is described in the Element.Mul declaration (.go)
-	// however, to benefit from the ADCX and ADOX carry chains
-	// we split the inner loops in 2:
-	// for i=0 to N-1
-	// 		for j=0 to N-1
-	// 		    (A,t[j])  := t[j] + x[j]*y[i] + A
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C + A
-
-	NO_LOCAL_POINTERS
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_1
-	MOVQ x+8(FP), SI
-
-	// x[0] -> DI
-	// x[1] -> R8
-	// x[2] -> R9
-	// x[3] -> R10
-	MOVQ 0(SI), DI
-	MOVQ 8(SI), R8
-	MOVQ 16(SI), R9
-	MOVQ 24(SI), R10
-	MOVQ y+16(FP), R11
-
-	// A -> BP
-	// t[0] -> R14
-	// t[1] -> R13
-	// t[2] -> CX
-	// t[3] -> BX
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 0(R11), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ DI, R14, R13
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ R8, AX, CX
-	ADOXQ AX, R13
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ R9, AX, BX
-	ADOXQ AX, CX
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 8(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R13
-	MULXQ R8, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, CX
-	MULXQ R9, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, BX
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 16(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R13
-	MULXQ R8, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, CX
-	MULXQ R9, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, BX
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 24(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R13
-	MULXQ R8, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, CX
-	MULXQ R9, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, BX
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// reduce element(R14,R13,CX,BX) using temp registers (SI,R12,R11,DI)
-	REDUCE(R14,R13,CX,BX,SI,R12,R11,DI)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R13, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	RET
-
-noAdx_1:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	MOVQ x+8(FP), AX
-	MOVQ AX, 8(SP)
-	MOVQ y+16(FP), AX
-	MOVQ AX, 16(SP)
-	CALL ·_mulGeneric(SB)
-	RET
-
-TEXT ·fromMont(SB), $8-8
-	NO_LOCAL_POINTERS
-
-	// the algorithm is described here
-	// https://hackmd.io/@gnark/modular_multiplication
-	// when y = 1 we have:
-	// for i=0 to N-1
-	// 		t[i] = x[i]
-	// for i=0 to N-1
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_2
-	MOVQ res+0(FP), DX
-	MOVQ 0(DX), R14
-	MOVQ 8(DX), R13
-	MOVQ 16(DX), CX
-	MOVQ 24(DX), BX
-	XORQ DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-
-	// reduce element(R14,R13,CX,BX) using temp registers (SI,DI,R8,R9)
-	REDUCE(R14,R13,CX,BX,SI,DI,R8,R9)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R13, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	RET
-
-noAdx_2:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	CALL ·_fromMontGeneric(SB)
-	RET
diff --git a/ecc/stark-curve/fp/element_ops_amd64.go b/ecc/stark-curve/fp/element_ops_amd64.go
index 6f16baf686..2ab1a98399 100644
--- a/ecc/stark-curve/fp/element_ops_amd64.go
+++ b/ecc/stark-curve/fp/element_ops_amd64.go
@@ -51,7 +51,8 @@ func (vector *Vector) Add(a, b Vector) {
 	if len(a) != len(b) || len(a) != len(*vector) {
 		panic("vector.Add: vectors don't have the same length")
 	}
-	addVec(&(*vector)[0], &a[0], &b[0], uint64(len(a)))
+	n := uint64(len(a))
+	addVec(&(*vector)[0], &a[0], &b[0], n)
 }
 
 //go:noescape
@@ -75,59 +76,123 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	if len(a) != len(*vector) {
 		panic("vector.ScalarMul: vectors don't have the same length")
 	}
-	scalarMulVec(&(*vector)[0], &a[0], b, uint64(len(a)))
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || uint64(len(a)) >= maxN {
+		// call scalarMulVecGeneric
+		scalarMulVecGeneric(*vector, a, b)
+		return
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	// the code for scalarMul is identical to mulVec; and it expects at least
+	// 2 elements in the vector to fill the Z registers
+	var bb [2]Element
+	bb[0] = *b
+	bb[1] = *b
+	const blockSize = 16
+	scalarMulVec(&(*vector)[0], &a[0], &bb[0], n/blockSize, qInvNeg)
+	if n%blockSize != 0 {
+		// call scalarMulVecGeneric on the rest
+		start := n - n%blockSize
+		scalarMulVecGeneric((*vector)[start:], a[start:], b)
+	}
+}
+
+//go:noescape
+func scalarMulVec(res, a, b *Element, n uint64, qInvNeg uint64)
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	const minN = 16 * 7 // AVX512 slower than generic for small n
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n <= minN || n >= maxN {
+		// call sumVecGeneric
+		sumVecGeneric(&res, *vector)
+		return
+	}
+	sumVec(&res, &(*vector)[0], uint64(len(*vector)))
+	return
 }
 
 //go:noescape
-func scalarMulVec(res, a, b *Element, n uint64)
+func sumVec(res *Element, a *Element, n uint64)
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	if n != uint64(len(other)) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n >= maxN {
+		// call innerProductVecGeneric
+		// note; we could split the vector into smaller chunks and call innerProductVec
+		innerProductVecGeneric(&res, *vector, other)
+		return
+	}
+	innerProdVec(&res[0], &(*vector)[0], &other[0], uint64(len(*vector)))
+
+	return
+}
+
+//go:noescape
+func innerProdVec(res *uint64, a, b *Element, n uint64)
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n >= maxN {
+		// call mulVecGeneric
+		mulVecGeneric(*vector, a, b)
+		return
+	}
+
+	const blockSize = 16
+	mulVec(&(*vector)[0], &a[0], &b[0], n/blockSize, qInvNeg)
+	if n%blockSize != 0 {
+		// call mulVecGeneric on the rest
+		start := n - n%blockSize
+		mulVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+
+}
+
+// Patterns use for transposing the vectors in mulVec
+var (
+	pattern1 = [8]uint64{0, 8, 1, 9, 2, 10, 3, 11}
+	pattern2 = [8]uint64{12, 4, 13, 5, 14, 6, 15, 7}
+	pattern3 = [8]uint64{0, 1, 8, 9, 2, 3, 10, 11}
+	pattern4 = [8]uint64{12, 13, 4, 5, 14, 15, 6, 7}
+)
+
+//go:noescape
+func mulVec(res, a, b *Element, n uint64, qInvNeg uint64)
 
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	mul(z, x, y)
 	return z
diff --git a/ecc/stark-curve/fp/element_ops_amd64.s b/ecc/stark-curve/fp/element_ops_amd64.s
index 914653b705..6c42136a7a 100644
--- a/ecc/stark-curve/fp/element_ops_amd64.s
+++ b/ecc/stark-curve/fp/element_ops_amd64.s
@@ -1,627 +1,6 @@
 // +build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+// We include the hash to force the Go compiler to recompile: 9425145785761608449
+#include "../../../field/asm/element_4w_amd64.s"
 
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $1
-DATA q<>+8(SB)/8, $0
-DATA q<>+16(SB)/8, $0
-DATA q<>+24(SB)/8, $0x0800000000000011
-GLOBL q<>(SB), (RODATA+NOPTR), $32
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0xffffffffffffffff
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, rb0, rb1, rb2, rb3) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-
-TEXT ·reduce(SB), NOSPLIT, $0-8
-	MOVQ res+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// MulBy3(x *Element)
-TEXT ·MulBy3(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// MulBy5(x *Element)
-TEXT ·MulBy5(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R15,DI,R8,R9)
-	REDUCE(DX,CX,BX,SI,R15,DI,R8,R9)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// MulBy13(x *Element)
-TEXT ·MulBy13(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
-
-	MOVQ DX, R11
-	MOVQ CX, R12
-	MOVQ BX, R13
-	MOVQ SI, R14
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ R11, DX
-	ADCQ R12, CX
-	ADCQ R13, BX
-	ADCQ R14, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// Butterfly(a, b *Element) sets a = a + b; b = a - b
-TEXT ·Butterfly(SB), NOSPLIT, $0-16
-	MOVQ    a+0(FP), AX
-	MOVQ    0(AX), CX
-	MOVQ    8(AX), BX
-	MOVQ    16(AX), SI
-	MOVQ    24(AX), DI
-	MOVQ    CX, R8
-	MOVQ    BX, R9
-	MOVQ    SI, R10
-	MOVQ    DI, R11
-	XORQ    AX, AX
-	MOVQ    b+8(FP), DX
-	ADDQ    0(DX), CX
-	ADCQ    8(DX), BX
-	ADCQ    16(DX), SI
-	ADCQ    24(DX), DI
-	SUBQ    0(DX), R8
-	SBBQ    8(DX), R9
-	SBBQ    16(DX), R10
-	SBBQ    24(DX), R11
-	MOVQ    $1, R12
-	MOVQ    $0, R13
-	MOVQ    $0, R14
-	MOVQ    $0x0800000000000011, R15
-	CMOVQCC AX, R12
-	CMOVQCC AX, R13
-	CMOVQCC AX, R14
-	CMOVQCC AX, R15
-	ADDQ    R12, R8
-	ADCQ    R13, R9
-	ADCQ    R14, R10
-	ADCQ    R15, R11
-	MOVQ    R8, 0(DX)
-	MOVQ    R9, 8(DX)
-	MOVQ    R10, 16(DX)
-	MOVQ    R11, 24(DX)
-
-	// reduce element(CX,BX,SI,DI) using temp registers (R8,R9,R10,R11)
-	REDUCE(CX,BX,SI,DI,R8,R9,R10,R11)
-
-	MOVQ a+0(FP), AX
-	MOVQ CX, 0(AX)
-	MOVQ BX, 8(AX)
-	MOVQ SI, 16(AX)
-	MOVQ DI, 24(AX)
-	RET
-
-// addVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] + b[0...n]
-TEXT ·addVec(SB), NOSPLIT, $0-32
-	MOVQ res+0(FP), CX
-	MOVQ a+8(FP), AX
-	MOVQ b+16(FP), DX
-	MOVQ n+24(FP), BX
-
-loop_1:
-	TESTQ BX, BX
-	JEQ   done_2 // n == 0, we are done
-
-	// a[0] -> SI
-	// a[1] -> DI
-	// a[2] -> R8
-	// a[3] -> R9
-	MOVQ 0(AX), SI
-	MOVQ 8(AX), DI
-	MOVQ 16(AX), R8
-	MOVQ 24(AX), R9
-	ADDQ 0(DX), SI
-	ADCQ 8(DX), DI
-	ADCQ 16(DX), R8
-	ADCQ 24(DX), R9
-
-	// reduce element(SI,DI,R8,R9) using temp registers (R10,R11,R12,R13)
-	REDUCE(SI,DI,R8,R9,R10,R11,R12,R13)
-
-	MOVQ SI, 0(CX)
-	MOVQ DI, 8(CX)
-	MOVQ R8, 16(CX)
-	MOVQ R9, 24(CX)
-
-	// increment pointers to visit next element
-	ADDQ $32, AX
-	ADDQ $32, DX
-	ADDQ $32, CX
-	DECQ BX      // decrement n
-	JMP  loop_1
-
-done_2:
-	RET
-
-// subVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] - b[0...n]
-TEXT ·subVec(SB), NOSPLIT, $0-32
-	MOVQ res+0(FP), CX
-	MOVQ a+8(FP), AX
-	MOVQ b+16(FP), DX
-	MOVQ n+24(FP), BX
-	XORQ SI, SI
-
-loop_3:
-	TESTQ BX, BX
-	JEQ   done_4 // n == 0, we are done
-
-	// a[0] -> DI
-	// a[1] -> R8
-	// a[2] -> R9
-	// a[3] -> R10
-	MOVQ 0(AX), DI
-	MOVQ 8(AX), R8
-	MOVQ 16(AX), R9
-	MOVQ 24(AX), R10
-	SUBQ 0(DX), DI
-	SBBQ 8(DX), R8
-	SBBQ 16(DX), R9
-	SBBQ 24(DX), R10
-
-	// reduce (a-b) mod q
-	// q[0] -> R11
-	// q[1] -> R12
-	// q[2] -> R13
-	// q[3] -> R14
-	MOVQ    $1, R11
-	MOVQ    $0, R12
-	MOVQ    $0, R13
-	MOVQ    $0x0800000000000011, R14
-	CMOVQCC SI, R11
-	CMOVQCC SI, R12
-	CMOVQCC SI, R13
-	CMOVQCC SI, R14
-
-	// add registers (q or 0) to a, and set to result
-	ADDQ R11, DI
-	ADCQ R12, R8
-	ADCQ R13, R9
-	ADCQ R14, R10
-	MOVQ DI, 0(CX)
-	MOVQ R8, 8(CX)
-	MOVQ R9, 16(CX)
-	MOVQ R10, 24(CX)
-
-	// increment pointers to visit next element
-	ADDQ $32, AX
-	ADDQ $32, DX
-	ADDQ $32, CX
-	DECQ BX      // decrement n
-	JMP  loop_3
-
-done_4:
-	RET
-
-// scalarMulVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] * b
-TEXT ·scalarMulVec(SB), $56-32
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_5
-	MOVQ a+8(FP), R11
-	MOVQ b+16(FP), R10
-	MOVQ n+24(FP), R12
-
-	// scalar[0] -> SI
-	// scalar[1] -> DI
-	// scalar[2] -> R8
-	// scalar[3] -> R9
-	MOVQ 0(R10), SI
-	MOVQ 8(R10), DI
-	MOVQ 16(R10), R8
-	MOVQ 24(R10), R9
-	MOVQ res+0(FP), R10
-
-loop_6:
-	TESTQ R12, R12
-	JEQ   done_7   // n == 0, we are done
-
-	// TODO @gbotrel this is generated from the same macro as the unit mul, we should refactor this in a single asm function
-	// A -> BP
-	// t[0] -> R14
-	// t[1] -> R15
-	// t[2] -> CX
-	// t[3] -> BX
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 0(R11), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ SI, R14, R15
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ DI, AX, CX
-	ADOXQ AX, R15
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ R8, AX, BX
-	ADOXQ AX, CX
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 8(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ SI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R15
-	MULXQ DI, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, CX
-	MULXQ R8, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, BX
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 16(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ SI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R15
-	MULXQ DI, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, CX
-	MULXQ R8, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, BX
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 24(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ SI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R15
-	MULXQ DI, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, CX
-	MULXQ R8, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, BX
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// reduce t mod q
-	// reduce element(R14,R15,CX,BX) using temp registers (R13,AX,DX,s0-8(SP))
-	REDUCE(R14,R15,CX,BX,R13,AX,DX,s0-8(SP))
-
-	MOVQ R14, 0(R10)
-	MOVQ R15, 8(R10)
-	MOVQ CX, 16(R10)
-	MOVQ BX, 24(R10)
-
-	// increment pointers to visit next element
-	ADDQ $32, R11
-	ADDQ $32, R10
-	DECQ R12      // decrement n
-	JMP  loop_6
-
-done_7:
-	RET
-
-noAdx_5:
-	MOVQ n+24(FP), DX
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	MOVQ DX, 8(SP)
-	MOVQ DX, 16(SP)
-	MOVQ a+8(FP), AX
-	MOVQ AX, 24(SP)
-	MOVQ DX, 32(SP)
-	MOVQ DX, 40(SP)
-	MOVQ b+16(FP), AX
-	MOVQ AX, 48(SP)
-	CALL ·scalarMulVecGeneric(SB)
-	RET
diff --git a/ecc/stark-curve/fp/element_ops_purego.go b/ecc/stark-curve/fp/element_ops_purego.go
index 4906d13e0c..19cb3649be 100644
--- a/ecc/stark-curve/fp/element_ops_purego.go
+++ b/ecc/stark-curve/fp/element_ops_purego.go
@@ -78,53 +78,32 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	scalarMulVecGeneric(*vector, a, b)
 }
 
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
+
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t0, t1, t2, t3 uint64
 	var u0, u1, u2, u3 uint64
diff --git a/ecc/stark-curve/fp/element_test.go b/ecc/stark-curve/fp/element_test.go
index 87e38f7c10..c33f3f21b6 100644
--- a/ecc/stark-curve/fp/element_test.go
+++ b/ecc/stark-curve/fp/element_test.go
@@ -637,7 +637,6 @@ func TestElementBitLen(t *testing.T) {
 	))
 
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
-
 }
 
 func TestElementButterflies(t *testing.T) {
@@ -707,77 +706,6 @@ func TestElementLexicographicallyLargest(t *testing.T) {
 
 }
 
-func TestElementVecOps(t *testing.T) {
-	assert := require.New(t)
-
-	const N = 7
-	a := make(Vector, N)
-	b := make(Vector, N)
-	c := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a[i].SetRandom()
-		b[i].SetRandom()
-	}
-
-	// Vector addition
-	c.Add(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Add(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector addition failed")
-	}
-
-	// Vector subtraction
-	c.Sub(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Sub(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector subtraction failed")
-	}
-
-	// Vector scaling
-	c.ScalarMul(a, &b[0])
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Mul(&a[i], &b[0])
-		assert.True(c[i].Equal(&expected), "Vector scaling failed")
-	}
-}
-
-func BenchmarkElementVecOps(b *testing.B) {
-	// note; to benchmark against "no asm" version, use the following
-	// build tag: -tags purego
-	const N = 1024
-	a1 := make(Vector, N)
-	b1 := make(Vector, N)
-	c1 := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a1[i].SetRandom()
-		b1[i].SetRandom()
-	}
-
-	b.Run("Add", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Add(a1, b1)
-		}
-	})
-
-	b.Run("Sub", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Sub(a1, b1)
-		}
-	})
-
-	b.Run("ScalarMul", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.ScalarMul(a1, &b1[0])
-		}
-	})
-}
-
 func TestElementAdd(t *testing.T) {
 	t.Parallel()
 	parameters := gopter.DefaultTestParameters()
@@ -2345,38 +2273,38 @@ func gen() gopter.Gen {
 	}
 }
 
-func genFull() gopter.Gen {
-	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+func genRandomFq(genParams *gopter.GenParameters) Element {
+	var g Element
 
-		genRandomFq := func() Element {
-			var g Element
+	g = Element{
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+	}
 
-			g = Element{
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-			}
+	if qElement[3] != ^uint64(0) {
+		g[3] %= (qElement[3] + 1)
+	}
 
-			if qElement[3] != ^uint64(0) {
-				g[3] %= (qElement[3] + 1)
-			}
+	for !g.smallerThanModulus() {
+		g = Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[3] != ^uint64(0) {
+			g[3] %= (qElement[3] + 1)
+		}
+	}
 
-			for !g.smallerThanModulus() {
-				g = Element{
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-				}
-				if qElement[3] != ^uint64(0) {
-					g[3] %= (qElement[3] + 1)
-				}
-			}
+	return g
+}
 
-			return g
-		}
-		a := genRandomFq()
+func genFull() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
 
 		var carry uint64
 		a[0], carry = bits.Add64(a[0], qElement[0], carry)
@@ -2389,6 +2317,14 @@ func genFull() gopter.Gen {
 	}
 }
 
+func genElement() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
+		genResult := gopter.NewGenResult(a, gopter.NoShrinker)
+		return genResult
+	}
+}
+
 func (z *Element) matchVeryBigInt(aHi uint64, aInt *big.Int) error {
 	var modulus big.Int
 	var aIntMod big.Int
diff --git a/ecc/stark-curve/fp/vector.go b/ecc/stark-curve/fp/vector.go
index 850b3603d8..c97b4283ce 100644
--- a/ecc/stark-curve/fp/vector.go
+++ b/ecc/stark-curve/fp/vector.go
@@ -226,6 +226,32 @@ func scalarMulVecGeneric(res, a Vector, b *Element) {
 	}
 }
 
+func sumVecGeneric(res *Element, a Vector) {
+	for i := 0; i < len(a); i++ {
+		res.Add(res, &a[i])
+	}
+}
+
+func innerProductVecGeneric(res *Element, a, b Vector) {
+	if len(a) != len(b) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	var tmp Element
+	for i := 0; i < len(a); i++ {
+		tmp.Mul(&a[i], &b[i])
+		res.Add(res, &tmp)
+	}
+}
+
+func mulVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Mul(&a[i], &b[i])
+	}
+}
+
 // TODO @gbotrel make a public package out of that.
 // execute executes the work function in parallel.
 // this is copy paste from internal/parallel/parallel.go
diff --git a/ecc/stark-curve/fp/vector_test.go b/ecc/stark-curve/fp/vector_test.go
index 5d88af91c0..12f17e21fb 100644
--- a/ecc/stark-curve/fp/vector_test.go
+++ b/ecc/stark-curve/fp/vector_test.go
@@ -18,10 +18,15 @@ package fp
 
 import (
 	"bytes"
+	"fmt"
 	"github.com/stretchr/testify/require"
+	"os"
 	"reflect"
 	"sort"
 	"testing"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/prop"
 )
 
 func TestVectorSort(t *testing.T) {
@@ -88,3 +93,279 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 	}
 	return <-chErr
 }
+
+func TestVectorOps(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = 2
+	} else {
+		parameters.MinSuccessfulTests = 10
+	}
+	properties := gopter.NewProperties(parameters)
+
+	addVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Add(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Add(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	subVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Sub(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Sub(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	scalarMulVector := func(a Vector, b Element) bool {
+		c := make(Vector, len(a))
+		c.ScalarMul(a, &b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b)
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sumVector := func(a Vector) bool {
+		var sum Element
+		computed := a.Sum()
+		for i := 0; i < len(a); i++ {
+			sum.Add(&sum, &a[i])
+		}
+
+		return sum.Equal(&computed)
+	}
+
+	innerProductVector := func(a, b Vector) bool {
+		computed := a.InnerProduct(b)
+		var innerProduct Element
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			innerProduct.Add(&innerProduct, &tmp)
+		}
+
+		return innerProduct.Equal(&computed)
+	}
+
+	mulVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		a[0].SetUint64(0x24)
+		b[0].SetUint64(0x42)
+		c.Mul(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sizes := []int{1, 2, 3, 4, 8, 9, 15, 16, 509, 510, 511, 512, 513, 514}
+	type genPair struct {
+		g1, g2 gopter.Gen
+		label  string
+	}
+
+	for _, size := range sizes {
+		generators := []genPair{
+			{genZeroVector(size), genZeroVector(size), "zero vectors"},
+			{genMaxVector(size), genMaxVector(size), "max vectors"},
+			{genVector(size), genVector(size), "random vectors"},
+			{genVector(size), genZeroVector(size), "random and zero vectors"},
+		}
+		for _, gp := range generators {
+			properties.Property(fmt.Sprintf("vector addition %d - %s", size, gp.label), prop.ForAll(
+				addVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector subtraction %d - %s", size, gp.label), prop.ForAll(
+				subVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector scalar multiplication %d - %s", size, gp.label), prop.ForAll(
+				scalarMulVector,
+				gp.g1,
+				genElement(),
+			))
+
+			properties.Property(fmt.Sprintf("vector sum %d - %s", size, gp.label), prop.ForAll(
+				sumVector,
+				gp.g1,
+			))
+
+			properties.Property(fmt.Sprintf("vector inner product %d - %s", size, gp.label), prop.ForAll(
+				innerProductVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector multiplication %d - %s", size, gp.label), prop.ForAll(
+				mulVector,
+				gp.g1,
+				gp.g2,
+			))
+		}
+	}
+
+	properties.TestingRun(t, gopter.NewFormatedReporter(false, 260, os.Stdout))
+}
+
+func BenchmarkVectorOps(b *testing.B) {
+	// note; to benchmark against "no asm" version, use the following
+	// build tag: -tags purego
+	const N = 1 << 24
+	a1 := make(Vector, N)
+	b1 := make(Vector, N)
+	c1 := make(Vector, N)
+	var mixer Element
+	mixer.SetRandom()
+	for i := 1; i < N; i++ {
+		a1[i-1].SetUint64(uint64(i)).
+			Mul(&a1[i-1], &mixer)
+		b1[i-1].SetUint64(^uint64(i)).
+			Mul(&b1[i-1], &mixer)
+	}
+
+	for n := 1 << 4; n <= N; n <<= 1 {
+		b.Run(fmt.Sprintf("add %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Add(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sub %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Sub(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("scalarMul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.ScalarMul(_a, &mixer)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sum %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.Sum()
+			}
+		})
+
+		b.Run(fmt.Sprintf("innerProduct %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.InnerProduct(_b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("mul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Mul(_a, _b)
+			}
+		})
+	}
+}
+
+func genZeroVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genMaxVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+
+		qMinusOne := qElement
+		qMinusOne[0]--
+
+		for i := 0; i < size; i++ {
+			g[i] = qMinusOne
+		}
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		mixer := Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[3] != ^uint64(0) {
+			mixer[3] %= (qElement[3] + 1)
+		}
+
+		for !mixer.smallerThanModulus() {
+			mixer = Element{
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+			}
+			if qElement[3] != ^uint64(0) {
+				mixer[3] %= (qElement[3] + 1)
+			}
+		}
+
+		for i := 1; i <= size; i++ {
+			g[i-1].SetUint64(uint64(i)).
+				Mul(&g[i-1], &mixer)
+		}
+
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/ecc/stark-curve/fr/asm.go b/ecc/stark-curve/fr/asm_adx.go
similarity index 100%
rename from ecc/stark-curve/fr/asm.go
rename to ecc/stark-curve/fr/asm_adx.go
diff --git a/ecc/stark-curve/fr/asm_avx.go b/ecc/stark-curve/fr/asm_avx.go
new file mode 100644
index 0000000000..955f559799
--- /dev/null
+++ b/ecc/stark-curve/fr/asm_avx.go
@@ -0,0 +1,27 @@
+//go:build !noavx
+// +build !noavx
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+import "golang.org/x/sys/cpu"
+
+var (
+	supportAvx512 = supportAdx && cpu.X86.HasAVX512 && cpu.X86.HasAVX512DQ
+	_             = supportAvx512
+)
diff --git a/ecc/stark-curve/fr/asm_noavx.go b/ecc/stark-curve/fr/asm_noavx.go
new file mode 100644
index 0000000000..e5a5b1f2cc
--- /dev/null
+++ b/ecc/stark-curve/fr/asm_noavx.go
@@ -0,0 +1,22 @@
+//go:build noavx
+// +build noavx
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+const supportAvx512 = false
diff --git a/ecc/stark-curve/fr/element.go b/ecc/stark-curve/fr/element.go
index a7ab8e2175..216e287ebb 100644
--- a/ecc/stark-curve/fr/element.go
+++ b/ecc/stark-curve/fr/element.go
@@ -81,6 +81,9 @@ func Modulus() *big.Int {
 // used for Montgomery reduction
 const qInvNeg uint64 = 13504954208620504625
 
+// mu = 2^288 / q needed for partial Barrett reduction
+const mu uint64 = 137438953471
+
 func init() {
 	_modulus.SetString("800000000000010ffffffffffffffffb781126dcae7b2321e66a241adc64d2f", 16)
 }
@@ -477,32 +480,8 @@ func (z *Element) Select(c int, x0 *Element, x1 *Element) *Element {
 // and is used for testing purposes.
 func _mulGeneric(z, x, y *Element) {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t [5]uint64
 	var D uint64
diff --git a/ecc/stark-curve/fr/element_mul_amd64.s b/ecc/stark-curve/fr/element_mul_amd64.s
deleted file mode 100644
index 8eb931e77a..0000000000
--- a/ecc/stark-curve/fr/element_mul_amd64.s
+++ /dev/null
@@ -1,487 +0,0 @@
-// +build !purego
-
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0x1e66a241adc64d2f
-DATA q<>+8(SB)/8, $0xb781126dcae7b232
-DATA q<>+16(SB)/8, $0xffffffffffffffff
-DATA q<>+24(SB)/8, $0x0800000000000010
-GLOBL q<>(SB), (RODATA+NOPTR), $32
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0xbb6b3c4ce8bde631
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, rb0, rb1, rb2, rb3) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-
-// mul(res, x, y *Element)
-TEXT ·mul(SB), $24-24
-
-	// the algorithm is described in the Element.Mul declaration (.go)
-	// however, to benefit from the ADCX and ADOX carry chains
-	// we split the inner loops in 2:
-	// for i=0 to N-1
-	// 		for j=0 to N-1
-	// 		    (A,t[j])  := t[j] + x[j]*y[i] + A
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C + A
-
-	NO_LOCAL_POINTERS
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_1
-	MOVQ x+8(FP), SI
-
-	// x[0] -> DI
-	// x[1] -> R8
-	// x[2] -> R9
-	// x[3] -> R10
-	MOVQ 0(SI), DI
-	MOVQ 8(SI), R8
-	MOVQ 16(SI), R9
-	MOVQ 24(SI), R10
-	MOVQ y+16(FP), R11
-
-	// A -> BP
-	// t[0] -> R14
-	// t[1] -> R13
-	// t[2] -> CX
-	// t[3] -> BX
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 0(R11), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ DI, R14, R13
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ R8, AX, CX
-	ADOXQ AX, R13
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ R9, AX, BX
-	ADOXQ AX, CX
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 8(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R13
-	MULXQ R8, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, CX
-	MULXQ R9, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, BX
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 16(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R13
-	MULXQ R8, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, CX
-	MULXQ R9, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, BX
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 24(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ DI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R13
-	MULXQ R8, AX, BP
-	ADOXQ AX, R13
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, CX
-	MULXQ R9, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, BX
-	MULXQ R10, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R12
-	ADCXQ R14, AX
-	MOVQ  R12, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// reduce element(R14,R13,CX,BX) using temp registers (SI,R12,R11,DI)
-	REDUCE(R14,R13,CX,BX,SI,R12,R11,DI)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R13, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	RET
-
-noAdx_1:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	MOVQ x+8(FP), AX
-	MOVQ AX, 8(SP)
-	MOVQ y+16(FP), AX
-	MOVQ AX, 16(SP)
-	CALL ·_mulGeneric(SB)
-	RET
-
-TEXT ·fromMont(SB), $8-8
-	NO_LOCAL_POINTERS
-
-	// the algorithm is described here
-	// https://hackmd.io/@gnark/modular_multiplication
-	// when y = 1 we have:
-	// for i=0 to N-1
-	// 		t[i] = x[i]
-	// for i=0 to N-1
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_2
-	MOVQ res+0(FP), DX
-	MOVQ 0(DX), R14
-	MOVQ 8(DX), R13
-	MOVQ 16(DX), CX
-	MOVQ 24(DX), BX
-	XORQ DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-	XORQ  DX, DX
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-	XORQ  AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, BP
-	ADCXQ R14, AX
-	MOVQ  BP, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R13, R14
-	MULXQ q<>+8(SB), AX, R13
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R13
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R13
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ AX, BX
-
-	// reduce element(R14,R13,CX,BX) using temp registers (SI,DI,R8,R9)
-	REDUCE(R14,R13,CX,BX,SI,DI,R8,R9)
-
-	MOVQ res+0(FP), AX
-	MOVQ R14, 0(AX)
-	MOVQ R13, 8(AX)
-	MOVQ CX, 16(AX)
-	MOVQ BX, 24(AX)
-	RET
-
-noAdx_2:
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	CALL ·_fromMontGeneric(SB)
-	RET
diff --git a/ecc/stark-curve/fr/element_ops_amd64.go b/ecc/stark-curve/fr/element_ops_amd64.go
index 21568255de..b653e80069 100644
--- a/ecc/stark-curve/fr/element_ops_amd64.go
+++ b/ecc/stark-curve/fr/element_ops_amd64.go
@@ -51,7 +51,8 @@ func (vector *Vector) Add(a, b Vector) {
 	if len(a) != len(b) || len(a) != len(*vector) {
 		panic("vector.Add: vectors don't have the same length")
 	}
-	addVec(&(*vector)[0], &a[0], &b[0], uint64(len(a)))
+	n := uint64(len(a))
+	addVec(&(*vector)[0], &a[0], &b[0], n)
 }
 
 //go:noescape
@@ -75,59 +76,123 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	if len(a) != len(*vector) {
 		panic("vector.ScalarMul: vectors don't have the same length")
 	}
-	scalarMulVec(&(*vector)[0], &a[0], b, uint64(len(a)))
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || uint64(len(a)) >= maxN {
+		// call scalarMulVecGeneric
+		scalarMulVecGeneric(*vector, a, b)
+		return
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	// the code for scalarMul is identical to mulVec; and it expects at least
+	// 2 elements in the vector to fill the Z registers
+	var bb [2]Element
+	bb[0] = *b
+	bb[1] = *b
+	const blockSize = 16
+	scalarMulVec(&(*vector)[0], &a[0], &bb[0], n/blockSize, qInvNeg)
+	if n%blockSize != 0 {
+		// call scalarMulVecGeneric on the rest
+		start := n - n%blockSize
+		scalarMulVecGeneric((*vector)[start:], a[start:], b)
+	}
+}
+
+//go:noescape
+func scalarMulVec(res, a, b *Element, n uint64, qInvNeg uint64)
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	const minN = 16 * 7 // AVX512 slower than generic for small n
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n <= minN || n >= maxN {
+		// call sumVecGeneric
+		sumVecGeneric(&res, *vector)
+		return
+	}
+	sumVec(&res, &(*vector)[0], uint64(len(*vector)))
+	return
 }
 
 //go:noescape
-func scalarMulVec(res, a, b *Element, n uint64)
+func sumVec(res *Element, a *Element, n uint64)
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	if n != uint64(len(other)) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n >= maxN {
+		// call innerProductVecGeneric
+		// note; we could split the vector into smaller chunks and call innerProductVec
+		innerProductVecGeneric(&res, *vector, other)
+		return
+	}
+	innerProdVec(&res[0], &(*vector)[0], &other[0], uint64(len(*vector)))
+
+	return
+}
+
+//go:noescape
+func innerProdVec(res *uint64, a, b *Element, n uint64)
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n >= maxN {
+		// call mulVecGeneric
+		mulVecGeneric(*vector, a, b)
+		return
+	}
+
+	const blockSize = 16
+	mulVec(&(*vector)[0], &a[0], &b[0], n/blockSize, qInvNeg)
+	if n%blockSize != 0 {
+		// call mulVecGeneric on the rest
+		start := n - n%blockSize
+		mulVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+
+}
+
+// Patterns use for transposing the vectors in mulVec
+var (
+	pattern1 = [8]uint64{0, 8, 1, 9, 2, 10, 3, 11}
+	pattern2 = [8]uint64{12, 4, 13, 5, 14, 6, 15, 7}
+	pattern3 = [8]uint64{0, 1, 8, 9, 2, 3, 10, 11}
+	pattern4 = [8]uint64{12, 13, 4, 5, 14, 15, 6, 7}
+)
+
+//go:noescape
+func mulVec(res, a, b *Element, n uint64, qInvNeg uint64)
 
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	mul(z, x, y)
 	return z
diff --git a/ecc/stark-curve/fr/element_ops_amd64.s b/ecc/stark-curve/fr/element_ops_amd64.s
index 245dcb8959..6c42136a7a 100644
--- a/ecc/stark-curve/fr/element_ops_amd64.s
+++ b/ecc/stark-curve/fr/element_ops_amd64.s
@@ -1,627 +1,6 @@
 // +build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+// We include the hash to force the Go compiler to recompile: 9425145785761608449
+#include "../../../field/asm/element_4w_amd64.s"
 
-#include "textflag.h"
-#include "funcdata.h"
-
-// modulus q
-DATA q<>+0(SB)/8, $0x1e66a241adc64d2f
-DATA q<>+8(SB)/8, $0xb781126dcae7b232
-DATA q<>+16(SB)/8, $0xffffffffffffffff
-DATA q<>+24(SB)/8, $0x0800000000000010
-GLOBL q<>(SB), (RODATA+NOPTR), $32
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, $0xbb6b3c4ce8bde631
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
-
-#define REDUCE(ra0, ra1, ra2, ra3, rb0, rb1, rb2, rb3) \
-	MOVQ    ra0, rb0;        \
-	SUBQ    q<>(SB), ra0;    \
-	MOVQ    ra1, rb1;        \
-	SBBQ    q<>+8(SB), ra1;  \
-	MOVQ    ra2, rb2;        \
-	SBBQ    q<>+16(SB), ra2; \
-	MOVQ    ra3, rb3;        \
-	SBBQ    q<>+24(SB), ra3; \
-	CMOVQCS rb0, ra0;        \
-	CMOVQCS rb1, ra1;        \
-	CMOVQCS rb2, ra2;        \
-	CMOVQCS rb3, ra3;        \
-
-TEXT ·reduce(SB), NOSPLIT, $0-8
-	MOVQ res+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// MulBy3(x *Element)
-TEXT ·MulBy3(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// MulBy5(x *Element)
-TEXT ·MulBy5(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R15,DI,R8,R9)
-	REDUCE(DX,CX,BX,SI,R15,DI,R8,R9)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// MulBy13(x *Element)
-TEXT ·MulBy13(SB), NOSPLIT, $0-8
-	MOVQ x+0(FP), AX
-	MOVQ 0(AX), DX
-	MOVQ 8(AX), CX
-	MOVQ 16(AX), BX
-	MOVQ 24(AX), SI
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
-	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
-
-	MOVQ DX, R11
-	MOVQ CX, R12
-	MOVQ BX, R13
-	MOVQ SI, R14
-	ADDQ DX, DX
-	ADCQ CX, CX
-	ADCQ BX, BX
-	ADCQ SI, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ R11, DX
-	ADCQ R12, CX
-	ADCQ R13, BX
-	ADCQ R14, SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	ADDQ 0(AX), DX
-	ADCQ 8(AX), CX
-	ADCQ 16(AX), BX
-	ADCQ 24(AX), SI
-
-	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
-	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
-
-	MOVQ DX, 0(AX)
-	MOVQ CX, 8(AX)
-	MOVQ BX, 16(AX)
-	MOVQ SI, 24(AX)
-	RET
-
-// Butterfly(a, b *Element) sets a = a + b; b = a - b
-TEXT ·Butterfly(SB), NOSPLIT, $0-16
-	MOVQ    a+0(FP), AX
-	MOVQ    0(AX), CX
-	MOVQ    8(AX), BX
-	MOVQ    16(AX), SI
-	MOVQ    24(AX), DI
-	MOVQ    CX, R8
-	MOVQ    BX, R9
-	MOVQ    SI, R10
-	MOVQ    DI, R11
-	XORQ    AX, AX
-	MOVQ    b+8(FP), DX
-	ADDQ    0(DX), CX
-	ADCQ    8(DX), BX
-	ADCQ    16(DX), SI
-	ADCQ    24(DX), DI
-	SUBQ    0(DX), R8
-	SBBQ    8(DX), R9
-	SBBQ    16(DX), R10
-	SBBQ    24(DX), R11
-	MOVQ    $0x1e66a241adc64d2f, R12
-	MOVQ    $0xb781126dcae7b232, R13
-	MOVQ    $0xffffffffffffffff, R14
-	MOVQ    $0x0800000000000010, R15
-	CMOVQCC AX, R12
-	CMOVQCC AX, R13
-	CMOVQCC AX, R14
-	CMOVQCC AX, R15
-	ADDQ    R12, R8
-	ADCQ    R13, R9
-	ADCQ    R14, R10
-	ADCQ    R15, R11
-	MOVQ    R8, 0(DX)
-	MOVQ    R9, 8(DX)
-	MOVQ    R10, 16(DX)
-	MOVQ    R11, 24(DX)
-
-	// reduce element(CX,BX,SI,DI) using temp registers (R8,R9,R10,R11)
-	REDUCE(CX,BX,SI,DI,R8,R9,R10,R11)
-
-	MOVQ a+0(FP), AX
-	MOVQ CX, 0(AX)
-	MOVQ BX, 8(AX)
-	MOVQ SI, 16(AX)
-	MOVQ DI, 24(AX)
-	RET
-
-// addVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] + b[0...n]
-TEXT ·addVec(SB), NOSPLIT, $0-32
-	MOVQ res+0(FP), CX
-	MOVQ a+8(FP), AX
-	MOVQ b+16(FP), DX
-	MOVQ n+24(FP), BX
-
-loop_1:
-	TESTQ BX, BX
-	JEQ   done_2 // n == 0, we are done
-
-	// a[0] -> SI
-	// a[1] -> DI
-	// a[2] -> R8
-	// a[3] -> R9
-	MOVQ 0(AX), SI
-	MOVQ 8(AX), DI
-	MOVQ 16(AX), R8
-	MOVQ 24(AX), R9
-	ADDQ 0(DX), SI
-	ADCQ 8(DX), DI
-	ADCQ 16(DX), R8
-	ADCQ 24(DX), R9
-
-	// reduce element(SI,DI,R8,R9) using temp registers (R10,R11,R12,R13)
-	REDUCE(SI,DI,R8,R9,R10,R11,R12,R13)
-
-	MOVQ SI, 0(CX)
-	MOVQ DI, 8(CX)
-	MOVQ R8, 16(CX)
-	MOVQ R9, 24(CX)
-
-	// increment pointers to visit next element
-	ADDQ $32, AX
-	ADDQ $32, DX
-	ADDQ $32, CX
-	DECQ BX      // decrement n
-	JMP  loop_1
-
-done_2:
-	RET
-
-// subVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] - b[0...n]
-TEXT ·subVec(SB), NOSPLIT, $0-32
-	MOVQ res+0(FP), CX
-	MOVQ a+8(FP), AX
-	MOVQ b+16(FP), DX
-	MOVQ n+24(FP), BX
-	XORQ SI, SI
-
-loop_3:
-	TESTQ BX, BX
-	JEQ   done_4 // n == 0, we are done
-
-	// a[0] -> DI
-	// a[1] -> R8
-	// a[2] -> R9
-	// a[3] -> R10
-	MOVQ 0(AX), DI
-	MOVQ 8(AX), R8
-	MOVQ 16(AX), R9
-	MOVQ 24(AX), R10
-	SUBQ 0(DX), DI
-	SBBQ 8(DX), R8
-	SBBQ 16(DX), R9
-	SBBQ 24(DX), R10
-
-	// reduce (a-b) mod q
-	// q[0] -> R11
-	// q[1] -> R12
-	// q[2] -> R13
-	// q[3] -> R14
-	MOVQ    $0x1e66a241adc64d2f, R11
-	MOVQ    $0xb781126dcae7b232, R12
-	MOVQ    $0xffffffffffffffff, R13
-	MOVQ    $0x0800000000000010, R14
-	CMOVQCC SI, R11
-	CMOVQCC SI, R12
-	CMOVQCC SI, R13
-	CMOVQCC SI, R14
-
-	// add registers (q or 0) to a, and set to result
-	ADDQ R11, DI
-	ADCQ R12, R8
-	ADCQ R13, R9
-	ADCQ R14, R10
-	MOVQ DI, 0(CX)
-	MOVQ R8, 8(CX)
-	MOVQ R9, 16(CX)
-	MOVQ R10, 24(CX)
-
-	// increment pointers to visit next element
-	ADDQ $32, AX
-	ADDQ $32, DX
-	ADDQ $32, CX
-	DECQ BX      // decrement n
-	JMP  loop_3
-
-done_4:
-	RET
-
-// scalarMulVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] * b
-TEXT ·scalarMulVec(SB), $56-32
-	CMPB ·supportAdx(SB), $1
-	JNE  noAdx_5
-	MOVQ a+8(FP), R11
-	MOVQ b+16(FP), R10
-	MOVQ n+24(FP), R12
-
-	// scalar[0] -> SI
-	// scalar[1] -> DI
-	// scalar[2] -> R8
-	// scalar[3] -> R9
-	MOVQ 0(R10), SI
-	MOVQ 8(R10), DI
-	MOVQ 16(R10), R8
-	MOVQ 24(R10), R9
-	MOVQ res+0(FP), R10
-
-loop_6:
-	TESTQ R12, R12
-	JEQ   done_7   // n == 0, we are done
-
-	// TODO @gbotrel this is generated from the same macro as the unit mul, we should refactor this in a single asm function
-	// A -> BP
-	// t[0] -> R14
-	// t[1] -> R15
-	// t[2] -> CX
-	// t[3] -> BX
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 0(R11), DX
-
-	// (A,t[0])  := x[0]*y[0] + A
-	MULXQ SI, R14, R15
-
-	// (A,t[1])  := x[1]*y[0] + A
-	MULXQ DI, AX, CX
-	ADOXQ AX, R15
-
-	// (A,t[2])  := x[2]*y[0] + A
-	MULXQ R8, AX, BX
-	ADOXQ AX, CX
-
-	// (A,t[3])  := x[3]*y[0] + A
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 8(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[1] + A
-	MULXQ SI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[1] + A
-	ADCXQ BP, R15
-	MULXQ DI, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[1] + A
-	ADCXQ BP, CX
-	MULXQ R8, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[1] + A
-	ADCXQ BP, BX
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 16(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[2] + A
-	MULXQ SI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[2] + A
-	ADCXQ BP, R15
-	MULXQ DI, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[2] + A
-	ADCXQ BP, CX
-	MULXQ R8, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[2] + A
-	ADCXQ BP, BX
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// clear the flags
-	XORQ AX, AX
-	MOVQ 24(R11), DX
-
-	// (A,t[0])  := t[0] + x[0]*y[3] + A
-	MULXQ SI, AX, BP
-	ADOXQ AX, R14
-
-	// (A,t[1])  := t[1] + x[1]*y[3] + A
-	ADCXQ BP, R15
-	MULXQ DI, AX, BP
-	ADOXQ AX, R15
-
-	// (A,t[2])  := t[2] + x[2]*y[3] + A
-	ADCXQ BP, CX
-	MULXQ R8, AX, BP
-	ADOXQ AX, CX
-
-	// (A,t[3])  := t[3] + x[3]*y[3] + A
-	ADCXQ BP, BX
-	MULXQ R9, AX, BP
-	ADOXQ AX, BX
-
-	// A += carries from ADCXQ and ADOXQ
-	MOVQ  $0, AX
-	ADCXQ AX, BP
-	ADOXQ AX, BP
-
-	// m := t[0]*q'[0] mod W
-	MOVQ  qInv0<>(SB), DX
-	IMULQ R14, DX
-
-	// clear the flags
-	XORQ AX, AX
-
-	// C,_ := t[0] + m*q[0]
-	MULXQ q<>+0(SB), AX, R13
-	ADCXQ R14, AX
-	MOVQ  R13, R14
-
-	// (C,t[0]) := t[1] + m*q[1] + C
-	ADCXQ R15, R14
-	MULXQ q<>+8(SB), AX, R15
-	ADOXQ AX, R14
-
-	// (C,t[1]) := t[2] + m*q[2] + C
-	ADCXQ CX, R15
-	MULXQ q<>+16(SB), AX, CX
-	ADOXQ AX, R15
-
-	// (C,t[2]) := t[3] + m*q[3] + C
-	ADCXQ BX, CX
-	MULXQ q<>+24(SB), AX, BX
-	ADOXQ AX, CX
-
-	// t[3] = C + A
-	MOVQ  $0, AX
-	ADCXQ AX, BX
-	ADOXQ BP, BX
-
-	// reduce t mod q
-	// reduce element(R14,R15,CX,BX) using temp registers (R13,AX,DX,s0-8(SP))
-	REDUCE(R14,R15,CX,BX,R13,AX,DX,s0-8(SP))
-
-	MOVQ R14, 0(R10)
-	MOVQ R15, 8(R10)
-	MOVQ CX, 16(R10)
-	MOVQ BX, 24(R10)
-
-	// increment pointers to visit next element
-	ADDQ $32, R11
-	ADDQ $32, R10
-	DECQ R12      // decrement n
-	JMP  loop_6
-
-done_7:
-	RET
-
-noAdx_5:
-	MOVQ n+24(FP), DX
-	MOVQ res+0(FP), AX
-	MOVQ AX, (SP)
-	MOVQ DX, 8(SP)
-	MOVQ DX, 16(SP)
-	MOVQ a+8(FP), AX
-	MOVQ AX, 24(SP)
-	MOVQ DX, 32(SP)
-	MOVQ DX, 40(SP)
-	MOVQ b+16(FP), AX
-	MOVQ AX, 48(SP)
-	CALL ·scalarMulVecGeneric(SB)
-	RET
diff --git a/ecc/stark-curve/fr/element_ops_purego.go b/ecc/stark-curve/fr/element_ops_purego.go
index b04f5202fd..2d0db69153 100644
--- a/ecc/stark-curve/fr/element_ops_purego.go
+++ b/ecc/stark-curve/fr/element_ops_purego.go
@@ -78,53 +78,32 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	scalarMulVecGeneric(*vector, a, b)
 }
 
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
+
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
 func (z *Element) Mul(x, y *Element) *Element {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-	//
-	// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-	// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-	//
-	// for i=0 to N-1
-	// 		(A,t[0]) := t[0] + x[0]*y[i]
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		t[N-1] = C + A
-	//
-	// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit
-	// of the modulus is zero (and not all of the remaining bits are set).
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t0, t1, t2, t3 uint64
 	var u0, u1, u2, u3 uint64
diff --git a/ecc/stark-curve/fr/element_test.go b/ecc/stark-curve/fr/element_test.go
index b81aff116e..fb10e5a55a 100644
--- a/ecc/stark-curve/fr/element_test.go
+++ b/ecc/stark-curve/fr/element_test.go
@@ -637,7 +637,6 @@ func TestElementBitLen(t *testing.T) {
 	))
 
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
-
 }
 
 func TestElementButterflies(t *testing.T) {
@@ -707,77 +706,6 @@ func TestElementLexicographicallyLargest(t *testing.T) {
 
 }
 
-func TestElementVecOps(t *testing.T) {
-	assert := require.New(t)
-
-	const N = 7
-	a := make(Vector, N)
-	b := make(Vector, N)
-	c := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a[i].SetRandom()
-		b[i].SetRandom()
-	}
-
-	// Vector addition
-	c.Add(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Add(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector addition failed")
-	}
-
-	// Vector subtraction
-	c.Sub(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Sub(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector subtraction failed")
-	}
-
-	// Vector scaling
-	c.ScalarMul(a, &b[0])
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Mul(&a[i], &b[0])
-		assert.True(c[i].Equal(&expected), "Vector scaling failed")
-	}
-}
-
-func BenchmarkElementVecOps(b *testing.B) {
-	// note; to benchmark against "no asm" version, use the following
-	// build tag: -tags purego
-	const N = 1024
-	a1 := make(Vector, N)
-	b1 := make(Vector, N)
-	c1 := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a1[i].SetRandom()
-		b1[i].SetRandom()
-	}
-
-	b.Run("Add", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Add(a1, b1)
-		}
-	})
-
-	b.Run("Sub", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Sub(a1, b1)
-		}
-	})
-
-	b.Run("ScalarMul", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.ScalarMul(a1, &b1[0])
-		}
-	})
-}
-
 func TestElementAdd(t *testing.T) {
 	t.Parallel()
 	parameters := gopter.DefaultTestParameters()
@@ -2297,38 +2225,38 @@ func gen() gopter.Gen {
 	}
 }
 
-func genFull() gopter.Gen {
-	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+func genRandomFq(genParams *gopter.GenParameters) Element {
+	var g Element
 
-		genRandomFq := func() Element {
-			var g Element
+	g = Element{
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+		genParams.NextUint64(),
+	}
 
-			g = Element{
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-				genParams.NextUint64(),
-			}
+	if qElement[3] != ^uint64(0) {
+		g[3] %= (qElement[3] + 1)
+	}
 
-			if qElement[3] != ^uint64(0) {
-				g[3] %= (qElement[3] + 1)
-			}
+	for !g.smallerThanModulus() {
+		g = Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[3] != ^uint64(0) {
+			g[3] %= (qElement[3] + 1)
+		}
+	}
 
-			for !g.smallerThanModulus() {
-				g = Element{
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-					genParams.NextUint64(),
-				}
-				if qElement[3] != ^uint64(0) {
-					g[3] %= (qElement[3] + 1)
-				}
-			}
+	return g
+}
 
-			return g
-		}
-		a := genRandomFq()
+func genFull() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
 
 		var carry uint64
 		a[0], carry = bits.Add64(a[0], qElement[0], carry)
@@ -2341,6 +2269,14 @@ func genFull() gopter.Gen {
 	}
 }
 
+func genElement() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
+		genResult := gopter.NewGenResult(a, gopter.NoShrinker)
+		return genResult
+	}
+}
+
 func (z *Element) matchVeryBigInt(aHi uint64, aInt *big.Int) error {
 	var modulus big.Int
 	var aIntMod big.Int
diff --git a/ecc/stark-curve/fr/vector.go b/ecc/stark-curve/fr/vector.go
index f39828547f..867cabbc3d 100644
--- a/ecc/stark-curve/fr/vector.go
+++ b/ecc/stark-curve/fr/vector.go
@@ -226,6 +226,32 @@ func scalarMulVecGeneric(res, a Vector, b *Element) {
 	}
 }
 
+func sumVecGeneric(res *Element, a Vector) {
+	for i := 0; i < len(a); i++ {
+		res.Add(res, &a[i])
+	}
+}
+
+func innerProductVecGeneric(res *Element, a, b Vector) {
+	if len(a) != len(b) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	var tmp Element
+	for i := 0; i < len(a); i++ {
+		tmp.Mul(&a[i], &b[i])
+		res.Add(res, &tmp)
+	}
+}
+
+func mulVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Mul(&a[i], &b[i])
+	}
+}
+
 // TODO @gbotrel make a public package out of that.
 // execute executes the work function in parallel.
 // this is copy paste from internal/parallel/parallel.go
diff --git a/ecc/stark-curve/fr/vector_test.go b/ecc/stark-curve/fr/vector_test.go
index e58f2d9a38..b6344c18b7 100644
--- a/ecc/stark-curve/fr/vector_test.go
+++ b/ecc/stark-curve/fr/vector_test.go
@@ -18,10 +18,15 @@ package fr
 
 import (
 	"bytes"
+	"fmt"
 	"github.com/stretchr/testify/require"
+	"os"
 	"reflect"
 	"sort"
 	"testing"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/prop"
 )
 
 func TestVectorSort(t *testing.T) {
@@ -88,3 +93,279 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 	}
 	return <-chErr
 }
+
+func TestVectorOps(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = 2
+	} else {
+		parameters.MinSuccessfulTests = 10
+	}
+	properties := gopter.NewProperties(parameters)
+
+	addVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Add(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Add(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	subVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Sub(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Sub(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	scalarMulVector := func(a Vector, b Element) bool {
+		c := make(Vector, len(a))
+		c.ScalarMul(a, &b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b)
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sumVector := func(a Vector) bool {
+		var sum Element
+		computed := a.Sum()
+		for i := 0; i < len(a); i++ {
+			sum.Add(&sum, &a[i])
+		}
+
+		return sum.Equal(&computed)
+	}
+
+	innerProductVector := func(a, b Vector) bool {
+		computed := a.InnerProduct(b)
+		var innerProduct Element
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			innerProduct.Add(&innerProduct, &tmp)
+		}
+
+		return innerProduct.Equal(&computed)
+	}
+
+	mulVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		a[0].SetUint64(0x24)
+		b[0].SetUint64(0x42)
+		c.Mul(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sizes := []int{1, 2, 3, 4, 8, 9, 15, 16, 509, 510, 511, 512, 513, 514}
+	type genPair struct {
+		g1, g2 gopter.Gen
+		label  string
+	}
+
+	for _, size := range sizes {
+		generators := []genPair{
+			{genZeroVector(size), genZeroVector(size), "zero vectors"},
+			{genMaxVector(size), genMaxVector(size), "max vectors"},
+			{genVector(size), genVector(size), "random vectors"},
+			{genVector(size), genZeroVector(size), "random and zero vectors"},
+		}
+		for _, gp := range generators {
+			properties.Property(fmt.Sprintf("vector addition %d - %s", size, gp.label), prop.ForAll(
+				addVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector subtraction %d - %s", size, gp.label), prop.ForAll(
+				subVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector scalar multiplication %d - %s", size, gp.label), prop.ForAll(
+				scalarMulVector,
+				gp.g1,
+				genElement(),
+			))
+
+			properties.Property(fmt.Sprintf("vector sum %d - %s", size, gp.label), prop.ForAll(
+				sumVector,
+				gp.g1,
+			))
+
+			properties.Property(fmt.Sprintf("vector inner product %d - %s", size, gp.label), prop.ForAll(
+				innerProductVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector multiplication %d - %s", size, gp.label), prop.ForAll(
+				mulVector,
+				gp.g1,
+				gp.g2,
+			))
+		}
+	}
+
+	properties.TestingRun(t, gopter.NewFormatedReporter(false, 260, os.Stdout))
+}
+
+func BenchmarkVectorOps(b *testing.B) {
+	// note; to benchmark against "no asm" version, use the following
+	// build tag: -tags purego
+	const N = 1 << 24
+	a1 := make(Vector, N)
+	b1 := make(Vector, N)
+	c1 := make(Vector, N)
+	var mixer Element
+	mixer.SetRandom()
+	for i := 1; i < N; i++ {
+		a1[i-1].SetUint64(uint64(i)).
+			Mul(&a1[i-1], &mixer)
+		b1[i-1].SetUint64(^uint64(i)).
+			Mul(&b1[i-1], &mixer)
+	}
+
+	for n := 1 << 4; n <= N; n <<= 1 {
+		b.Run(fmt.Sprintf("add %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Add(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sub %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Sub(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("scalarMul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.ScalarMul(_a, &mixer)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sum %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.Sum()
+			}
+		})
+
+		b.Run(fmt.Sprintf("innerProduct %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.InnerProduct(_b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("mul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Mul(_a, _b)
+			}
+		})
+	}
+}
+
+func genZeroVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genMaxVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+
+		qMinusOne := qElement
+		qMinusOne[0]--
+
+		for i := 0; i < size; i++ {
+			g[i] = qMinusOne
+		}
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		mixer := Element{
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+			genParams.NextUint64(),
+		}
+		if qElement[3] != ^uint64(0) {
+			mixer[3] %= (qElement[3] + 1)
+		}
+
+		for !mixer.smallerThanModulus() {
+			mixer = Element{
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+				genParams.NextUint64(),
+			}
+			if qElement[3] != ^uint64(0) {
+				mixer[3] %= (qElement[3] + 1)
+			}
+		}
+
+		for i := 1; i <= size; i++ {
+			g[i-1].SetUint64(uint64(i)).
+				Mul(&g[i-1], &mixer)
+		}
+
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/field/asm/.gitignore b/field/asm/.gitignore
new file mode 100644
index 0000000000..7c22f7f933
--- /dev/null
+++ b/field/asm/.gitignore
@@ -0,0 +1,6 @@
+# generated by integration tests
+element_2w_amd64.s
+element_3w_amd64.s
+element_7w_amd64.s
+element_8w_amd64.s
+*.h
\ No newline at end of file
diff --git a/field/asm/element_10w_amd64.s b/field/asm/element_10w_amd64.s
new file mode 100644
index 0000000000..e5f10dca8c
--- /dev/null
+++ b/field/asm/element_10w_amd64.s
@@ -0,0 +1,1187 @@
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+#include "textflag.h"
+#include "funcdata.h"
+#include "go_asm.h"
+
+#define REDUCE(ra0, ra1, ra2, ra3, ra4, ra5, ra6, ra7, ra8, ra9, rb0, rb1, rb2, rb3, rb4, rb5, rb6, rb7, rb8, rb9) \
+	MOVQ    ra0, rb0;              \
+	SUBQ    ·qElement(SB), ra0;    \
+	MOVQ    ra1, rb1;              \
+	SBBQ    ·qElement+8(SB), ra1;  \
+	MOVQ    ra2, rb2;              \
+	SBBQ    ·qElement+16(SB), ra2; \
+	MOVQ    ra3, rb3;              \
+	SBBQ    ·qElement+24(SB), ra3; \
+	MOVQ    ra4, rb4;              \
+	SBBQ    ·qElement+32(SB), ra4; \
+	MOVQ    ra5, rb5;              \
+	SBBQ    ·qElement+40(SB), ra5; \
+	MOVQ    ra6, rb6;              \
+	SBBQ    ·qElement+48(SB), ra6; \
+	MOVQ    ra7, rb7;              \
+	SBBQ    ·qElement+56(SB), ra7; \
+	MOVQ    ra8, rb8;              \
+	SBBQ    ·qElement+64(SB), ra8; \
+	MOVQ    ra9, rb9;              \
+	SBBQ    ·qElement+72(SB), ra9; \
+	CMOVQCS rb0, ra0;              \
+	CMOVQCS rb1, ra1;              \
+	CMOVQCS rb2, ra2;              \
+	CMOVQCS rb3, ra3;              \
+	CMOVQCS rb4, ra4;              \
+	CMOVQCS rb5, ra5;              \
+	CMOVQCS rb6, ra6;              \
+	CMOVQCS rb7, ra7;              \
+	CMOVQCS rb8, ra8;              \
+	CMOVQCS rb9, ra9;              \
+
+TEXT ·reduce(SB), $56-8
+	MOVQ res+0(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	MOVQ 32(AX), DI
+	MOVQ 40(AX), R8
+	MOVQ 48(AX), R9
+	MOVQ 56(AX), R10
+	MOVQ 64(AX), R11
+	MOVQ 72(AX), R12
+
+	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
+
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	MOVQ DI, 32(AX)
+	MOVQ R8, 40(AX)
+	MOVQ R9, 48(AX)
+	MOVQ R10, 56(AX)
+	MOVQ R11, 64(AX)
+	MOVQ R12, 72(AX)
+	RET
+
+// MulBy3(x *Element)
+TEXT ·MulBy3(SB), $56-8
+	MOVQ x+0(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	MOVQ 32(AX), DI
+	MOVQ 40(AX), R8
+	MOVQ 48(AX), R9
+	MOVQ 56(AX), R10
+	MOVQ 64(AX), R11
+	MOVQ 72(AX), R12
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+	ADCQ DI, DI
+	ADCQ R8, R8
+	ADCQ R9, R9
+	ADCQ R10, R10
+	ADCQ R11, R11
+	ADCQ R12, R12
+
+	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
+
+	ADDQ 0(AX), DX
+	ADCQ 8(AX), CX
+	ADCQ 16(AX), BX
+	ADCQ 24(AX), SI
+	ADCQ 32(AX), DI
+	ADCQ 40(AX), R8
+	ADCQ 48(AX), R9
+	ADCQ 56(AX), R10
+	ADCQ 64(AX), R11
+	ADCQ 72(AX), R12
+
+	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
+
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	MOVQ DI, 32(AX)
+	MOVQ R8, 40(AX)
+	MOVQ R9, 48(AX)
+	MOVQ R10, 56(AX)
+	MOVQ R11, 64(AX)
+	MOVQ R12, 72(AX)
+	RET
+
+// MulBy5(x *Element)
+TEXT ·MulBy5(SB), $56-8
+	MOVQ x+0(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	MOVQ 32(AX), DI
+	MOVQ 40(AX), R8
+	MOVQ 48(AX), R9
+	MOVQ 56(AX), R10
+	MOVQ 64(AX), R11
+	MOVQ 72(AX), R12
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+	ADCQ DI, DI
+	ADCQ R8, R8
+	ADCQ R9, R9
+	ADCQ R10, R10
+	ADCQ R11, R11
+	ADCQ R12, R12
+
+	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
+
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+	ADCQ DI, DI
+	ADCQ R8, R8
+	ADCQ R9, R9
+	ADCQ R10, R10
+	ADCQ R11, R11
+	ADCQ R12, R12
+
+	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
+
+	ADDQ 0(AX), DX
+	ADCQ 8(AX), CX
+	ADCQ 16(AX), BX
+	ADCQ 24(AX), SI
+	ADCQ 32(AX), DI
+	ADCQ 40(AX), R8
+	ADCQ 48(AX), R9
+	ADCQ 56(AX), R10
+	ADCQ 64(AX), R11
+	ADCQ 72(AX), R12
+
+	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
+
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	MOVQ DI, 32(AX)
+	MOVQ R8, 40(AX)
+	MOVQ R9, 48(AX)
+	MOVQ R10, 56(AX)
+	MOVQ R11, 64(AX)
+	MOVQ R12, 72(AX)
+	RET
+
+// MulBy13(x *Element)
+TEXT ·MulBy13(SB), $136-8
+	MOVQ x+0(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	MOVQ 32(AX), DI
+	MOVQ 40(AX), R8
+	MOVQ 48(AX), R9
+	MOVQ 56(AX), R10
+	MOVQ 64(AX), R11
+	MOVQ 72(AX), R12
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+	ADCQ DI, DI
+	ADCQ R8, R8
+	ADCQ R9, R9
+	ADCQ R10, R10
+	ADCQ R11, R11
+	ADCQ R12, R12
+
+	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
+
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+	ADCQ DI, DI
+	ADCQ R8, R8
+	ADCQ R9, R9
+	ADCQ R10, R10
+	ADCQ R11, R11
+	ADCQ R12, R12
+
+	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12) using temp registers (s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP),s11-96(SP),s12-104(SP),s13-112(SP),s14-120(SP),s15-128(SP),s16-136(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP),s11-96(SP),s12-104(SP),s13-112(SP),s14-120(SP),s15-128(SP),s16-136(SP))
+
+	MOVQ DX, s7-64(SP)
+	MOVQ CX, s8-72(SP)
+	MOVQ BX, s9-80(SP)
+	MOVQ SI, s10-88(SP)
+	MOVQ DI, s11-96(SP)
+	MOVQ R8, s12-104(SP)
+	MOVQ R9, s13-112(SP)
+	MOVQ R10, s14-120(SP)
+	MOVQ R11, s15-128(SP)
+	MOVQ R12, s16-136(SP)
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+	ADCQ DI, DI
+	ADCQ R8, R8
+	ADCQ R9, R9
+	ADCQ R10, R10
+	ADCQ R11, R11
+	ADCQ R12, R12
+
+	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
+
+	ADDQ s7-64(SP), DX
+	ADCQ s8-72(SP), CX
+	ADCQ s9-80(SP), BX
+	ADCQ s10-88(SP), SI
+	ADCQ s11-96(SP), DI
+	ADCQ s12-104(SP), R8
+	ADCQ s13-112(SP), R9
+	ADCQ s14-120(SP), R10
+	ADCQ s15-128(SP), R11
+	ADCQ s16-136(SP), R12
+
+	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
+
+	ADDQ 0(AX), DX
+	ADCQ 8(AX), CX
+	ADCQ 16(AX), BX
+	ADCQ 24(AX), SI
+	ADCQ 32(AX), DI
+	ADCQ 40(AX), R8
+	ADCQ 48(AX), R9
+	ADCQ 56(AX), R10
+	ADCQ 64(AX), R11
+	ADCQ 72(AX), R12
+
+	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
+
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	MOVQ DI, 32(AX)
+	MOVQ R8, 40(AX)
+	MOVQ R9, 48(AX)
+	MOVQ R10, 56(AX)
+	MOVQ R11, 64(AX)
+	MOVQ R12, 72(AX)
+	RET
+
+// Butterfly(a, b *Element) sets a = a + b; b = a - b
+TEXT ·Butterfly(SB), $56-16
+	MOVQ b+8(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	MOVQ 32(AX), DI
+	MOVQ 40(AX), R8
+	MOVQ 48(AX), R9
+	MOVQ 56(AX), R10
+	MOVQ 64(AX), R11
+	MOVQ 72(AX), R12
+	MOVQ a+0(FP), AX
+	ADDQ 0(AX), DX
+	ADCQ 8(AX), CX
+	ADCQ 16(AX), BX
+	ADCQ 24(AX), SI
+	ADCQ 32(AX), DI
+	ADCQ 40(AX), R8
+	ADCQ 48(AX), R9
+	ADCQ 56(AX), R10
+	ADCQ 64(AX), R11
+	ADCQ 72(AX), R12
+	MOVQ DX, R13
+	MOVQ CX, R14
+	MOVQ BX, R15
+	MOVQ SI, s0-8(SP)
+	MOVQ DI, s1-16(SP)
+	MOVQ R8, s2-24(SP)
+	MOVQ R9, s3-32(SP)
+	MOVQ R10, s4-40(SP)
+	MOVQ R11, s5-48(SP)
+	MOVQ R12, s6-56(SP)
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	MOVQ 32(AX), DI
+	MOVQ 40(AX), R8
+	MOVQ 48(AX), R9
+	MOVQ 56(AX), R10
+	MOVQ 64(AX), R11
+	MOVQ 72(AX), R12
+	MOVQ b+8(FP), AX
+	SUBQ 0(AX), DX
+	SBBQ 8(AX), CX
+	SBBQ 16(AX), BX
+	SBBQ 24(AX), SI
+	SBBQ 32(AX), DI
+	SBBQ 40(AX), R8
+	SBBQ 48(AX), R9
+	SBBQ 56(AX), R10
+	SBBQ 64(AX), R11
+	SBBQ 72(AX), R12
+	JCC  noReduce_1
+	MOVQ $const_q0, AX
+	ADDQ AX, DX
+	MOVQ $const_q1, AX
+	ADCQ AX, CX
+	MOVQ $const_q2, AX
+	ADCQ AX, BX
+	MOVQ $const_q3, AX
+	ADCQ AX, SI
+	MOVQ $const_q4, AX
+	ADCQ AX, DI
+	MOVQ $const_q5, AX
+	ADCQ AX, R8
+	MOVQ $const_q6, AX
+	ADCQ AX, R9
+	MOVQ $const_q7, AX
+	ADCQ AX, R10
+	MOVQ $const_q8, AX
+	ADCQ AX, R11
+	MOVQ $const_q9, AX
+	ADCQ AX, R12
+
+noReduce_1:
+	MOVQ b+8(FP), AX
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	MOVQ DI, 32(AX)
+	MOVQ R8, 40(AX)
+	MOVQ R9, 48(AX)
+	MOVQ R10, 56(AX)
+	MOVQ R11, 64(AX)
+	MOVQ R12, 72(AX)
+	MOVQ R13, DX
+	MOVQ R14, CX
+	MOVQ R15, BX
+	MOVQ s0-8(SP), SI
+	MOVQ s1-16(SP), DI
+	MOVQ s2-24(SP), R8
+	MOVQ s3-32(SP), R9
+	MOVQ s4-40(SP), R10
+	MOVQ s5-48(SP), R11
+	MOVQ s6-56(SP), R12
+
+	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP))
+
+	MOVQ a+0(FP), AX
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	MOVQ DI, 32(AX)
+	MOVQ R8, 40(AX)
+	MOVQ R9, 48(AX)
+	MOVQ R10, 56(AX)
+	MOVQ R11, 64(AX)
+	MOVQ R12, 72(AX)
+	RET
+
+// mul(res, x, y *Element)
+TEXT ·mul(SB), $64-24
+
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+	// See github.com/gnark-crypto/field/generator for more comments.
+
+	NO_LOCAL_POINTERS
+	CMPB ·supportAdx(SB), $1
+	JNE  noAdx_2
+	MOVQ x+8(FP), R12
+	MOVQ y+16(FP), R13
+
+	// A -> BP
+	// t[0] -> R14
+	// t[1] -> R15
+	// t[2] -> CX
+	// t[3] -> BX
+	// t[4] -> SI
+	// t[5] -> DI
+	// t[6] -> R8
+	// t[7] -> R9
+	// t[8] -> R10
+	// t[9] -> R11
+#define MACC(in0, in1, in2) \
+	ADCXQ in0, in1     \
+	MULXQ in2, AX, in0 \
+	ADOXQ AX, in1      \
+
+#define DIV_SHIFT() \
+	PUSHQ BP                         \
+	MOVQ  $const_qInvNeg, DX         \
+	IMULQ R14, DX                    \
+	XORQ  AX, AX                     \
+	MULXQ ·qElement+0(SB), AX, BP    \
+	ADCXQ R14, AX                    \
+	MOVQ  BP, R14                    \
+	POPQ  BP                         \
+	MACC(R15, R14, ·qElement+8(SB))  \
+	MACC(CX, R15, ·qElement+16(SB))  \
+	MACC(BX, CX, ·qElement+24(SB))   \
+	MACC(SI, BX, ·qElement+32(SB))   \
+	MACC(DI, SI, ·qElement+40(SB))   \
+	MACC(R8, DI, ·qElement+48(SB))   \
+	MACC(R9, R8, ·qElement+56(SB))   \
+	MACC(R10, R9, ·qElement+64(SB))  \
+	MACC(R11, R10, ·qElement+72(SB)) \
+	MOVQ  $0, AX                     \
+	ADCXQ AX, R11                    \
+	ADOXQ BP, R11                    \
+
+#define MUL_WORD_0() \
+	XORQ  AX, AX           \
+	MULXQ 0(R12), R14, R15 \
+	MULXQ 8(R12), AX, CX   \
+	ADOXQ AX, R15          \
+	MULXQ 16(R12), AX, BX  \
+	ADOXQ AX, CX           \
+	MULXQ 24(R12), AX, SI  \
+	ADOXQ AX, BX           \
+	MULXQ 32(R12), AX, DI  \
+	ADOXQ AX, SI           \
+	MULXQ 40(R12), AX, R8  \
+	ADOXQ AX, DI           \
+	MULXQ 48(R12), AX, R9  \
+	ADOXQ AX, R8           \
+	MULXQ 56(R12), AX, R10 \
+	ADOXQ AX, R9           \
+	MULXQ 64(R12), AX, R11 \
+	ADOXQ AX, R10          \
+	MULXQ 72(R12), AX, BP  \
+	ADOXQ AX, R11          \
+	MOVQ  $0, AX           \
+	ADOXQ AX, BP           \
+	DIV_SHIFT()            \
+
+#define MUL_WORD_N() \
+	XORQ  AX, AX           \
+	MULXQ 0(R12), AX, BP   \
+	ADOXQ AX, R14          \
+	MACC(BP, R15, 8(R12))  \
+	MACC(BP, CX, 16(R12))  \
+	MACC(BP, BX, 24(R12))  \
+	MACC(BP, SI, 32(R12))  \
+	MACC(BP, DI, 40(R12))  \
+	MACC(BP, R8, 48(R12))  \
+	MACC(BP, R9, 56(R12))  \
+	MACC(BP, R10, 64(R12)) \
+	MACC(BP, R11, 72(R12)) \
+	MOVQ  $0, AX           \
+	ADCXQ AX, BP           \
+	ADOXQ AX, BP           \
+	DIV_SHIFT()            \
+
+	// mul body
+	MOVQ 0(R13), DX
+	MUL_WORD_0()
+	MOVQ 8(R13), DX
+	MUL_WORD_N()
+	MOVQ 16(R13), DX
+	MUL_WORD_N()
+	MOVQ 24(R13), DX
+	MUL_WORD_N()
+	MOVQ 32(R13), DX
+	MUL_WORD_N()
+	MOVQ 40(R13), DX
+	MUL_WORD_N()
+	MOVQ 48(R13), DX
+	MUL_WORD_N()
+	MOVQ 56(R13), DX
+	MUL_WORD_N()
+	MOVQ 64(R13), DX
+	MUL_WORD_N()
+	MOVQ 72(R13), DX
+	MUL_WORD_N()
+
+	// reduce element(R14,R15,CX,BX,SI,DI,R8,R9,R10,R11) using temp registers (R12,R13,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP))
+	REDUCE(R14,R15,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP))
+
+	MOVQ res+0(FP), AX
+	MOVQ R14, 0(AX)
+	MOVQ R15, 8(AX)
+	MOVQ CX, 16(AX)
+	MOVQ BX, 24(AX)
+	MOVQ SI, 32(AX)
+	MOVQ DI, 40(AX)
+	MOVQ R8, 48(AX)
+	MOVQ R9, 56(AX)
+	MOVQ R10, 64(AX)
+	MOVQ R11, 72(AX)
+	RET
+
+noAdx_2:
+	MOVQ res+0(FP), AX
+	MOVQ AX, (SP)
+	MOVQ x+8(FP), AX
+	MOVQ AX, 8(SP)
+	MOVQ y+16(FP), AX
+	MOVQ AX, 16(SP)
+	CALL ·_mulGeneric(SB)
+	RET
+
+TEXT ·fromMont(SB), $64-8
+	NO_LOCAL_POINTERS
+
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+	// when y = 1 we have:
+	// for i=0 to N-1
+	// 		t[i] = x[i]
+	// for i=0 to N-1
+	// 		m := t[0]*q'[0] mod W
+	// 		C,_ := t[0] + m*q[0]
+	// 		for j=1 to N-1
+	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
+	// 		t[N-1] = C
+	CMPB ·supportAdx(SB), $1
+	JNE  noAdx_3
+	MOVQ res+0(FP), DX
+	MOVQ 0(DX), R14
+	MOVQ 8(DX), R15
+	MOVQ 16(DX), CX
+	MOVQ 24(DX), BX
+	MOVQ 32(DX), SI
+	MOVQ 40(DX), DI
+	MOVQ 48(DX), R8
+	MOVQ 56(DX), R9
+	MOVQ 64(DX), R10
+	MOVQ 72(DX), R11
+	XORQ DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+
+	// (C,t[5]) := t[6] + m*q[6] + C
+	ADCXQ R8, DI
+	MULXQ ·qElement+48(SB), AX, R8
+	ADOXQ AX, DI
+
+	// (C,t[6]) := t[7] + m*q[7] + C
+	ADCXQ R9, R8
+	MULXQ ·qElement+56(SB), AX, R9
+	ADOXQ AX, R8
+
+	// (C,t[7]) := t[8] + m*q[8] + C
+	ADCXQ R10, R9
+	MULXQ ·qElement+64(SB), AX, R10
+	ADOXQ AX, R9
+
+	// (C,t[8]) := t[9] + m*q[9] + C
+	ADCXQ R11, R10
+	MULXQ ·qElement+72(SB), AX, R11
+	ADOXQ AX, R10
+	MOVQ  $0, AX
+	ADCXQ AX, R11
+	ADOXQ AX, R11
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+
+	// (C,t[5]) := t[6] + m*q[6] + C
+	ADCXQ R8, DI
+	MULXQ ·qElement+48(SB), AX, R8
+	ADOXQ AX, DI
+
+	// (C,t[6]) := t[7] + m*q[7] + C
+	ADCXQ R9, R8
+	MULXQ ·qElement+56(SB), AX, R9
+	ADOXQ AX, R8
+
+	// (C,t[7]) := t[8] + m*q[8] + C
+	ADCXQ R10, R9
+	MULXQ ·qElement+64(SB), AX, R10
+	ADOXQ AX, R9
+
+	// (C,t[8]) := t[9] + m*q[9] + C
+	ADCXQ R11, R10
+	MULXQ ·qElement+72(SB), AX, R11
+	ADOXQ AX, R10
+	MOVQ  $0, AX
+	ADCXQ AX, R11
+	ADOXQ AX, R11
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+
+	// (C,t[5]) := t[6] + m*q[6] + C
+	ADCXQ R8, DI
+	MULXQ ·qElement+48(SB), AX, R8
+	ADOXQ AX, DI
+
+	// (C,t[6]) := t[7] + m*q[7] + C
+	ADCXQ R9, R8
+	MULXQ ·qElement+56(SB), AX, R9
+	ADOXQ AX, R8
+
+	// (C,t[7]) := t[8] + m*q[8] + C
+	ADCXQ R10, R9
+	MULXQ ·qElement+64(SB), AX, R10
+	ADOXQ AX, R9
+
+	// (C,t[8]) := t[9] + m*q[9] + C
+	ADCXQ R11, R10
+	MULXQ ·qElement+72(SB), AX, R11
+	ADOXQ AX, R10
+	MOVQ  $0, AX
+	ADCXQ AX, R11
+	ADOXQ AX, R11
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+
+	// (C,t[5]) := t[6] + m*q[6] + C
+	ADCXQ R8, DI
+	MULXQ ·qElement+48(SB), AX, R8
+	ADOXQ AX, DI
+
+	// (C,t[6]) := t[7] + m*q[7] + C
+	ADCXQ R9, R8
+	MULXQ ·qElement+56(SB), AX, R9
+	ADOXQ AX, R8
+
+	// (C,t[7]) := t[8] + m*q[8] + C
+	ADCXQ R10, R9
+	MULXQ ·qElement+64(SB), AX, R10
+	ADOXQ AX, R9
+
+	// (C,t[8]) := t[9] + m*q[9] + C
+	ADCXQ R11, R10
+	MULXQ ·qElement+72(SB), AX, R11
+	ADOXQ AX, R10
+	MOVQ  $0, AX
+	ADCXQ AX, R11
+	ADOXQ AX, R11
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+
+	// (C,t[5]) := t[6] + m*q[6] + C
+	ADCXQ R8, DI
+	MULXQ ·qElement+48(SB), AX, R8
+	ADOXQ AX, DI
+
+	// (C,t[6]) := t[7] + m*q[7] + C
+	ADCXQ R9, R8
+	MULXQ ·qElement+56(SB), AX, R9
+	ADOXQ AX, R8
+
+	// (C,t[7]) := t[8] + m*q[8] + C
+	ADCXQ R10, R9
+	MULXQ ·qElement+64(SB), AX, R10
+	ADOXQ AX, R9
+
+	// (C,t[8]) := t[9] + m*q[9] + C
+	ADCXQ R11, R10
+	MULXQ ·qElement+72(SB), AX, R11
+	ADOXQ AX, R10
+	MOVQ  $0, AX
+	ADCXQ AX, R11
+	ADOXQ AX, R11
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+
+	// (C,t[5]) := t[6] + m*q[6] + C
+	ADCXQ R8, DI
+	MULXQ ·qElement+48(SB), AX, R8
+	ADOXQ AX, DI
+
+	// (C,t[6]) := t[7] + m*q[7] + C
+	ADCXQ R9, R8
+	MULXQ ·qElement+56(SB), AX, R9
+	ADOXQ AX, R8
+
+	// (C,t[7]) := t[8] + m*q[8] + C
+	ADCXQ R10, R9
+	MULXQ ·qElement+64(SB), AX, R10
+	ADOXQ AX, R9
+
+	// (C,t[8]) := t[9] + m*q[9] + C
+	ADCXQ R11, R10
+	MULXQ ·qElement+72(SB), AX, R11
+	ADOXQ AX, R10
+	MOVQ  $0, AX
+	ADCXQ AX, R11
+	ADOXQ AX, R11
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+
+	// (C,t[5]) := t[6] + m*q[6] + C
+	ADCXQ R8, DI
+	MULXQ ·qElement+48(SB), AX, R8
+	ADOXQ AX, DI
+
+	// (C,t[6]) := t[7] + m*q[7] + C
+	ADCXQ R9, R8
+	MULXQ ·qElement+56(SB), AX, R9
+	ADOXQ AX, R8
+
+	// (C,t[7]) := t[8] + m*q[8] + C
+	ADCXQ R10, R9
+	MULXQ ·qElement+64(SB), AX, R10
+	ADOXQ AX, R9
+
+	// (C,t[8]) := t[9] + m*q[9] + C
+	ADCXQ R11, R10
+	MULXQ ·qElement+72(SB), AX, R11
+	ADOXQ AX, R10
+	MOVQ  $0, AX
+	ADCXQ AX, R11
+	ADOXQ AX, R11
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+
+	// (C,t[5]) := t[6] + m*q[6] + C
+	ADCXQ R8, DI
+	MULXQ ·qElement+48(SB), AX, R8
+	ADOXQ AX, DI
+
+	// (C,t[6]) := t[7] + m*q[7] + C
+	ADCXQ R9, R8
+	MULXQ ·qElement+56(SB), AX, R9
+	ADOXQ AX, R8
+
+	// (C,t[7]) := t[8] + m*q[8] + C
+	ADCXQ R10, R9
+	MULXQ ·qElement+64(SB), AX, R10
+	ADOXQ AX, R9
+
+	// (C,t[8]) := t[9] + m*q[9] + C
+	ADCXQ R11, R10
+	MULXQ ·qElement+72(SB), AX, R11
+	ADOXQ AX, R10
+	MOVQ  $0, AX
+	ADCXQ AX, R11
+	ADOXQ AX, R11
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+
+	// (C,t[5]) := t[6] + m*q[6] + C
+	ADCXQ R8, DI
+	MULXQ ·qElement+48(SB), AX, R8
+	ADOXQ AX, DI
+
+	// (C,t[6]) := t[7] + m*q[7] + C
+	ADCXQ R9, R8
+	MULXQ ·qElement+56(SB), AX, R9
+	ADOXQ AX, R8
+
+	// (C,t[7]) := t[8] + m*q[8] + C
+	ADCXQ R10, R9
+	MULXQ ·qElement+64(SB), AX, R10
+	ADOXQ AX, R9
+
+	// (C,t[8]) := t[9] + m*q[9] + C
+	ADCXQ R11, R10
+	MULXQ ·qElement+72(SB), AX, R11
+	ADOXQ AX, R10
+	MOVQ  $0, AX
+	ADCXQ AX, R11
+	ADOXQ AX, R11
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+
+	// (C,t[5]) := t[6] + m*q[6] + C
+	ADCXQ R8, DI
+	MULXQ ·qElement+48(SB), AX, R8
+	ADOXQ AX, DI
+
+	// (C,t[6]) := t[7] + m*q[7] + C
+	ADCXQ R9, R8
+	MULXQ ·qElement+56(SB), AX, R9
+	ADOXQ AX, R8
+
+	// (C,t[7]) := t[8] + m*q[8] + C
+	ADCXQ R10, R9
+	MULXQ ·qElement+64(SB), AX, R10
+	ADOXQ AX, R9
+
+	// (C,t[8]) := t[9] + m*q[9] + C
+	ADCXQ R11, R10
+	MULXQ ·qElement+72(SB), AX, R11
+	ADOXQ AX, R10
+	MOVQ  $0, AX
+	ADCXQ AX, R11
+	ADOXQ AX, R11
+
+	// reduce element(R14,R15,CX,BX,SI,DI,R8,R9,R10,R11) using temp registers (R12,R13,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP))
+	REDUCE(R14,R15,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP))
+
+	MOVQ res+0(FP), AX
+	MOVQ R14, 0(AX)
+	MOVQ R15, 8(AX)
+	MOVQ CX, 16(AX)
+	MOVQ BX, 24(AX)
+	MOVQ SI, 32(AX)
+	MOVQ DI, 40(AX)
+	MOVQ R8, 48(AX)
+	MOVQ R9, 56(AX)
+	MOVQ R10, 64(AX)
+	MOVQ R11, 72(AX)
+	RET
+
+noAdx_3:
+	MOVQ res+0(FP), AX
+	MOVQ AX, (SP)
+	CALL ·_fromMontGeneric(SB)
+	RET
diff --git a/field/asm/element_12w_amd64.s b/field/asm/element_12w_amd64.s
new file mode 100644
index 0000000000..52cf02adc1
--- /dev/null
+++ b/field/asm/element_12w_amd64.s
@@ -0,0 +1,1557 @@
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+#include "textflag.h"
+#include "funcdata.h"
+#include "go_asm.h"
+
+#define REDUCE(ra0, ra1, ra2, ra3, ra4, ra5, ra6, ra7, ra8, ra9, ra10, ra11, rb0, rb1, rb2, rb3, rb4, rb5, rb6, rb7, rb8, rb9, rb10, rb11) \
+	MOVQ    ra0, rb0;               \
+	SUBQ    ·qElement(SB), ra0;     \
+	MOVQ    ra1, rb1;               \
+	SBBQ    ·qElement+8(SB), ra1;   \
+	MOVQ    ra2, rb2;               \
+	SBBQ    ·qElement+16(SB), ra2;  \
+	MOVQ    ra3, rb3;               \
+	SBBQ    ·qElement+24(SB), ra3;  \
+	MOVQ    ra4, rb4;               \
+	SBBQ    ·qElement+32(SB), ra4;  \
+	MOVQ    ra5, rb5;               \
+	SBBQ    ·qElement+40(SB), ra5;  \
+	MOVQ    ra6, rb6;               \
+	SBBQ    ·qElement+48(SB), ra6;  \
+	MOVQ    ra7, rb7;               \
+	SBBQ    ·qElement+56(SB), ra7;  \
+	MOVQ    ra8, rb8;               \
+	SBBQ    ·qElement+64(SB), ra8;  \
+	MOVQ    ra9, rb9;               \
+	SBBQ    ·qElement+72(SB), ra9;  \
+	MOVQ    ra10, rb10;             \
+	SBBQ    ·qElement+80(SB), ra10; \
+	MOVQ    ra11, rb11;             \
+	SBBQ    ·qElement+88(SB), ra11; \
+	CMOVQCS rb0, ra0;               \
+	CMOVQCS rb1, ra1;               \
+	CMOVQCS rb2, ra2;               \
+	CMOVQCS rb3, ra3;               \
+	CMOVQCS rb4, ra4;               \
+	CMOVQCS rb5, ra5;               \
+	CMOVQCS rb6, ra6;               \
+	CMOVQCS rb7, ra7;               \
+	CMOVQCS rb8, ra8;               \
+	CMOVQCS rb9, ra9;               \
+	CMOVQCS rb10, ra10;             \
+	CMOVQCS rb11, ra11;             \
+
+TEXT ·reduce(SB), $88-8
+	MOVQ res+0(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	MOVQ 32(AX), DI
+	MOVQ 40(AX), R8
+	MOVQ 48(AX), R9
+	MOVQ 56(AX), R10
+	MOVQ 64(AX), R11
+	MOVQ 72(AX), R12
+	MOVQ 80(AX), R13
+	MOVQ 88(AX), R14
+
+	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
+
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	MOVQ DI, 32(AX)
+	MOVQ R8, 40(AX)
+	MOVQ R9, 48(AX)
+	MOVQ R10, 56(AX)
+	MOVQ R11, 64(AX)
+	MOVQ R12, 72(AX)
+	MOVQ R13, 80(AX)
+	MOVQ R14, 88(AX)
+	RET
+
+// MulBy3(x *Element)
+TEXT ·MulBy3(SB), $88-8
+	MOVQ x+0(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	MOVQ 32(AX), DI
+	MOVQ 40(AX), R8
+	MOVQ 48(AX), R9
+	MOVQ 56(AX), R10
+	MOVQ 64(AX), R11
+	MOVQ 72(AX), R12
+	MOVQ 80(AX), R13
+	MOVQ 88(AX), R14
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+	ADCQ DI, DI
+	ADCQ R8, R8
+	ADCQ R9, R9
+	ADCQ R10, R10
+	ADCQ R11, R11
+	ADCQ R12, R12
+	ADCQ R13, R13
+	ADCQ R14, R14
+
+	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
+
+	ADDQ 0(AX), DX
+	ADCQ 8(AX), CX
+	ADCQ 16(AX), BX
+	ADCQ 24(AX), SI
+	ADCQ 32(AX), DI
+	ADCQ 40(AX), R8
+	ADCQ 48(AX), R9
+	ADCQ 56(AX), R10
+	ADCQ 64(AX), R11
+	ADCQ 72(AX), R12
+	ADCQ 80(AX), R13
+	ADCQ 88(AX), R14
+
+	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
+
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	MOVQ DI, 32(AX)
+	MOVQ R8, 40(AX)
+	MOVQ R9, 48(AX)
+	MOVQ R10, 56(AX)
+	MOVQ R11, 64(AX)
+	MOVQ R12, 72(AX)
+	MOVQ R13, 80(AX)
+	MOVQ R14, 88(AX)
+	RET
+
+// MulBy5(x *Element)
+TEXT ·MulBy5(SB), $88-8
+	MOVQ x+0(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	MOVQ 32(AX), DI
+	MOVQ 40(AX), R8
+	MOVQ 48(AX), R9
+	MOVQ 56(AX), R10
+	MOVQ 64(AX), R11
+	MOVQ 72(AX), R12
+	MOVQ 80(AX), R13
+	MOVQ 88(AX), R14
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+	ADCQ DI, DI
+	ADCQ R8, R8
+	ADCQ R9, R9
+	ADCQ R10, R10
+	ADCQ R11, R11
+	ADCQ R12, R12
+	ADCQ R13, R13
+	ADCQ R14, R14
+
+	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
+
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+	ADCQ DI, DI
+	ADCQ R8, R8
+	ADCQ R9, R9
+	ADCQ R10, R10
+	ADCQ R11, R11
+	ADCQ R12, R12
+	ADCQ R13, R13
+	ADCQ R14, R14
+
+	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
+
+	ADDQ 0(AX), DX
+	ADCQ 8(AX), CX
+	ADCQ 16(AX), BX
+	ADCQ 24(AX), SI
+	ADCQ 32(AX), DI
+	ADCQ 40(AX), R8
+	ADCQ 48(AX), R9
+	ADCQ 56(AX), R10
+	ADCQ 64(AX), R11
+	ADCQ 72(AX), R12
+	ADCQ 80(AX), R13
+	ADCQ 88(AX), R14
+
+	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
+
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	MOVQ DI, 32(AX)
+	MOVQ R8, 40(AX)
+	MOVQ R9, 48(AX)
+	MOVQ R10, 56(AX)
+	MOVQ R11, 64(AX)
+	MOVQ R12, 72(AX)
+	MOVQ R13, 80(AX)
+	MOVQ R14, 88(AX)
+	RET
+
+// MulBy13(x *Element)
+TEXT ·MulBy13(SB), $184-8
+	MOVQ x+0(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	MOVQ 32(AX), DI
+	MOVQ 40(AX), R8
+	MOVQ 48(AX), R9
+	MOVQ 56(AX), R10
+	MOVQ 64(AX), R11
+	MOVQ 72(AX), R12
+	MOVQ 80(AX), R13
+	MOVQ 88(AX), R14
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+	ADCQ DI, DI
+	ADCQ R8, R8
+	ADCQ R9, R9
+	ADCQ R10, R10
+	ADCQ R11, R11
+	ADCQ R12, R12
+	ADCQ R13, R13
+	ADCQ R14, R14
+
+	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
+
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+	ADCQ DI, DI
+	ADCQ R8, R8
+	ADCQ R9, R9
+	ADCQ R10, R10
+	ADCQ R11, R11
+	ADCQ R12, R12
+	ADCQ R13, R13
+	ADCQ R14, R14
+
+	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14) using temp registers (s11-96(SP),s12-104(SP),s13-112(SP),s14-120(SP),s15-128(SP),s16-136(SP),s17-144(SP),s18-152(SP),s19-160(SP),s20-168(SP),s21-176(SP),s22-184(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,s11-96(SP),s12-104(SP),s13-112(SP),s14-120(SP),s15-128(SP),s16-136(SP),s17-144(SP),s18-152(SP),s19-160(SP),s20-168(SP),s21-176(SP),s22-184(SP))
+
+	MOVQ DX, s11-96(SP)
+	MOVQ CX, s12-104(SP)
+	MOVQ BX, s13-112(SP)
+	MOVQ SI, s14-120(SP)
+	MOVQ DI, s15-128(SP)
+	MOVQ R8, s16-136(SP)
+	MOVQ R9, s17-144(SP)
+	MOVQ R10, s18-152(SP)
+	MOVQ R11, s19-160(SP)
+	MOVQ R12, s20-168(SP)
+	MOVQ R13, s21-176(SP)
+	MOVQ R14, s22-184(SP)
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+	ADCQ DI, DI
+	ADCQ R8, R8
+	ADCQ R9, R9
+	ADCQ R10, R10
+	ADCQ R11, R11
+	ADCQ R12, R12
+	ADCQ R13, R13
+	ADCQ R14, R14
+
+	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
+
+	ADDQ s11-96(SP), DX
+	ADCQ s12-104(SP), CX
+	ADCQ s13-112(SP), BX
+	ADCQ s14-120(SP), SI
+	ADCQ s15-128(SP), DI
+	ADCQ s16-136(SP), R8
+	ADCQ s17-144(SP), R9
+	ADCQ s18-152(SP), R10
+	ADCQ s19-160(SP), R11
+	ADCQ s20-168(SP), R12
+	ADCQ s21-176(SP), R13
+	ADCQ s22-184(SP), R14
+
+	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
+
+	ADDQ 0(AX), DX
+	ADCQ 8(AX), CX
+	ADCQ 16(AX), BX
+	ADCQ 24(AX), SI
+	ADCQ 32(AX), DI
+	ADCQ 40(AX), R8
+	ADCQ 48(AX), R9
+	ADCQ 56(AX), R10
+	ADCQ 64(AX), R11
+	ADCQ 72(AX), R12
+	ADCQ 80(AX), R13
+	ADCQ 88(AX), R14
+
+	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
+
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	MOVQ DI, 32(AX)
+	MOVQ R8, 40(AX)
+	MOVQ R9, 48(AX)
+	MOVQ R10, 56(AX)
+	MOVQ R11, 64(AX)
+	MOVQ R12, 72(AX)
+	MOVQ R13, 80(AX)
+	MOVQ R14, 88(AX)
+	RET
+
+// Butterfly(a, b *Element) sets a = a + b; b = a - b
+TEXT ·Butterfly(SB), $88-16
+	MOVQ b+8(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	MOVQ 32(AX), DI
+	MOVQ 40(AX), R8
+	MOVQ 48(AX), R9
+	MOVQ 56(AX), R10
+	MOVQ 64(AX), R11
+	MOVQ 72(AX), R12
+	MOVQ 80(AX), R13
+	MOVQ 88(AX), R14
+	MOVQ a+0(FP), AX
+	ADDQ 0(AX), DX
+	ADCQ 8(AX), CX
+	ADCQ 16(AX), BX
+	ADCQ 24(AX), SI
+	ADCQ 32(AX), DI
+	ADCQ 40(AX), R8
+	ADCQ 48(AX), R9
+	ADCQ 56(AX), R10
+	ADCQ 64(AX), R11
+	ADCQ 72(AX), R12
+	ADCQ 80(AX), R13
+	ADCQ 88(AX), R14
+	MOVQ DX, R15
+	MOVQ CX, s0-8(SP)
+	MOVQ BX, s1-16(SP)
+	MOVQ SI, s2-24(SP)
+	MOVQ DI, s3-32(SP)
+	MOVQ R8, s4-40(SP)
+	MOVQ R9, s5-48(SP)
+	MOVQ R10, s6-56(SP)
+	MOVQ R11, s7-64(SP)
+	MOVQ R12, s8-72(SP)
+	MOVQ R13, s9-80(SP)
+	MOVQ R14, s10-88(SP)
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	MOVQ 32(AX), DI
+	MOVQ 40(AX), R8
+	MOVQ 48(AX), R9
+	MOVQ 56(AX), R10
+	MOVQ 64(AX), R11
+	MOVQ 72(AX), R12
+	MOVQ 80(AX), R13
+	MOVQ 88(AX), R14
+	MOVQ b+8(FP), AX
+	SUBQ 0(AX), DX
+	SBBQ 8(AX), CX
+	SBBQ 16(AX), BX
+	SBBQ 24(AX), SI
+	SBBQ 32(AX), DI
+	SBBQ 40(AX), R8
+	SBBQ 48(AX), R9
+	SBBQ 56(AX), R10
+	SBBQ 64(AX), R11
+	SBBQ 72(AX), R12
+	SBBQ 80(AX), R13
+	SBBQ 88(AX), R14
+	JCC  noReduce_1
+	MOVQ $const_q0, AX
+	ADDQ AX, DX
+	MOVQ $const_q1, AX
+	ADCQ AX, CX
+	MOVQ $const_q2, AX
+	ADCQ AX, BX
+	MOVQ $const_q3, AX
+	ADCQ AX, SI
+	MOVQ $const_q4, AX
+	ADCQ AX, DI
+	MOVQ $const_q5, AX
+	ADCQ AX, R8
+	MOVQ $const_q6, AX
+	ADCQ AX, R9
+	MOVQ $const_q7, AX
+	ADCQ AX, R10
+	MOVQ $const_q8, AX
+	ADCQ AX, R11
+	MOVQ $const_q9, AX
+	ADCQ AX, R12
+	MOVQ $const_q10, AX
+	ADCQ AX, R13
+	MOVQ $const_q11, AX
+	ADCQ AX, R14
+
+noReduce_1:
+	MOVQ b+8(FP), AX
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	MOVQ DI, 32(AX)
+	MOVQ R8, 40(AX)
+	MOVQ R9, 48(AX)
+	MOVQ R10, 56(AX)
+	MOVQ R11, 64(AX)
+	MOVQ R12, 72(AX)
+	MOVQ R13, 80(AX)
+	MOVQ R14, 88(AX)
+	MOVQ R15, DX
+	MOVQ s0-8(SP), CX
+	MOVQ s1-16(SP), BX
+	MOVQ s2-24(SP), SI
+	MOVQ s3-32(SP), DI
+	MOVQ s4-40(SP), R8
+	MOVQ s5-48(SP), R9
+	MOVQ s6-56(SP), R10
+	MOVQ s7-64(SP), R11
+	MOVQ s8-72(SP), R12
+	MOVQ s9-80(SP), R13
+	MOVQ s10-88(SP), R14
+
+	// reduce element(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP))
+
+	MOVQ a+0(FP), AX
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	MOVQ DI, 32(AX)
+	MOVQ R8, 40(AX)
+	MOVQ R9, 48(AX)
+	MOVQ R10, 56(AX)
+	MOVQ R11, 64(AX)
+	MOVQ R12, 72(AX)
+	MOVQ R13, 80(AX)
+	MOVQ R14, 88(AX)
+	RET
+
+// mul(res, x, y *Element)
+TEXT ·mul(SB), $96-24
+
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+	// See github.com/gnark-crypto/field/generator for more comments.
+
+	NO_LOCAL_POINTERS
+	CMPB ·supportAdx(SB), $1
+	JNE  noAdx_2
+	MOVQ x+8(FP), AX
+
+	// x[0] -> s0-8(SP)
+	// x[1] -> s1-16(SP)
+	// x[2] -> s2-24(SP)
+	// x[3] -> s3-32(SP)
+	// x[4] -> s4-40(SP)
+	// x[5] -> s5-48(SP)
+	// x[6] -> s6-56(SP)
+	// x[7] -> s7-64(SP)
+	// x[8] -> s8-72(SP)
+	// x[9] -> s9-80(SP)
+	// x[10] -> s10-88(SP)
+	// x[11] -> s11-96(SP)
+	MOVQ 0(AX), R14
+	MOVQ 8(AX), R15
+	MOVQ 16(AX), CX
+	MOVQ 24(AX), BX
+	MOVQ 32(AX), SI
+	MOVQ 40(AX), DI
+	MOVQ 48(AX), R8
+	MOVQ 56(AX), R9
+	MOVQ 64(AX), R10
+	MOVQ 72(AX), R11
+	MOVQ 80(AX), R12
+	MOVQ 88(AX), R13
+	MOVQ R14, s0-8(SP)
+	MOVQ R15, s1-16(SP)
+	MOVQ CX, s2-24(SP)
+	MOVQ BX, s3-32(SP)
+	MOVQ SI, s4-40(SP)
+	MOVQ DI, s5-48(SP)
+	MOVQ R8, s6-56(SP)
+	MOVQ R9, s7-64(SP)
+	MOVQ R10, s8-72(SP)
+	MOVQ R11, s9-80(SP)
+	MOVQ R12, s10-88(SP)
+	MOVQ R13, s11-96(SP)
+
+	// A -> BP
+	// t[0] -> R14
+	// t[1] -> R15
+	// t[2] -> CX
+	// t[3] -> BX
+	// t[4] -> SI
+	// t[5] -> DI
+	// t[6] -> R8
+	// t[7] -> R9
+	// t[8] -> R10
+	// t[9] -> R11
+	// t[10] -> R12
+	// t[11] -> R13
+#define MACC(in0, in1, in2) \
+	ADCXQ in0, in1     \
+	MULXQ in2, AX, in0 \
+	ADOXQ AX, in1      \
+
+#define DIV_SHIFT() \
+	PUSHQ BP                         \
+	MOVQ  $const_qInvNeg, DX         \
+	IMULQ R14, DX                    \
+	XORQ  AX, AX                     \
+	MULXQ ·qElement+0(SB), AX, BP    \
+	ADCXQ R14, AX                    \
+	MOVQ  BP, R14                    \
+	POPQ  BP                         \
+	MACC(R15, R14, ·qElement+8(SB))  \
+	MACC(CX, R15, ·qElement+16(SB))  \
+	MACC(BX, CX, ·qElement+24(SB))   \
+	MACC(SI, BX, ·qElement+32(SB))   \
+	MACC(DI, SI, ·qElement+40(SB))   \
+	MACC(R8, DI, ·qElement+48(SB))   \
+	MACC(R9, R8, ·qElement+56(SB))   \
+	MACC(R10, R9, ·qElement+64(SB))  \
+	MACC(R11, R10, ·qElement+72(SB)) \
+	MACC(R12, R11, ·qElement+80(SB)) \
+	MACC(R13, R12, ·qElement+88(SB)) \
+	MOVQ  $0, AX                     \
+	ADCXQ AX, R13                    \
+	ADOXQ BP, R13                    \
+
+#define MUL_WORD_0() \
+	XORQ  AX, AX              \
+	MULXQ s0-8(SP), R14, R15  \
+	MULXQ s1-16(SP), AX, CX   \
+	ADOXQ AX, R15             \
+	MULXQ s2-24(SP), AX, BX   \
+	ADOXQ AX, CX              \
+	MULXQ s3-32(SP), AX, SI   \
+	ADOXQ AX, BX              \
+	MULXQ s4-40(SP), AX, DI   \
+	ADOXQ AX, SI              \
+	MULXQ s5-48(SP), AX, R8   \
+	ADOXQ AX, DI              \
+	MULXQ s6-56(SP), AX, R9   \
+	ADOXQ AX, R8              \
+	MULXQ s7-64(SP), AX, R10  \
+	ADOXQ AX, R9              \
+	MULXQ s8-72(SP), AX, R11  \
+	ADOXQ AX, R10             \
+	MULXQ s9-80(SP), AX, R12  \
+	ADOXQ AX, R11             \
+	MULXQ s10-88(SP), AX, R13 \
+	ADOXQ AX, R12             \
+	MULXQ s11-96(SP), AX, BP  \
+	ADOXQ AX, R13             \
+	MOVQ  $0, AX              \
+	ADOXQ AX, BP              \
+	DIV_SHIFT()               \
+
+#define MUL_WORD_N() \
+	XORQ  AX, AX              \
+	MULXQ s0-8(SP), AX, BP    \
+	ADOXQ AX, R14             \
+	MACC(BP, R15, s1-16(SP))  \
+	MACC(BP, CX, s2-24(SP))   \
+	MACC(BP, BX, s3-32(SP))   \
+	MACC(BP, SI, s4-40(SP))   \
+	MACC(BP, DI, s5-48(SP))   \
+	MACC(BP, R8, s6-56(SP))   \
+	MACC(BP, R9, s7-64(SP))   \
+	MACC(BP, R10, s8-72(SP))  \
+	MACC(BP, R11, s9-80(SP))  \
+	MACC(BP, R12, s10-88(SP)) \
+	MACC(BP, R13, s11-96(SP)) \
+	MOVQ  $0, AX              \
+	ADCXQ AX, BP              \
+	ADOXQ AX, BP              \
+	DIV_SHIFT()               \
+
+	// mul body
+	MOVQ y+16(FP), AX
+	MOVQ 0(AX), DX
+	MUL_WORD_0()
+	MOVQ y+16(FP), AX
+	MOVQ 8(AX), DX
+	MUL_WORD_N()
+	MOVQ y+16(FP), AX
+	MOVQ 16(AX), DX
+	MUL_WORD_N()
+	MOVQ y+16(FP), AX
+	MOVQ 24(AX), DX
+	MUL_WORD_N()
+	MOVQ y+16(FP), AX
+	MOVQ 32(AX), DX
+	MUL_WORD_N()
+	MOVQ y+16(FP), AX
+	MOVQ 40(AX), DX
+	MUL_WORD_N()
+	MOVQ y+16(FP), AX
+	MOVQ 48(AX), DX
+	MUL_WORD_N()
+	MOVQ y+16(FP), AX
+	MOVQ 56(AX), DX
+	MUL_WORD_N()
+	MOVQ y+16(FP), AX
+	MOVQ 64(AX), DX
+	MUL_WORD_N()
+	MOVQ y+16(FP), AX
+	MOVQ 72(AX), DX
+	MUL_WORD_N()
+	MOVQ y+16(FP), AX
+	MOVQ 80(AX), DX
+	MUL_WORD_N()
+	MOVQ y+16(FP), AX
+	MOVQ 88(AX), DX
+	MUL_WORD_N()
+
+	// reduce element(R14,R15,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13) using temp registers (s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP),s11-96(SP))
+	REDUCE(R14,R15,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP),s11-96(SP))
+
+	MOVQ res+0(FP), AX
+	MOVQ R14, 0(AX)
+	MOVQ R15, 8(AX)
+	MOVQ CX, 16(AX)
+	MOVQ BX, 24(AX)
+	MOVQ SI, 32(AX)
+	MOVQ DI, 40(AX)
+	MOVQ R8, 48(AX)
+	MOVQ R9, 56(AX)
+	MOVQ R10, 64(AX)
+	MOVQ R11, 72(AX)
+	MOVQ R12, 80(AX)
+	MOVQ R13, 88(AX)
+	RET
+
+noAdx_2:
+	MOVQ res+0(FP), AX
+	MOVQ AX, (SP)
+	MOVQ x+8(FP), AX
+	MOVQ AX, 8(SP)
+	MOVQ y+16(FP), AX
+	MOVQ AX, 16(SP)
+	CALL ·_mulGeneric(SB)
+	RET
+
+TEXT ·fromMont(SB), $96-8
+	NO_LOCAL_POINTERS
+
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+	// when y = 1 we have:
+	// for i=0 to N-1
+	// 		t[i] = x[i]
+	// for i=0 to N-1
+	// 		m := t[0]*q'[0] mod W
+	// 		C,_ := t[0] + m*q[0]
+	// 		for j=1 to N-1
+	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
+	// 		t[N-1] = C
+	CMPB ·supportAdx(SB), $1
+	JNE  noAdx_3
+	MOVQ res+0(FP), DX
+	MOVQ 0(DX), R14
+	MOVQ 8(DX), R15
+	MOVQ 16(DX), CX
+	MOVQ 24(DX), BX
+	MOVQ 32(DX), SI
+	MOVQ 40(DX), DI
+	MOVQ 48(DX), R8
+	MOVQ 56(DX), R9
+	MOVQ 64(DX), R10
+	MOVQ 72(DX), R11
+	MOVQ 80(DX), R12
+	MOVQ 88(DX), R13
+	XORQ DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+
+	// (C,t[5]) := t[6] + m*q[6] + C
+	ADCXQ R8, DI
+	MULXQ ·qElement+48(SB), AX, R8
+	ADOXQ AX, DI
+
+	// (C,t[6]) := t[7] + m*q[7] + C
+	ADCXQ R9, R8
+	MULXQ ·qElement+56(SB), AX, R9
+	ADOXQ AX, R8
+
+	// (C,t[7]) := t[8] + m*q[8] + C
+	ADCXQ R10, R9
+	MULXQ ·qElement+64(SB), AX, R10
+	ADOXQ AX, R9
+
+	// (C,t[8]) := t[9] + m*q[9] + C
+	ADCXQ R11, R10
+	MULXQ ·qElement+72(SB), AX, R11
+	ADOXQ AX, R10
+
+	// (C,t[9]) := t[10] + m*q[10] + C
+	ADCXQ R12, R11
+	MULXQ ·qElement+80(SB), AX, R12
+	ADOXQ AX, R11
+
+	// (C,t[10]) := t[11] + m*q[11] + C
+	ADCXQ R13, R12
+	MULXQ ·qElement+88(SB), AX, R13
+	ADOXQ AX, R12
+	MOVQ  $0, AX
+	ADCXQ AX, R13
+	ADOXQ AX, R13
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+
+	// (C,t[5]) := t[6] + m*q[6] + C
+	ADCXQ R8, DI
+	MULXQ ·qElement+48(SB), AX, R8
+	ADOXQ AX, DI
+
+	// (C,t[6]) := t[7] + m*q[7] + C
+	ADCXQ R9, R8
+	MULXQ ·qElement+56(SB), AX, R9
+	ADOXQ AX, R8
+
+	// (C,t[7]) := t[8] + m*q[8] + C
+	ADCXQ R10, R9
+	MULXQ ·qElement+64(SB), AX, R10
+	ADOXQ AX, R9
+
+	// (C,t[8]) := t[9] + m*q[9] + C
+	ADCXQ R11, R10
+	MULXQ ·qElement+72(SB), AX, R11
+	ADOXQ AX, R10
+
+	// (C,t[9]) := t[10] + m*q[10] + C
+	ADCXQ R12, R11
+	MULXQ ·qElement+80(SB), AX, R12
+	ADOXQ AX, R11
+
+	// (C,t[10]) := t[11] + m*q[11] + C
+	ADCXQ R13, R12
+	MULXQ ·qElement+88(SB), AX, R13
+	ADOXQ AX, R12
+	MOVQ  $0, AX
+	ADCXQ AX, R13
+	ADOXQ AX, R13
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+
+	// (C,t[5]) := t[6] + m*q[6] + C
+	ADCXQ R8, DI
+	MULXQ ·qElement+48(SB), AX, R8
+	ADOXQ AX, DI
+
+	// (C,t[6]) := t[7] + m*q[7] + C
+	ADCXQ R9, R8
+	MULXQ ·qElement+56(SB), AX, R9
+	ADOXQ AX, R8
+
+	// (C,t[7]) := t[8] + m*q[8] + C
+	ADCXQ R10, R9
+	MULXQ ·qElement+64(SB), AX, R10
+	ADOXQ AX, R9
+
+	// (C,t[8]) := t[9] + m*q[9] + C
+	ADCXQ R11, R10
+	MULXQ ·qElement+72(SB), AX, R11
+	ADOXQ AX, R10
+
+	// (C,t[9]) := t[10] + m*q[10] + C
+	ADCXQ R12, R11
+	MULXQ ·qElement+80(SB), AX, R12
+	ADOXQ AX, R11
+
+	// (C,t[10]) := t[11] + m*q[11] + C
+	ADCXQ R13, R12
+	MULXQ ·qElement+88(SB), AX, R13
+	ADOXQ AX, R12
+	MOVQ  $0, AX
+	ADCXQ AX, R13
+	ADOXQ AX, R13
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+
+	// (C,t[5]) := t[6] + m*q[6] + C
+	ADCXQ R8, DI
+	MULXQ ·qElement+48(SB), AX, R8
+	ADOXQ AX, DI
+
+	// (C,t[6]) := t[7] + m*q[7] + C
+	ADCXQ R9, R8
+	MULXQ ·qElement+56(SB), AX, R9
+	ADOXQ AX, R8
+
+	// (C,t[7]) := t[8] + m*q[8] + C
+	ADCXQ R10, R9
+	MULXQ ·qElement+64(SB), AX, R10
+	ADOXQ AX, R9
+
+	// (C,t[8]) := t[9] + m*q[9] + C
+	ADCXQ R11, R10
+	MULXQ ·qElement+72(SB), AX, R11
+	ADOXQ AX, R10
+
+	// (C,t[9]) := t[10] + m*q[10] + C
+	ADCXQ R12, R11
+	MULXQ ·qElement+80(SB), AX, R12
+	ADOXQ AX, R11
+
+	// (C,t[10]) := t[11] + m*q[11] + C
+	ADCXQ R13, R12
+	MULXQ ·qElement+88(SB), AX, R13
+	ADOXQ AX, R12
+	MOVQ  $0, AX
+	ADCXQ AX, R13
+	ADOXQ AX, R13
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+
+	// (C,t[5]) := t[6] + m*q[6] + C
+	ADCXQ R8, DI
+	MULXQ ·qElement+48(SB), AX, R8
+	ADOXQ AX, DI
+
+	// (C,t[6]) := t[7] + m*q[7] + C
+	ADCXQ R9, R8
+	MULXQ ·qElement+56(SB), AX, R9
+	ADOXQ AX, R8
+
+	// (C,t[7]) := t[8] + m*q[8] + C
+	ADCXQ R10, R9
+	MULXQ ·qElement+64(SB), AX, R10
+	ADOXQ AX, R9
+
+	// (C,t[8]) := t[9] + m*q[9] + C
+	ADCXQ R11, R10
+	MULXQ ·qElement+72(SB), AX, R11
+	ADOXQ AX, R10
+
+	// (C,t[9]) := t[10] + m*q[10] + C
+	ADCXQ R12, R11
+	MULXQ ·qElement+80(SB), AX, R12
+	ADOXQ AX, R11
+
+	// (C,t[10]) := t[11] + m*q[11] + C
+	ADCXQ R13, R12
+	MULXQ ·qElement+88(SB), AX, R13
+	ADOXQ AX, R12
+	MOVQ  $0, AX
+	ADCXQ AX, R13
+	ADOXQ AX, R13
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+
+	// (C,t[5]) := t[6] + m*q[6] + C
+	ADCXQ R8, DI
+	MULXQ ·qElement+48(SB), AX, R8
+	ADOXQ AX, DI
+
+	// (C,t[6]) := t[7] + m*q[7] + C
+	ADCXQ R9, R8
+	MULXQ ·qElement+56(SB), AX, R9
+	ADOXQ AX, R8
+
+	// (C,t[7]) := t[8] + m*q[8] + C
+	ADCXQ R10, R9
+	MULXQ ·qElement+64(SB), AX, R10
+	ADOXQ AX, R9
+
+	// (C,t[8]) := t[9] + m*q[9] + C
+	ADCXQ R11, R10
+	MULXQ ·qElement+72(SB), AX, R11
+	ADOXQ AX, R10
+
+	// (C,t[9]) := t[10] + m*q[10] + C
+	ADCXQ R12, R11
+	MULXQ ·qElement+80(SB), AX, R12
+	ADOXQ AX, R11
+
+	// (C,t[10]) := t[11] + m*q[11] + C
+	ADCXQ R13, R12
+	MULXQ ·qElement+88(SB), AX, R13
+	ADOXQ AX, R12
+	MOVQ  $0, AX
+	ADCXQ AX, R13
+	ADOXQ AX, R13
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+
+	// (C,t[5]) := t[6] + m*q[6] + C
+	ADCXQ R8, DI
+	MULXQ ·qElement+48(SB), AX, R8
+	ADOXQ AX, DI
+
+	// (C,t[6]) := t[7] + m*q[7] + C
+	ADCXQ R9, R8
+	MULXQ ·qElement+56(SB), AX, R9
+	ADOXQ AX, R8
+
+	// (C,t[7]) := t[8] + m*q[8] + C
+	ADCXQ R10, R9
+	MULXQ ·qElement+64(SB), AX, R10
+	ADOXQ AX, R9
+
+	// (C,t[8]) := t[9] + m*q[9] + C
+	ADCXQ R11, R10
+	MULXQ ·qElement+72(SB), AX, R11
+	ADOXQ AX, R10
+
+	// (C,t[9]) := t[10] + m*q[10] + C
+	ADCXQ R12, R11
+	MULXQ ·qElement+80(SB), AX, R12
+	ADOXQ AX, R11
+
+	// (C,t[10]) := t[11] + m*q[11] + C
+	ADCXQ R13, R12
+	MULXQ ·qElement+88(SB), AX, R13
+	ADOXQ AX, R12
+	MOVQ  $0, AX
+	ADCXQ AX, R13
+	ADOXQ AX, R13
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+
+	// (C,t[5]) := t[6] + m*q[6] + C
+	ADCXQ R8, DI
+	MULXQ ·qElement+48(SB), AX, R8
+	ADOXQ AX, DI
+
+	// (C,t[6]) := t[7] + m*q[7] + C
+	ADCXQ R9, R8
+	MULXQ ·qElement+56(SB), AX, R9
+	ADOXQ AX, R8
+
+	// (C,t[7]) := t[8] + m*q[8] + C
+	ADCXQ R10, R9
+	MULXQ ·qElement+64(SB), AX, R10
+	ADOXQ AX, R9
+
+	// (C,t[8]) := t[9] + m*q[9] + C
+	ADCXQ R11, R10
+	MULXQ ·qElement+72(SB), AX, R11
+	ADOXQ AX, R10
+
+	// (C,t[9]) := t[10] + m*q[10] + C
+	ADCXQ R12, R11
+	MULXQ ·qElement+80(SB), AX, R12
+	ADOXQ AX, R11
+
+	// (C,t[10]) := t[11] + m*q[11] + C
+	ADCXQ R13, R12
+	MULXQ ·qElement+88(SB), AX, R13
+	ADOXQ AX, R12
+	MOVQ  $0, AX
+	ADCXQ AX, R13
+	ADOXQ AX, R13
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+
+	// (C,t[5]) := t[6] + m*q[6] + C
+	ADCXQ R8, DI
+	MULXQ ·qElement+48(SB), AX, R8
+	ADOXQ AX, DI
+
+	// (C,t[6]) := t[7] + m*q[7] + C
+	ADCXQ R9, R8
+	MULXQ ·qElement+56(SB), AX, R9
+	ADOXQ AX, R8
+
+	// (C,t[7]) := t[8] + m*q[8] + C
+	ADCXQ R10, R9
+	MULXQ ·qElement+64(SB), AX, R10
+	ADOXQ AX, R9
+
+	// (C,t[8]) := t[9] + m*q[9] + C
+	ADCXQ R11, R10
+	MULXQ ·qElement+72(SB), AX, R11
+	ADOXQ AX, R10
+
+	// (C,t[9]) := t[10] + m*q[10] + C
+	ADCXQ R12, R11
+	MULXQ ·qElement+80(SB), AX, R12
+	ADOXQ AX, R11
+
+	// (C,t[10]) := t[11] + m*q[11] + C
+	ADCXQ R13, R12
+	MULXQ ·qElement+88(SB), AX, R13
+	ADOXQ AX, R12
+	MOVQ  $0, AX
+	ADCXQ AX, R13
+	ADOXQ AX, R13
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+
+	// (C,t[5]) := t[6] + m*q[6] + C
+	ADCXQ R8, DI
+	MULXQ ·qElement+48(SB), AX, R8
+	ADOXQ AX, DI
+
+	// (C,t[6]) := t[7] + m*q[7] + C
+	ADCXQ R9, R8
+	MULXQ ·qElement+56(SB), AX, R9
+	ADOXQ AX, R8
+
+	// (C,t[7]) := t[8] + m*q[8] + C
+	ADCXQ R10, R9
+	MULXQ ·qElement+64(SB), AX, R10
+	ADOXQ AX, R9
+
+	// (C,t[8]) := t[9] + m*q[9] + C
+	ADCXQ R11, R10
+	MULXQ ·qElement+72(SB), AX, R11
+	ADOXQ AX, R10
+
+	// (C,t[9]) := t[10] + m*q[10] + C
+	ADCXQ R12, R11
+	MULXQ ·qElement+80(SB), AX, R12
+	ADOXQ AX, R11
+
+	// (C,t[10]) := t[11] + m*q[11] + C
+	ADCXQ R13, R12
+	MULXQ ·qElement+88(SB), AX, R13
+	ADOXQ AX, R12
+	MOVQ  $0, AX
+	ADCXQ AX, R13
+	ADOXQ AX, R13
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+
+	// (C,t[5]) := t[6] + m*q[6] + C
+	ADCXQ R8, DI
+	MULXQ ·qElement+48(SB), AX, R8
+	ADOXQ AX, DI
+
+	// (C,t[6]) := t[7] + m*q[7] + C
+	ADCXQ R9, R8
+	MULXQ ·qElement+56(SB), AX, R9
+	ADOXQ AX, R8
+
+	// (C,t[7]) := t[8] + m*q[8] + C
+	ADCXQ R10, R9
+	MULXQ ·qElement+64(SB), AX, R10
+	ADOXQ AX, R9
+
+	// (C,t[8]) := t[9] + m*q[9] + C
+	ADCXQ R11, R10
+	MULXQ ·qElement+72(SB), AX, R11
+	ADOXQ AX, R10
+
+	// (C,t[9]) := t[10] + m*q[10] + C
+	ADCXQ R12, R11
+	MULXQ ·qElement+80(SB), AX, R12
+	ADOXQ AX, R11
+
+	// (C,t[10]) := t[11] + m*q[11] + C
+	ADCXQ R13, R12
+	MULXQ ·qElement+88(SB), AX, R13
+	ADOXQ AX, R12
+	MOVQ  $0, AX
+	ADCXQ AX, R13
+	ADOXQ AX, R13
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+
+	// (C,t[5]) := t[6] + m*q[6] + C
+	ADCXQ R8, DI
+	MULXQ ·qElement+48(SB), AX, R8
+	ADOXQ AX, DI
+
+	// (C,t[6]) := t[7] + m*q[7] + C
+	ADCXQ R9, R8
+	MULXQ ·qElement+56(SB), AX, R9
+	ADOXQ AX, R8
+
+	// (C,t[7]) := t[8] + m*q[8] + C
+	ADCXQ R10, R9
+	MULXQ ·qElement+64(SB), AX, R10
+	ADOXQ AX, R9
+
+	// (C,t[8]) := t[9] + m*q[9] + C
+	ADCXQ R11, R10
+	MULXQ ·qElement+72(SB), AX, R11
+	ADOXQ AX, R10
+
+	// (C,t[9]) := t[10] + m*q[10] + C
+	ADCXQ R12, R11
+	MULXQ ·qElement+80(SB), AX, R12
+	ADOXQ AX, R11
+
+	// (C,t[10]) := t[11] + m*q[11] + C
+	ADCXQ R13, R12
+	MULXQ ·qElement+88(SB), AX, R13
+	ADOXQ AX, R12
+	MOVQ  $0, AX
+	ADCXQ AX, R13
+	ADOXQ AX, R13
+
+	// reduce element(R14,R15,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13) using temp registers (s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP),s11-96(SP))
+	REDUCE(R14,R15,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP),s5-48(SP),s6-56(SP),s7-64(SP),s8-72(SP),s9-80(SP),s10-88(SP),s11-96(SP))
+
+	MOVQ res+0(FP), AX
+	MOVQ R14, 0(AX)
+	MOVQ R15, 8(AX)
+	MOVQ CX, 16(AX)
+	MOVQ BX, 24(AX)
+	MOVQ SI, 32(AX)
+	MOVQ DI, 40(AX)
+	MOVQ R8, 48(AX)
+	MOVQ R9, 56(AX)
+	MOVQ R10, 64(AX)
+	MOVQ R11, 72(AX)
+	MOVQ R12, 80(AX)
+	MOVQ R13, 88(AX)
+	RET
+
+noAdx_3:
+	MOVQ res+0(FP), AX
+	MOVQ AX, (SP)
+	CALL ·_fromMontGeneric(SB)
+	RET
diff --git a/field/asm/element_4w_amd64.s b/field/asm/element_4w_amd64.s
new file mode 100644
index 0000000000..6f62d63102
--- /dev/null
+++ b/field/asm/element_4w_amd64.s
@@ -0,0 +1,2438 @@
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+#include "textflag.h"
+#include "funcdata.h"
+#include "go_asm.h"
+
+#define REDUCE(ra0, ra1, ra2, ra3, rb0, rb1, rb2, rb3) \
+	MOVQ    ra0, rb0;              \
+	SUBQ    ·qElement(SB), ra0;    \
+	MOVQ    ra1, rb1;              \
+	SBBQ    ·qElement+8(SB), ra1;  \
+	MOVQ    ra2, rb2;              \
+	SBBQ    ·qElement+16(SB), ra2; \
+	MOVQ    ra3, rb3;              \
+	SBBQ    ·qElement+24(SB), ra3; \
+	CMOVQCS rb0, ra0;              \
+	CMOVQCS rb1, ra1;              \
+	CMOVQCS rb2, ra2;              \
+	CMOVQCS rb3, ra3;              \
+
+TEXT ·reduce(SB), NOSPLIT, $0-8
+	MOVQ res+0(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+
+	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
+
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	RET
+
+// MulBy3(x *Element)
+TEXT ·MulBy3(SB), NOSPLIT, $0-8
+	MOVQ x+0(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+
+	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
+
+	ADDQ 0(AX), DX
+	ADCQ 8(AX), CX
+	ADCQ 16(AX), BX
+	ADCQ 24(AX), SI
+
+	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
+	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
+
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	RET
+
+// MulBy5(x *Element)
+TEXT ·MulBy5(SB), NOSPLIT, $0-8
+	MOVQ x+0(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+
+	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
+
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+
+	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
+	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
+
+	ADDQ 0(AX), DX
+	ADCQ 8(AX), CX
+	ADCQ 16(AX), BX
+	ADCQ 24(AX), SI
+
+	// reduce element(DX,CX,BX,SI) using temp registers (R15,DI,R8,R9)
+	REDUCE(DX,CX,BX,SI,R15,DI,R8,R9)
+
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	RET
+
+// MulBy13(x *Element)
+TEXT ·MulBy13(SB), NOSPLIT, $0-8
+	MOVQ x+0(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+
+	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
+
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+
+	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
+	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
+
+	MOVQ DX, R11
+	MOVQ CX, R12
+	MOVQ BX, R13
+	MOVQ SI, R14
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+
+	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
+
+	ADDQ R11, DX
+	ADCQ R12, CX
+	ADCQ R13, BX
+	ADCQ R14, SI
+
+	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
+
+	ADDQ 0(AX), DX
+	ADCQ 8(AX), CX
+	ADCQ 16(AX), BX
+	ADCQ 24(AX), SI
+
+	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
+
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	RET
+
+// Butterfly(a, b *Element) sets a = a + b; b = a - b
+TEXT ·Butterfly(SB), NOSPLIT, $0-16
+	MOVQ    a+0(FP), AX
+	MOVQ    0(AX), CX
+	MOVQ    8(AX), BX
+	MOVQ    16(AX), SI
+	MOVQ    24(AX), DI
+	MOVQ    CX, R8
+	MOVQ    BX, R9
+	MOVQ    SI, R10
+	MOVQ    DI, R11
+	XORQ    AX, AX
+	MOVQ    b+8(FP), DX
+	ADDQ    0(DX), CX
+	ADCQ    8(DX), BX
+	ADCQ    16(DX), SI
+	ADCQ    24(DX), DI
+	SUBQ    0(DX), R8
+	SBBQ    8(DX), R9
+	SBBQ    16(DX), R10
+	SBBQ    24(DX), R11
+	MOVQ    $const_q0, R12
+	MOVQ    $const_q1, R13
+	MOVQ    $const_q2, R14
+	MOVQ    $const_q3, R15
+	CMOVQCC AX, R12
+	CMOVQCC AX, R13
+	CMOVQCC AX, R14
+	CMOVQCC AX, R15
+	ADDQ    R12, R8
+	ADCQ    R13, R9
+	ADCQ    R14, R10
+	ADCQ    R15, R11
+	MOVQ    R8, 0(DX)
+	MOVQ    R9, 8(DX)
+	MOVQ    R10, 16(DX)
+	MOVQ    R11, 24(DX)
+
+	// reduce element(CX,BX,SI,DI) using temp registers (R8,R9,R10,R11)
+	REDUCE(CX,BX,SI,DI,R8,R9,R10,R11)
+
+	MOVQ a+0(FP), AX
+	MOVQ CX, 0(AX)
+	MOVQ BX, 8(AX)
+	MOVQ SI, 16(AX)
+	MOVQ DI, 24(AX)
+	RET
+
+// mul(res, x, y *Element)
+TEXT ·mul(SB), $24-24
+
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+	// See github.com/gnark-crypto/field/generator for more comments.
+
+	NO_LOCAL_POINTERS
+	CMPB ·supportAdx(SB), $1
+	JNE  noAdx_1
+	MOVQ x+8(FP), SI
+
+	// x[0] -> DI
+	// x[1] -> R8
+	// x[2] -> R9
+	// x[3] -> R10
+	MOVQ 0(SI), DI
+	MOVQ 8(SI), R8
+	MOVQ 16(SI), R9
+	MOVQ 24(SI), R10
+	MOVQ y+16(FP), R11
+
+	// A -> BP
+	// t[0] -> R14
+	// t[1] -> R13
+	// t[2] -> CX
+	// t[3] -> BX
+#define MACC(in0, in1, in2) \
+	ADCXQ in0, in1     \
+	MULXQ in2, AX, in0 \
+	ADOXQ AX, in1      \
+
+#define DIV_SHIFT() \
+	MOVQ  $const_qInvNeg, DX        \
+	IMULQ R14, DX                   \
+	XORQ  AX, AX                    \
+	MULXQ ·qElement+0(SB), AX, R12  \
+	ADCXQ R14, AX                   \
+	MOVQ  R12, R14                  \
+	MACC(R13, R14, ·qElement+8(SB)) \
+	MACC(CX, R13, ·qElement+16(SB)) \
+	MACC(BX, CX, ·qElement+24(SB))  \
+	MOVQ  $0, AX                    \
+	ADCXQ AX, BX                    \
+	ADOXQ BP, BX                    \
+
+#define MUL_WORD_0() \
+	XORQ  AX, AX       \
+	MULXQ DI, R14, R13 \
+	MULXQ R8, AX, CX   \
+	ADOXQ AX, R13      \
+	MULXQ R9, AX, BX   \
+	ADOXQ AX, CX       \
+	MULXQ R10, AX, BP  \
+	ADOXQ AX, BX       \
+	MOVQ  $0, AX       \
+	ADOXQ AX, BP       \
+	DIV_SHIFT()        \
+
+#define MUL_WORD_N() \
+	XORQ  AX, AX      \
+	MULXQ DI, AX, BP  \
+	ADOXQ AX, R14     \
+	MACC(BP, R13, R8) \
+	MACC(BP, CX, R9)  \
+	MACC(BP, BX, R10) \
+	MOVQ  $0, AX      \
+	ADCXQ AX, BP      \
+	ADOXQ AX, BP      \
+	DIV_SHIFT()       \
+
+	// mul body
+	MOVQ 0(R11), DX
+	MUL_WORD_0()
+	MOVQ 8(R11), DX
+	MUL_WORD_N()
+	MOVQ 16(R11), DX
+	MUL_WORD_N()
+	MOVQ 24(R11), DX
+	MUL_WORD_N()
+
+	// reduce element(R14,R13,CX,BX) using temp registers (SI,R12,R11,DI)
+	REDUCE(R14,R13,CX,BX,SI,R12,R11,DI)
+
+	MOVQ res+0(FP), AX
+	MOVQ R14, 0(AX)
+	MOVQ R13, 8(AX)
+	MOVQ CX, 16(AX)
+	MOVQ BX, 24(AX)
+	RET
+
+noAdx_1:
+	MOVQ res+0(FP), AX
+	MOVQ AX, (SP)
+	MOVQ x+8(FP), AX
+	MOVQ AX, 8(SP)
+	MOVQ y+16(FP), AX
+	MOVQ AX, 16(SP)
+	CALL ·_mulGeneric(SB)
+	RET
+
+TEXT ·fromMont(SB), $8-8
+	NO_LOCAL_POINTERS
+
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+	// when y = 1 we have:
+	// for i=0 to N-1
+	// 		t[i] = x[i]
+	// for i=0 to N-1
+	// 		m := t[0]*q'[0] mod W
+	// 		C,_ := t[0] + m*q[0]
+	// 		for j=1 to N-1
+	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
+	// 		t[N-1] = C
+	CMPB ·supportAdx(SB), $1
+	JNE  noAdx_2
+	MOVQ res+0(FP), DX
+	MOVQ 0(DX), R14
+	MOVQ 8(DX), R13
+	MOVQ 16(DX), CX
+	MOVQ 24(DX), BX
+	XORQ DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R13, R14
+	MULXQ ·qElement+8(SB), AX, R13
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R13
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R13
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+	MOVQ  $0, AX
+	ADCXQ AX, BX
+	ADOXQ AX, BX
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R13, R14
+	MULXQ ·qElement+8(SB), AX, R13
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R13
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R13
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+	MOVQ  $0, AX
+	ADCXQ AX, BX
+	ADOXQ AX, BX
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R13, R14
+	MULXQ ·qElement+8(SB), AX, R13
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R13
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R13
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+	MOVQ  $0, AX
+	ADCXQ AX, BX
+	ADOXQ AX, BX
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R13, R14
+	MULXQ ·qElement+8(SB), AX, R13
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R13
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R13
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+	MOVQ  $0, AX
+	ADCXQ AX, BX
+	ADOXQ AX, BX
+
+	// reduce element(R14,R13,CX,BX) using temp registers (SI,DI,R8,R9)
+	REDUCE(R14,R13,CX,BX,SI,DI,R8,R9)
+
+	MOVQ res+0(FP), AX
+	MOVQ R14, 0(AX)
+	MOVQ R13, 8(AX)
+	MOVQ CX, 16(AX)
+	MOVQ BX, 24(AX)
+	RET
+
+noAdx_2:
+	MOVQ res+0(FP), AX
+	MOVQ AX, (SP)
+	CALL ·_fromMontGeneric(SB)
+	RET
+
+// Vector operations are partially derived from Dag Arne Osvik's work in github.com/a16z/vectorized-fields
+
+// addVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] + b[0...n]
+TEXT ·addVec(SB), NOSPLIT, $0-32
+	MOVQ res+0(FP), CX
+	MOVQ a+8(FP), AX
+	MOVQ b+16(FP), DX
+	MOVQ n+24(FP), BX
+
+loop_3:
+	TESTQ BX, BX
+	JEQ   done_4 // n == 0, we are done
+
+	// a[0] -> SI
+	// a[1] -> DI
+	// a[2] -> R8
+	// a[3] -> R9
+	MOVQ       0(AX), SI
+	MOVQ       8(AX), DI
+	MOVQ       16(AX), R8
+	MOVQ       24(AX), R9
+	ADDQ       0(DX), SI
+	ADCQ       8(DX), DI
+	ADCQ       16(DX), R8
+	ADCQ       24(DX), R9
+	PREFETCHT0 2048(AX)
+	PREFETCHT0 2048(DX)
+
+	// reduce element(SI,DI,R8,R9) using temp registers (R10,R11,R12,R13)
+	REDUCE(SI,DI,R8,R9,R10,R11,R12,R13)
+
+	MOVQ SI, 0(CX)
+	MOVQ DI, 8(CX)
+	MOVQ R8, 16(CX)
+	MOVQ R9, 24(CX)
+
+	// increment pointers to visit next element
+	ADDQ $32, AX
+	ADDQ $32, DX
+	ADDQ $32, CX
+	DECQ BX      // decrement n
+	JMP  loop_3
+
+done_4:
+	RET
+
+// subVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] - b[0...n]
+TEXT ·subVec(SB), NOSPLIT, $0-32
+	MOVQ res+0(FP), CX
+	MOVQ a+8(FP), AX
+	MOVQ b+16(FP), DX
+	MOVQ n+24(FP), BX
+	XORQ SI, SI
+
+loop_5:
+	TESTQ BX, BX
+	JEQ   done_6 // n == 0, we are done
+
+	// a[0] -> DI
+	// a[1] -> R8
+	// a[2] -> R9
+	// a[3] -> R10
+	MOVQ       0(AX), DI
+	MOVQ       8(AX), R8
+	MOVQ       16(AX), R9
+	MOVQ       24(AX), R10
+	SUBQ       0(DX), DI
+	SBBQ       8(DX), R8
+	SBBQ       16(DX), R9
+	SBBQ       24(DX), R10
+	PREFETCHT0 2048(AX)
+	PREFETCHT0 2048(DX)
+
+	// reduce (a-b) mod q
+	// q[0] -> R11
+	// q[1] -> R12
+	// q[2] -> R13
+	// q[3] -> R14
+	MOVQ    $const_q0, R11
+	MOVQ    $const_q1, R12
+	MOVQ    $const_q2, R13
+	MOVQ    $const_q3, R14
+	CMOVQCC SI, R11
+	CMOVQCC SI, R12
+	CMOVQCC SI, R13
+	CMOVQCC SI, R14
+
+	// add registers (q or 0) to a, and set to result
+	ADDQ R11, DI
+	ADCQ R12, R8
+	ADCQ R13, R9
+	ADCQ R14, R10
+	MOVQ DI, 0(CX)
+	MOVQ R8, 8(CX)
+	MOVQ R9, 16(CX)
+	MOVQ R10, 24(CX)
+
+	// increment pointers to visit next element
+	ADDQ $32, AX
+	ADDQ $32, DX
+	ADDQ $32, CX
+	DECQ BX      // decrement n
+	JMP  loop_5
+
+done_6:
+	RET
+
+// sumVec(res, a *Element, n uint64) res = sum(a[0...n])
+TEXT ·sumVec(SB), NOSPLIT, $0-24
+
+	// Derived from https://github.com/a16z/vectorized-fields
+	// The idea is to use Z registers to accumulate the sum of elements, 8 by 8
+	// first, we handle the case where n % 8 != 0
+	// then, we loop over the elements 8 by 8 and accumulate the sum in the Z registers
+	// finally, we reduce the sum and store it in res
+	//
+	// when we move an element of a into a Z register, we use VPMOVZXDQ
+	// let's note w0...w3 the 4 64bits words of ai: w0 = ai[0], w1 = ai[1], w2 = ai[2], w3 = ai[3]
+	// VPMOVZXDQ(ai, Z0) will result in
+	// Z0= [hi(w3), lo(w3), hi(w2), lo(w2), hi(w1), lo(w1), hi(w0), lo(w0)]
+	// with hi(wi) the high 32 bits of wi and lo(wi) the low 32 bits of wi
+	// we can safely add 2^32+1 times Z registers constructed this way without overflow
+	// since each of this lo/hi bits are moved into a "64bits" slot
+	// N = 2^64-1 / 2^32-1 = 2^32+1
+	//
+	// we then propagate the carry using ADOXQ and ADCXQ
+	// r0 = w0l + lo(woh)
+	// r1 = carry + hi(woh) + w1l + lo(w1h)
+	// r2 = carry + hi(w1h) + w2l + lo(w2h)
+	// r3 = carry + hi(w2h) + w3l + lo(w3h)
+	// r4 = carry + hi(w3h)
+	// we then reduce the sum using a single-word Barrett reduction
+	// we pick mu = 2^288 / q; which correspond to 4.5 words max.
+	// meaning we must guarantee that r4 fits in 32bits.
+	// To do so, we reduce N to 2^32-1 (since r4 receives 2 carries max)
+
+	MOVQ a+8(FP), R14
+	MOVQ n+16(FP), R15
+
+	// initialize accumulators Z0, Z1, Z2, Z3, Z4, Z5, Z6, Z7
+	VXORPS    Z0, Z0, Z0
+	VMOVDQA64 Z0, Z1
+	VMOVDQA64 Z0, Z2
+	VMOVDQA64 Z0, Z3
+	VMOVDQA64 Z0, Z4
+	VMOVDQA64 Z0, Z5
+	VMOVDQA64 Z0, Z6
+	VMOVDQA64 Z0, Z7
+
+	// n % 8 -> CX
+	// n / 8 -> R15
+	MOVQ R15, CX
+	ANDQ $7, CX
+	SHRQ $3, R15
+
+loop_single_9:
+	TESTQ     CX, CX
+	JEQ       loop8by8_7    // n % 8 == 0, we are going to loop over 8 by 8
+	VPMOVZXDQ 0(R14), Z8
+	VPADDQ    Z8, Z0, Z0
+	ADDQ      $32, R14
+	DECQ      CX            // decrement nMod8
+	JMP       loop_single_9
+
+loop8by8_7:
+	TESTQ      R15, R15
+	JEQ        accumulate_10  // n == 0, we are going to accumulate
+	VPMOVZXDQ  0*32(R14), Z8
+	VPMOVZXDQ  1*32(R14), Z9
+	VPMOVZXDQ  2*32(R14), Z10
+	VPMOVZXDQ  3*32(R14), Z11
+	VPMOVZXDQ  4*32(R14), Z12
+	VPMOVZXDQ  5*32(R14), Z13
+	VPMOVZXDQ  6*32(R14), Z14
+	VPMOVZXDQ  7*32(R14), Z15
+	PREFETCHT0 4096(R14)
+	VPADDQ     Z8, Z0, Z0
+	VPADDQ     Z9, Z1, Z1
+	VPADDQ     Z10, Z2, Z2
+	VPADDQ     Z11, Z3, Z3
+	VPADDQ     Z12, Z4, Z4
+	VPADDQ     Z13, Z5, Z5
+	VPADDQ     Z14, Z6, Z6
+	VPADDQ     Z15, Z7, Z7
+
+	// increment pointers to visit next 8 elements
+	ADDQ $256, R14
+	DECQ R15        // decrement n
+	JMP  loop8by8_7
+
+accumulate_10:
+	// accumulate the 8 Z registers into Z0
+	VPADDQ Z7, Z6, Z6
+	VPADDQ Z6, Z5, Z5
+	VPADDQ Z5, Z4, Z4
+	VPADDQ Z4, Z3, Z3
+	VPADDQ Z3, Z2, Z2
+	VPADDQ Z2, Z1, Z1
+	VPADDQ Z1, Z0, Z0
+
+	// carry propagation
+	// lo(w0) -> BX
+	// hi(w0) -> SI
+	// lo(w1) -> DI
+	// hi(w1) -> R8
+	// lo(w2) -> R9
+	// hi(w2) -> R10
+	// lo(w3) -> R11
+	// hi(w3) -> R12
+	VMOVQ   X0, BX
+	VALIGNQ $1, Z0, Z0, Z0
+	VMOVQ   X0, SI
+	VALIGNQ $1, Z0, Z0, Z0
+	VMOVQ   X0, DI
+	VALIGNQ $1, Z0, Z0, Z0
+	VMOVQ   X0, R8
+	VALIGNQ $1, Z0, Z0, Z0
+	VMOVQ   X0, R9
+	VALIGNQ $1, Z0, Z0, Z0
+	VMOVQ   X0, R10
+	VALIGNQ $1, Z0, Z0, Z0
+	VMOVQ   X0, R11
+	VALIGNQ $1, Z0, Z0, Z0
+	VMOVQ   X0, R12
+
+	// lo(hi(wo)) -> R13
+	// lo(hi(w1)) -> CX
+	// lo(hi(w2)) -> R15
+	// lo(hi(w3)) -> R14
+#define SPLIT_LO_HI(in0, in1) \
+	MOVQ in1, in0         \
+	ANDQ $0xffffffff, in0 \
+	SHLQ $32, in0         \
+	SHRQ $32, in1         \
+
+	SPLIT_LO_HI(R13, SI)
+	SPLIT_LO_HI(CX, R8)
+	SPLIT_LO_HI(R15, R10)
+	SPLIT_LO_HI(R14, R12)
+
+	// r0 = w0l + lo(woh)
+	// r1 = carry + hi(woh) + w1l + lo(w1h)
+	// r2 = carry + hi(w1h) + w2l + lo(w2h)
+	// r3 = carry + hi(w2h) + w3l + lo(w3h)
+	// r4 = carry + hi(w3h)
+
+	XORQ  AX, AX   // clear the flags
+	ADOXQ R13, BX
+	ADOXQ CX, DI
+	ADCXQ SI, DI
+	ADOXQ R15, R9
+	ADCXQ R8, R9
+	ADOXQ R14, R11
+	ADCXQ R10, R11
+	ADOXQ AX, R12
+	ADCXQ AX, R12
+
+	// r[0] -> BX
+	// r[1] -> DI
+	// r[2] -> R9
+	// r[3] -> R11
+	// r[4] -> R12
+	// reduce using single-word Barrett
+	// see see Handbook of Applied Cryptography, Algorithm 14.42.
+	// mu=2^288 / q -> SI
+	MOVQ  $const_mu, SI
+	MOVQ  R11, AX
+	SHRQ  $32, R12, AX
+	MULQ  SI                       // high bits of res stored in DX
+	MULXQ ·qElement+0(SB), AX, SI
+	SUBQ  AX, BX
+	SBBQ  SI, DI
+	MULXQ ·qElement+16(SB), AX, SI
+	SBBQ  AX, R9
+	SBBQ  SI, R11
+	SBBQ  $0, R12
+	MULXQ ·qElement+8(SB), AX, SI
+	SUBQ  AX, DI
+	SBBQ  SI, R9
+	MULXQ ·qElement+24(SB), AX, SI
+	SBBQ  AX, R11
+	SBBQ  SI, R12
+	MOVQ  BX, R8
+	MOVQ  DI, R10
+	MOVQ  R9, R13
+	MOVQ  R11, CX
+	SUBQ  ·qElement+0(SB), BX
+	SBBQ  ·qElement+8(SB), DI
+	SBBQ  ·qElement+16(SB), R9
+	SBBQ  ·qElement+24(SB), R11
+	SBBQ  $0, R12
+	JCS   modReduced_11
+	MOVQ  BX, R8
+	MOVQ  DI, R10
+	MOVQ  R9, R13
+	MOVQ  R11, CX
+	SUBQ  ·qElement+0(SB), BX
+	SBBQ  ·qElement+8(SB), DI
+	SBBQ  ·qElement+16(SB), R9
+	SBBQ  ·qElement+24(SB), R11
+	SBBQ  $0, R12
+	JCS   modReduced_11
+	MOVQ  BX, R8
+	MOVQ  DI, R10
+	MOVQ  R9, R13
+	MOVQ  R11, CX
+
+modReduced_11:
+	MOVQ res+0(FP), SI
+	MOVQ R8, 0(SI)
+	MOVQ R10, 8(SI)
+	MOVQ R13, 16(SI)
+	MOVQ CX, 24(SI)
+
+done_8:
+	RET
+
+// innerProdVec(res, a,b *Element, n uint64) res = sum(a[0...n] * b[0...n])
+TEXT ·innerProdVec(SB), NOSPLIT, $0-32
+	MOVQ a+8(FP), R14
+	MOVQ b+16(FP), R15
+	MOVQ n+24(FP), CX
+
+	// Create mask for low dword in each qword
+	VPCMPEQB  Y0, Y0, Y0
+	VPMOVZXDQ Y0, Z5
+	VPXORQ    Z16, Z16, Z16
+	VMOVDQA64 Z16, Z17
+	VMOVDQA64 Z16, Z18
+	VMOVDQA64 Z16, Z19
+	VMOVDQA64 Z16, Z20
+	VMOVDQA64 Z16, Z21
+	VMOVDQA64 Z16, Z22
+	VMOVDQA64 Z16, Z23
+	VMOVDQA64 Z16, Z24
+	VMOVDQA64 Z16, Z25
+	VMOVDQA64 Z16, Z26
+	VMOVDQA64 Z16, Z27
+	VMOVDQA64 Z16, Z28
+	VMOVDQA64 Z16, Z29
+	VMOVDQA64 Z16, Z30
+	VMOVDQA64 Z16, Z31
+	TESTQ     CX, CX
+	JEQ       done_13       // n == 0, we are done
+
+loop_12:
+	TESTQ     CX, CX
+	JEQ       accumulate_14 // n == 0 we can accumulate
+	VPMOVZXDQ (R15), Z4
+	ADDQ      $32, R15
+
+	// we multiply and accumulate partial products of 4 bytes * 32 bytes
+#define MAC(in0, in1, in2) \
+	VPMULUDQ.BCST in0, Z4, Z2  \
+	VPSRLQ        $32, Z2, Z3  \
+	VPANDQ        Z5, Z2, Z2   \
+	VPADDQ        Z2, in1, in1 \
+	VPADDQ        Z3, in2, in2 \
+
+	MAC(0*4(R14), Z16, Z24)
+	MAC(1*4(R14), Z17, Z25)
+	MAC(2*4(R14), Z18, Z26)
+	MAC(3*4(R14), Z19, Z27)
+	MAC(4*4(R14), Z20, Z28)
+	MAC(5*4(R14), Z21, Z29)
+	MAC(6*4(R14), Z22, Z30)
+	MAC(7*4(R14), Z23, Z31)
+	ADDQ $32, R14
+	DECQ CX       // decrement n
+	JMP  loop_12
+
+accumulate_14:
+	// we accumulate the partial products into 544bits in Z1:Z0
+	MOVQ  $0x0000000000001555, AX
+	KMOVD AX, K1
+	MOVQ  $1, AX
+	KMOVD AX, K2
+
+	// store the least significant 32 bits of ACC (starts with A0L) in Z0
+	VALIGND.Z $16, Z16, Z16, K2, Z0
+	KSHIFTLW  $1, K2, K2
+	VPSRLQ    $32, Z16, Z2
+	VALIGND.Z $2, Z16, Z16, K1, Z16
+	VPADDQ    Z2, Z16, Z16
+	VPANDQ    Z5, Z24, Z2
+	VPADDQ    Z2, Z16, Z16
+	VPANDQ    Z5, Z17, Z2
+	VPADDQ    Z2, Z16, Z16
+	VALIGND   $15, Z16, Z16, K2, Z0
+	KSHIFTLW  $1, K2, K2
+
+	// macro to add partial products and store the result in Z0
+#define ADDPP(in0, in1, in2, in3, in4) \
+	VPSRLQ    $32, Z16, Z2              \
+	VALIGND.Z $2, Z16, Z16, K1, Z16     \
+	VPADDQ    Z2, Z16, Z16              \
+	VPSRLQ    $32, in0, in0             \
+	VPADDQ    in0, Z16, Z16             \
+	VPSRLQ    $32, in1, in1             \
+	VPADDQ    in1, Z16, Z16             \
+	VPANDQ    Z5, in2, Z2               \
+	VPADDQ    Z2, Z16, Z16              \
+	VPANDQ    Z5, in3, Z2               \
+	VPADDQ    Z2, Z16, Z16              \
+	VALIGND   $16-in4, Z16, Z16, K2, Z0 \
+	KADDW     K2, K2, K2                \
+
+	ADDPP(Z24, Z17, Z25, Z18, 2)
+	ADDPP(Z25, Z18, Z26, Z19, 3)
+	ADDPP(Z26, Z19, Z27, Z20, 4)
+	ADDPP(Z27, Z20, Z28, Z21, 5)
+	ADDPP(Z28, Z21, Z29, Z22, 6)
+	ADDPP(Z29, Z22, Z30, Z23, 7)
+	VPSRLQ    $32, Z16, Z2
+	VALIGND.Z $2, Z16, Z16, K1, Z16
+	VPADDQ    Z2, Z16, Z16
+	VPSRLQ    $32, Z30, Z30
+	VPADDQ    Z30, Z16, Z16
+	VPSRLQ    $32, Z23, Z23
+	VPADDQ    Z23, Z16, Z16
+	VPANDQ    Z5, Z31, Z2
+	VPADDQ    Z2, Z16, Z16
+	VALIGND   $16-8, Z16, Z16, K2, Z0
+	KSHIFTLW  $1, K2, K2
+	VPSRLQ    $32, Z16, Z2
+	VALIGND.Z $2, Z16, Z16, K1, Z16
+	VPADDQ    Z2, Z16, Z16
+	VPSRLQ    $32, Z31, Z31
+	VPADDQ    Z31, Z16, Z16
+	VALIGND   $16-9, Z16, Z16, K2, Z0
+	KSHIFTLW  $1, K2, K2
+
+#define ADDPP2(in0) \
+	VPSRLQ    $32, Z16, Z2              \
+	VALIGND.Z $2, Z16, Z16, K1, Z16     \
+	VPADDQ    Z2, Z16, Z16              \
+	VALIGND   $16-in0, Z16, Z16, K2, Z0 \
+	KSHIFTLW  $1, K2, K2                \
+
+	ADDPP2(10)
+	ADDPP2(11)
+	ADDPP2(12)
+	ADDPP2(13)
+	ADDPP2(14)
+	ADDPP2(15)
+	VPSRLQ      $32, Z16, Z2
+	VALIGND.Z   $2, Z16, Z16, K1, Z16
+	VPADDQ      Z2, Z16, Z16
+	VMOVDQA64.Z Z16, K1, Z1
+
+	// Extract the 4 least significant qwords of Z0
+	VMOVQ   X0, SI
+	VALIGNQ $1, Z0, Z1, Z0
+	VMOVQ   X0, DI
+	VALIGNQ $1, Z0, Z0, Z0
+	VMOVQ   X0, R8
+	VALIGNQ $1, Z0, Z0, Z0
+	VMOVQ   X0, R9
+	VALIGNQ $1, Z0, Z0, Z0
+	XORQ    BX, BX
+	MOVQ    $const_qInvNeg, DX
+	MULXQ   SI, DX, R10
+	MULXQ   ·qElement+0(SB), AX, R10
+	ADDQ    AX, SI
+	ADCQ    R10, DI
+	MULXQ   ·qElement+16(SB), AX, R10
+	ADCQ    AX, R8
+	ADCQ    R10, R9
+	ADCQ    $0, BX
+	MULXQ   ·qElement+8(SB), AX, R10
+	ADDQ    AX, DI
+	ADCQ    R10, R8
+	MULXQ   ·qElement+24(SB), AX, R10
+	ADCQ    AX, R9
+	ADCQ    R10, BX
+	ADCQ    $0, SI
+	MOVQ    $const_qInvNeg, DX
+	MULXQ   DI, DX, R10
+	MULXQ   ·qElement+0(SB), AX, R10
+	ADDQ    AX, DI
+	ADCQ    R10, R8
+	MULXQ   ·qElement+16(SB), AX, R10
+	ADCQ    AX, R9
+	ADCQ    R10, BX
+	ADCQ    $0, SI
+	MULXQ   ·qElement+8(SB), AX, R10
+	ADDQ    AX, R8
+	ADCQ    R10, R9
+	MULXQ   ·qElement+24(SB), AX, R10
+	ADCQ    AX, BX
+	ADCQ    R10, SI
+	ADCQ    $0, DI
+	MOVQ    $const_qInvNeg, DX
+	MULXQ   R8, DX, R10
+	MULXQ   ·qElement+0(SB), AX, R10
+	ADDQ    AX, R8
+	ADCQ    R10, R9
+	MULXQ   ·qElement+16(SB), AX, R10
+	ADCQ    AX, BX
+	ADCQ    R10, SI
+	ADCQ    $0, DI
+	MULXQ   ·qElement+8(SB), AX, R10
+	ADDQ    AX, R9
+	ADCQ    R10, BX
+	MULXQ   ·qElement+24(SB), AX, R10
+	ADCQ    AX, SI
+	ADCQ    R10, DI
+	ADCQ    $0, R8
+	MOVQ    $const_qInvNeg, DX
+	MULXQ   R9, DX, R10
+	MULXQ   ·qElement+0(SB), AX, R10
+	ADDQ    AX, R9
+	ADCQ    R10, BX
+	MULXQ   ·qElement+16(SB), AX, R10
+	ADCQ    AX, SI
+	ADCQ    R10, DI
+	ADCQ    $0, R8
+	MULXQ   ·qElement+8(SB), AX, R10
+	ADDQ    AX, BX
+	ADCQ    R10, SI
+	MULXQ   ·qElement+24(SB), AX, R10
+	ADCQ    AX, DI
+	ADCQ    R10, R8
+	ADCQ    $0, R9
+	VMOVQ   X0, AX
+	ADDQ    AX, BX
+	VALIGNQ $1, Z0, Z0, Z0
+	VMOVQ   X0, AX
+	ADCQ    AX, SI
+	VALIGNQ $1, Z0, Z0, Z0
+	VMOVQ   X0, AX
+	ADCQ    AX, DI
+	VALIGNQ $1, Z0, Z0, Z0
+	VMOVQ   X0, AX
+	ADCQ    AX, R8
+	VALIGNQ $1, Z0, Z0, Z0
+	VMOVQ   X0, AX
+	ADCQ    AX, R9
+
+	// Barrett reduction; see Handbook of Applied Cryptography, Algorithm 14.42.
+	MOVQ  R8, AX
+	SHRQ  $32, R9, AX
+	MOVQ  $const_mu, DX
+	MULQ  DX
+	MULXQ ·qElement+0(SB), AX, R10
+	SUBQ  AX, BX
+	SBBQ  R10, SI
+	MULXQ ·qElement+16(SB), AX, R10
+	SBBQ  AX, DI
+	SBBQ  R10, R8
+	SBBQ  $0, R9
+	MULXQ ·qElement+8(SB), AX, R10
+	SUBQ  AX, SI
+	SBBQ  R10, DI
+	MULXQ ·qElement+24(SB), AX, R10
+	SBBQ  AX, R8
+	SBBQ  R10, R9
+
+	// we need up to 2 conditional substractions to be < q
+	MOVQ res+0(FP), R11
+	MOVQ BX, 0(R11)
+	MOVQ SI, 8(R11)
+	MOVQ DI, 16(R11)
+	MOVQ R8, 24(R11)
+	SUBQ ·qElement+0(SB), BX
+	SBBQ ·qElement+8(SB), SI
+	SBBQ ·qElement+16(SB), DI
+	SBBQ ·qElement+24(SB), R8
+	SBBQ $0, R9
+	JCS  done_13
+	MOVQ BX, 0(R11)
+	MOVQ SI, 8(R11)
+	MOVQ DI, 16(R11)
+	MOVQ R8, 24(R11)
+	SUBQ ·qElement+0(SB), BX
+	SBBQ ·qElement+8(SB), SI
+	SBBQ ·qElement+16(SB), DI
+	SBBQ ·qElement+24(SB), R8
+	SBBQ $0, R9
+	JCS  done_13
+	MOVQ BX, 0(R11)
+	MOVQ SI, 8(R11)
+	MOVQ DI, 16(R11)
+	MOVQ R8, 24(R11)
+
+done_13:
+	RET
+
+TEXT ·scalarMulVec(SB), $8-40
+#define AVX_MUL_Q_LO() \
+	VPMULUDQ.BCST ·qElement+0(SB), Z9, Z10  \
+	VPADDQ        Z10, Z0, Z0               \
+	VPMULUDQ.BCST ·qElement+4(SB), Z9, Z11  \
+	VPADDQ        Z11, Z1, Z1               \
+	VPMULUDQ.BCST ·qElement+8(SB), Z9, Z12  \
+	VPADDQ        Z12, Z2, Z2               \
+	VPMULUDQ.BCST ·qElement+12(SB), Z9, Z13 \
+	VPADDQ        Z13, Z3, Z3               \
+
+#define AVX_MUL_Q_HI() \
+	VPMULUDQ.BCST ·qElement+16(SB), Z9, Z14 \
+	VPADDQ        Z14, Z4, Z4               \
+	VPMULUDQ.BCST ·qElement+20(SB), Z9, Z15 \
+	VPADDQ        Z15, Z5, Z5               \
+	VPMULUDQ.BCST ·qElement+24(SB), Z9, Z16 \
+	VPADDQ        Z16, Z6, Z6               \
+	VPMULUDQ.BCST ·qElement+28(SB), Z9, Z17 \
+	VPADDQ        Z17, Z7, Z7               \
+
+#define SHIFT_ADD_AND(in0, in1, in2, in3) \
+	VPSRLQ $32, in0, in1 \
+	VPADDQ in1, in2, in2 \
+	VPANDQ in3, in2, in0 \
+
+#define CARRY1() \
+	SHIFT_ADD_AND(Z0, Z10, Z1, Z8) \
+	SHIFT_ADD_AND(Z1, Z11, Z2, Z8) \
+	SHIFT_ADD_AND(Z2, Z12, Z3, Z8) \
+	SHIFT_ADD_AND(Z3, Z13, Z4, Z8) \
+
+#define CARRY2() \
+	SHIFT_ADD_AND(Z4, Z14, Z5, Z8) \
+	SHIFT_ADD_AND(Z5, Z15, Z6, Z8) \
+	SHIFT_ADD_AND(Z6, Z16, Z7, Z8) \
+	VPSRLQ $32, Z7, Z7             \
+
+#define CARRY3() \
+	VPSRLQ $32, Z0, Z10 \
+	VPANDQ Z8, Z0, Z0   \
+	VPADDQ Z10, Z1, Z1  \
+	VPSRLQ $32, Z1, Z11 \
+	VPANDQ Z8, Z1, Z1   \
+	VPADDQ Z11, Z2, Z2  \
+	VPSRLQ $32, Z2, Z12 \
+	VPANDQ Z8, Z2, Z2   \
+	VPADDQ Z12, Z3, Z3  \
+	VPSRLQ $32, Z3, Z13 \
+	VPANDQ Z8, Z3, Z3   \
+	VPADDQ Z13, Z4, Z4  \
+
+#define CARRY4() \
+	VPSRLQ $32, Z4, Z14 \
+	VPANDQ Z8, Z4, Z4   \
+	VPADDQ Z14, Z5, Z5  \
+	VPSRLQ $32, Z5, Z15 \
+	VPANDQ Z8, Z5, Z5   \
+	VPADDQ Z15, Z6, Z6  \
+	VPSRLQ $32, Z6, Z16 \
+	VPANDQ Z8, Z6, Z6   \
+	VPADDQ Z16, Z7, Z7  \
+
+	// t[0] -> R14
+	// t[1] -> R13
+	// t[2] -> CX
+	// t[3] -> BX
+	// y[0] -> DI
+	// y[1] -> R8
+	// y[2] -> R9
+	// y[3] -> R10
+	MOVQ res+0(FP), SI
+	MOVQ a+8(FP), R11
+	MOVQ b+16(FP), R15
+	MOVQ n+24(FP), R12
+	MOVQ 0(R15), DI
+	MOVQ 8(R15), R8
+	MOVQ 16(R15), R9
+	MOVQ 24(R15), R10
+	MOVQ R12, s0-8(SP)
+
+	// Create mask for low dword in each qword
+	VPCMPEQB  Y8, Y8, Y8
+	VPMOVZXDQ Y8, Z8
+	MOVQ      $0x5555, DX
+	KMOVD     DX, K1
+
+loop_16:
+	TESTQ     R12, R12
+	JEQ       done_15            // n == 0, we are done
+	MOVQ      0(R11), DX
+	VMOVDQU64 256+0*64(R11), Z16
+	VMOVDQU64 256+1*64(R11), Z17
+	VMOVDQU64 256+2*64(R11), Z18
+	VMOVDQU64 256+3*64(R11), Z19
+	VMOVDQU64 0(R15), Z24
+	VMOVDQU64 0(R15), Z25
+	VMOVDQU64 0(R15), Z26
+	VMOVDQU64 0(R15), Z27
+
+	// Transpose and expand x and y
+	VSHUFI64X2 $0x88, Z17, Z16, Z20
+	VSHUFI64X2 $0xdd, Z17, Z16, Z22
+	VSHUFI64X2 $0x88, Z19, Z18, Z21
+	VSHUFI64X2 $0xdd, Z19, Z18, Z23
+	VSHUFI64X2 $0x88, Z25, Z24, Z28
+	VSHUFI64X2 $0xdd, Z25, Z24, Z30
+	VSHUFI64X2 $0x88, Z27, Z26, Z29
+	VSHUFI64X2 $0xdd, Z27, Z26, Z31
+	VPERMQ     $0xd8, Z20, Z20
+	VPERMQ     $0xd8, Z21, Z21
+	VPERMQ     $0xd8, Z22, Z22
+	VPERMQ     $0xd8, Z23, Z23
+
+	// z[0] -> y * x[0]
+	MUL_WORD_0()
+	VPERMQ     $0xd8, Z28, Z28
+	VPERMQ     $0xd8, Z29, Z29
+	VPERMQ     $0xd8, Z30, Z30
+	VPERMQ     $0xd8, Z31, Z31
+	VSHUFI64X2 $0xd8, Z20, Z20, Z20
+	VSHUFI64X2 $0xd8, Z21, Z21, Z21
+	VSHUFI64X2 $0xd8, Z22, Z22, Z22
+	VSHUFI64X2 $0xd8, Z23, Z23, Z23
+
+	// z[0] -> y * x[1]
+	MOVQ       8(R11), DX
+	MUL_WORD_N()
+	VSHUFI64X2 $0xd8, Z28, Z28, Z28
+	VSHUFI64X2 $0xd8, Z29, Z29, Z29
+	VSHUFI64X2 $0xd8, Z30, Z30, Z30
+	VSHUFI64X2 $0xd8, Z31, Z31, Z31
+	VSHUFI64X2 $0x44, Z21, Z20, Z16
+	VSHUFI64X2 $0xee, Z21, Z20, Z18
+	VSHUFI64X2 $0x44, Z23, Z22, Z20
+	VSHUFI64X2 $0xee, Z23, Z22, Z22
+
+	// z[0] -> y * x[2]
+	MOVQ       16(R11), DX
+	MUL_WORD_N()
+	VSHUFI64X2 $0x44, Z29, Z28, Z24
+	VSHUFI64X2 $0xee, Z29, Z28, Z26
+	VSHUFI64X2 $0x44, Z31, Z30, Z28
+	VSHUFI64X2 $0xee, Z31, Z30, Z30
+	PREFETCHT0 1024(R11)
+	VPSRLQ     $32, Z16, Z17
+	VPSRLQ     $32, Z18, Z19
+	VPSRLQ     $32, Z20, Z21
+	VPSRLQ     $32, Z22, Z23
+	VPSRLQ     $32, Z24, Z25
+	VPSRLQ     $32, Z26, Z27
+	VPSRLQ     $32, Z28, Z29
+	VPSRLQ     $32, Z30, Z31
+
+	// z[0] -> y * x[3]
+	MOVQ   24(R11), DX
+	MUL_WORD_N()
+	VPANDQ Z8, Z16, Z16
+	VPANDQ Z8, Z18, Z18
+	VPANDQ Z8, Z20, Z20
+	VPANDQ Z8, Z22, Z22
+	VPANDQ Z8, Z24, Z24
+	VPANDQ Z8, Z26, Z26
+	VPANDQ Z8, Z28, Z28
+	VPANDQ Z8, Z30, Z30
+
+	// reduce element(R14,R13,CX,BX) using temp registers (BP,R12,AX,DX)
+	REDUCE(R14,R13,CX,BX,BP,R12,AX,DX)
+
+	// store output z[0]
+	MOVQ R14, 0(SI)
+	MOVQ R13, 8(SI)
+	MOVQ CX, 16(SI)
+	MOVQ BX, 24(SI)
+	ADDQ $32, R11
+	MOVQ 0(R11), DX
+
+	// For each 256-bit input value, each zmm register now represents a 32-bit input word zero-extended to 64 bits.
+	// Multiply y by doubleword 0 of x
+	VPMULUDQ      Z16, Z24, Z0
+	VPMULUDQ      Z16, Z25, Z1
+	VPMULUDQ      Z16, Z26, Z2
+	VPMULUDQ      Z16, Z27, Z3
+	VPMULUDQ      Z16, Z28, Z4
+	VPMULUDQ      Z16, Z29, Z5
+	VPMULUDQ      Z16, Z30, Z6
+	VPMULUDQ      Z16, Z31, Z7
+	VPMULUDQ.BCST qInvNeg+32(FP), Z0, Z9
+	VPSRLQ        $32, Z0, Z10
+	VPANDQ        Z8, Z0, Z0
+	VPADDQ        Z10, Z1, Z1
+	VPSRLQ        $32, Z1, Z11
+	VPANDQ        Z8, Z1, Z1
+	VPADDQ        Z11, Z2, Z2
+	VPSRLQ        $32, Z2, Z12
+	VPANDQ        Z8, Z2, Z2
+	VPADDQ        Z12, Z3, Z3
+	VPSRLQ        $32, Z3, Z13
+	VPANDQ        Z8, Z3, Z3
+	VPADDQ        Z13, Z4, Z4
+
+	// z[1] -> y * x[0]
+	MUL_WORD_0()
+	VPSRLQ        $32, Z4, Z14
+	VPANDQ        Z8, Z4, Z4
+	VPADDQ        Z14, Z5, Z5
+	VPSRLQ        $32, Z5, Z15
+	VPANDQ        Z8, Z5, Z5
+	VPADDQ        Z15, Z6, Z6
+	VPSRLQ        $32, Z6, Z16
+	VPANDQ        Z8, Z6, Z6
+	VPADDQ        Z16, Z7, Z7
+	VPMULUDQ.BCST ·qElement+0(SB), Z9, Z10
+	VPADDQ        Z10, Z0, Z0
+	VPMULUDQ.BCST ·qElement+4(SB), Z9, Z11
+	VPADDQ        Z11, Z1, Z1
+	VPMULUDQ.BCST ·qElement+8(SB), Z9, Z12
+	VPADDQ        Z12, Z2, Z2
+	VPMULUDQ.BCST ·qElement+12(SB), Z9, Z13
+	VPADDQ        Z13, Z3, Z3
+
+	// z[1] -> y * x[1]
+	MOVQ          8(R11), DX
+	MUL_WORD_N()
+	VPMULUDQ.BCST ·qElement+16(SB), Z9, Z14
+	VPADDQ        Z14, Z4, Z4
+	VPMULUDQ.BCST ·qElement+20(SB), Z9, Z15
+	VPADDQ        Z15, Z5, Z5
+	VPMULUDQ.BCST ·qElement+24(SB), Z9, Z16
+	VPADDQ        Z16, Z6, Z6
+	VPMULUDQ.BCST ·qElement+28(SB), Z9, Z10
+	VPADDQ        Z10, Z7, Z7
+	CARRY1()
+
+	// z[1] -> y * x[2]
+	MOVQ   16(R11), DX
+	MUL_WORD_N()
+	SHIFT_ADD_AND(Z4, Z14, Z5, Z8)
+	SHIFT_ADD_AND(Z5, Z15, Z6, Z8)
+	SHIFT_ADD_AND(Z6, Z16, Z7, Z8)
+	VPSRLQ $32, Z7, Z7
+
+	// Process doubleword 1 of x
+	VPMULUDQ Z17, Z24, Z10
+	VPADDQ   Z10, Z0, Z0
+	VPMULUDQ Z17, Z25, Z11
+	VPADDQ   Z11, Z1, Z1
+	VPMULUDQ Z17, Z26, Z12
+	VPADDQ   Z12, Z2, Z2
+	VPMULUDQ Z17, Z27, Z13
+	VPADDQ   Z13, Z3, Z3
+
+	// z[1] -> y * x[3]
+	MOVQ          24(R11), DX
+	MUL_WORD_N()
+	VPMULUDQ      Z17, Z28, Z14
+	VPADDQ        Z14, Z4, Z4
+	VPMULUDQ      Z17, Z29, Z15
+	VPADDQ        Z15, Z5, Z5
+	VPMULUDQ      Z17, Z30, Z16
+	VPADDQ        Z16, Z6, Z6
+	VPMULUDQ      Z17, Z31, Z17
+	VPADDQ        Z17, Z7, Z7
+	VPMULUDQ.BCST qInvNeg+32(FP), Z0, Z9
+
+	// reduce element(R14,R13,CX,BX) using temp registers (BP,R12,AX,DX)
+	REDUCE(R14,R13,CX,BX,BP,R12,AX,DX)
+
+	// store output z[1]
+	MOVQ R14, 32(SI)
+	MOVQ R13, 40(SI)
+	MOVQ CX, 48(SI)
+	MOVQ BX, 56(SI)
+	ADDQ $32, R11
+	MOVQ 0(R11), DX
+
+	// Move high dwords to zmm10-16, add each to the corresponding low dword (propagate 32-bit carries)
+	VPSRLQ $32, Z0, Z10
+	VPANDQ Z8, Z0, Z0
+	VPADDQ Z10, Z1, Z1
+	VPSRLQ $32, Z1, Z11
+	VPANDQ Z8, Z1, Z1
+	VPADDQ Z11, Z2, Z2
+	VPSRLQ $32, Z2, Z12
+	VPANDQ Z8, Z2, Z2
+	VPADDQ Z12, Z3, Z3
+	VPSRLQ $32, Z3, Z13
+	VPANDQ Z8, Z3, Z3
+	VPADDQ Z13, Z4, Z4
+	CARRY4()
+
+	// z[2] -> y * x[0]
+	MUL_WORD_0()
+	AVX_MUL_Q_LO()
+	AVX_MUL_Q_HI()
+
+	// z[2] -> y * x[1]
+	MOVQ 8(R11), DX
+	MUL_WORD_N()
+	CARRY1()
+	CARRY2()
+
+	// z[2] -> y * x[2]
+	MOVQ 16(R11), DX
+	MUL_WORD_N()
+
+	// Process doubleword 2 of x
+	VPMULUDQ      Z18, Z24, Z10
+	VPADDQ        Z10, Z0, Z0
+	VPMULUDQ      Z18, Z25, Z11
+	VPADDQ        Z11, Z1, Z1
+	VPMULUDQ      Z18, Z26, Z12
+	VPADDQ        Z12, Z2, Z2
+	VPMULUDQ      Z18, Z27, Z13
+	VPADDQ        Z13, Z3, Z3
+	VPMULUDQ      Z18, Z28, Z14
+	VPADDQ        Z14, Z4, Z4
+	VPMULUDQ      Z18, Z29, Z15
+	VPADDQ        Z15, Z5, Z5
+	VPMULUDQ      Z18, Z30, Z16
+	VPADDQ        Z16, Z6, Z6
+	VPMULUDQ      Z18, Z31, Z17
+	VPADDQ        Z17, Z7, Z7
+	VPMULUDQ.BCST qInvNeg+32(FP), Z0, Z9
+
+	// z[2] -> y * x[3]
+	MOVQ 24(R11), DX
+	MUL_WORD_N()
+
+	// Move high dwords to zmm10-16, add each to the corresponding low dword (propagate 32-bit carries)
+	CARRY3()
+
+	// reduce element(R14,R13,CX,BX) using temp registers (BP,R12,AX,DX)
+	REDUCE(R14,R13,CX,BX,BP,R12,AX,DX)
+
+	// store output z[2]
+	MOVQ R14, 64(SI)
+	MOVQ R13, 72(SI)
+	MOVQ CX, 80(SI)
+	MOVQ BX, 88(SI)
+	ADDQ $32, R11
+	MOVQ 0(R11), DX
+	CARRY4()
+	AVX_MUL_Q_LO()
+
+	// z[3] -> y * x[0]
+	MUL_WORD_0()
+	AVX_MUL_Q_HI()
+	CARRY1()
+	CARRY2()
+
+	// Process doubleword 3 of x
+	VPMULUDQ Z19, Z24, Z10
+	VPADDQ   Z10, Z0, Z0
+	VPMULUDQ Z19, Z25, Z11
+	VPADDQ   Z11, Z1, Z1
+	VPMULUDQ Z19, Z26, Z12
+	VPADDQ   Z12, Z2, Z2
+	VPMULUDQ Z19, Z27, Z13
+	VPADDQ   Z13, Z3, Z3
+
+	// z[3] -> y * x[1]
+	MOVQ     8(R11), DX
+	MUL_WORD_N()
+	VPMULUDQ Z19, Z28, Z14
+	VPADDQ   Z14, Z4, Z4
+	VPMULUDQ Z19, Z29, Z15
+	VPADDQ   Z15, Z5, Z5
+	VPMULUDQ Z19, Z30, Z16
+	VPADDQ   Z16, Z6, Z6
+	VPMULUDQ Z19, Z31, Z17
+	VPADDQ   Z17, Z7, Z7
+
+	// z[3] -> y * x[2]
+	MOVQ          16(R11), DX
+	MUL_WORD_N()
+	VPMULUDQ.BCST qInvNeg+32(FP), Z0, Z9
+	CARRY3()
+	CARRY4()
+
+	// z[3] -> y * x[3]
+	MOVQ 24(R11), DX
+	MUL_WORD_N()
+	AVX_MUL_Q_LO()
+	AVX_MUL_Q_HI()
+
+	// reduce element(R14,R13,CX,BX) using temp registers (BP,R12,AX,DX)
+	REDUCE(R14,R13,CX,BX,BP,R12,AX,DX)
+
+	// store output z[3]
+	MOVQ R14, 96(SI)
+	MOVQ R13, 104(SI)
+	MOVQ CX, 112(SI)
+	MOVQ BX, 120(SI)
+	ADDQ $32, R11
+	MOVQ 0(R11), DX
+
+	// Propagate carries and shift down by one dword
+	CARRY1()
+	CARRY2()
+
+	// Process doubleword 4 of x
+	VPMULUDQ Z20, Z24, Z10
+	VPADDQ   Z10, Z0, Z0
+	VPMULUDQ Z20, Z25, Z11
+	VPADDQ   Z11, Z1, Z1
+	VPMULUDQ Z20, Z26, Z12
+	VPADDQ   Z12, Z2, Z2
+	VPMULUDQ Z20, Z27, Z13
+	VPADDQ   Z13, Z3, Z3
+
+	// z[4] -> y * x[0]
+	MUL_WORD_0()
+	VPMULUDQ      Z20, Z28, Z14
+	VPADDQ        Z14, Z4, Z4
+	VPMULUDQ      Z20, Z29, Z15
+	VPADDQ        Z15, Z5, Z5
+	VPMULUDQ      Z20, Z30, Z16
+	VPADDQ        Z16, Z6, Z6
+	VPMULUDQ      Z20, Z31, Z17
+	VPADDQ        Z17, Z7, Z7
+	VPMULUDQ.BCST qInvNeg+32(FP), Z0, Z9
+
+	// z[4] -> y * x[1]
+	MOVQ 8(R11), DX
+	MUL_WORD_N()
+
+	// Move high dwords to zmm10-16, add each to the corresponding low dword (propagate 32-bit carries)
+	CARRY3()
+	CARRY4()
+
+	// z[4] -> y * x[2]
+	MOVQ 16(R11), DX
+	MUL_WORD_N()
+
+	// zmm7 keeps all 64 bits
+	AVX_MUL_Q_LO()
+	AVX_MUL_Q_HI()
+
+	// z[4] -> y * x[3]
+	MOVQ 24(R11), DX
+	MUL_WORD_N()
+
+	// Propagate carries and shift down by one dword
+	CARRY1()
+	CARRY2()
+
+	// reduce element(R14,R13,CX,BX) using temp registers (BP,R12,AX,DX)
+	REDUCE(R14,R13,CX,BX,BP,R12,AX,DX)
+
+	// store output z[4]
+	MOVQ R14, 128(SI)
+	MOVQ R13, 136(SI)
+	MOVQ CX, 144(SI)
+	MOVQ BX, 152(SI)
+	ADDQ $32, R11
+	MOVQ 0(R11), DX
+
+	// Process doubleword 5 of x
+	VPMULUDQ Z21, Z24, Z10
+	VPADDQ   Z10, Z0, Z0
+	VPMULUDQ Z21, Z25, Z11
+	VPADDQ   Z11, Z1, Z1
+	VPMULUDQ Z21, Z26, Z12
+	VPADDQ   Z12, Z2, Z2
+	VPMULUDQ Z21, Z27, Z13
+	VPADDQ   Z13, Z3, Z3
+	VPMULUDQ Z21, Z28, Z14
+	VPADDQ   Z14, Z4, Z4
+	VPMULUDQ Z21, Z29, Z15
+	VPADDQ   Z15, Z5, Z5
+	VPMULUDQ Z21, Z30, Z16
+	VPADDQ   Z16, Z6, Z6
+	VPMULUDQ Z21, Z31, Z17
+	VPADDQ   Z17, Z7, Z7
+
+	// z[5] -> y * x[0]
+	MUL_WORD_0()
+	VPMULUDQ.BCST qInvNeg+32(FP), Z0, Z9
+
+	// Move high dwords to zmm10-16, add each to the corresponding low dword (propagate 32-bit carries)
+	CARRY3()
+	CARRY4()
+
+	// z[5] -> y * x[1]
+	MOVQ 8(R11), DX
+	MUL_WORD_N()
+	AVX_MUL_Q_LO()
+	AVX_MUL_Q_HI()
+
+	// z[5] -> y * x[2]
+	MOVQ 16(R11), DX
+	MUL_WORD_N()
+	CARRY1()
+	CARRY2()
+
+	// z[5] -> y * x[3]
+	MOVQ 24(R11), DX
+	MUL_WORD_N()
+
+	// Process doubleword 6 of x
+	VPMULUDQ      Z22, Z24, Z10
+	VPADDQ        Z10, Z0, Z0
+	VPMULUDQ      Z22, Z25, Z11
+	VPADDQ        Z11, Z1, Z1
+	VPMULUDQ      Z22, Z26, Z12
+	VPADDQ        Z12, Z2, Z2
+	VPMULUDQ      Z22, Z27, Z13
+	VPADDQ        Z13, Z3, Z3
+	VPMULUDQ      Z22, Z28, Z14
+	VPADDQ        Z14, Z4, Z4
+	VPMULUDQ      Z22, Z29, Z15
+	VPADDQ        Z15, Z5, Z5
+	VPMULUDQ      Z22, Z30, Z16
+	VPADDQ        Z16, Z6, Z6
+	VPMULUDQ      Z22, Z31, Z17
+	VPADDQ        Z17, Z7, Z7
+	VPMULUDQ.BCST qInvNeg+32(FP), Z0, Z9
+
+	// reduce element(R14,R13,CX,BX) using temp registers (BP,R12,AX,DX)
+	REDUCE(R14,R13,CX,BX,BP,R12,AX,DX)
+
+	// store output z[5]
+	MOVQ R14, 160(SI)
+	MOVQ R13, 168(SI)
+	MOVQ CX, 176(SI)
+	MOVQ BX, 184(SI)
+	ADDQ $32, R11
+	MOVQ 0(R11), DX
+
+	// Move high dwords to zmm10-16, add each to the corresponding low dword (propagate 32-bit carries)
+	CARRY3()
+	CARRY4()
+
+	// z[6] -> y * x[0]
+	MUL_WORD_0()
+	AVX_MUL_Q_LO()
+	AVX_MUL_Q_HI()
+
+	// z[6] -> y * x[1]
+	MOVQ 8(R11), DX
+	MUL_WORD_N()
+	CARRY1()
+	CARRY2()
+
+	// z[6] -> y * x[2]
+	MOVQ 16(R11), DX
+	MUL_WORD_N()
+
+	// Process doubleword 7 of x
+	VPMULUDQ      Z23, Z24, Z10
+	VPADDQ        Z10, Z0, Z0
+	VPMULUDQ      Z23, Z25, Z11
+	VPADDQ        Z11, Z1, Z1
+	VPMULUDQ      Z23, Z26, Z12
+	VPADDQ        Z12, Z2, Z2
+	VPMULUDQ      Z23, Z27, Z13
+	VPADDQ        Z13, Z3, Z3
+	VPMULUDQ      Z23, Z28, Z14
+	VPADDQ        Z14, Z4, Z4
+	VPMULUDQ      Z23, Z29, Z15
+	VPADDQ        Z15, Z5, Z5
+	VPMULUDQ      Z23, Z30, Z16
+	VPADDQ        Z16, Z6, Z6
+	VPMULUDQ      Z23, Z31, Z17
+	VPADDQ        Z17, Z7, Z7
+	VPMULUDQ.BCST qInvNeg+32(FP), Z0, Z9
+
+	// z[6] -> y * x[3]
+	MOVQ 24(R11), DX
+	MUL_WORD_N()
+	CARRY3()
+
+	// reduce element(R14,R13,CX,BX) using temp registers (BP,R12,AX,DX)
+	REDUCE(R14,R13,CX,BX,BP,R12,AX,DX)
+
+	// store output z[6]
+	MOVQ R14, 192(SI)
+	MOVQ R13, 200(SI)
+	MOVQ CX, 208(SI)
+	MOVQ BX, 216(SI)
+	ADDQ $32, R11
+	MOVQ 0(R11), DX
+	CARRY4()
+	AVX_MUL_Q_LO()
+	AVX_MUL_Q_HI()
+
+	// z[7] -> y * x[0]
+	MUL_WORD_0()
+	CARRY1()
+	CARRY2()
+
+	// z[7] -> y * x[1]
+	MOVQ 8(R11), DX
+	MUL_WORD_N()
+
+	// Conditional subtraction of the modulus
+	VPERMD.BCST.Z ·qElement+0(SB), Z8, K1, Z10
+	VPERMD.BCST.Z ·qElement+4(SB), Z8, K1, Z11
+	VPERMD.BCST.Z ·qElement+8(SB), Z8, K1, Z12
+	VPERMD.BCST.Z ·qElement+12(SB), Z8, K1, Z13
+	VPERMD.BCST.Z ·qElement+16(SB), Z8, K1, Z14
+	VPERMD.BCST.Z ·qElement+20(SB), Z8, K1, Z15
+	VPERMD.BCST.Z ·qElement+24(SB), Z8, K1, Z16
+	VPERMD.BCST.Z ·qElement+28(SB), Z8, K1, Z17
+	VPSUBQ        Z10, Z0, Z10
+	VPSRLQ        $63, Z10, Z20
+	VPANDQ        Z8, Z10, Z10
+	VPSUBQ        Z11, Z1, Z11
+	VPSUBQ        Z20, Z11, Z11
+	VPSRLQ        $63, Z11, Z21
+	VPANDQ        Z8, Z11, Z11
+	VPSUBQ        Z12, Z2, Z12
+	VPSUBQ        Z21, Z12, Z12
+	VPSRLQ        $63, Z12, Z22
+	VPANDQ        Z8, Z12, Z12
+	VPSUBQ        Z13, Z3, Z13
+	VPSUBQ        Z22, Z13, Z13
+	VPSRLQ        $63, Z13, Z23
+	VPANDQ        Z8, Z13, Z13
+	VPSUBQ        Z14, Z4, Z14
+	VPSUBQ        Z23, Z14, Z14
+	VPSRLQ        $63, Z14, Z24
+	VPANDQ        Z8, Z14, Z14
+	VPSUBQ        Z15, Z5, Z15
+	VPSUBQ        Z24, Z15, Z15
+	VPSRLQ        $63, Z15, Z25
+	VPANDQ        Z8, Z15, Z15
+	VPSUBQ        Z16, Z6, Z16
+	VPSUBQ        Z25, Z16, Z16
+	VPSRLQ        $63, Z16, Z26
+	VPANDQ        Z8, Z16, Z16
+	VPSUBQ        Z17, Z7, Z17
+	VPSUBQ        Z26, Z17, Z17
+	VPMOVQ2M      Z17, K2
+	KNOTB         K2, K2
+	VMOVDQU64     Z10, K2, Z0
+	VMOVDQU64     Z11, K2, Z1
+	VMOVDQU64     Z12, K2, Z2
+	VMOVDQU64     Z13, K2, Z3
+	VMOVDQU64     Z14, K2, Z4
+
+	// z[7] -> y * x[2]
+	MOVQ      16(R11), DX
+	MUL_WORD_N()
+	VMOVDQU64 Z15, K2, Z5
+	VMOVDQU64 Z16, K2, Z6
+	VMOVDQU64 Z17, K2, Z7
+
+	// Transpose results back
+	VALIGND   $0, ·pattern1+0(SB), Z11, Z11
+	VALIGND   $0, ·pattern2+0(SB), Z12, Z12
+	VALIGND   $0, ·pattern3+0(SB), Z13, Z13
+	VALIGND   $0, ·pattern4+0(SB), Z14, Z14
+	VPSLLQ    $32, Z1, Z1
+	VPORQ     Z1, Z0, Z0
+	VPSLLQ    $32, Z3, Z3
+	VPORQ     Z3, Z2, Z1
+	VPSLLQ    $32, Z5, Z5
+	VPORQ     Z5, Z4, Z2
+	VPSLLQ    $32, Z7, Z7
+	VPORQ     Z7, Z6, Z3
+	VMOVDQU64 Z0, Z4
+	VMOVDQU64 Z2, Z6
+
+	// z[7] -> y * x[3]
+	MOVQ     24(R11), DX
+	MUL_WORD_N()
+	VPERMT2Q Z1, Z11, Z0
+	VPERMT2Q Z4, Z12, Z1
+	VPERMT2Q Z3, Z11, Z2
+	VPERMT2Q Z6, Z12, Z3
+
+	// reduce element(R14,R13,CX,BX) using temp registers (BP,R12,AX,DX)
+	REDUCE(R14,R13,CX,BX,BP,R12,AX,DX)
+
+	// store output z[7]
+	MOVQ      R14, 224(SI)
+	MOVQ      R13, 232(SI)
+	MOVQ      CX, 240(SI)
+	MOVQ      BX, 248(SI)
+	ADDQ      $288, R11
+	VMOVDQU64 Z0, Z4
+	VMOVDQU64 Z1, Z5
+	VPERMT2Q  Z2, Z13, Z0
+	VPERMT2Q  Z4, Z14, Z2
+	VPERMT2Q  Z3, Z13, Z1
+	VPERMT2Q  Z5, Z14, Z3
+
+	// Save AVX-512 results
+	VMOVDQU64 Z0, 256+0*64(SI)
+	VMOVDQU64 Z2, 256+1*64(SI)
+	VMOVDQU64 Z1, 256+2*64(SI)
+	VMOVDQU64 Z3, 256+3*64(SI)
+	ADDQ      $512, SI
+	MOVQ      s0-8(SP), R12
+	DECQ      R12              // decrement n
+	MOVQ      R12, s0-8(SP)
+	JMP       loop_16
+
+done_15:
+	RET
+
+TEXT ·mulVec(SB), $8-40
+	// t[0] -> R14
+	// t[1] -> R13
+	// t[2] -> CX
+	// t[3] -> BX
+	// y[0] -> DI
+	// y[1] -> R8
+	// y[2] -> R9
+	// y[3] -> R10
+	MOVQ res+0(FP), SI
+	MOVQ a+8(FP), R11
+	MOVQ b+16(FP), R15
+	MOVQ n+24(FP), R12
+	MOVQ R12, s0-8(SP)
+
+	// Create mask for low dword in each qword
+	VPCMPEQB  Y8, Y8, Y8
+	VPMOVZXDQ Y8, Z8
+	MOVQ      $0x5555, DX
+	KMOVD     DX, K1
+
+loop_18:
+	TESTQ     R12, R12
+	JEQ       done_17            // n == 0, we are done
+	MOVQ      0(R11), DX
+	VMOVDQU64 256+0*64(R11), Z16
+	VMOVDQU64 256+1*64(R11), Z17
+	VMOVDQU64 256+2*64(R11), Z18
+	VMOVDQU64 256+3*64(R11), Z19
+
+	// load input y[0]
+	MOVQ      0(R15), DI
+	MOVQ      8(R15), R8
+	MOVQ      16(R15), R9
+	MOVQ      24(R15), R10
+	VMOVDQU64 256+0*64(R15), Z24
+	VMOVDQU64 256+1*64(R15), Z25
+	VMOVDQU64 256+2*64(R15), Z26
+	VMOVDQU64 256+3*64(R15), Z27
+
+	// Transpose and expand x and y
+	VSHUFI64X2 $0x88, Z17, Z16, Z20
+	VSHUFI64X2 $0xdd, Z17, Z16, Z22
+	VSHUFI64X2 $0x88, Z19, Z18, Z21
+	VSHUFI64X2 $0xdd, Z19, Z18, Z23
+	VSHUFI64X2 $0x88, Z25, Z24, Z28
+	VSHUFI64X2 $0xdd, Z25, Z24, Z30
+	VSHUFI64X2 $0x88, Z27, Z26, Z29
+	VSHUFI64X2 $0xdd, Z27, Z26, Z31
+	VPERMQ     $0xd8, Z20, Z20
+	VPERMQ     $0xd8, Z21, Z21
+	VPERMQ     $0xd8, Z22, Z22
+	VPERMQ     $0xd8, Z23, Z23
+
+	// z[0] -> y * x[0]
+	MUL_WORD_0()
+	VPERMQ     $0xd8, Z28, Z28
+	VPERMQ     $0xd8, Z29, Z29
+	VPERMQ     $0xd8, Z30, Z30
+	VPERMQ     $0xd8, Z31, Z31
+	VSHUFI64X2 $0xd8, Z20, Z20, Z20
+	VSHUFI64X2 $0xd8, Z21, Z21, Z21
+	VSHUFI64X2 $0xd8, Z22, Z22, Z22
+	VSHUFI64X2 $0xd8, Z23, Z23, Z23
+
+	// z[0] -> y * x[1]
+	MOVQ       8(R11), DX
+	MUL_WORD_N()
+	VSHUFI64X2 $0xd8, Z28, Z28, Z28
+	VSHUFI64X2 $0xd8, Z29, Z29, Z29
+	VSHUFI64X2 $0xd8, Z30, Z30, Z30
+	VSHUFI64X2 $0xd8, Z31, Z31, Z31
+	VSHUFI64X2 $0x44, Z21, Z20, Z16
+	VSHUFI64X2 $0xee, Z21, Z20, Z18
+	VSHUFI64X2 $0x44, Z23, Z22, Z20
+	VSHUFI64X2 $0xee, Z23, Z22, Z22
+
+	// z[0] -> y * x[2]
+	MOVQ       16(R11), DX
+	MUL_WORD_N()
+	VSHUFI64X2 $0x44, Z29, Z28, Z24
+	VSHUFI64X2 $0xee, Z29, Z28, Z26
+	VSHUFI64X2 $0x44, Z31, Z30, Z28
+	VSHUFI64X2 $0xee, Z31, Z30, Z30
+	PREFETCHT0 1024(R11)
+	VPSRLQ     $32, Z16, Z17
+	VPSRLQ     $32, Z18, Z19
+	VPSRLQ     $32, Z20, Z21
+	VPSRLQ     $32, Z22, Z23
+	VPSRLQ     $32, Z24, Z25
+	VPSRLQ     $32, Z26, Z27
+	VPSRLQ     $32, Z28, Z29
+	VPSRLQ     $32, Z30, Z31
+
+	// z[0] -> y * x[3]
+	MOVQ   24(R11), DX
+	MUL_WORD_N()
+	VPANDQ Z8, Z16, Z16
+	VPANDQ Z8, Z18, Z18
+	VPANDQ Z8, Z20, Z20
+	VPANDQ Z8, Z22, Z22
+	VPANDQ Z8, Z24, Z24
+	VPANDQ Z8, Z26, Z26
+	VPANDQ Z8, Z28, Z28
+	VPANDQ Z8, Z30, Z30
+
+	// reduce element(R14,R13,CX,BX) using temp registers (BP,R12,AX,DX)
+	REDUCE(R14,R13,CX,BX,BP,R12,AX,DX)
+
+	// store output z[0]
+	MOVQ R14, 0(SI)
+	MOVQ R13, 8(SI)
+	MOVQ CX, 16(SI)
+	MOVQ BX, 24(SI)
+	ADDQ $32, R11
+	MOVQ 0(R11), DX
+
+	// For each 256-bit input value, each zmm register now represents a 32-bit input word zero-extended to 64 bits.
+	// Multiply y by doubleword 0 of x
+	VPMULUDQ   Z16, Z24, Z0
+	VPMULUDQ   Z16, Z25, Z1
+	VPMULUDQ   Z16, Z26, Z2
+	VPMULUDQ   Z16, Z27, Z3
+	VPMULUDQ   Z16, Z28, Z4
+	PREFETCHT0 1024(R15)
+	VPMULUDQ   Z16, Z29, Z5
+	VPMULUDQ   Z16, Z30, Z6
+	VPMULUDQ   Z16, Z31, Z7
+
+	// load input y[1]
+	MOVQ          32(R15), DI
+	MOVQ          40(R15), R8
+	MOVQ          48(R15), R9
+	MOVQ          56(R15), R10
+	VPMULUDQ.BCST qInvNeg+32(FP), Z0, Z9
+	VPSRLQ        $32, Z0, Z10
+	VPANDQ        Z8, Z0, Z0
+	VPADDQ        Z10, Z1, Z1
+	VPSRLQ        $32, Z1, Z11
+	VPANDQ        Z8, Z1, Z1
+	VPADDQ        Z11, Z2, Z2
+	VPSRLQ        $32, Z2, Z12
+	VPANDQ        Z8, Z2, Z2
+	VPADDQ        Z12, Z3, Z3
+	VPSRLQ        $32, Z3, Z13
+	VPANDQ        Z8, Z3, Z3
+	VPADDQ        Z13, Z4, Z4
+
+	// z[1] -> y * x[0]
+	MUL_WORD_0()
+	VPSRLQ        $32, Z4, Z14
+	VPANDQ        Z8, Z4, Z4
+	VPADDQ        Z14, Z5, Z5
+	VPSRLQ        $32, Z5, Z15
+	VPANDQ        Z8, Z5, Z5
+	VPADDQ        Z15, Z6, Z6
+	VPSRLQ        $32, Z6, Z16
+	VPANDQ        Z8, Z6, Z6
+	VPADDQ        Z16, Z7, Z7
+	VPMULUDQ.BCST ·qElement+0(SB), Z9, Z10
+	VPADDQ        Z10, Z0, Z0
+	VPMULUDQ.BCST ·qElement+4(SB), Z9, Z11
+	VPADDQ        Z11, Z1, Z1
+	VPMULUDQ.BCST ·qElement+8(SB), Z9, Z12
+	VPADDQ        Z12, Z2, Z2
+	VPMULUDQ.BCST ·qElement+12(SB), Z9, Z13
+	VPADDQ        Z13, Z3, Z3
+
+	// z[1] -> y * x[1]
+	MOVQ          8(R11), DX
+	MUL_WORD_N()
+	VPMULUDQ.BCST ·qElement+16(SB), Z9, Z14
+	VPADDQ        Z14, Z4, Z4
+	VPMULUDQ.BCST ·qElement+20(SB), Z9, Z15
+	VPADDQ        Z15, Z5, Z5
+	VPMULUDQ.BCST ·qElement+24(SB), Z9, Z16
+	VPADDQ        Z16, Z6, Z6
+	VPMULUDQ.BCST ·qElement+28(SB), Z9, Z10
+	VPADDQ        Z10, Z7, Z7
+	CARRY1()
+
+	// z[1] -> y * x[2]
+	MOVQ   16(R11), DX
+	MUL_WORD_N()
+	SHIFT_ADD_AND(Z4, Z14, Z5, Z8)
+	SHIFT_ADD_AND(Z5, Z15, Z6, Z8)
+	SHIFT_ADD_AND(Z6, Z16, Z7, Z8)
+	VPSRLQ $32, Z7, Z7
+
+	// Process doubleword 1 of x
+	VPMULUDQ Z17, Z24, Z10
+	VPADDQ   Z10, Z0, Z0
+	VPMULUDQ Z17, Z25, Z11
+	VPADDQ   Z11, Z1, Z1
+	VPMULUDQ Z17, Z26, Z12
+	VPADDQ   Z12, Z2, Z2
+	VPMULUDQ Z17, Z27, Z13
+	VPADDQ   Z13, Z3, Z3
+
+	// z[1] -> y * x[3]
+	MOVQ          24(R11), DX
+	MUL_WORD_N()
+	VPMULUDQ      Z17, Z28, Z14
+	VPADDQ        Z14, Z4, Z4
+	VPMULUDQ      Z17, Z29, Z15
+	VPADDQ        Z15, Z5, Z5
+	VPMULUDQ      Z17, Z30, Z16
+	VPADDQ        Z16, Z6, Z6
+	VPMULUDQ      Z17, Z31, Z17
+	VPADDQ        Z17, Z7, Z7
+	VPMULUDQ.BCST qInvNeg+32(FP), Z0, Z9
+
+	// reduce element(R14,R13,CX,BX) using temp registers (BP,R12,AX,DX)
+	REDUCE(R14,R13,CX,BX,BP,R12,AX,DX)
+
+	// store output z[1]
+	MOVQ R14, 32(SI)
+	MOVQ R13, 40(SI)
+	MOVQ CX, 48(SI)
+	MOVQ BX, 56(SI)
+	ADDQ $32, R11
+	MOVQ 0(R11), DX
+
+	// Move high dwords to zmm10-16, add each to the corresponding low dword (propagate 32-bit carries)
+	VPSRLQ $32, Z0, Z10
+	VPANDQ Z8, Z0, Z0
+	VPADDQ Z10, Z1, Z1
+	VPSRLQ $32, Z1, Z11
+	VPANDQ Z8, Z1, Z1
+	VPADDQ Z11, Z2, Z2
+	VPSRLQ $32, Z2, Z12
+	VPANDQ Z8, Z2, Z2
+	VPADDQ Z12, Z3, Z3
+
+	// load input y[2]
+	MOVQ   64(R15), DI
+	MOVQ   72(R15), R8
+	MOVQ   80(R15), R9
+	MOVQ   88(R15), R10
+	VPSRLQ $32, Z3, Z13
+	VPANDQ Z8, Z3, Z3
+	VPADDQ Z13, Z4, Z4
+	CARRY4()
+
+	// z[2] -> y * x[0]
+	MUL_WORD_0()
+	AVX_MUL_Q_LO()
+	AVX_MUL_Q_HI()
+
+	// z[2] -> y * x[1]
+	MOVQ 8(R11), DX
+	MUL_WORD_N()
+	CARRY1()
+	CARRY2()
+
+	// z[2] -> y * x[2]
+	MOVQ 16(R11), DX
+	MUL_WORD_N()
+
+	// Process doubleword 2 of x
+	VPMULUDQ      Z18, Z24, Z10
+	VPADDQ        Z10, Z0, Z0
+	VPMULUDQ      Z18, Z25, Z11
+	VPADDQ        Z11, Z1, Z1
+	VPMULUDQ      Z18, Z26, Z12
+	VPADDQ        Z12, Z2, Z2
+	VPMULUDQ      Z18, Z27, Z13
+	VPADDQ        Z13, Z3, Z3
+	VPMULUDQ      Z18, Z28, Z14
+	VPADDQ        Z14, Z4, Z4
+	VPMULUDQ      Z18, Z29, Z15
+	VPADDQ        Z15, Z5, Z5
+	VPMULUDQ      Z18, Z30, Z16
+	VPADDQ        Z16, Z6, Z6
+	VPMULUDQ      Z18, Z31, Z17
+	VPADDQ        Z17, Z7, Z7
+	VPMULUDQ.BCST qInvNeg+32(FP), Z0, Z9
+
+	// z[2] -> y * x[3]
+	MOVQ 24(R11), DX
+	MUL_WORD_N()
+
+	// Move high dwords to zmm10-16, add each to the corresponding low dword (propagate 32-bit carries)
+	CARRY3()
+
+	// reduce element(R14,R13,CX,BX) using temp registers (BP,R12,AX,DX)
+	REDUCE(R14,R13,CX,BX,BP,R12,AX,DX)
+
+	// store output z[2]
+	MOVQ R14, 64(SI)
+	MOVQ R13, 72(SI)
+	MOVQ CX, 80(SI)
+	MOVQ BX, 88(SI)
+	ADDQ $32, R11
+	MOVQ 0(R11), DX
+
+	// load input y[3]
+	MOVQ 96(R15), DI
+	MOVQ 104(R15), R8
+	MOVQ 112(R15), R9
+	MOVQ 120(R15), R10
+	CARRY4()
+	AVX_MUL_Q_LO()
+
+	// z[3] -> y * x[0]
+	MUL_WORD_0()
+	AVX_MUL_Q_HI()
+	CARRY1()
+	CARRY2()
+
+	// Process doubleword 3 of x
+	VPMULUDQ Z19, Z24, Z10
+	VPADDQ   Z10, Z0, Z0
+	VPMULUDQ Z19, Z25, Z11
+	VPADDQ   Z11, Z1, Z1
+	VPMULUDQ Z19, Z26, Z12
+	VPADDQ   Z12, Z2, Z2
+	VPMULUDQ Z19, Z27, Z13
+	VPADDQ   Z13, Z3, Z3
+
+	// z[3] -> y * x[1]
+	MOVQ     8(R11), DX
+	MUL_WORD_N()
+	VPMULUDQ Z19, Z28, Z14
+	VPADDQ   Z14, Z4, Z4
+	VPMULUDQ Z19, Z29, Z15
+	VPADDQ   Z15, Z5, Z5
+	VPMULUDQ Z19, Z30, Z16
+	VPADDQ   Z16, Z6, Z6
+	VPMULUDQ Z19, Z31, Z17
+	VPADDQ   Z17, Z7, Z7
+
+	// z[3] -> y * x[2]
+	MOVQ          16(R11), DX
+	MUL_WORD_N()
+	VPMULUDQ.BCST qInvNeg+32(FP), Z0, Z9
+	CARRY3()
+	CARRY4()
+
+	// z[3] -> y * x[3]
+	MOVQ 24(R11), DX
+	MUL_WORD_N()
+	AVX_MUL_Q_LO()
+	AVX_MUL_Q_HI()
+
+	// reduce element(R14,R13,CX,BX) using temp registers (BP,R12,AX,DX)
+	REDUCE(R14,R13,CX,BX,BP,R12,AX,DX)
+
+	// store output z[3]
+	MOVQ R14, 96(SI)
+	MOVQ R13, 104(SI)
+	MOVQ CX, 112(SI)
+	MOVQ BX, 120(SI)
+	ADDQ $32, R11
+	MOVQ 0(R11), DX
+
+	// Propagate carries and shift down by one dword
+	CARRY1()
+	CARRY2()
+
+	// load input y[4]
+	MOVQ 128(R15), DI
+	MOVQ 136(R15), R8
+	MOVQ 144(R15), R9
+	MOVQ 152(R15), R10
+
+	// Process doubleword 4 of x
+	VPMULUDQ Z20, Z24, Z10
+	VPADDQ   Z10, Z0, Z0
+	VPMULUDQ Z20, Z25, Z11
+	VPADDQ   Z11, Z1, Z1
+	VPMULUDQ Z20, Z26, Z12
+	VPADDQ   Z12, Z2, Z2
+	VPMULUDQ Z20, Z27, Z13
+	VPADDQ   Z13, Z3, Z3
+
+	// z[4] -> y * x[0]
+	MUL_WORD_0()
+	VPMULUDQ      Z20, Z28, Z14
+	VPADDQ        Z14, Z4, Z4
+	VPMULUDQ      Z20, Z29, Z15
+	VPADDQ        Z15, Z5, Z5
+	VPMULUDQ      Z20, Z30, Z16
+	VPADDQ        Z16, Z6, Z6
+	VPMULUDQ      Z20, Z31, Z17
+	VPADDQ        Z17, Z7, Z7
+	VPMULUDQ.BCST qInvNeg+32(FP), Z0, Z9
+
+	// z[4] -> y * x[1]
+	MOVQ 8(R11), DX
+	MUL_WORD_N()
+
+	// Move high dwords to zmm10-16, add each to the corresponding low dword (propagate 32-bit carries)
+	CARRY3()
+	CARRY4()
+
+	// z[4] -> y * x[2]
+	MOVQ 16(R11), DX
+	MUL_WORD_N()
+
+	// zmm7 keeps all 64 bits
+	AVX_MUL_Q_LO()
+	AVX_MUL_Q_HI()
+
+	// z[4] -> y * x[3]
+	MOVQ 24(R11), DX
+	MUL_WORD_N()
+
+	// Propagate carries and shift down by one dword
+	CARRY1()
+	CARRY2()
+
+	// reduce element(R14,R13,CX,BX) using temp registers (BP,R12,AX,DX)
+	REDUCE(R14,R13,CX,BX,BP,R12,AX,DX)
+
+	// store output z[4]
+	MOVQ R14, 128(SI)
+	MOVQ R13, 136(SI)
+	MOVQ CX, 144(SI)
+	MOVQ BX, 152(SI)
+	ADDQ $32, R11
+	MOVQ 0(R11), DX
+
+	// Process doubleword 5 of x
+	VPMULUDQ Z21, Z24, Z10
+	VPADDQ   Z10, Z0, Z0
+	VPMULUDQ Z21, Z25, Z11
+	VPADDQ   Z11, Z1, Z1
+	VPMULUDQ Z21, Z26, Z12
+	VPADDQ   Z12, Z2, Z2
+	VPMULUDQ Z21, Z27, Z13
+	VPADDQ   Z13, Z3, Z3
+
+	// load input y[5]
+	MOVQ     160(R15), DI
+	MOVQ     168(R15), R8
+	MOVQ     176(R15), R9
+	MOVQ     184(R15), R10
+	VPMULUDQ Z21, Z28, Z14
+	VPADDQ   Z14, Z4, Z4
+	VPMULUDQ Z21, Z29, Z15
+	VPADDQ   Z15, Z5, Z5
+	VPMULUDQ Z21, Z30, Z16
+	VPADDQ   Z16, Z6, Z6
+	VPMULUDQ Z21, Z31, Z17
+	VPADDQ   Z17, Z7, Z7
+
+	// z[5] -> y * x[0]
+	MUL_WORD_0()
+	VPMULUDQ.BCST qInvNeg+32(FP), Z0, Z9
+
+	// Move high dwords to zmm10-16, add each to the corresponding low dword (propagate 32-bit carries)
+	CARRY3()
+	CARRY4()
+
+	// z[5] -> y * x[1]
+	MOVQ 8(R11), DX
+	MUL_WORD_N()
+	AVX_MUL_Q_LO()
+	AVX_MUL_Q_HI()
+
+	// z[5] -> y * x[2]
+	MOVQ 16(R11), DX
+	MUL_WORD_N()
+	CARRY1()
+	CARRY2()
+
+	// z[5] -> y * x[3]
+	MOVQ 24(R11), DX
+	MUL_WORD_N()
+
+	// Process doubleword 6 of x
+	VPMULUDQ      Z22, Z24, Z10
+	VPADDQ        Z10, Z0, Z0
+	VPMULUDQ      Z22, Z25, Z11
+	VPADDQ        Z11, Z1, Z1
+	VPMULUDQ      Z22, Z26, Z12
+	VPADDQ        Z12, Z2, Z2
+	VPMULUDQ      Z22, Z27, Z13
+	VPADDQ        Z13, Z3, Z3
+	VPMULUDQ      Z22, Z28, Z14
+	VPADDQ        Z14, Z4, Z4
+	VPMULUDQ      Z22, Z29, Z15
+	VPADDQ        Z15, Z5, Z5
+	VPMULUDQ      Z22, Z30, Z16
+	VPADDQ        Z16, Z6, Z6
+	VPMULUDQ      Z22, Z31, Z17
+	VPADDQ        Z17, Z7, Z7
+	VPMULUDQ.BCST qInvNeg+32(FP), Z0, Z9
+
+	// reduce element(R14,R13,CX,BX) using temp registers (BP,R12,AX,DX)
+	REDUCE(R14,R13,CX,BX,BP,R12,AX,DX)
+
+	// store output z[5]
+	MOVQ R14, 160(SI)
+	MOVQ R13, 168(SI)
+	MOVQ CX, 176(SI)
+	MOVQ BX, 184(SI)
+	ADDQ $32, R11
+	MOVQ 0(R11), DX
+
+	// Move high dwords to zmm10-16, add each to the corresponding low dword (propagate 32-bit carries)
+	CARRY3()
+
+	// load input y[6]
+	MOVQ 192(R15), DI
+	MOVQ 200(R15), R8
+	MOVQ 208(R15), R9
+	MOVQ 216(R15), R10
+	CARRY4()
+
+	// z[6] -> y * x[0]
+	MUL_WORD_0()
+	AVX_MUL_Q_LO()
+	AVX_MUL_Q_HI()
+
+	// z[6] -> y * x[1]
+	MOVQ 8(R11), DX
+	MUL_WORD_N()
+	CARRY1()
+	CARRY2()
+
+	// z[6] -> y * x[2]
+	MOVQ 16(R11), DX
+	MUL_WORD_N()
+
+	// Process doubleword 7 of x
+	VPMULUDQ      Z23, Z24, Z10
+	VPADDQ        Z10, Z0, Z0
+	VPMULUDQ      Z23, Z25, Z11
+	VPADDQ        Z11, Z1, Z1
+	VPMULUDQ      Z23, Z26, Z12
+	VPADDQ        Z12, Z2, Z2
+	VPMULUDQ      Z23, Z27, Z13
+	VPADDQ        Z13, Z3, Z3
+	VPMULUDQ      Z23, Z28, Z14
+	VPADDQ        Z14, Z4, Z4
+	VPMULUDQ      Z23, Z29, Z15
+	VPADDQ        Z15, Z5, Z5
+	VPMULUDQ      Z23, Z30, Z16
+	VPADDQ        Z16, Z6, Z6
+	VPMULUDQ      Z23, Z31, Z17
+	VPADDQ        Z17, Z7, Z7
+	VPMULUDQ.BCST qInvNeg+32(FP), Z0, Z9
+
+	// z[6] -> y * x[3]
+	MOVQ 24(R11), DX
+	MUL_WORD_N()
+	CARRY3()
+
+	// reduce element(R14,R13,CX,BX) using temp registers (BP,R12,AX,DX)
+	REDUCE(R14,R13,CX,BX,BP,R12,AX,DX)
+
+	// store output z[6]
+	MOVQ R14, 192(SI)
+	MOVQ R13, 200(SI)
+	MOVQ CX, 208(SI)
+	MOVQ BX, 216(SI)
+	ADDQ $32, R11
+	MOVQ 0(R11), DX
+	CARRY4()
+
+	// load input y[7]
+	MOVQ 224(R15), DI
+	MOVQ 232(R15), R8
+	MOVQ 240(R15), R9
+	MOVQ 248(R15), R10
+	AVX_MUL_Q_LO()
+	AVX_MUL_Q_HI()
+
+	// z[7] -> y * x[0]
+	MUL_WORD_0()
+	CARRY1()
+	CARRY2()
+
+	// z[7] -> y * x[1]
+	MOVQ 8(R11), DX
+	MUL_WORD_N()
+
+	// Conditional subtraction of the modulus
+	VPERMD.BCST.Z ·qElement+0(SB), Z8, K1, Z10
+	VPERMD.BCST.Z ·qElement+4(SB), Z8, K1, Z11
+	VPERMD.BCST.Z ·qElement+8(SB), Z8, K1, Z12
+	VPERMD.BCST.Z ·qElement+12(SB), Z8, K1, Z13
+	VPERMD.BCST.Z ·qElement+16(SB), Z8, K1, Z14
+	VPERMD.BCST.Z ·qElement+20(SB), Z8, K1, Z15
+	VPERMD.BCST.Z ·qElement+24(SB), Z8, K1, Z16
+	VPERMD.BCST.Z ·qElement+28(SB), Z8, K1, Z17
+	VPSUBQ        Z10, Z0, Z10
+	VPSRLQ        $63, Z10, Z20
+	VPANDQ        Z8, Z10, Z10
+	VPSUBQ        Z11, Z1, Z11
+	VPSUBQ        Z20, Z11, Z11
+	VPSRLQ        $63, Z11, Z21
+	VPANDQ        Z8, Z11, Z11
+	VPSUBQ        Z12, Z2, Z12
+	VPSUBQ        Z21, Z12, Z12
+	VPSRLQ        $63, Z12, Z22
+	VPANDQ        Z8, Z12, Z12
+	VPSUBQ        Z13, Z3, Z13
+	VPSUBQ        Z22, Z13, Z13
+	VPSRLQ        $63, Z13, Z23
+	VPANDQ        Z8, Z13, Z13
+	VPSUBQ        Z14, Z4, Z14
+	VPSUBQ        Z23, Z14, Z14
+	VPSRLQ        $63, Z14, Z24
+	VPANDQ        Z8, Z14, Z14
+	VPSUBQ        Z15, Z5, Z15
+	VPSUBQ        Z24, Z15, Z15
+	VPSRLQ        $63, Z15, Z25
+	VPANDQ        Z8, Z15, Z15
+	VPSUBQ        Z16, Z6, Z16
+	VPSUBQ        Z25, Z16, Z16
+	VPSRLQ        $63, Z16, Z26
+	VPANDQ        Z8, Z16, Z16
+	VPSUBQ        Z17, Z7, Z17
+	VPSUBQ        Z26, Z17, Z17
+	VPMOVQ2M      Z17, K2
+	KNOTB         K2, K2
+	VMOVDQU64     Z10, K2, Z0
+	VMOVDQU64     Z11, K2, Z1
+	VMOVDQU64     Z12, K2, Z2
+	VMOVDQU64     Z13, K2, Z3
+	VMOVDQU64     Z14, K2, Z4
+
+	// z[7] -> y * x[2]
+	MOVQ      16(R11), DX
+	MUL_WORD_N()
+	VMOVDQU64 Z15, K2, Z5
+	VMOVDQU64 Z16, K2, Z6
+	VMOVDQU64 Z17, K2, Z7
+
+	// Transpose results back
+	VALIGND   $0, ·pattern1+0(SB), Z11, Z11
+	VALIGND   $0, ·pattern2+0(SB), Z12, Z12
+	VALIGND   $0, ·pattern3+0(SB), Z13, Z13
+	VALIGND   $0, ·pattern4+0(SB), Z14, Z14
+	VPSLLQ    $32, Z1, Z1
+	VPORQ     Z1, Z0, Z0
+	VPSLLQ    $32, Z3, Z3
+	VPORQ     Z3, Z2, Z1
+	VPSLLQ    $32, Z5, Z5
+	VPORQ     Z5, Z4, Z2
+	VPSLLQ    $32, Z7, Z7
+	VPORQ     Z7, Z6, Z3
+	VMOVDQU64 Z0, Z4
+	VMOVDQU64 Z2, Z6
+
+	// z[7] -> y * x[3]
+	MOVQ     24(R11), DX
+	MUL_WORD_N()
+	VPERMT2Q Z1, Z11, Z0
+	VPERMT2Q Z4, Z12, Z1
+	VPERMT2Q Z3, Z11, Z2
+	VPERMT2Q Z6, Z12, Z3
+
+	// reduce element(R14,R13,CX,BX) using temp registers (BP,R12,AX,DX)
+	REDUCE(R14,R13,CX,BX,BP,R12,AX,DX)
+
+	// store output z[7]
+	MOVQ      R14, 224(SI)
+	MOVQ      R13, 232(SI)
+	MOVQ      CX, 240(SI)
+	MOVQ      BX, 248(SI)
+	ADDQ      $288, R11
+	VMOVDQU64 Z0, Z4
+	VMOVDQU64 Z1, Z5
+	VPERMT2Q  Z2, Z13, Z0
+	VPERMT2Q  Z4, Z14, Z2
+	VPERMT2Q  Z3, Z13, Z1
+	VPERMT2Q  Z5, Z14, Z3
+
+	// Save AVX-512 results
+	VMOVDQU64 Z0, 256+0*64(SI)
+	VMOVDQU64 Z2, 256+1*64(SI)
+	VMOVDQU64 Z1, 256+2*64(SI)
+	VMOVDQU64 Z3, 256+3*64(SI)
+	ADDQ      $512, SI
+	ADDQ      $512, R15
+	MOVQ      s0-8(SP), R12
+	DECQ      R12              // decrement n
+	MOVQ      R12, s0-8(SP)
+	JMP       loop_18
+
+done_17:
+	RET
diff --git a/field/asm/element_5w_amd64.s b/field/asm/element_5w_amd64.s
new file mode 100644
index 0000000000..b3ccd84b14
--- /dev/null
+++ b/field/asm/element_5w_amd64.s
@@ -0,0 +1,563 @@
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+#include "textflag.h"
+#include "funcdata.h"
+#include "go_asm.h"
+
+#define REDUCE(ra0, ra1, ra2, ra3, ra4, rb0, rb1, rb2, rb3, rb4) \
+	MOVQ    ra0, rb0;              \
+	SUBQ    ·qElement(SB), ra0;    \
+	MOVQ    ra1, rb1;              \
+	SBBQ    ·qElement+8(SB), ra1;  \
+	MOVQ    ra2, rb2;              \
+	SBBQ    ·qElement+16(SB), ra2; \
+	MOVQ    ra3, rb3;              \
+	SBBQ    ·qElement+24(SB), ra3; \
+	MOVQ    ra4, rb4;              \
+	SBBQ    ·qElement+32(SB), ra4; \
+	CMOVQCS rb0, ra0;              \
+	CMOVQCS rb1, ra1;              \
+	CMOVQCS rb2, ra2;              \
+	CMOVQCS rb3, ra3;              \
+	CMOVQCS rb4, ra4;              \
+
+TEXT ·reduce(SB), NOSPLIT, $0-8
+	MOVQ res+0(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	MOVQ 32(AX), DI
+
+	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
+
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	MOVQ DI, 32(AX)
+	RET
+
+// MulBy3(x *Element)
+TEXT ·MulBy3(SB), NOSPLIT, $0-8
+	MOVQ x+0(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	MOVQ 32(AX), DI
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+	ADCQ DI, DI
+
+	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
+
+	ADDQ 0(AX), DX
+	ADCQ 8(AX), CX
+	ADCQ 16(AX), BX
+	ADCQ 24(AX), SI
+	ADCQ 32(AX), DI
+
+	// reduce element(DX,CX,BX,SI,DI) using temp registers (R13,R14,R15,R8,R9)
+	REDUCE(DX,CX,BX,SI,DI,R13,R14,R15,R8,R9)
+
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	MOVQ DI, 32(AX)
+	RET
+
+// MulBy5(x *Element)
+TEXT ·MulBy5(SB), NOSPLIT, $0-8
+	MOVQ x+0(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	MOVQ 32(AX), DI
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+	ADCQ DI, DI
+
+	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
+
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+	ADCQ DI, DI
+
+	// reduce element(DX,CX,BX,SI,DI) using temp registers (R13,R14,R15,R8,R9)
+	REDUCE(DX,CX,BX,SI,DI,R13,R14,R15,R8,R9)
+
+	ADDQ 0(AX), DX
+	ADCQ 8(AX), CX
+	ADCQ 16(AX), BX
+	ADCQ 24(AX), SI
+	ADCQ 32(AX), DI
+
+	// reduce element(DX,CX,BX,SI,DI) using temp registers (R10,R11,R12,R13,R14)
+	REDUCE(DX,CX,BX,SI,DI,R10,R11,R12,R13,R14)
+
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	MOVQ DI, 32(AX)
+	RET
+
+// MulBy13(x *Element)
+TEXT ·MulBy13(SB), $16-8
+	MOVQ x+0(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	MOVQ 32(AX), DI
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+	ADCQ DI, DI
+
+	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
+
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+	ADCQ DI, DI
+
+	// reduce element(DX,CX,BX,SI,DI) using temp registers (R13,R14,R15,s0-8(SP),s1-16(SP))
+	REDUCE(DX,CX,BX,SI,DI,R13,R14,R15,s0-8(SP),s1-16(SP))
+
+	MOVQ DX, R13
+	MOVQ CX, R14
+	MOVQ BX, R15
+	MOVQ SI, s0-8(SP)
+	MOVQ DI, s1-16(SP)
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+	ADCQ DI, DI
+
+	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
+
+	ADDQ R13, DX
+	ADCQ R14, CX
+	ADCQ R15, BX
+	ADCQ s0-8(SP), SI
+	ADCQ s1-16(SP), DI
+
+	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
+
+	ADDQ 0(AX), DX
+	ADCQ 8(AX), CX
+	ADCQ 16(AX), BX
+	ADCQ 24(AX), SI
+	ADCQ 32(AX), DI
+
+	// reduce element(DX,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12)
+
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	MOVQ DI, 32(AX)
+	RET
+
+// Butterfly(a, b *Element) sets a = a + b; b = a - b
+TEXT ·Butterfly(SB), $24-16
+	MOVQ    a+0(FP), AX
+	MOVQ    0(AX), CX
+	MOVQ    8(AX), BX
+	MOVQ    16(AX), SI
+	MOVQ    24(AX), DI
+	MOVQ    32(AX), R8
+	MOVQ    CX, R9
+	MOVQ    BX, R10
+	MOVQ    SI, R11
+	MOVQ    DI, R12
+	MOVQ    R8, R13
+	XORQ    AX, AX
+	MOVQ    b+8(FP), DX
+	ADDQ    0(DX), CX
+	ADCQ    8(DX), BX
+	ADCQ    16(DX), SI
+	ADCQ    24(DX), DI
+	ADCQ    32(DX), R8
+	SUBQ    0(DX), R9
+	SBBQ    8(DX), R10
+	SBBQ    16(DX), R11
+	SBBQ    24(DX), R12
+	SBBQ    32(DX), R13
+	MOVQ    CX, R14
+	MOVQ    BX, R15
+	MOVQ    SI, s0-8(SP)
+	MOVQ    DI, s1-16(SP)
+	MOVQ    R8, s2-24(SP)
+	MOVQ    $const_q0, CX
+	MOVQ    $const_q1, BX
+	MOVQ    $const_q2, SI
+	MOVQ    $const_q3, DI
+	MOVQ    $const_q4, R8
+	CMOVQCC AX, CX
+	CMOVQCC AX, BX
+	CMOVQCC AX, SI
+	CMOVQCC AX, DI
+	CMOVQCC AX, R8
+	ADDQ    CX, R9
+	ADCQ    BX, R10
+	ADCQ    SI, R11
+	ADCQ    DI, R12
+	ADCQ    R8, R13
+	MOVQ    R14, CX
+	MOVQ    R15, BX
+	MOVQ    s0-8(SP), SI
+	MOVQ    s1-16(SP), DI
+	MOVQ    s2-24(SP), R8
+	MOVQ    R9, 0(DX)
+	MOVQ    R10, 8(DX)
+	MOVQ    R11, 16(DX)
+	MOVQ    R12, 24(DX)
+	MOVQ    R13, 32(DX)
+
+	// reduce element(CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13)
+	REDUCE(CX,BX,SI,DI,R8,R9,R10,R11,R12,R13)
+
+	MOVQ a+0(FP), AX
+	MOVQ CX, 0(AX)
+	MOVQ BX, 8(AX)
+	MOVQ SI, 16(AX)
+	MOVQ DI, 24(AX)
+	MOVQ R8, 32(AX)
+	RET
+
+// mul(res, x, y *Element)
+TEXT ·mul(SB), $24-24
+
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+	// See github.com/gnark-crypto/field/generator for more comments.
+
+	NO_LOCAL_POINTERS
+	CMPB ·supportAdx(SB), $1
+	JNE  noAdx_1
+	MOVQ x+8(FP), DI
+
+	// x[0] -> R9
+	// x[1] -> R10
+	// x[2] -> R11
+	MOVQ 0(DI), R9
+	MOVQ 8(DI), R10
+	MOVQ 16(DI), R11
+	MOVQ y+16(FP), R12
+
+	// A -> BP
+	// t[0] -> R14
+	// t[1] -> R13
+	// t[2] -> CX
+	// t[3] -> BX
+	// t[4] -> SI
+#define MACC(in0, in1, in2) \
+	ADCXQ in0, in1     \
+	MULXQ in2, AX, in0 \
+	ADOXQ AX, in1      \
+
+#define DIV_SHIFT() \
+	MOVQ  $const_qInvNeg, DX        \
+	IMULQ R14, DX                   \
+	XORQ  AX, AX                    \
+	MULXQ ·qElement+0(SB), AX, R8   \
+	ADCXQ R14, AX                   \
+	MOVQ  R8, R14                   \
+	MACC(R13, R14, ·qElement+8(SB)) \
+	MACC(CX, R13, ·qElement+16(SB)) \
+	MACC(BX, CX, ·qElement+24(SB))  \
+	MACC(SI, BX, ·qElement+32(SB))  \
+	MOVQ  $0, AX                    \
+	ADCXQ AX, SI                    \
+	ADOXQ BP, SI                    \
+
+#define MUL_WORD_0() \
+	XORQ  AX, AX         \
+	MULXQ R9, R14, R13   \
+	MULXQ R10, AX, CX    \
+	ADOXQ AX, R13        \
+	MULXQ R11, AX, BX    \
+	ADOXQ AX, CX         \
+	MULXQ 24(DI), AX, SI \
+	ADOXQ AX, BX         \
+	MULXQ 32(DI), AX, BP \
+	ADOXQ AX, SI         \
+	MOVQ  $0, AX         \
+	ADOXQ AX, BP         \
+	DIV_SHIFT()          \
+
+#define MUL_WORD_N() \
+	XORQ  AX, AX         \
+	MULXQ R9, AX, BP     \
+	ADOXQ AX, R14        \
+	MACC(BP, R13, R10)   \
+	MACC(BP, CX, R11)    \
+	MACC(BP, BX, 24(DI)) \
+	MACC(BP, SI, 32(DI)) \
+	MOVQ  $0, AX         \
+	ADCXQ AX, BP         \
+	ADOXQ AX, BP         \
+	DIV_SHIFT()          \
+
+	// mul body
+	MOVQ 0(R12), DX
+	MUL_WORD_0()
+	MOVQ 8(R12), DX
+	MUL_WORD_N()
+	MOVQ 16(R12), DX
+	MUL_WORD_N()
+	MOVQ 24(R12), DX
+	MUL_WORD_N()
+	MOVQ 32(R12), DX
+	MUL_WORD_N()
+
+	// reduce element(R14,R13,CX,BX,SI) using temp registers (R8,DI,R12,R9,R10)
+	REDUCE(R14,R13,CX,BX,SI,R8,DI,R12,R9,R10)
+
+	MOVQ res+0(FP), AX
+	MOVQ R14, 0(AX)
+	MOVQ R13, 8(AX)
+	MOVQ CX, 16(AX)
+	MOVQ BX, 24(AX)
+	MOVQ SI, 32(AX)
+	RET
+
+noAdx_1:
+	MOVQ res+0(FP), AX
+	MOVQ AX, (SP)
+	MOVQ x+8(FP), AX
+	MOVQ AX, 8(SP)
+	MOVQ y+16(FP), AX
+	MOVQ AX, 16(SP)
+	CALL ·_mulGeneric(SB)
+	RET
+
+TEXT ·fromMont(SB), $8-8
+	NO_LOCAL_POINTERS
+
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+	// when y = 1 we have:
+	// for i=0 to N-1
+	// 		t[i] = x[i]
+	// for i=0 to N-1
+	// 		m := t[0]*q'[0] mod W
+	// 		C,_ := t[0] + m*q[0]
+	// 		for j=1 to N-1
+	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
+	// 		t[N-1] = C
+	CMPB ·supportAdx(SB), $1
+	JNE  noAdx_2
+	MOVQ res+0(FP), DX
+	MOVQ 0(DX), R14
+	MOVQ 8(DX), R13
+	MOVQ 16(DX), CX
+	MOVQ 24(DX), BX
+	MOVQ 32(DX), SI
+	XORQ DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R13, R14
+	MULXQ ·qElement+8(SB), AX, R13
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R13
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R13
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+	MOVQ  $0, AX
+	ADCXQ AX, SI
+	ADOXQ AX, SI
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R13, R14
+	MULXQ ·qElement+8(SB), AX, R13
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R13
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R13
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+	MOVQ  $0, AX
+	ADCXQ AX, SI
+	ADOXQ AX, SI
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R13, R14
+	MULXQ ·qElement+8(SB), AX, R13
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R13
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R13
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+	MOVQ  $0, AX
+	ADCXQ AX, SI
+	ADOXQ AX, SI
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R13, R14
+	MULXQ ·qElement+8(SB), AX, R13
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R13
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R13
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+	MOVQ  $0, AX
+	ADCXQ AX, SI
+	ADOXQ AX, SI
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R13, R14
+	MULXQ ·qElement+8(SB), AX, R13
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R13
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R13
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+	MOVQ  $0, AX
+	ADCXQ AX, SI
+	ADOXQ AX, SI
+
+	// reduce element(R14,R13,CX,BX,SI) using temp registers (DI,R8,R9,R10,R11)
+	REDUCE(R14,R13,CX,BX,SI,DI,R8,R9,R10,R11)
+
+	MOVQ res+0(FP), AX
+	MOVQ R14, 0(AX)
+	MOVQ R13, 8(AX)
+	MOVQ CX, 16(AX)
+	MOVQ BX, 24(AX)
+	MOVQ SI, 32(AX)
+	RET
+
+noAdx_2:
+	MOVQ res+0(FP), AX
+	MOVQ AX, (SP)
+	CALL ·_fromMontGeneric(SB)
+	RET
diff --git a/field/asm/element_6w_amd64.s b/field/asm/element_6w_amd64.s
new file mode 100644
index 0000000000..b8172b2870
--- /dev/null
+++ b/field/asm/element_6w_amd64.s
@@ -0,0 +1,670 @@
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+#include "textflag.h"
+#include "funcdata.h"
+#include "go_asm.h"
+
+#define REDUCE(ra0, ra1, ra2, ra3, ra4, ra5, rb0, rb1, rb2, rb3, rb4, rb5) \
+	MOVQ    ra0, rb0;              \
+	SUBQ    ·qElement(SB), ra0;    \
+	MOVQ    ra1, rb1;              \
+	SBBQ    ·qElement+8(SB), ra1;  \
+	MOVQ    ra2, rb2;              \
+	SBBQ    ·qElement+16(SB), ra2; \
+	MOVQ    ra3, rb3;              \
+	SBBQ    ·qElement+24(SB), ra3; \
+	MOVQ    ra4, rb4;              \
+	SBBQ    ·qElement+32(SB), ra4; \
+	MOVQ    ra5, rb5;              \
+	SBBQ    ·qElement+40(SB), ra5; \
+	CMOVQCS rb0, ra0;              \
+	CMOVQCS rb1, ra1;              \
+	CMOVQCS rb2, ra2;              \
+	CMOVQCS rb3, ra3;              \
+	CMOVQCS rb4, ra4;              \
+	CMOVQCS rb5, ra5;              \
+
+TEXT ·reduce(SB), NOSPLIT, $0-8
+	MOVQ res+0(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	MOVQ 32(AX), DI
+	MOVQ 40(AX), R8
+
+	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
+
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	MOVQ DI, 32(AX)
+	MOVQ R8, 40(AX)
+	RET
+
+// MulBy3(x *Element)
+TEXT ·MulBy3(SB), NOSPLIT, $0-8
+	MOVQ x+0(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	MOVQ 32(AX), DI
+	MOVQ 40(AX), R8
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+	ADCQ DI, DI
+	ADCQ R8, R8
+
+	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
+
+	ADDQ 0(AX), DX
+	ADCQ 8(AX), CX
+	ADCQ 16(AX), BX
+	ADCQ 24(AX), SI
+	ADCQ 32(AX), DI
+	ADCQ 40(AX), R8
+
+	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R15,R9,R10,R11,R12,R13)
+	REDUCE(DX,CX,BX,SI,DI,R8,R15,R9,R10,R11,R12,R13)
+
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	MOVQ DI, 32(AX)
+	MOVQ R8, 40(AX)
+	RET
+
+// MulBy5(x *Element)
+TEXT ·MulBy5(SB), NOSPLIT, $0-8
+	MOVQ x+0(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	MOVQ 32(AX), DI
+	MOVQ 40(AX), R8
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+	ADCQ DI, DI
+	ADCQ R8, R8
+
+	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
+
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+	ADCQ DI, DI
+	ADCQ R8, R8
+
+	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R15,R9,R10,R11,R12,R13)
+	REDUCE(DX,CX,BX,SI,DI,R8,R15,R9,R10,R11,R12,R13)
+
+	ADDQ 0(AX), DX
+	ADCQ 8(AX), CX
+	ADCQ 16(AX), BX
+	ADCQ 24(AX), SI
+	ADCQ 32(AX), DI
+	ADCQ 40(AX), R8
+
+	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R14,R15,R9,R10,R11,R12)
+	REDUCE(DX,CX,BX,SI,DI,R8,R14,R15,R9,R10,R11,R12)
+
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	MOVQ DI, 32(AX)
+	MOVQ R8, 40(AX)
+	RET
+
+// MulBy13(x *Element)
+TEXT ·MulBy13(SB), $40-8
+	MOVQ x+0(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	MOVQ 32(AX), DI
+	MOVQ 40(AX), R8
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+	ADCQ DI, DI
+	ADCQ R8, R8
+
+	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
+
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+	ADCQ DI, DI
+	ADCQ R8, R8
+
+	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP))
+	REDUCE(DX,CX,BX,SI,DI,R8,R15,s0-8(SP),s1-16(SP),s2-24(SP),s3-32(SP),s4-40(SP))
+
+	MOVQ DX, R15
+	MOVQ CX, s0-8(SP)
+	MOVQ BX, s1-16(SP)
+	MOVQ SI, s2-24(SP)
+	MOVQ DI, s3-32(SP)
+	MOVQ R8, s4-40(SP)
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+	ADCQ DI, DI
+	ADCQ R8, R8
+
+	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
+
+	ADDQ R15, DX
+	ADCQ s0-8(SP), CX
+	ADCQ s1-16(SP), BX
+	ADCQ s2-24(SP), SI
+	ADCQ s3-32(SP), DI
+	ADCQ s4-40(SP), R8
+
+	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
+
+	ADDQ 0(AX), DX
+	ADCQ 8(AX), CX
+	ADCQ 16(AX), BX
+	ADCQ 24(AX), SI
+	ADCQ 32(AX), DI
+	ADCQ 40(AX), R8
+
+	// reduce element(DX,CX,BX,SI,DI,R8) using temp registers (R9,R10,R11,R12,R13,R14)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14)
+
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	MOVQ DI, 32(AX)
+	MOVQ R8, 40(AX)
+	RET
+
+// Butterfly(a, b *Element) sets a = a + b; b = a - b
+TEXT ·Butterfly(SB), $48-16
+	MOVQ    a+0(FP), AX
+	MOVQ    0(AX), CX
+	MOVQ    8(AX), BX
+	MOVQ    16(AX), SI
+	MOVQ    24(AX), DI
+	MOVQ    32(AX), R8
+	MOVQ    40(AX), R9
+	MOVQ    CX, R10
+	MOVQ    BX, R11
+	MOVQ    SI, R12
+	MOVQ    DI, R13
+	MOVQ    R8, R14
+	MOVQ    R9, R15
+	XORQ    AX, AX
+	MOVQ    b+8(FP), DX
+	ADDQ    0(DX), CX
+	ADCQ    8(DX), BX
+	ADCQ    16(DX), SI
+	ADCQ    24(DX), DI
+	ADCQ    32(DX), R8
+	ADCQ    40(DX), R9
+	SUBQ    0(DX), R10
+	SBBQ    8(DX), R11
+	SBBQ    16(DX), R12
+	SBBQ    24(DX), R13
+	SBBQ    32(DX), R14
+	SBBQ    40(DX), R15
+	MOVQ    CX, s0-8(SP)
+	MOVQ    BX, s1-16(SP)
+	MOVQ    SI, s2-24(SP)
+	MOVQ    DI, s3-32(SP)
+	MOVQ    R8, s4-40(SP)
+	MOVQ    R9, s5-48(SP)
+	MOVQ    $const_q0, CX
+	MOVQ    $const_q1, BX
+	MOVQ    $const_q2, SI
+	MOVQ    $const_q3, DI
+	MOVQ    $const_q4, R8
+	MOVQ    $const_q5, R9
+	CMOVQCC AX, CX
+	CMOVQCC AX, BX
+	CMOVQCC AX, SI
+	CMOVQCC AX, DI
+	CMOVQCC AX, R8
+	CMOVQCC AX, R9
+	ADDQ    CX, R10
+	ADCQ    BX, R11
+	ADCQ    SI, R12
+	ADCQ    DI, R13
+	ADCQ    R8, R14
+	ADCQ    R9, R15
+	MOVQ    s0-8(SP), CX
+	MOVQ    s1-16(SP), BX
+	MOVQ    s2-24(SP), SI
+	MOVQ    s3-32(SP), DI
+	MOVQ    s4-40(SP), R8
+	MOVQ    s5-48(SP), R9
+	MOVQ    R10, 0(DX)
+	MOVQ    R11, 8(DX)
+	MOVQ    R12, 16(DX)
+	MOVQ    R13, 24(DX)
+	MOVQ    R14, 32(DX)
+	MOVQ    R15, 40(DX)
+
+	// reduce element(CX,BX,SI,DI,R8,R9) using temp registers (R10,R11,R12,R13,R14,R15)
+	REDUCE(CX,BX,SI,DI,R8,R9,R10,R11,R12,R13,R14,R15)
+
+	MOVQ a+0(FP), AX
+	MOVQ CX, 0(AX)
+	MOVQ BX, 8(AX)
+	MOVQ SI, 16(AX)
+	MOVQ DI, 24(AX)
+	MOVQ R8, 32(AX)
+	MOVQ R9, 40(AX)
+	RET
+
+// mul(res, x, y *Element)
+TEXT ·mul(SB), $24-24
+
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+	// See github.com/gnark-crypto/field/generator for more comments.
+
+	NO_LOCAL_POINTERS
+	CMPB ·supportAdx(SB), $1
+	JNE  noAdx_1
+	MOVQ x+8(FP), R8
+
+	// x[0] -> R10
+	// x[1] -> R11
+	// x[2] -> R12
+	MOVQ 0(R8), R10
+	MOVQ 8(R8), R11
+	MOVQ 16(R8), R12
+	MOVQ y+16(FP), R13
+
+	// A -> BP
+	// t[0] -> R14
+	// t[1] -> R15
+	// t[2] -> CX
+	// t[3] -> BX
+	// t[4] -> SI
+	// t[5] -> DI
+#define MACC(in0, in1, in2) \
+	ADCXQ in0, in1     \
+	MULXQ in2, AX, in0 \
+	ADOXQ AX, in1      \
+
+#define DIV_SHIFT() \
+	MOVQ  $const_qInvNeg, DX        \
+	IMULQ R14, DX                   \
+	XORQ  AX, AX                    \
+	MULXQ ·qElement+0(SB), AX, R9   \
+	ADCXQ R14, AX                   \
+	MOVQ  R9, R14                   \
+	MACC(R15, R14, ·qElement+8(SB)) \
+	MACC(CX, R15, ·qElement+16(SB)) \
+	MACC(BX, CX, ·qElement+24(SB))  \
+	MACC(SI, BX, ·qElement+32(SB))  \
+	MACC(DI, SI, ·qElement+40(SB))  \
+	MOVQ  $0, AX                    \
+	ADCXQ AX, DI                    \
+	ADOXQ BP, DI                    \
+
+#define MUL_WORD_0() \
+	XORQ  AX, AX         \
+	MULXQ R10, R14, R15  \
+	MULXQ R11, AX, CX    \
+	ADOXQ AX, R15        \
+	MULXQ R12, AX, BX    \
+	ADOXQ AX, CX         \
+	MULXQ 24(R8), AX, SI \
+	ADOXQ AX, BX         \
+	MULXQ 32(R8), AX, DI \
+	ADOXQ AX, SI         \
+	MULXQ 40(R8), AX, BP \
+	ADOXQ AX, DI         \
+	MOVQ  $0, AX         \
+	ADOXQ AX, BP         \
+	DIV_SHIFT()          \
+
+#define MUL_WORD_N() \
+	XORQ  AX, AX         \
+	MULXQ R10, AX, BP    \
+	ADOXQ AX, R14        \
+	MACC(BP, R15, R11)   \
+	MACC(BP, CX, R12)    \
+	MACC(BP, BX, 24(R8)) \
+	MACC(BP, SI, 32(R8)) \
+	MACC(BP, DI, 40(R8)) \
+	MOVQ  $0, AX         \
+	ADCXQ AX, BP         \
+	ADOXQ AX, BP         \
+	DIV_SHIFT()          \
+
+	// mul body
+	MOVQ 0(R13), DX
+	MUL_WORD_0()
+	MOVQ 8(R13), DX
+	MUL_WORD_N()
+	MOVQ 16(R13), DX
+	MUL_WORD_N()
+	MOVQ 24(R13), DX
+	MUL_WORD_N()
+	MOVQ 32(R13), DX
+	MUL_WORD_N()
+	MOVQ 40(R13), DX
+	MUL_WORD_N()
+
+	// reduce element(R14,R15,CX,BX,SI,DI) using temp registers (R9,R8,R13,R10,R11,R12)
+	REDUCE(R14,R15,CX,BX,SI,DI,R9,R8,R13,R10,R11,R12)
+
+	MOVQ res+0(FP), AX
+	MOVQ R14, 0(AX)
+	MOVQ R15, 8(AX)
+	MOVQ CX, 16(AX)
+	MOVQ BX, 24(AX)
+	MOVQ SI, 32(AX)
+	MOVQ DI, 40(AX)
+	RET
+
+noAdx_1:
+	MOVQ res+0(FP), AX
+	MOVQ AX, (SP)
+	MOVQ x+8(FP), AX
+	MOVQ AX, 8(SP)
+	MOVQ y+16(FP), AX
+	MOVQ AX, 16(SP)
+	CALL ·_mulGeneric(SB)
+	RET
+
+TEXT ·fromMont(SB), $8-8
+	NO_LOCAL_POINTERS
+
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+	// when y = 1 we have:
+	// for i=0 to N-1
+	// 		t[i] = x[i]
+	// for i=0 to N-1
+	// 		m := t[0]*q'[0] mod W
+	// 		C,_ := t[0] + m*q[0]
+	// 		for j=1 to N-1
+	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
+	// 		t[N-1] = C
+	CMPB ·supportAdx(SB), $1
+	JNE  noAdx_2
+	MOVQ res+0(FP), DX
+	MOVQ 0(DX), R14
+	MOVQ 8(DX), R15
+	MOVQ 16(DX), CX
+	MOVQ 24(DX), BX
+	MOVQ 32(DX), SI
+	MOVQ 40(DX), DI
+	XORQ DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+	MOVQ  $0, AX
+	ADCXQ AX, DI
+	ADOXQ AX, DI
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+	MOVQ  $0, AX
+	ADCXQ AX, DI
+	ADOXQ AX, DI
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+	MOVQ  $0, AX
+	ADCXQ AX, DI
+	ADOXQ AX, DI
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+	MOVQ  $0, AX
+	ADCXQ AX, DI
+	ADOXQ AX, DI
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+	MOVQ  $0, AX
+	ADCXQ AX, DI
+	ADOXQ AX, DI
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  $const_qInvNeg, DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ ·qElement+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ ·qElement+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ ·qElement+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ ·qElement+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// (C,t[3]) := t[4] + m*q[4] + C
+	ADCXQ SI, BX
+	MULXQ ·qElement+32(SB), AX, SI
+	ADOXQ AX, BX
+
+	// (C,t[4]) := t[5] + m*q[5] + C
+	ADCXQ DI, SI
+	MULXQ ·qElement+40(SB), AX, DI
+	ADOXQ AX, SI
+	MOVQ  $0, AX
+	ADCXQ AX, DI
+	ADOXQ AX, DI
+
+	// reduce element(R14,R15,CX,BX,SI,DI) using temp registers (R8,R9,R10,R11,R12,R13)
+	REDUCE(R14,R15,CX,BX,SI,DI,R8,R9,R10,R11,R12,R13)
+
+	MOVQ res+0(FP), AX
+	MOVQ R14, 0(AX)
+	MOVQ R15, 8(AX)
+	MOVQ CX, 16(AX)
+	MOVQ BX, 24(AX)
+	MOVQ SI, 32(AX)
+	MOVQ DI, 40(AX)
+	RET
+
+noAdx_2:
+	MOVQ res+0(FP), AX
+	MOVQ AX, (SP)
+	CALL ·_fromMontGeneric(SB)
+	RET
diff --git a/field/generator/asm/amd64/asm_macros.go b/field/generator/asm/amd64/asm_macros.go
index 45d324c948..b2c6341cf5 100644
--- a/field/generator/asm/amd64/asm_macros.go
+++ b/field/generator/asm/amd64/asm_macros.go
@@ -61,37 +61,25 @@ func (f *FFAmd64) ReduceElement(t, scratch []amd64.Register) {
 	f.WriteLn("")
 }
 
-// TODO @gbotrel: figure out if interleaving MOVQ and SUBQ or CMOVQ and MOVQ instructions makes sense
-const tmplDefines = `
-
-// modulus q
-{{- range $i, $w := .Q}}
-DATA q<>+{{mul $i 8}}(SB)/8, {{imm $w}}
-{{- end}}
-GLOBL q<>(SB), (RODATA+NOPTR), ${{mul 8 $.NbWords}}
-
-// qInv0 q'[0]
-DATA qInv0<>(SB)/8, {{$qinv0 := index .QInverse 0}}{{imm $qinv0}}
-GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
+const tmplReduceDefine = `
 
 #define REDUCE(	{{- range $i := .NbWordsIndexesFull}}ra{{$i}},{{- end}}
 				{{- range $i := .NbWordsIndexesFull}}rb{{$i}}{{- if ne $.NbWordsLastIndex $i}},{{- end}}{{- end}}) \
 	MOVQ ra0, rb0;  \
-	SUBQ    q<>(SB), ra0; \
+	SUBQ    ·qElement(SB), ra0; \
 	{{- range $i := .NbWordsIndexesNoZero}}
 	MOVQ ra{{$i}}, rb{{$i}};  \
-	SBBQ  q<>+{{mul $i 8}}(SB), ra{{$i}}; \
+	SBBQ  ·qElement+{{mul $i 8}}(SB), ra{{$i}}; \
 	{{- end}}
 	{{- range $i := .NbWordsIndexesFull}}
 	CMOVQCS rb{{$i}}, ra{{$i}};  \
 	{{- end}}
-
 `
 
-func (f *FFAmd64) GenerateDefines() {
+func (f *FFAmd64) GenerateReduceDefine() {
 	tmpl := template.Must(template.New("").
 		Funcs(helpers()).
-		Parse(tmplDefines))
+		Parse(tmplReduceDefine))
 
 	// execute template
 	var buf bytes.Buffer
diff --git a/field/generator/asm/amd64/build.go b/field/generator/asm/amd64/build.go
index b760ad3e3f..ccf41c4e83 100644
--- a/field/generator/asm/amd64/build.go
+++ b/field/generator/asm/amd64/build.go
@@ -17,28 +17,58 @@ package amd64
 
 import (
 	"fmt"
+	"hash/fnv"
 	"io"
+	"os"
+	"path/filepath"
 	"strings"
 
-	"github.com/consensys/bavard"
-
 	"github.com/consensys/bavard/amd64"
 	"github.com/consensys/gnark-crypto/field/generator/config"
 )
 
 const SmallModulus = 6
+const (
+	ElementASMFileName = "element_%dw_amd64.s"
+)
 
-func NewFFAmd64(w io.Writer, F *config.FieldConfig) *FFAmd64 {
-	return &FFAmd64{F, amd64.NewAmd64(w), 0, 0}
+func NewFFAmd64(w io.Writer, nbWords int) *FFAmd64 {
+	F := &FFAmd64{
+		amd64.NewAmd64(w),
+		0,
+		0,
+		nbWords,
+		nbWords - 1,
+		make([]int, nbWords),
+		make([]int, nbWords-1),
+		make(map[string]defineFn),
+	}
+
+	// indexes (template helpers)
+	for i := 0; i < F.NbWords; i++ {
+		F.NbWordsIndexesFull[i] = i
+		if i > 0 {
+			F.NbWordsIndexesNoZero[i-1] = i
+		}
+	}
+
+	return F
 }
 
 type FFAmd64 struct {
-	*config.FieldConfig
+	// *config.FieldConfig
 	*amd64.Amd64
-	nbElementsOnStack int
-	maxOnStack        int
+	nbElementsOnStack    int
+	maxOnStack           int
+	NbWords              int
+	NbWordsLastIndex     int
+	NbWordsIndexesFull   []int
+	NbWordsIndexesNoZero []int
+	mDefines             map[string]defineFn
 }
 
+type defineFn func(args ...amd64.Register)
+
 func (f *FFAmd64) StackSize(maxNbRegistersNeeded, nbRegistersReserved, minStackSize int) int {
 	got := amd64.NbRegisters - nbRegistersReserved
 	r := got - maxNbRegistersNeeded
@@ -49,6 +79,64 @@ func (f *FFAmd64) StackSize(maxNbRegistersNeeded, nbRegistersReserved, minStackS
 	return max(r, minStackSize)
 }
 
+func (f *FFAmd64) DefineFn(name string) (fn defineFn, err error) {
+	fn, ok := f.mDefines[name]
+	if !ok {
+		return nil, fmt.Errorf("function %s not defined", name)
+	}
+	return fn, nil
+}
+
+func (f *FFAmd64) Define(name string, nbInputs int, fn defineFn) defineFn {
+
+	inputs := make([]string, nbInputs)
+	for i := 0; i < nbInputs; i++ {
+		inputs[i] = fmt.Sprintf("in%d", i)
+	}
+	name = strings.ToUpper(name)
+
+	for _, ok := f.mDefines[name]; ok; {
+		// name already exist, for code generation purpose we add a suffix
+		// should happen only with e2 deprecated functions
+		fmt.Println("WARNING: function name already defined, adding suffix")
+		i := 0
+		for {
+			newName := fmt.Sprintf("%s_%d", name, i)
+			if _, ok := f.mDefines[newName]; !ok {
+				name = newName
+				goto startDefine
+			}
+			i++
+		}
+	}
+startDefine:
+
+	f.StartDefine()
+	f.WriteLn("#define " + name + "(" + strings.Join(inputs, ", ") + ")")
+	inputsRegisters := make([]amd64.Register, nbInputs)
+	for i := 0; i < nbInputs; i++ {
+		inputsRegisters[i] = amd64.Register(inputs[i])
+	}
+	fn(inputsRegisters...)
+	f.EndDefine()
+	f.WriteLn("")
+
+	toReturn := func(args ...amd64.Register) {
+		if len(args) != nbInputs {
+			panic("invalid number of arguments")
+		}
+		inputsStr := make([]string, len(args))
+		for i := 0; i < len(args); i++ {
+			inputsStr[i] = string(args[i])
+		}
+		f.WriteLn(name + "(" + strings.Join(inputsStr, ", ") + ")")
+	}
+
+	f.mDefines[name] = toReturn
+
+	return toReturn
+}
+
 func max(a, b int) int {
 	if a > b {
 		return a
@@ -128,24 +216,68 @@ func (f *FFAmd64) PopN(registers *amd64.Registers, forceStack ...bool) []amd64.R
 }
 
 func (f *FFAmd64) qAt(index int) string {
-	return fmt.Sprintf("q<>+%d(SB)", index*8)
+	return fmt.Sprintf("·qElement+%d(SB)", index*8)
+}
+
+func (f *FFAmd64) qAt_bcst(index int) string {
+	return fmt.Sprintf("·qElement+%d(SB)", index*4)
 }
 
 func (f *FFAmd64) qInv0() string {
-	return "qInv0<>(SB)"
+	return "$const_qInvNeg"
+}
+
+func (f *FFAmd64) mu() string {
+	return "$const_mu"
+}
+
+func GenerateFieldWrapper(w io.Writer, F *config.FieldConfig, asmDirBuildPath, asmDirIncludePath string) error {
+	// for each field we generate the defines for the modulus and the montgomery constant
+	f := NewFFAmd64(w, F.NbWords)
+
+	// we add the defines first, then the common asm, then the global variable section
+	// to enable correct compilations with #include in order.
+	f.WriteLn("")
+
+	hashAndInclude := func(fileName string) error {
+		// we hash the file content and include the hash in comment of the generated file
+		// to force the Go compiler to recompile the file if the content has changed
+		fData, err := os.ReadFile(filepath.Join(asmDirBuildPath, fileName))
+		if err != nil {
+			return err
+		}
+		// hash the file using FNV
+		hasher := fnv.New64()
+		hasher.Write(fData)
+		hash := hasher.Sum64()
+
+		f.WriteLn("// Code generated by gnark-crypto/generator. DO NOT EDIT.")
+		f.WriteLn(fmt.Sprintf("// We include the hash to force the Go compiler to recompile: %d", hash))
+		f.WriteLn(fmt.Sprintf("#include \"%s\"\n", filepath.Join(asmDirIncludePath, fileName)))
+
+		return nil
+	}
+
+	toInclude := fmt.Sprintf(ElementASMFileName, F.NbWords)
+	if err := hashAndInclude(toInclude); err != nil {
+		return err
+	}
+
+	return nil
 }
 
-// Generate generates assembly code for the base field provided to goff
+// GenerateCommonASM generates assembly code for the base field provided to goff
 // see internal/templates/ops*
-func Generate(w io.Writer, F *config.FieldConfig) error {
-	f := NewFFAmd64(w, F)
-	f.WriteLn(bavard.Apache2Header("ConsenSys Software Inc.", 2020))
+func GenerateCommonASM(w io.Writer, nbWords int, hasVector bool) error {
+	f := NewFFAmd64(w, nbWords)
+	f.Comment("Code generated by gnark-crypto/generator. DO NOT EDIT.")
 
 	f.WriteLn("#include \"textflag.h\"")
 	f.WriteLn("#include \"funcdata.h\"")
+	f.WriteLn("#include \"go_asm.h\"")
 	f.WriteLn("")
 
-	f.GenerateDefines()
+	f.GenerateReduceDefine()
 
 	// reduce
 	f.generateReduce()
@@ -158,48 +290,24 @@ func Generate(w io.Writer, F *config.FieldConfig) error {
 	// fft butterflies
 	f.generateButterfly()
 
-	// generate vector operations for "small" modulus
-	if f.NbWords == 4 {
-		f.generateAddVec()
-		f.generateSubVec()
-		f.generateScalarMulVec()
-	}
-
-	return nil
-}
-
-func GenerateMul(w io.Writer, F *config.FieldConfig) error {
-	f := NewFFAmd64(w, F)
-	f.WriteLn(bavard.Apache2Header("ConsenSys Software Inc.", 2020))
-
-	f.WriteLn("#include \"textflag.h\"")
-	f.WriteLn("#include \"funcdata.h\"")
-	f.WriteLn("")
-	f.GenerateDefines()
-
 	// mul
 	f.generateMul(false)
 
 	// from mont
 	f.generateFromMont(false)
 
-	return nil
-}
-
-func GenerateMulADX(w io.Writer, F *config.FieldConfig) error {
-	f := NewFFAmd64(w, F)
-	f.WriteLn(bavard.Apache2Header("ConsenSys Software Inc.", 2020))
+	if hasVector {
+		f.WriteLn("")
+		f.Comment("Vector operations are partially derived from Dag Arne Osvik's work in github.com/a16z/vectorized-fields")
+		f.WriteLn("")
 
-	f.WriteLn("#include \"textflag.h\"")
-	f.WriteLn("#include \"funcdata.h\"")
-	f.WriteLn("")
-	f.GenerateDefines()
-
-	// mul
-	f.generateMul(true)
-
-	// from mont
-	f.generateFromMont(true)
+		f.generateAddVec()
+		f.generateSubVec()
+		f.generateSumVec()
+		f.generateInnerProduct()
+		f.generateMulVec("scalarMulVec")
+		f.generateMulVec("mulVec")
+	}
 
 	return nil
 }
diff --git a/field/generator/asm/amd64/element_butterfly.go b/field/generator/asm/amd64/element_butterfly.go
index 2d996754ae..8792b6dce3 100644
--- a/field/generator/asm/amd64/element_butterfly.go
+++ b/field/generator/asm/amd64/element_butterfly.go
@@ -14,6 +14,8 @@
 
 package amd64
 
+import "fmt"
+
 // Butterfly sets
 // a = a + b
 // b = a - b
@@ -56,7 +58,9 @@ func (f *FFAmd64) generateButterfly() {
 		if f.NbWords >= 5 {
 			// q is on the stack, can't use for CMOVQCC
 			f.Mov(t0, q) // save t0
-			f.Mov(f.Q, t0)
+			for i := 0; i < f.NbWords; i++ {
+				f.MOVQ(fmt.Sprintf("$const_q%d", i), t0[i])
+			}
 			for i := 0; i < f.NbWords; i++ {
 				f.CMOVQCC(a, t0[i])
 			}
@@ -64,7 +68,9 @@ func (f *FFAmd64) generateButterfly() {
 			f.Add(t0, t1)
 			f.Mov(q, t0) // restore t0
 		} else {
-			f.Mov(f.Q, q)
+			for i := 0; i < f.NbWords; i++ {
+				f.MOVQ(fmt.Sprintf("$const_q%d", i), q[i])
+			}
 			for i := 0; i < f.NbWords; i++ {
 				f.CMOVQCC(a, q[i])
 			}
@@ -110,10 +116,11 @@ func (f *FFAmd64) generateButterfly() {
 		noReduce := f.NewLabel("noReduce")
 		f.JCC(noReduce)
 		q := r
-		f.MOVQ(f.Q[0], q)
+		f.MOVQ("$const_q0", q)
+
 		f.ADDQ(q, t0[0])
 		for i := 1; i < f.NbWords; i++ {
-			f.MOVQ(f.Q[i], q)
+			f.MOVQ(fmt.Sprintf("$const_q%d", i), q)
 			f.ADCQ(q, t0[i])
 		}
 		f.LABEL(noReduce)
diff --git a/field/generator/asm/amd64/element_frommont.go b/field/generator/asm/amd64/element_frommont.go
index 79b717dccc..de9d0e3c46 100644
--- a/field/generator/asm/amd64/element_frommont.go
+++ b/field/generator/asm/amd64/element_frommont.go
@@ -42,8 +42,8 @@ func (f *FFAmd64) generateFromMont(forceADX bool) {
 		f.WriteLn("NO_LOCAL_POINTERS")
 	}
 	f.WriteLn(`
-	// the algorithm is described here
-	// https://hackmd.io/@gnark/modular_multiplication
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS" 
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 	// when y = 1 we have: 
 	// for i=0 to N-1
 	// 		t[i] = x[i]
diff --git a/field/generator/asm/amd64/element_mul.go b/field/generator/asm/amd64/element_mul.go
index df63f1ad4b..55f816c267 100644
--- a/field/generator/asm/amd64/element_mul.go
+++ b/field/generator/asm/amd64/element_mul.go
@@ -20,6 +20,18 @@ import (
 	"github.com/consensys/bavard/amd64"
 )
 
+// Registers used when f.NbWords == 4
+// for the multiplication.
+// They are re-referenced in defines in the vectorized operations.
+var mul4Registers = []amd64.Register{
+	// t
+	amd64.R14, amd64.R13, amd64.CX, amd64.BX,
+	// x
+	amd64.DI, amd64.R8, amd64.R9, amd64.R10,
+	// tr
+	amd64.R12,
+}
+
 // MulADX uses AX, DX and BP
 // sets x * y into t, without modular reduction
 // x() will have more accesses than y()
@@ -40,69 +52,50 @@ func (f *FFAmd64) MulADX(registers *amd64.Registers, x, y func(int) string, t []
 	f.LabelRegisters("A", A)
 	f.LabelRegisters("t", t...)
 
-	for i := 0; i < f.NbWords; i++ {
-		f.Comment("clear the flags")
-		f.XORQ(amd64.AX, amd64.AX)
-
-		f.MOVQ(y(i), amd64.DX)
-
-		// for j=0 to N-1
-		//    (A,t[j])  := t[j] + x[j]*y[i] + A
-		if i == 0 {
-			for j := 0; j < f.NbWords; j++ {
-				f.Comment(fmt.Sprintf("(A,t[%[1]d])  := x[%[1]d]*y[%[2]d] + A", j, i))
-
-				if j == 0 && f.NbWords == 1 {
-					f.MULXQ(x(j), t[j], A)
-				} else if j == 0 {
-					f.MULXQ(x(j), t[j], t[j+1])
-				} else {
-					highBits := A
-					if j != f.NbWordsLastIndex {
-						highBits = t[j+1]
-					}
-					f.MULXQ(x(j), amd64.AX, highBits)
-					f.ADOXQ(amd64.AX, t[j])
-				}
+	if f.NbWords == 4 && hasFreeRegister {
+		// ensure the registers match the "hardcoded ones" in mul4Registers for the vecops
+		match := true
+		for i := 0; i < 4; i++ {
+			if mul4Registers[i] != t[i] {
+				match = false
+				fmt.Printf("expected %s, got t[%d] %s\n", mul4Registers[i], i, t[i])
 			}
-		} else {
-			for j := 0; j < f.NbWords; j++ {
-				f.Comment(fmt.Sprintf("(A,t[%[1]d])  := t[%[1]d] + x[%[1]d]*y[%[2]d] + A", j, i))
-
-				if j != 0 {
-					f.ADCXQ(A, t[j])
-				}
-				f.MULXQ(x(j), amd64.AX, A)
-				f.ADOXQ(amd64.AX, t[j])
+			if mul4Registers[i+4] != amd64.Register(x(i)) {
+				match = false
+				fmt.Printf("expected %s, got x[%d] %s\n", mul4Registers[i+4], i, x(i))
 			}
 		}
-
-		f.Comment("A += carries from ADCXQ and ADOXQ")
-		f.MOVQ(0, amd64.AX)
-		if i != 0 {
-			f.ADCXQ(amd64.AX, A)
+		if tr != mul4Registers[8] {
+			match = false
+			fmt.Printf("expected %s, got tr %s\n", mul4Registers[8], tr)
 		}
-		f.ADOXQ(amd64.AX, A)
+		if !match {
+			panic("registers do not match hardcoded ones")
+		}
+	}
+
+	mac := f.Define("MACC", 3, func(args ...amd64.Register) {
+		in0 := args[0]
+		in1 := args[1]
+		in2 := args[2]
+		f.ADCXQ(in0, in1)
+		f.MULXQ(in2, amd64.AX, in0)
+		f.ADOXQ(amd64.AX, in1)
+	})
 
+	divShift := f.Define("DIV_SHIFT", 0, func(_ ...amd64.Register) {
 		if !hasFreeRegister {
 			f.PUSHQ(A)
 		}
-
 		// m := t[0]*q'[0] mod W
-		f.Comment("m := t[0]*q'[0] mod W")
 		m := amd64.DX
-		// f.MOVQ(t[0], m)
-		// f.MULXQ(f.qInv0(), m, amd64.AX)
 		f.MOVQ(f.qInv0(), m)
 		f.IMULQ(t[0], m)
 
 		// clear the carry flags
-		f.Comment("clear the flags")
 		f.XORQ(amd64.AX, amd64.AX)
 
 		// C,_ := t[0] + m*q[0]
-		f.Comment("C,_ := t[0] + m*q[0]")
-
 		f.MULXQ(f.qAt(0), amd64.AX, tr)
 		f.ADCXQ(t[0], amd64.AX)
 		f.MOVQ(tr, t[0])
@@ -110,20 +103,68 @@ func (f *FFAmd64) MulADX(registers *amd64.Registers, x, y func(int) string, t []
 		if !hasFreeRegister {
 			f.POPQ(A)
 		}
+
 		// for j=1 to N-1
-		//    (C,t[j-1]) := t[j] + m*q[j] + C
+		//
+		//	(C,t[j-1]) := t[j] + m*q[j] + C
 		for j := 1; j < f.NbWords; j++ {
-			f.Comment(fmt.Sprintf("(C,t[%[1]d]) := t[%[2]d] + m*q[%[2]d] + C", j-1, j))
-			f.ADCXQ(t[j], t[j-1])
-			f.MULXQ(f.qAt(j), amd64.AX, t[j])
-			f.ADOXQ(amd64.AX, t[j-1])
+			mac(t[j], t[j-1], amd64.Register(f.qAt(j)))
 		}
 
-		f.Comment(fmt.Sprintf("t[%d] = C + A", f.NbWordsLastIndex))
 		f.MOVQ(0, amd64.AX)
 		f.ADCXQ(amd64.AX, t[f.NbWordsLastIndex])
 		f.ADOXQ(A, t[f.NbWordsLastIndex])
 
+	})
+
+	mulWord0 := f.Define("MUL_WORD_0", 0, func(_ ...amd64.Register) {
+		f.XORQ(amd64.AX, amd64.AX)
+		// for j=0 to N-1
+		//    (A,t[j])  := t[j] + x[j]*y[i] + A
+		for j := 0; j < f.NbWords; j++ {
+			if j == 0 && f.NbWords == 1 {
+				f.MULXQ(x(j), t[j], A)
+			} else if j == 0 {
+				f.MULXQ(x(j), t[j], t[j+1])
+			} else {
+				highBits := A
+				if j != f.NbWordsLastIndex {
+					highBits = t[j+1]
+				}
+				f.MULXQ(x(j), amd64.AX, highBits)
+				f.ADOXQ(amd64.AX, t[j])
+			}
+		}
+		f.MOVQ(0, amd64.AX)
+		f.ADOXQ(amd64.AX, A)
+		divShift()
+	})
+
+	mulWordN := f.Define("MUL_WORD_N", 0, func(args ...amd64.Register) {
+		f.XORQ(amd64.AX, amd64.AX)
+		// for j=0 to N-1
+		//    (A,t[j])  := t[j] + x[j]*y[i] + A
+		f.MULXQ(x(0), amd64.AX, A)
+		f.ADOXQ(amd64.AX, t[0])
+		for j := 1; j < f.NbWords; j++ {
+			mac(A, t[j], amd64.Register(x(j)))
+		}
+		f.MOVQ(0, amd64.AX)
+		f.ADCXQ(amd64.AX, A)
+		f.ADOXQ(amd64.AX, A)
+		divShift()
+	})
+
+	f.Comment("mul body")
+
+	for i := 0; i < f.NbWords; i++ {
+		f.MOVQ(y(i), amd64.DX)
+
+		if i == 0 {
+			mulWord0()
+		} else {
+			mulWordN()
+		}
 	}
 
 	if hasFreeRegister {
@@ -152,19 +193,11 @@ func (f *FFAmd64) generateMul(forceADX bool) {
 	registers := f.FnHeader("mul", stackSize, argSize, reserved...)
 	defer f.AssertCleanStack(stackSize, minStackSize)
 
-	f.WriteLn(fmt.Sprintf(`
-	// the algorithm is described in the %s.Mul declaration (.go)
-	// however, to benefit from the ADCX and ADOX carry chains
-	// we split the inner loops in 2:
-	// for i=0 to N-1
-	// 		for j=0 to N-1
-	// 		    (A,t[j])  := t[j] + x[j]*y[i] + A
-	// 		m := t[0]*q'[0] mod W
-	// 		C,_ := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
-	// 		t[N-1] = C + A
-	`, f.ElementName))
+	f.WriteLn(`
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS" 
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+	// See github.com/gnark-crypto/field/generator for more comments.
+	`)
 	if stackSize > 0 {
 		f.WriteLn("NO_LOCAL_POINTERS")
 	}
diff --git a/field/generator/asm/amd64/element_vec.go b/field/generator/asm/amd64/element_vec.go
index 05c2cf3f19..c67137d6cb 100644
--- a/field/generator/asm/amd64/element_vec.go
+++ b/field/generator/asm/amd64/element_vec.go
@@ -14,7 +14,12 @@
 
 package amd64
 
-import "github.com/consensys/bavard/amd64"
+import (
+	"fmt"
+	"strconv"
+
+	"github.com/consensys/bavard/amd64"
+)
 
 // addVec res = a + b
 // func addVec(res, a, b *{{.ElementName}}, n uint64)
@@ -53,13 +58,14 @@ func (f *FFAmd64) generateAddVec() {
 	f.LabelRegisters("a", a...)
 	f.Mov(addrA, a)
 	f.Add(addrB, a)
+	f.WriteLn(fmt.Sprintf("PREFETCHT0 2048(%[1]s)", addrA))
+	f.WriteLn(fmt.Sprintf("PREFETCHT0 2048(%[1]s)", addrB))
 
 	// reduce a
 	f.ReduceElement(a, t)
 
 	// save a into res
 	f.Mov(a, addrRes)
-
 	f.Comment("increment pointers to visit next element")
 	f.ADDQ("$32", addrA)
 	f.ADDQ("$32", addrB)
@@ -117,11 +123,15 @@ func (f *FFAmd64) generateSubVec() {
 	f.LabelRegisters("a", a...)
 	f.Mov(addrA, a)
 	f.Sub(addrB, a)
+	f.WriteLn(fmt.Sprintf("PREFETCHT0 2048(%[1]s)", addrA))
+	f.WriteLn(fmt.Sprintf("PREFETCHT0 2048(%[1]s)", addrB))
 
 	// reduce a
 	f.Comment("reduce (a-b) mod q")
 	f.LabelRegisters("q", q...)
-	f.Mov(f.Q, q)
+	for i := 0; i < f.NbWords; i++ {
+		f.MOVQ(fmt.Sprintf("$const_q%d", i), q[i])
+	}
 	for i := 0; i < f.NbWords; i++ {
 		f.CMOVQCC(zero, q[i])
 	}
@@ -149,94 +159,1341 @@ func (f *FFAmd64) generateSubVec() {
 
 }
 
-// scalarMulVec res = a * b
-// func scalarMulVec(res, a, b *{{.ElementName}}, n uint64)
-func (f *FFAmd64) generateScalarMulVec() {
-	f.Comment("scalarMulVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] * b")
+// sumVec res = sum(a[0...n])
+func (f *FFAmd64) generateSumVec() {
+	f.Comment("sumVec(res, a *Element, n uint64) res = sum(a[0...n])")
+
+	const argSize = 3 * 8
+	stackSize := f.StackSize(f.NbWords*3+2, 0, 0)
+	registers := f.FnHeader("sumVec", stackSize, argSize, amd64.DX, amd64.AX)
+	defer f.AssertCleanStack(stackSize, 0)
+
+	f.WriteLn(`
+	// Derived from https://github.com/a16z/vectorized-fields
+	// The idea is to use Z registers to accumulate the sum of elements, 8 by 8
+	// first, we handle the case where n % 8 != 0
+	// then, we loop over the elements 8 by 8 and accumulate the sum in the Z registers
+	// finally, we reduce the sum and store it in res
+	// 
+	// when we move an element of a into a Z register, we use VPMOVZXDQ
+	// let's note w0...w3 the 4 64bits words of ai: w0 = ai[0], w1 = ai[1], w2 = ai[2], w3 = ai[3]
+	// VPMOVZXDQ(ai, Z0) will result in 
+	// Z0= [hi(w3), lo(w3), hi(w2), lo(w2), hi(w1), lo(w1), hi(w0), lo(w0)]
+	// with hi(wi) the high 32 bits of wi and lo(wi) the low 32 bits of wi
+	// we can safely add 2^32+1 times Z registers constructed this way without overflow
+	// since each of this lo/hi bits are moved into a "64bits" slot
+	// N = 2^64-1 / 2^32-1 = 2^32+1
+	//
+	// we then propagate the carry using ADOXQ and ADCXQ
+	// r0 = w0l + lo(woh)
+	// r1 = carry + hi(woh) + w1l + lo(w1h)
+	// r2 = carry + hi(w1h) + w2l + lo(w2h)
+	// r3 = carry + hi(w2h) + w3l + lo(w3h)
+	// r4 = carry + hi(w3h)
+	// we then reduce the sum using a single-word Barrett reduction
+	// we pick mu = 2^288 / q; which correspond to 4.5 words max.
+	// meaning we must guarantee that r4 fits in 32bits.
+	// To do so, we reduce N to 2^32-1 (since r4 receives 2 carries max)
+	`)
+
+	// registers & labels we need
+	addrA := f.Pop(&registers)
+	n := f.Pop(&registers)
+	nMod8 := f.Pop(&registers)
+
+	loop := f.NewLabel("loop8by8")
+	done := f.NewLabel("done")
+	loopSingle := f.NewLabel("loop_single")
+	accumulate := f.NewLabel("accumulate")
+
+	// AVX512 registers
+	Z0 := amd64.Register("Z0")
+	Z1 := amd64.Register("Z1")
+	Z2 := amd64.Register("Z2")
+	Z3 := amd64.Register("Z3")
+	Z4 := amd64.Register("Z4")
+	Z5 := amd64.Register("Z5")
+	Z6 := amd64.Register("Z6")
+	Z7 := amd64.Register("Z7")
+	Z8 := amd64.Register("Z8")
+
+	X0 := amd64.Register("X0")
+
+	// load arguments
+	f.MOVQ("a+8(FP)", addrA)
+	f.MOVQ("n+16(FP)", n)
+
+	f.Comment("initialize accumulators Z0, Z1, Z2, Z3, Z4, Z5, Z6, Z7")
+	f.VXORPS(Z0, Z0, Z0)
+	f.VMOVDQA64(Z0, Z1)
+	f.VMOVDQA64(Z0, Z2)
+	f.VMOVDQA64(Z0, Z3)
+	f.VMOVDQA64(Z0, Z4)
+	f.VMOVDQA64(Z0, Z5)
+	f.VMOVDQA64(Z0, Z6)
+	f.VMOVDQA64(Z0, Z7)
+
+	// note: we don't need to handle the case n==0; handled by caller already.
+	// f.TESTQ(n, n)
+	// f.JEQ(done, "n == 0, we are done")
+
+	f.LabelRegisters("n % 8", nMod8)
+	f.LabelRegisters("n / 8", n)
+	f.MOVQ(n, nMod8)
+	f.ANDQ("$7", nMod8) // nMod8 = n % 8
+	f.SHRQ("$3", n)     // len = n / 8
+
+	f.LABEL(loopSingle)
+	f.TESTQ(nMod8, nMod8)
+	f.JEQ(loop, "n % 8 == 0, we are going to loop over 8 by 8")
+
+	f.VPMOVZXDQ("0("+addrA+")", Z8)
+	f.VPADDQ(Z8, Z0, Z0)
+	f.ADDQ("$32", addrA)
+
+	f.DECQ(nMod8, "decrement nMod8")
+	f.JMP(loopSingle)
+
+	f.Push(&registers, nMod8) // we don't need tmp0
+
+	f.LABEL(loop)
+	f.TESTQ(n, n)
+	f.JEQ(accumulate, "n == 0, we are going to accumulate")
+
+	for i := 0; i < 8; i++ {
+		r := fmt.Sprintf("Z%d", i+8)
+		f.VPMOVZXDQ(fmt.Sprintf("%d*32("+string(addrA)+")", i), r)
+	}
+
+	f.WriteLn(fmt.Sprintf("PREFETCHT0 4096(%[1]s)", addrA))
+	for i := 0; i < 8; i++ {
+		r := fmt.Sprintf("Z%d", i)
+		f.VPADDQ(fmt.Sprintf("Z%d", i+8), r, r)
+	}
+
+	f.Comment("increment pointers to visit next 8 elements")
+	f.ADDQ("$256", addrA)
+	f.DECQ(n, "decrement n")
+	f.JMP(loop)
+
+	f.Push(&registers, n, addrA)
+
+	f.LABEL(accumulate)
+
+	f.Comment("accumulate the 8 Z registers into Z0")
+	f.VPADDQ(Z7, Z6, Z6)
+	f.VPADDQ(Z6, Z5, Z5)
+	f.VPADDQ(Z5, Z4, Z4)
+	f.VPADDQ(Z4, Z3, Z3)
+	f.VPADDQ(Z3, Z2, Z2)
+	f.VPADDQ(Z2, Z1, Z1)
+	f.VPADDQ(Z1, Z0, Z0)
+
+	w0l := f.Pop(&registers)
+	w0h := f.Pop(&registers)
+	w1l := f.Pop(&registers)
+	w1h := f.Pop(&registers)
+	w2l := f.Pop(&registers)
+	w2h := f.Pop(&registers)
+	w3l := f.Pop(&registers)
+	w3h := f.Pop(&registers)
+	low0h := f.Pop(&registers)
+	low1h := f.Pop(&registers)
+	low2h := f.Pop(&registers)
+	low3h := f.Pop(&registers)
+
+	// Propagate carries
+	f.Comment("carry propagation")
+
+	f.LabelRegisters("lo(w0)", w0l)
+	f.LabelRegisters("hi(w0)", w0h)
+	f.LabelRegisters("lo(w1)", w1l)
+	f.LabelRegisters("hi(w1)", w1h)
+	f.LabelRegisters("lo(w2)", w2l)
+	f.LabelRegisters("hi(w2)", w2h)
+	f.LabelRegisters("lo(w3)", w3l)
+	f.LabelRegisters("hi(w3)", w3h)
+
+	f.VMOVQ(X0, w0l)
+	f.VALIGNQ("$1", Z0, Z0, Z0)
+	f.VMOVQ(X0, w0h)
+	f.VALIGNQ("$1", Z0, Z0, Z0)
+	f.VMOVQ(X0, w1l)
+	f.VALIGNQ("$1", Z0, Z0, Z0)
+	f.VMOVQ(X0, w1h)
+	f.VALIGNQ("$1", Z0, Z0, Z0)
+	f.VMOVQ(X0, w2l)
+	f.VALIGNQ("$1", Z0, Z0, Z0)
+	f.VMOVQ(X0, w2h)
+	f.VALIGNQ("$1", Z0, Z0, Z0)
+	f.VMOVQ(X0, w3l)
+	f.VALIGNQ("$1", Z0, Z0, Z0)
+	f.VMOVQ(X0, w3h)
+
+	f.LabelRegisters("lo(hi(wo))", low0h)
+	f.LabelRegisters("lo(hi(w1))", low1h)
+	f.LabelRegisters("lo(hi(w2))", low2h)
+	f.LabelRegisters("lo(hi(w3))", low3h)
+
+	type hilo struct {
+		hi, lo amd64.Register
+	}
+
+	splitLoHi := f.Define("SPLIT_LO_HI", 2, func(args ...amd64.Register) {
+		lo := args[0]
+		hi := args[1]
+		f.MOVQ(hi, lo)
+		f.ANDQ("$0xffffffff", lo)
+		f.SHLQ("$32", lo)
+		f.SHRQ("$32", hi)
+	})
+
+	for _, v := range []hilo{{w0h, low0h}, {w1h, low1h}, {w2h, low2h}, {w3h, low3h}} {
+		splitLoHi(v.lo, v.hi)
+	}
+
+	f.WriteLn(`
+	// r0 = w0l + lo(woh)
+	// r1 = carry + hi(woh) + w1l + lo(w1h)
+	// r2 = carry + hi(w1h) + w2l + lo(w2h)
+	// r3 = carry + hi(w2h) + w3l + lo(w3h)
+	// r4 = carry + hi(w3h)
+	`)
+	f.XORQ(amd64.AX, amd64.AX, "clear the flags")
+	f.ADOXQ(low0h, w0l)
+
+	f.ADOXQ(low1h, w1l)
+	f.ADCXQ(w0h, w1l)
+
+	f.ADOXQ(low2h, w2l)
+	f.ADCXQ(w1h, w2l)
+
+	f.ADOXQ(low3h, w3l)
+	f.ADCXQ(w2h, w3l)
+
+	f.ADOXQ(amd64.AX, w3h)
+	f.ADCXQ(amd64.AX, w3h)
+
+	r0 := w0l
+	r1 := w1l
+	r2 := w2l
+	r3 := w3l
+	r4 := w3h
+
+	r := []amd64.Register{r0, r1, r2, r3, r4}
+	f.LabelRegisters("r", r...)
+	// we don't need w0h, w1h, w2h anymore
+	f.Push(&registers, w0h, w1h, w2h)
+	// we don't need the low bits anymore
+	f.Push(&registers, low0h, low1h, low2h, low3h)
+
+	// Reduce using single-word Barrett
+	mu := f.Pop(&registers)
+
+	f.Comment("reduce using single-word Barrett")
+	f.Comment("see see Handbook of Applied Cryptography, Algorithm 14.42.")
+	f.LabelRegisters("mu=2^288 / q", mu)
+	f.MOVQ(f.mu(), mu)
+	f.MOVQ(r3, amd64.AX)
+	f.SHRQw("$32", r4, amd64.AX)
+	f.MULQ(mu, "high bits of res stored in DX")
+
+	f.MULXQ(f.qAt(0), amd64.AX, mu)
+	f.SUBQ(amd64.AX, r0)
+	f.SBBQ(mu, r1)
+
+	f.MULXQ(f.qAt(2), amd64.AX, mu)
+	f.SBBQ(amd64.AX, r2)
+	f.SBBQ(mu, r3)
+	f.SBBQ("$0", r4)
+
+	f.MULXQ(f.qAt(1), amd64.AX, mu)
+	f.SUBQ(amd64.AX, r1)
+	f.SBBQ(mu, r2)
+
+	f.MULXQ(f.qAt(3), amd64.AX, mu)
+	f.SBBQ(amd64.AX, r3)
+	f.SBBQ(mu, r4)
+
+	// we need up to 2 conditional substractions to be < q
+	modReduced := f.NewLabel("modReduced")
+	t := f.PopN(&registers)
+	f.Mov(r[:4], t) // backup r0 to r3 (our result)
+
+	// sub modulus
+	f.SUBQ(f.qAt(0), r0)
+	f.SBBQ(f.qAt(1), r1)
+	f.SBBQ(f.qAt(2), r2)
+	f.SBBQ(f.qAt(3), r3)
+	f.SBBQ("$0", r4)
+
+	// if borrow, we go to mod reduced
+	f.JCS(modReduced)
+	f.Mov(r, t)
+	f.SUBQ(f.qAt(0), r0)
+	f.SBBQ(f.qAt(1), r1)
+	f.SBBQ(f.qAt(2), r2)
+	f.SBBQ(f.qAt(3), r3)
+	f.SBBQ("$0", r4)
+
+	// if borrow, we skip to the end
+	f.JCS(modReduced)
+	f.Mov(r, t)
+
+	f.LABEL(modReduced)
+	addrRes := mu
+	f.MOVQ("res+0(FP)", addrRes)
+	f.Mov(t, addrRes)
+
+	f.LABEL(done)
+
+	f.RET()
+	f.Push(&registers, mu)
+	f.Push(&registers, w0l, w1l, w2l, w3l, w3h)
+}
+
+func (f *FFAmd64) generateInnerProduct() {
+	f.Comment("innerProdVec(res, a,b *Element, n uint64) res = sum(a[0...n] * b[0...n])")
 
 	const argSize = 4 * 8
-	const minStackSize = 7 * 8 // 2 slices (3 words each) + pointer to the scalar
-	stackSize := f.StackSize(f.NbWords*2+3, 2, minStackSize)
-	reserved := []amd64.Register{amd64.DX, amd64.AX}
-	registers := f.FnHeader("scalarMulVec", stackSize, argSize, reserved...)
-	defer f.AssertCleanStack(stackSize, minStackSize)
-
-	// labels & registers we need
-	noAdx := f.NewLabel("noAdx")
+	stackSize := f.StackSize(f.NbWords*3+2, 0, 0)
+	registers := f.FnHeader("innerProdVec", stackSize, argSize, amd64.DX, amd64.AX)
+	defer f.AssertCleanStack(stackSize, 0)
+
+	// registers & labels we need
+	PX := f.Pop(&registers)
+	PY := f.Pop(&registers)
+	LEN := f.Pop(&registers)
+
 	loop := f.NewLabel("loop")
 	done := f.NewLabel("done")
+	AddPP := f.NewLabel("accumulate")
 
-	t := registers.PopN(f.NbWords)
-	scalar := registers.PopN(f.NbWords)
+	// AVX512 registers
+	PPL := amd64.Register("Z2")
+	PPH := amd64.Register("Z3")
+	Y := amd64.Register("Z4")
+	LSW := amd64.Register("Z5")
 
-	addrB := registers.Pop()
-	addrA := registers.Pop()
-	addrRes := addrB
-	len := registers.Pop()
+	ACC := amd64.Register("Z16")
+	A0L := amd64.Register("Z16")
+	A1L := amd64.Register("Z17")
+	A2L := amd64.Register("Z18")
+	A3L := amd64.Register("Z19")
+	A4L := amd64.Register("Z20")
+	A5L := amd64.Register("Z21")
+	A6L := amd64.Register("Z22")
+	A7L := amd64.Register("Z23")
+	A0H := amd64.Register("Z24")
+	A1H := amd64.Register("Z25")
+	A2H := amd64.Register("Z26")
+	A3H := amd64.Register("Z27")
+	A4H := amd64.Register("Z28")
+	A5H := amd64.Register("Z29")
+	A6H := amd64.Register("Z30")
+	A7H := amd64.Register("Z31")
 
-	// check ADX instruction support
-	f.CMPB("·supportAdx(SB)", 1)
-	f.JNE(noAdx)
+	// load arguments
+	f.MOVQ("a+8(FP)", PX)
+	f.MOVQ("b+16(FP)", PY)
+	f.MOVQ("n+24(FP)", LEN)
 
-	f.MOVQ("a+8(FP)", addrA)
-	f.MOVQ("b+16(FP)", addrB)
-	f.MOVQ("n+24(FP)", len)
+	f.Comment("Create mask for low dword in each qword")
+	f.VPCMPEQB("Y0", "Y0", "Y0")
+	f.VPMOVZXDQ("Y0", LSW)
+
+	// Clear accumulator registers
+	f.VPXORQ(A0L, A0L, A0L)
+	f.VMOVDQA64(A0L, A1L)
+	f.VMOVDQA64(A0L, A2L)
+	f.VMOVDQA64(A0L, A3L)
+	f.VMOVDQA64(A0L, A4L)
+	f.VMOVDQA64(A0L, A5L)
+	f.VMOVDQA64(A0L, A6L)
+	f.VMOVDQA64(A0L, A7L)
+	f.VMOVDQA64(A0L, A0H)
+	f.VMOVDQA64(A0L, A1H)
+	f.VMOVDQA64(A0L, A2H)
+	f.VMOVDQA64(A0L, A3H)
+	f.VMOVDQA64(A0L, A4H)
+	f.VMOVDQA64(A0L, A5H)
+	f.VMOVDQA64(A0L, A6H)
+	f.VMOVDQA64(A0L, A7H)
+
+	// note: we don't need to handle the case n==0; handled by caller already.
+	f.TESTQ(LEN, LEN)
+	f.JEQ(done, "n == 0, we are done")
+
+	f.LABEL(loop)
+	f.TESTQ(LEN, LEN)
+	f.JEQ(AddPP, "n == 0 we can accumulate")
+
+	f.VPMOVZXDQ("("+PY+")", Y)
+
+	f.ADDQ("$32", PY)
+
+	f.Comment("we multiply and accumulate partial products of 4 bytes * 32 bytes")
+
+	mac := f.Define("MAC", 3, func(inputs ...amd64.Register) {
+		opLeft := inputs[0]
+		lo := inputs[1]
+		hi := inputs[2]
+
+		f.VPMULUDQ_BCST(opLeft, Y, PPL)
+		f.VPSRLQ("$32", PPL, PPH)
+		f.VPANDQ(LSW, PPL, PPL)
+		f.VPADDQ(PPL, lo, lo)
+		f.VPADDQ(PPH, hi, hi)
+	})
 
-	// we store b, the scalar, fully in registers
-	f.LabelRegisters("scalar", scalar...)
-	f.Mov(addrB, scalar)
+	mac("0*4("+PX+")", A0L, A0H)
+	mac("1*4("+PX+")", A1L, A1H)
+	mac("2*4("+PX+")", A2L, A2H)
+	mac("3*4("+PX+")", A3L, A3H)
+	mac("4*4("+PX+")", A4L, A4H)
+	mac("5*4("+PX+")", A5L, A5H)
+	mac("6*4("+PX+")", A6L, A6H)
+	mac("7*4("+PX+")", A7L, A7H)
 
-	xat := func(i int) string {
-		return string(scalar[i])
+	f.ADDQ("$32", PX)
+
+	f.DECQ(LEN, "decrement n")
+	f.JMP(loop)
+
+	f.Push(&registers, LEN, PX, PY)
+
+	f.LABEL(AddPP)
+	f.Comment("we accumulate the partial products into 544bits in Z1:Z0")
+
+	f.MOVQ(uint64(0x1555), amd64.AX)
+	f.KMOVD(amd64.AX, "K1")
+
+	f.MOVQ(uint64(1), amd64.AX)
+	f.KMOVD(amd64.AX, "K2")
+
+	// ACC starts with the value of A0L
+
+	f.Comment("store the least significant 32 bits of ACC (starts with A0L) in Z0")
+	f.VALIGND_Z("$16", ACC, ACC, "K2", "Z0")
+	f.KSHIFTLW("$1", "K2", "K2")
+
+	f.VPSRLQ("$32", ACC, PPL)
+	f.VALIGND_Z("$2", ACC, ACC, "K1", ACC)
+	f.VPADDQ(PPL, ACC, ACC)
+
+	f.VPANDQ(LSW, A0H, PPL)
+	f.VPADDQ(PPL, ACC, ACC)
+
+	f.VPANDQ(LSW, A1L, PPL)
+	f.VPADDQ(PPL, ACC, ACC)
+
+	// Word 1 of z is ready
+	f.VALIGND("$15", ACC, ACC, "K2", "Z0")
+	f.KSHIFTLW("$1", "K2", "K2")
+
+	f.Comment("macro to add partial products and store the result in Z0")
+	addPP := f.Define("ADDPP", 5, func(inputs ...amd64.Register) {
+		AxH := inputs[0]
+		AyL := inputs[1]
+		AyH := inputs[2]
+		AzL := inputs[3]
+		I := inputs[4]
+		f.VPSRLQ("$32", ACC, PPL)
+		f.VALIGND_Z("$2", ACC, ACC, "K1", ACC)
+		f.VPADDQ(PPL, ACC, ACC)
+		f.VPSRLQ("$32", AxH, AxH)
+		f.VPADDQ(AxH, ACC, ACC)
+		f.VPSRLQ("$32", AyL, AyL)
+		f.VPADDQ(AyL, ACC, ACC)
+		f.VPANDQ(LSW, AyH, PPL)
+		f.VPADDQ(PPL, ACC, ACC)
+		f.VPANDQ(LSW, AzL, PPL)
+		f.VPADDQ(PPL, ACC, ACC)
+		f.VALIGND("$16-"+I, ACC, ACC, "K2", "Z0")
+		f.KADDW("K2", "K2", "K2")
+	})
+
+	addPP(A0H, A1L, A1H, A2L, "2")
+	addPP(A1H, A2L, A2H, A3L, "3")
+	addPP(A2H, A3L, A3H, A4L, "4")
+	addPP(A3H, A4L, A4H, A5L, "5")
+	addPP(A4H, A5L, A5H, A6L, "6")
+	addPP(A5H, A6L, A6H, A7L, "7")
+	f.VPSRLQ("$32", ACC, PPL)
+	f.VALIGND_Z("$2", ACC, ACC, "K1", ACC)
+	f.VPADDQ(PPL, ACC, ACC)
+	f.VPSRLQ("$32", A6H, A6H)
+	f.VPADDQ(A6H, ACC, ACC)
+	f.VPSRLQ("$32", A7L, A7L)
+	f.VPADDQ(A7L, ACC, ACC)
+	f.VPANDQ(LSW, A7H, PPL)
+	f.VPADDQ(PPL, ACC, ACC)
+	f.VALIGND("$16-8", ACC, ACC, "K2", "Z0")
+	f.KSHIFTLW("$1", "K2", "K2")
+
+	f.VPSRLQ("$32", ACC, PPL)
+	f.VALIGND_Z("$2", ACC, ACC, "K1", ACC)
+	f.VPADDQ(PPL, ACC, ACC)
+	f.VPSRLQ("$32", A7H, A7H)
+	f.VPADDQ(A7H, ACC, ACC)
+	f.VALIGND("$16-9", ACC, ACC, "K2", "Z0")
+	f.KSHIFTLW("$1", "K2", "K2")
+
+	addPP2 := f.Define("ADDPP2", 1, func(args ...amd64.Register) {
+		f.VPSRLQ("$32", ACC, PPL)
+		f.VALIGND_Z("$2", ACC, ACC, "K1", ACC)
+		f.VPADDQ(PPL, ACC, ACC)
+		f.VALIGND("$16-"+args[0], ACC, ACC, "K2", "Z0")
+		f.KSHIFTLW("$1", "K2", "K2")
+	})
+
+	addPP2("10")
+	addPP2("11")
+	addPP2("12")
+	addPP2("13")
+	addPP2("14")
+	addPP2("15")
+
+	f.VPSRLQ("$32", ACC, PPL)
+	f.VALIGND_Z("$2", ACC, ACC, "K1", ACC)
+	f.VPADDQ(PPL, ACC, ACC)
+	f.VMOVDQA64_Z(ACC, "K1", "Z1")
+
+	T0 := f.Pop(&registers)
+	T1 := f.Pop(&registers)
+	T2 := f.Pop(&registers)
+	T3 := f.Pop(&registers)
+	T4 := f.Pop(&registers)
+
+	f.Comment("Extract the 4 least significant qwords of Z0")
+	f.VMOVQ("X0", T1)
+	f.VALIGNQ("$1", "Z0", "Z1", "Z0")
+	f.VMOVQ("X0", T2)
+	f.VALIGNQ("$1", "Z0", "Z0", "Z0")
+	f.VMOVQ("X0", T3)
+	f.VALIGNQ("$1", "Z0", "Z0", "Z0")
+	f.VMOVQ("X0", T4)
+	f.VALIGNQ("$1", "Z0", "Z0", "Z0")
+	f.XORQ(T0, T0)
+
+	PH := f.Pop(&registers)
+	PL := amd64.AX
+	f.MOVQ(f.qInv0(), amd64.DX)
+	f.MULXQ(T1, amd64.DX, PH)
+	f.MULXQ(f.qAt(0), PL, PH)
+	f.ADDQ(PL, T1)
+	f.ADCQ(PH, T2)
+	f.MULXQ(f.qAt(2), PL, PH)
+	f.ADCQ(PL, T3)
+	f.ADCQ(PH, T4)
+	f.ADCQ("$0", T0)
+	f.MULXQ(f.qAt(1), PL, PH)
+	f.ADDQ(PL, T2)
+	f.ADCQ(PH, T3)
+	f.MULXQ(f.qAt(3), PL, PH)
+	f.ADCQ(PL, T4)
+	f.ADCQ(PH, T0)
+	f.ADCQ("$0", T1)
+
+	f.MOVQ(f.qInv0(), amd64.DX)
+	f.MULXQ(T2, amd64.DX, PH)
+
+	f.MULXQ(f.qAt(0), PL, PH)
+	f.ADDQ(PL, T2)
+	f.ADCQ(PH, T3)
+	f.MULXQ(f.qAt(2), PL, PH)
+	f.ADCQ(PL, T4)
+	f.ADCQ(PH, T0)
+	f.ADCQ("$0", T1)
+	f.MULXQ(f.qAt(1), PL, PH)
+	f.ADDQ(PL, T3)
+	f.ADCQ(PH, T4)
+	f.MULXQ(f.qAt(3), PL, PH)
+	f.ADCQ(PL, T0)
+	f.ADCQ(PH, T1)
+	f.ADCQ("$0", T2)
+
+	f.MOVQ(f.qInv0(), amd64.DX)
+
+	f.MULXQ(T3, amd64.DX, PH)
+
+	f.MULXQ(f.qAt(0), PL, PH)
+	f.ADDQ(PL, T3)
+	f.ADCQ(PH, T4)
+	f.MULXQ(f.qAt(2), PL, PH)
+	f.ADCQ(PL, T0)
+	f.ADCQ(PH, T1)
+	f.ADCQ("$0", T2)
+	f.MULXQ(f.qAt(1), PL, PH)
+	f.ADDQ(PL, T4)
+	f.ADCQ(PH, T0)
+	f.MULXQ(f.qAt(3), PL, PH)
+	f.ADCQ(PL, T1)
+	f.ADCQ(PH, T2)
+	f.ADCQ("$0", T3)
+
+	f.MOVQ(f.qInv0(), amd64.DX)
+
+	f.MULXQ(T4, amd64.DX, PH)
+
+	f.MULXQ(f.qAt(0), PL, PH)
+	f.ADDQ(PL, T4)
+	f.ADCQ(PH, T0)
+	f.MULXQ(f.qAt(2), PL, PH)
+	f.ADCQ(PL, T1)
+	f.ADCQ(PH, T2)
+	f.ADCQ("$0", T3)
+	f.MULXQ(f.qAt(1), PL, PH)
+	f.ADDQ(PL, T0)
+	f.ADCQ(PH, T1)
+	f.MULXQ(f.qAt(3), PL, PH)
+	f.ADCQ(PL, T2)
+	f.ADCQ(PH, T3)
+	f.ADCQ("$0", T4)
+
+	// Add the remaining 5 qwords (9 dwords) from zmm0
+
+	f.VMOVQ("X0", PL)
+	f.ADDQ(PL, T0)
+	f.VALIGNQ("$1", "Z0", "Z0", "Z0")
+	f.VMOVQ("X0", PL)
+	f.ADCQ(PL, T1)
+	f.VALIGNQ("$1", "Z0", "Z0", "Z0")
+	f.VMOVQ("X0", PL)
+	f.ADCQ(PL, T2)
+	f.VALIGNQ("$1", "Z0", "Z0", "Z0")
+	f.VMOVQ("X0", PL)
+	f.ADCQ(PL, T3)
+	f.VALIGNQ("$1", "Z0", "Z0", "Z0")
+	f.VMOVQ("X0", PL)
+	f.ADCQ(PL, T4)
+
+	f.Comment("Barrett reduction; see Handbook of Applied Cryptography, Algorithm 14.42.")
+	f.MOVQ(T3, amd64.AX)
+	f.SHRQw("$32", T4, amd64.AX)
+	f.MOVQ(f.mu(), amd64.DX)
+	f.MULQ(amd64.DX)
+
+	f.MULXQ(f.qAt(0), PL, PH)
+	f.SUBQ(PL, T0)
+	f.SBBQ(PH, T1)
+	f.MULXQ(f.qAt(2), PL, PH)
+	f.SBBQ(PL, T2)
+	f.SBBQ(PH, T3)
+	f.SBBQ("$0", T4)
+	f.MULXQ(f.qAt(1), PL, PH)
+	f.SUBQ(PL, T1)
+	f.SBBQ(PH, T2)
+	f.MULXQ(f.qAt(3), PL, PH)
+	f.SBBQ(PL, T3)
+	f.SBBQ(PH, T4)
+
+	f.Comment("we need up to 2 conditional substractions to be < q")
+
+	PZ := f.Pop(&registers)
+	f.MOVQ("res+0(FP)", PZ)
+	t := []amd64.Register{T0, T1, T2, T3}
+	f.Mov(t, PZ)
+
+	// sub q
+	f.SUBQ(f.qAt(0), T0)
+	f.SBBQ(f.qAt(1), T1)
+	f.SBBQ(f.qAt(2), T2)
+	f.SBBQ(f.qAt(3), T3)
+	f.SBBQ("$0", T4)
+
+	// if borrow, we go to done
+	f.JCS(done)
+
+	f.Mov(t, PZ)
+
+	f.SUBQ(f.qAt(0), T0)
+	f.SBBQ(f.qAt(1), T1)
+	f.SBBQ(f.qAt(2), T2)
+	f.SBBQ(f.qAt(3), T3)
+	f.SBBQ("$0", T4)
+
+	f.JCS(done)
+
+	f.Mov(t, PZ)
+
+	f.LABEL(done)
+
+	f.RET()
+}
+
+func (f *FFAmd64) generateMulVec(funcName string) {
+	scalarMul := funcName != "mulVec"
+
+	const argSize = 5 * 8
+	stackSize := f.StackSize(6+f.NbWords, 2, 8)
+	reserved := make([]amd64.Register, len(mul4Registers)+2)
+	copy(reserved, mul4Registers)
+	reserved[len(mul4Registers)] = amd64.AX
+	reserved[len(mul4Registers)+1] = amd64.DX
+	registers := f.FnHeader(funcName, stackSize, argSize, reserved...)
+	defer f.AssertCleanStack(stackSize, 0)
+
+	// to simplify the generated assembly, we only handle n/16 (and do blocks of 16 muls).
+	// that is if n%16 != 0, we let the caller (Go) handle the remaining elements.
+	LEN := f.Pop(&registers, true)
+	PZ := f.Pop(&registers)
+	PX := f.Pop(&registers)
+	PY := f.Pop(&registers)
+
+	zi := func(i int) amd64.Register {
+		return amd64.Register("Z" + strconv.Itoa(i))
 	}
 
-	f.MOVQ("res+0(FP)", addrRes)
+	// AVX_MUL_Q_LO:
+	AVX_MUL_Q_LO, err := f.DefineFn("AVX_MUL_Q_LO")
+	if err != nil {
+		AVX_MUL_Q_LO = f.Define("AVX_MUL_Q_LO", 0, func(args ...amd64.Register) {
+			for i := 0; i < 4; i++ {
+				f.VPMULUDQ_BCST(f.qAt_bcst(i), "Z9", zi(10+i))
+				f.VPADDQ(zi(10+i), zi(i), zi(i))
+			}
+		})
+	}
+
+	// AVX_MUL_Q_HI:
+	AVX_MUL_Q_HI, err := f.DefineFn("AVX_MUL_Q_HI")
+	if err != nil {
+		AVX_MUL_Q_HI = f.Define("AVX_MUL_Q_HI", 0, func(args ...amd64.Register) {
+			for i := 0; i < 4; i++ {
+				f.VPMULUDQ_BCST(f.qAt_bcst(i+4), "Z9", zi(14+i))
+				f.VPADDQ(zi(14+i), zi(i+4), zi(i+4))
+			}
+		})
+	}
+
+	SHIFT_ADD_AND, err := f.DefineFn("SHIFT_ADD_AND")
+	if err != nil {
+		SHIFT_ADD_AND = f.Define("SHIFT_ADD_AND", 4, func(args ...amd64.Register) {
+			in0 := args[0]
+			in1 := args[1]
+			in2 := args[2]
+			in3 := args[3]
+			f.VPSRLQ("$32", in0, in1)
+			f.VPADDQ(in1, in2, in2)
+			f.VPANDQ(in3, in2, in0)
+		})
+	}
+
+	// CARRY1:
+	CARRY1, err := f.DefineFn("CARRY1")
+	if err != nil {
+		CARRY1 = f.Define("CARRY1", 0, func(args ...amd64.Register) {
+			for i := 0; i < 4; i++ {
+				SHIFT_ADD_AND(zi(i), zi(10+i), zi(i+1), "Z8")
+			}
+		})
+	}
+
+	// CARRY2:
+	CARRY2, err := f.DefineFn("CARRY2")
+	if err != nil {
+		CARRY2 = f.Define("CARRY2", 0, func(args ...amd64.Register) {
+			for i := 0; i < 3; i++ {
+				SHIFT_ADD_AND(zi(i+4), zi(14+i), zi(i+5), "Z8")
+			}
+			f.VPSRLQ("$32", "Z7", "Z7")
+		})
+	}
+
+	// CARRY3:
+	CARRY3, err := f.DefineFn("CARRY3")
+	if err != nil {
+		CARRY3 = f.Define("CARRY3", 0, func(args ...amd64.Register) {
+			for i := 0; i < 4; i++ {
+				f.VPSRLQ("$32", zi(i), zi(10+i))
+				f.VPANDQ("Z8", zi(i), zi(i))
+				f.VPADDQ(zi(10+i), zi(i+1), zi(i+1))
+			}
+		})
+	}
+
+	// CARRY4:
+	CARRY4, err := f.DefineFn("CARRY4")
+	if err != nil {
+		CARRY4 = f.Define("CARRY4", 0, func(args ...amd64.Register) {
+			for i := 0; i < 3; i++ {
+				f.VPSRLQ("$32", zi(i+4), zi(14+i))
+				f.VPANDQ("Z8", zi(i+4), zi(i+4))
+				f.VPADDQ(zi(14+i), zi(i+5), zi(i+5))
+			}
+		})
+	}
+
+	// we use the same registers as defined in the mul.
+	t := mul4Registers[:4]
+	f.LabelRegisters("t", t...)
+	y := mul4Registers[4:8]
+	f.LabelRegisters("y", y...)
+	tr := mul4Registers[8]
+	A := amd64.BP // note, BP is used in the mul defines.
+
+	// reuse defines from the mul function
+	mulWord0, err := f.DefineFn("MUL_WORD_0")
+	if err != nil {
+		panic(err)
+	}
+	mulWordN, err := f.DefineFn("MUL_WORD_N")
+	if err != nil {
+		panic(err)
+	}
+
+	zIndex := 0
+
+	loadInput := func() {
+		if scalarMul {
+			return
+		}
+		f.Comment(fmt.Sprintf("load input y[%d]", zIndex))
+		f.Mov(PY, y, zIndex*4)
+	}
+
+	mulXi := func(wordIndex int) {
+		f.Comment(fmt.Sprintf("z[%d] -> y * x[%d]", zIndex, wordIndex))
+		if wordIndex == 0 {
+			mulWord0()
+		} else {
+			f.MOVQ(amd64.Register(PX.At(wordIndex)), amd64.DX)
+			mulWordN()
+		}
+	}
+
+	storeOutput := func() {
+		scratch := []amd64.Register{A, tr, amd64.AX, amd64.DX}
+		f.ReduceElement(t, scratch)
+
+		f.Comment(fmt.Sprintf("store output z[%d]", zIndex))
+		f.Mov(t, PZ, 0, zIndex*4)
+		if zIndex == 7 {
+			f.ADDQ("$288", PX)
+		} else {
+			f.ADDQ("$32", PX)
+			f.MOVQ(amd64.Register(PX.At(0)), amd64.DX)
+		}
+		zIndex++
+	}
+
+	done := f.NewLabel("done")
+	loop := f.NewLabel("loop")
+
+	f.MOVQ("res+0(FP)", PZ)
+	f.MOVQ("a+8(FP)", PX)
+	f.MOVQ("b+16(FP)", PY)
+	f.MOVQ("n+24(FP)", tr)
+
+	if scalarMul {
+		// for scalar mul we move the scalar only once in registers.
+		f.Mov(PY, y)
+	}
+
+	// we process 16 elements at a time, Go caller divided len by 16.
+	f.MOVQ(tr, LEN)
+
+	f.Comment("Create mask for low dword in each qword")
+
+	f.VPCMPEQB("Y8", "Y8", "Y8")
+	f.VPMOVZXDQ("Y8", "Z8")
+	f.MOVQ("$0x5555", amd64.DX)
+	f.KMOVD(amd64.DX, "K1")
 
 	f.LABEL(loop)
-	f.TESTQ(len, len)
+	// f.MOVQ(LEN, tr)
+	f.TESTQ(tr, tr)
 	f.JEQ(done, "n == 0, we are done")
 
-	yat := func(i int) string {
-		return addrA.At(i)
+	f.MOVQ(amd64.Register(PX.At(0)), amd64.DX)
+	f.VMOVDQU64("256+0*64("+PX+")", "Z16")
+	f.VMOVDQU64("256+1*64("+PX+")", "Z17")
+	f.VMOVDQU64("256+2*64("+PX+")", "Z18")
+	f.VMOVDQU64("256+3*64("+PX+")", "Z19")
+
+	loadInput()
+	if scalarMul {
+		f.VMOVDQU64("0("+PY+")", "Z24")
+		f.VMOVDQU64("0("+PY+")", "Z25")
+		f.VMOVDQU64("0("+PY+")", "Z26")
+		f.VMOVDQU64("0("+PY+")", "Z27")
+	} else {
+		f.VMOVDQU64("256+0*64("+PY+")", "Z24")
+		f.VMOVDQU64("256+1*64("+PY+")", "Z25")
+		f.VMOVDQU64("256+2*64("+PY+")", "Z26")
+		f.VMOVDQU64("256+3*64("+PY+")", "Z27")
 	}
 
-	f.Comment("TODO @gbotrel this is generated from the same macro as the unit mul, we should refactor this in a single asm function")
+	f.Comment("Transpose and expand x and y")
 
-	f.MulADX(&registers, xat, yat, t)
+	// Step 1
 
-	// registers.Push(addrA)
+	f.VSHUFI64X2("$0x88", "Z17", "Z16", "Z20")
+	f.VSHUFI64X2("$0xdd", "Z17", "Z16", "Z22")
+	f.VSHUFI64X2("$0x88", "Z19", "Z18", "Z21")
+	f.VSHUFI64X2("$0xdd", "Z19", "Z18", "Z23")
 
-	// reduce; we need at least 4 extra registers
-	registers.Push(amd64.AX, amd64.DX)
-	f.Comment("reduce t mod q")
-	f.Reduce(&registers, t)
-	f.Mov(t, addrRes)
+	f.VSHUFI64X2("$0x88", "Z25", "Z24", "Z28")
+	f.VSHUFI64X2("$0xdd", "Z25", "Z24", "Z30")
+	f.VSHUFI64X2("$0x88", "Z27", "Z26", "Z29")
+	f.VSHUFI64X2("$0xdd", "Z27", "Z26", "Z31")
 
-	f.Comment("increment pointers to visit next element")
-	f.ADDQ("$32", addrA)
-	f.ADDQ("$32", addrRes)
-	f.DECQ(len, "decrement n")
+	// Step 2
+
+	f.VPERMQ("$0xd8", "Z20", "Z20")
+	f.VPERMQ("$0xd8", "Z21", "Z21")
+	f.VPERMQ("$0xd8", "Z22", "Z22")
+	f.VPERMQ("$0xd8", "Z23", "Z23")
+
+	mulXi(0)
+
+	f.VPERMQ("$0xd8", "Z28", "Z28")
+	f.VPERMQ("$0xd8", "Z29", "Z29")
+	f.VPERMQ("$0xd8", "Z30", "Z30")
+	f.VPERMQ("$0xd8", "Z31", "Z31")
+
+	// Step 3
+
+	for i := 20; i <= 23; i++ {
+		f.VSHUFI64X2("$0xd8", zi(i), zi(i), zi(i))
+	}
+
+	mulXi(1)
+
+	for i := 28; i <= 31; i++ {
+		f.VSHUFI64X2("$0xd8", zi(i), zi(i), zi(i))
+	}
+
+	// Step 4
+
+	f.VSHUFI64X2("$0x44", "Z21", "Z20", "Z16")
+	f.VSHUFI64X2("$0xee", "Z21", "Z20", "Z18")
+	f.VSHUFI64X2("$0x44", "Z23", "Z22", "Z20")
+	f.VSHUFI64X2("$0xee", "Z23", "Z22", "Z22")
+
+	mulXi(2)
+	f.VSHUFI64X2("$0x44", "Z29", "Z28", "Z24")
+	f.VSHUFI64X2("$0xee", "Z29", "Z28", "Z26")
+	f.VSHUFI64X2("$0x44", "Z31", "Z30", "Z28")
+	f.VSHUFI64X2("$0xee", "Z31", "Z30", "Z30")
+
+	f.WriteLn("PREFETCHT0 1024(" + string(PX) + ")")
+
+	// Step 5
+
+	f.VPSRLQ("$32", "Z16", "Z17")
+	f.VPSRLQ("$32", "Z18", "Z19")
+	f.VPSRLQ("$32", "Z20", "Z21")
+	f.VPSRLQ("$32", "Z22", "Z23")
+
+	for i := 24; i <= 30; i += 2 {
+		f.VPSRLQ("$32", zi(i), zi(i+1))
+	}
+	mulXi(3)
+
+	for i := 16; i <= 30; i += 2 {
+		f.VPANDQ("Z8", zi(i), zi(i))
+	}
+
+	storeOutput()
+
+	f.Comment("For each 256-bit input value, each zmm register now represents a 32-bit input word zero-extended to 64 bits.")
+	f.Comment("Multiply y by doubleword 0 of x")
+
+	for i := 0; i < 8; i++ {
+		f.VPMULUDQ("Z16", zi(24+i), zi(i))
+		if i == 4 {
+			if !scalarMul {
+				f.WriteLn("PREFETCHT0 1024(" + string(PY) + ")")
+			}
+		}
+	}
+
+	loadInput()
+
+	f.VPMULUDQ_BCST("qInvNeg+32(FP)", "Z0", "Z9")
+
+	for i := 0; i < 4; i++ {
+		f.VPSRLQ("$32", zi(i), zi(10+i))
+		f.VPANDQ("Z8", zi(i), zi(i))
+		f.VPADDQ(zi(10+i), zi(i+1), zi(i+1))
+
+	}
+
+	mulXi(0)
+
+	for i := 0; i < 3; i++ {
+		f.VPSRLQ("$32", zi(4+i), zi(14+i))
+		f.VPANDQ("Z8", zi(4+i), zi(4+i))
+		f.VPADDQ(zi(14+i), zi(5+i), zi(5+i))
+
+	}
+
+	for i := 0; i < 4; i++ {
+		f.VPMULUDQ_BCST(f.qAt_bcst(i), "Z9", zi(10+i))
+		f.VPADDQ(zi(10+i), zi(i), zi(i))
+	}
+
+	mulXi(1)
+
+	f.VPMULUDQ_BCST(f.qAt_bcst(4), "Z9", "Z14")
+	f.VPADDQ("Z14", "Z4", "Z4")
+
+	f.VPMULUDQ_BCST(f.qAt_bcst(5), "Z9", "Z15")
+	f.VPADDQ("Z15", "Z5", "Z5")
+
+	f.VPMULUDQ_BCST(f.qAt_bcst(6), "Z9", "Z16")
+	f.VPADDQ("Z16", "Z6", "Z6")
+
+	f.VPMULUDQ_BCST(f.qAt_bcst(7), "Z9", "Z10")
+	f.VPADDQ("Z10", "Z7", "Z7")
+
+	CARRY1()
+
+	mulXi(2)
+
+	for i := 0; i < 3; i++ {
+		SHIFT_ADD_AND(zi(4+i), zi(14+i), zi(5+i), "Z8")
+	}
+	f.VPSRLQ("$32", "Z7", "Z7")
+
+	f.Comment("Process doubleword 1 of x")
+
+	for i := 0; i < 4; i++ {
+		f.VPMULUDQ("Z17", zi(24+i), zi(10+i))
+		f.VPADDQ(zi(10+i), zi(i), zi(i))
+
+	}
+
+	mulXi(3)
+
+	for i := 0; i < 4; i++ {
+		f.VPMULUDQ("Z17", zi(28+i), zi(14+i))
+		f.VPADDQ(zi(14+i), zi(4+i), zi(4+i))
+
+	}
+
+	f.VPMULUDQ_BCST("qInvNeg+32(FP)", "Z0", "Z9")
+
+	storeOutput()
+
+	f.Comment("Move high dwords to zmm10-16, add each to the corresponding low dword (propagate 32-bit carries)")
+
+	for i := 0; i < 3; i++ {
+		f.VPSRLQ("$32", zi(i), zi(10+i))
+		f.VPANDQ("Z8", zi(i), zi(i))
+		f.VPADDQ(zi(10+i), zi(i+1), zi(i+1))
+	}
+	loadInput()
+
+	f.VPSRLQ("$32", "Z3", "Z13")
+	f.VPANDQ("Z8", "Z3", "Z3")
+	f.VPADDQ("Z13", "Z4", "Z4")
+
+	CARRY4()
+	mulXi(0)
+
+	AVX_MUL_Q_LO()
+
+	AVX_MUL_Q_HI()
+	mulXi(1)
+
+	CARRY1()
+
+	CARRY2()
+	mulXi(2)
+
+	f.Comment("Process doubleword 2 of x")
+
+	for i := 0; i < 4; i++ {
+		f.VPMULUDQ("Z18", zi(24+i), zi(10+i))
+		f.VPADDQ(zi(10+i), zi(i), zi(i))
+	}
+
+	for i := 0; i < 4; i++ {
+		f.VPMULUDQ("Z18", zi(28+i), zi(14+i))
+		f.VPADDQ(zi(14+i), zi(4+i), zi(4+i))
+
+	}
+
+	f.VPMULUDQ_BCST("qInvNeg+32(FP)", "Z0", "Z9")
+
+	mulXi(3)
+
+	f.Comment("Move high dwords to zmm10-16, add each to the corresponding low dword (propagate 32-bit carries)")
+	CARRY3()
+
+	storeOutput()
+	loadInput()
+
+	CARRY4()
+
+	AVX_MUL_Q_LO()
+
+	mulXi(0)
+	AVX_MUL_Q_HI()
+
+	CARRY1()
+	CARRY2()
+
+	f.Comment("Process doubleword 3 of x")
+
+	for i := 0; i < 4; i++ {
+		f.VPMULUDQ("Z19", zi(24+i), zi(10+i))
+		f.VPADDQ(zi(10+i), zi(i), zi(i))
+
+	}
+
+	mulXi(1)
+
+	for i := 0; i < 4; i++ {
+		f.VPMULUDQ("Z19", zi(28+i), zi(14+i))
+		f.VPADDQ(zi(14+i), zi(4+i), zi(4+i))
+
+	}
+	mulXi(2)
+	f.VPMULUDQ_BCST("qInvNeg+32(FP)", "Z0", "Z9")
+
+	// Move high dwords to zmm10-16, add each to the corresponding low dword (propagate 32-bit carries)
+	CARRY3()
+	CARRY4()
+	mulXi(3)
+
+	AVX_MUL_Q_LO()
+
+	AVX_MUL_Q_HI()
+
+	storeOutput()
+
+	f.Comment("Propagate carries and shift down by one dword")
+	CARRY1()
+
+	CARRY2()
+
+	loadInput()
+
+	f.Comment("Process doubleword 4 of x")
+
+	for i := 0; i < 4; i++ {
+		f.VPMULUDQ("Z20", zi(24+i), zi(10+i))
+		f.VPADDQ(zi(10+i), zi(i), zi(i))
+
+	}
+	mulXi(0)
+	for i := 0; i < 4; i++ {
+		f.VPMULUDQ("Z20", zi(28+i), zi(14+i))
+		f.VPADDQ(zi(14+i), zi(4+i), zi(4+i))
+
+	}
+
+	f.VPMULUDQ_BCST("qInvNeg+32(FP)", "Z0", "Z9")
+	mulXi(1)
+
+	f.Comment("Move high dwords to zmm10-16, add each to the corresponding low dword (propagate 32-bit carries)")
+
+	CARRY3()
+
+	CARRY4()
+	mulXi(2)
+
+	f.Comment("zmm7 keeps all 64 bits")
+
+	AVX_MUL_Q_LO()
+
+	AVX_MUL_Q_HI()
+
+	mulXi(3)
+
+	f.Comment("Propagate carries and shift down by one dword")
+
+	CARRY1()
+
+	CARRY2()
+
+	storeOutput()
+
+	f.Comment("Process doubleword 5 of x")
+
+	for i := 0; i < 4; i++ {
+		f.VPMULUDQ("Z21", zi(24+i), zi(10+i))
+		f.VPADDQ(zi(10+i), zi(i), zi(i))
+
+	}
+	loadInput()
+	for i := 0; i < 4; i++ {
+		f.VPMULUDQ("Z21", zi(28+i), zi(14+i))
+		f.VPADDQ(zi(14+i), zi(4+i), zi(4+i))
+
+	}
+
+	mulXi(0)
+
+	f.VPMULUDQ_BCST("qInvNeg+32(FP)", "Z0", "Z9")
+
+	f.Comment("Move high dwords to zmm10-16, add each to the corresponding low dword (propagate 32-bit carries)")
+	CARRY3()
+
+	CARRY4()
+
+	mulXi(1)
+
+	AVX_MUL_Q_LO()
+
+	AVX_MUL_Q_HI()
+
+	mulXi(2)
+
+	CARRY1()
+
+	CARRY2()
+
+	mulXi(3)
+
+	f.Comment("Process doubleword 6 of x")
+
+	for i := 0; i < 8; i++ {
+		f.VPMULUDQ("Z22", zi(24+i), zi(10+i))
+		f.VPADDQ(zi(10+i), zi(i), zi(i))
+	}
+
+	f.VPMULUDQ_BCST("qInvNeg+32(FP)", "Z0", "Z9")
+
+	storeOutput()
+
+	f.Comment("Move high dwords to zmm10-16, add each to the corresponding low dword (propagate 32-bit carries)")
+	CARRY3()
+	loadInput()
+	CARRY4()
+
+	mulXi(0)
+
+	AVX_MUL_Q_LO()
+
+	AVX_MUL_Q_HI()
+
+	mulXi(1)
+
+	CARRY1()
+
+	CARRY2()
+
+	mulXi(2)
+
+	f.Comment("Process doubleword 7 of x")
+	for i := 0; i < 4; i++ {
+		f.VPMULUDQ("Z23", zi(24+i), zi(10+i))
+		f.VPADDQ(zi(10+i), zi(i), zi(i))
+
+	}
+
+	for i := 0; i < 4; i++ {
+		f.VPMULUDQ("Z23", zi(28+i), zi(14+i))
+		f.VPADDQ(zi(14+i), zi(4+i), zi(4+i))
+
+	}
+	f.VPMULUDQ_BCST("qInvNeg+32(FP)", "Z0", "Z9")
+
+	mulXi(3)
+
+	CARRY3()
+	storeOutput()
+	CARRY4()
+
+	loadInput()
+
+	AVX_MUL_Q_LO()
+
+	AVX_MUL_Q_HI()
+
+	mulXi(0)
+
+	CARRY1()
+
+	CARRY2()
+
+	mulXi(1)
+
+	f.Comment("Conditional subtraction of the modulus")
+
+	for i := 0; i < 8; i++ {
+		f.VPERMD_BCST_Z(f.qAt_bcst(i), "Z8", "K1", zi(10+i))
+	}
+
+	for i := 0; i < 8; i++ {
+		f.VPSUBQ(zi(10+i), zi(i), zi(10+i))
+		if i > 0 {
+			f.VPSUBQ(zi(20+i-1), zi(10+i), zi(10+i))
+		}
+		if i != 7 {
+			f.VPSRLQ("$63", zi(10+i), zi(20+i))
+			f.VPANDQ("Z8", zi(10+i), zi(10+i))
+		}
+
+	}
+
+	f.VPMOVQ2M("Z17", "K2")
+	f.KNOTB("K2", "K2")
+
+	for i := 0; i < 8; i++ {
+		f.VMOVDQU64k(zi(10+i), "K2", zi(i))
+		if i == 4 {
+			mulXi(2)
+		}
+	}
+
+	f.Comment("Transpose results back")
+
+	f.WriteLn("VALIGND $0, ·pattern1+0(SB), Z11, Z11")
+	f.WriteLn("VALIGND $0, ·pattern2+0(SB), Z12, Z12")
+	f.WriteLn("VALIGND $0, ·pattern3+0(SB), Z13, Z13")
+	f.WriteLn("VALIGND $0, ·pattern4+0(SB), Z14, Z14")
+
+	for i := 0; i < 4; i++ {
+		f.VPSLLQ("$32", zi(2*i+1), zi(2*i+1))
+		f.VPORQ(zi(2*i+1), zi(2*i), zi(i))
+	}
+
+	f.VMOVDQU64("Z0", "Z4")
+	f.VMOVDQU64("Z2", "Z6")
+
+	mulXi(3)
+	f.VPERMT2Q("Z1", "Z11", "Z0")
+	f.VPERMT2Q("Z4", "Z12", "Z1")
+	f.VPERMT2Q("Z3", "Z11", "Z2")
+	f.VPERMT2Q("Z6", "Z12", "Z3")
+
+	// Step 3
+	storeOutput()
+
+	f.VMOVDQU64("Z0", "Z4")
+	f.VMOVDQU64("Z1", "Z5")
+	f.VPERMT2Q("Z2", "Z13", "Z0")
+	f.VPERMT2Q("Z4", "Z14", "Z2")
+	f.VPERMT2Q("Z3", "Z13", "Z1")
+	f.VPERMT2Q("Z5", "Z14", "Z3")
+
+	f.Comment("Save AVX-512 results")
+
+	f.VMOVDQU64("Z0", "256+0*64("+PZ+")")
+	f.VMOVDQU64("Z2", "256+1*64("+PZ+")")
+	f.VMOVDQU64("Z1", "256+2*64("+PZ+")")
+	f.VMOVDQU64("Z3", "256+3*64("+PZ+")")
+	f.ADDQ("$512", PZ)
+
+	if !scalarMul {
+		f.ADDQ("$512", PY)
+	}
+
+	f.MOVQ(LEN, tr)
+	f.DECQ(tr, "decrement n")
+	f.MOVQ(tr, LEN)
 	f.JMP(loop)
 
 	f.LABEL(done)
-	f.RET()
 
-	// no ADX support
-	f.LABEL(noAdx)
-
-	f.MOVQ("n+24(FP)", amd64.DX)
-
-	f.MOVQ("res+0(FP)", amd64.AX)
-	f.MOVQ(amd64.AX, "(SP)")
-	f.MOVQ(amd64.DX, "8(SP)")  // len
-	f.MOVQ(amd64.DX, "16(SP)") // cap
-	f.MOVQ("a+8(FP)", amd64.AX)
-	f.MOVQ(amd64.AX, "24(SP)")
-	f.MOVQ(amd64.DX, "32(SP)") // len
-	f.MOVQ(amd64.DX, "40(SP)") // cap
-	f.MOVQ("b+16(FP)", amd64.AX)
-	f.MOVQ(amd64.AX, "48(SP)")
-	f.WriteLn("CALL ·scalarMulVecGeneric(SB)")
 	f.RET()
 
+	f.Push(&registers, LEN)
+
 }
diff --git a/field/generator/config/field_config.go b/field/generator/config/field_config.go
index 457a89d7d2..6d24aab743 100644
--- a/field/generator/config/field_config.go
+++ b/field/generator/config/field_config.go
@@ -51,7 +51,9 @@ type FieldConfig struct {
 	Q                         []uint64
 	QInverse                  []uint64
 	QMinusOneHalvedP          []uint64 // ((q-1) / 2 ) + 1
+	Mu                        uint64   // mu = 2^288 / q for 4.5 word barrett reduction
 	ASM                       bool
+	ASMVector                 bool
 	RSquare                   []uint64
 	One, Thirteen             []uint64
 	LegendreExponent          string // big.Int to base16 string
@@ -260,6 +262,16 @@ func NewFieldConfig(packageName, elementName, modulus string, useAddChain bool)
 	// moduli that meet the condition F.NoCarry
 	// asm code generation for moduli with more than 6 words can be optimized further
 	F.ASM = F.NoCarry && F.NbWords <= 12 && F.NbWords > 1
+	F.ASMVector = F.ASM && F.NbWords == 4 && F.NbBits > 225
+
+	// setting Mu 2^288 / q
+	if F.NbWords == 4 {
+		_mu := big.NewInt(1)
+		_mu.Lsh(_mu, 288)
+		_mu.Div(_mu, &bModulus)
+		muSlice := toUint64Slice(_mu, F.NbWords)
+		F.Mu = muSlice[0]
+	}
 
 	return F, nil
 }
diff --git a/field/generator/generator.go b/field/generator/generator.go
index e149ac9ae0..0150897677 100644
--- a/field/generator/generator.go
+++ b/field/generator/generator.go
@@ -22,7 +22,7 @@ import (
 //
 //	fp, _ = config.NewField("fp", "Element", fpModulus")
 //	generator.GenerateFF(fp, filepath.Join(baseDir, "fp"))
-func GenerateFF(F *config.FieldConfig, outputDir string) error {
+func GenerateFF(F *config.FieldConfig, outputDir, asmDirBuildPath, asmDirIncludePath string) error {
 	// source file templates
 	sourceFiles := []string{
 		element.Base,
@@ -73,6 +73,8 @@ func GenerateFF(F *config.FieldConfig, outputDir string) error {
 	}
 	_ = os.Remove(filepath.Join(outputDir, "asm.go"))
 	_ = os.Remove(filepath.Join(outputDir, "asm_noadx.go"))
+	_ = os.Remove(filepath.Join(outputDir, "avx.go"))
+	_ = os.Remove(filepath.Join(outputDir, "noavx.go"))
 
 	funcs := template.FuncMap{}
 	if F.UseAddChain {
@@ -137,33 +139,7 @@ func GenerateFF(F *config.FieldConfig, outputDir string) error {
 
 			_, _ = io.WriteString(f, "// +build !purego\n")
 
-			if err := amd64.Generate(f, F); err != nil {
-				_ = f.Close()
-				return err
-			}
-			_ = f.Close()
-
-			// run asmfmt
-			// run go fmt on whole directory
-			cmd := exec.Command("asmfmt", "-w", pathSrc)
-			cmd.Stdout = os.Stdout
-			cmd.Stderr = os.Stderr
-			if err := cmd.Run(); err != nil {
-				return err
-			}
-		}
-
-		{
-			pathSrc := filepath.Join(outputDir, eName+"_mul_amd64.s")
-			fmt.Println("generating", pathSrc)
-			f, err := os.Create(pathSrc)
-			if err != nil {
-				return err
-			}
-
-			_, _ = io.WriteString(f, "// +build !purego\n")
-
-			if err := amd64.GenerateMul(f, F); err != nil {
+			if err := amd64.GenerateFieldWrapper(f, F, asmDirBuildPath, asmDirIncludePath); err != nil {
 				_ = f.Close()
 				return err
 			}
@@ -234,7 +210,7 @@ func GenerateFF(F *config.FieldConfig, outputDir string) error {
 		src := []string{
 			element.Asm,
 		}
-		pathSrc := filepath.Join(outputDir, "asm.go")
+		pathSrc := filepath.Join(outputDir, "asm_adx.go")
 		bavardOptsCpy := make([]func(*bavard.Bavard) error, len(bavardOpts))
 		copy(bavardOptsCpy, bavardOpts)
 		bavardOptsCpy = append(bavardOptsCpy, bavard.BuildTag("!noadx"))
@@ -256,6 +232,34 @@ func GenerateFF(F *config.FieldConfig, outputDir string) error {
 		}
 	}
 
+	if F.ASMVector {
+		// generate asm.go and asm_noadx.go
+		src := []string{
+			element.Avx,
+		}
+		pathSrc := filepath.Join(outputDir, "asm_avx.go")
+		bavardOptsCpy := make([]func(*bavard.Bavard) error, len(bavardOpts))
+		copy(bavardOptsCpy, bavardOpts)
+		bavardOptsCpy = append(bavardOptsCpy, bavard.BuildTag("!noavx"))
+		if err := bavard.GenerateFromString(pathSrc, src, F, bavardOptsCpy...); err != nil {
+			return err
+		}
+	}
+
+	if F.ASMVector {
+		// generate asm.go and asm_noadx.go
+		src := []string{
+			element.NoAvx,
+		}
+		pathSrc := filepath.Join(outputDir, "asm_noavx.go")
+		bavardOptsCpy := make([]func(*bavard.Bavard) error, len(bavardOpts))
+		copy(bavardOptsCpy, bavardOpts)
+		bavardOptsCpy = append(bavardOptsCpy, bavard.BuildTag("noavx"))
+		if err := bavard.GenerateFromString(pathSrc, src, F, bavardOptsCpy...); err != nil {
+			return err
+		}
+	}
+
 	// run go fmt on whole directory
 	cmd := exec.Command("gofmt", "-s", "-w", outputDir)
 	cmd.Stdout = os.Stdout
@@ -274,3 +278,31 @@ func shorten(input string) string {
 	}
 	return input
 }
+
+func GenerateCommonASM(nbWords int, asmDir string, hasVector bool) error {
+	os.MkdirAll(asmDir, 0755)
+	pathSrc := filepath.Join(asmDir, fmt.Sprintf(amd64.ElementASMFileName, nbWords))
+
+	fmt.Println("generating", pathSrc)
+	f, err := os.Create(pathSrc)
+	if err != nil {
+		return err
+	}
+
+	if err := amd64.GenerateCommonASM(f, nbWords, hasVector); err != nil {
+		_ = f.Close()
+		return err
+	}
+	_ = f.Close()
+
+	// run asmfmt
+	// run go fmt on whole directory
+	cmd := exec.Command("asmfmt", "-w", pathSrc)
+	cmd.Stdout = os.Stdout
+	cmd.Stderr = os.Stderr
+	if err := cmd.Run(); err != nil {
+		return err
+	}
+
+	return nil
+}
diff --git a/field/generator/generator_test.go b/field/generator/generator_test.go
index e107a0e85f..85b79cfdbe 100644
--- a/field/generator/generator_test.go
+++ b/field/generator/generator_test.go
@@ -21,27 +21,32 @@ import (
 	"os"
 	"os/exec"
 	"path/filepath"
+	"strings"
 	"testing"
 
 	field "github.com/consensys/gnark-crypto/field/generator/config"
+	"github.com/stretchr/testify/require"
+	"golang.org/x/sync/errgroup"
 )
 
 // integration test will create modulus for various field sizes and run tests
 
 const rootDir = "integration_test"
+const asmDir = "../asm"
 
 func TestIntegration(t *testing.T) {
+	assert := require.New(t)
+
 	os.RemoveAll(rootDir)
 	err := os.MkdirAll(rootDir, 0700)
 	defer os.RemoveAll(rootDir)
-	if err != nil {
-		t.Fatal(err)
-	}
+	assert.NoError(err)
 
 	var bits []int
 	for i := 64; i <= 448; i += 64 {
 		bits = append(bits, i-3, i-2, i-1, i, i+1)
 	}
+	bits = append(bits, 224, 225, 226)
 
 	moduli := make(map[string]string)
 	for _, i := range bits {
@@ -73,17 +78,18 @@ func TestIntegration(t *testing.T) {
 	moduli["e_nocarry_edge_0127"] = "170141183460469231731687303715884105727"
 	moduli["e_nocarry_edge_1279"] = "10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729087"
 
+	assert.NoError(GenerateCommonASM(2, asmDir, false))
+	assert.NoError(GenerateCommonASM(3, asmDir, false))
+	assert.NoError(GenerateCommonASM(7, asmDir, false))
+	assert.NoError(GenerateCommonASM(8, asmDir, false))
+
 	for elementName, modulus := range moduli {
 		var fIntegration *field.FieldConfig
 		// generate field
 		childDir := filepath.Join(rootDir, elementName)
 		fIntegration, err = field.NewFieldConfig("integration", elementName, modulus, false)
-		if err != nil {
-			t.Fatal(elementName, err)
-		}
-		if err = GenerateFF(fIntegration, childDir); err != nil {
-			t.Fatal(elementName, err)
-		}
+		assert.NoError(err)
+		assert.NoError(GenerateFF(fIntegration, childDir, asmDir, "../../../asm"))
 	}
 
 	// run go test
@@ -91,14 +97,39 @@ func TestIntegration(t *testing.T) {
 	if err != nil {
 		t.Fatal(err)
 	}
-	packageDir := filepath.Join(wd, rootDir) + string(filepath.Separator) + "..."
-	cmd := exec.Command("go", "test", packageDir)
-	if err := cmd.Run(); err != nil {
-		if exitErr, ok := err.(*exec.ExitError); ok {
-			t.Fatal(string(exitErr.Stderr))
-		} else {
-			t.Fatal(err)
+	packageDir := filepath.Join(wd, rootDir) // + string(filepath.Separator) + "..."
+
+	// list all subdirectories in package dir
+	var subDirs []string
+	err = filepath.Walk(packageDir, func(path string, info os.FileInfo, err error) error {
+		if info.IsDir() && path != packageDir {
+			subDirs = append(subDirs, path)
 		}
+		return nil
+	})
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	errGroup := errgroup.Group{}
+
+	for _, subDir := range subDirs {
+		// run go test in parallel
+		errGroup.Go(func() error {
+			cmd := exec.Command("go", "test")
+			cmd.Dir = subDir
+			var stdouterr strings.Builder
+			cmd.Stdout = &stdouterr
+			cmd.Stderr = &stdouterr
+			if err := cmd.Run(); err != nil {
+				return fmt.Errorf("go test failed, output:\n%s\n%s", stdouterr.String(), err)
+			}
+			return nil
+		})
+	}
+
+	if err := errGroup.Wait(); err != nil {
+		t.Fatal(err)
 	}
 
 }
diff --git a/field/generator/internal/templates/element/asm.go b/field/generator/internal/templates/element/asm.go
index c1027f148a..ed7fac7b40 100644
--- a/field/generator/internal/templates/element/asm.go
+++ b/field/generator/internal/templates/element/asm.go
@@ -10,6 +10,19 @@ var (
 )
 `
 
+const Avx = `
+import 	"golang.org/x/sys/cpu"
+
+var (
+	supportAvx512 = supportAdx && cpu.X86.HasAVX512 && cpu.X86.HasAVX512DQ
+	_ = supportAvx512
+)
+`
+
+const NoAvx = `
+const supportAvx512 = false
+`
+
 // AsmNoAdx ...
 const AsmNoAdx = `
 
diff --git a/field/generator/internal/templates/element/base.go b/field/generator/internal/templates/element/base.go
index 7690f06573..7dc8bffc4e 100644
--- a/field/generator/internal/templates/element/base.go
+++ b/field/generator/internal/templates/element/base.go
@@ -49,7 +49,7 @@ const (
 {{- end}}
 )
 
-var q{{.ElementName}} = {{.ElementName}}{
+var qElement = {{.ElementName}}{
 	{{- range $i := $.NbWordsIndexesFull}}
 	q{{$i}},{{end}}
 }
@@ -68,6 +68,12 @@ func Modulus() *big.Int {
 // used for Montgomery reduction
 const qInvNeg uint64 = {{index .QInverse 0}}
 
+{{- if eq .NbWords 4}}
+// mu = 2^288 / q needed for partial Barrett reduction
+const mu uint64 = {{.Mu}}
+{{- end}}
+
+
 func init() {
 	_modulus.SetString("{{.ModulusHex}}", 16)
 }
diff --git a/field/generator/internal/templates/element/mul_cios.go b/field/generator/internal/templates/element/mul_cios.go
index 070d07ec80..6fb554c3bd 100644
--- a/field/generator/internal/templates/element/mul_cios.go
+++ b/field/generator/internal/templates/element/mul_cios.go
@@ -2,6 +2,9 @@ package element
 
 // MulCIOS text book CIOS works for all modulus.
 //
+// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+//
 // There are couple of variations to the multiplication (and squaring) algorithms.
 //
 // All versions are derived from the Montgomery CIOS algorithm: see
@@ -126,49 +129,7 @@ const MulCIOS = `
 
 const MulDoc = `
 {{define "mul_doc noCarry"}}
-// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-// 
-// The algorithm:
-// 
-// for i=0 to N-1
-// 		C := 0
-// 		for j=0 to N-1
-// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-// 		(t[N+1],t[N]) := t[N] + C
-//		
-// 		C := 0
-// 		m := t[0]*q'[0] mod D
-// 		(C,_) := t[0] + m*q[0]
-// 		for j=1 to N-1
-// 			(C,t[j-1]) := t[j] + m*q[j] + C
-//		
-// 		(C,t[N-1]) := t[N] + C
-// 		t[N] := t[N+1] + C
-//
-// → N is the number of machine words needed to store the modulus q
-// → D is the word size. For example, on a 64-bit architecture D is 2	64
-// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-// → t is a temporary array of size N+2 
-// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
-{{- if .noCarry}}
-// 
-// As described here https://hackmd.io/@gnark/modular_multiplication we can get rid of one carry chain and simplify:
-// (also described in https://eprint.iacr.org/2022/1400.pdf annex)
-//
-// for i=0 to N-1
-// 		(A,t[0]) := t[0] + x[0]*y[i] 
-// 		m := t[0]*q'[0] mod W
-// 		C,_ := t[0] + m*q[0]
-// 		for j=1 to N-1
-// 			(A,t[j])  := t[j] + x[j]*y[i] + A
-// 			(C,t[j-1]) := t[j] + m*q[j] + C
-//		
-// 		t[N-1] = C + A
-//
-// This optimization saves 5N + 2 additions in the algorithm, and can be used whenever the highest bit 
-// of the modulus is zero (and not all of the remaining bits are set).
-{{- end}}
+// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS" 
+// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 {{ end }}
 `
diff --git a/field/generator/internal/templates/element/mul_nocarry.go b/field/generator/internal/templates/element/mul_nocarry.go
index 0ec89f7a8c..14740fd4af 100644
--- a/field/generator/internal/templates/element/mul_nocarry.go
+++ b/field/generator/internal/templates/element/mul_nocarry.go
@@ -1,6 +1,8 @@
 package element
 
-// MulNoCarry see https://eprint.iacr.org/2022/1400.pdf annex for more info on the algorithm
+// MulNoCarry
+// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 // Note that these templates are optimized for arm64 target, since x86 benefits from assembly impl.
 const MulNoCarry = `
 {{ define "mul_nocarry" }}
diff --git a/field/generator/internal/templates/element/ops_asm.go b/field/generator/internal/templates/element/ops_asm.go
index ffa7231e15..1d1408e264 100644
--- a/field/generator/internal/templates/element/ops_asm.go
+++ b/field/generator/internal/templates/element/ops_asm.go
@@ -29,14 +29,15 @@ func reduce(res *{{.ElementName}})
 //go:noescape
 func Butterfly(a, b *{{.ElementName}})
 
-{{- if eq .NbWords 4}}
+{{- if .ASMVector}}
 // Add adds two vectors element-wise and stores the result in self.
 // It panics if the vectors don't have the same length.
 func (vector *Vector) Add(a, b Vector) {
 	if len(a) != len(b) || len(a) != len(*vector) {
 		panic("vector.Add: vectors don't have the same length")
 	}
-	addVec(&(*vector)[0], &a[0], &b[0], uint64(len(a)))
+		n := uint64(len(a))
+	addVec(&(*vector)[0], &a[0], &b[0], n)
 }
 
 //go:noescape
@@ -60,11 +61,116 @@ func (vector *Vector) ScalarMul(a Vector, b *{{.ElementName}}) {
 	if len(a) != len(*vector) {
 		panic("vector.ScalarMul: vectors don't have the same length")
 	}
-	scalarMulVec(&(*vector)[0], &a[0], b, uint64(len(a)))
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || uint64(len(a)) >= maxN {
+		// call scalarMulVecGeneric
+		scalarMulVecGeneric(*vector, a, b)
+		return
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	// the code for scalarMul is identical to mulVec; and it expects at least 
+	// 2 elements in the vector to fill the Z registers
+	var bb  [2]{{.ElementName}}
+	bb[0] = *b
+	bb[1] = *b
+	const blockSize = 16
+	scalarMulVec(&(*vector)[0], &a[0], &bb[0], n/blockSize, qInvNeg)
+	if n % blockSize != 0 {
+		// call scalarMulVecGeneric on the rest
+		start := n - n % blockSize
+		scalarMulVecGeneric((*vector)[start:], a[start:], b)
+	}
+}
+
+//go:noescape
+func scalarMulVec(res, a, b *{{.ElementName}}, n uint64, qInvNeg uint64)
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res {{.ElementName}}) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	const minN = 16*7 // AVX512 slower than generic for small n
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n <= minN || n >= maxN {
+		// call sumVecGeneric
+		sumVecGeneric(&res, *vector)
+		return
+	}
+	sumVec(&res, &(*vector)[0], uint64(len(*vector)))
+	return
 }
 
 //go:noescape
-func scalarMulVec(res, a, b *{{.ElementName}}, n uint64)
+func sumVec(res *{{.ElementName}}, a *{{.ElementName}}, n uint64)
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res {{.ElementName}}) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	if n != uint64(len(other)) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n >= maxN {
+		// call innerProductVecGeneric
+		// note; we could split the vector into smaller chunks and call innerProductVec
+		innerProductVecGeneric(&res, *vector, other)
+		return
+	}
+	innerProdVec(&res[0], &(*vector)[0], &other[0], uint64(len(*vector)))
+
+	return
+}
+
+//go:noescape
+func innerProdVec(res *uint64, a,b *{{.ElementName}}, n uint64)
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n >= maxN {
+		// call mulVecGeneric
+		mulVecGeneric(*vector, a, b)
+		return
+	}
+
+	const blockSize = 16
+	mulVec(&(*vector)[0], &a[0], &b[0], n/blockSize, qInvNeg)
+	if n % blockSize != 0 {
+		// call mulVecGeneric on the rest
+		start := n - n % blockSize
+		mulVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+	
+}
+
+// Patterns use for transposing the vectors in mulVec
+var (
+	pattern1 = [8]uint64{0, 8, 1, 9, 2, 10, 3, 11}
+	pattern2 = [8]uint64{12, 4, 13, 5, 14, 6, 15, 7}
+	pattern3 = [8]uint64{0, 1, 8, 9, 2, 3, 10, 11}
+	pattern4 = [8]uint64{12, 13, 4, 5, 14, 15, 6, 7}
+)
+
+//go:noescape
+func mulVec(res, a, b *{{.ElementName}}, n uint64, qInvNeg uint64)
+
 {{- end}}
 
 // Mul z = x * y (mod q)
diff --git a/field/generator/internal/templates/element/ops_purego.go b/field/generator/internal/templates/element/ops_purego.go
index a4fde0d053..fe3cead3c4 100644
--- a/field/generator/internal/templates/element/ops_purego.go
+++ b/field/generator/internal/templates/element/ops_purego.go
@@ -50,7 +50,7 @@ func reduce(z *{{.ElementName}})  {
 	_reduceGeneric(z)
 }
 
-{{- if eq .NbWords 4}}
+{{- if .ASMVector}}
 // Add adds two vectors element-wise and stores the result in self.
 // It panics if the vectors don't have the same length.
 func (vector *Vector) Add(a, b Vector) {
@@ -68,6 +68,26 @@ func (vector *Vector) Sub(a, b Vector) {
 func (vector *Vector) ScalarMul(a Vector, b *{{.ElementName}}) {
 	scalarMulVecGeneric(*vector, a, b)
 }
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res {{.ElementName}}) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res {{.ElementName}}) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
+
 {{- end}}
 
 // Mul z = x * y (mod q)
diff --git a/field/generator/internal/templates/element/tests.go b/field/generator/internal/templates/element/tests.go
index 416b3f30e6..d09dbeb7e5 100644
--- a/field/generator/internal/templates/element/tests.go
+++ b/field/generator/internal/templates/element/tests.go
@@ -331,14 +331,14 @@ func init() {
 	staticTestValues = append(staticTestValues, rSquare) 			// r²
 	var e, one {{.ElementName}}
 	one.SetOne()
-	e.Sub(&q{{.ElementName}}, &one)
+	e.Sub(&qElement, &one)
 	staticTestValues = append(staticTestValues, e) 	// q - 1
 	e.Double(&one)
 	staticTestValues = append(staticTestValues, e) 	// 2 
 
 
 	{
-		a := q{{.ElementName}}
+		a := qElement
 		a[0]--
 		staticTestValues = append(staticTestValues, a)
 	}
@@ -354,14 +354,14 @@ func init() {
 	{{- end}}
 
 	{
-		a := q{{.ElementName}}
+		a := qElement
 		a[{{.NbWordsLastIndex}}]--
 		staticTestValues = append(staticTestValues, a)
 	}
 
 	{{- if ne .NbWords 1}}
 	{
-		a := q{{.ElementName}}
+		a := qElement
 		a[{{.NbWordsLastIndex}}]--
 		a[0]++
 		staticTestValues = append(staticTestValues, a)
@@ -369,7 +369,7 @@ func init() {
 	{{- end}}
 
 	{
-		a := q{{.ElementName}}
+		a := qElement
 		a[{{.NbWordsLastIndex}}] = 0
 		staticTestValues = append(staticTestValues, a)
 	}
@@ -653,8 +653,6 @@ func Test{{toTitle .ElementName}}BitLen(t *testing.T) {
 	))
 
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
-
-	
 }
 
 
@@ -728,78 +726,6 @@ func Test{{toTitle .ElementName}}LexicographicallyLargest(t *testing.T) {
 	
 }
 
-func Test{{toTitle .ElementName}}VecOps(t *testing.T) {
-	assert := require.New(t)
-
-	const N = 7
-	a := make(Vector, N)
-	b := make(Vector, N)
-	c := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a[i].SetRandom()
-		b[i].SetRandom()
-	}
-
-	// Vector addition
-	c.Add(a, b)
-	for i := 0; i < N; i++ {
-		var expected {{.ElementName}}
-		expected.Add(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector addition failed")
-	}
-
-	// Vector subtraction
-	c.Sub(a, b)
-	for i := 0; i < N; i++ {
-		var expected {{.ElementName}}
-		expected.Sub(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector subtraction failed")
-	}
-
-	// Vector scaling
-	c.ScalarMul(a, &b[0])
-	for i := 0; i < N; i++ {
-		var expected {{.ElementName}}
-		expected.Mul(&a[i], &b[0])
-		assert.True(c[i].Equal(&expected), "Vector scaling failed")
-	}
-}
-
-func Benchmark{{toTitle .ElementName}}VecOps(b *testing.B) {
-	// note; to benchmark against "no asm" version, use the following
-	// build tag: -tags purego
-	const N = 1024
-	a1 := make(Vector, N)
-	b1 := make(Vector, N)
-	c1 := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a1[i].SetRandom()
-		b1[i].SetRandom()
-	}
-
-
-	b.Run("Add", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Add(a1, b1)
-		}
-	})
-
-	b.Run("Sub", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Sub(a1, b1)
-		}
-	})
-
-	b.Run("ScalarMul", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.ScalarMul(a1, &b1[0])
-		}
-	})
-}
-
 
 {{template "testBinaryOp" dict "all" . "Op" "Add"}}
 {{template "testBinaryOp" dict "all" . "Op" "Sub"}}
@@ -1651,8 +1577,8 @@ func gen() gopter.Gen {
 			{{- range $i := .NbWordsIndexesFull}}
 			genParams.NextUint64(),{{end}}
 		}
-		if q{{.ElementName}}[{{.NbWordsLastIndex}}] != ^uint64(0) {
-			g.element[{{.NbWordsLastIndex}}] %= (q{{.ElementName}}[{{.NbWordsLastIndex}}] +1 )
+		if qElement[{{.NbWordsLastIndex}}] != ^uint64(0) {
+			g.element[{{.NbWordsLastIndex}}] %= (qElement[{{.NbWordsLastIndex}}] +1 )
 		}
 		
 
@@ -1661,8 +1587,8 @@ func gen() gopter.Gen {
 				{{- range $i := .NbWordsIndexesFull}}
 				genParams.NextUint64(),{{end}}
 			}
-			if q{{.ElementName}}[{{.NbWordsLastIndex}}] != ^uint64(0) {
-				g.element[{{.NbWordsLastIndex}}] %= (q{{.ElementName}}[{{.NbWordsLastIndex}}] +1 )
+			if qElement[{{.NbWordsLastIndex}}] != ^uint64(0) {
+				g.element[{{.NbWordsLastIndex}}] %= (qElement[{{.NbWordsLastIndex}}] +1 )
 			}
 		}
 
@@ -1672,42 +1598,42 @@ func gen() gopter.Gen {
 	}
 }
 
+func genRandomFq(genParams *gopter.GenParameters) {{.ElementName}} {
+	var g {{.ElementName}}
 
-func genFull() gopter.Gen {
-	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+	g = {{.ElementName}}{
+		{{- range $i := .NbWordsIndexesFull}}
+		genParams.NextUint64(),{{end}}
+	}
 
-		genRandomFq := func() {{.ElementName}} {
-			var g {{.ElementName}}
+	if qElement[{{.NbWordsLastIndex}}] != ^uint64(0) {
+		g[{{.NbWordsLastIndex}}] %= (qElement[{{.NbWordsLastIndex}}] +1 )
+	}
 
-			g = {{.ElementName}}{
-				{{- range $i := .NbWordsIndexesFull}}
-				genParams.NextUint64(),{{end}}
-			}
+	for !g.smallerThanModulus() {
+		g = {{.ElementName}}{
+			{{- range $i := .NbWordsIndexesFull}}
+			genParams.NextUint64(),{{end}}
+		}
+		if qElement[{{.NbWordsLastIndex}}] != ^uint64(0) {
+			g[{{.NbWordsLastIndex}}] %= (qElement[{{.NbWordsLastIndex}}] +1 )
+		}
+	}
 
-			if q{{.ElementName}}[{{.NbWordsLastIndex}}] != ^uint64(0) {
-				g[{{.NbWordsLastIndex}}] %= (q{{.ElementName}}[{{.NbWordsLastIndex}}] +1 )
-			}
+	return g 
+}
 
-			for !g.smallerThanModulus() {
-				g = {{.ElementName}}{
-					{{- range $i := .NbWordsIndexesFull}}
-					genParams.NextUint64(),{{end}}
-				}
-				if q{{.ElementName}}[{{.NbWordsLastIndex}}] != ^uint64(0) {
-					g[{{.NbWordsLastIndex}}] %= (q{{.ElementName}}[{{.NbWordsLastIndex}}] +1 )
-				}
-			}
 
-			return g 
-		}
-		a := genRandomFq()
+func genFull() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
 
 		var carry uint64
 		{{- range $i := .NbWordsIndexesFull}}
 			{{- if eq $i $.NbWordsLastIndex}}
-			a[{{$i}}], _ = bits.Add64(a[{{$i}}], q{{$.ElementName}}[{{$i}}], carry)
+			a[{{$i}}], _ = bits.Add64(a[{{$i}}], qElement[{{$i}}], carry)
 			{{- else}}
-			a[{{$i}}], carry = bits.Add64(a[{{$i}}], q{{$.ElementName}}[{{$i}}], carry)
+			a[{{$i}}], carry = bits.Add64(a[{{$i}}], qElement[{{$i}}], carry)
 			{{- end}}
 		{{- end}}
 		
@@ -1715,6 +1641,15 @@ func genFull() gopter.Gen {
 		return genResult
 	}
 }
+
+func gen{{.ElementName}}() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
+		genResult := gopter.NewGenResult(a, gopter.NoShrinker)
+		return genResult
+	}
+}
+
 {{if $.UsingP20Inverse}}
 func (z *{{.ElementName}}) matchVeryBigInt(aHi uint64, aInt *big.Int) error {
 	var modulus big.Int
diff --git a/field/generator/internal/templates/element/tests_vector.go b/field/generator/internal/templates/element/tests_vector.go
index 14a7c3e50e..41187a2caa 100644
--- a/field/generator/internal/templates/element/tests_vector.go
+++ b/field/generator/internal/templates/element/tests_vector.go
@@ -9,9 +9,12 @@ import (
 	"sort"
 	"reflect"
 	"bytes"
-)
-
+	"os"
+	"fmt"
 
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/prop"
+)
 
 func TestVectorSort(t *testing.T) {
 	assert := require.New(t)
@@ -69,8 +72,6 @@ func TestVectorEmptyRoundTrip(t *testing.T) {
 	assert.True(reflect.DeepEqual(v3,v2))
 }
 
-
-
 func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 	r := bytes.NewReader(data)
 	_, err, chErr := vector.AsyncReadFrom(r)
@@ -80,4 +81,280 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 	return <-chErr
 }
 
+
+
+func TestVectorOps(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = 2
+	} else {
+		parameters.MinSuccessfulTests = 10
+	}
+	properties := gopter.NewProperties(parameters)
+
+	addVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Add(a, b)
+		
+		for i := 0; i < len(a); i++ {
+			var tmp {{.ElementName}}
+			tmp.Add(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	subVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Sub(a, b)
+		
+		for i := 0; i < len(a); i++ {
+			var tmp {{.ElementName}}
+			tmp.Sub(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	scalarMulVector := func(a Vector, b {{.ElementName}}) bool {
+		c := make(Vector, len(a))
+		c.ScalarMul(a, &b)
+		
+		for i := 0; i < len(a); i++ {
+			var tmp {{.ElementName}}
+			tmp.Mul(&a[i], &b)
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sumVector := func(a Vector) bool {
+		var sum {{.ElementName}}
+		computed := a.Sum()
+		for i := 0; i < len(a); i++ {
+			sum.Add(&sum, &a[i])
+		}
+
+		return sum.Equal(&computed)
+	}
+
+	innerProductVector := func(a, b Vector) bool {
+		computed := a.InnerProduct(b)
+		var innerProduct {{.ElementName}}
+		for i := 0; i < len(a); i++ {
+			var tmp {{.ElementName}}
+			tmp.Mul(&a[i], &b[i])
+			innerProduct.Add(&innerProduct, &tmp)
+		}
+
+		return innerProduct.Equal(&computed)
+	}
+
+	mulVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		a[0].SetUint64(0x24)
+		b[0].SetUint64(0x42)
+		c.Mul(a, b)
+		
+		for i := 0; i < len(a); i++ {
+			var tmp {{.ElementName}}
+			tmp.Mul(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sizes := []int{1, 2, 3, 4,8,9,15,16, 509, 510, 511, 512, 513, 514}
+	type genPair struct {
+		g1, g2 gopter.Gen
+		label string
+	}
+	
+	for _, size := range sizes {
+		generators := []genPair{
+			{genZeroVector(size), genZeroVector(size), "zero vectors"},
+			{genMaxVector(size), genMaxVector(size), "max vectors"},
+			{genVector(size), genVector(size), "random vectors"},
+			{genVector(size), genZeroVector(size), "random and zero vectors"},
+		}	
+		for _, gp := range generators {
+			properties.Property(fmt.Sprintf("vector addition %d - %s", size, gp.label), prop.ForAll(
+				addVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector subtraction %d - %s", size, gp.label), prop.ForAll(
+				subVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector scalar multiplication %d - %s", size, gp.label), prop.ForAll(
+				scalarMulVector,
+				gp.g1,
+				gen{{.ElementName}}(),
+			))
+
+			properties.Property(fmt.Sprintf("vector sum %d - %s", size, gp.label), prop.ForAll(
+				sumVector,
+				gp.g1,
+			))
+
+			properties.Property(fmt.Sprintf("vector inner product %d - %s", size, gp.label), prop.ForAll(
+				innerProductVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector multiplication %d - %s", size, gp.label), prop.ForAll(
+				mulVector,
+				gp.g1,
+				gp.g2,
+			))
+		}
+	}
+
+	properties.TestingRun(t, gopter.NewFormatedReporter(false, 260, os.Stdout))
+}
+
+
+func BenchmarkVectorOps(b *testing.B) {
+	// note; to benchmark against "no asm" version, use the following
+	// build tag: -tags purego
+	const N = 1<<24
+	a1 := make(Vector, N)
+	b1 := make(Vector, N)
+	c1 := make(Vector, N)
+	var mixer {{.ElementName}}
+	mixer.SetRandom()
+	for i := 1; i < N; i++ {
+		a1[i-1].SetUint64(uint64(i)).
+			Mul(&a1[i-1], &mixer)
+		b1[i-1].SetUint64(^uint64(i)).
+			Mul(&b1[i-1], &mixer)
+	}
+
+	for n:= 1<<4; n <= N; n <<= 1 {
+		b.Run(fmt.Sprintf("add %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Add(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sub %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Sub(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("scalarMul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.ScalarMul(_a, &mixer)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sum %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.Sum()
+			}
+		})
+
+		b.Run(fmt.Sprintf("innerProduct %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.InnerProduct(_b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("mul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Mul(_a, _b)
+			}
+		})
+	}
+}
+
+func genZeroVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genMaxVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+
+		qMinusOne := qElement
+		qMinusOne[0]--
+
+		for i := 0; i < size; i++ {
+			g[i] = qMinusOne
+		}
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		mixer := {{.ElementName}}{
+			{{- range $i := .NbWordsIndexesFull}}
+			genParams.NextUint64(),{{end}}
+		}
+		if qElement[{{.NbWordsLastIndex}}] != ^uint64(0) {
+			mixer[{{.NbWordsLastIndex}}] %= (qElement[{{.NbWordsLastIndex}}] +1 )
+		}
+		
+
+		for !mixer.smallerThanModulus() {
+			mixer = {{.ElementName}}{
+				{{- range $i := .NbWordsIndexesFull}}
+				genParams.NextUint64(),{{end}}
+			}
+			if qElement[{{.NbWordsLastIndex}}] != ^uint64(0) {
+				mixer[{{.NbWordsLastIndex}}] %= (qElement[{{.NbWordsLastIndex}}] +1 )
+			}
+		}
+
+		for i := 1; i <= size; i++ {
+			g[i-1].SetUint64(uint64(i)).
+				Mul(&g[i-1], &mixer)
+		}
+
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
 `
diff --git a/field/generator/internal/templates/element/vector.go b/field/generator/internal/templates/element/vector.go
index 8f06b54c9f..6407a024d5 100644
--- a/field/generator/internal/templates/element/vector.go
+++ b/field/generator/internal/templates/element/vector.go
@@ -174,7 +174,6 @@ func (vector Vector) String() string {
     return sbb.String()
 }
 
-
 // Len is the number of elements in the collection.
 func (vector Vector) Len() int {
 	return len(vector)
@@ -193,7 +192,7 @@ func (vector Vector) Swap(i, j int) {
 
 
 {{/* For 4 elements, we have a special assembly path and copy this in ops_pure.go */}}
-{{- if ne .NbWords 4}}
+{{- if not .ASMVector}}
 // Add adds two vectors element-wise and stores the result in self.
 // It panics if the vectors don't have the same length.
 func (vector *Vector) Add(a, b Vector) {
@@ -211,6 +210,26 @@ func (vector *Vector) Sub(a, b Vector) {
 func (vector *Vector) ScalarMul(a Vector, b *{{.ElementName}}) {
 	scalarMulVecGeneric(*vector, a, b)
 }
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res {{.ElementName}}) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res {{.ElementName}}) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
+
 {{- end}}
 
 
@@ -242,6 +261,32 @@ func scalarMulVecGeneric(res, a Vector, b *{{.ElementName}}) {
 	}
 }
 
+func sumVecGeneric(res *{{.ElementName}}, a Vector) {
+	for i := 0; i < len(a); i++ {
+		res.Add(res, &a[i])
+	}
+}
+
+func innerProductVecGeneric(res *{{.ElementName}},a, b Vector) {
+	if len(a) != len(b) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	var tmp {{.ElementName}}
+	for i := 0; i < len(a); i++ {
+		tmp.Mul(&a[i], &b[i])
+		res.Add(res, &tmp)
+	}
+}
+
+func mulVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Mul(&a[i], &b[i])
+	}
+}
+
 // TODO @gbotrel make a public package out of that.
 // execute executes the work function in parallel.
 // this is copy paste from internal/parallel/parallel.go
diff --git a/field/goff/cmd/root.go b/field/goff/cmd/root.go
index 15ed94fc02..849e26da76 100644
--- a/field/goff/cmd/root.go
+++ b/field/goff/cmd/root.go
@@ -71,7 +71,14 @@ func cmdGenerate(cmd *cobra.Command, args []string) {
 		fmt.Printf("\n%s\n", err.Error())
 		os.Exit(-1)
 	}
-	if err := generator.GenerateFF(F, fOutputDir); err != nil {
+
+	asmDir := filepath.Join(fOutputDir, "asm")
+	if err := generator.GenerateCommonASM(F.NbWords, asmDir, F.ASMVector); err != nil {
+		fmt.Printf("\n%s\n", err.Error())
+		os.Exit(-1)
+	}
+
+	if err := generator.GenerateFF(F, fOutputDir, asmDir, "asm/"); err != nil {
 		fmt.Printf("\n%s\n", err.Error())
 		os.Exit(-1)
 	}
diff --git a/field/goldilocks/element.go b/field/goldilocks/element.go
index 3afe5c4474..8dd4d69919 100644
--- a/field/goldilocks/element.go
+++ b/field/goldilocks/element.go
@@ -412,32 +412,8 @@ func (z *Element) Select(c int, x0 *Element, x1 *Element) *Element {
 // and is used for testing purposes.
 func _mulGeneric(z, x, y *Element) {
 
-	// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
-	// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
-	//
-	// The algorithm:
-	//
-	// for i=0 to N-1
-	// 		C := 0
-	// 		for j=0 to N-1
-	// 			(C,t[j]) := t[j] + x[j]*y[i] + C
-	// 		(t[N+1],t[N]) := t[N] + C
-	//
-	// 		C := 0
-	// 		m := t[0]*q'[0] mod D
-	// 		(C,_) := t[0] + m*q[0]
-	// 		for j=1 to N-1
-	// 			(C,t[j-1]) := t[j] + m*q[j] + C
-	//
-	// 		(C,t[N-1]) := t[N] + C
-	// 		t[N] := t[N+1] + C
-	//
-	// → N is the number of machine words needed to store the modulus q
-	// → D is the word size. For example, on a 64-bit architecture D is 2	64
-	// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
-	// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
-	// → t is a temporary array of size N+2
-	// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
 
 	var t [2]uint64
 	var D uint64
diff --git a/field/goldilocks/element_test.go b/field/goldilocks/element_test.go
index 339fb4ea61..454d057dbf 100644
--- a/field/goldilocks/element_test.go
+++ b/field/goldilocks/element_test.go
@@ -582,7 +582,6 @@ func TestElementBitLen(t *testing.T) {
 	))
 
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
-
 }
 
 func TestElementButterflies(t *testing.T) {
@@ -652,77 +651,6 @@ func TestElementLexicographicallyLargest(t *testing.T) {
 
 }
 
-func TestElementVecOps(t *testing.T) {
-	assert := require.New(t)
-
-	const N = 7
-	a := make(Vector, N)
-	b := make(Vector, N)
-	c := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a[i].SetRandom()
-		b[i].SetRandom()
-	}
-
-	// Vector addition
-	c.Add(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Add(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector addition failed")
-	}
-
-	// Vector subtraction
-	c.Sub(a, b)
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Sub(&a[i], &b[i])
-		assert.True(c[i].Equal(&expected), "Vector subtraction failed")
-	}
-
-	// Vector scaling
-	c.ScalarMul(a, &b[0])
-	for i := 0; i < N; i++ {
-		var expected Element
-		expected.Mul(&a[i], &b[0])
-		assert.True(c[i].Equal(&expected), "Vector scaling failed")
-	}
-}
-
-func BenchmarkElementVecOps(b *testing.B) {
-	// note; to benchmark against "no asm" version, use the following
-	// build tag: -tags purego
-	const N = 1024
-	a1 := make(Vector, N)
-	b1 := make(Vector, N)
-	c1 := make(Vector, N)
-	for i := 0; i < N; i++ {
-		a1[i].SetRandom()
-		b1[i].SetRandom()
-	}
-
-	b.Run("Add", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Add(a1, b1)
-		}
-	})
-
-	b.Run("Sub", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.Sub(a1, b1)
-		}
-	})
-
-	b.Run("ScalarMul", func(b *testing.B) {
-		b.ResetTimer()
-		for i := 0; i < b.N; i++ {
-			c1.ScalarMul(a1, &b1[0])
-		}
-	})
-}
-
 func TestElementAdd(t *testing.T) {
 	t.Parallel()
 	parameters := gopter.DefaultTestParameters()
@@ -2284,32 +2212,32 @@ func gen() gopter.Gen {
 	}
 }
 
-func genFull() gopter.Gen {
-	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+func genRandomFq(genParams *gopter.GenParameters) Element {
+	var g Element
 
-		genRandomFq := func() Element {
-			var g Element
+	g = Element{
+		genParams.NextUint64(),
+	}
 
-			g = Element{
-				genParams.NextUint64(),
-			}
+	if qElement[0] != ^uint64(0) {
+		g[0] %= (qElement[0] + 1)
+	}
 
-			if qElement[0] != ^uint64(0) {
-				g[0] %= (qElement[0] + 1)
-			}
+	for !g.smallerThanModulus() {
+		g = Element{
+			genParams.NextUint64(),
+		}
+		if qElement[0] != ^uint64(0) {
+			g[0] %= (qElement[0] + 1)
+		}
+	}
 
-			for !g.smallerThanModulus() {
-				g = Element{
-					genParams.NextUint64(),
-				}
-				if qElement[0] != ^uint64(0) {
-					g[0] %= (qElement[0] + 1)
-				}
-			}
+	return g
+}
 
-			return g
-		}
-		a := genRandomFq()
+func genFull() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
 
 		var carry uint64
 		a[0], _ = bits.Add64(a[0], qElement[0], carry)
@@ -2318,3 +2246,11 @@ func genFull() gopter.Gen {
 		return genResult
 	}
 }
+
+func genElement() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
+		genResult := gopter.NewGenResult(a, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/field/goldilocks/internal/main.go b/field/goldilocks/internal/main.go
index 4f5bacd3f8..e9f8749a5b 100644
--- a/field/goldilocks/internal/main.go
+++ b/field/goldilocks/internal/main.go
@@ -14,7 +14,7 @@ func main() {
 	if err != nil {
 		panic(err)
 	}
-	if err := generator.GenerateFF(goldilocks, "../"); err != nil {
+	if err := generator.GenerateFF(goldilocks, "../", "", ""); err != nil {
 		panic(err)
 	}
 	fmt.Println("successfully generated goldilocks field")
diff --git a/field/goldilocks/vector.go b/field/goldilocks/vector.go
index 3de71afb88..7411cb7bf7 100644
--- a/field/goldilocks/vector.go
+++ b/field/goldilocks/vector.go
@@ -214,6 +214,25 @@ func (vector *Vector) ScalarMul(a Vector, b *Element) {
 	scalarMulVecGeneric(*vector, a, b)
 }
 
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
+
 func addVecGeneric(res, a, b Vector) {
 	if len(a) != len(b) || len(a) != len(res) {
 		panic("vector.Add: vectors don't have the same length")
@@ -241,6 +260,32 @@ func scalarMulVecGeneric(res, a Vector, b *Element) {
 	}
 }
 
+func sumVecGeneric(res *Element, a Vector) {
+	for i := 0; i < len(a); i++ {
+		res.Add(res, &a[i])
+	}
+}
+
+func innerProductVecGeneric(res *Element, a, b Vector) {
+	if len(a) != len(b) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	var tmp Element
+	for i := 0; i < len(a); i++ {
+		tmp.Mul(&a[i], &b[i])
+		res.Add(res, &tmp)
+	}
+}
+
+func mulVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Mul(&a[i], &b[i])
+	}
+}
+
 // TODO @gbotrel make a public package out of that.
 // execute executes the work function in parallel.
 // this is copy paste from internal/parallel/parallel.go
diff --git a/field/goldilocks/vector_test.go b/field/goldilocks/vector_test.go
index e1ce6992c3..8d45c0f5dc 100644
--- a/field/goldilocks/vector_test.go
+++ b/field/goldilocks/vector_test.go
@@ -18,10 +18,15 @@ package goldilocks
 
 import (
 	"bytes"
+	"fmt"
 	"github.com/stretchr/testify/require"
+	"os"
 	"reflect"
 	"sort"
 	"testing"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/prop"
 )
 
 func TestVectorSort(t *testing.T) {
@@ -88,3 +93,273 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 	}
 	return <-chErr
 }
+
+func TestVectorOps(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = 2
+	} else {
+		parameters.MinSuccessfulTests = 10
+	}
+	properties := gopter.NewProperties(parameters)
+
+	addVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Add(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Add(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	subVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Sub(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Sub(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	scalarMulVector := func(a Vector, b Element) bool {
+		c := make(Vector, len(a))
+		c.ScalarMul(a, &b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b)
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sumVector := func(a Vector) bool {
+		var sum Element
+		computed := a.Sum()
+		for i := 0; i < len(a); i++ {
+			sum.Add(&sum, &a[i])
+		}
+
+		return sum.Equal(&computed)
+	}
+
+	innerProductVector := func(a, b Vector) bool {
+		computed := a.InnerProduct(b)
+		var innerProduct Element
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			innerProduct.Add(&innerProduct, &tmp)
+		}
+
+		return innerProduct.Equal(&computed)
+	}
+
+	mulVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		a[0].SetUint64(0x24)
+		b[0].SetUint64(0x42)
+		c.Mul(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sizes := []int{1, 2, 3, 4, 8, 9, 15, 16, 509, 510, 511, 512, 513, 514}
+	type genPair struct {
+		g1, g2 gopter.Gen
+		label  string
+	}
+
+	for _, size := range sizes {
+		generators := []genPair{
+			{genZeroVector(size), genZeroVector(size), "zero vectors"},
+			{genMaxVector(size), genMaxVector(size), "max vectors"},
+			{genVector(size), genVector(size), "random vectors"},
+			{genVector(size), genZeroVector(size), "random and zero vectors"},
+		}
+		for _, gp := range generators {
+			properties.Property(fmt.Sprintf("vector addition %d - %s", size, gp.label), prop.ForAll(
+				addVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector subtraction %d - %s", size, gp.label), prop.ForAll(
+				subVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector scalar multiplication %d - %s", size, gp.label), prop.ForAll(
+				scalarMulVector,
+				gp.g1,
+				genElement(),
+			))
+
+			properties.Property(fmt.Sprintf("vector sum %d - %s", size, gp.label), prop.ForAll(
+				sumVector,
+				gp.g1,
+			))
+
+			properties.Property(fmt.Sprintf("vector inner product %d - %s", size, gp.label), prop.ForAll(
+				innerProductVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector multiplication %d - %s", size, gp.label), prop.ForAll(
+				mulVector,
+				gp.g1,
+				gp.g2,
+			))
+		}
+	}
+
+	properties.TestingRun(t, gopter.NewFormatedReporter(false, 260, os.Stdout))
+}
+
+func BenchmarkVectorOps(b *testing.B) {
+	// note; to benchmark against "no asm" version, use the following
+	// build tag: -tags purego
+	const N = 1 << 24
+	a1 := make(Vector, N)
+	b1 := make(Vector, N)
+	c1 := make(Vector, N)
+	var mixer Element
+	mixer.SetRandom()
+	for i := 1; i < N; i++ {
+		a1[i-1].SetUint64(uint64(i)).
+			Mul(&a1[i-1], &mixer)
+		b1[i-1].SetUint64(^uint64(i)).
+			Mul(&b1[i-1], &mixer)
+	}
+
+	for n := 1 << 4; n <= N; n <<= 1 {
+		b.Run(fmt.Sprintf("add %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Add(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sub %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Sub(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("scalarMul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.ScalarMul(_a, &mixer)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sum %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.Sum()
+			}
+		})
+
+		b.Run(fmt.Sprintf("innerProduct %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.InnerProduct(_b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("mul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Mul(_a, _b)
+			}
+		})
+	}
+}
+
+func genZeroVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genMaxVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+
+		qMinusOne := qElement
+		qMinusOne[0]--
+
+		for i := 0; i < size; i++ {
+			g[i] = qMinusOne
+		}
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		mixer := Element{
+			genParams.NextUint64(),
+		}
+		if qElement[0] != ^uint64(0) {
+			mixer[0] %= (qElement[0] + 1)
+		}
+
+		for !mixer.smallerThanModulus() {
+			mixer = Element{
+				genParams.NextUint64(),
+			}
+			if qElement[0] != ^uint64(0) {
+				mixer[0] %= (qElement[0] + 1)
+			}
+		}
+
+		for i := 1; i <= size; i++ {
+			g[i-1].SetUint64(uint64(i)).
+				Mul(&g[i-1], &mixer)
+		}
+
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/go.mod b/go.mod
index 1cc1f399bb..b5486971f2 100644
--- a/go.mod
+++ b/go.mod
@@ -4,12 +4,13 @@ go 1.22
 
 require (
 	github.com/bits-and-blooms/bitset v1.14.2
-	github.com/consensys/bavard v0.1.15
+	github.com/consensys/bavard v0.1.22
 	github.com/leanovate/gopter v0.2.11
 	github.com/mmcloughlin/addchain v0.4.0
 	github.com/spf13/cobra v1.8.1
 	github.com/stretchr/testify v1.9.0
 	golang.org/x/crypto v0.26.0
+	golang.org/x/sync v0.1.0
 	golang.org/x/sys v0.24.0
 	gopkg.in/yaml.v2 v2.4.0
 )
diff --git a/go.sum b/go.sum
index 2c324c00b1..26af63d69f 100644
--- a/go.sum
+++ b/go.sum
@@ -55,8 +55,8 @@ github.com/client9/misspell v0.3.4/go.mod h1:qj6jICC3Q7zFZvVWo7KLAzC3yx5G7kyvSDk
 github.com/cncf/udpa/go v0.0.0-20191209042840-269d4d468f6f/go.mod h1:M8M6+tZqaGXZJjfX53e64911xZQV5JYwmTeXPW+k8Sc=
 github.com/cncf/udpa/go v0.0.0-20200629203442-efcf912fb354/go.mod h1:WmhPx2Nbnhtbo57+VJT5O0JRkEi1Wbu0z5j0R8u5Hbk=
 github.com/cncf/udpa/go v0.0.0-20201120205902-5459f2c99403/go.mod h1:WmhPx2Nbnhtbo57+VJT5O0JRkEi1Wbu0z5j0R8u5Hbk=
-github.com/consensys/bavard v0.1.15 h1:fxv2mg1afRMJvZgpwEgLmyr2MsQwaAYcyKf31UBHzw4=
-github.com/consensys/bavard v0.1.15/go.mod h1:9ItSMtA/dXMAiL7BG6bqW2m3NdSEObYWoH223nGHukI=
+github.com/consensys/bavard v0.1.22 h1:Uw2CGvbXSZWhqK59X0VG/zOjpTFuOMcPLStrp1ihI0A=
+github.com/consensys/bavard v0.1.22/go.mod h1:k/zVjHHC4B+PQy1Pg7fgvG3ALicQw540Crag8qx+dZs=
 github.com/coreos/go-semver v0.3.0/go.mod h1:nnelYz7RCh+5ahJtPPxZlU+153eP4D4r3EedlOD2RNk=
 github.com/coreos/go-systemd/v22 v22.3.2/go.mod h1:Y58oyj3AT4RCenI/lSvhwexgC+NSVTIJ3seZv2GcEnc=
 github.com/cpuguy83/go-md2man/v2 v2.0.0/go.mod h1:maD7wRr/U5Z6m/iR4s+kqSMx2CaBsrgA7czyZG/E6dU=
@@ -384,6 +384,7 @@ golang.org/x/sync v0.0.0-20201020160332-67f06af15bc9/go.mod h1:RxMgew5VJxzue5/jJ
 golang.org/x/sync v0.0.0-20201207232520-09787c993a3a/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
 golang.org/x/sync v0.0.0-20210220032951-036812b2e83c/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
 golang.org/x/sync v0.0.0-20220722155255-886fb9371eb4/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
+golang.org/x/sync v0.1.0 h1:wsuoTGHzEhffawBOhz5CYhcrV4IdKZbEyZjBMuTp12o=
 golang.org/x/sync v0.1.0/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
 golang.org/x/sys v0.0.0-20180823144017-11551d06cbcc/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY=
 golang.org/x/sys v0.0.0-20180830151530-49385e6e1522/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY=
diff --git a/internal/generator/main.go b/internal/generator/main.go
index 389f96c2e0..3d7cd9c0ab 100644
--- a/internal/generator/main.go
+++ b/internal/generator/main.go
@@ -43,28 +43,55 @@ var bgen = bavard.NewBatchGenerator(copyrightHolder, copyrightYear, "consensys/g
 
 //go:generate go run main.go
 func main() {
-	var wg sync.WaitGroup
 
+	// first we loop through the field arithmetic we must generate.
+	// then, we create the common files (only once) for the assembly code.
+	asmDirBuildPath := filepath.Join(baseDir, "field", "asm")
+	asmDirIncludePath := filepath.Join("../../../", "field", "asm")
+
+	// generate common assembly files depending on field number of words
+	mCommon := make(map[int]bool)
+	mVec := make(map[int]bool)
+
+	for i, conf := range config.Curves {
+		var err error
+		// generate base field
+		conf.Fp, err = field.NewFieldConfig("fp", "Element", conf.FpModulus, true)
+		assertNoError(err)
+
+		conf.Fr, err = field.NewFieldConfig("fr", "Element", conf.FrModulus, !conf.Equal(config.STARK_CURVE))
+		assertNoError(err)
+
+		mCommon[conf.Fr.NbWords] = true
+		mCommon[conf.Fp.NbWords] = true
+
+		if conf.Fr.ASMVector {
+			mVec[conf.Fr.NbWords] = true
+		}
+		if conf.Fp.ASMVector {
+			mVec[conf.Fp.NbWords] = true
+		}
+
+		config.Curves[i] = conf
+	}
+
+	for nbWords := range mCommon {
+		assertNoError(generator.GenerateCommonASM(nbWords, asmDirBuildPath, mVec[nbWords]))
+	}
+
+	var wg sync.WaitGroup
 	for _, conf := range config.Curves {
 		wg.Add(1)
 		// for each curve, generate the needed files
 		go func(conf config.Curve) {
 			defer wg.Done()
-			var err error
 
 			curveDir := filepath.Join(baseDir, "ecc", conf.Name)
 
-			// generate base field
-			conf.Fp, err = field.NewFieldConfig("fp", "Element", conf.FpModulus, true)
-			assertNoError(err)
-
-			conf.Fr, err = field.NewFieldConfig("fr", "Element", conf.FrModulus, !conf.Equal(config.STARK_CURVE))
-			assertNoError(err)
-
 			conf.FpUnusedBits = 64 - (conf.Fp.NbBits % 64)
 
-			assertNoError(generator.GenerateFF(conf.Fr, filepath.Join(curveDir, "fr")))
-			assertNoError(generator.GenerateFF(conf.Fp, filepath.Join(curveDir, "fp")))
+			assertNoError(generator.GenerateFF(conf.Fr, filepath.Join(curveDir, "fr"), asmDirBuildPath, asmDirIncludePath))
+			assertNoError(generator.GenerateFF(conf.Fp, filepath.Join(curveDir, "fp"), asmDirBuildPath, asmDirIncludePath))
 
 			// generate ecdsa
 			assertNoError(ecdsa.Generate(conf, curveDir, bgen))
diff --git a/internal/generator/tower/asm/amd64/e2.go b/internal/generator/tower/asm/amd64/e2.go
index 5fb3ea969b..e3564861a9 100644
--- a/internal/generator/tower/asm/amd64/e2.go
+++ b/internal/generator/tower/asm/amd64/e2.go
@@ -35,7 +35,7 @@ type Fq2Amd64 struct {
 // NewFq2Amd64 ...
 func NewFq2Amd64(w io.Writer, F *field.FieldConfig, config config.Curve) *Fq2Amd64 {
 	return &Fq2Amd64{
-		amd64.NewFFAmd64(w, F),
+		amd64.NewFFAmd64(w, F.NbWords),
 		config,
 		w,
 		F,
@@ -48,8 +48,9 @@ func (fq2 *Fq2Amd64) Generate(forceADXCheck bool) error {
 
 	fq2.WriteLn("#include \"textflag.h\"")
 	fq2.WriteLn("#include \"funcdata.h\"")
+	fq2.WriteLn("#include \"go_asm.h\"")
 
-	fq2.GenerateDefines()
+	fq2.GenerateReduceDefine()
 	if fq2.config.Equal(config.BN254) {
 		fq2.generateMulDefine()
 	}
@@ -174,7 +175,7 @@ func (fq2 *Fq2Amd64) generateNegE2() {
 
 	// z = x - q
 	for i := 0; i < fq2.NbWords; i++ {
-		fq2.MOVQ(fq2.Q[i], q)
+		fq2.MOVQ(fq2.F.Q[i], q)
 		if i == 0 {
 			fq2.SUBQ(t[i], q)
 		} else {
@@ -208,7 +209,7 @@ func (fq2 *Fq2Amd64) generateNegE2() {
 
 	// z = x - q
 	for i := 0; i < fq2.NbWords; i++ {
-		fq2.MOVQ(fq2.Q[i], q)
+		fq2.MOVQ(fq2.F.Q[i], q)
 		if i == 0 {
 			fq2.SUBQ(t[i], q)
 		} else {
@@ -272,7 +273,7 @@ func (fq2 *Fq2Amd64) modReduceAfterSub(registers *ramd64.Registers, zero ramd64.
 }
 
 func (fq2 *Fq2Amd64) modReduceAfterSubScratch(zero ramd64.Register, t, scratch []ramd64.Register) {
-	fq2.Mov(fq2.Q, scratch)
+	fq2.Mov(fq2.F.Q, scratch)
 	for i := 0; i < fq2.NbWords; i++ {
 		fq2.CMOVQCC(zero, scratch[i])
 	}
diff --git a/internal/generator/tower/asm/amd64/e2_bn254.go b/internal/generator/tower/asm/amd64/e2_bn254.go
index 8213381096..c894c2c684 100644
--- a/internal/generator/tower/asm/amd64/e2_bn254.go
+++ b/internal/generator/tower/asm/amd64/e2_bn254.go
@@ -305,11 +305,10 @@ func (fq2 *Fq2Amd64) generateMulDefine() {
 		return string(op2[i])
 	}
 
-	wd := writerDefine{fq2.w}
-	tw := gamd64.NewFFAmd64(&wd, fq2.F)
+	wd := writerDefine{fq2.w, 0, false}
+	tw := gamd64.NewFFAmd64(&wd, fq2.F.NbWords)
 
 	_, _ = io.WriteString(fq2.w, "// this code is generated and identical to fp.Mul(...)\n")
-	_, _ = io.WriteString(fq2.w, "#define MUL() \\ \n")
 	tw.MulADX(&r, xat, yat, res)
 }
 
@@ -339,10 +338,25 @@ func (fq2 *Fq2Amd64) mulElement() {
 }
 
 type writerDefine struct {
-	w io.Writer
+	w       io.Writer
+	cptXORQ int
+	first   bool
 }
 
 func (w *writerDefine) Write(p []byte) (n int, err error) {
+	// TODO @gbotrel temporary hack to re-use new struct in mul;
+	// then if it's the first time we are here, we print the header
+	if strings.Contains(string(p), "mul body") {
+		w.first = true
+		n, err = io.WriteString(w.w, "#define MUL() \\ \n")
+		if err != nil {
+			return
+		}
+	}
+	if !w.first {
+		return w.w.Write(p)
+	}
+
 	line := string(p)
 	line = strings.TrimSpace(line)
 	if strings.HasPrefix(line, "//") {
diff --git a/internal/generator/tower/template/fq12over6over2/amd64.fq2.go.tmpl b/internal/generator/tower/template/fq12over6over2/amd64.fq2.go.tmpl
index 74efb87e10..cebb6827b1 100644
--- a/internal/generator/tower/template/fq12over6over2/amd64.fq2.go.tmpl
+++ b/internal/generator/tower/template/fq12over6over2/amd64.fq2.go.tmpl
@@ -1,3 +1,25 @@
+import (
+	"github.com/consensys/gnark-crypto/ecc/{{.Name}}/fp"
+)
+
+// q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
+// used for Montgomery reduction
+const qInvNeg uint64 = {{index .Fp.QInverse 0}}
+
+// Field modulus q (Fp)
+const (
+	{{- range $i := $.Fp.NbWordsIndexesFull}}
+		q{{$i}} uint64 = {{index $.Fp.Q $i}}
+		{{- if eq $.Fp.NbWords 1}}
+			q uint64 = q0
+		{{- end}}
+	{{- end}}
+	)
+
+var qElement = fp.Element { 
+	{{- range $i := $.Fp.NbWordsIndexesFull}}
+	q{{$i}},{{end}}
+}
 
 //go:noescape
 func addE2(res,x,y *E2)

From 40622b0750202ca3185f7c894331baccec50a0a1 Mon Sep 17 00:00:00 2001
From: Gautam Botrel <gautam.botrel@gmail.com>
Date: Mon, 7 Oct 2024 11:56:25 -0500
Subject: [PATCH 078/114] test: fix windows build

---
 field/generator/generator_test.go | 5 +++--
 field/goff/cmd/root.go            | 2 +-
 field/goldilocks/internal/main.go | 2 +-
 internal/generator/main.go        | 4 ++--
 4 files changed, 7 insertions(+), 6 deletions(-)

diff --git a/field/generator/generator_test.go b/field/generator/generator_test.go
index 85b79cfdbe..2c4b055f65 100644
--- a/field/generator/generator_test.go
+++ b/field/generator/generator_test.go
@@ -32,10 +32,11 @@ import (
 // integration test will create modulus for various field sizes and run tests
 
 const rootDir = "integration_test"
-const asmDir = "../asm"
 
 func TestIntegration(t *testing.T) {
 	assert := require.New(t)
+	asmDir := filepath.Join("..", "asm")
+	asmDirIncludePath := filepath.Join("..", "..", "..", "asm")
 
 	os.RemoveAll(rootDir)
 	err := os.MkdirAll(rootDir, 0700)
@@ -89,7 +90,7 @@ func TestIntegration(t *testing.T) {
 		childDir := filepath.Join(rootDir, elementName)
 		fIntegration, err = field.NewFieldConfig("integration", elementName, modulus, false)
 		assert.NoError(err)
-		assert.NoError(GenerateFF(fIntegration, childDir, asmDir, "../../../asm"))
+		assert.NoError(GenerateFF(fIntegration, childDir, asmDir, asmDirIncludePath))
 	}
 
 	// run go test
diff --git a/field/goff/cmd/root.go b/field/goff/cmd/root.go
index 849e26da76..58d36dbdee 100644
--- a/field/goff/cmd/root.go
+++ b/field/goff/cmd/root.go
@@ -78,7 +78,7 @@ func cmdGenerate(cmd *cobra.Command, args []string) {
 		os.Exit(-1)
 	}
 
-	if err := generator.GenerateFF(F, fOutputDir, asmDir, "asm/"); err != nil {
+	if err := generator.GenerateFF(F, fOutputDir, asmDir, "asm"); err != nil {
 		fmt.Printf("\n%s\n", err.Error())
 		os.Exit(-1)
 	}
diff --git a/field/goldilocks/internal/main.go b/field/goldilocks/internal/main.go
index e9f8749a5b..04d5d75305 100644
--- a/field/goldilocks/internal/main.go
+++ b/field/goldilocks/internal/main.go
@@ -14,7 +14,7 @@ func main() {
 	if err != nil {
 		panic(err)
 	}
-	if err := generator.GenerateFF(goldilocks, "../", "", ""); err != nil {
+	if err := generator.GenerateFF(goldilocks, "..", "", ""); err != nil {
 		panic(err)
 	}
 	fmt.Println("successfully generated goldilocks field")
diff --git a/internal/generator/main.go b/internal/generator/main.go
index 3d7cd9c0ab..be5b29f518 100644
--- a/internal/generator/main.go
+++ b/internal/generator/main.go
@@ -36,7 +36,6 @@ import (
 const (
 	copyrightHolder = "Consensys Software Inc."
 	copyrightYear   = 2020
-	baseDir         = "../../"
 )
 
 var bgen = bavard.NewBatchGenerator(copyrightHolder, copyrightYear, "consensys/gnark-crypto")
@@ -44,10 +43,11 @@ var bgen = bavard.NewBatchGenerator(copyrightHolder, copyrightYear, "consensys/g
 //go:generate go run main.go
 func main() {
 
+	baseDir := filepath.Join("..", "..")
 	// first we loop through the field arithmetic we must generate.
 	// then, we create the common files (only once) for the assembly code.
 	asmDirBuildPath := filepath.Join(baseDir, "field", "asm")
-	asmDirIncludePath := filepath.Join("../../../", "field", "asm")
+	asmDirIncludePath := filepath.Join(baseDir, "..", "field", "asm")
 
 	// generate common assembly files depending on field number of words
 	mCommon := make(map[int]bool)

From acecab72083c6a3991172fc280b7e41ecec9e3f6 Mon Sep 17 00:00:00 2001
From: Gautam Botrel <gautam.botrel@gmail.com>
Date: Mon, 7 Oct 2024 12:17:26 -0500
Subject: [PATCH 079/114] test: fix windows build

---
 field/generator/asm/amd64/build.go | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/field/generator/asm/amd64/build.go b/field/generator/asm/amd64/build.go
index ccf41c4e83..9f2e44bd1a 100644
--- a/field/generator/asm/amd64/build.go
+++ b/field/generator/asm/amd64/build.go
@@ -253,7 +253,12 @@ func GenerateFieldWrapper(w io.Writer, F *config.FieldConfig, asmDirBuildPath, a
 
 		f.WriteLn("// Code generated by gnark-crypto/generator. DO NOT EDIT.")
 		f.WriteLn(fmt.Sprintf("// We include the hash to force the Go compiler to recompile: %d", hash))
-		f.WriteLn(fmt.Sprintf("#include \"%s\"\n", filepath.Join(asmDirIncludePath, fileName)))
+		includePath := filepath.Join(asmDirIncludePath, fileName)
+		// on windows, we replace the "\" by "/"
+		if filepath.Separator == '\\' {
+			includePath = strings.ReplaceAll(includePath, "\\", "/")
+		}
+		f.WriteLn(fmt.Sprintf("#include \"%s\"\n", includePath))
 
 		return nil
 	}

From de674b4c64e955612c351fb16117ff4f89700a46 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Tue, 8 Oct 2024 13:00:12 +0200
Subject: [PATCH 080/114] feat: example shplonk

---
 ecc/bls12-377/shplonk/example_test.go | 63 +++++++++++++++++++++++++++
 1 file changed, 63 insertions(+)
 create mode 100644 ecc/bls12-377/shplonk/example_test.go

diff --git a/ecc/bls12-377/shplonk/example_test.go b/ecc/bls12-377/shplonk/example_test.go
new file mode 100644
index 0000000000..e913991e42
--- /dev/null
+++ b/ecc/bls12-377/shplonk/example_test.go
@@ -0,0 +1,63 @@
+package shplonk
+
+import (
+	"crypto/sha256"
+	"fmt"
+
+	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls12-377/kzg"
+)
+
+// This example shows how to batch open a list of polynomials on a set of points,
+// where each polynomial is opened on its own set of point.
+// That is the i-th polynomial f_i is opened on  set of point S_i.
+func Example_batchOpen() {
+
+	const nbPolynomials = 10
+
+	// sample a list of points and a list of polynomials. The i-th polynomial
+	// is opened on the i-th set of points, there might be several points per set.
+	points := make([][]fr.Element, nbPolynomials)
+	polynomials := make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
+
+		polynomials[i] = make([]fr.Element, 20+2*i) // random size
+		for j := 0; j < 20+2*i; j++ {
+			polynomials[i][j].SetRandom()
+		}
+
+		points[i] = make([]fr.Element, i+1) // random number of point
+		for j := 0; j < i+1; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+
+	// Create commitments for each polynomials
+	var err error
+	digests := make([]kzg.Digest, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
+		digests[i], err = kzg.Commit(polynomials[i], testSrs.Pk)
+		if err != nil {
+			panic(err)
+		}
+	}
+
+	// hash function that is used for the challenge derivation in Fiat Shamir
+	hf := sha256.New()
+
+	// ceate an opening proof of polynomials[i] on the set points[i]
+	openingProof, err := BatchOpen(polynomials, digests, points, hf, testSrs.Pk)
+	if err != nil {
+		panic(err)
+	}
+
+	// we verify the proof. If the proof is correct, then openingProof[i][j] contains
+	// the evaluation of the polynomials[i] on points[i][j]
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	if err != nil {
+		panic(err)
+	}
+
+	fmt.Println("verified")
+	// output: verified
+}

From 5fc53f3014ee49c028cb80666b79d3f1236d7d4f Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Tue, 8 Oct 2024 13:06:50 +0200
Subject: [PATCH 081/114] feat: code gen

---
 ecc/bls12-377/shplonk/example_test.go         | 16 ++++
 ecc/bls12-381/shplonk/example_test.go         | 79 +++++++++++++++++++
 ecc/bls24-315/shplonk/example_test.go         | 79 +++++++++++++++++++
 ecc/bls24-317/shplonk/example_test.go         | 79 +++++++++++++++++++
 ecc/bn254/shplonk/example_test.go             | 79 +++++++++++++++++++
 ecc/bw6-633/shplonk/example_test.go           | 79 +++++++++++++++++++
 ecc/bw6-761/shplonk/example_test.go           | 79 +++++++++++++++++++
 internal/generator/shplonk/generator.go       |  1 +
 .../shplonk/template/example_test.go.tmpl     | 61 ++++++++++++++
 9 files changed, 552 insertions(+)
 create mode 100644 ecc/bls12-381/shplonk/example_test.go
 create mode 100644 ecc/bls24-315/shplonk/example_test.go
 create mode 100644 ecc/bls24-317/shplonk/example_test.go
 create mode 100644 ecc/bn254/shplonk/example_test.go
 create mode 100644 ecc/bw6-633/shplonk/example_test.go
 create mode 100644 ecc/bw6-761/shplonk/example_test.go
 create mode 100644 internal/generator/shplonk/template/example_test.go.tmpl

diff --git a/ecc/bls12-377/shplonk/example_test.go b/ecc/bls12-377/shplonk/example_test.go
index e913991e42..88c7e07c8d 100644
--- a/ecc/bls12-377/shplonk/example_test.go
+++ b/ecc/bls12-377/shplonk/example_test.go
@@ -1,3 +1,19 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
 package shplonk
 
 import (
diff --git a/ecc/bls12-381/shplonk/example_test.go b/ecc/bls12-381/shplonk/example_test.go
new file mode 100644
index 0000000000..f575f56875
--- /dev/null
+++ b/ecc/bls12-381/shplonk/example_test.go
@@ -0,0 +1,79 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"crypto/sha256"
+	"fmt"
+
+	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls12-381/kzg"
+)
+
+// This example shows how to batch open a list of polynomials on a set of points,
+// where each polynomial is opened on its own set of point.
+// That is the i-th polynomial f_i is opened on  set of point S_i.
+func Example_batchOpen() {
+
+	const nbPolynomials = 10
+
+	// sample a list of points and a list of polynomials. The i-th polynomial
+	// is opened on the i-th set of points, there might be several points per set.
+	points := make([][]fr.Element, nbPolynomials)
+	polynomials := make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
+
+		polynomials[i] = make([]fr.Element, 20+2*i) // random size
+		for j := 0; j < 20+2*i; j++ {
+			polynomials[i][j].SetRandom()
+		}
+
+		points[i] = make([]fr.Element, i+1) // random number of point
+		for j := 0; j < i+1; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+
+	// Create commitments for each polynomials
+	var err error
+	digests := make([]kzg.Digest, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
+		digests[i], err = kzg.Commit(polynomials[i], testSrs.Pk)
+		if err != nil {
+			panic(err)
+		}
+	}
+
+	// hash function that is used for the challenge derivation in Fiat Shamir
+	hf := sha256.New()
+
+	// ceate an opening proof of polynomials[i] on the set points[i]
+	openingProof, err := BatchOpen(polynomials, digests, points, hf, testSrs.Pk)
+	if err != nil {
+		panic(err)
+	}
+
+	// we verify the proof. If the proof is correct, then openingProof[i][j] contains
+	// the evaluation of the polynomials[i] on points[i][j]
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	if err != nil {
+		panic(err)
+	}
+
+	fmt.Println("verified")
+	// output: verified
+}
diff --git a/ecc/bls24-315/shplonk/example_test.go b/ecc/bls24-315/shplonk/example_test.go
new file mode 100644
index 0000000000..2185a37ccb
--- /dev/null
+++ b/ecc/bls24-315/shplonk/example_test.go
@@ -0,0 +1,79 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"crypto/sha256"
+	"fmt"
+
+	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls24-315/kzg"
+)
+
+// This example shows how to batch open a list of polynomials on a set of points,
+// where each polynomial is opened on its own set of point.
+// That is the i-th polynomial f_i is opened on  set of point S_i.
+func Example_batchOpen() {
+
+	const nbPolynomials = 10
+
+	// sample a list of points and a list of polynomials. The i-th polynomial
+	// is opened on the i-th set of points, there might be several points per set.
+	points := make([][]fr.Element, nbPolynomials)
+	polynomials := make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
+
+		polynomials[i] = make([]fr.Element, 20+2*i) // random size
+		for j := 0; j < 20+2*i; j++ {
+			polynomials[i][j].SetRandom()
+		}
+
+		points[i] = make([]fr.Element, i+1) // random number of point
+		for j := 0; j < i+1; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+
+	// Create commitments for each polynomials
+	var err error
+	digests := make([]kzg.Digest, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
+		digests[i], err = kzg.Commit(polynomials[i], testSrs.Pk)
+		if err != nil {
+			panic(err)
+		}
+	}
+
+	// hash function that is used for the challenge derivation in Fiat Shamir
+	hf := sha256.New()
+
+	// ceate an opening proof of polynomials[i] on the set points[i]
+	openingProof, err := BatchOpen(polynomials, digests, points, hf, testSrs.Pk)
+	if err != nil {
+		panic(err)
+	}
+
+	// we verify the proof. If the proof is correct, then openingProof[i][j] contains
+	// the evaluation of the polynomials[i] on points[i][j]
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	if err != nil {
+		panic(err)
+	}
+
+	fmt.Println("verified")
+	// output: verified
+}
diff --git a/ecc/bls24-317/shplonk/example_test.go b/ecc/bls24-317/shplonk/example_test.go
new file mode 100644
index 0000000000..237b13ef60
--- /dev/null
+++ b/ecc/bls24-317/shplonk/example_test.go
@@ -0,0 +1,79 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"crypto/sha256"
+	"fmt"
+
+	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls24-317/kzg"
+)
+
+// This example shows how to batch open a list of polynomials on a set of points,
+// where each polynomial is opened on its own set of point.
+// That is the i-th polynomial f_i is opened on  set of point S_i.
+func Example_batchOpen() {
+
+	const nbPolynomials = 10
+
+	// sample a list of points and a list of polynomials. The i-th polynomial
+	// is opened on the i-th set of points, there might be several points per set.
+	points := make([][]fr.Element, nbPolynomials)
+	polynomials := make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
+
+		polynomials[i] = make([]fr.Element, 20+2*i) // random size
+		for j := 0; j < 20+2*i; j++ {
+			polynomials[i][j].SetRandom()
+		}
+
+		points[i] = make([]fr.Element, i+1) // random number of point
+		for j := 0; j < i+1; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+
+	// Create commitments for each polynomials
+	var err error
+	digests := make([]kzg.Digest, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
+		digests[i], err = kzg.Commit(polynomials[i], testSrs.Pk)
+		if err != nil {
+			panic(err)
+		}
+	}
+
+	// hash function that is used for the challenge derivation in Fiat Shamir
+	hf := sha256.New()
+
+	// ceate an opening proof of polynomials[i] on the set points[i]
+	openingProof, err := BatchOpen(polynomials, digests, points, hf, testSrs.Pk)
+	if err != nil {
+		panic(err)
+	}
+
+	// we verify the proof. If the proof is correct, then openingProof[i][j] contains
+	// the evaluation of the polynomials[i] on points[i][j]
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	if err != nil {
+		panic(err)
+	}
+
+	fmt.Println("verified")
+	// output: verified
+}
diff --git a/ecc/bn254/shplonk/example_test.go b/ecc/bn254/shplonk/example_test.go
new file mode 100644
index 0000000000..e839ce1e16
--- /dev/null
+++ b/ecc/bn254/shplonk/example_test.go
@@ -0,0 +1,79 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"crypto/sha256"
+	"fmt"
+
+	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
+	"github.com/consensys/gnark-crypto/ecc/bn254/kzg"
+)
+
+// This example shows how to batch open a list of polynomials on a set of points,
+// where each polynomial is opened on its own set of point.
+// That is the i-th polynomial f_i is opened on  set of point S_i.
+func Example_batchOpen() {
+
+	const nbPolynomials = 10
+
+	// sample a list of points and a list of polynomials. The i-th polynomial
+	// is opened on the i-th set of points, there might be several points per set.
+	points := make([][]fr.Element, nbPolynomials)
+	polynomials := make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
+
+		polynomials[i] = make([]fr.Element, 20+2*i) // random size
+		for j := 0; j < 20+2*i; j++ {
+			polynomials[i][j].SetRandom()
+		}
+
+		points[i] = make([]fr.Element, i+1) // random number of point
+		for j := 0; j < i+1; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+
+	// Create commitments for each polynomials
+	var err error
+	digests := make([]kzg.Digest, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
+		digests[i], err = kzg.Commit(polynomials[i], testSrs.Pk)
+		if err != nil {
+			panic(err)
+		}
+	}
+
+	// hash function that is used for the challenge derivation in Fiat Shamir
+	hf := sha256.New()
+
+	// ceate an opening proof of polynomials[i] on the set points[i]
+	openingProof, err := BatchOpen(polynomials, digests, points, hf, testSrs.Pk)
+	if err != nil {
+		panic(err)
+	}
+
+	// we verify the proof. If the proof is correct, then openingProof[i][j] contains
+	// the evaluation of the polynomials[i] on points[i][j]
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	if err != nil {
+		panic(err)
+	}
+
+	fmt.Println("verified")
+	// output: verified
+}
diff --git a/ecc/bw6-633/shplonk/example_test.go b/ecc/bw6-633/shplonk/example_test.go
new file mode 100644
index 0000000000..d13fd51dfe
--- /dev/null
+++ b/ecc/bw6-633/shplonk/example_test.go
@@ -0,0 +1,79 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"crypto/sha256"
+	"fmt"
+
+	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
+	"github.com/consensys/gnark-crypto/ecc/bw6-633/kzg"
+)
+
+// This example shows how to batch open a list of polynomials on a set of points,
+// where each polynomial is opened on its own set of point.
+// That is the i-th polynomial f_i is opened on  set of point S_i.
+func Example_batchOpen() {
+
+	const nbPolynomials = 10
+
+	// sample a list of points and a list of polynomials. The i-th polynomial
+	// is opened on the i-th set of points, there might be several points per set.
+	points := make([][]fr.Element, nbPolynomials)
+	polynomials := make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
+
+		polynomials[i] = make([]fr.Element, 20+2*i) // random size
+		for j := 0; j < 20+2*i; j++ {
+			polynomials[i][j].SetRandom()
+		}
+
+		points[i] = make([]fr.Element, i+1) // random number of point
+		for j := 0; j < i+1; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+
+	// Create commitments for each polynomials
+	var err error
+	digests := make([]kzg.Digest, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
+		digests[i], err = kzg.Commit(polynomials[i], testSrs.Pk)
+		if err != nil {
+			panic(err)
+		}
+	}
+
+	// hash function that is used for the challenge derivation in Fiat Shamir
+	hf := sha256.New()
+
+	// ceate an opening proof of polynomials[i] on the set points[i]
+	openingProof, err := BatchOpen(polynomials, digests, points, hf, testSrs.Pk)
+	if err != nil {
+		panic(err)
+	}
+
+	// we verify the proof. If the proof is correct, then openingProof[i][j] contains
+	// the evaluation of the polynomials[i] on points[i][j]
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	if err != nil {
+		panic(err)
+	}
+
+	fmt.Println("verified")
+	// output: verified
+}
diff --git a/ecc/bw6-761/shplonk/example_test.go b/ecc/bw6-761/shplonk/example_test.go
new file mode 100644
index 0000000000..6beff08c10
--- /dev/null
+++ b/ecc/bw6-761/shplonk/example_test.go
@@ -0,0 +1,79 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package shplonk
+
+import (
+	"crypto/sha256"
+	"fmt"
+
+	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
+	"github.com/consensys/gnark-crypto/ecc/bw6-761/kzg"
+)
+
+// This example shows how to batch open a list of polynomials on a set of points,
+// where each polynomial is opened on its own set of point.
+// That is the i-th polynomial f_i is opened on  set of point S_i.
+func Example_batchOpen() {
+
+	const nbPolynomials = 10
+
+	// sample a list of points and a list of polynomials. The i-th polynomial
+	// is opened on the i-th set of points, there might be several points per set.
+	points := make([][]fr.Element, nbPolynomials)
+	polynomials := make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
+
+		polynomials[i] = make([]fr.Element, 20+2*i) // random size
+		for j := 0; j < 20+2*i; j++ {
+			polynomials[i][j].SetRandom()
+		}
+
+		points[i] = make([]fr.Element, i+1) // random number of point
+		for j := 0; j < i+1; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+
+	// Create commitments for each polynomials
+	var err error
+	digests := make([]kzg.Digest, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
+		digests[i], err = kzg.Commit(polynomials[i], testSrs.Pk)
+		if err != nil {
+			panic(err)
+		}
+	}
+
+	// hash function that is used for the challenge derivation in Fiat Shamir
+	hf := sha256.New()
+
+	// ceate an opening proof of polynomials[i] on the set points[i]
+	openingProof, err := BatchOpen(polynomials, digests, points, hf, testSrs.Pk)
+	if err != nil {
+		panic(err)
+	}
+
+	// we verify the proof. If the proof is correct, then openingProof[i][j] contains
+	// the evaluation of the polynomials[i] on points[i][j]
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	if err != nil {
+		panic(err)
+	}
+
+	fmt.Println("verified")
+	// output: verified
+}
diff --git a/internal/generator/shplonk/generator.go b/internal/generator/shplonk/generator.go
index 94e1118300..15d72c2589 100644
--- a/internal/generator/shplonk/generator.go
+++ b/internal/generator/shplonk/generator.go
@@ -16,6 +16,7 @@ func Generate(conf config.Curve, baseDir string, bgen *bavard.BatchGenerator) er
 		{File: filepath.Join(baseDir, "shplonk.go"), Templates: []string{"shplonk.go.tmpl"}},
 		{File: filepath.Join(baseDir, "shplonk_test.go"), Templates: []string{"shplonk.test.go.tmpl"}},
 		{File: filepath.Join(baseDir, "marshal.go"), Templates: []string{"marshal.go.tmpl"}},
+		{File: filepath.Join(baseDir, "example_test.go"), Templates: []string{"example_test.go.tmpl"}},
 		// {File: filepath.Join(baseDir, "utils.go"), Templates: []string{"utils.go.tmpl"}},
 	}
 	return bgen.Generate(conf, conf.Package, "./shplonk/template/", entries...)
diff --git a/internal/generator/shplonk/template/example_test.go.tmpl b/internal/generator/shplonk/template/example_test.go.tmpl
new file mode 100644
index 0000000000..6a492b522e
--- /dev/null
+++ b/internal/generator/shplonk/template/example_test.go.tmpl
@@ -0,0 +1,61 @@
+import (
+	"crypto/sha256"
+	"fmt"
+
+	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/fr"
+	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/kzg"
+)
+
+// This example shows how to batch open a list of polynomials on a set of points,
+// where each polynomial is opened on its own set of point.
+// That is the i-th polynomial f_i is opened on  set of point S_i.
+func Example_batchOpen() {
+
+	const nbPolynomials = 10
+
+	// sample a list of points and a list of polynomials. The i-th polynomial
+	// is opened on the i-th set of points, there might be several points per set.
+	points := make([][]fr.Element, nbPolynomials)
+	polynomials := make([][]fr.Element, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
+
+		polynomials[i] = make([]fr.Element, 20+2*i) // random size
+		for j := 0; j < 20+2*i; j++ {
+			polynomials[i][j].SetRandom()
+		}
+
+		points[i] = make([]fr.Element, i+1) // random number of point
+		for j := 0; j < i+1; j++ {
+			points[i][j].SetRandom()
+		}
+	}
+
+	// Create commitments for each polynomials
+	var err error
+	digests := make([]kzg.Digest, nbPolynomials)
+	for i := 0; i < nbPolynomials; i++ {
+		digests[i], err = kzg.Commit(polynomials[i], testSrs.Pk)
+		if err != nil {
+			panic(err)
+		}
+	}
+
+	// hash function that is used for the challenge derivation in Fiat Shamir
+	hf := sha256.New()
+
+	// ceate an opening proof of polynomials[i] on the set points[i]
+	openingProof, err := BatchOpen(polynomials, digests, points, hf, testSrs.Pk)
+	if err != nil {
+		panic(err)
+	}
+
+	// we verify the proof. If the proof is correct, then openingProof[i][j] contains
+	// the evaluation of the polynomials[i] on points[i][j]
+	err = BatchVerify(openingProof, digests, points, hf, testSrs.Vk)
+	if err != nil {
+		panic(err)
+	}
+
+	fmt.Println("verified")
+	// output: verified
+}

From 5cf6c02ad5b47db3a02b8dccbb1c611901a6fc8b Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Tue, 8 Oct 2024 17:09:55 +0200
Subject: [PATCH 082/114] feat: example fflonk

---
 ecc/bls12-377/fflonk/example_test.go | 68 ++++++++++++++++++++++++++++
 1 file changed, 68 insertions(+)
 create mode 100644 ecc/bls12-377/fflonk/example_test.go

diff --git a/ecc/bls12-377/fflonk/example_test.go b/ecc/bls12-377/fflonk/example_test.go
new file mode 100644
index 0000000000..8ef443e87d
--- /dev/null
+++ b/ecc/bls12-377/fflonk/example_test.go
@@ -0,0 +1,68 @@
+package fflonk
+
+import (
+	"crypto/sha256"
+
+	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls12-377/kzg"
+)
+
+// This example demonstrates how to open a list of polynomials on a list of points.
+func Example_batchOpen() {
+
+	// sample a list of polynomials, we have 5 packs of polynomials,
+	// each pack will be opened on its own set of points.
+	nbPacks := 5
+
+	// The first set of polynomials contains 2 polynomials, the second 3, etc.
+	// The i-th set of polynomials is opened on the i-th set of points. The first
+	// set of point contains 4 points, the second 5, etc.
+	nbPolynomialsPerPack := []int{2, 3, 4, 5, 6}
+	nbPointsPerPack := []int{4, 5, 6, 7, 8}
+	points := make([][]fr.Element, nbPacks)
+	polynomials := make([][][]fr.Element, nbPacks)
+	for i := 0; i < nbPacks; i++ {
+		polynomials[i] = make([][]fr.Element, nbPolynomialsPerPack[i])
+		for j := 0; j < nbPointsPerPack[i]; j++ {
+
+			// random size for the polynomials
+			polynomials[i][j] = make([]fr.Element, j+10)
+		}
+
+		// random number of points per pack
+		points[i] = make([]fr.Element, i+5)
+	}
+
+	// commit to the folded Polynomials. In each pack, we fold the polynomials in a similar way
+	// as in the FFT. If the given pack contains 3 polynomials P1,P2,P3, the folded polynomial
+	// that we commit to is P1(X^t)+XP2(X^t)+X^2P3(X^t) where t is the smallest number dividing
+	// r-1 bounding above the number of polynomials, which is 3 here.
+	var err error
+	digests := make([]kzg.Digest, nbPacks)
+	for i := 0; i < nbPacks; i++ {
+		digests[i], err = FoldAndCommit(polynomials[i], testSrs.Pk)
+		if err != nil {
+			panic(err)
+		}
+	}
+
+	// compute the opening proof. We first pick a hash function that will be used for the FS challenge
+	// derivation.
+	hf := sha256.New()
+	proof, err := BatchOpen(polynomials, digests, points, hf, testSrs.Pk)
+	if err != nil {
+		panic(err)
+	}
+
+	// Check the opening proof. The claimed values of the i-th pack of polynomials are the evaluation
+	// of the i-th pack of polynomials, evaluated on the t-th powers of points[i], where t is the smallest
+	// integer bounding above the number of polynomials in the pack that divides r-1, the field on which
+	// the polynomials are defined.
+	//
+	// For instance, proof.ClaimedValues[i][j][k] contains the evaluation of the j-th polynomial of the i-th
+	// pack, on points[i][k]^t, where t is defined as above.
+	err = BatchVerify(proof, digests, points, hf, testSrs.Vk)
+	if err != nil {
+		panic(err)
+	}
+}

From 6b5bc8d083ea13e4015a9cb1202491b1038e6a42 Mon Sep 17 00:00:00 2001
From: Thomas Piellard <thomas.piellard@consensys.net>
Date: Tue, 8 Oct 2024 17:23:22 +0200
Subject: [PATCH 083/114] feat: code gen

---
 ecc/bls12-377/fflonk/example_test.go          | 16 ++++
 ecc/bls12-381/fflonk/example_test.go          | 84 +++++++++++++++++++
 ecc/bls24-315/fflonk/example_test.go          | 84 +++++++++++++++++++
 ecc/bls24-317/fflonk/example_test.go          | 84 +++++++++++++++++++
 ecc/bn254/fflonk/example_test.go              | 84 +++++++++++++++++++
 ecc/bw6-633/fflonk/example_test.go            | 84 +++++++++++++++++++
 ecc/bw6-761/fflonk/example_test.go            | 84 +++++++++++++++++++
 internal/generator/fflonk/generator.go        |  1 +
 .../fflonk/template/example_test.go.tmpl      | 66 +++++++++++++++
 9 files changed, 587 insertions(+)
 create mode 100644 ecc/bls12-381/fflonk/example_test.go
 create mode 100644 ecc/bls24-315/fflonk/example_test.go
 create mode 100644 ecc/bls24-317/fflonk/example_test.go
 create mode 100644 ecc/bn254/fflonk/example_test.go
 create mode 100644 ecc/bw6-633/fflonk/example_test.go
 create mode 100644 ecc/bw6-761/fflonk/example_test.go
 create mode 100644 internal/generator/fflonk/template/example_test.go.tmpl

diff --git a/ecc/bls12-377/fflonk/example_test.go b/ecc/bls12-377/fflonk/example_test.go
index 8ef443e87d..43bde4e804 100644
--- a/ecc/bls12-377/fflonk/example_test.go
+++ b/ecc/bls12-377/fflonk/example_test.go
@@ -1,3 +1,19 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
 package fflonk
 
 import (
diff --git a/ecc/bls12-381/fflonk/example_test.go b/ecc/bls12-381/fflonk/example_test.go
new file mode 100644
index 0000000000..61bd6079f4
--- /dev/null
+++ b/ecc/bls12-381/fflonk/example_test.go
@@ -0,0 +1,84 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"crypto/sha256"
+
+	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls12-381/kzg"
+)
+
+// This example demonstrates how to open a list of polynomials on a list of points.
+func Example_batchOpen() {
+
+	// sample a list of polynomials, we have 5 packs of polynomials,
+	// each pack will be opened on its own set of points.
+	nbPacks := 5
+
+	// The first set of polynomials contains 2 polynomials, the second 3, etc.
+	// The i-th set of polynomials is opened on the i-th set of points. The first
+	// set of point contains 4 points, the second 5, etc.
+	nbPolynomialsPerPack := []int{2, 3, 4, 5, 6}
+	nbPointsPerPack := []int{4, 5, 6, 7, 8}
+	points := make([][]fr.Element, nbPacks)
+	polynomials := make([][][]fr.Element, nbPacks)
+	for i := 0; i < nbPacks; i++ {
+		polynomials[i] = make([][]fr.Element, nbPolynomialsPerPack[i])
+		for j := 0; j < nbPointsPerPack[i]; j++ {
+
+			// random size for the polynomials
+			polynomials[i][j] = make([]fr.Element, j+10)
+		}
+
+		// random number of points per pack
+		points[i] = make([]fr.Element, i+5)
+	}
+
+	// commit to the folded Polynomials. In each pack, we fold the polynomials in a similar way
+	// as in the FFT. If the given pack contains 3 polynomials P1,P2,P3, the folded polynomial
+	// that we commit to is P1(X^t)+XP2(X^t)+X^2P3(X^t) where t is the smallest number dividing
+	// r-1 bounding above the number of polynomials, which is 3 here.
+	var err error
+	digests := make([]kzg.Digest, nbPacks)
+	for i := 0; i < nbPacks; i++ {
+		digests[i], err = FoldAndCommit(polynomials[i], testSrs.Pk)
+		if err != nil {
+			panic(err)
+		}
+	}
+
+	// compute the opening proof. We first pick a hash function that will be used for the FS challenge
+	// derivation.
+	hf := sha256.New()
+	proof, err := BatchOpen(polynomials, digests, points, hf, testSrs.Pk)
+	if err != nil {
+		panic(err)
+	}
+
+	// Check the opening proof. The claimed values of the i-th pack of polynomials are the evaluation
+	// of the i-th pack of polynomials, evaluated on the t-th powers of points[i], where t is the smallest
+	// integer bounding above the number of polynomials in the pack that divides r-1, the field on which
+	// the polynomials are defined.
+	//
+	// For instance, proof.ClaimedValues[i][j][k] contains the evaluation of the j-th polynomial of the i-th
+	// pack, on points[i][k]^t, where t is defined as above.
+	err = BatchVerify(proof, digests, points, hf, testSrs.Vk)
+	if err != nil {
+		panic(err)
+	}
+}
diff --git a/ecc/bls24-315/fflonk/example_test.go b/ecc/bls24-315/fflonk/example_test.go
new file mode 100644
index 0000000000..ffc84295c6
--- /dev/null
+++ b/ecc/bls24-315/fflonk/example_test.go
@@ -0,0 +1,84 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"crypto/sha256"
+
+	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls24-315/kzg"
+)
+
+// This example demonstrates how to open a list of polynomials on a list of points.
+func Example_batchOpen() {
+
+	// sample a list of polynomials, we have 5 packs of polynomials,
+	// each pack will be opened on its own set of points.
+	nbPacks := 5
+
+	// The first set of polynomials contains 2 polynomials, the second 3, etc.
+	// The i-th set of polynomials is opened on the i-th set of points. The first
+	// set of point contains 4 points, the second 5, etc.
+	nbPolynomialsPerPack := []int{2, 3, 4, 5, 6}
+	nbPointsPerPack := []int{4, 5, 6, 7, 8}
+	points := make([][]fr.Element, nbPacks)
+	polynomials := make([][][]fr.Element, nbPacks)
+	for i := 0; i < nbPacks; i++ {
+		polynomials[i] = make([][]fr.Element, nbPolynomialsPerPack[i])
+		for j := 0; j < nbPointsPerPack[i]; j++ {
+
+			// random size for the polynomials
+			polynomials[i][j] = make([]fr.Element, j+10)
+		}
+
+		// random number of points per pack
+		points[i] = make([]fr.Element, i+5)
+	}
+
+	// commit to the folded Polynomials. In each pack, we fold the polynomials in a similar way
+	// as in the FFT. If the given pack contains 3 polynomials P1,P2,P3, the folded polynomial
+	// that we commit to is P1(X^t)+XP2(X^t)+X^2P3(X^t) where t is the smallest number dividing
+	// r-1 bounding above the number of polynomials, which is 3 here.
+	var err error
+	digests := make([]kzg.Digest, nbPacks)
+	for i := 0; i < nbPacks; i++ {
+		digests[i], err = FoldAndCommit(polynomials[i], testSrs.Pk)
+		if err != nil {
+			panic(err)
+		}
+	}
+
+	// compute the opening proof. We first pick a hash function that will be used for the FS challenge
+	// derivation.
+	hf := sha256.New()
+	proof, err := BatchOpen(polynomials, digests, points, hf, testSrs.Pk)
+	if err != nil {
+		panic(err)
+	}
+
+	// Check the opening proof. The claimed values of the i-th pack of polynomials are the evaluation
+	// of the i-th pack of polynomials, evaluated on the t-th powers of points[i], where t is the smallest
+	// integer bounding above the number of polynomials in the pack that divides r-1, the field on which
+	// the polynomials are defined.
+	//
+	// For instance, proof.ClaimedValues[i][j][k] contains the evaluation of the j-th polynomial of the i-th
+	// pack, on points[i][k]^t, where t is defined as above.
+	err = BatchVerify(proof, digests, points, hf, testSrs.Vk)
+	if err != nil {
+		panic(err)
+	}
+}
diff --git a/ecc/bls24-317/fflonk/example_test.go b/ecc/bls24-317/fflonk/example_test.go
new file mode 100644
index 0000000000..3d58b2b5aa
--- /dev/null
+++ b/ecc/bls24-317/fflonk/example_test.go
@@ -0,0 +1,84 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"crypto/sha256"
+
+	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls24-317/kzg"
+)
+
+// This example demonstrates how to open a list of polynomials on a list of points.
+func Example_batchOpen() {
+
+	// sample a list of polynomials, we have 5 packs of polynomials,
+	// each pack will be opened on its own set of points.
+	nbPacks := 5
+
+	// The first set of polynomials contains 2 polynomials, the second 3, etc.
+	// The i-th set of polynomials is opened on the i-th set of points. The first
+	// set of point contains 4 points, the second 5, etc.
+	nbPolynomialsPerPack := []int{2, 3, 4, 5, 6}
+	nbPointsPerPack := []int{4, 5, 6, 7, 8}
+	points := make([][]fr.Element, nbPacks)
+	polynomials := make([][][]fr.Element, nbPacks)
+	for i := 0; i < nbPacks; i++ {
+		polynomials[i] = make([][]fr.Element, nbPolynomialsPerPack[i])
+		for j := 0; j < nbPointsPerPack[i]; j++ {
+
+			// random size for the polynomials
+			polynomials[i][j] = make([]fr.Element, j+10)
+		}
+
+		// random number of points per pack
+		points[i] = make([]fr.Element, i+5)
+	}
+
+	// commit to the folded Polynomials. In each pack, we fold the polynomials in a similar way
+	// as in the FFT. If the given pack contains 3 polynomials P1,P2,P3, the folded polynomial
+	// that we commit to is P1(X^t)+XP2(X^t)+X^2P3(X^t) where t is the smallest number dividing
+	// r-1 bounding above the number of polynomials, which is 3 here.
+	var err error
+	digests := make([]kzg.Digest, nbPacks)
+	for i := 0; i < nbPacks; i++ {
+		digests[i], err = FoldAndCommit(polynomials[i], testSrs.Pk)
+		if err != nil {
+			panic(err)
+		}
+	}
+
+	// compute the opening proof. We first pick a hash function that will be used for the FS challenge
+	// derivation.
+	hf := sha256.New()
+	proof, err := BatchOpen(polynomials, digests, points, hf, testSrs.Pk)
+	if err != nil {
+		panic(err)
+	}
+
+	// Check the opening proof. The claimed values of the i-th pack of polynomials are the evaluation
+	// of the i-th pack of polynomials, evaluated on the t-th powers of points[i], where t is the smallest
+	// integer bounding above the number of polynomials in the pack that divides r-1, the field on which
+	// the polynomials are defined.
+	//
+	// For instance, proof.ClaimedValues[i][j][k] contains the evaluation of the j-th polynomial of the i-th
+	// pack, on points[i][k]^t, where t is defined as above.
+	err = BatchVerify(proof, digests, points, hf, testSrs.Vk)
+	if err != nil {
+		panic(err)
+	}
+}
diff --git a/ecc/bn254/fflonk/example_test.go b/ecc/bn254/fflonk/example_test.go
new file mode 100644
index 0000000000..a3c26b50b2
--- /dev/null
+++ b/ecc/bn254/fflonk/example_test.go
@@ -0,0 +1,84 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"crypto/sha256"
+
+	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
+	"github.com/consensys/gnark-crypto/ecc/bn254/kzg"
+)
+
+// This example demonstrates how to open a list of polynomials on a list of points.
+func Example_batchOpen() {
+
+	// sample a list of polynomials, we have 5 packs of polynomials,
+	// each pack will be opened on its own set of points.
+	nbPacks := 5
+
+	// The first set of polynomials contains 2 polynomials, the second 3, etc.
+	// The i-th set of polynomials is opened on the i-th set of points. The first
+	// set of point contains 4 points, the second 5, etc.
+	nbPolynomialsPerPack := []int{2, 3, 4, 5, 6}
+	nbPointsPerPack := []int{4, 5, 6, 7, 8}
+	points := make([][]fr.Element, nbPacks)
+	polynomials := make([][][]fr.Element, nbPacks)
+	for i := 0; i < nbPacks; i++ {
+		polynomials[i] = make([][]fr.Element, nbPolynomialsPerPack[i])
+		for j := 0; j < nbPointsPerPack[i]; j++ {
+
+			// random size for the polynomials
+			polynomials[i][j] = make([]fr.Element, j+10)
+		}
+
+		// random number of points per pack
+		points[i] = make([]fr.Element, i+5)
+	}
+
+	// commit to the folded Polynomials. In each pack, we fold the polynomials in a similar way
+	// as in the FFT. If the given pack contains 3 polynomials P1,P2,P3, the folded polynomial
+	// that we commit to is P1(X^t)+XP2(X^t)+X^2P3(X^t) where t is the smallest number dividing
+	// r-1 bounding above the number of polynomials, which is 3 here.
+	var err error
+	digests := make([]kzg.Digest, nbPacks)
+	for i := 0; i < nbPacks; i++ {
+		digests[i], err = FoldAndCommit(polynomials[i], testSrs.Pk)
+		if err != nil {
+			panic(err)
+		}
+	}
+
+	// compute the opening proof. We first pick a hash function that will be used for the FS challenge
+	// derivation.
+	hf := sha256.New()
+	proof, err := BatchOpen(polynomials, digests, points, hf, testSrs.Pk)
+	if err != nil {
+		panic(err)
+	}
+
+	// Check the opening proof. The claimed values of the i-th pack of polynomials are the evaluation
+	// of the i-th pack of polynomials, evaluated on the t-th powers of points[i], where t is the smallest
+	// integer bounding above the number of polynomials in the pack that divides r-1, the field on which
+	// the polynomials are defined.
+	//
+	// For instance, proof.ClaimedValues[i][j][k] contains the evaluation of the j-th polynomial of the i-th
+	// pack, on points[i][k]^t, where t is defined as above.
+	err = BatchVerify(proof, digests, points, hf, testSrs.Vk)
+	if err != nil {
+		panic(err)
+	}
+}
diff --git a/ecc/bw6-633/fflonk/example_test.go b/ecc/bw6-633/fflonk/example_test.go
new file mode 100644
index 0000000000..c02b2b8ae8
--- /dev/null
+++ b/ecc/bw6-633/fflonk/example_test.go
@@ -0,0 +1,84 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"crypto/sha256"
+
+	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
+	"github.com/consensys/gnark-crypto/ecc/bw6-633/kzg"
+)
+
+// This example demonstrates how to open a list of polynomials on a list of points.
+func Example_batchOpen() {
+
+	// sample a list of polynomials, we have 5 packs of polynomials,
+	// each pack will be opened on its own set of points.
+	nbPacks := 5
+
+	// The first set of polynomials contains 2 polynomials, the second 3, etc.
+	// The i-th set of polynomials is opened on the i-th set of points. The first
+	// set of point contains 4 points, the second 5, etc.
+	nbPolynomialsPerPack := []int{2, 3, 4, 5, 6}
+	nbPointsPerPack := []int{4, 5, 6, 7, 8}
+	points := make([][]fr.Element, nbPacks)
+	polynomials := make([][][]fr.Element, nbPacks)
+	for i := 0; i < nbPacks; i++ {
+		polynomials[i] = make([][]fr.Element, nbPolynomialsPerPack[i])
+		for j := 0; j < nbPointsPerPack[i]; j++ {
+
+			// random size for the polynomials
+			polynomials[i][j] = make([]fr.Element, j+10)
+		}
+
+		// random number of points per pack
+		points[i] = make([]fr.Element, i+5)
+	}
+
+	// commit to the folded Polynomials. In each pack, we fold the polynomials in a similar way
+	// as in the FFT. If the given pack contains 3 polynomials P1,P2,P3, the folded polynomial
+	// that we commit to is P1(X^t)+XP2(X^t)+X^2P3(X^t) where t is the smallest number dividing
+	// r-1 bounding above the number of polynomials, which is 3 here.
+	var err error
+	digests := make([]kzg.Digest, nbPacks)
+	for i := 0; i < nbPacks; i++ {
+		digests[i], err = FoldAndCommit(polynomials[i], testSrs.Pk)
+		if err != nil {
+			panic(err)
+		}
+	}
+
+	// compute the opening proof. We first pick a hash function that will be used for the FS challenge
+	// derivation.
+	hf := sha256.New()
+	proof, err := BatchOpen(polynomials, digests, points, hf, testSrs.Pk)
+	if err != nil {
+		panic(err)
+	}
+
+	// Check the opening proof. The claimed values of the i-th pack of polynomials are the evaluation
+	// of the i-th pack of polynomials, evaluated on the t-th powers of points[i], where t is the smallest
+	// integer bounding above the number of polynomials in the pack that divides r-1, the field on which
+	// the polynomials are defined.
+	//
+	// For instance, proof.ClaimedValues[i][j][k] contains the evaluation of the j-th polynomial of the i-th
+	// pack, on points[i][k]^t, where t is defined as above.
+	err = BatchVerify(proof, digests, points, hf, testSrs.Vk)
+	if err != nil {
+		panic(err)
+	}
+}
diff --git a/ecc/bw6-761/fflonk/example_test.go b/ecc/bw6-761/fflonk/example_test.go
new file mode 100644
index 0000000000..ea35977108
--- /dev/null
+++ b/ecc/bw6-761/fflonk/example_test.go
@@ -0,0 +1,84 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fflonk
+
+import (
+	"crypto/sha256"
+
+	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
+	"github.com/consensys/gnark-crypto/ecc/bw6-761/kzg"
+)
+
+// This example demonstrates how to open a list of polynomials on a list of points.
+func Example_batchOpen() {
+
+	// sample a list of polynomials, we have 5 packs of polynomials,
+	// each pack will be opened on its own set of points.
+	nbPacks := 5
+
+	// The first set of polynomials contains 2 polynomials, the second 3, etc.
+	// The i-th set of polynomials is opened on the i-th set of points. The first
+	// set of point contains 4 points, the second 5, etc.
+	nbPolynomialsPerPack := []int{2, 3, 4, 5, 6}
+	nbPointsPerPack := []int{4, 5, 6, 7, 8}
+	points := make([][]fr.Element, nbPacks)
+	polynomials := make([][][]fr.Element, nbPacks)
+	for i := 0; i < nbPacks; i++ {
+		polynomials[i] = make([][]fr.Element, nbPolynomialsPerPack[i])
+		for j := 0; j < nbPointsPerPack[i]; j++ {
+
+			// random size for the polynomials
+			polynomials[i][j] = make([]fr.Element, j+10)
+		}
+
+		// random number of points per pack
+		points[i] = make([]fr.Element, i+5)
+	}
+
+	// commit to the folded Polynomials. In each pack, we fold the polynomials in a similar way
+	// as in the FFT. If the given pack contains 3 polynomials P1,P2,P3, the folded polynomial
+	// that we commit to is P1(X^t)+XP2(X^t)+X^2P3(X^t) where t is the smallest number dividing
+	// r-1 bounding above the number of polynomials, which is 3 here.
+	var err error
+	digests := make([]kzg.Digest, nbPacks)
+	for i := 0; i < nbPacks; i++ {
+		digests[i], err = FoldAndCommit(polynomials[i], testSrs.Pk)
+		if err != nil {
+			panic(err)
+		}
+	}
+
+	// compute the opening proof. We first pick a hash function that will be used for the FS challenge
+	// derivation.
+	hf := sha256.New()
+	proof, err := BatchOpen(polynomials, digests, points, hf, testSrs.Pk)
+	if err != nil {
+		panic(err)
+	}
+
+	// Check the opening proof. The claimed values of the i-th pack of polynomials are the evaluation
+	// of the i-th pack of polynomials, evaluated on the t-th powers of points[i], where t is the smallest
+	// integer bounding above the number of polynomials in the pack that divides r-1, the field on which
+	// the polynomials are defined.
+	//
+	// For instance, proof.ClaimedValues[i][j][k] contains the evaluation of the j-th polynomial of the i-th
+	// pack, on points[i][k]^t, where t is defined as above.
+	err = BatchVerify(proof, digests, points, hf, testSrs.Vk)
+	if err != nil {
+		panic(err)
+	}
+}
diff --git a/internal/generator/fflonk/generator.go b/internal/generator/fflonk/generator.go
index 875c129dd8..5eba0c6a95 100644
--- a/internal/generator/fflonk/generator.go
+++ b/internal/generator/fflonk/generator.go
@@ -16,6 +16,7 @@ func Generate(conf config.Curve, baseDir string, bgen *bavard.BatchGenerator) er
 		{File: filepath.Join(baseDir, "fflonk.go"), Templates: []string{"fflonk.go.tmpl"}},
 		{File: filepath.Join(baseDir, "fflonk_test.go"), Templates: []string{"fflonk.test.go.tmpl"}},
 		{File: filepath.Join(baseDir, "marshal.go"), Templates: []string{"marshal.go.tmpl"}},
+		{File: filepath.Join(baseDir, "example_test.go"), Templates: []string{"example_test.go.tmpl"}},
 	}
 	return bgen.Generate(conf, conf.Package, "./fflonk/template/", entries...)
 
diff --git a/internal/generator/fflonk/template/example_test.go.tmpl b/internal/generator/fflonk/template/example_test.go.tmpl
new file mode 100644
index 0000000000..050a5f23eb
--- /dev/null
+++ b/internal/generator/fflonk/template/example_test.go.tmpl
@@ -0,0 +1,66 @@
+import (
+	"crypto/sha256"
+
+	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/fr"
+	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/kzg"
+)
+
+// This example demonstrates how to open a list of polynomials on a list of points.
+func Example_batchOpen() {
+
+	// sample a list of polynomials, we have 5 packs of polynomials,
+	// each pack will be opened on its own set of points.
+	nbPacks := 5
+
+	// The first set of polynomials contains 2 polynomials, the second 3, etc.
+	// The i-th set of polynomials is opened on the i-th set of points. The first
+	// set of point contains 4 points, the second 5, etc.
+	nbPolynomialsPerPack := []int{2, 3, 4, 5, 6}
+	nbPointsPerPack := []int{4, 5, 6, 7, 8}
+	points := make([][]fr.Element, nbPacks)
+	polynomials := make([][][]fr.Element, nbPacks)
+	for i := 0; i < nbPacks; i++ {
+		polynomials[i] = make([][]fr.Element, nbPolynomialsPerPack[i])
+		for j := 0; j < nbPointsPerPack[i]; j++ {
+
+			// random size for the polynomials
+			polynomials[i][j] = make([]fr.Element, j+10)
+		}
+
+		// random number of points per pack
+		points[i] = make([]fr.Element, i+5)
+	}
+
+	// commit to the folded Polynomials. In each pack, we fold the polynomials in a similar way
+	// as in the FFT. If the given pack contains 3 polynomials P1,P2,P3, the folded polynomial
+	// that we commit to is P1(X^t)+XP2(X^t)+X^2P3(X^t) where t is the smallest number dividing
+	// r-1 bounding above the number of polynomials, which is 3 here.
+	var err error
+	digests := make([]kzg.Digest, nbPacks)
+	for i := 0; i < nbPacks; i++ {
+		digests[i], err = FoldAndCommit(polynomials[i], testSrs.Pk)
+		if err != nil {
+			panic(err)
+		}
+	}
+
+	// compute the opening proof. We first pick a hash function that will be used for the FS challenge
+	// derivation.
+	hf := sha256.New()
+	proof, err := BatchOpen(polynomials, digests, points, hf, testSrs.Pk)
+	if err != nil {
+		panic(err)
+	}
+
+	// Check the opening proof. The claimed values of the i-th pack of polynomials are the evaluation
+	// of the i-th pack of polynomials, evaluated on the t-th powers of points[i], where t is the smallest
+	// integer bounding above the number of polynomials in the pack that divides r-1, the field on which
+	// the polynomials are defined.
+	//
+	// For instance, proof.ClaimedValues[i][j][k] contains the evaluation of the j-th polynomial of the i-th
+	// pack, on points[i][k]^t, where t is defined as above.
+	err = BatchVerify(proof, digests, points, hf, testSrs.Vk)
+	if err != nil {
+		panic(err)
+	}
+}

From 441b06ec40703b25e2c866ce3ef1c46cb6f1aadd Mon Sep 17 00:00:00 2001
From: Ivo Kubjas <ivo.kubjas@consensys.net>
Date: Thu, 10 Oct 2024 09:47:59 +0200
Subject: [PATCH 084/114] fix: buffer sufficient size (#551)

---
 ecc/bls12-377/shplonk/shplonk.go                    | 5 +++++
 ecc/bls12-381/shplonk/shplonk.go                    | 5 +++++
 ecc/bls24-315/shplonk/shplonk.go                    | 5 +++++
 ecc/bls24-317/shplonk/shplonk.go                    | 5 +++++
 ecc/bn254/shplonk/shplonk.go                        | 5 +++++
 ecc/bw6-633/shplonk/shplonk.go                      | 5 +++++
 ecc/bw6-761/shplonk/shplonk.go                      | 5 +++++
 internal/generator/shplonk/template/shplonk.go.tmpl | 5 +++++
 8 files changed, 40 insertions(+)

diff --git a/ecc/bls12-377/shplonk/shplonk.go b/ecc/bls12-377/shplonk/shplonk.go
index f2faa6d860..2124ccc6ac 100644
--- a/ecc/bls12-377/shplonk/shplonk.go
+++ b/ecc/bls12-377/shplonk/shplonk.go
@@ -80,6 +80,11 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 			maxSizePolys = len(polynomials[i])
 		}
 	}
+	for i := range points {
+		if len(points[i])+1 > maxSizePolys {
+			maxSizePolys = len(points[i]) + 1
+		}
+	}
 	nbPoints := 0
 	sizeSi := make([]int, len(points))
 	for i := 0; i < nbPolynomials; i++ {
diff --git a/ecc/bls12-381/shplonk/shplonk.go b/ecc/bls12-381/shplonk/shplonk.go
index d5adfa3f07..9c7a0de36d 100644
--- a/ecc/bls12-381/shplonk/shplonk.go
+++ b/ecc/bls12-381/shplonk/shplonk.go
@@ -80,6 +80,11 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 			maxSizePolys = len(polynomials[i])
 		}
 	}
+	for i := range points {
+		if len(points[i])+1 > maxSizePolys {
+			maxSizePolys = len(points[i]) + 1
+		}
+	}
 	nbPoints := 0
 	sizeSi := make([]int, len(points))
 	for i := 0; i < nbPolynomials; i++ {
diff --git a/ecc/bls24-315/shplonk/shplonk.go b/ecc/bls24-315/shplonk/shplonk.go
index 825c756cf3..f583310e1a 100644
--- a/ecc/bls24-315/shplonk/shplonk.go
+++ b/ecc/bls24-315/shplonk/shplonk.go
@@ -80,6 +80,11 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 			maxSizePolys = len(polynomials[i])
 		}
 	}
+	for i := range points {
+		if len(points[i])+1 > maxSizePolys {
+			maxSizePolys = len(points[i]) + 1
+		}
+	}
 	nbPoints := 0
 	sizeSi := make([]int, len(points))
 	for i := 0; i < nbPolynomials; i++ {
diff --git a/ecc/bls24-317/shplonk/shplonk.go b/ecc/bls24-317/shplonk/shplonk.go
index 33640bb695..9e3642463b 100644
--- a/ecc/bls24-317/shplonk/shplonk.go
+++ b/ecc/bls24-317/shplonk/shplonk.go
@@ -80,6 +80,11 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 			maxSizePolys = len(polynomials[i])
 		}
 	}
+	for i := range points {
+		if len(points[i])+1 > maxSizePolys {
+			maxSizePolys = len(points[i]) + 1
+		}
+	}
 	nbPoints := 0
 	sizeSi := make([]int, len(points))
 	for i := 0; i < nbPolynomials; i++ {
diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
index 90c7ea5bb1..1c6e6ad849 100644
--- a/ecc/bn254/shplonk/shplonk.go
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -80,6 +80,11 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 			maxSizePolys = len(polynomials[i])
 		}
 	}
+	for i := range points {
+		if len(points[i])+1 > maxSizePolys {
+			maxSizePolys = len(points[i]) + 1
+		}
+	}
 	nbPoints := 0
 	sizeSi := make([]int, len(points))
 	for i := 0; i < nbPolynomials; i++ {
diff --git a/ecc/bw6-633/shplonk/shplonk.go b/ecc/bw6-633/shplonk/shplonk.go
index af23c6ec58..56375f157f 100644
--- a/ecc/bw6-633/shplonk/shplonk.go
+++ b/ecc/bw6-633/shplonk/shplonk.go
@@ -80,6 +80,11 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 			maxSizePolys = len(polynomials[i])
 		}
 	}
+	for i := range points {
+		if len(points[i])+1 > maxSizePolys {
+			maxSizePolys = len(points[i]) + 1
+		}
+	}
 	nbPoints := 0
 	sizeSi := make([]int, len(points))
 	for i := 0; i < nbPolynomials; i++ {
diff --git a/ecc/bw6-761/shplonk/shplonk.go b/ecc/bw6-761/shplonk/shplonk.go
index b02bcd5451..aec562df5c 100644
--- a/ecc/bw6-761/shplonk/shplonk.go
+++ b/ecc/bw6-761/shplonk/shplonk.go
@@ -80,6 +80,11 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 			maxSizePolys = len(polynomials[i])
 		}
 	}
+	for i := range points {
+		if len(points[i])+1 > maxSizePolys {
+			maxSizePolys = len(points[i]) + 1
+		}
+	}
 	nbPoints := 0
 	sizeSi := make([]int, len(points))
 	for i := 0; i < nbPolynomials; i++ {
diff --git a/internal/generator/shplonk/template/shplonk.go.tmpl b/internal/generator/shplonk/template/shplonk.go.tmpl
index 94f83cc92f..0215fab854 100644
--- a/internal/generator/shplonk/template/shplonk.go.tmpl
+++ b/internal/generator/shplonk/template/shplonk.go.tmpl
@@ -62,6 +62,11 @@ func BatchOpen(polynomials [][]fr.Element, digests []kzg.Digest, points [][]fr.E
 			maxSizePolys = len(polynomials[i])
 		}
 	}
+	for i := range points {
+		if len(points[i])+1 > maxSizePolys {
+			maxSizePolys = len(points[i]) + 1
+		}
+	}
 	nbPoints := 0
 	sizeSi := make([]int, len(points))
 	for i := 0; i < nbPolynomials; i++ {

From 6f6fded2379d109d11a8bea20622bed19010d1e9 Mon Sep 17 00:00:00 2001
From: Arya Tabaie <arya.pourtabatabaie@gmail.com>
Date: Tue, 15 Oct 2024 14:16:38 -0500
Subject: [PATCH 085/114] Set `setInfinity` public (#552)

* feat: public setInfinity

* fix: s->S in tests

* build: generate

---------

Co-authored-by: Arya Tabaie <15056835+Tabaie@users.noreply.github.com>
---
 ecc/bls12-377/g1.go                           | 10 +++---
 ecc/bls12-377/g1_test.go                      |  2 +-
 ecc/bls12-377/g2.go                           | 10 +++---
 ecc/bls12-377/g2_test.go                      |  2 +-
 ecc/bls12-377/multiexp_affine.go              | 24 ++++++-------
 ecc/bls12-377/multiexp_jacobian.go            | 12 +++----
 ecc/bls12-377/multiexp_test.go                | 36 +++++++++----------
 ecc/bls12-381/g1.go                           | 10 +++---
 ecc/bls12-381/g1_test.go                      |  2 +-
 ecc/bls12-381/g2.go                           | 10 +++---
 ecc/bls12-381/g2_test.go                      |  2 +-
 ecc/bls12-381/multiexp_affine.go              | 24 ++++++-------
 ecc/bls12-381/multiexp_jacobian.go            | 12 +++----
 ecc/bls12-381/multiexp_test.go                | 36 +++++++++----------
 ecc/bls24-315/g1.go                           | 10 +++---
 ecc/bls24-315/g1_test.go                      |  2 +-
 ecc/bls24-315/g2.go                           | 10 +++---
 ecc/bls24-315/g2_test.go                      |  2 +-
 ecc/bls24-315/multiexp_affine.go              | 24 ++++++-------
 ecc/bls24-315/multiexp_jacobian.go            | 12 +++----
 ecc/bls24-315/multiexp_test.go                | 36 +++++++++----------
 ecc/bls24-317/g1.go                           | 10 +++---
 ecc/bls24-317/g1_test.go                      |  2 +-
 ecc/bls24-317/g2.go                           | 10 +++---
 ecc/bls24-317/g2_test.go                      |  2 +-
 ecc/bls24-317/multiexp_affine.go              | 24 ++++++-------
 ecc/bls24-317/multiexp_jacobian.go            | 12 +++----
 ecc/bls24-317/multiexp_test.go                | 36 +++++++++----------
 ecc/bn254/g1.go                               | 10 +++---
 ecc/bn254/g1_test.go                          |  2 +-
 ecc/bn254/g2.go                               | 10 +++---
 ecc/bn254/g2_test.go                          |  2 +-
 ecc/bn254/multiexp_affine.go                  | 24 ++++++-------
 ecc/bn254/multiexp_jacobian.go                | 12 +++----
 ecc/bn254/multiexp_test.go                    | 36 +++++++++----------
 ecc/bw6-633/g1.go                             | 10 +++---
 ecc/bw6-633/g1_test.go                        |  2 +-
 ecc/bw6-633/g2.go                             | 10 +++---
 ecc/bw6-633/g2_test.go                        |  2 +-
 ecc/bw6-633/multiexp_affine.go                | 24 ++++++-------
 ecc/bw6-633/multiexp_jacobian.go              | 12 +++----
 ecc/bw6-633/multiexp_test.go                  | 36 +++++++++----------
 ecc/bw6-761/g1.go                             | 10 +++---
 ecc/bw6-761/g1_test.go                        |  2 +-
 ecc/bw6-761/g2.go                             | 10 +++---
 ecc/bw6-761/g2_test.go                        |  2 +-
 ecc/bw6-761/multiexp_affine.go                | 24 ++++++-------
 ecc/bw6-761/multiexp_jacobian.go              | 12 +++----
 ecc/bw6-761/multiexp_test.go                  | 36 +++++++++----------
 ecc/secp256k1/g1.go                           | 10 +++---
 ecc/secp256k1/g1_test.go                      |  2 +-
 ecc/secp256k1/multiexp_affine.go              | 12 +++----
 ecc/secp256k1/multiexp_jacobian.go            |  6 ++--
 ecc/secp256k1/multiexp_test.go                | 18 +++++-----
 .../ecc/template/multiexp_affine.go.tmpl      | 12 +++----
 .../ecc/template/multiexp_jacobian.go.tmpl    |  6 ++--
 internal/generator/ecc/template/point.go.tmpl | 10 +++---
 .../ecc/template/tests/multiexp.go.tmpl       | 18 +++++-----
 .../ecc/template/tests/point.go.tmpl          |  2 +-
 59 files changed, 384 insertions(+), 384 deletions(-)

diff --git a/ecc/bls12-377/g1.go b/ecc/bls12-377/g1.go
index b0c8bcb523..a99d6c81d6 100644
--- a/ecc/bls12-377/g1.go
+++ b/ecc/bls12-377/g1.go
@@ -49,9 +49,9 @@ func (p *G1Affine) Set(a *G1Affine) *G1Affine {
 	return p
 }
 
-// setInfinity sets p to the infinity point, which is encoded as (0,0).
+// SetInfinity sets p to the infinity point, which is encoded as (0,0).
 // N.B.: (0,0) is never on the curve for j=0 curves (Y²=X³+B).
-func (p *G1Affine) setInfinity() *G1Affine {
+func (p *G1Affine) SetInfinity() *G1Affine {
 	p.X.SetZero()
 	p.Y.SetZero()
 	return p
@@ -99,7 +99,7 @@ func (p *G1Affine) Add(a, b *G1Affine) *G1Affine {
 			return p.FromJacobian(&q)
 		} else {
 			// if b == -a, we return 0
-			return p.setInfinity()
+			return p.SetInfinity()
 		}
 	}
 	var H, HH, I, J, r, V fp.Element
@@ -723,8 +723,8 @@ func (p *g1JacExtended) Set(q *g1JacExtended) *g1JacExtended {
 	return p
 }
 
-// setInfinity sets p to the infinity point (1,1,0,0).
-func (p *g1JacExtended) setInfinity() *g1JacExtended {
+// SetInfinity sets p to the infinity point (1,1,0,0).
+func (p *g1JacExtended) SetInfinity() *g1JacExtended {
 	p.X.SetOne()
 	p.Y.SetOne()
 	p.ZZ = fp.Element{}
diff --git a/ecc/bls12-377/g1_test.go b/ecc/bls12-377/g1_test.go
index d06b56297d..54afb43909 100644
--- a/ecc/bls12-377/g1_test.go
+++ b/ecc/bls12-377/g1_test.go
@@ -270,7 +270,7 @@ func TestG1AffineOps(t *testing.T) {
 			g := g1GenAff
 			s.BigInt(&sInt)
 			op1.ScalarMultiplication(&g, &sInt)
-			op2.setInfinity()
+			op2.SetInfinity()
 
 			op1.Add(&op1, &op2)
 			op2.Add(&op2, &op1)
diff --git a/ecc/bls12-377/g2.go b/ecc/bls12-377/g2.go
index 4162460343..3401a43a0f 100644
--- a/ecc/bls12-377/g2.go
+++ b/ecc/bls12-377/g2.go
@@ -55,9 +55,9 @@ func (p *G2Affine) Set(a *G2Affine) *G2Affine {
 	return p
 }
 
-// setInfinity sets p to the infinity point, which is encoded as (0,0).
+// SetInfinity sets p to the infinity point, which is encoded as (0,0).
 // N.B.: (0,0) is never on the curve for j=0 curves (Y²=X³+B).
-func (p *G2Affine) setInfinity() *G2Affine {
+func (p *G2Affine) SetInfinity() *G2Affine {
 	p.X.SetZero()
 	p.Y.SetZero()
 	return p
@@ -105,7 +105,7 @@ func (p *G2Affine) Add(a, b *G2Affine) *G2Affine {
 			return p.FromJacobian(&q)
 		} else {
 			// if b == -a, we return 0
-			return p.setInfinity()
+			return p.SetInfinity()
 		}
 	}
 	var H, HH, I, J, r, V fptower.E2
@@ -671,8 +671,8 @@ func (p *g2JacExtended) Set(q *g2JacExtended) *g2JacExtended {
 	return p
 }
 
-// setInfinity sets p to the infinity point (1,1,0,0).
-func (p *g2JacExtended) setInfinity() *g2JacExtended {
+// SetInfinity sets p to the infinity point (1,1,0,0).
+func (p *g2JacExtended) SetInfinity() *g2JacExtended {
 	p.X.SetOne()
 	p.Y.SetOne()
 	p.ZZ = fptower.E2{}
diff --git a/ecc/bls12-377/g2_test.go b/ecc/bls12-377/g2_test.go
index 4bd4b9a82f..78a4c50954 100644
--- a/ecc/bls12-377/g2_test.go
+++ b/ecc/bls12-377/g2_test.go
@@ -271,7 +271,7 @@ func TestG2AffineOps(t *testing.T) {
 			g := g2GenAff
 			s.BigInt(&sInt)
 			op1.ScalarMultiplication(&g, &sInt)
-			op2.setInfinity()
+			op2.SetInfinity()
 
 			op1.Add(&op1, &op2)
 			op2.Add(&op2, &op1)
diff --git a/ecc/bls12-377/multiexp_affine.go b/ecc/bls12-377/multiexp_affine.go
index 10f68ca4de..fcb768be9f 100644
--- a/ecc/bls12-377/multiexp_affine.go
+++ b/ecc/bls12-377/multiexp_affine.go
@@ -63,7 +63,7 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 	var buckets B // in G1Affine coordinates, infinity point is represented as (0,0), no need to init
 	var bucketsJE BJE
 	for i := 0; i < len(buckets); i++ {
-		bucketsJE[i].setInfinity()
+		bucketsJE[i].SetInfinity()
 	}
 
 	// setup for the batch affine;
@@ -106,7 +106,7 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 				bucketsJE[op.bucketID].addMixed(&op.point)
 				return
 			}
-			BK.setInfinity()
+			BK.SetInfinity()
 			return
 		}
 
@@ -134,12 +134,12 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 				if isAdd {
 					bucketsJE[bucketID].addMixed(PP)
 				} else {
-					BK.setInfinity()
+					BK.SetInfinity()
 				}
 				return
 			}
 			if isAdd {
-				BK.setInfinity()
+				BK.SetInfinity()
 			} else {
 				bucketsJE[bucketID].subMixed(PP)
 			}
@@ -221,8 +221,8 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 	// reduce buckets into total
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 	var runningSum, total g1JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		runningSum.addMixed(&buckets[k])
 		if !bucketsJE[k].IsInfinity() {
@@ -390,7 +390,7 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 	var buckets B // in G2Affine coordinates, infinity point is represented as (0,0), no need to init
 	var bucketsJE BJE
 	for i := 0; i < len(buckets); i++ {
-		bucketsJE[i].setInfinity()
+		bucketsJE[i].SetInfinity()
 	}
 
 	// setup for the batch affine;
@@ -433,7 +433,7 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 				bucketsJE[op.bucketID].addMixed(&op.point)
 				return
 			}
-			BK.setInfinity()
+			BK.SetInfinity()
 			return
 		}
 
@@ -461,12 +461,12 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 				if isAdd {
 					bucketsJE[bucketID].addMixed(PP)
 				} else {
-					BK.setInfinity()
+					BK.SetInfinity()
 				}
 				return
 			}
 			if isAdd {
-				BK.setInfinity()
+				BK.SetInfinity()
 			} else {
 				bucketsJE[bucketID].subMixed(PP)
 			}
@@ -548,8 +548,8 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 	// reduce buckets into total
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 	var runningSum, total g2JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		runningSum.addMixed(&buckets[k])
 		if !bucketsJE[k].IsInfinity() {
diff --git a/ecc/bls12-377/multiexp_jacobian.go b/ecc/bls12-377/multiexp_jacobian.go
index 9b2c3d2e2e..1c20a8b05b 100644
--- a/ecc/bls12-377/multiexp_jacobian.go
+++ b/ecc/bls12-377/multiexp_jacobian.go
@@ -30,7 +30,7 @@ func processChunkG1Jacobian[B ibg1JacExtended](chunk uint64,
 
 	var buckets B
 	for i := 0; i < len(buckets); i++ {
-		buckets[i].setInfinity()
+		buckets[i].SetInfinity()
 	}
 
 	// for each scalars, get the digit corresponding to the chunk we're processing.
@@ -53,8 +53,8 @@ func processChunkG1Jacobian[B ibg1JacExtended](chunk uint64,
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 
 	var runningSum, total g1JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		if !buckets[k].IsInfinity() {
 			runningSum.add(&buckets[k])
@@ -119,7 +119,7 @@ func processChunkG2Jacobian[B ibg2JacExtended](chunk uint64,
 
 	var buckets B
 	for i := 0; i < len(buckets); i++ {
-		buckets[i].setInfinity()
+		buckets[i].SetInfinity()
 	}
 
 	// for each scalars, get the digit corresponding to the chunk we're processing.
@@ -142,8 +142,8 @@ func processChunkG2Jacobian[B ibg2JacExtended](chunk uint64,
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 
 	var runningSum, total g2JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		if !buckets[k].IsInfinity() {
 			runningSum.add(&buckets[k])
diff --git a/ecc/bls12-377/multiexp_test.go b/ecc/bls12-377/multiexp_test.go
index 4d387cf87d..059cf586c3 100644
--- a/ecc/bls12-377/multiexp_test.go
+++ b/ecc/bls12-377/multiexp_test.go
@@ -57,10 +57,10 @@ func TestMultiExpG1(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	// final scalar to use in double and add method (without mixer factor)
 	// n(n+1)(2n+1)/6  (sum of the squares from 1 to n)
@@ -154,7 +154,7 @@ func TestMultiExpG1(t *testing.T) {
 			for i := 1; i <= nbSamples; i++ {
 				sampleScalars[i-1].SetUint64(uint64(i)).
 					Mul(&sampleScalars[i-1], &mixer)
-				samplePointsZero[i-1].setInfinity()
+				samplePointsZero[i-1].SetInfinity()
 			}
 
 			results := make([]G1Jac, len(cRange))
@@ -241,10 +241,10 @@ func TestCrossMultiExpG1(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	var sampleScalars [nbSamples]fr.Element
 	fillBenchScalars(sampleScalars[:])
@@ -471,10 +471,10 @@ func TestMultiExpG2(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	// final scalar to use in double and add method (without mixer factor)
 	// n(n+1)(2n+1)/6  (sum of the squares from 1 to n)
@@ -566,7 +566,7 @@ func TestMultiExpG2(t *testing.T) {
 			for i := 1; i <= nbSamples; i++ {
 				sampleScalars[i-1].SetUint64(uint64(i)).
 					Mul(&sampleScalars[i-1], &mixer)
-				samplePointsZero[i-1].setInfinity()
+				samplePointsZero[i-1].SetInfinity()
 			}
 
 			results := make([]G2Jac, len(cRange))
@@ -653,10 +653,10 @@ func TestCrossMultiExpG2(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	var sampleScalars [nbSamples]fr.Element
 	fillBenchScalars(sampleScalars[:])
diff --git a/ecc/bls12-381/g1.go b/ecc/bls12-381/g1.go
index 50ab4713e3..88ac32c77a 100644
--- a/ecc/bls12-381/g1.go
+++ b/ecc/bls12-381/g1.go
@@ -49,9 +49,9 @@ func (p *G1Affine) Set(a *G1Affine) *G1Affine {
 	return p
 }
 
-// setInfinity sets p to the infinity point, which is encoded as (0,0).
+// SetInfinity sets p to the infinity point, which is encoded as (0,0).
 // N.B.: (0,0) is never on the curve for j=0 curves (Y²=X³+B).
-func (p *G1Affine) setInfinity() *G1Affine {
+func (p *G1Affine) SetInfinity() *G1Affine {
 	p.X.SetZero()
 	p.Y.SetZero()
 	return p
@@ -99,7 +99,7 @@ func (p *G1Affine) Add(a, b *G1Affine) *G1Affine {
 			return p.FromJacobian(&q)
 		} else {
 			// if b == -a, we return 0
-			return p.setInfinity()
+			return p.SetInfinity()
 		}
 	}
 	var H, HH, I, J, r, V fp.Element
@@ -724,8 +724,8 @@ func (p *g1JacExtended) Set(q *g1JacExtended) *g1JacExtended {
 	return p
 }
 
-// setInfinity sets p to the infinity point (1,1,0,0).
-func (p *g1JacExtended) setInfinity() *g1JacExtended {
+// SetInfinity sets p to the infinity point (1,1,0,0).
+func (p *g1JacExtended) SetInfinity() *g1JacExtended {
 	p.X.SetOne()
 	p.Y.SetOne()
 	p.ZZ = fp.Element{}
diff --git a/ecc/bls12-381/g1_test.go b/ecc/bls12-381/g1_test.go
index 7dc98ec19b..5a07ae406a 100644
--- a/ecc/bls12-381/g1_test.go
+++ b/ecc/bls12-381/g1_test.go
@@ -270,7 +270,7 @@ func TestG1AffineOps(t *testing.T) {
 			g := g1GenAff
 			s.BigInt(&sInt)
 			op1.ScalarMultiplication(&g, &sInt)
-			op2.setInfinity()
+			op2.SetInfinity()
 
 			op1.Add(&op1, &op2)
 			op2.Add(&op2, &op1)
diff --git a/ecc/bls12-381/g2.go b/ecc/bls12-381/g2.go
index 424d939d5e..d4d7fa1c92 100644
--- a/ecc/bls12-381/g2.go
+++ b/ecc/bls12-381/g2.go
@@ -55,9 +55,9 @@ func (p *G2Affine) Set(a *G2Affine) *G2Affine {
 	return p
 }
 
-// setInfinity sets p to the infinity point, which is encoded as (0,0).
+// SetInfinity sets p to the infinity point, which is encoded as (0,0).
 // N.B.: (0,0) is never on the curve for j=0 curves (Y²=X³+B).
-func (p *G2Affine) setInfinity() *G2Affine {
+func (p *G2Affine) SetInfinity() *G2Affine {
 	p.X.SetZero()
 	p.Y.SetZero()
 	return p
@@ -105,7 +105,7 @@ func (p *G2Affine) Add(a, b *G2Affine) *G2Affine {
 			return p.FromJacobian(&q)
 		} else {
 			// if b == -a, we return 0
-			return p.setInfinity()
+			return p.SetInfinity()
 		}
 	}
 	var H, HH, I, J, r, V fptower.E2
@@ -672,8 +672,8 @@ func (p *g2JacExtended) Set(q *g2JacExtended) *g2JacExtended {
 	return p
 }
 
-// setInfinity sets p to the infinity point (1,1,0,0).
-func (p *g2JacExtended) setInfinity() *g2JacExtended {
+// SetInfinity sets p to the infinity point (1,1,0,0).
+func (p *g2JacExtended) SetInfinity() *g2JacExtended {
 	p.X.SetOne()
 	p.Y.SetOne()
 	p.ZZ = fptower.E2{}
diff --git a/ecc/bls12-381/g2_test.go b/ecc/bls12-381/g2_test.go
index 122713eb51..fe3b1a9b51 100644
--- a/ecc/bls12-381/g2_test.go
+++ b/ecc/bls12-381/g2_test.go
@@ -271,7 +271,7 @@ func TestG2AffineOps(t *testing.T) {
 			g := g2GenAff
 			s.BigInt(&sInt)
 			op1.ScalarMultiplication(&g, &sInt)
-			op2.setInfinity()
+			op2.SetInfinity()
 
 			op1.Add(&op1, &op2)
 			op2.Add(&op2, &op1)
diff --git a/ecc/bls12-381/multiexp_affine.go b/ecc/bls12-381/multiexp_affine.go
index 1b71b7ab45..9988b02544 100644
--- a/ecc/bls12-381/multiexp_affine.go
+++ b/ecc/bls12-381/multiexp_affine.go
@@ -63,7 +63,7 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 	var buckets B // in G1Affine coordinates, infinity point is represented as (0,0), no need to init
 	var bucketsJE BJE
 	for i := 0; i < len(buckets); i++ {
-		bucketsJE[i].setInfinity()
+		bucketsJE[i].SetInfinity()
 	}
 
 	// setup for the batch affine;
@@ -106,7 +106,7 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 				bucketsJE[op.bucketID].addMixed(&op.point)
 				return
 			}
-			BK.setInfinity()
+			BK.SetInfinity()
 			return
 		}
 
@@ -134,12 +134,12 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 				if isAdd {
 					bucketsJE[bucketID].addMixed(PP)
 				} else {
-					BK.setInfinity()
+					BK.SetInfinity()
 				}
 				return
 			}
 			if isAdd {
-				BK.setInfinity()
+				BK.SetInfinity()
 			} else {
 				bucketsJE[bucketID].subMixed(PP)
 			}
@@ -221,8 +221,8 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 	// reduce buckets into total
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 	var runningSum, total g1JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		runningSum.addMixed(&buckets[k])
 		if !bucketsJE[k].IsInfinity() {
@@ -390,7 +390,7 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 	var buckets B // in G2Affine coordinates, infinity point is represented as (0,0), no need to init
 	var bucketsJE BJE
 	for i := 0; i < len(buckets); i++ {
-		bucketsJE[i].setInfinity()
+		bucketsJE[i].SetInfinity()
 	}
 
 	// setup for the batch affine;
@@ -433,7 +433,7 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 				bucketsJE[op.bucketID].addMixed(&op.point)
 				return
 			}
-			BK.setInfinity()
+			BK.SetInfinity()
 			return
 		}
 
@@ -461,12 +461,12 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 				if isAdd {
 					bucketsJE[bucketID].addMixed(PP)
 				} else {
-					BK.setInfinity()
+					BK.SetInfinity()
 				}
 				return
 			}
 			if isAdd {
-				BK.setInfinity()
+				BK.SetInfinity()
 			} else {
 				bucketsJE[bucketID].subMixed(PP)
 			}
@@ -548,8 +548,8 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 	// reduce buckets into total
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 	var runningSum, total g2JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		runningSum.addMixed(&buckets[k])
 		if !bucketsJE[k].IsInfinity() {
diff --git a/ecc/bls12-381/multiexp_jacobian.go b/ecc/bls12-381/multiexp_jacobian.go
index 80b042d8d3..da3445bd69 100644
--- a/ecc/bls12-381/multiexp_jacobian.go
+++ b/ecc/bls12-381/multiexp_jacobian.go
@@ -30,7 +30,7 @@ func processChunkG1Jacobian[B ibg1JacExtended](chunk uint64,
 
 	var buckets B
 	for i := 0; i < len(buckets); i++ {
-		buckets[i].setInfinity()
+		buckets[i].SetInfinity()
 	}
 
 	// for each scalars, get the digit corresponding to the chunk we're processing.
@@ -53,8 +53,8 @@ func processChunkG1Jacobian[B ibg1JacExtended](chunk uint64,
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 
 	var runningSum, total g1JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		if !buckets[k].IsInfinity() {
 			runningSum.add(&buckets[k])
@@ -119,7 +119,7 @@ func processChunkG2Jacobian[B ibg2JacExtended](chunk uint64,
 
 	var buckets B
 	for i := 0; i < len(buckets); i++ {
-		buckets[i].setInfinity()
+		buckets[i].SetInfinity()
 	}
 
 	// for each scalars, get the digit corresponding to the chunk we're processing.
@@ -142,8 +142,8 @@ func processChunkG2Jacobian[B ibg2JacExtended](chunk uint64,
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 
 	var runningSum, total g2JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		if !buckets[k].IsInfinity() {
 			runningSum.add(&buckets[k])
diff --git a/ecc/bls12-381/multiexp_test.go b/ecc/bls12-381/multiexp_test.go
index 367af5148e..60ced46ca3 100644
--- a/ecc/bls12-381/multiexp_test.go
+++ b/ecc/bls12-381/multiexp_test.go
@@ -57,10 +57,10 @@ func TestMultiExpG1(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	// final scalar to use in double and add method (without mixer factor)
 	// n(n+1)(2n+1)/6  (sum of the squares from 1 to n)
@@ -154,7 +154,7 @@ func TestMultiExpG1(t *testing.T) {
 			for i := 1; i <= nbSamples; i++ {
 				sampleScalars[i-1].SetUint64(uint64(i)).
 					Mul(&sampleScalars[i-1], &mixer)
-				samplePointsZero[i-1].setInfinity()
+				samplePointsZero[i-1].SetInfinity()
 			}
 
 			results := make([]G1Jac, len(cRange))
@@ -241,10 +241,10 @@ func TestCrossMultiExpG1(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	var sampleScalars [nbSamples]fr.Element
 	fillBenchScalars(sampleScalars[:])
@@ -471,10 +471,10 @@ func TestMultiExpG2(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	// final scalar to use in double and add method (without mixer factor)
 	// n(n+1)(2n+1)/6  (sum of the squares from 1 to n)
@@ -566,7 +566,7 @@ func TestMultiExpG2(t *testing.T) {
 			for i := 1; i <= nbSamples; i++ {
 				sampleScalars[i-1].SetUint64(uint64(i)).
 					Mul(&sampleScalars[i-1], &mixer)
-				samplePointsZero[i-1].setInfinity()
+				samplePointsZero[i-1].SetInfinity()
 			}
 
 			results := make([]G2Jac, len(cRange))
@@ -653,10 +653,10 @@ func TestCrossMultiExpG2(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	var sampleScalars [nbSamples]fr.Element
 	fillBenchScalars(sampleScalars[:])
diff --git a/ecc/bls24-315/g1.go b/ecc/bls24-315/g1.go
index 52de0e1d6e..91d995c8cb 100644
--- a/ecc/bls24-315/g1.go
+++ b/ecc/bls24-315/g1.go
@@ -49,9 +49,9 @@ func (p *G1Affine) Set(a *G1Affine) *G1Affine {
 	return p
 }
 
-// setInfinity sets p to the infinity point, which is encoded as (0,0).
+// SetInfinity sets p to the infinity point, which is encoded as (0,0).
 // N.B.: (0,0) is never on the curve for j=0 curves (Y²=X³+B).
-func (p *G1Affine) setInfinity() *G1Affine {
+func (p *G1Affine) SetInfinity() *G1Affine {
 	p.X.SetZero()
 	p.Y.SetZero()
 	return p
@@ -99,7 +99,7 @@ func (p *G1Affine) Add(a, b *G1Affine) *G1Affine {
 			return p.FromJacobian(&q)
 		} else {
 			// if b == -a, we return 0
-			return p.setInfinity()
+			return p.SetInfinity()
 		}
 	}
 	var H, HH, I, J, r, V fp.Element
@@ -725,8 +725,8 @@ func (p *g1JacExtended) Set(q *g1JacExtended) *g1JacExtended {
 	return p
 }
 
-// setInfinity sets p to the infinity point (1,1,0,0).
-func (p *g1JacExtended) setInfinity() *g1JacExtended {
+// SetInfinity sets p to the infinity point (1,1,0,0).
+func (p *g1JacExtended) SetInfinity() *g1JacExtended {
 	p.X.SetOne()
 	p.Y.SetOne()
 	p.ZZ = fp.Element{}
diff --git a/ecc/bls24-315/g1_test.go b/ecc/bls24-315/g1_test.go
index 6a1cafa115..84ea681f05 100644
--- a/ecc/bls24-315/g1_test.go
+++ b/ecc/bls24-315/g1_test.go
@@ -270,7 +270,7 @@ func TestG1AffineOps(t *testing.T) {
 			g := g1GenAff
 			s.BigInt(&sInt)
 			op1.ScalarMultiplication(&g, &sInt)
-			op2.setInfinity()
+			op2.SetInfinity()
 
 			op1.Add(&op1, &op2)
 			op2.Add(&op2, &op1)
diff --git a/ecc/bls24-315/g2.go b/ecc/bls24-315/g2.go
index e5df7637c1..dd08636ea9 100644
--- a/ecc/bls24-315/g2.go
+++ b/ecc/bls24-315/g2.go
@@ -55,9 +55,9 @@ func (p *G2Affine) Set(a *G2Affine) *G2Affine {
 	return p
 }
 
-// setInfinity sets p to the infinity point, which is encoded as (0,0).
+// SetInfinity sets p to the infinity point, which is encoded as (0,0).
 // N.B.: (0,0) is never on the curve for j=0 curves (Y²=X³+B).
-func (p *G2Affine) setInfinity() *G2Affine {
+func (p *G2Affine) SetInfinity() *G2Affine {
 	p.X.SetZero()
 	p.Y.SetZero()
 	return p
@@ -105,7 +105,7 @@ func (p *G2Affine) Add(a, b *G2Affine) *G2Affine {
 			return p.FromJacobian(&q)
 		} else {
 			// if b == -a, we return 0
-			return p.setInfinity()
+			return p.SetInfinity()
 		}
 	}
 	var H, HH, I, J, r, V fptower.E4
@@ -687,8 +687,8 @@ func (p *g2JacExtended) Set(q *g2JacExtended) *g2JacExtended {
 	return p
 }
 
-// setInfinity sets p to the infinity point (1,1,0,0).
-func (p *g2JacExtended) setInfinity() *g2JacExtended {
+// SetInfinity sets p to the infinity point (1,1,0,0).
+func (p *g2JacExtended) SetInfinity() *g2JacExtended {
 	p.X.SetOne()
 	p.Y.SetOne()
 	p.ZZ = fptower.E4{}
diff --git a/ecc/bls24-315/g2_test.go b/ecc/bls24-315/g2_test.go
index 43e953e318..34a97df9d9 100644
--- a/ecc/bls24-315/g2_test.go
+++ b/ecc/bls24-315/g2_test.go
@@ -271,7 +271,7 @@ func TestG2AffineOps(t *testing.T) {
 			g := g2GenAff
 			s.BigInt(&sInt)
 			op1.ScalarMultiplication(&g, &sInt)
-			op2.setInfinity()
+			op2.SetInfinity()
 
 			op1.Add(&op1, &op2)
 			op2.Add(&op2, &op1)
diff --git a/ecc/bls24-315/multiexp_affine.go b/ecc/bls24-315/multiexp_affine.go
index 2938a409e7..c020191bdd 100644
--- a/ecc/bls24-315/multiexp_affine.go
+++ b/ecc/bls24-315/multiexp_affine.go
@@ -63,7 +63,7 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 	var buckets B // in G1Affine coordinates, infinity point is represented as (0,0), no need to init
 	var bucketsJE BJE
 	for i := 0; i < len(buckets); i++ {
-		bucketsJE[i].setInfinity()
+		bucketsJE[i].SetInfinity()
 	}
 
 	// setup for the batch affine;
@@ -106,7 +106,7 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 				bucketsJE[op.bucketID].addMixed(&op.point)
 				return
 			}
-			BK.setInfinity()
+			BK.SetInfinity()
 			return
 		}
 
@@ -134,12 +134,12 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 				if isAdd {
 					bucketsJE[bucketID].addMixed(PP)
 				} else {
-					BK.setInfinity()
+					BK.SetInfinity()
 				}
 				return
 			}
 			if isAdd {
-				BK.setInfinity()
+				BK.SetInfinity()
 			} else {
 				bucketsJE[bucketID].subMixed(PP)
 			}
@@ -221,8 +221,8 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 	// reduce buckets into total
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 	var runningSum, total g1JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		runningSum.addMixed(&buckets[k])
 		if !bucketsJE[k].IsInfinity() {
@@ -390,7 +390,7 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 	var buckets B // in G2Affine coordinates, infinity point is represented as (0,0), no need to init
 	var bucketsJE BJE
 	for i := 0; i < len(buckets); i++ {
-		bucketsJE[i].setInfinity()
+		bucketsJE[i].SetInfinity()
 	}
 
 	// setup for the batch affine;
@@ -433,7 +433,7 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 				bucketsJE[op.bucketID].addMixed(&op.point)
 				return
 			}
-			BK.setInfinity()
+			BK.SetInfinity()
 			return
 		}
 
@@ -461,12 +461,12 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 				if isAdd {
 					bucketsJE[bucketID].addMixed(PP)
 				} else {
-					BK.setInfinity()
+					BK.SetInfinity()
 				}
 				return
 			}
 			if isAdd {
-				BK.setInfinity()
+				BK.SetInfinity()
 			} else {
 				bucketsJE[bucketID].subMixed(PP)
 			}
@@ -548,8 +548,8 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 	// reduce buckets into total
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 	var runningSum, total g2JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		runningSum.addMixed(&buckets[k])
 		if !bucketsJE[k].IsInfinity() {
diff --git a/ecc/bls24-315/multiexp_jacobian.go b/ecc/bls24-315/multiexp_jacobian.go
index 76d08a460c..8ffc4d04ae 100644
--- a/ecc/bls24-315/multiexp_jacobian.go
+++ b/ecc/bls24-315/multiexp_jacobian.go
@@ -30,7 +30,7 @@ func processChunkG1Jacobian[B ibg1JacExtended](chunk uint64,
 
 	var buckets B
 	for i := 0; i < len(buckets); i++ {
-		buckets[i].setInfinity()
+		buckets[i].SetInfinity()
 	}
 
 	// for each scalars, get the digit corresponding to the chunk we're processing.
@@ -53,8 +53,8 @@ func processChunkG1Jacobian[B ibg1JacExtended](chunk uint64,
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 
 	var runningSum, total g1JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		if !buckets[k].IsInfinity() {
 			runningSum.add(&buckets[k])
@@ -119,7 +119,7 @@ func processChunkG2Jacobian[B ibg2JacExtended](chunk uint64,
 
 	var buckets B
 	for i := 0; i < len(buckets); i++ {
-		buckets[i].setInfinity()
+		buckets[i].SetInfinity()
 	}
 
 	// for each scalars, get the digit corresponding to the chunk we're processing.
@@ -142,8 +142,8 @@ func processChunkG2Jacobian[B ibg2JacExtended](chunk uint64,
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 
 	var runningSum, total g2JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		if !buckets[k].IsInfinity() {
 			runningSum.add(&buckets[k])
diff --git a/ecc/bls24-315/multiexp_test.go b/ecc/bls24-315/multiexp_test.go
index 9b091a337e..2c46aa2286 100644
--- a/ecc/bls24-315/multiexp_test.go
+++ b/ecc/bls24-315/multiexp_test.go
@@ -57,10 +57,10 @@ func TestMultiExpG1(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	// final scalar to use in double and add method (without mixer factor)
 	// n(n+1)(2n+1)/6  (sum of the squares from 1 to n)
@@ -154,7 +154,7 @@ func TestMultiExpG1(t *testing.T) {
 			for i := 1; i <= nbSamples; i++ {
 				sampleScalars[i-1].SetUint64(uint64(i)).
 					Mul(&sampleScalars[i-1], &mixer)
-				samplePointsZero[i-1].setInfinity()
+				samplePointsZero[i-1].SetInfinity()
 			}
 
 			results := make([]G1Jac, len(cRange))
@@ -241,10 +241,10 @@ func TestCrossMultiExpG1(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	var sampleScalars [nbSamples]fr.Element
 	fillBenchScalars(sampleScalars[:])
@@ -471,10 +471,10 @@ func TestMultiExpG2(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	// final scalar to use in double and add method (without mixer factor)
 	// n(n+1)(2n+1)/6  (sum of the squares from 1 to n)
@@ -566,7 +566,7 @@ func TestMultiExpG2(t *testing.T) {
 			for i := 1; i <= nbSamples; i++ {
 				sampleScalars[i-1].SetUint64(uint64(i)).
 					Mul(&sampleScalars[i-1], &mixer)
-				samplePointsZero[i-1].setInfinity()
+				samplePointsZero[i-1].SetInfinity()
 			}
 
 			results := make([]G2Jac, len(cRange))
@@ -653,10 +653,10 @@ func TestCrossMultiExpG2(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	var sampleScalars [nbSamples]fr.Element
 	fillBenchScalars(sampleScalars[:])
diff --git a/ecc/bls24-317/g1.go b/ecc/bls24-317/g1.go
index 18585821f1..890a7de492 100644
--- a/ecc/bls24-317/g1.go
+++ b/ecc/bls24-317/g1.go
@@ -49,9 +49,9 @@ func (p *G1Affine) Set(a *G1Affine) *G1Affine {
 	return p
 }
 
-// setInfinity sets p to the infinity point, which is encoded as (0,0).
+// SetInfinity sets p to the infinity point, which is encoded as (0,0).
 // N.B.: (0,0) is never on the curve for j=0 curves (Y²=X³+B).
-func (p *G1Affine) setInfinity() *G1Affine {
+func (p *G1Affine) SetInfinity() *G1Affine {
 	p.X.SetZero()
 	p.Y.SetZero()
 	return p
@@ -99,7 +99,7 @@ func (p *G1Affine) Add(a, b *G1Affine) *G1Affine {
 			return p.FromJacobian(&q)
 		} else {
 			// if b == -a, we return 0
-			return p.setInfinity()
+			return p.SetInfinity()
 		}
 	}
 	var H, HH, I, J, r, V fp.Element
@@ -726,8 +726,8 @@ func (p *g1JacExtended) Set(q *g1JacExtended) *g1JacExtended {
 	return p
 }
 
-// setInfinity sets p to the infinity point (1,1,0,0).
-func (p *g1JacExtended) setInfinity() *g1JacExtended {
+// SetInfinity sets p to the infinity point (1,1,0,0).
+func (p *g1JacExtended) SetInfinity() *g1JacExtended {
 	p.X.SetOne()
 	p.Y.SetOne()
 	p.ZZ = fp.Element{}
diff --git a/ecc/bls24-317/g1_test.go b/ecc/bls24-317/g1_test.go
index 5c2154b6e1..fbf290d972 100644
--- a/ecc/bls24-317/g1_test.go
+++ b/ecc/bls24-317/g1_test.go
@@ -270,7 +270,7 @@ func TestG1AffineOps(t *testing.T) {
 			g := g1GenAff
 			s.BigInt(&sInt)
 			op1.ScalarMultiplication(&g, &sInt)
-			op2.setInfinity()
+			op2.SetInfinity()
 
 			op1.Add(&op1, &op2)
 			op2.Add(&op2, &op1)
diff --git a/ecc/bls24-317/g2.go b/ecc/bls24-317/g2.go
index 4384dcc16c..b34c68acd6 100644
--- a/ecc/bls24-317/g2.go
+++ b/ecc/bls24-317/g2.go
@@ -55,9 +55,9 @@ func (p *G2Affine) Set(a *G2Affine) *G2Affine {
 	return p
 }
 
-// setInfinity sets p to the infinity point, which is encoded as (0,0).
+// SetInfinity sets p to the infinity point, which is encoded as (0,0).
 // N.B.: (0,0) is never on the curve for j=0 curves (Y²=X³+B).
-func (p *G2Affine) setInfinity() *G2Affine {
+func (p *G2Affine) SetInfinity() *G2Affine {
 	p.X.SetZero()
 	p.Y.SetZero()
 	return p
@@ -105,7 +105,7 @@ func (p *G2Affine) Add(a, b *G2Affine) *G2Affine {
 			return p.FromJacobian(&q)
 		} else {
 			// if b == -a, we return 0
-			return p.setInfinity()
+			return p.SetInfinity()
 		}
 	}
 	var H, HH, I, J, r, V fptower.E4
@@ -687,8 +687,8 @@ func (p *g2JacExtended) Set(q *g2JacExtended) *g2JacExtended {
 	return p
 }
 
-// setInfinity sets p to the infinity point (1,1,0,0).
-func (p *g2JacExtended) setInfinity() *g2JacExtended {
+// SetInfinity sets p to the infinity point (1,1,0,0).
+func (p *g2JacExtended) SetInfinity() *g2JacExtended {
 	p.X.SetOne()
 	p.Y.SetOne()
 	p.ZZ = fptower.E4{}
diff --git a/ecc/bls24-317/g2_test.go b/ecc/bls24-317/g2_test.go
index 9424bac50e..69f7745503 100644
--- a/ecc/bls24-317/g2_test.go
+++ b/ecc/bls24-317/g2_test.go
@@ -271,7 +271,7 @@ func TestG2AffineOps(t *testing.T) {
 			g := g2GenAff
 			s.BigInt(&sInt)
 			op1.ScalarMultiplication(&g, &sInt)
-			op2.setInfinity()
+			op2.SetInfinity()
 
 			op1.Add(&op1, &op2)
 			op2.Add(&op2, &op1)
diff --git a/ecc/bls24-317/multiexp_affine.go b/ecc/bls24-317/multiexp_affine.go
index 47b693fbd9..b05471f593 100644
--- a/ecc/bls24-317/multiexp_affine.go
+++ b/ecc/bls24-317/multiexp_affine.go
@@ -63,7 +63,7 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 	var buckets B // in G1Affine coordinates, infinity point is represented as (0,0), no need to init
 	var bucketsJE BJE
 	for i := 0; i < len(buckets); i++ {
-		bucketsJE[i].setInfinity()
+		bucketsJE[i].SetInfinity()
 	}
 
 	// setup for the batch affine;
@@ -106,7 +106,7 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 				bucketsJE[op.bucketID].addMixed(&op.point)
 				return
 			}
-			BK.setInfinity()
+			BK.SetInfinity()
 			return
 		}
 
@@ -134,12 +134,12 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 				if isAdd {
 					bucketsJE[bucketID].addMixed(PP)
 				} else {
-					BK.setInfinity()
+					BK.SetInfinity()
 				}
 				return
 			}
 			if isAdd {
-				BK.setInfinity()
+				BK.SetInfinity()
 			} else {
 				bucketsJE[bucketID].subMixed(PP)
 			}
@@ -221,8 +221,8 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 	// reduce buckets into total
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 	var runningSum, total g1JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		runningSum.addMixed(&buckets[k])
 		if !bucketsJE[k].IsInfinity() {
@@ -390,7 +390,7 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 	var buckets B // in G2Affine coordinates, infinity point is represented as (0,0), no need to init
 	var bucketsJE BJE
 	for i := 0; i < len(buckets); i++ {
-		bucketsJE[i].setInfinity()
+		bucketsJE[i].SetInfinity()
 	}
 
 	// setup for the batch affine;
@@ -433,7 +433,7 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 				bucketsJE[op.bucketID].addMixed(&op.point)
 				return
 			}
-			BK.setInfinity()
+			BK.SetInfinity()
 			return
 		}
 
@@ -461,12 +461,12 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 				if isAdd {
 					bucketsJE[bucketID].addMixed(PP)
 				} else {
-					BK.setInfinity()
+					BK.SetInfinity()
 				}
 				return
 			}
 			if isAdd {
-				BK.setInfinity()
+				BK.SetInfinity()
 			} else {
 				bucketsJE[bucketID].subMixed(PP)
 			}
@@ -548,8 +548,8 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 	// reduce buckets into total
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 	var runningSum, total g2JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		runningSum.addMixed(&buckets[k])
 		if !bucketsJE[k].IsInfinity() {
diff --git a/ecc/bls24-317/multiexp_jacobian.go b/ecc/bls24-317/multiexp_jacobian.go
index c7178af022..04a8103691 100644
--- a/ecc/bls24-317/multiexp_jacobian.go
+++ b/ecc/bls24-317/multiexp_jacobian.go
@@ -30,7 +30,7 @@ func processChunkG1Jacobian[B ibg1JacExtended](chunk uint64,
 
 	var buckets B
 	for i := 0; i < len(buckets); i++ {
-		buckets[i].setInfinity()
+		buckets[i].SetInfinity()
 	}
 
 	// for each scalars, get the digit corresponding to the chunk we're processing.
@@ -53,8 +53,8 @@ func processChunkG1Jacobian[B ibg1JacExtended](chunk uint64,
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 
 	var runningSum, total g1JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		if !buckets[k].IsInfinity() {
 			runningSum.add(&buckets[k])
@@ -119,7 +119,7 @@ func processChunkG2Jacobian[B ibg2JacExtended](chunk uint64,
 
 	var buckets B
 	for i := 0; i < len(buckets); i++ {
-		buckets[i].setInfinity()
+		buckets[i].SetInfinity()
 	}
 
 	// for each scalars, get the digit corresponding to the chunk we're processing.
@@ -142,8 +142,8 @@ func processChunkG2Jacobian[B ibg2JacExtended](chunk uint64,
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 
 	var runningSum, total g2JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		if !buckets[k].IsInfinity() {
 			runningSum.add(&buckets[k])
diff --git a/ecc/bls24-317/multiexp_test.go b/ecc/bls24-317/multiexp_test.go
index d92cd72816..75a6f165db 100644
--- a/ecc/bls24-317/multiexp_test.go
+++ b/ecc/bls24-317/multiexp_test.go
@@ -57,10 +57,10 @@ func TestMultiExpG1(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	// final scalar to use in double and add method (without mixer factor)
 	// n(n+1)(2n+1)/6  (sum of the squares from 1 to n)
@@ -154,7 +154,7 @@ func TestMultiExpG1(t *testing.T) {
 			for i := 1; i <= nbSamples; i++ {
 				sampleScalars[i-1].SetUint64(uint64(i)).
 					Mul(&sampleScalars[i-1], &mixer)
-				samplePointsZero[i-1].setInfinity()
+				samplePointsZero[i-1].SetInfinity()
 			}
 
 			results := make([]G1Jac, len(cRange))
@@ -241,10 +241,10 @@ func TestCrossMultiExpG1(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	var sampleScalars [nbSamples]fr.Element
 	fillBenchScalars(sampleScalars[:])
@@ -471,10 +471,10 @@ func TestMultiExpG2(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	// final scalar to use in double and add method (without mixer factor)
 	// n(n+1)(2n+1)/6  (sum of the squares from 1 to n)
@@ -566,7 +566,7 @@ func TestMultiExpG2(t *testing.T) {
 			for i := 1; i <= nbSamples; i++ {
 				sampleScalars[i-1].SetUint64(uint64(i)).
 					Mul(&sampleScalars[i-1], &mixer)
-				samplePointsZero[i-1].setInfinity()
+				samplePointsZero[i-1].SetInfinity()
 			}
 
 			results := make([]G2Jac, len(cRange))
@@ -653,10 +653,10 @@ func TestCrossMultiExpG2(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	var sampleScalars [nbSamples]fr.Element
 	fillBenchScalars(sampleScalars[:])
diff --git a/ecc/bn254/g1.go b/ecc/bn254/g1.go
index fc484aac95..14dfeef86b 100644
--- a/ecc/bn254/g1.go
+++ b/ecc/bn254/g1.go
@@ -49,9 +49,9 @@ func (p *G1Affine) Set(a *G1Affine) *G1Affine {
 	return p
 }
 
-// setInfinity sets p to the infinity point, which is encoded as (0,0).
+// SetInfinity sets p to the infinity point, which is encoded as (0,0).
 // N.B.: (0,0) is never on the curve for j=0 curves (Y²=X³+B).
-func (p *G1Affine) setInfinity() *G1Affine {
+func (p *G1Affine) SetInfinity() *G1Affine {
 	p.X.SetZero()
 	p.Y.SetZero()
 	return p
@@ -99,7 +99,7 @@ func (p *G1Affine) Add(a, b *G1Affine) *G1Affine {
 			return p.FromJacobian(&q)
 		} else {
 			// if b == -a, we return 0
-			return p.setInfinity()
+			return p.SetInfinity()
 		}
 	}
 	var H, HH, I, J, r, V fp.Element
@@ -695,8 +695,8 @@ func (p *g1JacExtended) Set(q *g1JacExtended) *g1JacExtended {
 	return p
 }
 
-// setInfinity sets p to the infinity point (1,1,0,0).
-func (p *g1JacExtended) setInfinity() *g1JacExtended {
+// SetInfinity sets p to the infinity point (1,1,0,0).
+func (p *g1JacExtended) SetInfinity() *g1JacExtended {
 	p.X.SetOne()
 	p.Y.SetOne()
 	p.ZZ = fp.Element{}
diff --git a/ecc/bn254/g1_test.go b/ecc/bn254/g1_test.go
index 910bfd499b..9354444ee3 100644
--- a/ecc/bn254/g1_test.go
+++ b/ecc/bn254/g1_test.go
@@ -270,7 +270,7 @@ func TestG1AffineOps(t *testing.T) {
 			g := g1GenAff
 			s.BigInt(&sInt)
 			op1.ScalarMultiplication(&g, &sInt)
-			op2.setInfinity()
+			op2.SetInfinity()
 
 			op1.Add(&op1, &op2)
 			op2.Add(&op2, &op1)
diff --git a/ecc/bn254/g2.go b/ecc/bn254/g2.go
index 5635224d94..24561bb28c 100644
--- a/ecc/bn254/g2.go
+++ b/ecc/bn254/g2.go
@@ -55,9 +55,9 @@ func (p *G2Affine) Set(a *G2Affine) *G2Affine {
 	return p
 }
 
-// setInfinity sets p to the infinity point, which is encoded as (0,0).
+// SetInfinity sets p to the infinity point, which is encoded as (0,0).
 // N.B.: (0,0) is never on the curve for j=0 curves (Y²=X³+B).
-func (p *G2Affine) setInfinity() *G2Affine {
+func (p *G2Affine) SetInfinity() *G2Affine {
 	p.X.SetZero()
 	p.Y.SetZero()
 	return p
@@ -105,7 +105,7 @@ func (p *G2Affine) Add(a, b *G2Affine) *G2Affine {
 			return p.FromJacobian(&q)
 		} else {
 			// if b == -a, we return 0
-			return p.setInfinity()
+			return p.SetInfinity()
 		}
 	}
 	var H, HH, I, J, r, V fptower.E2
@@ -676,8 +676,8 @@ func (p *g2JacExtended) Set(q *g2JacExtended) *g2JacExtended {
 	return p
 }
 
-// setInfinity sets p to the infinity point (1,1,0,0).
-func (p *g2JacExtended) setInfinity() *g2JacExtended {
+// SetInfinity sets p to the infinity point (1,1,0,0).
+func (p *g2JacExtended) SetInfinity() *g2JacExtended {
 	p.X.SetOne()
 	p.Y.SetOne()
 	p.ZZ = fptower.E2{}
diff --git a/ecc/bn254/g2_test.go b/ecc/bn254/g2_test.go
index c6ee502367..f998e7550d 100644
--- a/ecc/bn254/g2_test.go
+++ b/ecc/bn254/g2_test.go
@@ -270,7 +270,7 @@ func TestG2AffineOps(t *testing.T) {
 			g := g2GenAff
 			s.BigInt(&sInt)
 			op1.ScalarMultiplication(&g, &sInt)
-			op2.setInfinity()
+			op2.SetInfinity()
 
 			op1.Add(&op1, &op2)
 			op2.Add(&op2, &op1)
diff --git a/ecc/bn254/multiexp_affine.go b/ecc/bn254/multiexp_affine.go
index 6c66595bce..f3a929a635 100644
--- a/ecc/bn254/multiexp_affine.go
+++ b/ecc/bn254/multiexp_affine.go
@@ -63,7 +63,7 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 	var buckets B // in G1Affine coordinates, infinity point is represented as (0,0), no need to init
 	var bucketsJE BJE
 	for i := 0; i < len(buckets); i++ {
-		bucketsJE[i].setInfinity()
+		bucketsJE[i].SetInfinity()
 	}
 
 	// setup for the batch affine;
@@ -106,7 +106,7 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 				bucketsJE[op.bucketID].addMixed(&op.point)
 				return
 			}
-			BK.setInfinity()
+			BK.SetInfinity()
 			return
 		}
 
@@ -134,12 +134,12 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 				if isAdd {
 					bucketsJE[bucketID].addMixed(PP)
 				} else {
-					BK.setInfinity()
+					BK.SetInfinity()
 				}
 				return
 			}
 			if isAdd {
-				BK.setInfinity()
+				BK.SetInfinity()
 			} else {
 				bucketsJE[bucketID].subMixed(PP)
 			}
@@ -221,8 +221,8 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 	// reduce buckets into total
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 	var runningSum, total g1JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		runningSum.addMixed(&buckets[k])
 		if !bucketsJE[k].IsInfinity() {
@@ -390,7 +390,7 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 	var buckets B // in G2Affine coordinates, infinity point is represented as (0,0), no need to init
 	var bucketsJE BJE
 	for i := 0; i < len(buckets); i++ {
-		bucketsJE[i].setInfinity()
+		bucketsJE[i].SetInfinity()
 	}
 
 	// setup for the batch affine;
@@ -433,7 +433,7 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 				bucketsJE[op.bucketID].addMixed(&op.point)
 				return
 			}
-			BK.setInfinity()
+			BK.SetInfinity()
 			return
 		}
 
@@ -461,12 +461,12 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 				if isAdd {
 					bucketsJE[bucketID].addMixed(PP)
 				} else {
-					BK.setInfinity()
+					BK.SetInfinity()
 				}
 				return
 			}
 			if isAdd {
-				BK.setInfinity()
+				BK.SetInfinity()
 			} else {
 				bucketsJE[bucketID].subMixed(PP)
 			}
@@ -548,8 +548,8 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 	// reduce buckets into total
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 	var runningSum, total g2JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		runningSum.addMixed(&buckets[k])
 		if !bucketsJE[k].IsInfinity() {
diff --git a/ecc/bn254/multiexp_jacobian.go b/ecc/bn254/multiexp_jacobian.go
index f9a3df9d30..199b781ca3 100644
--- a/ecc/bn254/multiexp_jacobian.go
+++ b/ecc/bn254/multiexp_jacobian.go
@@ -30,7 +30,7 @@ func processChunkG1Jacobian[B ibg1JacExtended](chunk uint64,
 
 	var buckets B
 	for i := 0; i < len(buckets); i++ {
-		buckets[i].setInfinity()
+		buckets[i].SetInfinity()
 	}
 
 	// for each scalars, get the digit corresponding to the chunk we're processing.
@@ -53,8 +53,8 @@ func processChunkG1Jacobian[B ibg1JacExtended](chunk uint64,
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 
 	var runningSum, total g1JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		if !buckets[k].IsInfinity() {
 			runningSum.add(&buckets[k])
@@ -121,7 +121,7 @@ func processChunkG2Jacobian[B ibg2JacExtended](chunk uint64,
 
 	var buckets B
 	for i := 0; i < len(buckets); i++ {
-		buckets[i].setInfinity()
+		buckets[i].SetInfinity()
 	}
 
 	// for each scalars, get the digit corresponding to the chunk we're processing.
@@ -144,8 +144,8 @@ func processChunkG2Jacobian[B ibg2JacExtended](chunk uint64,
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 
 	var runningSum, total g2JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		if !buckets[k].IsInfinity() {
 			runningSum.add(&buckets[k])
diff --git a/ecc/bn254/multiexp_test.go b/ecc/bn254/multiexp_test.go
index 89cf9074b2..4c8303ad61 100644
--- a/ecc/bn254/multiexp_test.go
+++ b/ecc/bn254/multiexp_test.go
@@ -57,10 +57,10 @@ func TestMultiExpG1(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	// final scalar to use in double and add method (without mixer factor)
 	// n(n+1)(2n+1)/6  (sum of the squares from 1 to n)
@@ -154,7 +154,7 @@ func TestMultiExpG1(t *testing.T) {
 			for i := 1; i <= nbSamples; i++ {
 				sampleScalars[i-1].SetUint64(uint64(i)).
 					Mul(&sampleScalars[i-1], &mixer)
-				samplePointsZero[i-1].setInfinity()
+				samplePointsZero[i-1].SetInfinity()
 			}
 
 			results := make([]G1Jac, len(cRange))
@@ -241,10 +241,10 @@ func TestCrossMultiExpG1(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	var sampleScalars [nbSamples]fr.Element
 	fillBenchScalars(sampleScalars[:])
@@ -471,10 +471,10 @@ func TestMultiExpG2(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	// final scalar to use in double and add method (without mixer factor)
 	// n(n+1)(2n+1)/6  (sum of the squares from 1 to n)
@@ -566,7 +566,7 @@ func TestMultiExpG2(t *testing.T) {
 			for i := 1; i <= nbSamples; i++ {
 				sampleScalars[i-1].SetUint64(uint64(i)).
 					Mul(&sampleScalars[i-1], &mixer)
-				samplePointsZero[i-1].setInfinity()
+				samplePointsZero[i-1].SetInfinity()
 			}
 
 			results := make([]G2Jac, len(cRange))
@@ -653,10 +653,10 @@ func TestCrossMultiExpG2(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	var sampleScalars [nbSamples]fr.Element
 	fillBenchScalars(sampleScalars[:])
diff --git a/ecc/bw6-633/g1.go b/ecc/bw6-633/g1.go
index db4e88dcaa..196053c960 100644
--- a/ecc/bw6-633/g1.go
+++ b/ecc/bw6-633/g1.go
@@ -49,9 +49,9 @@ func (p *G1Affine) Set(a *G1Affine) *G1Affine {
 	return p
 }
 
-// setInfinity sets p to the infinity point, which is encoded as (0,0).
+// SetInfinity sets p to the infinity point, which is encoded as (0,0).
 // N.B.: (0,0) is never on the curve for j=0 curves (Y²=X³+B).
-func (p *G1Affine) setInfinity() *G1Affine {
+func (p *G1Affine) SetInfinity() *G1Affine {
 	p.X.SetZero()
 	p.Y.SetZero()
 	return p
@@ -99,7 +99,7 @@ func (p *G1Affine) Add(a, b *G1Affine) *G1Affine {
 			return p.FromJacobian(&q)
 		} else {
 			// if b == -a, we return 0
-			return p.setInfinity()
+			return p.SetInfinity()
 		}
 	}
 	var H, HH, I, J, r, V fp.Element
@@ -748,8 +748,8 @@ func (p *g1JacExtended) Set(q *g1JacExtended) *g1JacExtended {
 	return p
 }
 
-// setInfinity sets p to the infinity point (1,1,0,0).
-func (p *g1JacExtended) setInfinity() *g1JacExtended {
+// SetInfinity sets p to the infinity point (1,1,0,0).
+func (p *g1JacExtended) SetInfinity() *g1JacExtended {
 	p.X.SetOne()
 	p.Y.SetOne()
 	p.ZZ = fp.Element{}
diff --git a/ecc/bw6-633/g1_test.go b/ecc/bw6-633/g1_test.go
index e5b93006dc..af7c526f48 100644
--- a/ecc/bw6-633/g1_test.go
+++ b/ecc/bw6-633/g1_test.go
@@ -270,7 +270,7 @@ func TestG1AffineOps(t *testing.T) {
 			g := g1GenAff
 			s.BigInt(&sInt)
 			op1.ScalarMultiplication(&g, &sInt)
-			op2.setInfinity()
+			op2.SetInfinity()
 
 			op1.Add(&op1, &op2)
 			op2.Add(&op2, &op1)
diff --git a/ecc/bw6-633/g2.go b/ecc/bw6-633/g2.go
index 6dfbaa0033..611753c678 100644
--- a/ecc/bw6-633/g2.go
+++ b/ecc/bw6-633/g2.go
@@ -55,9 +55,9 @@ func (p *G2Affine) Set(a *G2Affine) *G2Affine {
 	return p
 }
 
-// setInfinity sets p to the infinity point, which is encoded as (0,0).
+// SetInfinity sets p to the infinity point, which is encoded as (0,0).
 // N.B.: (0,0) is never on the curve for j=0 curves (Y²=X³+B).
-func (p *G2Affine) setInfinity() *G2Affine {
+func (p *G2Affine) SetInfinity() *G2Affine {
 	p.X.SetZero()
 	p.Y.SetZero()
 	return p
@@ -105,7 +105,7 @@ func (p *G2Affine) Add(a, b *G2Affine) *G2Affine {
 			return p.FromJacobian(&q)
 		} else {
 			// if b == -a, we return 0
-			return p.setInfinity()
+			return p.SetInfinity()
 		}
 	}
 	var H, HH, I, J, r, V fp.Element
@@ -678,8 +678,8 @@ func (p *g2JacExtended) Set(q *g2JacExtended) *g2JacExtended {
 	return p
 }
 
-// setInfinity sets p to the infinity point (1,1,0,0).
-func (p *g2JacExtended) setInfinity() *g2JacExtended {
+// SetInfinity sets p to the infinity point (1,1,0,0).
+func (p *g2JacExtended) SetInfinity() *g2JacExtended {
 	p.X.SetOne()
 	p.Y.SetOne()
 	p.ZZ = fp.Element{}
diff --git a/ecc/bw6-633/g2_test.go b/ecc/bw6-633/g2_test.go
index 04a3efe6de..611318c9eb 100644
--- a/ecc/bw6-633/g2_test.go
+++ b/ecc/bw6-633/g2_test.go
@@ -257,7 +257,7 @@ func TestG2AffineOps(t *testing.T) {
 			g := g2GenAff
 			s.BigInt(&sInt)
 			op1.ScalarMultiplication(&g, &sInt)
-			op2.setInfinity()
+			op2.SetInfinity()
 
 			op1.Add(&op1, &op2)
 			op2.Add(&op2, &op1)
diff --git a/ecc/bw6-633/multiexp_affine.go b/ecc/bw6-633/multiexp_affine.go
index aaba66f9f1..73e875fa8b 100644
--- a/ecc/bw6-633/multiexp_affine.go
+++ b/ecc/bw6-633/multiexp_affine.go
@@ -62,7 +62,7 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 	var buckets B // in G1Affine coordinates, infinity point is represented as (0,0), no need to init
 	var bucketsJE BJE
 	for i := 0; i < len(buckets); i++ {
-		bucketsJE[i].setInfinity()
+		bucketsJE[i].SetInfinity()
 	}
 
 	// setup for the batch affine;
@@ -105,7 +105,7 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 				bucketsJE[op.bucketID].addMixed(&op.point)
 				return
 			}
-			BK.setInfinity()
+			BK.SetInfinity()
 			return
 		}
 
@@ -133,12 +133,12 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 				if isAdd {
 					bucketsJE[bucketID].addMixed(PP)
 				} else {
-					BK.setInfinity()
+					BK.SetInfinity()
 				}
 				return
 			}
 			if isAdd {
-				BK.setInfinity()
+				BK.SetInfinity()
 			} else {
 				bucketsJE[bucketID].subMixed(PP)
 			}
@@ -220,8 +220,8 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 	// reduce buckets into total
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 	var runningSum, total g1JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		runningSum.addMixed(&buckets[k])
 		if !bucketsJE[k].IsInfinity() {
@@ -329,7 +329,7 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 	var buckets B // in G2Affine coordinates, infinity point is represented as (0,0), no need to init
 	var bucketsJE BJE
 	for i := 0; i < len(buckets); i++ {
-		bucketsJE[i].setInfinity()
+		bucketsJE[i].SetInfinity()
 	}
 
 	// setup for the batch affine;
@@ -372,7 +372,7 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 				bucketsJE[op.bucketID].addMixed(&op.point)
 				return
 			}
-			BK.setInfinity()
+			BK.SetInfinity()
 			return
 		}
 
@@ -400,12 +400,12 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 				if isAdd {
 					bucketsJE[bucketID].addMixed(PP)
 				} else {
-					BK.setInfinity()
+					BK.SetInfinity()
 				}
 				return
 			}
 			if isAdd {
-				BK.setInfinity()
+				BK.SetInfinity()
 			} else {
 				bucketsJE[bucketID].subMixed(PP)
 			}
@@ -487,8 +487,8 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 	// reduce buckets into total
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 	var runningSum, total g2JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		runningSum.addMixed(&buckets[k])
 		if !bucketsJE[k].IsInfinity() {
diff --git a/ecc/bw6-633/multiexp_jacobian.go b/ecc/bw6-633/multiexp_jacobian.go
index ffd7d0a5cc..fce9735a1c 100644
--- a/ecc/bw6-633/multiexp_jacobian.go
+++ b/ecc/bw6-633/multiexp_jacobian.go
@@ -30,7 +30,7 @@ func processChunkG1Jacobian[B ibg1JacExtended](chunk uint64,
 
 	var buckets B
 	for i := 0; i < len(buckets); i++ {
-		buckets[i].setInfinity()
+		buckets[i].SetInfinity()
 	}
 
 	// for each scalars, get the digit corresponding to the chunk we're processing.
@@ -53,8 +53,8 @@ func processChunkG1Jacobian[B ibg1JacExtended](chunk uint64,
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 
 	var runningSum, total g1JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		if !buckets[k].IsInfinity() {
 			runningSum.add(&buckets[k])
@@ -103,7 +103,7 @@ func processChunkG2Jacobian[B ibg2JacExtended](chunk uint64,
 
 	var buckets B
 	for i := 0; i < len(buckets); i++ {
-		buckets[i].setInfinity()
+		buckets[i].SetInfinity()
 	}
 
 	// for each scalars, get the digit corresponding to the chunk we're processing.
@@ -126,8 +126,8 @@ func processChunkG2Jacobian[B ibg2JacExtended](chunk uint64,
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 
 	var runningSum, total g2JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		if !buckets[k].IsInfinity() {
 			runningSum.add(&buckets[k])
diff --git a/ecc/bw6-633/multiexp_test.go b/ecc/bw6-633/multiexp_test.go
index c6c4e86a9b..2de5f7b732 100644
--- a/ecc/bw6-633/multiexp_test.go
+++ b/ecc/bw6-633/multiexp_test.go
@@ -57,10 +57,10 @@ func TestMultiExpG1(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	// final scalar to use in double and add method (without mixer factor)
 	// n(n+1)(2n+1)/6  (sum of the squares from 1 to n)
@@ -154,7 +154,7 @@ func TestMultiExpG1(t *testing.T) {
 			for i := 1; i <= nbSamples; i++ {
 				sampleScalars[i-1].SetUint64(uint64(i)).
 					Mul(&sampleScalars[i-1], &mixer)
-				samplePointsZero[i-1].setInfinity()
+				samplePointsZero[i-1].SetInfinity()
 			}
 
 			results := make([]G1Jac, len(cRange))
@@ -241,10 +241,10 @@ func TestCrossMultiExpG1(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	var sampleScalars [nbSamples]fr.Element
 	fillBenchScalars(sampleScalars[:])
@@ -471,10 +471,10 @@ func TestMultiExpG2(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	// final scalar to use in double and add method (without mixer factor)
 	// n(n+1)(2n+1)/6  (sum of the squares from 1 to n)
@@ -566,7 +566,7 @@ func TestMultiExpG2(t *testing.T) {
 			for i := 1; i <= nbSamples; i++ {
 				sampleScalars[i-1].SetUint64(uint64(i)).
 					Mul(&sampleScalars[i-1], &mixer)
-				samplePointsZero[i-1].setInfinity()
+				samplePointsZero[i-1].SetInfinity()
 			}
 
 			results := make([]G2Jac, len(cRange))
@@ -653,10 +653,10 @@ func TestCrossMultiExpG2(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	var sampleScalars [nbSamples]fr.Element
 	fillBenchScalars(sampleScalars[:])
diff --git a/ecc/bw6-761/g1.go b/ecc/bw6-761/g1.go
index d1939254c9..beef3e2aca 100644
--- a/ecc/bw6-761/g1.go
+++ b/ecc/bw6-761/g1.go
@@ -49,9 +49,9 @@ func (p *G1Affine) Set(a *G1Affine) *G1Affine {
 	return p
 }
 
-// setInfinity sets p to the infinity point, which is encoded as (0,0).
+// SetInfinity sets p to the infinity point, which is encoded as (0,0).
 // N.B.: (0,0) is never on the curve for j=0 curves (Y²=X³+B).
-func (p *G1Affine) setInfinity() *G1Affine {
+func (p *G1Affine) SetInfinity() *G1Affine {
 	p.X.SetZero()
 	p.Y.SetZero()
 	return p
@@ -99,7 +99,7 @@ func (p *G1Affine) Add(a, b *G1Affine) *G1Affine {
 			return p.FromJacobian(&q)
 		} else {
 			// if b == -a, we return 0
-			return p.setInfinity()
+			return p.SetInfinity()
 		}
 	}
 	var H, HH, I, J, r, V fp.Element
@@ -760,8 +760,8 @@ func (p *g1JacExtended) Set(q *g1JacExtended) *g1JacExtended {
 	return p
 }
 
-// setInfinity sets p to the infinity point (1,1,0,0).
-func (p *g1JacExtended) setInfinity() *g1JacExtended {
+// SetInfinity sets p to the infinity point (1,1,0,0).
+func (p *g1JacExtended) SetInfinity() *g1JacExtended {
 	p.X.SetOne()
 	p.Y.SetOne()
 	p.ZZ = fp.Element{}
diff --git a/ecc/bw6-761/g1_test.go b/ecc/bw6-761/g1_test.go
index c2c47846f9..620504f07f 100644
--- a/ecc/bw6-761/g1_test.go
+++ b/ecc/bw6-761/g1_test.go
@@ -270,7 +270,7 @@ func TestG1AffineOps(t *testing.T) {
 			g := g1GenAff
 			s.BigInt(&sInt)
 			op1.ScalarMultiplication(&g, &sInt)
-			op2.setInfinity()
+			op2.SetInfinity()
 
 			op1.Add(&op1, &op2)
 			op2.Add(&op2, &op1)
diff --git a/ecc/bw6-761/g2.go b/ecc/bw6-761/g2.go
index 57ea684685..832811a70e 100644
--- a/ecc/bw6-761/g2.go
+++ b/ecc/bw6-761/g2.go
@@ -55,9 +55,9 @@ func (p *G2Affine) Set(a *G2Affine) *G2Affine {
 	return p
 }
 
-// setInfinity sets p to the infinity point, which is encoded as (0,0).
+// SetInfinity sets p to the infinity point, which is encoded as (0,0).
 // N.B.: (0,0) is never on the curve for j=0 curves (Y²=X³+B).
-func (p *G2Affine) setInfinity() *G2Affine {
+func (p *G2Affine) SetInfinity() *G2Affine {
 	p.X.SetZero()
 	p.Y.SetZero()
 	return p
@@ -105,7 +105,7 @@ func (p *G2Affine) Add(a, b *G2Affine) *G2Affine {
 			return p.FromJacobian(&q)
 		} else {
 			// if b == -a, we return 0
-			return p.setInfinity()
+			return p.SetInfinity()
 		}
 	}
 	var H, HH, I, J, r, V fp.Element
@@ -686,8 +686,8 @@ func (p *g2JacExtended) Set(q *g2JacExtended) *g2JacExtended {
 	return p
 }
 
-// setInfinity sets p to the infinity point (1,1,0,0).
-func (p *g2JacExtended) setInfinity() *g2JacExtended {
+// SetInfinity sets p to the infinity point (1,1,0,0).
+func (p *g2JacExtended) SetInfinity() *g2JacExtended {
 	p.X.SetOne()
 	p.Y.SetOne()
 	p.ZZ = fp.Element{}
diff --git a/ecc/bw6-761/g2_test.go b/ecc/bw6-761/g2_test.go
index 18307cbdfa..e14f8ada59 100644
--- a/ecc/bw6-761/g2_test.go
+++ b/ecc/bw6-761/g2_test.go
@@ -257,7 +257,7 @@ func TestG2AffineOps(t *testing.T) {
 			g := g2GenAff
 			s.BigInt(&sInt)
 			op1.ScalarMultiplication(&g, &sInt)
-			op2.setInfinity()
+			op2.SetInfinity()
 
 			op1.Add(&op1, &op2)
 			op2.Add(&op2, &op1)
diff --git a/ecc/bw6-761/multiexp_affine.go b/ecc/bw6-761/multiexp_affine.go
index fd68dd7f50..f8427f4ba0 100644
--- a/ecc/bw6-761/multiexp_affine.go
+++ b/ecc/bw6-761/multiexp_affine.go
@@ -62,7 +62,7 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 	var buckets B // in G1Affine coordinates, infinity point is represented as (0,0), no need to init
 	var bucketsJE BJE
 	for i := 0; i < len(buckets); i++ {
-		bucketsJE[i].setInfinity()
+		bucketsJE[i].SetInfinity()
 	}
 
 	// setup for the batch affine;
@@ -105,7 +105,7 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 				bucketsJE[op.bucketID].addMixed(&op.point)
 				return
 			}
-			BK.setInfinity()
+			BK.SetInfinity()
 			return
 		}
 
@@ -133,12 +133,12 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 				if isAdd {
 					bucketsJE[bucketID].addMixed(PP)
 				} else {
-					BK.setInfinity()
+					BK.SetInfinity()
 				}
 				return
 			}
 			if isAdd {
-				BK.setInfinity()
+				BK.SetInfinity()
 			} else {
 				bucketsJE[bucketID].subMixed(PP)
 			}
@@ -220,8 +220,8 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 	// reduce buckets into total
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 	var runningSum, total g1JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		runningSum.addMixed(&buckets[k])
 		if !bucketsJE[k].IsInfinity() {
@@ -329,7 +329,7 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 	var buckets B // in G2Affine coordinates, infinity point is represented as (0,0), no need to init
 	var bucketsJE BJE
 	for i := 0; i < len(buckets); i++ {
-		bucketsJE[i].setInfinity()
+		bucketsJE[i].SetInfinity()
 	}
 
 	// setup for the batch affine;
@@ -372,7 +372,7 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 				bucketsJE[op.bucketID].addMixed(&op.point)
 				return
 			}
-			BK.setInfinity()
+			BK.SetInfinity()
 			return
 		}
 
@@ -400,12 +400,12 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 				if isAdd {
 					bucketsJE[bucketID].addMixed(PP)
 				} else {
-					BK.setInfinity()
+					BK.SetInfinity()
 				}
 				return
 			}
 			if isAdd {
-				BK.setInfinity()
+				BK.SetInfinity()
 			} else {
 				bucketsJE[bucketID].subMixed(PP)
 			}
@@ -487,8 +487,8 @@ func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP
 	// reduce buckets into total
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 	var runningSum, total g2JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		runningSum.addMixed(&buckets[k])
 		if !bucketsJE[k].IsInfinity() {
diff --git a/ecc/bw6-761/multiexp_jacobian.go b/ecc/bw6-761/multiexp_jacobian.go
index cb9b215db5..cb022606f9 100644
--- a/ecc/bw6-761/multiexp_jacobian.go
+++ b/ecc/bw6-761/multiexp_jacobian.go
@@ -30,7 +30,7 @@ func processChunkG1Jacobian[B ibg1JacExtended](chunk uint64,
 
 	var buckets B
 	for i := 0; i < len(buckets); i++ {
-		buckets[i].setInfinity()
+		buckets[i].SetInfinity()
 	}
 
 	// for each scalars, get the digit corresponding to the chunk we're processing.
@@ -53,8 +53,8 @@ func processChunkG1Jacobian[B ibg1JacExtended](chunk uint64,
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 
 	var runningSum, total g1JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		if !buckets[k].IsInfinity() {
 			runningSum.add(&buckets[k])
@@ -105,7 +105,7 @@ func processChunkG2Jacobian[B ibg2JacExtended](chunk uint64,
 
 	var buckets B
 	for i := 0; i < len(buckets); i++ {
-		buckets[i].setInfinity()
+		buckets[i].SetInfinity()
 	}
 
 	// for each scalars, get the digit corresponding to the chunk we're processing.
@@ -128,8 +128,8 @@ func processChunkG2Jacobian[B ibg2JacExtended](chunk uint64,
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 
 	var runningSum, total g2JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		if !buckets[k].IsInfinity() {
 			runningSum.add(&buckets[k])
diff --git a/ecc/bw6-761/multiexp_test.go b/ecc/bw6-761/multiexp_test.go
index 57242a6bd1..f4da37fc2e 100644
--- a/ecc/bw6-761/multiexp_test.go
+++ b/ecc/bw6-761/multiexp_test.go
@@ -57,10 +57,10 @@ func TestMultiExpG1(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	// final scalar to use in double and add method (without mixer factor)
 	// n(n+1)(2n+1)/6  (sum of the squares from 1 to n)
@@ -154,7 +154,7 @@ func TestMultiExpG1(t *testing.T) {
 			for i := 1; i <= nbSamples; i++ {
 				sampleScalars[i-1].SetUint64(uint64(i)).
 					Mul(&sampleScalars[i-1], &mixer)
-				samplePointsZero[i-1].setInfinity()
+				samplePointsZero[i-1].SetInfinity()
 			}
 
 			results := make([]G1Jac, len(cRange))
@@ -241,10 +241,10 @@ func TestCrossMultiExpG1(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	var sampleScalars [nbSamples]fr.Element
 	fillBenchScalars(sampleScalars[:])
@@ -471,10 +471,10 @@ func TestMultiExpG2(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	// final scalar to use in double and add method (without mixer factor)
 	// n(n+1)(2n+1)/6  (sum of the squares from 1 to n)
@@ -566,7 +566,7 @@ func TestMultiExpG2(t *testing.T) {
 			for i := 1; i <= nbSamples; i++ {
 				sampleScalars[i-1].SetUint64(uint64(i)).
 					Mul(&sampleScalars[i-1], &mixer)
-				samplePointsZero[i-1].setInfinity()
+				samplePointsZero[i-1].SetInfinity()
 			}
 
 			results := make([]G2Jac, len(cRange))
@@ -653,10 +653,10 @@ func TestCrossMultiExpG2(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	var sampleScalars [nbSamples]fr.Element
 	fillBenchScalars(sampleScalars[:])
diff --git a/ecc/secp256k1/g1.go b/ecc/secp256k1/g1.go
index 625e4f5f0a..d747e4d9bd 100644
--- a/ecc/secp256k1/g1.go
+++ b/ecc/secp256k1/g1.go
@@ -49,9 +49,9 @@ func (p *G1Affine) Set(a *G1Affine) *G1Affine {
 	return p
 }
 
-// setInfinity sets p to the infinity point, which is encoded as (0,0).
+// SetInfinity sets p to the infinity point, which is encoded as (0,0).
 // N.B.: (0,0) is never on the curve for j=0 curves (Y²=X³+B).
-func (p *G1Affine) setInfinity() *G1Affine {
+func (p *G1Affine) SetInfinity() *G1Affine {
 	p.X.SetZero()
 	p.Y.SetZero()
 	return p
@@ -99,7 +99,7 @@ func (p *G1Affine) Add(a, b *G1Affine) *G1Affine {
 			return p.FromJacobian(&q)
 		} else {
 			// if b == -a, we return 0
-			return p.setInfinity()
+			return p.SetInfinity()
 		}
 	}
 	var H, HH, I, J, r, V fp.Element
@@ -694,8 +694,8 @@ func (p *g1JacExtended) Set(q *g1JacExtended) *g1JacExtended {
 	return p
 }
 
-// setInfinity sets p to the infinity point (1,1,0,0).
-func (p *g1JacExtended) setInfinity() *g1JacExtended {
+// SetInfinity sets p to the infinity point (1,1,0,0).
+func (p *g1JacExtended) SetInfinity() *g1JacExtended {
 	p.X.SetOne()
 	p.Y.SetOne()
 	p.ZZ = fp.Element{}
diff --git a/ecc/secp256k1/g1_test.go b/ecc/secp256k1/g1_test.go
index dd31e0ee54..a4fa37fb57 100644
--- a/ecc/secp256k1/g1_test.go
+++ b/ecc/secp256k1/g1_test.go
@@ -272,7 +272,7 @@ func TestG1AffineOps(t *testing.T) {
 			g := g1GenAff
 			s.BigInt(&sInt)
 			op1.ScalarMultiplication(&g, &sInt)
-			op2.setInfinity()
+			op2.SetInfinity()
 
 			op1.Add(&op1, &op2)
 			op2.Add(&op2, &op1)
diff --git a/ecc/secp256k1/multiexp_affine.go b/ecc/secp256k1/multiexp_affine.go
index e865e90e13..64bdcf759a 100644
--- a/ecc/secp256k1/multiexp_affine.go
+++ b/ecc/secp256k1/multiexp_affine.go
@@ -62,7 +62,7 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 	var buckets B // in G1Affine coordinates, infinity point is represented as (0,0), no need to init
 	var bucketsJE BJE
 	for i := 0; i < len(buckets); i++ {
-		bucketsJE[i].setInfinity()
+		bucketsJE[i].SetInfinity()
 	}
 
 	// setup for the batch affine;
@@ -105,7 +105,7 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 				bucketsJE[op.bucketID].addMixed(&op.point)
 				return
 			}
-			BK.setInfinity()
+			BK.SetInfinity()
 			return
 		}
 
@@ -133,12 +133,12 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 				if isAdd {
 					bucketsJE[bucketID].addMixed(PP)
 				} else {
-					BK.setInfinity()
+					BK.SetInfinity()
 				}
 				return
 			}
 			if isAdd {
-				BK.setInfinity()
+				BK.SetInfinity()
 			} else {
 				bucketsJE[bucketID].subMixed(PP)
 			}
@@ -220,8 +220,8 @@ func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP
 	// reduce buckets into total
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 	var runningSum, total g1JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		runningSum.addMixed(&buckets[k])
 		if !bucketsJE[k].IsInfinity() {
diff --git a/ecc/secp256k1/multiexp_jacobian.go b/ecc/secp256k1/multiexp_jacobian.go
index bbbc17b0d0..69b25b089f 100644
--- a/ecc/secp256k1/multiexp_jacobian.go
+++ b/ecc/secp256k1/multiexp_jacobian.go
@@ -30,7 +30,7 @@ func processChunkG1Jacobian[B ibg1JacExtended](chunk uint64,
 
 	var buckets B
 	for i := 0; i < len(buckets); i++ {
-		buckets[i].setInfinity()
+		buckets[i].SetInfinity()
 	}
 
 	// for each scalars, get the digit corresponding to the chunk we're processing.
@@ -53,8 +53,8 @@ func processChunkG1Jacobian[B ibg1JacExtended](chunk uint64,
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 
 	var runningSum, total g1JacExtended
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		if !buckets[k].IsInfinity() {
 			runningSum.add(&buckets[k])
diff --git a/ecc/secp256k1/multiexp_test.go b/ecc/secp256k1/multiexp_test.go
index ebc2c5002b..3f2c2c7908 100644
--- a/ecc/secp256k1/multiexp_test.go
+++ b/ecc/secp256k1/multiexp_test.go
@@ -57,10 +57,10 @@ func TestMultiExpG1(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	// final scalar to use in double and add method (without mixer factor)
 	// n(n+1)(2n+1)/6  (sum of the squares from 1 to n)
@@ -154,7 +154,7 @@ func TestMultiExpG1(t *testing.T) {
 			for i := 1; i <= nbSamples; i++ {
 				sampleScalars[i-1].SetUint64(uint64(i)).
 					Mul(&sampleScalars[i-1], &mixer)
-				samplePointsZero[i-1].setInfinity()
+				samplePointsZero[i-1].SetInfinity()
 			}
 
 			results := make([]G1Jac, len(cRange))
@@ -241,10 +241,10 @@ func TestCrossMultiExpG1(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	var sampleScalars [nbSamples]fr.Element
 	fillBenchScalars(sampleScalars[:])
diff --git a/internal/generator/ecc/template/multiexp_affine.go.tmpl b/internal/generator/ecc/template/multiexp_affine.go.tmpl
index 9f206a86d4..4b3b732964 100644
--- a/internal/generator/ecc/template/multiexp_affine.go.tmpl
+++ b/internal/generator/ecc/template/multiexp_affine.go.tmpl
@@ -64,7 +64,7 @@ func processChunk{{ $.UPointName }}BatchAffine[BJE ib{{ $.TJacobianExtended }},B
 	var buckets B // in {{ $.TAffine }} coordinates, infinity point is represented as (0,0), no need to init
 	var bucketsJE BJE
 	for i := 0; i < len(buckets); i++ {
-		bucketsJE[i].setInfinity()
+		bucketsJE[i].SetInfinity()
 	}
 
 	// setup for the batch affine;
@@ -107,7 +107,7 @@ func processChunk{{ $.UPointName }}BatchAffine[BJE ib{{ $.TJacobianExtended }},B
 				bucketsJE[op.bucketID].addMixed(&op.point)
 				return
 			}
-			BK.setInfinity()
+			BK.SetInfinity()
 			return
 		}
 
@@ -135,12 +135,12 @@ func processChunk{{ $.UPointName }}BatchAffine[BJE ib{{ $.TJacobianExtended }},B
 				if isAdd {
 					bucketsJE[bucketID].addMixed(PP)
 				} else {
-					BK.setInfinity()
+					BK.SetInfinity()
 				}
 				return
 			}
 			if isAdd {
-				BK.setInfinity()
+				BK.SetInfinity()
 			} else {
 				bucketsJE[bucketID].subMixed(PP)
 			}
@@ -225,8 +225,8 @@ func processChunk{{ $.UPointName }}BatchAffine[BJE ib{{ $.TJacobianExtended }},B
 	// reduce buckets into total
 	// total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 	var runningSum, total {{ $.TJacobianExtended }}
-	runningSum.setInfinity()
-	total.setInfinity()
+	runningSum.SetInfinity()
+	total.SetInfinity()
 	for k := len(buckets) - 1; k >= 0; k-- {
 		runningSum.addMixed(&buckets[k])
 		if !bucketsJE[k].IsInfinity() {
diff --git a/internal/generator/ecc/template/multiexp_jacobian.go.tmpl b/internal/generator/ecc/template/multiexp_jacobian.go.tmpl
index 39a6b55c72..cd7947345e 100644
--- a/internal/generator/ecc/template/multiexp_jacobian.go.tmpl
+++ b/internal/generator/ecc/template/multiexp_jacobian.go.tmpl
@@ -31,7 +31,7 @@ func processChunk{{ $.UPointName }}Jacobian[B ib{{ $.TJacobianExtended }}](chunk
 
    var buckets B
    for i := 0 ; i < len(buckets); i++ {
-	   buckets[i].setInfinity()
+	   buckets[i].SetInfinity()
    }
 
    // for each scalars, get the digit corresponding to the chunk we're processing.
@@ -55,8 +55,8 @@ func processChunk{{ $.UPointName }}Jacobian[B ib{{ $.TJacobianExtended }}](chunk
    // total =  bucket[0] + 2*bucket[1] + 3*bucket[2] ... + n*bucket[n-1]
 
    var runningSum, total {{ $.TJacobianExtended }}
-   runningSum.setInfinity()
-   total.setInfinity()
+   runningSum.SetInfinity()
+   total.SetInfinity()
    for k := len(buckets) - 1; k >= 0; k-- {
 	   if !buckets[k].IsInfinity() {
 		   runningSum.add(&buckets[k])
diff --git a/internal/generator/ecc/template/point.go.tmpl b/internal/generator/ecc/template/point.go.tmpl
index 4a06f1a5ac..22bf4e6f38 100644
--- a/internal/generator/ecc/template/point.go.tmpl
+++ b/internal/generator/ecc/template/point.go.tmpl
@@ -58,9 +58,9 @@ func (p *{{ $TAffine }}) Set(a *{{ $TAffine }}) *{{ $TAffine }} {
        return p
 }
 
-// setInfinity sets p to the infinity point, which is encoded as (0,0).
+// SetInfinity sets p to the infinity point, which is encoded as (0,0).
 // N.B.: (0,0) is never on the curve for j=0 curves (Y²=X³+B).
-func (p *{{ $TAffine }}) setInfinity() *{{ $TAffine }} {
+func (p *{{ $TAffine }}) SetInfinity() *{{ $TAffine }} {
 	p.X.SetZero()
 	p.Y.SetZero()
 	return p
@@ -117,7 +117,7 @@ func (p *{{ $TAffine }}) Add(a, b *{{ $TAffine }}) *{{ $TAffine }} {
 			return p.FromJacobian(&q)
 		} else {
 			// if b == -a, we return 0
-			return p.setInfinity()
+			return p.SetInfinity()
 		}
 	}
 	var H, HH, I, J, r, V {{.CoordType}}
@@ -1284,8 +1284,8 @@ func (p *{{ $TJacobianExtended }}) Set(q *{{ $TJacobianExtended }}) *{{ $TJacobi
 	return p
 }
 
-// setInfinity sets p to the infinity point (1,1,0,0).
-func (p *{{ $TJacobianExtended }}) setInfinity() *{{ $TJacobianExtended }} {
+// SetInfinity sets p to the infinity point (1,1,0,0).
+func (p *{{ $TJacobianExtended }}) SetInfinity() *{{ $TJacobianExtended }} {
 	p.X.SetOne()
 	p.Y.SetOne()
 	p.ZZ = {{.CoordType}}{}
diff --git a/internal/generator/ecc/template/tests/multiexp.go.tmpl b/internal/generator/ecc/template/tests/multiexp.go.tmpl
index fa678fd7f6..912b251352 100644
--- a/internal/generator/ecc/template/tests/multiexp.go.tmpl
+++ b/internal/generator/ecc/template/tests/multiexp.go.tmpl
@@ -59,10 +59,10 @@ func TestMultiExp{{$.UPointName}}(t *testing.T) {
 	}
 
     // sprinkle some points at infinity
-    samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-    samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-    samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-    samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+    samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+    samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+    samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+    samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 	// final scalar to use in double and add method (without mixer factor)
 	// n(n+1)(2n+1)/6  (sum of the squares from 1 to n)
@@ -166,7 +166,7 @@ func TestMultiExp{{$.UPointName}}(t *testing.T) {
 			for i := 1; i <= nbSamples; i++ {
 				sampleScalars[i-1].SetUint64(uint64(i)).
 					Mul(&sampleScalars[i-1], &mixer)
-				samplePointsZero[i-1].setInfinity()
+				samplePointsZero[i-1].SetInfinity()
 			}
 
 			results := make([]{{ $.TJacobian }}, len(cRange))
@@ -257,10 +257,10 @@ func TestCrossMultiExp{{ $.UPointName }}(t *testing.T) {
 	}
 
 	// sprinkle some points at infinity
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
-	samplePoints[rand.N(nbSamples)].setInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
+	samplePoints[rand.N(nbSamples)].SetInfinity() //#nosec G404 weak rng is fine here
 
 
 	var sampleScalars [nbSamples]fr.Element
diff --git a/internal/generator/ecc/template/tests/point.go.tmpl b/internal/generator/ecc/template/tests/point.go.tmpl
index ee4fdb615a..cb54d3791c 100644
--- a/internal/generator/ecc/template/tests/point.go.tmpl
+++ b/internal/generator/ecc/template/tests/point.go.tmpl
@@ -309,7 +309,7 @@ func Test{{ $TAffine }}Ops(t *testing.T) {
                     g := {{ toLower .PointName }}GenAff
                     s.BigInt(&sInt)
                     op1.ScalarMultiplication(&g, &sInt)
-                    op2.setInfinity()
+                    op2.SetInfinity()
 
                     op1.Add(&op1, &op2)
                     op2.Add(&op2, &op1)

From 3976874e9fef34fb2da630e1f1d4f77cec0f5ee4 Mon Sep 17 00:00:00 2001
From: Gautam Botrel <gautam.botrel@gmail.com>
Date: Wed, 23 Oct 2024 11:03:42 -0500
Subject: [PATCH 086/114] docs: document batchAddAfine func (#555)

---
 ecc/bls12-377/g1.go                           | 48 ++++++++++++-------
 ecc/bls12-377/g2.go                           | 48 ++++++++++++-------
 ecc/bls12-381/g1.go                           | 48 ++++++++++++-------
 ecc/bls12-381/g2.go                           | 48 ++++++++++++-------
 ecc/bls24-315/g1.go                           | 48 ++++++++++++-------
 ecc/bls24-315/g2.go                           | 48 ++++++++++++-------
 ecc/bls24-317/g1.go                           | 48 ++++++++++++-------
 ecc/bls24-317/g2.go                           | 48 ++++++++++++-------
 ecc/bn254/g1.go                               | 48 ++++++++++++-------
 ecc/bn254/g2.go                               | 48 ++++++++++++-------
 ecc/bw6-633/g1.go                             | 48 ++++++++++++-------
 ecc/bw6-633/g2.go                             | 48 ++++++++++++-------
 ecc/bw6-761/g1.go                             | 48 ++++++++++++-------
 ecc/bw6-761/g2.go                             | 48 ++++++++++++-------
 ecc/secp256k1/g1.go                           | 48 ++++++++++++-------
 internal/generator/ecc/template/point.go.tmpl | 47 +++++++++++-------
 16 files changed, 495 insertions(+), 272 deletions(-)

diff --git a/ecc/bls12-377/g1.go b/ecc/bls12-377/g1.go
index a99d6c81d6..9563f30667 100644
--- a/ecc/bls12-377/g1.go
+++ b/ecc/bls12-377/g1.go
@@ -1161,12 +1161,24 @@ func BatchScalarMultiplicationG1(base *G1Affine, scalars []fr.Element) []G1Affin
 func batchAddG1Affine[TP pG1Affine, TPP ppG1Affine, TC cG1Affine](R *TPP, P *TP, batchSize int) {
 	var lambda, lambdain TC
 
-	// add part
+	// from https://docs.zkproof.org/pages/standards/accepted-workshop3/proposal-turbo_plonk.pdf
+	// affine point addition formula
+	// R(X1, Y1) + P(X2, Y2) = Q(X3, Y3)
+	// λ  = (Y2 - Y1) / (X2 - X1)
+	// X3 = λ² - (X1 + X2)
+	// Y3 = λ * (X1 - X3) - Y1
+
+	// first we compute the 1 / (X2 - X1) for all points using Montgomery batch inversion trick
+
+	// X2 - X1
 	for j := 0; j < batchSize; j++ {
 		lambdain[j].Sub(&(*P)[j].X, &(*R)[j].X)
 	}
 
-	// invert denominator using montgomery batch invert technique
+	// montgomery batch inversion;
+	// lambda[0] = 1 / (P[0].X - R[0].X)
+	// lambda[1] = 1 / (P[1].X - R[1].X)
+	// ...
 	{
 		var accumulator fp.Element
 		lambda[0].SetOne()
@@ -1186,22 +1198,24 @@ func batchAddG1Affine[TP pG1Affine, TPP ppG1Affine, TC cG1Affine](R *TPP, P *TP,
 		lambda[0].Set(&accumulator)
 	}
 
-	var d fp.Element
-	var rr G1Affine
+	var t fp.Element
+	var Q G1Affine
 
-	// add part
 	for j := 0; j < batchSize; j++ {
-		// computa lambda
-		d.Sub(&(*P)[j].Y, &(*R)[j].Y)
-		lambda[j].Mul(&lambda[j], &d)
-
-		// compute X, Y
-		rr.X.Square(&lambda[j])
-		rr.X.Sub(&rr.X, &(*R)[j].X)
-		rr.X.Sub(&rr.X, &(*P)[j].X)
-		d.Sub(&(*R)[j].X, &rr.X)
-		rr.Y.Mul(&lambda[j], &d)
-		rr.Y.Sub(&rr.Y, &(*R)[j].Y)
-		(*R)[j].Set(&rr)
+		// λ  = (Y2 - Y1) / (X2 - X1)
+		t.Sub(&(*P)[j].Y, &(*R)[j].Y)
+		lambda[j].Mul(&lambda[j], &t)
+
+		// X3 = λ² - (X1 + X2)
+		Q.X.Square(&lambda[j])
+		Q.X.Sub(&Q.X, &(*R)[j].X)
+		Q.X.Sub(&Q.X, &(*P)[j].X)
+
+		// Y3 = λ * (X1 - X3) - Y1
+		t.Sub(&(*R)[j].X, &Q.X)
+		Q.Y.Mul(&lambda[j], &t)
+		Q.Y.Sub(&Q.Y, &(*R)[j].Y)
+
+		(*R)[j].Set(&Q)
 	}
 }
diff --git a/ecc/bls12-377/g2.go b/ecc/bls12-377/g2.go
index 3401a43a0f..29bf5e5e9e 100644
--- a/ecc/bls12-377/g2.go
+++ b/ecc/bls12-377/g2.go
@@ -1087,12 +1087,24 @@ func BatchScalarMultiplicationG2(base *G2Affine, scalars []fr.Element) []G2Affin
 func batchAddG2Affine[TP pG2Affine, TPP ppG2Affine, TC cG2Affine](R *TPP, P *TP, batchSize int) {
 	var lambda, lambdain TC
 
-	// add part
+	// from https://docs.zkproof.org/pages/standards/accepted-workshop3/proposal-turbo_plonk.pdf
+	// affine point addition formula
+	// R(X1, Y1) + P(X2, Y2) = Q(X3, Y3)
+	// λ  = (Y2 - Y1) / (X2 - X1)
+	// X3 = λ² - (X1 + X2)
+	// Y3 = λ * (X1 - X3) - Y1
+
+	// first we compute the 1 / (X2 - X1) for all points using Montgomery batch inversion trick
+
+	// X2 - X1
 	for j := 0; j < batchSize; j++ {
 		lambdain[j].Sub(&(*P)[j].X, &(*R)[j].X)
 	}
 
-	// invert denominator using montgomery batch invert technique
+	// montgomery batch inversion;
+	// lambda[0] = 1 / (P[0].X - R[0].X)
+	// lambda[1] = 1 / (P[1].X - R[1].X)
+	// ...
 	{
 		var accumulator fptower.E2
 		lambda[0].SetOne()
@@ -1112,23 +1124,25 @@ func batchAddG2Affine[TP pG2Affine, TPP ppG2Affine, TC cG2Affine](R *TPP, P *TP,
 		lambda[0].Set(&accumulator)
 	}
 
-	var d fptower.E2
-	var rr G2Affine
+	var t fptower.E2
+	var Q G2Affine
 
-	// add part
 	for j := 0; j < batchSize; j++ {
-		// computa lambda
-		d.Sub(&(*P)[j].Y, &(*R)[j].Y)
-		lambda[j].Mul(&lambda[j], &d)
-
-		// compute X, Y
-		rr.X.Square(&lambda[j])
-		rr.X.Sub(&rr.X, &(*R)[j].X)
-		rr.X.Sub(&rr.X, &(*P)[j].X)
-		d.Sub(&(*R)[j].X, &rr.X)
-		rr.Y.Mul(&lambda[j], &d)
-		rr.Y.Sub(&rr.Y, &(*R)[j].Y)
-		(*R)[j].Set(&rr)
+		// λ  = (Y2 - Y1) / (X2 - X1)
+		t.Sub(&(*P)[j].Y, &(*R)[j].Y)
+		lambda[j].Mul(&lambda[j], &t)
+
+		// X3 = λ² - (X1 + X2)
+		Q.X.Square(&lambda[j])
+		Q.X.Sub(&Q.X, &(*R)[j].X)
+		Q.X.Sub(&Q.X, &(*P)[j].X)
+
+		// Y3 = λ * (X1 - X3) - Y1
+		t.Sub(&(*R)[j].X, &Q.X)
+		Q.Y.Mul(&lambda[j], &t)
+		Q.Y.Sub(&Q.Y, &(*R)[j].Y)
+
+		(*R)[j].Set(&Q)
 	}
 }
 
diff --git a/ecc/bls12-381/g1.go b/ecc/bls12-381/g1.go
index 88ac32c77a..c626d848f6 100644
--- a/ecc/bls12-381/g1.go
+++ b/ecc/bls12-381/g1.go
@@ -1162,12 +1162,24 @@ func BatchScalarMultiplicationG1(base *G1Affine, scalars []fr.Element) []G1Affin
 func batchAddG1Affine[TP pG1Affine, TPP ppG1Affine, TC cG1Affine](R *TPP, P *TP, batchSize int) {
 	var lambda, lambdain TC
 
-	// add part
+	// from https://docs.zkproof.org/pages/standards/accepted-workshop3/proposal-turbo_plonk.pdf
+	// affine point addition formula
+	// R(X1, Y1) + P(X2, Y2) = Q(X3, Y3)
+	// λ  = (Y2 - Y1) / (X2 - X1)
+	// X3 = λ² - (X1 + X2)
+	// Y3 = λ * (X1 - X3) - Y1
+
+	// first we compute the 1 / (X2 - X1) for all points using Montgomery batch inversion trick
+
+	// X2 - X1
 	for j := 0; j < batchSize; j++ {
 		lambdain[j].Sub(&(*P)[j].X, &(*R)[j].X)
 	}
 
-	// invert denominator using montgomery batch invert technique
+	// montgomery batch inversion;
+	// lambda[0] = 1 / (P[0].X - R[0].X)
+	// lambda[1] = 1 / (P[1].X - R[1].X)
+	// ...
 	{
 		var accumulator fp.Element
 		lambda[0].SetOne()
@@ -1187,22 +1199,24 @@ func batchAddG1Affine[TP pG1Affine, TPP ppG1Affine, TC cG1Affine](R *TPP, P *TP,
 		lambda[0].Set(&accumulator)
 	}
 
-	var d fp.Element
-	var rr G1Affine
+	var t fp.Element
+	var Q G1Affine
 
-	// add part
 	for j := 0; j < batchSize; j++ {
-		// computa lambda
-		d.Sub(&(*P)[j].Y, &(*R)[j].Y)
-		lambda[j].Mul(&lambda[j], &d)
-
-		// compute X, Y
-		rr.X.Square(&lambda[j])
-		rr.X.Sub(&rr.X, &(*R)[j].X)
-		rr.X.Sub(&rr.X, &(*P)[j].X)
-		d.Sub(&(*R)[j].X, &rr.X)
-		rr.Y.Mul(&lambda[j], &d)
-		rr.Y.Sub(&rr.Y, &(*R)[j].Y)
-		(*R)[j].Set(&rr)
+		// λ  = (Y2 - Y1) / (X2 - X1)
+		t.Sub(&(*P)[j].Y, &(*R)[j].Y)
+		lambda[j].Mul(&lambda[j], &t)
+
+		// X3 = λ² - (X1 + X2)
+		Q.X.Square(&lambda[j])
+		Q.X.Sub(&Q.X, &(*R)[j].X)
+		Q.X.Sub(&Q.X, &(*P)[j].X)
+
+		// Y3 = λ * (X1 - X3) - Y1
+		t.Sub(&(*R)[j].X, &Q.X)
+		Q.Y.Mul(&lambda[j], &t)
+		Q.Y.Sub(&Q.Y, &(*R)[j].Y)
+
+		(*R)[j].Set(&Q)
 	}
 }
diff --git a/ecc/bls12-381/g2.go b/ecc/bls12-381/g2.go
index d4d7fa1c92..38f262cb8c 100644
--- a/ecc/bls12-381/g2.go
+++ b/ecc/bls12-381/g2.go
@@ -1088,12 +1088,24 @@ func BatchScalarMultiplicationG2(base *G2Affine, scalars []fr.Element) []G2Affin
 func batchAddG2Affine[TP pG2Affine, TPP ppG2Affine, TC cG2Affine](R *TPP, P *TP, batchSize int) {
 	var lambda, lambdain TC
 
-	// add part
+	// from https://docs.zkproof.org/pages/standards/accepted-workshop3/proposal-turbo_plonk.pdf
+	// affine point addition formula
+	// R(X1, Y1) + P(X2, Y2) = Q(X3, Y3)
+	// λ  = (Y2 - Y1) / (X2 - X1)
+	// X3 = λ² - (X1 + X2)
+	// Y3 = λ * (X1 - X3) - Y1
+
+	// first we compute the 1 / (X2 - X1) for all points using Montgomery batch inversion trick
+
+	// X2 - X1
 	for j := 0; j < batchSize; j++ {
 		lambdain[j].Sub(&(*P)[j].X, &(*R)[j].X)
 	}
 
-	// invert denominator using montgomery batch invert technique
+	// montgomery batch inversion;
+	// lambda[0] = 1 / (P[0].X - R[0].X)
+	// lambda[1] = 1 / (P[1].X - R[1].X)
+	// ...
 	{
 		var accumulator fptower.E2
 		lambda[0].SetOne()
@@ -1113,23 +1125,25 @@ func batchAddG2Affine[TP pG2Affine, TPP ppG2Affine, TC cG2Affine](R *TPP, P *TP,
 		lambda[0].Set(&accumulator)
 	}
 
-	var d fptower.E2
-	var rr G2Affine
+	var t fptower.E2
+	var Q G2Affine
 
-	// add part
 	for j := 0; j < batchSize; j++ {
-		// computa lambda
-		d.Sub(&(*P)[j].Y, &(*R)[j].Y)
-		lambda[j].Mul(&lambda[j], &d)
-
-		// compute X, Y
-		rr.X.Square(&lambda[j])
-		rr.X.Sub(&rr.X, &(*R)[j].X)
-		rr.X.Sub(&rr.X, &(*P)[j].X)
-		d.Sub(&(*R)[j].X, &rr.X)
-		rr.Y.Mul(&lambda[j], &d)
-		rr.Y.Sub(&rr.Y, &(*R)[j].Y)
-		(*R)[j].Set(&rr)
+		// λ  = (Y2 - Y1) / (X2 - X1)
+		t.Sub(&(*P)[j].Y, &(*R)[j].Y)
+		lambda[j].Mul(&lambda[j], &t)
+
+		// X3 = λ² - (X1 + X2)
+		Q.X.Square(&lambda[j])
+		Q.X.Sub(&Q.X, &(*R)[j].X)
+		Q.X.Sub(&Q.X, &(*P)[j].X)
+
+		// Y3 = λ * (X1 - X3) - Y1
+		t.Sub(&(*R)[j].X, &Q.X)
+		Q.Y.Mul(&lambda[j], &t)
+		Q.Y.Sub(&Q.Y, &(*R)[j].Y)
+
+		(*R)[j].Set(&Q)
 	}
 }
 
diff --git a/ecc/bls24-315/g1.go b/ecc/bls24-315/g1.go
index 91d995c8cb..0e1cc2ff8c 100644
--- a/ecc/bls24-315/g1.go
+++ b/ecc/bls24-315/g1.go
@@ -1163,12 +1163,24 @@ func BatchScalarMultiplicationG1(base *G1Affine, scalars []fr.Element) []G1Affin
 func batchAddG1Affine[TP pG1Affine, TPP ppG1Affine, TC cG1Affine](R *TPP, P *TP, batchSize int) {
 	var lambda, lambdain TC
 
-	// add part
+	// from https://docs.zkproof.org/pages/standards/accepted-workshop3/proposal-turbo_plonk.pdf
+	// affine point addition formula
+	// R(X1, Y1) + P(X2, Y2) = Q(X3, Y3)
+	// λ  = (Y2 - Y1) / (X2 - X1)
+	// X3 = λ² - (X1 + X2)
+	// Y3 = λ * (X1 - X3) - Y1
+
+	// first we compute the 1 / (X2 - X1) for all points using Montgomery batch inversion trick
+
+	// X2 - X1
 	for j := 0; j < batchSize; j++ {
 		lambdain[j].Sub(&(*P)[j].X, &(*R)[j].X)
 	}
 
-	// invert denominator using montgomery batch invert technique
+	// montgomery batch inversion;
+	// lambda[0] = 1 / (P[0].X - R[0].X)
+	// lambda[1] = 1 / (P[1].X - R[1].X)
+	// ...
 	{
 		var accumulator fp.Element
 		lambda[0].SetOne()
@@ -1188,22 +1200,24 @@ func batchAddG1Affine[TP pG1Affine, TPP ppG1Affine, TC cG1Affine](R *TPP, P *TP,
 		lambda[0].Set(&accumulator)
 	}
 
-	var d fp.Element
-	var rr G1Affine
+	var t fp.Element
+	var Q G1Affine
 
-	// add part
 	for j := 0; j < batchSize; j++ {
-		// computa lambda
-		d.Sub(&(*P)[j].Y, &(*R)[j].Y)
-		lambda[j].Mul(&lambda[j], &d)
-
-		// compute X, Y
-		rr.X.Square(&lambda[j])
-		rr.X.Sub(&rr.X, &(*R)[j].X)
-		rr.X.Sub(&rr.X, &(*P)[j].X)
-		d.Sub(&(*R)[j].X, &rr.X)
-		rr.Y.Mul(&lambda[j], &d)
-		rr.Y.Sub(&rr.Y, &(*R)[j].Y)
-		(*R)[j].Set(&rr)
+		// λ  = (Y2 - Y1) / (X2 - X1)
+		t.Sub(&(*P)[j].Y, &(*R)[j].Y)
+		lambda[j].Mul(&lambda[j], &t)
+
+		// X3 = λ² - (X1 + X2)
+		Q.X.Square(&lambda[j])
+		Q.X.Sub(&Q.X, &(*R)[j].X)
+		Q.X.Sub(&Q.X, &(*P)[j].X)
+
+		// Y3 = λ * (X1 - X3) - Y1
+		t.Sub(&(*R)[j].X, &Q.X)
+		Q.Y.Mul(&lambda[j], &t)
+		Q.Y.Sub(&Q.Y, &(*R)[j].Y)
+
+		(*R)[j].Set(&Q)
 	}
 }
diff --git a/ecc/bls24-315/g2.go b/ecc/bls24-315/g2.go
index dd08636ea9..8250d2b5aa 100644
--- a/ecc/bls24-315/g2.go
+++ b/ecc/bls24-315/g2.go
@@ -1103,12 +1103,24 @@ func BatchScalarMultiplicationG2(base *G2Affine, scalars []fr.Element) []G2Affin
 func batchAddG2Affine[TP pG2Affine, TPP ppG2Affine, TC cG2Affine](R *TPP, P *TP, batchSize int) {
 	var lambda, lambdain TC
 
-	// add part
+	// from https://docs.zkproof.org/pages/standards/accepted-workshop3/proposal-turbo_plonk.pdf
+	// affine point addition formula
+	// R(X1, Y1) + P(X2, Y2) = Q(X3, Y3)
+	// λ  = (Y2 - Y1) / (X2 - X1)
+	// X3 = λ² - (X1 + X2)
+	// Y3 = λ * (X1 - X3) - Y1
+
+	// first we compute the 1 / (X2 - X1) for all points using Montgomery batch inversion trick
+
+	// X2 - X1
 	for j := 0; j < batchSize; j++ {
 		lambdain[j].Sub(&(*P)[j].X, &(*R)[j].X)
 	}
 
-	// invert denominator using montgomery batch invert technique
+	// montgomery batch inversion;
+	// lambda[0] = 1 / (P[0].X - R[0].X)
+	// lambda[1] = 1 / (P[1].X - R[1].X)
+	// ...
 	{
 		var accumulator fptower.E4
 		lambda[0].SetOne()
@@ -1128,23 +1140,25 @@ func batchAddG2Affine[TP pG2Affine, TPP ppG2Affine, TC cG2Affine](R *TPP, P *TP,
 		lambda[0].Set(&accumulator)
 	}
 
-	var d fptower.E4
-	var rr G2Affine
+	var t fptower.E4
+	var Q G2Affine
 
-	// add part
 	for j := 0; j < batchSize; j++ {
-		// computa lambda
-		d.Sub(&(*P)[j].Y, &(*R)[j].Y)
-		lambda[j].Mul(&lambda[j], &d)
-
-		// compute X, Y
-		rr.X.Square(&lambda[j])
-		rr.X.Sub(&rr.X, &(*R)[j].X)
-		rr.X.Sub(&rr.X, &(*P)[j].X)
-		d.Sub(&(*R)[j].X, &rr.X)
-		rr.Y.Mul(&lambda[j], &d)
-		rr.Y.Sub(&rr.Y, &(*R)[j].Y)
-		(*R)[j].Set(&rr)
+		// λ  = (Y2 - Y1) / (X2 - X1)
+		t.Sub(&(*P)[j].Y, &(*R)[j].Y)
+		lambda[j].Mul(&lambda[j], &t)
+
+		// X3 = λ² - (X1 + X2)
+		Q.X.Square(&lambda[j])
+		Q.X.Sub(&Q.X, &(*R)[j].X)
+		Q.X.Sub(&Q.X, &(*P)[j].X)
+
+		// Y3 = λ * (X1 - X3) - Y1
+		t.Sub(&(*R)[j].X, &Q.X)
+		Q.Y.Mul(&lambda[j], &t)
+		Q.Y.Sub(&Q.Y, &(*R)[j].Y)
+
+		(*R)[j].Set(&Q)
 	}
 }
 
diff --git a/ecc/bls24-317/g1.go b/ecc/bls24-317/g1.go
index 890a7de492..8240303dd9 100644
--- a/ecc/bls24-317/g1.go
+++ b/ecc/bls24-317/g1.go
@@ -1164,12 +1164,24 @@ func BatchScalarMultiplicationG1(base *G1Affine, scalars []fr.Element) []G1Affin
 func batchAddG1Affine[TP pG1Affine, TPP ppG1Affine, TC cG1Affine](R *TPP, P *TP, batchSize int) {
 	var lambda, lambdain TC
 
-	// add part
+	// from https://docs.zkproof.org/pages/standards/accepted-workshop3/proposal-turbo_plonk.pdf
+	// affine point addition formula
+	// R(X1, Y1) + P(X2, Y2) = Q(X3, Y3)
+	// λ  = (Y2 - Y1) / (X2 - X1)
+	// X3 = λ² - (X1 + X2)
+	// Y3 = λ * (X1 - X3) - Y1
+
+	// first we compute the 1 / (X2 - X1) for all points using Montgomery batch inversion trick
+
+	// X2 - X1
 	for j := 0; j < batchSize; j++ {
 		lambdain[j].Sub(&(*P)[j].X, &(*R)[j].X)
 	}
 
-	// invert denominator using montgomery batch invert technique
+	// montgomery batch inversion;
+	// lambda[0] = 1 / (P[0].X - R[0].X)
+	// lambda[1] = 1 / (P[1].X - R[1].X)
+	// ...
 	{
 		var accumulator fp.Element
 		lambda[0].SetOne()
@@ -1189,22 +1201,24 @@ func batchAddG1Affine[TP pG1Affine, TPP ppG1Affine, TC cG1Affine](R *TPP, P *TP,
 		lambda[0].Set(&accumulator)
 	}
 
-	var d fp.Element
-	var rr G1Affine
+	var t fp.Element
+	var Q G1Affine
 
-	// add part
 	for j := 0; j < batchSize; j++ {
-		// computa lambda
-		d.Sub(&(*P)[j].Y, &(*R)[j].Y)
-		lambda[j].Mul(&lambda[j], &d)
-
-		// compute X, Y
-		rr.X.Square(&lambda[j])
-		rr.X.Sub(&rr.X, &(*R)[j].X)
-		rr.X.Sub(&rr.X, &(*P)[j].X)
-		d.Sub(&(*R)[j].X, &rr.X)
-		rr.Y.Mul(&lambda[j], &d)
-		rr.Y.Sub(&rr.Y, &(*R)[j].Y)
-		(*R)[j].Set(&rr)
+		// λ  = (Y2 - Y1) / (X2 - X1)
+		t.Sub(&(*P)[j].Y, &(*R)[j].Y)
+		lambda[j].Mul(&lambda[j], &t)
+
+		// X3 = λ² - (X1 + X2)
+		Q.X.Square(&lambda[j])
+		Q.X.Sub(&Q.X, &(*R)[j].X)
+		Q.X.Sub(&Q.X, &(*P)[j].X)
+
+		// Y3 = λ * (X1 - X3) - Y1
+		t.Sub(&(*R)[j].X, &Q.X)
+		Q.Y.Mul(&lambda[j], &t)
+		Q.Y.Sub(&Q.Y, &(*R)[j].Y)
+
+		(*R)[j].Set(&Q)
 	}
 }
diff --git a/ecc/bls24-317/g2.go b/ecc/bls24-317/g2.go
index b34c68acd6..9f51ce2141 100644
--- a/ecc/bls24-317/g2.go
+++ b/ecc/bls24-317/g2.go
@@ -1103,12 +1103,24 @@ func BatchScalarMultiplicationG2(base *G2Affine, scalars []fr.Element) []G2Affin
 func batchAddG2Affine[TP pG2Affine, TPP ppG2Affine, TC cG2Affine](R *TPP, P *TP, batchSize int) {
 	var lambda, lambdain TC
 
-	// add part
+	// from https://docs.zkproof.org/pages/standards/accepted-workshop3/proposal-turbo_plonk.pdf
+	// affine point addition formula
+	// R(X1, Y1) + P(X2, Y2) = Q(X3, Y3)
+	// λ  = (Y2 - Y1) / (X2 - X1)
+	// X3 = λ² - (X1 + X2)
+	// Y3 = λ * (X1 - X3) - Y1
+
+	// first we compute the 1 / (X2 - X1) for all points using Montgomery batch inversion trick
+
+	// X2 - X1
 	for j := 0; j < batchSize; j++ {
 		lambdain[j].Sub(&(*P)[j].X, &(*R)[j].X)
 	}
 
-	// invert denominator using montgomery batch invert technique
+	// montgomery batch inversion;
+	// lambda[0] = 1 / (P[0].X - R[0].X)
+	// lambda[1] = 1 / (P[1].X - R[1].X)
+	// ...
 	{
 		var accumulator fptower.E4
 		lambda[0].SetOne()
@@ -1128,23 +1140,25 @@ func batchAddG2Affine[TP pG2Affine, TPP ppG2Affine, TC cG2Affine](R *TPP, P *TP,
 		lambda[0].Set(&accumulator)
 	}
 
-	var d fptower.E4
-	var rr G2Affine
+	var t fptower.E4
+	var Q G2Affine
 
-	// add part
 	for j := 0; j < batchSize; j++ {
-		// computa lambda
-		d.Sub(&(*P)[j].Y, &(*R)[j].Y)
-		lambda[j].Mul(&lambda[j], &d)
-
-		// compute X, Y
-		rr.X.Square(&lambda[j])
-		rr.X.Sub(&rr.X, &(*R)[j].X)
-		rr.X.Sub(&rr.X, &(*P)[j].X)
-		d.Sub(&(*R)[j].X, &rr.X)
-		rr.Y.Mul(&lambda[j], &d)
-		rr.Y.Sub(&rr.Y, &(*R)[j].Y)
-		(*R)[j].Set(&rr)
+		// λ  = (Y2 - Y1) / (X2 - X1)
+		t.Sub(&(*P)[j].Y, &(*R)[j].Y)
+		lambda[j].Mul(&lambda[j], &t)
+
+		// X3 = λ² - (X1 + X2)
+		Q.X.Square(&lambda[j])
+		Q.X.Sub(&Q.X, &(*R)[j].X)
+		Q.X.Sub(&Q.X, &(*P)[j].X)
+
+		// Y3 = λ * (X1 - X3) - Y1
+		t.Sub(&(*R)[j].X, &Q.X)
+		Q.Y.Mul(&lambda[j], &t)
+		Q.Y.Sub(&Q.Y, &(*R)[j].Y)
+
+		(*R)[j].Set(&Q)
 	}
 }
 
diff --git a/ecc/bn254/g1.go b/ecc/bn254/g1.go
index 14dfeef86b..e2c4a1d96d 100644
--- a/ecc/bn254/g1.go
+++ b/ecc/bn254/g1.go
@@ -1133,12 +1133,24 @@ func BatchScalarMultiplicationG1(base *G1Affine, scalars []fr.Element) []G1Affin
 func batchAddG1Affine[TP pG1Affine, TPP ppG1Affine, TC cG1Affine](R *TPP, P *TP, batchSize int) {
 	var lambda, lambdain TC
 
-	// add part
+	// from https://docs.zkproof.org/pages/standards/accepted-workshop3/proposal-turbo_plonk.pdf
+	// affine point addition formula
+	// R(X1, Y1) + P(X2, Y2) = Q(X3, Y3)
+	// λ  = (Y2 - Y1) / (X2 - X1)
+	// X3 = λ² - (X1 + X2)
+	// Y3 = λ * (X1 - X3) - Y1
+
+	// first we compute the 1 / (X2 - X1) for all points using Montgomery batch inversion trick
+
+	// X2 - X1
 	for j := 0; j < batchSize; j++ {
 		lambdain[j].Sub(&(*P)[j].X, &(*R)[j].X)
 	}
 
-	// invert denominator using montgomery batch invert technique
+	// montgomery batch inversion;
+	// lambda[0] = 1 / (P[0].X - R[0].X)
+	// lambda[1] = 1 / (P[1].X - R[1].X)
+	// ...
 	{
 		var accumulator fp.Element
 		lambda[0].SetOne()
@@ -1158,22 +1170,24 @@ func batchAddG1Affine[TP pG1Affine, TPP ppG1Affine, TC cG1Affine](R *TPP, P *TP,
 		lambda[0].Set(&accumulator)
 	}
 
-	var d fp.Element
-	var rr G1Affine
+	var t fp.Element
+	var Q G1Affine
 
-	// add part
 	for j := 0; j < batchSize; j++ {
-		// computa lambda
-		d.Sub(&(*P)[j].Y, &(*R)[j].Y)
-		lambda[j].Mul(&lambda[j], &d)
-
-		// compute X, Y
-		rr.X.Square(&lambda[j])
-		rr.X.Sub(&rr.X, &(*R)[j].X)
-		rr.X.Sub(&rr.X, &(*P)[j].X)
-		d.Sub(&(*R)[j].X, &rr.X)
-		rr.Y.Mul(&lambda[j], &d)
-		rr.Y.Sub(&rr.Y, &(*R)[j].Y)
-		(*R)[j].Set(&rr)
+		// λ  = (Y2 - Y1) / (X2 - X1)
+		t.Sub(&(*P)[j].Y, &(*R)[j].Y)
+		lambda[j].Mul(&lambda[j], &t)
+
+		// X3 = λ² - (X1 + X2)
+		Q.X.Square(&lambda[j])
+		Q.X.Sub(&Q.X, &(*R)[j].X)
+		Q.X.Sub(&Q.X, &(*P)[j].X)
+
+		// Y3 = λ * (X1 - X3) - Y1
+		t.Sub(&(*R)[j].X, &Q.X)
+		Q.Y.Mul(&lambda[j], &t)
+		Q.Y.Sub(&Q.Y, &(*R)[j].Y)
+
+		(*R)[j].Set(&Q)
 	}
 }
diff --git a/ecc/bn254/g2.go b/ecc/bn254/g2.go
index 24561bb28c..54addc34d2 100644
--- a/ecc/bn254/g2.go
+++ b/ecc/bn254/g2.go
@@ -1092,12 +1092,24 @@ func BatchScalarMultiplicationG2(base *G2Affine, scalars []fr.Element) []G2Affin
 func batchAddG2Affine[TP pG2Affine, TPP ppG2Affine, TC cG2Affine](R *TPP, P *TP, batchSize int) {
 	var lambda, lambdain TC
 
-	// add part
+	// from https://docs.zkproof.org/pages/standards/accepted-workshop3/proposal-turbo_plonk.pdf
+	// affine point addition formula
+	// R(X1, Y1) + P(X2, Y2) = Q(X3, Y3)
+	// λ  = (Y2 - Y1) / (X2 - X1)
+	// X3 = λ² - (X1 + X2)
+	// Y3 = λ * (X1 - X3) - Y1
+
+	// first we compute the 1 / (X2 - X1) for all points using Montgomery batch inversion trick
+
+	// X2 - X1
 	for j := 0; j < batchSize; j++ {
 		lambdain[j].Sub(&(*P)[j].X, &(*R)[j].X)
 	}
 
-	// invert denominator using montgomery batch invert technique
+	// montgomery batch inversion;
+	// lambda[0] = 1 / (P[0].X - R[0].X)
+	// lambda[1] = 1 / (P[1].X - R[1].X)
+	// ...
 	{
 		var accumulator fptower.E2
 		lambda[0].SetOne()
@@ -1117,23 +1129,25 @@ func batchAddG2Affine[TP pG2Affine, TPP ppG2Affine, TC cG2Affine](R *TPP, P *TP,
 		lambda[0].Set(&accumulator)
 	}
 
-	var d fptower.E2
-	var rr G2Affine
+	var t fptower.E2
+	var Q G2Affine
 
-	// add part
 	for j := 0; j < batchSize; j++ {
-		// computa lambda
-		d.Sub(&(*P)[j].Y, &(*R)[j].Y)
-		lambda[j].Mul(&lambda[j], &d)
-
-		// compute X, Y
-		rr.X.Square(&lambda[j])
-		rr.X.Sub(&rr.X, &(*R)[j].X)
-		rr.X.Sub(&rr.X, &(*P)[j].X)
-		d.Sub(&(*R)[j].X, &rr.X)
-		rr.Y.Mul(&lambda[j], &d)
-		rr.Y.Sub(&rr.Y, &(*R)[j].Y)
-		(*R)[j].Set(&rr)
+		// λ  = (Y2 - Y1) / (X2 - X1)
+		t.Sub(&(*P)[j].Y, &(*R)[j].Y)
+		lambda[j].Mul(&lambda[j], &t)
+
+		// X3 = λ² - (X1 + X2)
+		Q.X.Square(&lambda[j])
+		Q.X.Sub(&Q.X, &(*R)[j].X)
+		Q.X.Sub(&Q.X, &(*P)[j].X)
+
+		// Y3 = λ * (X1 - X3) - Y1
+		t.Sub(&(*R)[j].X, &Q.X)
+		Q.Y.Mul(&lambda[j], &t)
+		Q.Y.Sub(&Q.Y, &(*R)[j].Y)
+
+		(*R)[j].Set(&Q)
 	}
 }
 
diff --git a/ecc/bw6-633/g1.go b/ecc/bw6-633/g1.go
index 196053c960..6491867a3f 100644
--- a/ecc/bw6-633/g1.go
+++ b/ecc/bw6-633/g1.go
@@ -1186,12 +1186,24 @@ func BatchScalarMultiplicationG1(base *G1Affine, scalars []fr.Element) []G1Affin
 func batchAddG1Affine[TP pG1Affine, TPP ppG1Affine, TC cG1Affine](R *TPP, P *TP, batchSize int) {
 	var lambda, lambdain TC
 
-	// add part
+	// from https://docs.zkproof.org/pages/standards/accepted-workshop3/proposal-turbo_plonk.pdf
+	// affine point addition formula
+	// R(X1, Y1) + P(X2, Y2) = Q(X3, Y3)
+	// λ  = (Y2 - Y1) / (X2 - X1)
+	// X3 = λ² - (X1 + X2)
+	// Y3 = λ * (X1 - X3) - Y1
+
+	// first we compute the 1 / (X2 - X1) for all points using Montgomery batch inversion trick
+
+	// X2 - X1
 	for j := 0; j < batchSize; j++ {
 		lambdain[j].Sub(&(*P)[j].X, &(*R)[j].X)
 	}
 
-	// invert denominator using montgomery batch invert technique
+	// montgomery batch inversion;
+	// lambda[0] = 1 / (P[0].X - R[0].X)
+	// lambda[1] = 1 / (P[1].X - R[1].X)
+	// ...
 	{
 		var accumulator fp.Element
 		lambda[0].SetOne()
@@ -1211,22 +1223,24 @@ func batchAddG1Affine[TP pG1Affine, TPP ppG1Affine, TC cG1Affine](R *TPP, P *TP,
 		lambda[0].Set(&accumulator)
 	}
 
-	var d fp.Element
-	var rr G1Affine
+	var t fp.Element
+	var Q G1Affine
 
-	// add part
 	for j := 0; j < batchSize; j++ {
-		// computa lambda
-		d.Sub(&(*P)[j].Y, &(*R)[j].Y)
-		lambda[j].Mul(&lambda[j], &d)
-
-		// compute X, Y
-		rr.X.Square(&lambda[j])
-		rr.X.Sub(&rr.X, &(*R)[j].X)
-		rr.X.Sub(&rr.X, &(*P)[j].X)
-		d.Sub(&(*R)[j].X, &rr.X)
-		rr.Y.Mul(&lambda[j], &d)
-		rr.Y.Sub(&rr.Y, &(*R)[j].Y)
-		(*R)[j].Set(&rr)
+		// λ  = (Y2 - Y1) / (X2 - X1)
+		t.Sub(&(*P)[j].Y, &(*R)[j].Y)
+		lambda[j].Mul(&lambda[j], &t)
+
+		// X3 = λ² - (X1 + X2)
+		Q.X.Square(&lambda[j])
+		Q.X.Sub(&Q.X, &(*R)[j].X)
+		Q.X.Sub(&Q.X, &(*P)[j].X)
+
+		// Y3 = λ * (X1 - X3) - Y1
+		t.Sub(&(*R)[j].X, &Q.X)
+		Q.Y.Mul(&lambda[j], &t)
+		Q.Y.Sub(&Q.Y, &(*R)[j].Y)
+
+		(*R)[j].Set(&Q)
 	}
 }
diff --git a/ecc/bw6-633/g2.go b/ecc/bw6-633/g2.go
index 611753c678..a6e7268de1 100644
--- a/ecc/bw6-633/g2.go
+++ b/ecc/bw6-633/g2.go
@@ -1094,12 +1094,24 @@ func BatchScalarMultiplicationG2(base *G2Affine, scalars []fr.Element) []G2Affin
 func batchAddG2Affine[TP pG2Affine, TPP ppG2Affine, TC cG2Affine](R *TPP, P *TP, batchSize int) {
 	var lambda, lambdain TC
 
-	// add part
+	// from https://docs.zkproof.org/pages/standards/accepted-workshop3/proposal-turbo_plonk.pdf
+	// affine point addition formula
+	// R(X1, Y1) + P(X2, Y2) = Q(X3, Y3)
+	// λ  = (Y2 - Y1) / (X2 - X1)
+	// X3 = λ² - (X1 + X2)
+	// Y3 = λ * (X1 - X3) - Y1
+
+	// first we compute the 1 / (X2 - X1) for all points using Montgomery batch inversion trick
+
+	// X2 - X1
 	for j := 0; j < batchSize; j++ {
 		lambdain[j].Sub(&(*P)[j].X, &(*R)[j].X)
 	}
 
-	// invert denominator using montgomery batch invert technique
+	// montgomery batch inversion;
+	// lambda[0] = 1 / (P[0].X - R[0].X)
+	// lambda[1] = 1 / (P[1].X - R[1].X)
+	// ...
 	{
 		var accumulator fp.Element
 		lambda[0].SetOne()
@@ -1119,23 +1131,25 @@ func batchAddG2Affine[TP pG2Affine, TPP ppG2Affine, TC cG2Affine](R *TPP, P *TP,
 		lambda[0].Set(&accumulator)
 	}
 
-	var d fp.Element
-	var rr G2Affine
+	var t fp.Element
+	var Q G2Affine
 
-	// add part
 	for j := 0; j < batchSize; j++ {
-		// computa lambda
-		d.Sub(&(*P)[j].Y, &(*R)[j].Y)
-		lambda[j].Mul(&lambda[j], &d)
-
-		// compute X, Y
-		rr.X.Square(&lambda[j])
-		rr.X.Sub(&rr.X, &(*R)[j].X)
-		rr.X.Sub(&rr.X, &(*P)[j].X)
-		d.Sub(&(*R)[j].X, &rr.X)
-		rr.Y.Mul(&lambda[j], &d)
-		rr.Y.Sub(&rr.Y, &(*R)[j].Y)
-		(*R)[j].Set(&rr)
+		// λ  = (Y2 - Y1) / (X2 - X1)
+		t.Sub(&(*P)[j].Y, &(*R)[j].Y)
+		lambda[j].Mul(&lambda[j], &t)
+
+		// X3 = λ² - (X1 + X2)
+		Q.X.Square(&lambda[j])
+		Q.X.Sub(&Q.X, &(*R)[j].X)
+		Q.X.Sub(&Q.X, &(*P)[j].X)
+
+		// Y3 = λ * (X1 - X3) - Y1
+		t.Sub(&(*R)[j].X, &Q.X)
+		Q.Y.Mul(&lambda[j], &t)
+		Q.Y.Sub(&Q.Y, &(*R)[j].Y)
+
+		(*R)[j].Set(&Q)
 	}
 }
 
diff --git a/ecc/bw6-761/g1.go b/ecc/bw6-761/g1.go
index beef3e2aca..a25082de81 100644
--- a/ecc/bw6-761/g1.go
+++ b/ecc/bw6-761/g1.go
@@ -1198,12 +1198,24 @@ func BatchScalarMultiplicationG1(base *G1Affine, scalars []fr.Element) []G1Affin
 func batchAddG1Affine[TP pG1Affine, TPP ppG1Affine, TC cG1Affine](R *TPP, P *TP, batchSize int) {
 	var lambda, lambdain TC
 
-	// add part
+	// from https://docs.zkproof.org/pages/standards/accepted-workshop3/proposal-turbo_plonk.pdf
+	// affine point addition formula
+	// R(X1, Y1) + P(X2, Y2) = Q(X3, Y3)
+	// λ  = (Y2 - Y1) / (X2 - X1)
+	// X3 = λ² - (X1 + X2)
+	// Y3 = λ * (X1 - X3) - Y1
+
+	// first we compute the 1 / (X2 - X1) for all points using Montgomery batch inversion trick
+
+	// X2 - X1
 	for j := 0; j < batchSize; j++ {
 		lambdain[j].Sub(&(*P)[j].X, &(*R)[j].X)
 	}
 
-	// invert denominator using montgomery batch invert technique
+	// montgomery batch inversion;
+	// lambda[0] = 1 / (P[0].X - R[0].X)
+	// lambda[1] = 1 / (P[1].X - R[1].X)
+	// ...
 	{
 		var accumulator fp.Element
 		lambda[0].SetOne()
@@ -1223,22 +1235,24 @@ func batchAddG1Affine[TP pG1Affine, TPP ppG1Affine, TC cG1Affine](R *TPP, P *TP,
 		lambda[0].Set(&accumulator)
 	}
 
-	var d fp.Element
-	var rr G1Affine
+	var t fp.Element
+	var Q G1Affine
 
-	// add part
 	for j := 0; j < batchSize; j++ {
-		// computa lambda
-		d.Sub(&(*P)[j].Y, &(*R)[j].Y)
-		lambda[j].Mul(&lambda[j], &d)
-
-		// compute X, Y
-		rr.X.Square(&lambda[j])
-		rr.X.Sub(&rr.X, &(*R)[j].X)
-		rr.X.Sub(&rr.X, &(*P)[j].X)
-		d.Sub(&(*R)[j].X, &rr.X)
-		rr.Y.Mul(&lambda[j], &d)
-		rr.Y.Sub(&rr.Y, &(*R)[j].Y)
-		(*R)[j].Set(&rr)
+		// λ  = (Y2 - Y1) / (X2 - X1)
+		t.Sub(&(*P)[j].Y, &(*R)[j].Y)
+		lambda[j].Mul(&lambda[j], &t)
+
+		// X3 = λ² - (X1 + X2)
+		Q.X.Square(&lambda[j])
+		Q.X.Sub(&Q.X, &(*R)[j].X)
+		Q.X.Sub(&Q.X, &(*P)[j].X)
+
+		// Y3 = λ * (X1 - X3) - Y1
+		t.Sub(&(*R)[j].X, &Q.X)
+		Q.Y.Mul(&lambda[j], &t)
+		Q.Y.Sub(&Q.Y, &(*R)[j].Y)
+
+		(*R)[j].Set(&Q)
 	}
 }
diff --git a/ecc/bw6-761/g2.go b/ecc/bw6-761/g2.go
index 832811a70e..b14e9da70b 100644
--- a/ecc/bw6-761/g2.go
+++ b/ecc/bw6-761/g2.go
@@ -1102,12 +1102,24 @@ func BatchScalarMultiplicationG2(base *G2Affine, scalars []fr.Element) []G2Affin
 func batchAddG2Affine[TP pG2Affine, TPP ppG2Affine, TC cG2Affine](R *TPP, P *TP, batchSize int) {
 	var lambda, lambdain TC
 
-	// add part
+	// from https://docs.zkproof.org/pages/standards/accepted-workshop3/proposal-turbo_plonk.pdf
+	// affine point addition formula
+	// R(X1, Y1) + P(X2, Y2) = Q(X3, Y3)
+	// λ  = (Y2 - Y1) / (X2 - X1)
+	// X3 = λ² - (X1 + X2)
+	// Y3 = λ * (X1 - X3) - Y1
+
+	// first we compute the 1 / (X2 - X1) for all points using Montgomery batch inversion trick
+
+	// X2 - X1
 	for j := 0; j < batchSize; j++ {
 		lambdain[j].Sub(&(*P)[j].X, &(*R)[j].X)
 	}
 
-	// invert denominator using montgomery batch invert technique
+	// montgomery batch inversion;
+	// lambda[0] = 1 / (P[0].X - R[0].X)
+	// lambda[1] = 1 / (P[1].X - R[1].X)
+	// ...
 	{
 		var accumulator fp.Element
 		lambda[0].SetOne()
@@ -1127,23 +1139,25 @@ func batchAddG2Affine[TP pG2Affine, TPP ppG2Affine, TC cG2Affine](R *TPP, P *TP,
 		lambda[0].Set(&accumulator)
 	}
 
-	var d fp.Element
-	var rr G2Affine
+	var t fp.Element
+	var Q G2Affine
 
-	// add part
 	for j := 0; j < batchSize; j++ {
-		// computa lambda
-		d.Sub(&(*P)[j].Y, &(*R)[j].Y)
-		lambda[j].Mul(&lambda[j], &d)
-
-		// compute X, Y
-		rr.X.Square(&lambda[j])
-		rr.X.Sub(&rr.X, &(*R)[j].X)
-		rr.X.Sub(&rr.X, &(*P)[j].X)
-		d.Sub(&(*R)[j].X, &rr.X)
-		rr.Y.Mul(&lambda[j], &d)
-		rr.Y.Sub(&rr.Y, &(*R)[j].Y)
-		(*R)[j].Set(&rr)
+		// λ  = (Y2 - Y1) / (X2 - X1)
+		t.Sub(&(*P)[j].Y, &(*R)[j].Y)
+		lambda[j].Mul(&lambda[j], &t)
+
+		// X3 = λ² - (X1 + X2)
+		Q.X.Square(&lambda[j])
+		Q.X.Sub(&Q.X, &(*R)[j].X)
+		Q.X.Sub(&Q.X, &(*P)[j].X)
+
+		// Y3 = λ * (X1 - X3) - Y1
+		t.Sub(&(*R)[j].X, &Q.X)
+		Q.Y.Mul(&lambda[j], &t)
+		Q.Y.Sub(&Q.Y, &(*R)[j].Y)
+
+		(*R)[j].Set(&Q)
 	}
 }
 
diff --git a/ecc/secp256k1/g1.go b/ecc/secp256k1/g1.go
index d747e4d9bd..c5714c3324 100644
--- a/ecc/secp256k1/g1.go
+++ b/ecc/secp256k1/g1.go
@@ -1132,12 +1132,24 @@ func BatchScalarMultiplicationG1(base *G1Affine, scalars []fr.Element) []G1Affin
 func batchAddG1Affine[TP pG1Affine, TPP ppG1Affine, TC cG1Affine](R *TPP, P *TP, batchSize int) {
 	var lambda, lambdain TC
 
-	// add part
+	// from https://docs.zkproof.org/pages/standards/accepted-workshop3/proposal-turbo_plonk.pdf
+	// affine point addition formula
+	// R(X1, Y1) + P(X2, Y2) = Q(X3, Y3)
+	// λ  = (Y2 - Y1) / (X2 - X1)
+	// X3 = λ² - (X1 + X2)
+	// Y3 = λ * (X1 - X3) - Y1
+
+	// first we compute the 1 / (X2 - X1) for all points using Montgomery batch inversion trick
+
+	// X2 - X1
 	for j := 0; j < batchSize; j++ {
 		lambdain[j].Sub(&(*P)[j].X, &(*R)[j].X)
 	}
 
-	// invert denominator using montgomery batch invert technique
+	// montgomery batch inversion;
+	// lambda[0] = 1 / (P[0].X - R[0].X)
+	// lambda[1] = 1 / (P[1].X - R[1].X)
+	// ...
 	{
 		var accumulator fp.Element
 		lambda[0].SetOne()
@@ -1157,22 +1169,24 @@ func batchAddG1Affine[TP pG1Affine, TPP ppG1Affine, TC cG1Affine](R *TPP, P *TP,
 		lambda[0].Set(&accumulator)
 	}
 
-	var d fp.Element
-	var rr G1Affine
+	var t fp.Element
+	var Q G1Affine
 
-	// add part
 	for j := 0; j < batchSize; j++ {
-		// computa lambda
-		d.Sub(&(*P)[j].Y, &(*R)[j].Y)
-		lambda[j].Mul(&lambda[j], &d)
-
-		// compute X, Y
-		rr.X.Square(&lambda[j])
-		rr.X.Sub(&rr.X, &(*R)[j].X)
-		rr.X.Sub(&rr.X, &(*P)[j].X)
-		d.Sub(&(*R)[j].X, &rr.X)
-		rr.Y.Mul(&lambda[j], &d)
-		rr.Y.Sub(&rr.Y, &(*R)[j].Y)
-		(*R)[j].Set(&rr)
+		// λ  = (Y2 - Y1) / (X2 - X1)
+		t.Sub(&(*P)[j].Y, &(*R)[j].Y)
+		lambda[j].Mul(&lambda[j], &t)
+
+		// X3 = λ² - (X1 + X2)
+		Q.X.Square(&lambda[j])
+		Q.X.Sub(&Q.X, &(*R)[j].X)
+		Q.X.Sub(&Q.X, &(*P)[j].X)
+
+		// Y3 = λ * (X1 - X3) - Y1
+		t.Sub(&(*R)[j].X, &Q.X)
+		Q.Y.Mul(&lambda[j], &t)
+		Q.Y.Sub(&Q.Y, &(*R)[j].Y)
+
+		(*R)[j].Set(&Q)
 	}
 }
diff --git a/internal/generator/ecc/template/point.go.tmpl b/internal/generator/ecc/template/point.go.tmpl
index 22bf4e6f38..961a9e89b3 100644
--- a/internal/generator/ecc/template/point.go.tmpl
+++ b/internal/generator/ecc/template/point.go.tmpl
@@ -1739,13 +1739,24 @@ func BatchScalarMultiplication{{ toUpper .PointName }}(base *{{ $TAffine }}, sca
 func batchAdd{{ $TAffine }}[TP p{{ $TAffine }}, TPP pp{{ $TAffine }}, TC c{{ $TAffine }}](R *TPP,P *TP, batchSize int) {
 	var lambda, lambdain TC
 
+	// from https://docs.zkproof.org/pages/standards/accepted-workshop3/proposal-turbo_plonk.pdf
+	// affine point addition formula
+	// R(X1, Y1) + P(X2, Y2) = Q(X3, Y3)
+	// λ  = (Y2 - Y1) / (X2 - X1)
+	// X3 = λ² - (X1 + X2)
+	// Y3 = λ * (X1 - X3) - Y1
 
-	// add part
+	// first we compute the 1 / (X2 - X1) for all points using Montgomery batch inversion trick
+
+	// X2 - X1
 	for j := 0; j < batchSize; j++ {
 		lambdain[j].Sub(&(*P)[j].X, &(*R)[j].X)
 	}
 
-	// invert denominator using montgomery batch invert technique
+	// montgomery batch inversion; 
+	// lambda[0] = 1 / (P[0].X - R[0].X)
+	// lambda[1] = 1 / (P[1].X - R[1].X)
+	// ...
 	{
 		var accumulator {{.CoordType}}
 		lambda[0].SetOne()
@@ -1765,23 +1776,25 @@ func batchAdd{{ $TAffine }}[TP p{{ $TAffine }}, TPP pp{{ $TAffine }}, TC c{{ $TA
 		lambda[0].Set(&accumulator)
 	}
 
-	var d {{.CoordType}}
-	var rr {{ $TAffine }}
+	var t {{.CoordType}}
+	var Q {{ $TAffine }}
 
-	// add part
 	for j := 0; j < batchSize; j++ {
-		// computa lambda
-		d.Sub(&(*P)[j].Y, &(*R)[j].Y)
-		lambda[j].Mul(&lambda[j], &d)
-
-		// compute X, Y
-		rr.X.Square(&lambda[j])
-		rr.X.Sub(&rr.X, &(*R)[j].X)
-		rr.X.Sub(&rr.X, &(*P)[j].X)
-		d.Sub(&(*R)[j].X, &rr.X)
-		rr.Y.Mul(&lambda[j], &d)
-		rr.Y.Sub(&rr.Y, &(*R)[j].Y)
-		(*R)[j].Set(&rr)
+		// λ  = (Y2 - Y1) / (X2 - X1)
+		t.Sub(&(*P)[j].Y, &(*R)[j].Y)
+		lambda[j].Mul(&lambda[j], &t)
+
+		// X3 = λ² - (X1 + X2)
+		Q.X.Square(&lambda[j])
+		Q.X.Sub(&Q.X, &(*R)[j].X)
+		Q.X.Sub(&Q.X, &(*P)[j].X)
+
+		// Y3 = λ * (X1 - X3) - Y1
+		t.Sub(&(*R)[j].X, &Q.X)
+		Q.Y.Mul(&lambda[j], &t)
+		Q.Y.Sub(&Q.Y, &(*R)[j].Y)
+
+		(*R)[j].Set(&Q)
 	}
 }
 

From 37b2cbd0023e53386258750a3e0dd16d45edc2cf Mon Sep 17 00:00:00 2001
From: Youssef El Housni <youssef.elhousni@consensys.net>
Date: Mon, 28 Oct 2024 15:58:30 -0400
Subject: [PATCH 087/114] perf: subgroup check (#557)

---
 ecc/bls12-377/g1.go                           |   6 +-
 ecc/bls12-377/g1_test.go                      |   2 +-
 ecc/bls12-377/g2.go                           |   6 +-
 ecc/bls12-377/g2_test.go                      |   2 +-
 ecc/bls12-381/g1.go                           |   6 +-
 ecc/bls12-381/g1_test.go                      |   2 +-
 ecc/bls12-381/g2.go                           |   6 +-
 ecc/bls12-381/g2_test.go                      |   2 +-
 ecc/bls24-315/g1.go                           |  10 +-
 ecc/bls24-315/g1_test.go                      |   2 +-
 ecc/bls24-315/g2.go                           |  10 +-
 ecc/bls24-315/g2_test.go                      |   2 +-
 ecc/bls24-317/g1.go                           |  10 +-
 ecc/bls24-317/g1_test.go                      |   2 +-
 ecc/bls24-317/g2.go                           |  10 +-
 ecc/bls24-317/g2_test.go                      |   2 +-
 ecc/bn254/g1_test.go                          |   2 +-
 ecc/bn254/g2.go                               |   4 +-
 ecc/bn254/g2_test.go                          |   2 +-
 ecc/bw6-633/g1.go                             |  26 +--
 ecc/bw6-633/g1_test.go                        |   2 +-
 ecc/bw6-633/g2.go                             |  32 ++--
 ecc/bw6-633/g2_test.go                        |   2 +-
 ecc/bw6-761/g1.go                             |  28 +--
 ecc/bw6-761/g1_test.go                        |   2 +-
 ecc/bw6-761/g2.go                             |  28 +--
 ecc/bw6-761/g2_test.go                        |   2 +-
 ecc/secp256k1/g1_test.go                      |   2 +-
 internal/generator/ecc/template/point.go.tmpl | 162 +++++++++---------
 .../ecc/template/tests/point.go.tmpl          |   2 +-
 30 files changed, 188 insertions(+), 188 deletions(-)

diff --git a/ecc/bls12-377/g1.go b/ecc/bls12-377/g1.go
index 9563f30667..0cf4f746fd 100644
--- a/ecc/bls12-377/g1.go
+++ b/ecc/bls12-377/g1.go
@@ -493,8 +493,8 @@ func (p *G1Jac) IsInSubGroup() bool {
 	var res G1Jac
 
 	res.phi(p).
-		ScalarMultiplication(&res, &xGen).
-		ScalarMultiplication(&res, &xGen).
+		mulWindowed(&res, &xGen).
+		mulWindowed(&res, &xGen).
 		AddAssign(p)
 
 	return res.IsOnCurve() && res.Z.IsZero()
@@ -630,7 +630,7 @@ func (p *G1Affine) ClearCofactor(a *G1Affine) *G1Affine {
 func (p *G1Jac) ClearCofactor(q *G1Jac) *G1Jac {
 	// cf https://eprint.iacr.org/2019/403.pdf, 5
 	var res G1Jac
-	res.ScalarMultiplication(q, &xGen).Neg(&res).AddAssign(q)
+	res.mulWindowed(q, &xGen).Neg(&res).AddAssign(q)
 	p.Set(&res)
 	return p
 
diff --git a/ecc/bls12-377/g1_test.go b/ecc/bls12-377/g1_test.go
index 54afb43909..a110a1bf57 100644
--- a/ecc/bls12-377/g1_test.go
+++ b/ecc/bls12-377/g1_test.go
@@ -111,7 +111,7 @@ func TestG1AffineIsOnCurve(t *testing.T) {
 			var op1, op2 G1Jac
 			op1 = fuzzG1Jac(&g1Gen, a)
 			_r := fr.Modulus()
-			op2.ScalarMultiplication(&op1, _r)
+			op2.mulWindowed(&op1, _r)
 			return op1.IsInSubGroup() && op2.Z.IsZero()
 		},
 		GenFp(),
diff --git a/ecc/bls12-377/g2.go b/ecc/bls12-377/g2.go
index 29bf5e5e9e..5cb8240d80 100644
--- a/ecc/bls12-377/g2.go
+++ b/ecc/bls12-377/g2.go
@@ -494,7 +494,7 @@ func (p *G2Jac) IsOnCurve() bool {
 func (p *G2Jac) IsInSubGroup() bool {
 	var res, tmp G2Jac
 	tmp.psi(p)
-	res.ScalarMultiplication(p, &xGen).
+	res.mulWindowed(p, &xGen).
 		SubAssign(&tmp)
 
 	return res.IsOnCurve() && res.Z.IsZero()
@@ -638,8 +638,8 @@ func (p *G2Affine) ClearCofactor(a *G2Affine) *G2Affine {
 func (p *G2Jac) ClearCofactor(q *G2Jac) *G2Jac {
 	// https://eprint.iacr.org/2017/419.pdf, 4.1
 	var xg, xxg, res, t G2Jac
-	xg.ScalarMultiplication(q, &xGen)
-	xxg.ScalarMultiplication(&xg, &xGen)
+	xg.mulWindowed(q, &xGen)
+	xxg.mulWindowed(&xg, &xGen)
 
 	res.Set(&xxg).
 		SubAssign(&xg).
diff --git a/ecc/bls12-377/g2_test.go b/ecc/bls12-377/g2_test.go
index 78a4c50954..f18dcdf9d4 100644
--- a/ecc/bls12-377/g2_test.go
+++ b/ecc/bls12-377/g2_test.go
@@ -125,7 +125,7 @@ func TestG2AffineIsOnCurve(t *testing.T) {
 			var op1, op2 G2Jac
 			op1 = fuzzG2Jac(&g2Gen, a)
 			_r := fr.Modulus()
-			op2.ScalarMultiplication(&op1, _r)
+			op2.mulWindowed(&op1, _r)
 			return op1.IsInSubGroup() && op2.Z.IsZero()
 		},
 		GenE2(),
diff --git a/ecc/bls12-381/g1.go b/ecc/bls12-381/g1.go
index c626d848f6..9ecf220da7 100644
--- a/ecc/bls12-381/g1.go
+++ b/ecc/bls12-381/g1.go
@@ -494,8 +494,8 @@ func (p *G1Jac) IsInSubGroup() bool {
 	var res G1Jac
 
 	res.phi(p).
-		ScalarMultiplication(&res, &xGen).
-		ScalarMultiplication(&res, &xGen).
+		mulWindowed(&res, &xGen).
+		mulWindowed(&res, &xGen).
 		AddAssign(p)
 
 	return res.IsOnCurve() && res.Z.IsZero()
@@ -631,7 +631,7 @@ func (p *G1Affine) ClearCofactor(a *G1Affine) *G1Affine {
 func (p *G1Jac) ClearCofactor(q *G1Jac) *G1Jac {
 	// cf https://eprint.iacr.org/2019/403.pdf, 5
 	var res G1Jac
-	res.ScalarMultiplication(q, &xGen).AddAssign(q)
+	res.mulWindowed(q, &xGen).AddAssign(q)
 	p.Set(&res)
 	return p
 
diff --git a/ecc/bls12-381/g1_test.go b/ecc/bls12-381/g1_test.go
index 5a07ae406a..507fa71160 100644
--- a/ecc/bls12-381/g1_test.go
+++ b/ecc/bls12-381/g1_test.go
@@ -111,7 +111,7 @@ func TestG1AffineIsOnCurve(t *testing.T) {
 			var op1, op2 G1Jac
 			op1 = fuzzG1Jac(&g1Gen, a)
 			_r := fr.Modulus()
-			op2.ScalarMultiplication(&op1, _r)
+			op2.mulWindowed(&op1, _r)
 			return op1.IsInSubGroup() && op2.Z.IsZero()
 		},
 		GenFp(),
diff --git a/ecc/bls12-381/g2.go b/ecc/bls12-381/g2.go
index 38f262cb8c..51b03fc595 100644
--- a/ecc/bls12-381/g2.go
+++ b/ecc/bls12-381/g2.go
@@ -495,7 +495,7 @@ func (p *G2Jac) IsOnCurve() bool {
 func (p *G2Jac) IsInSubGroup() bool {
 	var res, tmp G2Jac
 	tmp.psi(p)
-	res.ScalarMultiplication(p, &xGen).
+	res.mulWindowed(p, &xGen).
 		AddAssign(&tmp)
 
 	return res.IsOnCurve() && res.Z.IsZero()
@@ -639,8 +639,8 @@ func (p *G2Affine) ClearCofactor(a *G2Affine) *G2Affine {
 func (p *G2Jac) ClearCofactor(q *G2Jac) *G2Jac {
 	// https://eprint.iacr.org/2017/419.pdf, 4.1
 	var xg, xxg, res, t G2Jac
-	xg.ScalarMultiplication(q, &xGen).Neg(&xg)
-	xxg.ScalarMultiplication(&xg, &xGen).Neg(&xxg)
+	xg.mulWindowed(q, &xGen).Neg(&xg)
+	xxg.mulWindowed(&xg, &xGen).Neg(&xxg)
 
 	res.Set(&xxg).
 		SubAssign(&xg).
diff --git a/ecc/bls12-381/g2_test.go b/ecc/bls12-381/g2_test.go
index fe3b1a9b51..d15ac8715a 100644
--- a/ecc/bls12-381/g2_test.go
+++ b/ecc/bls12-381/g2_test.go
@@ -125,7 +125,7 @@ func TestG2AffineIsOnCurve(t *testing.T) {
 			var op1, op2 G2Jac
 			op1 = fuzzG2Jac(&g2Gen, a)
 			_r := fr.Modulus()
-			op2.ScalarMultiplication(&op1, _r)
+			op2.mulWindowed(&op1, _r)
 			return op1.IsInSubGroup() && op2.Z.IsZero()
 		},
 		GenE2(),
diff --git a/ecc/bls24-315/g1.go b/ecc/bls24-315/g1.go
index 0e1cc2ff8c..ab872e9986 100644
--- a/ecc/bls24-315/g1.go
+++ b/ecc/bls24-315/g1.go
@@ -493,10 +493,10 @@ func (p *G1Jac) IsInSubGroup() bool {
 
 	var res G1Jac
 	res.phi(p).
-		ScalarMultiplication(&res, &xGen).
-		ScalarMultiplication(&res, &xGen).
-		ScalarMultiplication(&res, &xGen).
-		ScalarMultiplication(&res, &xGen).
+		mulWindowed(&res, &xGen).
+		mulWindowed(&res, &xGen).
+		mulWindowed(&res, &xGen).
+		mulWindowed(&res, &xGen).
 		AddAssign(p)
 
 	return res.IsOnCurve() && res.Z.IsZero()
@@ -632,7 +632,7 @@ func (p *G1Affine) ClearCofactor(a *G1Affine) *G1Affine {
 func (p *G1Jac) ClearCofactor(q *G1Jac) *G1Jac {
 	// cf https://eprint.iacr.org/2019/403.pdf, 5
 	var res G1Jac
-	res.ScalarMultiplication(q, &xGen).AddAssign(q)
+	res.mulWindowed(q, &xGen).AddAssign(q)
 	p.Set(&res)
 	return p
 
diff --git a/ecc/bls24-315/g1_test.go b/ecc/bls24-315/g1_test.go
index 84ea681f05..8f99519348 100644
--- a/ecc/bls24-315/g1_test.go
+++ b/ecc/bls24-315/g1_test.go
@@ -111,7 +111,7 @@ func TestG1AffineIsOnCurve(t *testing.T) {
 			var op1, op2 G1Jac
 			op1 = fuzzG1Jac(&g1Gen, a)
 			_r := fr.Modulus()
-			op2.ScalarMultiplication(&op1, _r)
+			op2.mulWindowed(&op1, _r)
 			return op1.IsInSubGroup() && op2.Z.IsZero()
 		},
 		GenFp(),
diff --git a/ecc/bls24-315/g2.go b/ecc/bls24-315/g2.go
index 8250d2b5aa..ad3b75b7c0 100644
--- a/ecc/bls24-315/g2.go
+++ b/ecc/bls24-315/g2.go
@@ -495,7 +495,7 @@ func (p *G2Jac) IsOnCurve() bool {
 func (p *G2Jac) IsInSubGroup() bool {
 	var res, tmp G2Jac
 	tmp.psi(p)
-	res.ScalarMultiplication(p, &xGen).
+	res.mulWindowed(p, &xGen).
 		AddAssign(&tmp)
 
 	return res.IsOnCurve() && res.Z.IsZero()
@@ -642,10 +642,10 @@ func (p *G2Jac) ClearCofactor(q *G2Jac) *G2Jac {
 	// multiply by (3x⁴-3)*cofacor
 
 	var xg, xxg, xxxg, xxxxg, res, t G2Jac
-	xg.ScalarMultiplication(q, &xGen).Neg(&xg).SubAssign(q)
-	xxg.ScalarMultiplication(&xg, &xGen).Neg(&xxg)
-	xxxg.ScalarMultiplication(&xxg, &xGen).Neg(&xxxg)
-	xxxxg.ScalarMultiplication(&xxxg, &xGen).Neg(&xxxxg)
+	xg.mulWindowed(q, &xGen).Neg(&xg).SubAssign(q)
+	xxg.mulWindowed(&xg, &xGen).Neg(&xxg)
+	xxxg.mulWindowed(&xxg, &xGen).Neg(&xxxg)
+	xxxxg.mulWindowed(&xxxg, &xGen).Neg(&xxxxg)
 
 	res.Set(&xxxxg).
 		SubAssign(q)
diff --git a/ecc/bls24-315/g2_test.go b/ecc/bls24-315/g2_test.go
index 34a97df9d9..a42966a99c 100644
--- a/ecc/bls24-315/g2_test.go
+++ b/ecc/bls24-315/g2_test.go
@@ -125,7 +125,7 @@ func TestG2AffineIsOnCurve(t *testing.T) {
 			var op1, op2 G2Jac
 			op1 = fuzzG2Jac(&g2Gen, a)
 			_r := fr.Modulus()
-			op2.ScalarMultiplication(&op1, _r)
+			op2.mulWindowed(&op1, _r)
 			return op1.IsInSubGroup() && op2.Z.IsZero()
 		},
 		GenE4(),
diff --git a/ecc/bls24-317/g1.go b/ecc/bls24-317/g1.go
index 8240303dd9..b0a28327b9 100644
--- a/ecc/bls24-317/g1.go
+++ b/ecc/bls24-317/g1.go
@@ -494,10 +494,10 @@ func (p *G1Jac) IsInSubGroup() bool {
 
 	var res G1Jac
 	res.phi(p).
-		ScalarMultiplication(&res, &xGen).
-		ScalarMultiplication(&res, &xGen).
-		ScalarMultiplication(&res, &xGen).
-		ScalarMultiplication(&res, &xGen).
+		mulWindowed(&res, &xGen).
+		mulWindowed(&res, &xGen).
+		mulWindowed(&res, &xGen).
+		mulWindowed(&res, &xGen).
 		AddAssign(p)
 
 	return res.IsOnCurve() && res.Z.IsZero()
@@ -633,7 +633,7 @@ func (p *G1Affine) ClearCofactor(a *G1Affine) *G1Affine {
 func (p *G1Jac) ClearCofactor(q *G1Jac) *G1Jac {
 	// cf https://eprint.iacr.org/2019/403.pdf, 5
 	var res G1Jac
-	res.ScalarMultiplication(q, &xGen).Neg(&res).AddAssign(q)
+	res.mulWindowed(q, &xGen).Neg(&res).AddAssign(q)
 	p.Set(&res)
 	return p
 
diff --git a/ecc/bls24-317/g1_test.go b/ecc/bls24-317/g1_test.go
index fbf290d972..c64e8ccef4 100644
--- a/ecc/bls24-317/g1_test.go
+++ b/ecc/bls24-317/g1_test.go
@@ -111,7 +111,7 @@ func TestG1AffineIsOnCurve(t *testing.T) {
 			var op1, op2 G1Jac
 			op1 = fuzzG1Jac(&g1Gen, a)
 			_r := fr.Modulus()
-			op2.ScalarMultiplication(&op1, _r)
+			op2.mulWindowed(&op1, _r)
 			return op1.IsInSubGroup() && op2.Z.IsZero()
 		},
 		GenFp(),
diff --git a/ecc/bls24-317/g2.go b/ecc/bls24-317/g2.go
index 9f51ce2141..2def434850 100644
--- a/ecc/bls24-317/g2.go
+++ b/ecc/bls24-317/g2.go
@@ -495,7 +495,7 @@ func (p *G2Jac) IsOnCurve() bool {
 func (p *G2Jac) IsInSubGroup() bool {
 	var res, tmp G2Jac
 	tmp.psi(p)
-	res.ScalarMultiplication(p, &xGen).
+	res.mulWindowed(p, &xGen).
 		SubAssign(&tmp)
 
 	return res.IsOnCurve() && res.Z.IsZero()
@@ -642,10 +642,10 @@ func (p *G2Jac) ClearCofactor(q *G2Jac) *G2Jac {
 	// multiply by (3x⁴-3)*cofacor
 
 	var xg, xxg, xxxg, xxxxg, res, t G2Jac
-	xg.ScalarMultiplication(q, &xGen).SubAssign(q)
-	xxg.ScalarMultiplication(&xg, &xGen)
-	xxxg.ScalarMultiplication(&xxg, &xGen)
-	xxxxg.ScalarMultiplication(&xxxg, &xGen)
+	xg.mulWindowed(q, &xGen).SubAssign(q)
+	xxg.mulWindowed(&xg, &xGen)
+	xxxg.mulWindowed(&xxg, &xGen)
+	xxxxg.mulWindowed(&xxxg, &xGen)
 
 	res.Set(&xxxxg).
 		SubAssign(q)
diff --git a/ecc/bls24-317/g2_test.go b/ecc/bls24-317/g2_test.go
index 69f7745503..cd8a859095 100644
--- a/ecc/bls24-317/g2_test.go
+++ b/ecc/bls24-317/g2_test.go
@@ -125,7 +125,7 @@ func TestG2AffineIsOnCurve(t *testing.T) {
 			var op1, op2 G2Jac
 			op1 = fuzzG2Jac(&g2Gen, a)
 			_r := fr.Modulus()
-			op2.ScalarMultiplication(&op1, _r)
+			op2.mulWindowed(&op1, _r)
 			return op1.IsInSubGroup() && op2.Z.IsZero()
 		},
 		GenE4(),
diff --git a/ecc/bn254/g1_test.go b/ecc/bn254/g1_test.go
index 9354444ee3..a358dbcc86 100644
--- a/ecc/bn254/g1_test.go
+++ b/ecc/bn254/g1_test.go
@@ -111,7 +111,7 @@ func TestG1AffineIsOnCurve(t *testing.T) {
 			var op1, op2 G1Jac
 			op1 = fuzzG1Jac(&g1Gen, a)
 			_r := fr.Modulus()
-			op2.ScalarMultiplication(&op1, _r)
+			op2.mulWindowed(&op1, _r)
 			return op1.IsInSubGroup() && op2.Z.IsZero()
 		},
 		GenFp(),
diff --git a/ecc/bn254/g2.go b/ecc/bn254/g2.go
index 54addc34d2..83c00364d5 100644
--- a/ecc/bn254/g2.go
+++ b/ecc/bn254/g2.go
@@ -493,7 +493,7 @@ func (p *G2Jac) IsOnCurve() bool {
 // [r]P == 0 <==> [x₀+1]P + ψ([x₀]P) + ψ²([x₀]P) = ψ³([2x₀]P)
 func (p *G2Jac) IsInSubGroup() bool {
 	var a, b, c, res G2Jac
-	a.ScalarMultiplication(p, &xGen)
+	a.mulWindowed(p, &xGen)
 	b.psi(&a)
 	a.AddAssign(p)
 	res.psi(&b)
@@ -646,7 +646,7 @@ func (p *G2Jac) ClearCofactor(q *G2Jac) *G2Jac {
 	// cf http://cacr.uwaterloo.ca/techreports/2011/cacr2011-26.pdf, 6.1
 	var points [4]G2Jac
 
-	points[0].ScalarMultiplication(q, &xGen)
+	points[0].mulWindowed(q, &xGen)
 
 	points[1].Double(&points[0]).
 		AddAssign(&points[0]).
diff --git a/ecc/bn254/g2_test.go b/ecc/bn254/g2_test.go
index f998e7550d..a9a153a7c3 100644
--- a/ecc/bn254/g2_test.go
+++ b/ecc/bn254/g2_test.go
@@ -124,7 +124,7 @@ func TestG2AffineIsOnCurve(t *testing.T) {
 			var op1, op2 G2Jac
 			op1 = fuzzG2Jac(&g2Gen, a)
 			_r := fr.Modulus()
-			op2.ScalarMultiplication(&op1, _r)
+			op2.mulWindowed(&op1, _r)
 			return op1.IsInSubGroup() && op2.Z.IsZero()
 		},
 		GenE2(),
diff --git a/ecc/bw6-633/g1.go b/ecc/bw6-633/g1.go
index 6491867a3f..a40bcfc6f8 100644
--- a/ecc/bw6-633/g1.go
+++ b/ecc/bw6-633/g1.go
@@ -489,11 +489,11 @@ func (p *G1Jac) IsOnCurve() bool {
 func (p *G1Jac) IsInSubGroup() bool {
 
 	var uP, u4P, u5P, q, r G1Jac
-	uP.ScalarMultiplication(p, &xGen)
-	u4P.ScalarMultiplication(&uP, &xGen).
-		ScalarMultiplication(&u4P, &xGen).
-		ScalarMultiplication(&u4P, &xGen)
-	u5P.ScalarMultiplication(&u4P, &xGen)
+	uP.mulWindowed(p, &xGen)
+	u4P.mulWindowed(&uP, &xGen).
+		mulWindowed(&u4P, &xGen).
+		mulWindowed(&u4P, &xGen)
+	u5P.mulWindowed(&u4P, &xGen)
 	q.Set(p).SubAssign(&uP)
 	r.phi(&q).SubAssign(&uP).
 		AddAssign(&u4P).
@@ -640,20 +640,20 @@ func (p *G1Jac) ClearCofactor(q *G1Jac) *G1Jac {
 	ht.SetInt64(7)
 	v.Mul(&xGen, &xGen).Add(&v, &one).Mul(&v, &uPlusOne)
 
-	uP.ScalarMultiplication(q, &xGen).Neg(&uP)
+	uP.mulWindowed(q, &xGen).Neg(&uP)
 	vP.Set(q).SubAssign(&uP).
-		ScalarMultiplication(&vP, &v)
-	wP.ScalarMultiplication(&vP, &uMinusOne).Neg(&wP).
+		mulWindowed(&vP, &v)
+	wP.mulWindowed(&vP, &uMinusOne).Neg(&wP).
 		AddAssign(&uP)
-	L0.ScalarMultiplication(&wP, &d1)
-	tmp.ScalarMultiplication(&vP, &ht)
+	L0.mulWindowed(&wP, &d1)
+	tmp.mulWindowed(&vP, &ht)
 	L0.AddAssign(&tmp)
 	tmp.Double(q)
 	L0.AddAssign(&tmp)
-	L1.Set(&uP).AddAssign(q).ScalarMultiplication(&L1, &d1)
-	tmp.ScalarMultiplication(&vP, &d2)
+	L1.Set(&uP).AddAssign(q).mulWindowed(&L1, &d1)
+	tmp.mulWindowed(&vP, &d2)
 	L1.AddAssign(&tmp)
-	tmp.ScalarMultiplication(q, &ht)
+	tmp.mulWindowed(q, &ht)
 	L1.AddAssign(&tmp)
 
 	p.phi(&L1).AddAssign(&L0)
diff --git a/ecc/bw6-633/g1_test.go b/ecc/bw6-633/g1_test.go
index af7c526f48..52e7955454 100644
--- a/ecc/bw6-633/g1_test.go
+++ b/ecc/bw6-633/g1_test.go
@@ -111,7 +111,7 @@ func TestG1AffineIsOnCurve(t *testing.T) {
 			var op1, op2 G1Jac
 			op1 = fuzzG1Jac(&g1Gen, a)
 			_r := fr.Modulus()
-			op2.ScalarMultiplication(&op1, _r)
+			op2.mulWindowed(&op1, _r)
 			return op1.IsInSubGroup() && op2.Z.IsZero()
 		},
 		GenFp(),
diff --git a/ecc/bw6-633/g2.go b/ecc/bw6-633/g2.go
index a6e7268de1..7e55beadf2 100644
--- a/ecc/bw6-633/g2.go
+++ b/ecc/bw6-633/g2.go
@@ -495,11 +495,11 @@ func (p *G2Jac) IsOnCurve() bool {
 func (p *G2Jac) IsInSubGroup() bool {
 
 	var uP, u4P, u5P, q, r G2Jac
-	uP.ScalarMultiplication(p, &xGen)
-	u4P.ScalarMultiplication(&uP, &xGen).
-		ScalarMultiplication(&u4P, &xGen).
-		ScalarMultiplication(&u4P, &xGen)
-	u5P.ScalarMultiplication(&u4P, &xGen)
+	uP.mulWindowed(p, &xGen)
+	u4P.mulWindowed(&uP, &xGen).
+		mulWindowed(&u4P, &xGen).
+		mulWindowed(&u4P, &xGen)
+	u5P.mulWindowed(&u4P, &xGen)
 	q.Set(p).SubAssign(&uP)
 	r.phi(&q).SubAssign(&uP).
 		AddAssign(&u4P).
@@ -641,11 +641,11 @@ func (p *G2Jac) ClearCofactor(q *G2Jac) *G2Jac {
 	d1.SetInt64(13)
 	d3.SetInt64(5) // negative
 
-	uP.ScalarMultiplication(q, &xGen) // negative
-	u2P.ScalarMultiplication(&uP, &xGen)
-	u3P.ScalarMultiplication(&u2P, &xGen) // negative
-	u4P.ScalarMultiplication(&u3P, &xGen)
-	u5P.ScalarMultiplication(&u4P, &xGen) // negative
+	uP.mulWindowed(q, &xGen) // negative
+	u2P.mulWindowed(&uP, &xGen)
+	u3P.mulWindowed(&u2P, &xGen) // negative
+	u4P.mulWindowed(&u3P, &xGen)
+	u5P.mulWindowed(&u4P, &xGen) // negative
 	vP.Set(&u2P).AddAssign(&uP).
 		AddAssign(&u3P).
 		Double(&vP).
@@ -653,15 +653,15 @@ func (p *G2Jac) ClearCofactor(q *G2Jac) *G2Jac {
 		AddAssign(q)
 	wP.Set(&uP).SubAssign(&u4P).SubAssign(&u5P)
 	xP.Set(q).AddAssign(&vP)
-	L0.Set(&uP).SubAssign(q).ScalarMultiplication(&L0, &d1)
-	tmp.ScalarMultiplication(&xP, &d3)
+	L0.Set(&uP).SubAssign(q).mulWindowed(&L0, &d1)
+	tmp.mulWindowed(&xP, &d3)
 	L0.AddAssign(&tmp)
-	tmp.ScalarMultiplication(q, &ht) // negative
+	tmp.mulWindowed(q, &ht) // negative
 	L0.SubAssign(&tmp)
-	L1.ScalarMultiplication(&wP, &d1)
-	tmp.ScalarMultiplication(&vP, &ht)
+	L1.mulWindowed(&wP, &d1)
+	tmp.mulWindowed(&vP, &ht)
 	L1.AddAssign(&tmp)
-	tmp.ScalarMultiplication(q, &d3)
+	tmp.mulWindowed(q, &d3)
 	L1.AddAssign(&tmp)
 
 	p.phi(&L1).AddAssign(&L0)
diff --git a/ecc/bw6-633/g2_test.go b/ecc/bw6-633/g2_test.go
index 611318c9eb..5ecdebd9d8 100644
--- a/ecc/bw6-633/g2_test.go
+++ b/ecc/bw6-633/g2_test.go
@@ -111,7 +111,7 @@ func TestG2AffineIsOnCurve(t *testing.T) {
 			var op1, op2 G2Jac
 			op1 = fuzzG2Jac(&g2Gen, a)
 			_r := fr.Modulus()
-			op2.ScalarMultiplication(&op1, _r)
+			op2.mulWindowed(&op1, _r)
 			return op1.IsInSubGroup() && op2.Z.IsZero()
 		},
 		GenFp(),
diff --git a/ecc/bw6-761/g1.go b/ecc/bw6-761/g1.go
index a25082de81..2f4196f73c 100644
--- a/ecc/bw6-761/g1.go
+++ b/ecc/bw6-761/g1.go
@@ -494,13 +494,13 @@ func (p *G1Jac) IsInSubGroup() bool {
 
 	var res, phip G1Jac
 	phip.phi(p)
-	res.ScalarMultiplication(&phip, &xGen).
+	res.mulWindowed(&phip, &xGen).
 		SubAssign(&phip).
-		ScalarMultiplication(&res, &xGen).
-		ScalarMultiplication(&res, &xGen).
+		mulWindowed(&res, &xGen).
+		mulWindowed(&res, &xGen).
 		AddAssign(&phip)
 
-	phip.ScalarMultiplication(p, &xGen).AddAssign(p).AddAssign(&res)
+	phip.mulWindowed(p, &xGen).AddAssign(p).AddAssign(&res)
 
 	return phip.IsOnCurve() && phip.Z.IsZero()
 
@@ -637,9 +637,9 @@ func (p *G1Jac) ClearCofactor(q *G1Jac) *G1Jac {
 	// https://eprint.iacr.org/2020/351.pdf
 	var points [4]G1Jac
 	points[0].Set(q)
-	points[1].ScalarMultiplication(q, &xGen)
-	points[2].ScalarMultiplication(&points[1], &xGen)
-	points[3].ScalarMultiplication(&points[2], &xGen)
+	points[1].mulWindowed(q, &xGen)
+	points[2].mulWindowed(&points[1], &xGen)
+	points[3].mulWindowed(&points[2], &xGen)
 
 	var scalars [7]big.Int
 	scalars[0].SetInt64(103)
@@ -652,18 +652,18 @@ func (p *G1Jac) ClearCofactor(q *G1Jac) *G1Jac {
 	scalars[6].SetInt64(130)
 
 	var p1, p2, tmp G1Jac
-	p1.ScalarMultiplication(&points[3], &scalars[0])
-	tmp.ScalarMultiplication(&points[2], &scalars[1]).Neg(&tmp)
+	p1.mulWindowed(&points[3], &scalars[0])
+	tmp.mulWindowed(&points[2], &scalars[1]).Neg(&tmp)
 	p1.AddAssign(&tmp)
-	tmp.ScalarMultiplication(&points[1], &scalars[2]).Neg(&tmp)
+	tmp.mulWindowed(&points[1], &scalars[2]).Neg(&tmp)
 	p1.AddAssign(&tmp)
-	tmp.ScalarMultiplication(&points[0], &scalars[3])
+	tmp.mulWindowed(&points[0], &scalars[3])
 	p1.AddAssign(&tmp)
 
-	p2.ScalarMultiplication(&points[2], &scalars[4])
-	tmp.ScalarMultiplication(&points[1], &scalars[5])
+	p2.mulWindowed(&points[2], &scalars[4])
+	tmp.mulWindowed(&points[1], &scalars[5])
 	p2.AddAssign(&tmp)
-	tmp.ScalarMultiplication(&points[0], &scalars[6])
+	tmp.mulWindowed(&points[0], &scalars[6])
 	p2.AddAssign(&tmp)
 	p2.phi(&p2)
 
diff --git a/ecc/bw6-761/g1_test.go b/ecc/bw6-761/g1_test.go
index 620504f07f..e6f79f4dde 100644
--- a/ecc/bw6-761/g1_test.go
+++ b/ecc/bw6-761/g1_test.go
@@ -111,7 +111,7 @@ func TestG1AffineIsOnCurve(t *testing.T) {
 			var op1, op2 G1Jac
 			op1 = fuzzG1Jac(&g1Gen, a)
 			_r := fr.Modulus()
-			op2.ScalarMultiplication(&op1, _r)
+			op2.mulWindowed(&op1, _r)
 			return op1.IsInSubGroup() && op2.Z.IsZero()
 		},
 		GenFp(),
diff --git a/ecc/bw6-761/g2.go b/ecc/bw6-761/g2.go
index b14e9da70b..72ed4b08bd 100644
--- a/ecc/bw6-761/g2.go
+++ b/ecc/bw6-761/g2.go
@@ -500,13 +500,13 @@ func (p *G2Jac) IsInSubGroup() bool {
 
 	var res, phip G2Jac
 	phip.phi(p)
-	res.ScalarMultiplication(&phip, &xGen).
+	res.mulWindowed(&phip, &xGen).
 		SubAssign(&phip).
-		ScalarMultiplication(&res, &xGen).
-		ScalarMultiplication(&res, &xGen).
+		mulWindowed(&res, &xGen).
+		mulWindowed(&res, &xGen).
 		AddAssign(&phip)
 
-	phip.ScalarMultiplication(p, &xGen).AddAssign(p).AddAssign(&res)
+	phip.mulWindowed(p, &xGen).AddAssign(p).AddAssign(&res)
 
 	return phip.IsOnCurve() && phip.Z.IsZero()
 
@@ -641,9 +641,9 @@ func (p *G2Affine) ClearCofactor(a *G2Affine) *G2Affine {
 func (p *G2Jac) ClearCofactor(q *G2Jac) *G2Jac {
 	var points [4]G2Jac
 	points[0].Set(q)
-	points[1].ScalarMultiplication(q, &xGen)
-	points[2].ScalarMultiplication(&points[1], &xGen)
-	points[3].ScalarMultiplication(&points[2], &xGen)
+	points[1].mulWindowed(q, &xGen)
+	points[2].mulWindowed(&points[1], &xGen)
+	points[3].mulWindowed(&points[2], &xGen)
 
 	var scalars [7]big.Int
 	scalars[0].SetInt64(103)
@@ -656,18 +656,18 @@ func (p *G2Jac) ClearCofactor(q *G2Jac) *G2Jac {
 	scalars[6].SetInt64(109)
 
 	var p1, p2, tmp G2Jac
-	p1.ScalarMultiplication(&points[3], &scalars[0])
-	tmp.ScalarMultiplication(&points[2], &scalars[1]).Neg(&tmp)
+	p1.mulWindowed(&points[3], &scalars[0])
+	tmp.mulWindowed(&points[2], &scalars[1]).Neg(&tmp)
 	p1.AddAssign(&tmp)
-	tmp.ScalarMultiplication(&points[1], &scalars[2]).Neg(&tmp)
+	tmp.mulWindowed(&points[1], &scalars[2]).Neg(&tmp)
 	p1.AddAssign(&tmp)
-	tmp.ScalarMultiplication(&points[0], &scalars[3])
+	tmp.mulWindowed(&points[0], &scalars[3])
 	p1.AddAssign(&tmp)
 
-	p2.ScalarMultiplication(&points[2], &scalars[4])
-	tmp.ScalarMultiplication(&points[1], &scalars[5]).Neg(&tmp)
+	p2.mulWindowed(&points[2], &scalars[4])
+	tmp.mulWindowed(&points[1], &scalars[5]).Neg(&tmp)
 	p2.AddAssign(&tmp)
-	tmp.ScalarMultiplication(&points[0], &scalars[6]).Neg(&tmp)
+	tmp.mulWindowed(&points[0], &scalars[6]).Neg(&tmp)
 	p2.AddAssign(&tmp)
 	p2.phi(&p2).phi(&p2)
 
diff --git a/ecc/bw6-761/g2_test.go b/ecc/bw6-761/g2_test.go
index e14f8ada59..1de4bd3956 100644
--- a/ecc/bw6-761/g2_test.go
+++ b/ecc/bw6-761/g2_test.go
@@ -111,7 +111,7 @@ func TestG2AffineIsOnCurve(t *testing.T) {
 			var op1, op2 G2Jac
 			op1 = fuzzG2Jac(&g2Gen, a)
 			_r := fr.Modulus()
-			op2.ScalarMultiplication(&op1, _r)
+			op2.mulWindowed(&op1, _r)
 			return op1.IsInSubGroup() && op2.Z.IsZero()
 		},
 		GenFp(),
diff --git a/ecc/secp256k1/g1_test.go b/ecc/secp256k1/g1_test.go
index a4fa37fb57..2acef064ae 100644
--- a/ecc/secp256k1/g1_test.go
+++ b/ecc/secp256k1/g1_test.go
@@ -113,7 +113,7 @@ func TestG1AffineIsOnCurve(t *testing.T) {
 			var op1, op2 G1Jac
 			op1 = fuzzG1Jac(&g1Gen, a)
 			_r := fr.Modulus()
-			op2.ScalarMultiplication(&op1, _r)
+			op2.mulWindowed(&op1, _r)
 			return op1.IsInSubGroup() && op2.Z.IsZero()
 		},
 		GenFp(),
diff --git a/internal/generator/ecc/template/point.go.tmpl b/internal/generator/ecc/template/point.go.tmpl
index 961a9e89b3..82e60b6369 100644
--- a/internal/generator/ecc/template/point.go.tmpl
+++ b/internal/generator/ecc/template/point.go.tmpl
@@ -559,7 +559,7 @@ func (p *{{ $TJacobian }}) IsOnCurve() bool {
         // [r]P == 0 <==> [x₀+1]P + ψ([x₀]P) + ψ²([x₀]P) = ψ³([2x₀]P)
 		func (p *{{ $TJacobian }}) IsInSubGroup() bool {
             var a, b, c, res G2Jac
-            a.ScalarMultiplication(p, &xGen)
+            a.mulWindowed(p, &xGen)
             b.psi(&a)
             a.AddAssign(p)
             res.psi(&b)
@@ -585,20 +585,20 @@ func (p *{{ $TJacobian }}) IsOnCurve() bool {
 
 		var res, phip {{ $TJacobian }}
 		phip.phi(p)
-		res.ScalarMultiplication(&phip, &xGen).
+		res.mulWindowed(&phip, &xGen).
 			SubAssign(&phip).
-			ScalarMultiplication(&res, &xGen).
-			ScalarMultiplication(&res, &xGen).
+			mulWindowed(&res, &xGen).
+			mulWindowed(&res, &xGen).
 			AddAssign(&phip)
 
-		phip.ScalarMultiplication(p, &xGen).AddAssign(p).AddAssign(&res)
+		phip.mulWindowed(p, &xGen).AddAssign(p).AddAssign(&res)
 
 		return phip.IsOnCurve() && phip.Z.IsZero()
     {{ else}}
 	func (p *{{ $TJacobian }}) IsInSubGroup() bool {
 
 		var res {{ $TJacobian }}
-        res.ScalarMultiplication(p, fr.Modulus())
+        res.mulWindowed(p, fr.Modulus())
 		return res.IsOnCurve() && res.Z.IsZero()
     {{ end}}
 
@@ -610,11 +610,11 @@ func (p *{{ $TJacobian }}) IsOnCurve() bool {
 	func (p *{{ $TJacobian }}) IsInSubGroup() bool {
 
         var uP, u4P, u5P, q, r {{ $TJacobian }}
-        uP.ScalarMultiplication(p, &xGen)
-        u4P.ScalarMultiplication(&uP, &xGen).
-            ScalarMultiplication(&u4P, &xGen).
-            ScalarMultiplication(&u4P, &xGen)
-        u5P.ScalarMultiplication(&u4P, &xGen)
+        uP.mulWindowed(p, &xGen)
+        u4P.mulWindowed(&uP, &xGen).
+            mulWindowed(&u4P, &xGen).
+            mulWindowed(&u4P, &xGen)
+        u5P.mulWindowed(&u4P, &xGen)
         q.Set(p).SubAssign(&uP)
         r.phi(&q).SubAssign(&uP).
             AddAssign(&u4P).
@@ -624,7 +624,7 @@ func (p *{{ $TJacobian }}) IsOnCurve() bool {
 	func (p *{{ $TJacobian }}) IsInSubGroup() bool {
 
         var r {{ $TJacobian }}
-        r.ScalarMultiplication(p, fr.Modulus())
+        r.mulWindowed(p, fr.Modulus())
     {{ end}}
 		return r.IsOnCurve() && r.Z.IsZero()
 	}
@@ -641,16 +641,16 @@ func (p *{{ $TJacobian }}) IsOnCurve() bool {
 
             var res {{ $TJacobian }}
             res.phi(p).
-                ScalarMultiplication(&res, &xGen).
-                ScalarMultiplication(&res, &xGen).
-                ScalarMultiplication(&res, &xGen).
-                ScalarMultiplication(&res, &xGen).
+                mulWindowed(&res, &xGen).
+                mulWindowed(&res, &xGen).
+                mulWindowed(&res, &xGen).
+                mulWindowed(&res, &xGen).
                 AddAssign(p)
     {{ else}}
 	func (p *{{ $TJacobian }}) IsInSubGroup() bool {
 
         var res {{ $TJacobian }}
-        res.ScalarMultiplication(p, fr.Modulus())
+        res.mulWindowed(p, fr.Modulus())
 		return res.IsOnCurve() && res.Z.IsZero()
     {{ end}}
 
@@ -665,7 +665,7 @@ func (p *{{ $TJacobian }}) IsOnCurve() bool {
         func (p *{{ $TJacobian }}) IsInSubGroup() bool {
             var res, tmp {{ $TJacobian }}
             tmp.psi(p)
-            res.ScalarMultiplication(p, &xGen).
+            res.mulWindowed(p, &xGen).
             {{ if eq .Name "bls24-315"}}
                 AddAssign(&tmp)
             {{ else }}
@@ -689,11 +689,11 @@ func (p *{{ $TJacobian }}) IsOnCurve() bool {
             var res {{ $TJacobian }}
             {{ if .GLV}}
             res.phi(p).
-                ScalarMultiplication(&res, &xGen).
-                ScalarMultiplication(&res, &xGen).
+                mulWindowed(&res, &xGen).
+                mulWindowed(&res, &xGen).
                 AddAssign(p)
             {{ else}}
-            res.ScalarMultiplication(p, fr.Modulus())
+            res.mulWindowed(p, fr.Modulus())
             {{ end}}
 
             return res.IsOnCurve() && res.Z.IsZero()
@@ -708,7 +708,7 @@ func (p *{{ $TJacobian }}) IsOnCurve() bool {
             func (p *{{ $TJacobian }}) IsInSubGroup() bool {
                 var res, tmp {{ $TJacobian }}
                 tmp.psi(p)
-                res.ScalarMultiplication(p, &xGen).
+                res.mulWindowed(p, &xGen).
                     AddAssign(&tmp)
 
                 return res.IsOnCurve() && res.Z.IsZero()
@@ -720,7 +720,7 @@ func (p *{{ $TJacobian }}) IsOnCurve() bool {
             func (p *{{ $TJacobian }}) IsInSubGroup() bool {
                 var res, tmp {{ $TJacobian }}
                 tmp.psi(p)
-                res.ScalarMultiplication(p, &xGen).
+                res.mulWindowed(p, &xGen).
                     SubAssign(&tmp)
 
                 return res.IsOnCurve() && res.Z.IsZero()
@@ -893,13 +893,13 @@ func (p *{{$TJacobian}}) ClearCofactor(q *{{$TJacobian}}) *{{$TJacobian}} {
 {{- if or (eq .Name "bls12-381") (eq .Name "bls24-315")}}
 	// cf https://eprint.iacr.org/2019/403.pdf, 5
 	var res {{$TJacobian}}
-	res.ScalarMultiplication(q, &xGen).AddAssign(q)
+	res.mulWindowed(q, &xGen).AddAssign(q)
 	p.Set(&res)
 	return p
 {{else if or (eq .Name "bls12-377") (eq .Name "bls24-317")}}
 	// cf https://eprint.iacr.org/2019/403.pdf, 5
 	var res {{$TJacobian}}
-	res.ScalarMultiplication(q, &xGen).Neg(&res).AddAssign(q)
+	res.mulWindowed(q, &xGen).Neg(&res).AddAssign(q)
 	p.Set(&res)
 	return p
 {{else if eq .Name "bw6-761"}}
@@ -907,9 +907,9 @@ func (p *{{$TJacobian}}) ClearCofactor(q *{{$TJacobian}}) *{{$TJacobian}} {
 	// https://eprint.iacr.org/2020/351.pdf
 	var points [4]{{$TJacobian}}
 	points[0].Set(q)
-	points[1].ScalarMultiplication(q, &xGen)
-	points[2].ScalarMultiplication(&points[1], &xGen)
-	points[3].ScalarMultiplication(&points[2], &xGen)
+	points[1].mulWindowed(q, &xGen)
+	points[2].mulWindowed(&points[1], &xGen)
+	points[3].mulWindowed(&points[2], &xGen)
 
 	var scalars [7]big.Int
 	scalars[0].SetInt64(103)
@@ -922,18 +922,18 @@ func (p *{{$TJacobian}}) ClearCofactor(q *{{$TJacobian}}) *{{$TJacobian}} {
 	scalars[6].SetInt64(130)
 
 	var p1, p2, tmp {{$TJacobian}}
-	p1.ScalarMultiplication(&points[3], &scalars[0])
-	tmp.ScalarMultiplication(&points[2], &scalars[1]).Neg(&tmp)
+	p1.mulWindowed(&points[3], &scalars[0])
+	tmp.mulWindowed(&points[2], &scalars[1]).Neg(&tmp)
 	p1.AddAssign(&tmp)
-	tmp.ScalarMultiplication(&points[1], &scalars[2]).Neg(&tmp)
+	tmp.mulWindowed(&points[1], &scalars[2]).Neg(&tmp)
 	p1.AddAssign(&tmp)
-	tmp.ScalarMultiplication(&points[0], &scalars[3])
+	tmp.mulWindowed(&points[0], &scalars[3])
 	p1.AddAssign(&tmp)
 
-	p2.ScalarMultiplication(&points[2], &scalars[4])
-	tmp.ScalarMultiplication(&points[1], &scalars[5])
+	p2.mulWindowed(&points[2], &scalars[4])
+	tmp.mulWindowed(&points[1], &scalars[5])
 	p2.AddAssign(&tmp)
-	tmp.ScalarMultiplication(&points[0], &scalars[6])
+	tmp.mulWindowed(&points[0], &scalars[6])
 	p2.AddAssign(&tmp)
 	p2.phi(&p2)
 
@@ -941,7 +941,7 @@ func (p *{{$TJacobian}}) ClearCofactor(q *{{$TJacobian}}) *{{$TJacobian}} {
 {{ else}}
     var c1 big.Int
     c1.SetString("26642435879335816683987677701488073867751118270052650655942102502312977592501693353047140953112195348280268661194876", 10)
-    p.ScalarMultiplication(q, &c1)
+    p.mulWindowed(q, &c1)
 {{ end}}
 
 	return p
@@ -957,27 +957,27 @@ func (p *{{$TJacobian}}) ClearCofactor(q *{{$TJacobian}}) *{{$TJacobian}} {
 	ht.SetInt64(7)
 	v.Mul(&xGen, &xGen).Add(&v, &one).Mul(&v, &uPlusOne)
 
-	uP.ScalarMultiplication(q, &xGen).Neg(&uP)
+	uP.mulWindowed(q, &xGen).Neg(&uP)
 	vP.Set(q).SubAssign(&uP).
-        ScalarMultiplication(&vP, &v)
-	wP.ScalarMultiplication(&vP, &uMinusOne).Neg(&wP).
+        mulWindowed(&vP, &v)
+	wP.mulWindowed(&vP, &uMinusOne).Neg(&wP).
         AddAssign(&uP)
-	L0.ScalarMultiplication(&wP, &d1)
-	tmp.ScalarMultiplication(&vP, &ht)
+	L0.mulWindowed(&wP, &d1)
+	tmp.mulWindowed(&vP, &ht)
 	L0.AddAssign(&tmp)
 	tmp.Double(q)
 	L0.AddAssign(&tmp)
-	L1.Set(&uP).AddAssign(q).ScalarMultiplication(&L1, &d1)
-	tmp.ScalarMultiplication(&vP, &d2)
+	L1.Set(&uP).AddAssign(q).mulWindowed(&L1, &d1)
+	tmp.mulWindowed(&vP, &d2)
 	L1.AddAssign(&tmp)
-	tmp.ScalarMultiplication(q, &ht)
+	tmp.mulWindowed(q, &ht)
 	L1.AddAssign(&tmp)
 
 	p.phi(&L1).AddAssign(&L0)
 {{ else}}
     var c1 big.Int
     c1.SetString("516166855112631370346774477030598579858367278343565509012644853411927535599366632765988905418773", 10)
-    p.ScalarMultiplication(q, &c1)
+    p.mulWindowed(q, &c1)
 {{ end}}
 
     return p
@@ -991,7 +991,7 @@ func (p *{{$TJacobian}}) ClearCofactor(q *{{$TJacobian}}) *{{$TJacobian}} {
 	// cf http://cacr.uwaterloo.ca/techreports/2011/cacr2011-26.pdf, 6.1
 	var points [4]{{$TJacobian}}
 
-	points[0].ScalarMultiplication(q, &xGen)
+	points[0].mulWindowed(q, &xGen)
 
 	points[1].Double(&points[0]).
 		AddAssign(&points[0]).
@@ -1012,8 +1012,8 @@ func (p *{{$TJacobian}}) ClearCofactor(q *{{$TJacobian}}) *{{$TJacobian}} {
 {{else if eq .Name "bls12-381"}}
 	// https://eprint.iacr.org/2017/419.pdf, 4.1
 	var xg, xxg, res, t G2Jac
-	xg.ScalarMultiplication(q, &xGen).Neg(&xg)
-	xxg.ScalarMultiplication(&xg, &xGen).Neg(&xxg)
+	xg.mulWindowed(q, &xGen).Neg(&xg)
+	xxg.mulWindowed(&xg, &xGen).Neg(&xxg)
 
 	res.Set(&xxg).
 		SubAssign(&xg).
@@ -1037,8 +1037,8 @@ func (p *{{$TJacobian}}) ClearCofactor(q *{{$TJacobian}}) *{{$TJacobian}} {
 {{else if eq .Name "bls12-377"}}
     // https://eprint.iacr.org/2017/419.pdf, 4.1
 	var xg, xxg, res, t G2Jac
-	xg.ScalarMultiplication(q, &xGen)
-	xxg.ScalarMultiplication(&xg, &xGen)
+	xg.mulWindowed(q, &xGen)
+	xxg.mulWindowed(&xg, &xGen)
 
 	res.Set(&xxg).
 		SubAssign(&xg).
@@ -1064,16 +1064,16 @@ func (p *{{$TJacobian}}) ClearCofactor(q *{{$TJacobian}}) *{{$TJacobian}} {
 	// multiply by (3x⁴-3)*cofacor
     {{ if eq .Name "bls24-315"}}
 	var xg, xxg, xxxg, xxxxg, res, t G2Jac
-	xg.ScalarMultiplication(q, &xGen).Neg(&xg).SubAssign(q)
-	xxg.ScalarMultiplication(&xg, &xGen).Neg(&xxg)
-	xxxg.ScalarMultiplication(&xxg, &xGen).Neg(&xxxg)
-	xxxxg.ScalarMultiplication(&xxxg, &xGen).Neg(&xxxxg)
+	xg.mulWindowed(q, &xGen).Neg(&xg).SubAssign(q)
+	xxg.mulWindowed(&xg, &xGen).Neg(&xxg)
+	xxxg.mulWindowed(&xxg, &xGen).Neg(&xxxg)
+	xxxxg.mulWindowed(&xxxg, &xGen).Neg(&xxxxg)
     {{ else }}
 	var xg, xxg, xxxg, xxxxg, res, t G2Jac
-	xg.ScalarMultiplication(q, &xGen).SubAssign(q)
-	xxg.ScalarMultiplication(&xg, &xGen)
-	xxxg.ScalarMultiplication(&xxg, &xGen)
-	xxxxg.ScalarMultiplication(&xxxg, &xGen)
+	xg.mulWindowed(q, &xGen).SubAssign(q)
+	xxg.mulWindowed(&xg, &xGen)
+	xxxg.mulWindowed(&xxg, &xGen)
+	xxxxg.mulWindowed(&xxxg, &xGen)
     {{ end }}
 
 	res.Set(&xxxxg).
@@ -1109,9 +1109,9 @@ func (p *{{$TJacobian}}) ClearCofactor(q *{{$TJacobian}}) *{{$TJacobian}} {
 {{- if .GLV}}
 	var points [4]{{$TJacobian}}
 	points[0].Set(q)
-	points[1].ScalarMultiplication(q, &xGen)
-	points[2].ScalarMultiplication(&points[1], &xGen)
-	points[3].ScalarMultiplication(&points[2], &xGen)
+	points[1].mulWindowed(q, &xGen)
+	points[2].mulWindowed(&points[1], &xGen)
+	points[3].mulWindowed(&points[2], &xGen)
 
 	var scalars [7]big.Int
 	scalars[0].SetInt64(103)
@@ -1124,18 +1124,18 @@ func (p *{{$TJacobian}}) ClearCofactor(q *{{$TJacobian}}) *{{$TJacobian}} {
 	scalars[6].SetInt64(109)
 
 	var p1, p2, tmp {{$TJacobian}}
-	p1.ScalarMultiplication(&points[3], &scalars[0])
-	tmp.ScalarMultiplication(&points[2], &scalars[1]).Neg(&tmp)
+	p1.mulWindowed(&points[3], &scalars[0])
+	tmp.mulWindowed(&points[2], &scalars[1]).Neg(&tmp)
 	p1.AddAssign(&tmp)
-	tmp.ScalarMultiplication(&points[1], &scalars[2]).Neg(&tmp)
+	tmp.mulWindowed(&points[1], &scalars[2]).Neg(&tmp)
 	p1.AddAssign(&tmp)
-	tmp.ScalarMultiplication(&points[0], &scalars[3])
+	tmp.mulWindowed(&points[0], &scalars[3])
 	p1.AddAssign(&tmp)
 
-	p2.ScalarMultiplication(&points[2], &scalars[4])
-	tmp.ScalarMultiplication(&points[1], &scalars[5]).Neg(&tmp)
+	p2.mulWindowed(&points[2], &scalars[4])
+	tmp.mulWindowed(&points[1], &scalars[5]).Neg(&tmp)
 	p2.AddAssign(&tmp)
-	tmp.ScalarMultiplication(&points[0], &scalars[6]).Neg(&tmp)
+	tmp.mulWindowed(&points[0], &scalars[6]).Neg(&tmp)
 	p2.AddAssign(&tmp)
 	p2.phi(&p2).phi(&p2)
 
@@ -1143,7 +1143,7 @@ func (p *{{$TJacobian}}) ClearCofactor(q *{{$TJacobian}}) *{{$TJacobian}} {
 {{else}}
     var c2 big.Int
     c2.SetString("26642435879335816683987677701488073867751118270052650655942102502312977592501693353047140953112195348280268661194869", 10)
-    p.ScalarMultiplication(q, &c2)
+    p.mulWindowed(q, &c2)
 {{end}}
 
 	return p
@@ -1155,11 +1155,11 @@ func (p *{{$TJacobian}}) ClearCofactor(q *{{$TJacobian}}) *{{$TJacobian}} {
 	d1.SetInt64(13)
 	d3.SetInt64(5) // negative
 
-	uP.ScalarMultiplication(q, &xGen) // negative
-	u2P.ScalarMultiplication(&uP, &xGen)
-	u3P.ScalarMultiplication(&u2P, &xGen) // negative
-	u4P.ScalarMultiplication(&u3P, &xGen)
-	u5P.ScalarMultiplication(&u4P, &xGen) // negative
+	uP.mulWindowed(q, &xGen) // negative
+	u2P.mulWindowed(&uP, &xGen)
+	u3P.mulWindowed(&u2P, &xGen) // negative
+	u4P.mulWindowed(&u3P, &xGen)
+	u5P.mulWindowed(&u4P, &xGen) // negative
 	vP.Set(&u2P).AddAssign(&uP).
 	    AddAssign(&u3P).
 	    Double(&vP).
@@ -1167,22 +1167,22 @@ func (p *{{$TJacobian}}) ClearCofactor(q *{{$TJacobian}}) *{{$TJacobian}} {
 	    AddAssign(q)
 	wP.Set(&uP).SubAssign(&u4P).SubAssign(&u5P)
     xP.Set(q).AddAssign(&vP)
-	L0.Set(&uP).SubAssign(q).ScalarMultiplication(&L0, &d1)
-	tmp.ScalarMultiplication(&xP, &d3)
+	L0.Set(&uP).SubAssign(q).mulWindowed(&L0, &d1)
+	tmp.mulWindowed(&xP, &d3)
 	L0.AddAssign(&tmp)
-    tmp.ScalarMultiplication(q, &ht) // negative
+    tmp.mulWindowed(q, &ht) // negative
 	L0.SubAssign(&tmp)
-	L1.ScalarMultiplication(&wP, &d1)
-	tmp.ScalarMultiplication(&vP, &ht)
+	L1.mulWindowed(&wP, &d1)
+	tmp.mulWindowed(&vP, &ht)
 	L1.AddAssign(&tmp)
-	tmp.ScalarMultiplication(q, &d3)
+	tmp.mulWindowed(q, &d3)
 	L1.AddAssign(&tmp)
 
 	p.phi(&L1).AddAssign(&L0)
 {{else}}
     var c2 big.Int
     c2.SetString("516166855112631370346774477030598579858367278343565509012644853411927535599366632765988905418768", 10)
-    p.ScalarMultiplication(q, &c2)
+    p.mulWindowed(q, &c2)
 {{end}}
 
 	return p
diff --git a/internal/generator/ecc/template/tests/point.go.tmpl b/internal/generator/ecc/template/tests/point.go.tmpl
index cb54d3791c..1cbc953030 100644
--- a/internal/generator/ecc/template/tests/point.go.tmpl
+++ b/internal/generator/ecc/template/tests/point.go.tmpl
@@ -144,7 +144,7 @@ func Test{{ $TAffine }}IsOnCurve(t *testing.T) {
             var op1, op2 {{ $TJacobian }}
 			op1 = fuzz{{ $TJacobian }}(&{{.PointName}}Gen, a)
             _r := fr.Modulus()
-            op2.ScalarMultiplication(&op1, _r)
+            op2.mulWindowed(&op1, _r)
 			return op1.IsInSubGroup() && op2.Z.IsZero()
 		},
 		{{$fuzzer}},

From 03e007d865c081adce4ef702aedf07866a4a1a86 Mon Sep 17 00:00:00 2001
From: ThomasPiellard <thomas.piellard@consensys.net>
Date: Fri, 22 Nov 2024 19:11:07 +0100
Subject: [PATCH 088/114] Feat/poseidon2 (#553)

---
 ecc/bls12-377/fr/poseidon2/poseidon2.go       | 259 ++++++++++++++++++
 ecc/bls12-377/fr/poseidon2/poseidon2_test.go  |  78 ++++++
 ecc/bls12-381/fr/poseidon2/poseidon2.go       | 257 +++++++++++++++++
 ecc/bls12-381/fr/poseidon2/poseidon2_test.go  |  78 ++++++
 ecc/bls24-315/fr/poseidon2/poseidon2.go       | 257 +++++++++++++++++
 ecc/bls24-315/fr/poseidon2/poseidon2_test.go  |  78 ++++++
 ecc/bls24-317/fr/poseidon2/poseidon2.go       | 258 +++++++++++++++++
 ecc/bls24-317/fr/poseidon2/poseidon2_test.go  |  78 ++++++
 ecc/bn254/fr/poseidon2/poseidon2.go           | 257 +++++++++++++++++
 ecc/bn254/fr/poseidon2/poseidon2_test.go      |  78 ++++++
 ecc/bw6-633/fr/poseidon2/poseidon2.go         | 257 +++++++++++++++++
 ecc/bw6-633/fr/poseidon2/poseidon2_test.go    |  78 ++++++
 ecc/bw6-761/fr/poseidon2/poseidon2.go         | 257 +++++++++++++++++
 ecc/bw6-761/fr/poseidon2/poseidon2_test.go    |  78 ++++++
 .../crypto/hash/poseidon2/generate.go         |  20 ++
 .../hash/poseidon2/template/poseidon2.go.tmpl | 252 +++++++++++++++++
 .../poseidon2/template/poseidon2.test.go.tmpl |  60 ++++
 internal/generator/main.go                    |   4 +
 18 files changed, 2684 insertions(+)
 create mode 100644 ecc/bls12-377/fr/poseidon2/poseidon2.go
 create mode 100644 ecc/bls12-377/fr/poseidon2/poseidon2_test.go
 create mode 100644 ecc/bls12-381/fr/poseidon2/poseidon2.go
 create mode 100644 ecc/bls12-381/fr/poseidon2/poseidon2_test.go
 create mode 100644 ecc/bls24-315/fr/poseidon2/poseidon2.go
 create mode 100644 ecc/bls24-315/fr/poseidon2/poseidon2_test.go
 create mode 100644 ecc/bls24-317/fr/poseidon2/poseidon2.go
 create mode 100644 ecc/bls24-317/fr/poseidon2/poseidon2_test.go
 create mode 100644 ecc/bn254/fr/poseidon2/poseidon2.go
 create mode 100644 ecc/bn254/fr/poseidon2/poseidon2_test.go
 create mode 100644 ecc/bw6-633/fr/poseidon2/poseidon2.go
 create mode 100644 ecc/bw6-633/fr/poseidon2/poseidon2_test.go
 create mode 100644 ecc/bw6-761/fr/poseidon2/poseidon2.go
 create mode 100644 ecc/bw6-761/fr/poseidon2/poseidon2_test.go
 create mode 100644 internal/generator/crypto/hash/poseidon2/generate.go
 create mode 100644 internal/generator/crypto/hash/poseidon2/template/poseidon2.go.tmpl
 create mode 100644 internal/generator/crypto/hash/poseidon2/template/poseidon2.test.go.tmpl

diff --git a/ecc/bls12-377/fr/poseidon2/poseidon2.go b/ecc/bls12-377/fr/poseidon2/poseidon2.go
new file mode 100644
index 0000000000..89e51de1d1
--- /dev/null
+++ b/ecc/bls12-377/fr/poseidon2/poseidon2.go
@@ -0,0 +1,259 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package poseidon2
+
+import (
+	"errors"
+	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
+	"golang.org/x/crypto/sha3"
+)
+
+var (
+	ErrInvalidSizebuffer = errors.New("the size of the input should match the size of the hash buffer")
+)
+
+// reference implementation: https://github.com/HorizenLabs/poseidon2/blob/main/plain_implementations/src/poseidon2/poseidon2.rs
+// specifications: https://github.com/argumentcomputer/neptune/blob/main/spec/poseidon_spec.pdf
+// origina paper: https://eprint.iacr.org/2023/323.pdf
+
+// parameters describing the poseidon2 implementation
+type parameters struct {
+	// len(preimage)+len(digest)=len(preimage)+ceil(log(2*<security_level>/r))
+	t int
+
+	// number of full rounds (even number)
+	rF int
+
+	// number of partial rounds
+	rP int
+
+	// diagonal elements of the internal matrices, minus one
+	diagInternalMatrices []fr.Element
+
+	// round keys
+	roundKeys [][]fr.Element
+}
+
+// Hash stores the buffer of the poseidon2 permutation and provides poseidon2 permutation
+// methods on the buffer
+type Hash struct {
+
+	// parameters describing the
+	params parameters
+}
+
+// NewHash returns a new hash instance allowing to apply the poseidon2 permutation
+func NewHash(t, rf, rp int, seed string) Hash {
+	params := parameters{t: t, rF: rf, rP: rp}
+	params.roundKeys = InitRC(seed, rf, rp, t)
+	res := Hash{params: params}
+	return res
+}
+
+// InitRC initiate round keys. Only one entry is non zero for the internal
+// rounds, cf https://eprint.iacr.org/2023/323.pdf page 9
+func InitRC(seed string, rf, rp, t int) [][]fr.Element {
+
+	bseed := ([]byte)(seed)
+	hash := sha3.NewLegacyKeccak256()
+	_, _ = hash.Write(bseed)
+	rnd := hash.Sum(nil) // pre hash before use
+	hash.Reset()
+	_, _ = hash.Write(rnd)
+
+	roundKeys := make([][]fr.Element, rf+rp)
+	for i := 0; i < rf/2; i++ {
+		roundKeys[i] = make([]fr.Element, t)
+		for j := 0; j < t; j++ {
+			rnd = hash.Sum(nil)
+			roundKeys[i][j].SetBytes(rnd)
+			hash.Reset()
+			_, _ = hash.Write(rnd)
+		}
+	}
+	for i := 0; i < rp; i++ {
+		roundKeys[i] = make([]fr.Element, 1)
+		rnd = hash.Sum(nil)
+		roundKeys[i][0].SetBytes(rnd)
+		hash.Reset()
+		_, _ = hash.Write(rnd)
+	}
+	for i := 0; i < rf/2; i++ {
+		roundKeys[i] = make([]fr.Element, t)
+		for j := 0; j < t; j++ {
+			rnd = hash.Sum(nil)
+			roundKeys[i][j].SetBytes(rnd)
+			hash.Reset()
+			_, _ = hash.Write(rnd)
+		}
+	}
+	return roundKeys
+}
+
+// sBox applies the sBox on buffer[index]
+func (h *Hash) sBox(index int, input []fr.Element) {
+	var tmp fr.Element
+	tmp.Set(&input[index])
+
+	// sbox degree is 17
+	input[index].Square(&input[index]).
+		Square(&input[index]).
+		Square(&input[index]).
+		Square(&input[index]).
+		Mul(&input[index], &tmp)
+
+}
+
+// matMulM4 computes
+// s <- M4*s
+// where M4=
+// (5 7 1 3)
+// (4 6 1 1)
+// (1 3 5 7)
+// (1 1 4 6)
+// on chunks of 4 elemts on each part of the buffer
+// see https://eprint.iacr.org/2023/323.pdf appendix B for the addition chain
+func (h *Hash) matMulM4InPlace(s []fr.Element) {
+	c := len(s) / 4
+	for i := 0; i < c; i++ {
+		var t0, t1, t2, t3, t4, t5, t6, t7 fr.Element
+		t0.Add(&s[4*i], &s[4*i+1])               // s0+s1
+		t1.Add(&s[4*i+2], &s[4*i+3])             // s2+s3
+		t2.Double(&s[4*i+1]).Add(&t2, &t1)       // 2s1+t1
+		t3.Double(&s[4*i+3]).Add(&t3, &t0)       // 2s3+t0
+		t4.Double(&t1).Double(&t4).Add(&t4, &t3) // 4t1+t3
+		t5.Double(&t0).Double(&t5).Add(&t5, &t2) // 4t0+t2
+		t6.Add(&t3, &t5)                         // t3+t4
+		t7.Add(&t2, &t4)                         // t2+t4
+		s[4*i].Set(&t6)
+		s[4*i+1].Set(&t5)
+		s[4*i+2].Set(&t7)
+		s[4*i+3].Set(&t4)
+	}
+}
+
+// when t=2,3 the buffer is multiplied by circ(2,1) and circ(2,1,1)
+// see https://eprint.iacr.org/2023/323.pdf page 15, case t=2,3
+//
+// when t=0[4], the buffer is multiplied by circ(2M4,M4,..,M4)
+// see https://eprint.iacr.org/2023/323.pdf
+func (h *Hash) matMulExternalInPlace(input []fr.Element) {
+
+	if h.params.t == 2 {
+		var tmp fr.Element
+		tmp.Add(&input[0], &input[1])
+		input[0].Add(&tmp, &input[0])
+		input[1].Add(&tmp, &input[1])
+	} else if h.params.t == 3 {
+		var tmp fr.Element
+		tmp.Add(&input[0], &input[1]).
+			Add(&tmp, &input[2])
+		input[0].Add(&tmp, &input[0])
+		input[1].Add(&tmp, &input[1])
+		input[2].Add(&tmp, &input[2])
+	} else if h.params.t == 4 {
+		h.matMulM4InPlace(input)
+	} else {
+		// at this stage t is supposed to be a multiple of 4
+		// the MDS matrix is circ(2M4,M4,..,M4)
+		h.matMulM4InPlace(input)
+		tmp := make([]fr.Element, 4)
+		for i := 0; i < h.params.t/4; i++ {
+			tmp[0].Add(&tmp[0], &input[4*i])
+			tmp[1].Add(&tmp[1], &input[4*i+1])
+			tmp[2].Add(&tmp[2], &input[4*i+2])
+			tmp[3].Add(&tmp[3], &input[4*i+3])
+		}
+		for i := 0; i < h.params.t/4; i++ {
+			input[4*i].Add(&input[4*i], &tmp[0])
+			input[4*i+1].Add(&input[4*i], &tmp[1])
+			input[4*i+2].Add(&input[4*i], &tmp[2])
+			input[4*i+3].Add(&input[4*i], &tmp[3])
+		}
+	}
+}
+
+// when t=2,3 the matrix are respectibely [[2,1][1,3]] and [[2,1,1][1,2,1][1,1,3]]
+// otherwise the matrix is filled with ones except on the diagonal,
+func (h *Hash) matMulInternalInPlace(input []fr.Element) {
+	if h.params.t == 2 {
+		var sum fr.Element
+		sum.Add(&input[0], &input[1])
+		input[0].Add(&input[0], &sum)
+		input[1].Double(&input[1]).Add(&input[1], &sum)
+	} else if h.params.t == 3 {
+		var sum fr.Element
+		sum.Add(&input[0], &input[1]).Add(&sum, &input[2])
+		input[0].Add(&input[0], &sum)
+		input[1].Add(&input[1], &sum)
+		input[2].Double(&input[2]).Add(&input[2], &sum)
+	} else {
+		var sum fr.Element
+		sum.Set(&input[0])
+		for i := 1; i < h.params.t; i++ {
+			sum.Add(&sum, &input[i])
+		}
+		for i := 0; i < h.params.t; i++ {
+			input[i].Mul(&input[i], &h.params.diagInternalMatrices[i]).
+				Add(&input[i], &sum)
+		}
+	}
+}
+
+// addRoundKeyInPlace adds the round-th key to the buffer
+func (h *Hash) addRoundKeyInPlace(round int, input []fr.Element) {
+	for i := 0; i < len(h.params.roundKeys[round]); i++ {
+		input[i].Add(&input[i], &h.params.roundKeys[round][i])
+	}
+}
+
+// Permutation applies the permutation on input, and stores the result in input.
+func (h *Hash) Permutation(input []fr.Element) error {
+	if len(input) != h.params.t {
+		return ErrInvalidSizebuffer
+	}
+
+	// external matrix multiplication, cf https://eprint.iacr.org/2023/323.pdf page 14 (part 6)
+	h.matMulExternalInPlace(input)
+
+	rf := h.params.rF / 2
+	for i := 0; i < rf; i++ {
+		// one round = matMulExternal(sBox_Full(addRoundKey))
+		h.addRoundKeyInPlace(i, input)
+		for j := 0; j < h.params.t; j++ {
+			h.sBox(j, input)
+		}
+		h.matMulExternalInPlace(input)
+	}
+
+	for i := rf; i < rf+h.params.rP; i++ {
+		// one round = matMulInternal(sBox_sparse(addRoundKey))
+		h.addRoundKeyInPlace(i, input)
+		h.sBox(0, input)
+		h.matMulInternalInPlace(input)
+	}
+	for i := rf + h.params.rP; i < h.params.rF+h.params.rP; i++ {
+		// one round = matMulExternal(sBox_Full(addRoundKey))
+		h.addRoundKeyInPlace(i, input)
+		for j := 0; j < h.params.t; j++ {
+			h.sBox(j, input)
+		}
+		h.matMulExternalInPlace(input)
+	}
+
+	return nil
+}
diff --git a/ecc/bls12-377/fr/poseidon2/poseidon2_test.go b/ecc/bls12-377/fr/poseidon2/poseidon2_test.go
new file mode 100644
index 0000000000..3c99a43c92
--- /dev/null
+++ b/ecc/bls12-377/fr/poseidon2/poseidon2_test.go
@@ -0,0 +1,78 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package poseidon2
+
+import (
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
+)
+
+func TestExternalMatrix(t *testing.T) {
+
+	var expected [4][4]fr.Element
+	expected[0][0].SetUint64(5)
+	expected[0][1].SetUint64(4)
+	expected[0][2].SetUint64(1)
+	expected[0][3].SetUint64(1)
+
+	expected[1][0].SetUint64(7)
+	expected[1][1].SetUint64(6)
+	expected[1][2].SetUint64(3)
+	expected[1][3].SetUint64(1)
+
+	expected[2][0].SetUint64(1)
+	expected[2][1].SetUint64(1)
+	expected[2][2].SetUint64(5)
+	expected[2][3].SetUint64(4)
+
+	expected[3][0].SetUint64(3)
+	expected[3][1].SetUint64(1)
+	expected[3][2].SetUint64(7)
+	expected[3][3].SetUint64(6)
+
+	h := NewHash(4, 8, 56, "seed")
+	var tmp [4]fr.Element
+	for i := 0; i < 4; i++ {
+		for j := 0; j < 4; j++ {
+			tmp[j].SetUint64(0)
+			if i == j {
+				tmp[j].SetOne()
+			}
+		}
+		// h.Write(tmp[:])
+		h.matMulExternalInPlace(tmp[:])
+		for j := 0; j < 4; j++ {
+			if !tmp[j].Equal(&expected[i][j]) {
+				t.Fatal("error matMul4")
+			}
+		}
+	}
+
+}
+
+func BenchmarkPoseidon2(b *testing.B) {
+	h := NewHash(3, 8, 56, "seed")
+	var tmp [3]fr.Element
+	tmp[0].SetRandom()
+	tmp[1].SetRandom()
+	tmp[2].SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		h.Permutation(tmp[:])
+	}
+}
diff --git a/ecc/bls12-381/fr/poseidon2/poseidon2.go b/ecc/bls12-381/fr/poseidon2/poseidon2.go
new file mode 100644
index 0000000000..a3bf1b14de
--- /dev/null
+++ b/ecc/bls12-381/fr/poseidon2/poseidon2.go
@@ -0,0 +1,257 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package poseidon2
+
+import (
+	"errors"
+	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
+	"golang.org/x/crypto/sha3"
+)
+
+var (
+	ErrInvalidSizebuffer = errors.New("the size of the input should match the size of the hash buffer")
+)
+
+// reference implementation: https://github.com/HorizenLabs/poseidon2/blob/main/plain_implementations/src/poseidon2/poseidon2.rs
+// specifications: https://github.com/argumentcomputer/neptune/blob/main/spec/poseidon_spec.pdf
+// origina paper: https://eprint.iacr.org/2023/323.pdf
+
+// parameters describing the poseidon2 implementation
+type parameters struct {
+	// len(preimage)+len(digest)=len(preimage)+ceil(log(2*<security_level>/r))
+	t int
+
+	// number of full rounds (even number)
+	rF int
+
+	// number of partial rounds
+	rP int
+
+	// diagonal elements of the internal matrices, minus one
+	diagInternalMatrices []fr.Element
+
+	// round keys
+	roundKeys [][]fr.Element
+}
+
+// Hash stores the buffer of the poseidon2 permutation and provides poseidon2 permutation
+// methods on the buffer
+type Hash struct {
+
+	// parameters describing the
+	params parameters
+}
+
+// NewHash returns a new hash instance allowing to apply the poseidon2 permutation
+func NewHash(t, rf, rp int, seed string) Hash {
+	params := parameters{t: t, rF: rf, rP: rp}
+	params.roundKeys = InitRC(seed, rf, rp, t)
+	res := Hash{params: params}
+	return res
+}
+
+// InitRC initiate round keys. Only one entry is non zero for the internal
+// rounds, cf https://eprint.iacr.org/2023/323.pdf page 9
+func InitRC(seed string, rf, rp, t int) [][]fr.Element {
+
+	bseed := ([]byte)(seed)
+	hash := sha3.NewLegacyKeccak256()
+	_, _ = hash.Write(bseed)
+	rnd := hash.Sum(nil) // pre hash before use
+	hash.Reset()
+	_, _ = hash.Write(rnd)
+
+	roundKeys := make([][]fr.Element, rf+rp)
+	for i := 0; i < rf/2; i++ {
+		roundKeys[i] = make([]fr.Element, t)
+		for j := 0; j < t; j++ {
+			rnd = hash.Sum(nil)
+			roundKeys[i][j].SetBytes(rnd)
+			hash.Reset()
+			_, _ = hash.Write(rnd)
+		}
+	}
+	for i := 0; i < rp; i++ {
+		roundKeys[i] = make([]fr.Element, 1)
+		rnd = hash.Sum(nil)
+		roundKeys[i][0].SetBytes(rnd)
+		hash.Reset()
+		_, _ = hash.Write(rnd)
+	}
+	for i := 0; i < rf/2; i++ {
+		roundKeys[i] = make([]fr.Element, t)
+		for j := 0; j < t; j++ {
+			rnd = hash.Sum(nil)
+			roundKeys[i][j].SetBytes(rnd)
+			hash.Reset()
+			_, _ = hash.Write(rnd)
+		}
+	}
+	return roundKeys
+}
+
+// sBox applies the sBox on buffer[index]
+func (h *Hash) sBox(index int, input []fr.Element) {
+	var tmp fr.Element
+	tmp.Set(&input[index])
+
+	// sbox degree is 5
+	input[index].Square(&input[index]).
+		Square(&input[index]).
+		Mul(&input[index], &tmp)
+
+}
+
+// matMulM4 computes
+// s <- M4*s
+// where M4=
+// (5 7 1 3)
+// (4 6 1 1)
+// (1 3 5 7)
+// (1 1 4 6)
+// on chunks of 4 elemts on each part of the buffer
+// see https://eprint.iacr.org/2023/323.pdf appendix B for the addition chain
+func (h *Hash) matMulM4InPlace(s []fr.Element) {
+	c := len(s) / 4
+	for i := 0; i < c; i++ {
+		var t0, t1, t2, t3, t4, t5, t6, t7 fr.Element
+		t0.Add(&s[4*i], &s[4*i+1])               // s0+s1
+		t1.Add(&s[4*i+2], &s[4*i+3])             // s2+s3
+		t2.Double(&s[4*i+1]).Add(&t2, &t1)       // 2s1+t1
+		t3.Double(&s[4*i+3]).Add(&t3, &t0)       // 2s3+t0
+		t4.Double(&t1).Double(&t4).Add(&t4, &t3) // 4t1+t3
+		t5.Double(&t0).Double(&t5).Add(&t5, &t2) // 4t0+t2
+		t6.Add(&t3, &t5)                         // t3+t4
+		t7.Add(&t2, &t4)                         // t2+t4
+		s[4*i].Set(&t6)
+		s[4*i+1].Set(&t5)
+		s[4*i+2].Set(&t7)
+		s[4*i+3].Set(&t4)
+	}
+}
+
+// when t=2,3 the buffer is multiplied by circ(2,1) and circ(2,1,1)
+// see https://eprint.iacr.org/2023/323.pdf page 15, case t=2,3
+//
+// when t=0[4], the buffer is multiplied by circ(2M4,M4,..,M4)
+// see https://eprint.iacr.org/2023/323.pdf
+func (h *Hash) matMulExternalInPlace(input []fr.Element) {
+
+	if h.params.t == 2 {
+		var tmp fr.Element
+		tmp.Add(&input[0], &input[1])
+		input[0].Add(&tmp, &input[0])
+		input[1].Add(&tmp, &input[1])
+	} else if h.params.t == 3 {
+		var tmp fr.Element
+		tmp.Add(&input[0], &input[1]).
+			Add(&tmp, &input[2])
+		input[0].Add(&tmp, &input[0])
+		input[1].Add(&tmp, &input[1])
+		input[2].Add(&tmp, &input[2])
+	} else if h.params.t == 4 {
+		h.matMulM4InPlace(input)
+	} else {
+		// at this stage t is supposed to be a multiple of 4
+		// the MDS matrix is circ(2M4,M4,..,M4)
+		h.matMulM4InPlace(input)
+		tmp := make([]fr.Element, 4)
+		for i := 0; i < h.params.t/4; i++ {
+			tmp[0].Add(&tmp[0], &input[4*i])
+			tmp[1].Add(&tmp[1], &input[4*i+1])
+			tmp[2].Add(&tmp[2], &input[4*i+2])
+			tmp[3].Add(&tmp[3], &input[4*i+3])
+		}
+		for i := 0; i < h.params.t/4; i++ {
+			input[4*i].Add(&input[4*i], &tmp[0])
+			input[4*i+1].Add(&input[4*i], &tmp[1])
+			input[4*i+2].Add(&input[4*i], &tmp[2])
+			input[4*i+3].Add(&input[4*i], &tmp[3])
+		}
+	}
+}
+
+// when t=2,3 the matrix are respectibely [[2,1][1,3]] and [[2,1,1][1,2,1][1,1,3]]
+// otherwise the matrix is filled with ones except on the diagonal,
+func (h *Hash) matMulInternalInPlace(input []fr.Element) {
+	if h.params.t == 2 {
+		var sum fr.Element
+		sum.Add(&input[0], &input[1])
+		input[0].Add(&input[0], &sum)
+		input[1].Double(&input[1]).Add(&input[1], &sum)
+	} else if h.params.t == 3 {
+		var sum fr.Element
+		sum.Add(&input[0], &input[1]).Add(&sum, &input[2])
+		input[0].Add(&input[0], &sum)
+		input[1].Add(&input[1], &sum)
+		input[2].Double(&input[2]).Add(&input[2], &sum)
+	} else {
+		var sum fr.Element
+		sum.Set(&input[0])
+		for i := 1; i < h.params.t; i++ {
+			sum.Add(&sum, &input[i])
+		}
+		for i := 0; i < h.params.t; i++ {
+			input[i].Mul(&input[i], &h.params.diagInternalMatrices[i]).
+				Add(&input[i], &sum)
+		}
+	}
+}
+
+// addRoundKeyInPlace adds the round-th key to the buffer
+func (h *Hash) addRoundKeyInPlace(round int, input []fr.Element) {
+	for i := 0; i < len(h.params.roundKeys[round]); i++ {
+		input[i].Add(&input[i], &h.params.roundKeys[round][i])
+	}
+}
+
+// Permutation applies the permutation on input, and stores the result in input.
+func (h *Hash) Permutation(input []fr.Element) error {
+	if len(input) != h.params.t {
+		return ErrInvalidSizebuffer
+	}
+
+	// external matrix multiplication, cf https://eprint.iacr.org/2023/323.pdf page 14 (part 6)
+	h.matMulExternalInPlace(input)
+
+	rf := h.params.rF / 2
+	for i := 0; i < rf; i++ {
+		// one round = matMulExternal(sBox_Full(addRoundKey))
+		h.addRoundKeyInPlace(i, input)
+		for j := 0; j < h.params.t; j++ {
+			h.sBox(j, input)
+		}
+		h.matMulExternalInPlace(input)
+	}
+
+	for i := rf; i < rf+h.params.rP; i++ {
+		// one round = matMulInternal(sBox_sparse(addRoundKey))
+		h.addRoundKeyInPlace(i, input)
+		h.sBox(0, input)
+		h.matMulInternalInPlace(input)
+	}
+	for i := rf + h.params.rP; i < h.params.rF+h.params.rP; i++ {
+		// one round = matMulExternal(sBox_Full(addRoundKey))
+		h.addRoundKeyInPlace(i, input)
+		for j := 0; j < h.params.t; j++ {
+			h.sBox(j, input)
+		}
+		h.matMulExternalInPlace(input)
+	}
+
+	return nil
+}
diff --git a/ecc/bls12-381/fr/poseidon2/poseidon2_test.go b/ecc/bls12-381/fr/poseidon2/poseidon2_test.go
new file mode 100644
index 0000000000..c41de997cc
--- /dev/null
+++ b/ecc/bls12-381/fr/poseidon2/poseidon2_test.go
@@ -0,0 +1,78 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package poseidon2
+
+import (
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
+)
+
+func TestExternalMatrix(t *testing.T) {
+
+	var expected [4][4]fr.Element
+	expected[0][0].SetUint64(5)
+	expected[0][1].SetUint64(4)
+	expected[0][2].SetUint64(1)
+	expected[0][3].SetUint64(1)
+
+	expected[1][0].SetUint64(7)
+	expected[1][1].SetUint64(6)
+	expected[1][2].SetUint64(3)
+	expected[1][3].SetUint64(1)
+
+	expected[2][0].SetUint64(1)
+	expected[2][1].SetUint64(1)
+	expected[2][2].SetUint64(5)
+	expected[2][3].SetUint64(4)
+
+	expected[3][0].SetUint64(3)
+	expected[3][1].SetUint64(1)
+	expected[3][2].SetUint64(7)
+	expected[3][3].SetUint64(6)
+
+	h := NewHash(4, 8, 56, "seed")
+	var tmp [4]fr.Element
+	for i := 0; i < 4; i++ {
+		for j := 0; j < 4; j++ {
+			tmp[j].SetUint64(0)
+			if i == j {
+				tmp[j].SetOne()
+			}
+		}
+		// h.Write(tmp[:])
+		h.matMulExternalInPlace(tmp[:])
+		for j := 0; j < 4; j++ {
+			if !tmp[j].Equal(&expected[i][j]) {
+				t.Fatal("error matMul4")
+			}
+		}
+	}
+
+}
+
+func BenchmarkPoseidon2(b *testing.B) {
+	h := NewHash(3, 8, 56, "seed")
+	var tmp [3]fr.Element
+	tmp[0].SetRandom()
+	tmp[1].SetRandom()
+	tmp[2].SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		h.Permutation(tmp[:])
+	}
+}
diff --git a/ecc/bls24-315/fr/poseidon2/poseidon2.go b/ecc/bls24-315/fr/poseidon2/poseidon2.go
new file mode 100644
index 0000000000..6f0f4fdb32
--- /dev/null
+++ b/ecc/bls24-315/fr/poseidon2/poseidon2.go
@@ -0,0 +1,257 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package poseidon2
+
+import (
+	"errors"
+	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
+	"golang.org/x/crypto/sha3"
+)
+
+var (
+	ErrInvalidSizebuffer = errors.New("the size of the input should match the size of the hash buffer")
+)
+
+// reference implementation: https://github.com/HorizenLabs/poseidon2/blob/main/plain_implementations/src/poseidon2/poseidon2.rs
+// specifications: https://github.com/argumentcomputer/neptune/blob/main/spec/poseidon_spec.pdf
+// origina paper: https://eprint.iacr.org/2023/323.pdf
+
+// parameters describing the poseidon2 implementation
+type parameters struct {
+	// len(preimage)+len(digest)=len(preimage)+ceil(log(2*<security_level>/r))
+	t int
+
+	// number of full rounds (even number)
+	rF int
+
+	// number of partial rounds
+	rP int
+
+	// diagonal elements of the internal matrices, minus one
+	diagInternalMatrices []fr.Element
+
+	// round keys
+	roundKeys [][]fr.Element
+}
+
+// Hash stores the buffer of the poseidon2 permutation and provides poseidon2 permutation
+// methods on the buffer
+type Hash struct {
+
+	// parameters describing the
+	params parameters
+}
+
+// NewHash returns a new hash instance allowing to apply the poseidon2 permutation
+func NewHash(t, rf, rp int, seed string) Hash {
+	params := parameters{t: t, rF: rf, rP: rp}
+	params.roundKeys = InitRC(seed, rf, rp, t)
+	res := Hash{params: params}
+	return res
+}
+
+// InitRC initiate round keys. Only one entry is non zero for the internal
+// rounds, cf https://eprint.iacr.org/2023/323.pdf page 9
+func InitRC(seed string, rf, rp, t int) [][]fr.Element {
+
+	bseed := ([]byte)(seed)
+	hash := sha3.NewLegacyKeccak256()
+	_, _ = hash.Write(bseed)
+	rnd := hash.Sum(nil) // pre hash before use
+	hash.Reset()
+	_, _ = hash.Write(rnd)
+
+	roundKeys := make([][]fr.Element, rf+rp)
+	for i := 0; i < rf/2; i++ {
+		roundKeys[i] = make([]fr.Element, t)
+		for j := 0; j < t; j++ {
+			rnd = hash.Sum(nil)
+			roundKeys[i][j].SetBytes(rnd)
+			hash.Reset()
+			_, _ = hash.Write(rnd)
+		}
+	}
+	for i := 0; i < rp; i++ {
+		roundKeys[i] = make([]fr.Element, 1)
+		rnd = hash.Sum(nil)
+		roundKeys[i][0].SetBytes(rnd)
+		hash.Reset()
+		_, _ = hash.Write(rnd)
+	}
+	for i := 0; i < rf/2; i++ {
+		roundKeys[i] = make([]fr.Element, t)
+		for j := 0; j < t; j++ {
+			rnd = hash.Sum(nil)
+			roundKeys[i][j].SetBytes(rnd)
+			hash.Reset()
+			_, _ = hash.Write(rnd)
+		}
+	}
+	return roundKeys
+}
+
+// sBox applies the sBox on buffer[index]
+func (h *Hash) sBox(index int, input []fr.Element) {
+	var tmp fr.Element
+	tmp.Set(&input[index])
+
+	// sbox degree is 5
+	input[index].Square(&input[index]).
+		Square(&input[index]).
+		Mul(&input[index], &tmp)
+
+}
+
+// matMulM4 computes
+// s <- M4*s
+// where M4=
+// (5 7 1 3)
+// (4 6 1 1)
+// (1 3 5 7)
+// (1 1 4 6)
+// on chunks of 4 elemts on each part of the buffer
+// see https://eprint.iacr.org/2023/323.pdf appendix B for the addition chain
+func (h *Hash) matMulM4InPlace(s []fr.Element) {
+	c := len(s) / 4
+	for i := 0; i < c; i++ {
+		var t0, t1, t2, t3, t4, t5, t6, t7 fr.Element
+		t0.Add(&s[4*i], &s[4*i+1])               // s0+s1
+		t1.Add(&s[4*i+2], &s[4*i+3])             // s2+s3
+		t2.Double(&s[4*i+1]).Add(&t2, &t1)       // 2s1+t1
+		t3.Double(&s[4*i+3]).Add(&t3, &t0)       // 2s3+t0
+		t4.Double(&t1).Double(&t4).Add(&t4, &t3) // 4t1+t3
+		t5.Double(&t0).Double(&t5).Add(&t5, &t2) // 4t0+t2
+		t6.Add(&t3, &t5)                         // t3+t4
+		t7.Add(&t2, &t4)                         // t2+t4
+		s[4*i].Set(&t6)
+		s[4*i+1].Set(&t5)
+		s[4*i+2].Set(&t7)
+		s[4*i+3].Set(&t4)
+	}
+}
+
+// when t=2,3 the buffer is multiplied by circ(2,1) and circ(2,1,1)
+// see https://eprint.iacr.org/2023/323.pdf page 15, case t=2,3
+//
+// when t=0[4], the buffer is multiplied by circ(2M4,M4,..,M4)
+// see https://eprint.iacr.org/2023/323.pdf
+func (h *Hash) matMulExternalInPlace(input []fr.Element) {
+
+	if h.params.t == 2 {
+		var tmp fr.Element
+		tmp.Add(&input[0], &input[1])
+		input[0].Add(&tmp, &input[0])
+		input[1].Add(&tmp, &input[1])
+	} else if h.params.t == 3 {
+		var tmp fr.Element
+		tmp.Add(&input[0], &input[1]).
+			Add(&tmp, &input[2])
+		input[0].Add(&tmp, &input[0])
+		input[1].Add(&tmp, &input[1])
+		input[2].Add(&tmp, &input[2])
+	} else if h.params.t == 4 {
+		h.matMulM4InPlace(input)
+	} else {
+		// at this stage t is supposed to be a multiple of 4
+		// the MDS matrix is circ(2M4,M4,..,M4)
+		h.matMulM4InPlace(input)
+		tmp := make([]fr.Element, 4)
+		for i := 0; i < h.params.t/4; i++ {
+			tmp[0].Add(&tmp[0], &input[4*i])
+			tmp[1].Add(&tmp[1], &input[4*i+1])
+			tmp[2].Add(&tmp[2], &input[4*i+2])
+			tmp[3].Add(&tmp[3], &input[4*i+3])
+		}
+		for i := 0; i < h.params.t/4; i++ {
+			input[4*i].Add(&input[4*i], &tmp[0])
+			input[4*i+1].Add(&input[4*i], &tmp[1])
+			input[4*i+2].Add(&input[4*i], &tmp[2])
+			input[4*i+3].Add(&input[4*i], &tmp[3])
+		}
+	}
+}
+
+// when t=2,3 the matrix are respectibely [[2,1][1,3]] and [[2,1,1][1,2,1][1,1,3]]
+// otherwise the matrix is filled with ones except on the diagonal,
+func (h *Hash) matMulInternalInPlace(input []fr.Element) {
+	if h.params.t == 2 {
+		var sum fr.Element
+		sum.Add(&input[0], &input[1])
+		input[0].Add(&input[0], &sum)
+		input[1].Double(&input[1]).Add(&input[1], &sum)
+	} else if h.params.t == 3 {
+		var sum fr.Element
+		sum.Add(&input[0], &input[1]).Add(&sum, &input[2])
+		input[0].Add(&input[0], &sum)
+		input[1].Add(&input[1], &sum)
+		input[2].Double(&input[2]).Add(&input[2], &sum)
+	} else {
+		var sum fr.Element
+		sum.Set(&input[0])
+		for i := 1; i < h.params.t; i++ {
+			sum.Add(&sum, &input[i])
+		}
+		for i := 0; i < h.params.t; i++ {
+			input[i].Mul(&input[i], &h.params.diagInternalMatrices[i]).
+				Add(&input[i], &sum)
+		}
+	}
+}
+
+// addRoundKeyInPlace adds the round-th key to the buffer
+func (h *Hash) addRoundKeyInPlace(round int, input []fr.Element) {
+	for i := 0; i < len(h.params.roundKeys[round]); i++ {
+		input[i].Add(&input[i], &h.params.roundKeys[round][i])
+	}
+}
+
+// Permutation applies the permutation on input, and stores the result in input.
+func (h *Hash) Permutation(input []fr.Element) error {
+	if len(input) != h.params.t {
+		return ErrInvalidSizebuffer
+	}
+
+	// external matrix multiplication, cf https://eprint.iacr.org/2023/323.pdf page 14 (part 6)
+	h.matMulExternalInPlace(input)
+
+	rf := h.params.rF / 2
+	for i := 0; i < rf; i++ {
+		// one round = matMulExternal(sBox_Full(addRoundKey))
+		h.addRoundKeyInPlace(i, input)
+		for j := 0; j < h.params.t; j++ {
+			h.sBox(j, input)
+		}
+		h.matMulExternalInPlace(input)
+	}
+
+	for i := rf; i < rf+h.params.rP; i++ {
+		// one round = matMulInternal(sBox_sparse(addRoundKey))
+		h.addRoundKeyInPlace(i, input)
+		h.sBox(0, input)
+		h.matMulInternalInPlace(input)
+	}
+	for i := rf + h.params.rP; i < h.params.rF+h.params.rP; i++ {
+		// one round = matMulExternal(sBox_Full(addRoundKey))
+		h.addRoundKeyInPlace(i, input)
+		for j := 0; j < h.params.t; j++ {
+			h.sBox(j, input)
+		}
+		h.matMulExternalInPlace(input)
+	}
+
+	return nil
+}
diff --git a/ecc/bls24-315/fr/poseidon2/poseidon2_test.go b/ecc/bls24-315/fr/poseidon2/poseidon2_test.go
new file mode 100644
index 0000000000..eaade1b7f8
--- /dev/null
+++ b/ecc/bls24-315/fr/poseidon2/poseidon2_test.go
@@ -0,0 +1,78 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package poseidon2
+
+import (
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
+)
+
+func TestExternalMatrix(t *testing.T) {
+
+	var expected [4][4]fr.Element
+	expected[0][0].SetUint64(5)
+	expected[0][1].SetUint64(4)
+	expected[0][2].SetUint64(1)
+	expected[0][3].SetUint64(1)
+
+	expected[1][0].SetUint64(7)
+	expected[1][1].SetUint64(6)
+	expected[1][2].SetUint64(3)
+	expected[1][3].SetUint64(1)
+
+	expected[2][0].SetUint64(1)
+	expected[2][1].SetUint64(1)
+	expected[2][2].SetUint64(5)
+	expected[2][3].SetUint64(4)
+
+	expected[3][0].SetUint64(3)
+	expected[3][1].SetUint64(1)
+	expected[3][2].SetUint64(7)
+	expected[3][3].SetUint64(6)
+
+	h := NewHash(4, 8, 56, "seed")
+	var tmp [4]fr.Element
+	for i := 0; i < 4; i++ {
+		for j := 0; j < 4; j++ {
+			tmp[j].SetUint64(0)
+			if i == j {
+				tmp[j].SetOne()
+			}
+		}
+		// h.Write(tmp[:])
+		h.matMulExternalInPlace(tmp[:])
+		for j := 0; j < 4; j++ {
+			if !tmp[j].Equal(&expected[i][j]) {
+				t.Fatal("error matMul4")
+			}
+		}
+	}
+
+}
+
+func BenchmarkPoseidon2(b *testing.B) {
+	h := NewHash(3, 8, 56, "seed")
+	var tmp [3]fr.Element
+	tmp[0].SetRandom()
+	tmp[1].SetRandom()
+	tmp[2].SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		h.Permutation(tmp[:])
+	}
+}
diff --git a/ecc/bls24-317/fr/poseidon2/poseidon2.go b/ecc/bls24-317/fr/poseidon2/poseidon2.go
new file mode 100644
index 0000000000..5a9a72a721
--- /dev/null
+++ b/ecc/bls24-317/fr/poseidon2/poseidon2.go
@@ -0,0 +1,258 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package poseidon2
+
+import (
+	"errors"
+	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
+	"golang.org/x/crypto/sha3"
+)
+
+var (
+	ErrInvalidSizebuffer = errors.New("the size of the input should match the size of the hash buffer")
+)
+
+// reference implementation: https://github.com/HorizenLabs/poseidon2/blob/main/plain_implementations/src/poseidon2/poseidon2.rs
+// specifications: https://github.com/argumentcomputer/neptune/blob/main/spec/poseidon_spec.pdf
+// origina paper: https://eprint.iacr.org/2023/323.pdf
+
+// parameters describing the poseidon2 implementation
+type parameters struct {
+	// len(preimage)+len(digest)=len(preimage)+ceil(log(2*<security_level>/r))
+	t int
+
+	// number of full rounds (even number)
+	rF int
+
+	// number of partial rounds
+	rP int
+
+	// diagonal elements of the internal matrices, minus one
+	diagInternalMatrices []fr.Element
+
+	// round keys
+	roundKeys [][]fr.Element
+}
+
+// Hash stores the buffer of the poseidon2 permutation and provides poseidon2 permutation
+// methods on the buffer
+type Hash struct {
+
+	// parameters describing the
+	params parameters
+}
+
+// NewHash returns a new hash instance allowing to apply the poseidon2 permutation
+func NewHash(t, rf, rp int, seed string) Hash {
+	params := parameters{t: t, rF: rf, rP: rp}
+	params.roundKeys = InitRC(seed, rf, rp, t)
+	res := Hash{params: params}
+	return res
+}
+
+// InitRC initiate round keys. Only one entry is non zero for the internal
+// rounds, cf https://eprint.iacr.org/2023/323.pdf page 9
+func InitRC(seed string, rf, rp, t int) [][]fr.Element {
+
+	bseed := ([]byte)(seed)
+	hash := sha3.NewLegacyKeccak256()
+	_, _ = hash.Write(bseed)
+	rnd := hash.Sum(nil) // pre hash before use
+	hash.Reset()
+	_, _ = hash.Write(rnd)
+
+	roundKeys := make([][]fr.Element, rf+rp)
+	for i := 0; i < rf/2; i++ {
+		roundKeys[i] = make([]fr.Element, t)
+		for j := 0; j < t; j++ {
+			rnd = hash.Sum(nil)
+			roundKeys[i][j].SetBytes(rnd)
+			hash.Reset()
+			_, _ = hash.Write(rnd)
+		}
+	}
+	for i := 0; i < rp; i++ {
+		roundKeys[i] = make([]fr.Element, 1)
+		rnd = hash.Sum(nil)
+		roundKeys[i][0].SetBytes(rnd)
+		hash.Reset()
+		_, _ = hash.Write(rnd)
+	}
+	for i := 0; i < rf/2; i++ {
+		roundKeys[i] = make([]fr.Element, t)
+		for j := 0; j < t; j++ {
+			rnd = hash.Sum(nil)
+			roundKeys[i][j].SetBytes(rnd)
+			hash.Reset()
+			_, _ = hash.Write(rnd)
+		}
+	}
+	return roundKeys
+}
+
+// sBox applies the sBox on buffer[index]
+func (h *Hash) sBox(index int, input []fr.Element) {
+	var tmp fr.Element
+	tmp.Set(&input[index])
+
+	// sbox degree is 7
+	input[index].Square(&input[index]).
+		Mul(&input[index], &tmp).
+		Square(&input[index]).
+		Mul(&input[index], &tmp)
+
+}
+
+// matMulM4 computes
+// s <- M4*s
+// where M4=
+// (5 7 1 3)
+// (4 6 1 1)
+// (1 3 5 7)
+// (1 1 4 6)
+// on chunks of 4 elemts on each part of the buffer
+// see https://eprint.iacr.org/2023/323.pdf appendix B for the addition chain
+func (h *Hash) matMulM4InPlace(s []fr.Element) {
+	c := len(s) / 4
+	for i := 0; i < c; i++ {
+		var t0, t1, t2, t3, t4, t5, t6, t7 fr.Element
+		t0.Add(&s[4*i], &s[4*i+1])               // s0+s1
+		t1.Add(&s[4*i+2], &s[4*i+3])             // s2+s3
+		t2.Double(&s[4*i+1]).Add(&t2, &t1)       // 2s1+t1
+		t3.Double(&s[4*i+3]).Add(&t3, &t0)       // 2s3+t0
+		t4.Double(&t1).Double(&t4).Add(&t4, &t3) // 4t1+t3
+		t5.Double(&t0).Double(&t5).Add(&t5, &t2) // 4t0+t2
+		t6.Add(&t3, &t5)                         // t3+t4
+		t7.Add(&t2, &t4)                         // t2+t4
+		s[4*i].Set(&t6)
+		s[4*i+1].Set(&t5)
+		s[4*i+2].Set(&t7)
+		s[4*i+3].Set(&t4)
+	}
+}
+
+// when t=2,3 the buffer is multiplied by circ(2,1) and circ(2,1,1)
+// see https://eprint.iacr.org/2023/323.pdf page 15, case t=2,3
+//
+// when t=0[4], the buffer is multiplied by circ(2M4,M4,..,M4)
+// see https://eprint.iacr.org/2023/323.pdf
+func (h *Hash) matMulExternalInPlace(input []fr.Element) {
+
+	if h.params.t == 2 {
+		var tmp fr.Element
+		tmp.Add(&input[0], &input[1])
+		input[0].Add(&tmp, &input[0])
+		input[1].Add(&tmp, &input[1])
+	} else if h.params.t == 3 {
+		var tmp fr.Element
+		tmp.Add(&input[0], &input[1]).
+			Add(&tmp, &input[2])
+		input[0].Add(&tmp, &input[0])
+		input[1].Add(&tmp, &input[1])
+		input[2].Add(&tmp, &input[2])
+	} else if h.params.t == 4 {
+		h.matMulM4InPlace(input)
+	} else {
+		// at this stage t is supposed to be a multiple of 4
+		// the MDS matrix is circ(2M4,M4,..,M4)
+		h.matMulM4InPlace(input)
+		tmp := make([]fr.Element, 4)
+		for i := 0; i < h.params.t/4; i++ {
+			tmp[0].Add(&tmp[0], &input[4*i])
+			tmp[1].Add(&tmp[1], &input[4*i+1])
+			tmp[2].Add(&tmp[2], &input[4*i+2])
+			tmp[3].Add(&tmp[3], &input[4*i+3])
+		}
+		for i := 0; i < h.params.t/4; i++ {
+			input[4*i].Add(&input[4*i], &tmp[0])
+			input[4*i+1].Add(&input[4*i], &tmp[1])
+			input[4*i+2].Add(&input[4*i], &tmp[2])
+			input[4*i+3].Add(&input[4*i], &tmp[3])
+		}
+	}
+}
+
+// when t=2,3 the matrix are respectibely [[2,1][1,3]] and [[2,1,1][1,2,1][1,1,3]]
+// otherwise the matrix is filled with ones except on the diagonal,
+func (h *Hash) matMulInternalInPlace(input []fr.Element) {
+	if h.params.t == 2 {
+		var sum fr.Element
+		sum.Add(&input[0], &input[1])
+		input[0].Add(&input[0], &sum)
+		input[1].Double(&input[1]).Add(&input[1], &sum)
+	} else if h.params.t == 3 {
+		var sum fr.Element
+		sum.Add(&input[0], &input[1]).Add(&sum, &input[2])
+		input[0].Add(&input[0], &sum)
+		input[1].Add(&input[1], &sum)
+		input[2].Double(&input[2]).Add(&input[2], &sum)
+	} else {
+		var sum fr.Element
+		sum.Set(&input[0])
+		for i := 1; i < h.params.t; i++ {
+			sum.Add(&sum, &input[i])
+		}
+		for i := 0; i < h.params.t; i++ {
+			input[i].Mul(&input[i], &h.params.diagInternalMatrices[i]).
+				Add(&input[i], &sum)
+		}
+	}
+}
+
+// addRoundKeyInPlace adds the round-th key to the buffer
+func (h *Hash) addRoundKeyInPlace(round int, input []fr.Element) {
+	for i := 0; i < len(h.params.roundKeys[round]); i++ {
+		input[i].Add(&input[i], &h.params.roundKeys[round][i])
+	}
+}
+
+// Permutation applies the permutation on input, and stores the result in input.
+func (h *Hash) Permutation(input []fr.Element) error {
+	if len(input) != h.params.t {
+		return ErrInvalidSizebuffer
+	}
+
+	// external matrix multiplication, cf https://eprint.iacr.org/2023/323.pdf page 14 (part 6)
+	h.matMulExternalInPlace(input)
+
+	rf := h.params.rF / 2
+	for i := 0; i < rf; i++ {
+		// one round = matMulExternal(sBox_Full(addRoundKey))
+		h.addRoundKeyInPlace(i, input)
+		for j := 0; j < h.params.t; j++ {
+			h.sBox(j, input)
+		}
+		h.matMulExternalInPlace(input)
+	}
+
+	for i := rf; i < rf+h.params.rP; i++ {
+		// one round = matMulInternal(sBox_sparse(addRoundKey))
+		h.addRoundKeyInPlace(i, input)
+		h.sBox(0, input)
+		h.matMulInternalInPlace(input)
+	}
+	for i := rf + h.params.rP; i < h.params.rF+h.params.rP; i++ {
+		// one round = matMulExternal(sBox_Full(addRoundKey))
+		h.addRoundKeyInPlace(i, input)
+		for j := 0; j < h.params.t; j++ {
+			h.sBox(j, input)
+		}
+		h.matMulExternalInPlace(input)
+	}
+
+	return nil
+}
diff --git a/ecc/bls24-317/fr/poseidon2/poseidon2_test.go b/ecc/bls24-317/fr/poseidon2/poseidon2_test.go
new file mode 100644
index 0000000000..f41efef59a
--- /dev/null
+++ b/ecc/bls24-317/fr/poseidon2/poseidon2_test.go
@@ -0,0 +1,78 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package poseidon2
+
+import (
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
+)
+
+func TestExternalMatrix(t *testing.T) {
+
+	var expected [4][4]fr.Element
+	expected[0][0].SetUint64(5)
+	expected[0][1].SetUint64(4)
+	expected[0][2].SetUint64(1)
+	expected[0][3].SetUint64(1)
+
+	expected[1][0].SetUint64(7)
+	expected[1][1].SetUint64(6)
+	expected[1][2].SetUint64(3)
+	expected[1][3].SetUint64(1)
+
+	expected[2][0].SetUint64(1)
+	expected[2][1].SetUint64(1)
+	expected[2][2].SetUint64(5)
+	expected[2][3].SetUint64(4)
+
+	expected[3][0].SetUint64(3)
+	expected[3][1].SetUint64(1)
+	expected[3][2].SetUint64(7)
+	expected[3][3].SetUint64(6)
+
+	h := NewHash(4, 8, 56, "seed")
+	var tmp [4]fr.Element
+	for i := 0; i < 4; i++ {
+		for j := 0; j < 4; j++ {
+			tmp[j].SetUint64(0)
+			if i == j {
+				tmp[j].SetOne()
+			}
+		}
+		// h.Write(tmp[:])
+		h.matMulExternalInPlace(tmp[:])
+		for j := 0; j < 4; j++ {
+			if !tmp[j].Equal(&expected[i][j]) {
+				t.Fatal("error matMul4")
+			}
+		}
+	}
+
+}
+
+func BenchmarkPoseidon2(b *testing.B) {
+	h := NewHash(3, 8, 56, "seed")
+	var tmp [3]fr.Element
+	tmp[0].SetRandom()
+	tmp[1].SetRandom()
+	tmp[2].SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		h.Permutation(tmp[:])
+	}
+}
diff --git a/ecc/bn254/fr/poseidon2/poseidon2.go b/ecc/bn254/fr/poseidon2/poseidon2.go
new file mode 100644
index 0000000000..dd3302de4c
--- /dev/null
+++ b/ecc/bn254/fr/poseidon2/poseidon2.go
@@ -0,0 +1,257 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package poseidon2
+
+import (
+	"errors"
+	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
+	"golang.org/x/crypto/sha3"
+)
+
+var (
+	ErrInvalidSizebuffer = errors.New("the size of the input should match the size of the hash buffer")
+)
+
+// reference implementation: https://github.com/HorizenLabs/poseidon2/blob/main/plain_implementations/src/poseidon2/poseidon2.rs
+// specifications: https://github.com/argumentcomputer/neptune/blob/main/spec/poseidon_spec.pdf
+// origina paper: https://eprint.iacr.org/2023/323.pdf
+
+// parameters describing the poseidon2 implementation
+type parameters struct {
+	// len(preimage)+len(digest)=len(preimage)+ceil(log(2*<security_level>/r))
+	t int
+
+	// number of full rounds (even number)
+	rF int
+
+	// number of partial rounds
+	rP int
+
+	// diagonal elements of the internal matrices, minus one
+	diagInternalMatrices []fr.Element
+
+	// round keys
+	roundKeys [][]fr.Element
+}
+
+// Hash stores the buffer of the poseidon2 permutation and provides poseidon2 permutation
+// methods on the buffer
+type Hash struct {
+
+	// parameters describing the
+	params parameters
+}
+
+// NewHash returns a new hash instance allowing to apply the poseidon2 permutation
+func NewHash(t, rf, rp int, seed string) Hash {
+	params := parameters{t: t, rF: rf, rP: rp}
+	params.roundKeys = InitRC(seed, rf, rp, t)
+	res := Hash{params: params}
+	return res
+}
+
+// InitRC initiate round keys. Only one entry is non zero for the internal
+// rounds, cf https://eprint.iacr.org/2023/323.pdf page 9
+func InitRC(seed string, rf, rp, t int) [][]fr.Element {
+
+	bseed := ([]byte)(seed)
+	hash := sha3.NewLegacyKeccak256()
+	_, _ = hash.Write(bseed)
+	rnd := hash.Sum(nil) // pre hash before use
+	hash.Reset()
+	_, _ = hash.Write(rnd)
+
+	roundKeys := make([][]fr.Element, rf+rp)
+	for i := 0; i < rf/2; i++ {
+		roundKeys[i] = make([]fr.Element, t)
+		for j := 0; j < t; j++ {
+			rnd = hash.Sum(nil)
+			roundKeys[i][j].SetBytes(rnd)
+			hash.Reset()
+			_, _ = hash.Write(rnd)
+		}
+	}
+	for i := 0; i < rp; i++ {
+		roundKeys[i] = make([]fr.Element, 1)
+		rnd = hash.Sum(nil)
+		roundKeys[i][0].SetBytes(rnd)
+		hash.Reset()
+		_, _ = hash.Write(rnd)
+	}
+	for i := 0; i < rf/2; i++ {
+		roundKeys[i] = make([]fr.Element, t)
+		for j := 0; j < t; j++ {
+			rnd = hash.Sum(nil)
+			roundKeys[i][j].SetBytes(rnd)
+			hash.Reset()
+			_, _ = hash.Write(rnd)
+		}
+	}
+	return roundKeys
+}
+
+// sBox applies the sBox on buffer[index]
+func (h *Hash) sBox(index int, input []fr.Element) {
+	var tmp fr.Element
+	tmp.Set(&input[index])
+
+	// sbox degree is 5
+	input[index].Square(&input[index]).
+		Square(&input[index]).
+		Mul(&input[index], &tmp)
+
+}
+
+// matMulM4 computes
+// s <- M4*s
+// where M4=
+// (5 7 1 3)
+// (4 6 1 1)
+// (1 3 5 7)
+// (1 1 4 6)
+// on chunks of 4 elemts on each part of the buffer
+// see https://eprint.iacr.org/2023/323.pdf appendix B for the addition chain
+func (h *Hash) matMulM4InPlace(s []fr.Element) {
+	c := len(s) / 4
+	for i := 0; i < c; i++ {
+		var t0, t1, t2, t3, t4, t5, t6, t7 fr.Element
+		t0.Add(&s[4*i], &s[4*i+1])               // s0+s1
+		t1.Add(&s[4*i+2], &s[4*i+3])             // s2+s3
+		t2.Double(&s[4*i+1]).Add(&t2, &t1)       // 2s1+t1
+		t3.Double(&s[4*i+3]).Add(&t3, &t0)       // 2s3+t0
+		t4.Double(&t1).Double(&t4).Add(&t4, &t3) // 4t1+t3
+		t5.Double(&t0).Double(&t5).Add(&t5, &t2) // 4t0+t2
+		t6.Add(&t3, &t5)                         // t3+t4
+		t7.Add(&t2, &t4)                         // t2+t4
+		s[4*i].Set(&t6)
+		s[4*i+1].Set(&t5)
+		s[4*i+2].Set(&t7)
+		s[4*i+3].Set(&t4)
+	}
+}
+
+// when t=2,3 the buffer is multiplied by circ(2,1) and circ(2,1,1)
+// see https://eprint.iacr.org/2023/323.pdf page 15, case t=2,3
+//
+// when t=0[4], the buffer is multiplied by circ(2M4,M4,..,M4)
+// see https://eprint.iacr.org/2023/323.pdf
+func (h *Hash) matMulExternalInPlace(input []fr.Element) {
+
+	if h.params.t == 2 {
+		var tmp fr.Element
+		tmp.Add(&input[0], &input[1])
+		input[0].Add(&tmp, &input[0])
+		input[1].Add(&tmp, &input[1])
+	} else if h.params.t == 3 {
+		var tmp fr.Element
+		tmp.Add(&input[0], &input[1]).
+			Add(&tmp, &input[2])
+		input[0].Add(&tmp, &input[0])
+		input[1].Add(&tmp, &input[1])
+		input[2].Add(&tmp, &input[2])
+	} else if h.params.t == 4 {
+		h.matMulM4InPlace(input)
+	} else {
+		// at this stage t is supposed to be a multiple of 4
+		// the MDS matrix is circ(2M4,M4,..,M4)
+		h.matMulM4InPlace(input)
+		tmp := make([]fr.Element, 4)
+		for i := 0; i < h.params.t/4; i++ {
+			tmp[0].Add(&tmp[0], &input[4*i])
+			tmp[1].Add(&tmp[1], &input[4*i+1])
+			tmp[2].Add(&tmp[2], &input[4*i+2])
+			tmp[3].Add(&tmp[3], &input[4*i+3])
+		}
+		for i := 0; i < h.params.t/4; i++ {
+			input[4*i].Add(&input[4*i], &tmp[0])
+			input[4*i+1].Add(&input[4*i], &tmp[1])
+			input[4*i+2].Add(&input[4*i], &tmp[2])
+			input[4*i+3].Add(&input[4*i], &tmp[3])
+		}
+	}
+}
+
+// when t=2,3 the matrix are respectibely [[2,1][1,3]] and [[2,1,1][1,2,1][1,1,3]]
+// otherwise the matrix is filled with ones except on the diagonal,
+func (h *Hash) matMulInternalInPlace(input []fr.Element) {
+	if h.params.t == 2 {
+		var sum fr.Element
+		sum.Add(&input[0], &input[1])
+		input[0].Add(&input[0], &sum)
+		input[1].Double(&input[1]).Add(&input[1], &sum)
+	} else if h.params.t == 3 {
+		var sum fr.Element
+		sum.Add(&input[0], &input[1]).Add(&sum, &input[2])
+		input[0].Add(&input[0], &sum)
+		input[1].Add(&input[1], &sum)
+		input[2].Double(&input[2]).Add(&input[2], &sum)
+	} else {
+		var sum fr.Element
+		sum.Set(&input[0])
+		for i := 1; i < h.params.t; i++ {
+			sum.Add(&sum, &input[i])
+		}
+		for i := 0; i < h.params.t; i++ {
+			input[i].Mul(&input[i], &h.params.diagInternalMatrices[i]).
+				Add(&input[i], &sum)
+		}
+	}
+}
+
+// addRoundKeyInPlace adds the round-th key to the buffer
+func (h *Hash) addRoundKeyInPlace(round int, input []fr.Element) {
+	for i := 0; i < len(h.params.roundKeys[round]); i++ {
+		input[i].Add(&input[i], &h.params.roundKeys[round][i])
+	}
+}
+
+// Permutation applies the permutation on input, and stores the result in input.
+func (h *Hash) Permutation(input []fr.Element) error {
+	if len(input) != h.params.t {
+		return ErrInvalidSizebuffer
+	}
+
+	// external matrix multiplication, cf https://eprint.iacr.org/2023/323.pdf page 14 (part 6)
+	h.matMulExternalInPlace(input)
+
+	rf := h.params.rF / 2
+	for i := 0; i < rf; i++ {
+		// one round = matMulExternal(sBox_Full(addRoundKey))
+		h.addRoundKeyInPlace(i, input)
+		for j := 0; j < h.params.t; j++ {
+			h.sBox(j, input)
+		}
+		h.matMulExternalInPlace(input)
+	}
+
+	for i := rf; i < rf+h.params.rP; i++ {
+		// one round = matMulInternal(sBox_sparse(addRoundKey))
+		h.addRoundKeyInPlace(i, input)
+		h.sBox(0, input)
+		h.matMulInternalInPlace(input)
+	}
+	for i := rf + h.params.rP; i < h.params.rF+h.params.rP; i++ {
+		// one round = matMulExternal(sBox_Full(addRoundKey))
+		h.addRoundKeyInPlace(i, input)
+		for j := 0; j < h.params.t; j++ {
+			h.sBox(j, input)
+		}
+		h.matMulExternalInPlace(input)
+	}
+
+	return nil
+}
diff --git a/ecc/bn254/fr/poseidon2/poseidon2_test.go b/ecc/bn254/fr/poseidon2/poseidon2_test.go
new file mode 100644
index 0000000000..91fa4cd47c
--- /dev/null
+++ b/ecc/bn254/fr/poseidon2/poseidon2_test.go
@@ -0,0 +1,78 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package poseidon2
+
+import (
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
+)
+
+func TestExternalMatrix(t *testing.T) {
+
+	var expected [4][4]fr.Element
+	expected[0][0].SetUint64(5)
+	expected[0][1].SetUint64(4)
+	expected[0][2].SetUint64(1)
+	expected[0][3].SetUint64(1)
+
+	expected[1][0].SetUint64(7)
+	expected[1][1].SetUint64(6)
+	expected[1][2].SetUint64(3)
+	expected[1][3].SetUint64(1)
+
+	expected[2][0].SetUint64(1)
+	expected[2][1].SetUint64(1)
+	expected[2][2].SetUint64(5)
+	expected[2][3].SetUint64(4)
+
+	expected[3][0].SetUint64(3)
+	expected[3][1].SetUint64(1)
+	expected[3][2].SetUint64(7)
+	expected[3][3].SetUint64(6)
+
+	h := NewHash(4, 8, 56, "seed")
+	var tmp [4]fr.Element
+	for i := 0; i < 4; i++ {
+		for j := 0; j < 4; j++ {
+			tmp[j].SetUint64(0)
+			if i == j {
+				tmp[j].SetOne()
+			}
+		}
+		// h.Write(tmp[:])
+		h.matMulExternalInPlace(tmp[:])
+		for j := 0; j < 4; j++ {
+			if !tmp[j].Equal(&expected[i][j]) {
+				t.Fatal("error matMul4")
+			}
+		}
+	}
+
+}
+
+func BenchmarkPoseidon2(b *testing.B) {
+	h := NewHash(3, 8, 56, "seed")
+	var tmp [3]fr.Element
+	tmp[0].SetRandom()
+	tmp[1].SetRandom()
+	tmp[2].SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		h.Permutation(tmp[:])
+	}
+}
diff --git a/ecc/bw6-633/fr/poseidon2/poseidon2.go b/ecc/bw6-633/fr/poseidon2/poseidon2.go
new file mode 100644
index 0000000000..4415e87ed5
--- /dev/null
+++ b/ecc/bw6-633/fr/poseidon2/poseidon2.go
@@ -0,0 +1,257 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package poseidon2
+
+import (
+	"errors"
+	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
+	"golang.org/x/crypto/sha3"
+)
+
+var (
+	ErrInvalidSizebuffer = errors.New("the size of the input should match the size of the hash buffer")
+)
+
+// reference implementation: https://github.com/HorizenLabs/poseidon2/blob/main/plain_implementations/src/poseidon2/poseidon2.rs
+// specifications: https://github.com/argumentcomputer/neptune/blob/main/spec/poseidon_spec.pdf
+// origina paper: https://eprint.iacr.org/2023/323.pdf
+
+// parameters describing the poseidon2 implementation
+type parameters struct {
+	// len(preimage)+len(digest)=len(preimage)+ceil(log(2*<security_level>/r))
+	t int
+
+	// number of full rounds (even number)
+	rF int
+
+	// number of partial rounds
+	rP int
+
+	// diagonal elements of the internal matrices, minus one
+	diagInternalMatrices []fr.Element
+
+	// round keys
+	roundKeys [][]fr.Element
+}
+
+// Hash stores the buffer of the poseidon2 permutation and provides poseidon2 permutation
+// methods on the buffer
+type Hash struct {
+
+	// parameters describing the
+	params parameters
+}
+
+// NewHash returns a new hash instance allowing to apply the poseidon2 permutation
+func NewHash(t, rf, rp int, seed string) Hash {
+	params := parameters{t: t, rF: rf, rP: rp}
+	params.roundKeys = InitRC(seed, rf, rp, t)
+	res := Hash{params: params}
+	return res
+}
+
+// InitRC initiate round keys. Only one entry is non zero for the internal
+// rounds, cf https://eprint.iacr.org/2023/323.pdf page 9
+func InitRC(seed string, rf, rp, t int) [][]fr.Element {
+
+	bseed := ([]byte)(seed)
+	hash := sha3.NewLegacyKeccak256()
+	_, _ = hash.Write(bseed)
+	rnd := hash.Sum(nil) // pre hash before use
+	hash.Reset()
+	_, _ = hash.Write(rnd)
+
+	roundKeys := make([][]fr.Element, rf+rp)
+	for i := 0; i < rf/2; i++ {
+		roundKeys[i] = make([]fr.Element, t)
+		for j := 0; j < t; j++ {
+			rnd = hash.Sum(nil)
+			roundKeys[i][j].SetBytes(rnd)
+			hash.Reset()
+			_, _ = hash.Write(rnd)
+		}
+	}
+	for i := 0; i < rp; i++ {
+		roundKeys[i] = make([]fr.Element, 1)
+		rnd = hash.Sum(nil)
+		roundKeys[i][0].SetBytes(rnd)
+		hash.Reset()
+		_, _ = hash.Write(rnd)
+	}
+	for i := 0; i < rf/2; i++ {
+		roundKeys[i] = make([]fr.Element, t)
+		for j := 0; j < t; j++ {
+			rnd = hash.Sum(nil)
+			roundKeys[i][j].SetBytes(rnd)
+			hash.Reset()
+			_, _ = hash.Write(rnd)
+		}
+	}
+	return roundKeys
+}
+
+// sBox applies the sBox on buffer[index]
+func (h *Hash) sBox(index int, input []fr.Element) {
+	var tmp fr.Element
+	tmp.Set(&input[index])
+
+	// sbox degree is 5
+	input[index].Square(&input[index]).
+		Square(&input[index]).
+		Mul(&input[index], &tmp)
+
+}
+
+// matMulM4 computes
+// s <- M4*s
+// where M4=
+// (5 7 1 3)
+// (4 6 1 1)
+// (1 3 5 7)
+// (1 1 4 6)
+// on chunks of 4 elemts on each part of the buffer
+// see https://eprint.iacr.org/2023/323.pdf appendix B for the addition chain
+func (h *Hash) matMulM4InPlace(s []fr.Element) {
+	c := len(s) / 4
+	for i := 0; i < c; i++ {
+		var t0, t1, t2, t3, t4, t5, t6, t7 fr.Element
+		t0.Add(&s[4*i], &s[4*i+1])               // s0+s1
+		t1.Add(&s[4*i+2], &s[4*i+3])             // s2+s3
+		t2.Double(&s[4*i+1]).Add(&t2, &t1)       // 2s1+t1
+		t3.Double(&s[4*i+3]).Add(&t3, &t0)       // 2s3+t0
+		t4.Double(&t1).Double(&t4).Add(&t4, &t3) // 4t1+t3
+		t5.Double(&t0).Double(&t5).Add(&t5, &t2) // 4t0+t2
+		t6.Add(&t3, &t5)                         // t3+t4
+		t7.Add(&t2, &t4)                         // t2+t4
+		s[4*i].Set(&t6)
+		s[4*i+1].Set(&t5)
+		s[4*i+2].Set(&t7)
+		s[4*i+3].Set(&t4)
+	}
+}
+
+// when t=2,3 the buffer is multiplied by circ(2,1) and circ(2,1,1)
+// see https://eprint.iacr.org/2023/323.pdf page 15, case t=2,3
+//
+// when t=0[4], the buffer is multiplied by circ(2M4,M4,..,M4)
+// see https://eprint.iacr.org/2023/323.pdf
+func (h *Hash) matMulExternalInPlace(input []fr.Element) {
+
+	if h.params.t == 2 {
+		var tmp fr.Element
+		tmp.Add(&input[0], &input[1])
+		input[0].Add(&tmp, &input[0])
+		input[1].Add(&tmp, &input[1])
+	} else if h.params.t == 3 {
+		var tmp fr.Element
+		tmp.Add(&input[0], &input[1]).
+			Add(&tmp, &input[2])
+		input[0].Add(&tmp, &input[0])
+		input[1].Add(&tmp, &input[1])
+		input[2].Add(&tmp, &input[2])
+	} else if h.params.t == 4 {
+		h.matMulM4InPlace(input)
+	} else {
+		// at this stage t is supposed to be a multiple of 4
+		// the MDS matrix is circ(2M4,M4,..,M4)
+		h.matMulM4InPlace(input)
+		tmp := make([]fr.Element, 4)
+		for i := 0; i < h.params.t/4; i++ {
+			tmp[0].Add(&tmp[0], &input[4*i])
+			tmp[1].Add(&tmp[1], &input[4*i+1])
+			tmp[2].Add(&tmp[2], &input[4*i+2])
+			tmp[3].Add(&tmp[3], &input[4*i+3])
+		}
+		for i := 0; i < h.params.t/4; i++ {
+			input[4*i].Add(&input[4*i], &tmp[0])
+			input[4*i+1].Add(&input[4*i], &tmp[1])
+			input[4*i+2].Add(&input[4*i], &tmp[2])
+			input[4*i+3].Add(&input[4*i], &tmp[3])
+		}
+	}
+}
+
+// when t=2,3 the matrix are respectibely [[2,1][1,3]] and [[2,1,1][1,2,1][1,1,3]]
+// otherwise the matrix is filled with ones except on the diagonal,
+func (h *Hash) matMulInternalInPlace(input []fr.Element) {
+	if h.params.t == 2 {
+		var sum fr.Element
+		sum.Add(&input[0], &input[1])
+		input[0].Add(&input[0], &sum)
+		input[1].Double(&input[1]).Add(&input[1], &sum)
+	} else if h.params.t == 3 {
+		var sum fr.Element
+		sum.Add(&input[0], &input[1]).Add(&sum, &input[2])
+		input[0].Add(&input[0], &sum)
+		input[1].Add(&input[1], &sum)
+		input[2].Double(&input[2]).Add(&input[2], &sum)
+	} else {
+		var sum fr.Element
+		sum.Set(&input[0])
+		for i := 1; i < h.params.t; i++ {
+			sum.Add(&sum, &input[i])
+		}
+		for i := 0; i < h.params.t; i++ {
+			input[i].Mul(&input[i], &h.params.diagInternalMatrices[i]).
+				Add(&input[i], &sum)
+		}
+	}
+}
+
+// addRoundKeyInPlace adds the round-th key to the buffer
+func (h *Hash) addRoundKeyInPlace(round int, input []fr.Element) {
+	for i := 0; i < len(h.params.roundKeys[round]); i++ {
+		input[i].Add(&input[i], &h.params.roundKeys[round][i])
+	}
+}
+
+// Permutation applies the permutation on input, and stores the result in input.
+func (h *Hash) Permutation(input []fr.Element) error {
+	if len(input) != h.params.t {
+		return ErrInvalidSizebuffer
+	}
+
+	// external matrix multiplication, cf https://eprint.iacr.org/2023/323.pdf page 14 (part 6)
+	h.matMulExternalInPlace(input)
+
+	rf := h.params.rF / 2
+	for i := 0; i < rf; i++ {
+		// one round = matMulExternal(sBox_Full(addRoundKey))
+		h.addRoundKeyInPlace(i, input)
+		for j := 0; j < h.params.t; j++ {
+			h.sBox(j, input)
+		}
+		h.matMulExternalInPlace(input)
+	}
+
+	for i := rf; i < rf+h.params.rP; i++ {
+		// one round = matMulInternal(sBox_sparse(addRoundKey))
+		h.addRoundKeyInPlace(i, input)
+		h.sBox(0, input)
+		h.matMulInternalInPlace(input)
+	}
+	for i := rf + h.params.rP; i < h.params.rF+h.params.rP; i++ {
+		// one round = matMulExternal(sBox_Full(addRoundKey))
+		h.addRoundKeyInPlace(i, input)
+		for j := 0; j < h.params.t; j++ {
+			h.sBox(j, input)
+		}
+		h.matMulExternalInPlace(input)
+	}
+
+	return nil
+}
diff --git a/ecc/bw6-633/fr/poseidon2/poseidon2_test.go b/ecc/bw6-633/fr/poseidon2/poseidon2_test.go
new file mode 100644
index 0000000000..4bf1e0f1bf
--- /dev/null
+++ b/ecc/bw6-633/fr/poseidon2/poseidon2_test.go
@@ -0,0 +1,78 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package poseidon2
+
+import (
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
+)
+
+func TestExternalMatrix(t *testing.T) {
+
+	var expected [4][4]fr.Element
+	expected[0][0].SetUint64(5)
+	expected[0][1].SetUint64(4)
+	expected[0][2].SetUint64(1)
+	expected[0][3].SetUint64(1)
+
+	expected[1][0].SetUint64(7)
+	expected[1][1].SetUint64(6)
+	expected[1][2].SetUint64(3)
+	expected[1][3].SetUint64(1)
+
+	expected[2][0].SetUint64(1)
+	expected[2][1].SetUint64(1)
+	expected[2][2].SetUint64(5)
+	expected[2][3].SetUint64(4)
+
+	expected[3][0].SetUint64(3)
+	expected[3][1].SetUint64(1)
+	expected[3][2].SetUint64(7)
+	expected[3][3].SetUint64(6)
+
+	h := NewHash(4, 8, 56, "seed")
+	var tmp [4]fr.Element
+	for i := 0; i < 4; i++ {
+		for j := 0; j < 4; j++ {
+			tmp[j].SetUint64(0)
+			if i == j {
+				tmp[j].SetOne()
+			}
+		}
+		// h.Write(tmp[:])
+		h.matMulExternalInPlace(tmp[:])
+		for j := 0; j < 4; j++ {
+			if !tmp[j].Equal(&expected[i][j]) {
+				t.Fatal("error matMul4")
+			}
+		}
+	}
+
+}
+
+func BenchmarkPoseidon2(b *testing.B) {
+	h := NewHash(3, 8, 56, "seed")
+	var tmp [3]fr.Element
+	tmp[0].SetRandom()
+	tmp[1].SetRandom()
+	tmp[2].SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		h.Permutation(tmp[:])
+	}
+}
diff --git a/ecc/bw6-761/fr/poseidon2/poseidon2.go b/ecc/bw6-761/fr/poseidon2/poseidon2.go
new file mode 100644
index 0000000000..80283bcf46
--- /dev/null
+++ b/ecc/bw6-761/fr/poseidon2/poseidon2.go
@@ -0,0 +1,257 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package poseidon2
+
+import (
+	"errors"
+	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
+	"golang.org/x/crypto/sha3"
+)
+
+var (
+	ErrInvalidSizebuffer = errors.New("the size of the input should match the size of the hash buffer")
+)
+
+// reference implementation: https://github.com/HorizenLabs/poseidon2/blob/main/plain_implementations/src/poseidon2/poseidon2.rs
+// specifications: https://github.com/argumentcomputer/neptune/blob/main/spec/poseidon_spec.pdf
+// origina paper: https://eprint.iacr.org/2023/323.pdf
+
+// parameters describing the poseidon2 implementation
+type parameters struct {
+	// len(preimage)+len(digest)=len(preimage)+ceil(log(2*<security_level>/r))
+	t int
+
+	// number of full rounds (even number)
+	rF int
+
+	// number of partial rounds
+	rP int
+
+	// diagonal elements of the internal matrices, minus one
+	diagInternalMatrices []fr.Element
+
+	// round keys
+	roundKeys [][]fr.Element
+}
+
+// Hash stores the buffer of the poseidon2 permutation and provides poseidon2 permutation
+// methods on the buffer
+type Hash struct {
+
+	// parameters describing the
+	params parameters
+}
+
+// NewHash returns a new hash instance allowing to apply the poseidon2 permutation
+func NewHash(t, rf, rp int, seed string) Hash {
+	params := parameters{t: t, rF: rf, rP: rp}
+	params.roundKeys = InitRC(seed, rf, rp, t)
+	res := Hash{params: params}
+	return res
+}
+
+// InitRC initiate round keys. Only one entry is non zero for the internal
+// rounds, cf https://eprint.iacr.org/2023/323.pdf page 9
+func InitRC(seed string, rf, rp, t int) [][]fr.Element {
+
+	bseed := ([]byte)(seed)
+	hash := sha3.NewLegacyKeccak256()
+	_, _ = hash.Write(bseed)
+	rnd := hash.Sum(nil) // pre hash before use
+	hash.Reset()
+	_, _ = hash.Write(rnd)
+
+	roundKeys := make([][]fr.Element, rf+rp)
+	for i := 0; i < rf/2; i++ {
+		roundKeys[i] = make([]fr.Element, t)
+		for j := 0; j < t; j++ {
+			rnd = hash.Sum(nil)
+			roundKeys[i][j].SetBytes(rnd)
+			hash.Reset()
+			_, _ = hash.Write(rnd)
+		}
+	}
+	for i := 0; i < rp; i++ {
+		roundKeys[i] = make([]fr.Element, 1)
+		rnd = hash.Sum(nil)
+		roundKeys[i][0].SetBytes(rnd)
+		hash.Reset()
+		_, _ = hash.Write(rnd)
+	}
+	for i := 0; i < rf/2; i++ {
+		roundKeys[i] = make([]fr.Element, t)
+		for j := 0; j < t; j++ {
+			rnd = hash.Sum(nil)
+			roundKeys[i][j].SetBytes(rnd)
+			hash.Reset()
+			_, _ = hash.Write(rnd)
+		}
+	}
+	return roundKeys
+}
+
+// sBox applies the sBox on buffer[index]
+func (h *Hash) sBox(index int, input []fr.Element) {
+	var tmp fr.Element
+	tmp.Set(&input[index])
+
+	// sbox degree is 5
+	input[index].Square(&input[index]).
+		Square(&input[index]).
+		Mul(&input[index], &tmp)
+
+}
+
+// matMulM4 computes
+// s <- M4*s
+// where M4=
+// (5 7 1 3)
+// (4 6 1 1)
+// (1 3 5 7)
+// (1 1 4 6)
+// on chunks of 4 elemts on each part of the buffer
+// see https://eprint.iacr.org/2023/323.pdf appendix B for the addition chain
+func (h *Hash) matMulM4InPlace(s []fr.Element) {
+	c := len(s) / 4
+	for i := 0; i < c; i++ {
+		var t0, t1, t2, t3, t4, t5, t6, t7 fr.Element
+		t0.Add(&s[4*i], &s[4*i+1])               // s0+s1
+		t1.Add(&s[4*i+2], &s[4*i+3])             // s2+s3
+		t2.Double(&s[4*i+1]).Add(&t2, &t1)       // 2s1+t1
+		t3.Double(&s[4*i+3]).Add(&t3, &t0)       // 2s3+t0
+		t4.Double(&t1).Double(&t4).Add(&t4, &t3) // 4t1+t3
+		t5.Double(&t0).Double(&t5).Add(&t5, &t2) // 4t0+t2
+		t6.Add(&t3, &t5)                         // t3+t4
+		t7.Add(&t2, &t4)                         // t2+t4
+		s[4*i].Set(&t6)
+		s[4*i+1].Set(&t5)
+		s[4*i+2].Set(&t7)
+		s[4*i+3].Set(&t4)
+	}
+}
+
+// when t=2,3 the buffer is multiplied by circ(2,1) and circ(2,1,1)
+// see https://eprint.iacr.org/2023/323.pdf page 15, case t=2,3
+//
+// when t=0[4], the buffer is multiplied by circ(2M4,M4,..,M4)
+// see https://eprint.iacr.org/2023/323.pdf
+func (h *Hash) matMulExternalInPlace(input []fr.Element) {
+
+	if h.params.t == 2 {
+		var tmp fr.Element
+		tmp.Add(&input[0], &input[1])
+		input[0].Add(&tmp, &input[0])
+		input[1].Add(&tmp, &input[1])
+	} else if h.params.t == 3 {
+		var tmp fr.Element
+		tmp.Add(&input[0], &input[1]).
+			Add(&tmp, &input[2])
+		input[0].Add(&tmp, &input[0])
+		input[1].Add(&tmp, &input[1])
+		input[2].Add(&tmp, &input[2])
+	} else if h.params.t == 4 {
+		h.matMulM4InPlace(input)
+	} else {
+		// at this stage t is supposed to be a multiple of 4
+		// the MDS matrix is circ(2M4,M4,..,M4)
+		h.matMulM4InPlace(input)
+		tmp := make([]fr.Element, 4)
+		for i := 0; i < h.params.t/4; i++ {
+			tmp[0].Add(&tmp[0], &input[4*i])
+			tmp[1].Add(&tmp[1], &input[4*i+1])
+			tmp[2].Add(&tmp[2], &input[4*i+2])
+			tmp[3].Add(&tmp[3], &input[4*i+3])
+		}
+		for i := 0; i < h.params.t/4; i++ {
+			input[4*i].Add(&input[4*i], &tmp[0])
+			input[4*i+1].Add(&input[4*i], &tmp[1])
+			input[4*i+2].Add(&input[4*i], &tmp[2])
+			input[4*i+3].Add(&input[4*i], &tmp[3])
+		}
+	}
+}
+
+// when t=2,3 the matrix are respectibely [[2,1][1,3]] and [[2,1,1][1,2,1][1,1,3]]
+// otherwise the matrix is filled with ones except on the diagonal,
+func (h *Hash) matMulInternalInPlace(input []fr.Element) {
+	if h.params.t == 2 {
+		var sum fr.Element
+		sum.Add(&input[0], &input[1])
+		input[0].Add(&input[0], &sum)
+		input[1].Double(&input[1]).Add(&input[1], &sum)
+	} else if h.params.t == 3 {
+		var sum fr.Element
+		sum.Add(&input[0], &input[1]).Add(&sum, &input[2])
+		input[0].Add(&input[0], &sum)
+		input[1].Add(&input[1], &sum)
+		input[2].Double(&input[2]).Add(&input[2], &sum)
+	} else {
+		var sum fr.Element
+		sum.Set(&input[0])
+		for i := 1; i < h.params.t; i++ {
+			sum.Add(&sum, &input[i])
+		}
+		for i := 0; i < h.params.t; i++ {
+			input[i].Mul(&input[i], &h.params.diagInternalMatrices[i]).
+				Add(&input[i], &sum)
+		}
+	}
+}
+
+// addRoundKeyInPlace adds the round-th key to the buffer
+func (h *Hash) addRoundKeyInPlace(round int, input []fr.Element) {
+	for i := 0; i < len(h.params.roundKeys[round]); i++ {
+		input[i].Add(&input[i], &h.params.roundKeys[round][i])
+	}
+}
+
+// Permutation applies the permutation on input, and stores the result in input.
+func (h *Hash) Permutation(input []fr.Element) error {
+	if len(input) != h.params.t {
+		return ErrInvalidSizebuffer
+	}
+
+	// external matrix multiplication, cf https://eprint.iacr.org/2023/323.pdf page 14 (part 6)
+	h.matMulExternalInPlace(input)
+
+	rf := h.params.rF / 2
+	for i := 0; i < rf; i++ {
+		// one round = matMulExternal(sBox_Full(addRoundKey))
+		h.addRoundKeyInPlace(i, input)
+		for j := 0; j < h.params.t; j++ {
+			h.sBox(j, input)
+		}
+		h.matMulExternalInPlace(input)
+	}
+
+	for i := rf; i < rf+h.params.rP; i++ {
+		// one round = matMulInternal(sBox_sparse(addRoundKey))
+		h.addRoundKeyInPlace(i, input)
+		h.sBox(0, input)
+		h.matMulInternalInPlace(input)
+	}
+	for i := rf + h.params.rP; i < h.params.rF+h.params.rP; i++ {
+		// one round = matMulExternal(sBox_Full(addRoundKey))
+		h.addRoundKeyInPlace(i, input)
+		for j := 0; j < h.params.t; j++ {
+			h.sBox(j, input)
+		}
+		h.matMulExternalInPlace(input)
+	}
+
+	return nil
+}
diff --git a/ecc/bw6-761/fr/poseidon2/poseidon2_test.go b/ecc/bw6-761/fr/poseidon2/poseidon2_test.go
new file mode 100644
index 0000000000..acb3ea1cef
--- /dev/null
+++ b/ecc/bw6-761/fr/poseidon2/poseidon2_test.go
@@ -0,0 +1,78 @@
+// Copyright 2020 Consensys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package poseidon2
+
+import (
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
+)
+
+func TestExternalMatrix(t *testing.T) {
+
+	var expected [4][4]fr.Element
+	expected[0][0].SetUint64(5)
+	expected[0][1].SetUint64(4)
+	expected[0][2].SetUint64(1)
+	expected[0][3].SetUint64(1)
+
+	expected[1][0].SetUint64(7)
+	expected[1][1].SetUint64(6)
+	expected[1][2].SetUint64(3)
+	expected[1][3].SetUint64(1)
+
+	expected[2][0].SetUint64(1)
+	expected[2][1].SetUint64(1)
+	expected[2][2].SetUint64(5)
+	expected[2][3].SetUint64(4)
+
+	expected[3][0].SetUint64(3)
+	expected[3][1].SetUint64(1)
+	expected[3][2].SetUint64(7)
+	expected[3][3].SetUint64(6)
+
+	h := NewHash(4, 8, 56, "seed")
+	var tmp [4]fr.Element
+	for i := 0; i < 4; i++ {
+		for j := 0; j < 4; j++ {
+			tmp[j].SetUint64(0)
+			if i == j {
+				tmp[j].SetOne()
+			}
+		}
+		// h.Write(tmp[:])
+		h.matMulExternalInPlace(tmp[:])
+		for j := 0; j < 4; j++ {
+			if !tmp[j].Equal(&expected[i][j]) {
+				t.Fatal("error matMul4")
+			}
+		}
+	}
+
+}
+
+func BenchmarkPoseidon2(b *testing.B) {
+	h := NewHash(3, 8, 56, "seed")
+	var tmp [3]fr.Element
+	tmp[0].SetRandom()
+	tmp[1].SetRandom()
+	tmp[2].SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		h.Permutation(tmp[:])
+	}
+}
diff --git a/internal/generator/crypto/hash/poseidon2/generate.go b/internal/generator/crypto/hash/poseidon2/generate.go
new file mode 100644
index 0000000000..2c05bb08eb
--- /dev/null
+++ b/internal/generator/crypto/hash/poseidon2/generate.go
@@ -0,0 +1,20 @@
+package poseidon2
+
+import (
+	"path/filepath"
+
+	"github.com/consensys/bavard"
+	"github.com/consensys/gnark-crypto/internal/generator/config"
+)
+
+func Generate(conf config.Curve, baseDir string, bgen *bavard.BatchGenerator) error {
+
+	conf.Package = "poseidon2"
+	entries := []bavard.Entry{
+		{File: filepath.Join(baseDir, "poseidon2.go"), Templates: []string{"poseidon2.go.tmpl"}},
+		{File: filepath.Join(baseDir, "poseidon2_test.go"), Templates: []string{"poseidon2.test.go.tmpl"}},
+	}
+
+	return bgen.Generate(conf, conf.Package, "./crypto/hash/poseidon2/template", entries...)
+
+}
diff --git a/internal/generator/crypto/hash/poseidon2/template/poseidon2.go.tmpl b/internal/generator/crypto/hash/poseidon2/template/poseidon2.go.tmpl
new file mode 100644
index 0000000000..346db87726
--- /dev/null
+++ b/internal/generator/crypto/hash/poseidon2/template/poseidon2.go.tmpl
@@ -0,0 +1,252 @@
+import (
+	"errors"
+	"golang.org/x/crypto/sha3"
+	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/fr"
+)
+
+var (
+	ErrInvalidSizebuffer = errors.New("the size of the input should match the size of the hash buffer")
+)
+
+// reference implementation: https://github.com/HorizenLabs/poseidon2/blob/main/plain_implementations/src/poseidon2/poseidon2.rs
+// specifications: https://github.com/argumentcomputer/neptune/blob/main/spec/poseidon_spec.pdf
+// origina paper: https://eprint.iacr.org/2023/323.pdf
+
+// parameters describing the poseidon2 implementation
+type parameters struct {
+	// len(preimage)+len(digest)=len(preimage)+ceil(log(2*<security_level>/r))
+	t int
+
+	// number of full rounds (even number)
+	rF int
+
+	// number of partial rounds
+	rP int
+
+	// diagonal elements of the internal matrices, minus one
+	diagInternalMatrices []fr.Element
+
+	// round keys
+	roundKeys [][]fr.Element
+}
+
+// Hash stores the buffer of the poseidon2 permutation and provides poseidon2 permutation
+// methods on the buffer
+type Hash struct {
+
+	// parameters describing the
+	params parameters
+}
+
+// NewHash returns a new hash instance allowing to apply the poseidon2 permutation
+func NewHash(t, rf, rp int, seed string) Hash {
+	params := parameters{t: t, rF: rf, rP: rp}
+	params.roundKeys = InitRC(seed, rf, rp, t)
+	res := Hash{params: params}
+	return res
+}
+
+// InitRC initiate round keys. Only one entry is non zero for the internal
+// rounds, cf https://eprint.iacr.org/2023/323.pdf page 9
+func InitRC(seed string, rf, rp, t int) [][]fr.Element {
+
+	bseed := ([]byte)(seed)
+	hash := sha3.NewLegacyKeccak256()
+	_, _ = hash.Write(bseed)
+	rnd := hash.Sum(nil) // pre hash before use
+	hash.Reset()
+	_, _ = hash.Write(rnd)
+
+	roundKeys := make([][]fr.Element, rf+rp)
+	for i := 0; i < rf/2; i++ {
+		roundKeys[i] = make([]fr.Element, t)
+		for j := 0; j < t; j++ {
+			rnd = hash.Sum(nil)
+			roundKeys[i][j].SetBytes(rnd)
+			hash.Reset()
+			_, _ = hash.Write(rnd)
+		}
+	}
+	for i := 0; i < rp; i++ {
+		roundKeys[i] = make([]fr.Element, 1)
+		rnd = hash.Sum(nil)
+		roundKeys[i][0].SetBytes(rnd)
+		hash.Reset()
+		_, _ = hash.Write(rnd)
+	}
+	for i := 0; i < rf/2; i++ {
+		roundKeys[i] = make([]fr.Element, t)
+		for j := 0; j < t; j++ {
+			rnd = hash.Sum(nil)
+			roundKeys[i][j].SetBytes(rnd)
+			hash.Reset()
+			_, _ = hash.Write(rnd)
+		}
+	}
+	return roundKeys
+}
+
+// sBox applies the sBox on buffer[index]
+func (h *Hash) sBox(index int, input []fr.Element) {
+	var tmp fr.Element
+	tmp.Set(&input[index])
+	{{ if eq .Name "bls12-377" }}
+	// sbox degree is 17
+	input[index].Square(&input[index]).
+		Square(&input[index]).
+		Square(&input[index]).
+		Square(&input[index]).
+		Mul(&input[index], &tmp)
+	{{ else if eq .Name "bls24-317" }}
+	// sbox degree is 7
+	input[index].Square(&input[index]).
+		Mul(&input[index], &tmp).
+		Square(&input[index]).
+		Mul(&input[index], &tmp)
+	{{ else }}
+	// sbox degree is 5
+	input[index].Square(&input[index]).
+		Square(&input[index]).
+		Mul(&input[index], &tmp)
+	{{ end }}
+}
+
+// matMulM4 computes
+// s <- M4*s
+// where M4=
+// (5 7 1 3)
+// (4 6 1 1)
+// (1 3 5 7)
+// (1 1 4 6)
+// on chunks of 4 elemts on each part of the buffer
+// see https://eprint.iacr.org/2023/323.pdf appendix B for the addition chain
+func (h *Hash) matMulM4InPlace(s []fr.Element) {
+	c := len(s) / 4
+	for i := 0; i < c; i++ {
+		var t0, t1, t2, t3, t4, t5, t6, t7 fr.Element
+		t0.Add(&s[4*i], &s[4*i+1])               // s0+s1
+		t1.Add(&s[4*i+2], &s[4*i+3])             // s2+s3
+		t2.Double(&s[4*i+1]).Add(&t2, &t1)       // 2s1+t1
+		t3.Double(&s[4*i+3]).Add(&t3, &t0)       // 2s3+t0
+		t4.Double(&t1).Double(&t4).Add(&t4, &t3) // 4t1+t3
+		t5.Double(&t0).Double(&t5).Add(&t5, &t2) // 4t0+t2
+		t6.Add(&t3, &t5)                         // t3+t4
+		t7.Add(&t2, &t4)                         // t2+t4
+		s[4*i].Set(&t6)
+		s[4*i+1].Set(&t5)
+		s[4*i+2].Set(&t7)
+		s[4*i+3].Set(&t4)
+	}
+}
+
+// when t=2,3 the buffer is multiplied by circ(2,1) and circ(2,1,1)
+// see https://eprint.iacr.org/2023/323.pdf page 15, case t=2,3
+//
+// when t=0[4], the buffer is multiplied by circ(2M4,M4,..,M4)
+// see https://eprint.iacr.org/2023/323.pdf
+func (h *Hash) matMulExternalInPlace(input []fr.Element) {
+
+	if h.params.t == 2 {
+		var tmp fr.Element
+		tmp.Add(&input[0], &input[1])
+		input[0].Add(&tmp, &input[0])
+		input[1].Add(&tmp, &input[1])
+	} else if h.params.t == 3 {
+		var tmp fr.Element
+		tmp.Add(&input[0], &input[1]).
+			Add(&tmp, &input[2])
+		input[0].Add(&tmp, &input[0])
+		input[1].Add(&tmp, &input[1])
+		input[2].Add(&tmp, &input[2])
+	} else if h.params.t == 4 {
+		h.matMulM4InPlace(input)
+	} else {
+		// at this stage t is supposed to be a multiple of 4
+		// the MDS matrix is circ(2M4,M4,..,M4)
+		h.matMulM4InPlace(input)
+		tmp := make([]fr.Element, 4)
+		for i := 0; i < h.params.t/4; i++ {
+			tmp[0].Add(&tmp[0], &input[4*i])
+			tmp[1].Add(&tmp[1], &input[4*i+1])
+			tmp[2].Add(&tmp[2], &input[4*i+2])
+			tmp[3].Add(&tmp[3], &input[4*i+3])
+		}
+		for i := 0; i < h.params.t/4; i++ {
+			input[4*i].Add(&input[4*i], &tmp[0])
+			input[4*i+1].Add(&input[4*i], &tmp[1])
+			input[4*i+2].Add(&input[4*i], &tmp[2])
+			input[4*i+3].Add(&input[4*i], &tmp[3])
+		}
+	}
+}
+
+// when t=2,3 the matrix are respectibely [[2,1][1,3]] and [[2,1,1][1,2,1][1,1,3]]
+// otherwise the matrix is filled with ones except on the diagonal,
+func (h *Hash) matMulInternalInPlace(input []fr.Element) {
+	if h.params.t == 2 {
+		var sum fr.Element
+		sum.Add(&input[0], &input[1])
+		input[0].Add(&input[0], &sum)
+		input[1].Double(&input[1]).Add(&input[1], &sum)
+	} else if h.params.t == 3 {
+		var sum fr.Element
+		sum.Add(&input[0], &input[1]).Add(&sum, &input[2])
+		input[0].Add(&input[0], &sum)
+		input[1].Add(&input[1], &sum)
+		input[2].Double(&input[2]).Add(&input[2], &sum)
+	} else {
+		var sum fr.Element
+		sum.Set(&input[0])
+		for i := 1; i < h.params.t; i++ {
+			sum.Add(&sum, &input[i])
+		}
+		for i := 0; i < h.params.t; i++ {
+			input[i].Mul(&input[i], &h.params.diagInternalMatrices[i]).
+				Add(&input[i], &sum)
+		}
+	}
+}
+
+// addRoundKeyInPlace adds the round-th key to the buffer
+func (h *Hash) addRoundKeyInPlace(round int, input []fr.Element) {
+	for i := 0; i < len(h.params.roundKeys[round]); i++ {
+		input[i].Add(&input[i], &h.params.roundKeys[round][i])
+	}
+}
+
+// Permutation applies the permutation on input, and stores the result in input.
+func (h *Hash) Permutation(input []fr.Element) error {
+	if len(input) != h.params.t {
+		return ErrInvalidSizebuffer
+	}
+
+	// external matrix multiplication, cf https://eprint.iacr.org/2023/323.pdf page 14 (part 6)
+	h.matMulExternalInPlace(input)
+
+	rf := h.params.rF / 2
+	for i := 0; i < rf; i++ {
+		// one round = matMulExternal(sBox_Full(addRoundKey))
+		h.addRoundKeyInPlace(i, input)
+		for j := 0; j < h.params.t; j++ {
+			h.sBox(j, input)
+		}
+		h.matMulExternalInPlace(input)
+	}
+
+	for i := rf; i < rf+h.params.rP; i++ {
+		// one round = matMulInternal(sBox_sparse(addRoundKey))
+		h.addRoundKeyInPlace(i, input)
+		h.sBox(0, input)
+		h.matMulInternalInPlace(input)
+	}
+	for i := rf + h.params.rP; i < h.params.rF+h.params.rP; i++ {
+		// one round = matMulExternal(sBox_Full(addRoundKey))
+		h.addRoundKeyInPlace(i, input)
+		for j := 0; j < h.params.t; j++ {
+			h.sBox(j, input)
+		}
+		h.matMulExternalInPlace(input)
+	}
+
+	return nil
+}
diff --git a/internal/generator/crypto/hash/poseidon2/template/poseidon2.test.go.tmpl b/internal/generator/crypto/hash/poseidon2/template/poseidon2.test.go.tmpl
new file mode 100644
index 0000000000..809fc11c67
--- /dev/null
+++ b/internal/generator/crypto/hash/poseidon2/template/poseidon2.test.go.tmpl
@@ -0,0 +1,60 @@
+import (
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/fr"
+)
+
+func TestExternalMatrix(t *testing.T) {
+
+	var expected [4][4]fr.Element
+	expected[0][0].SetUint64(5)
+	expected[0][1].SetUint64(4)
+	expected[0][2].SetUint64(1)
+	expected[0][3].SetUint64(1)
+
+	expected[1][0].SetUint64(7)
+	expected[1][1].SetUint64(6)
+	expected[1][2].SetUint64(3)
+	expected[1][3].SetUint64(1)
+
+	expected[2][0].SetUint64(1)
+	expected[2][1].SetUint64(1)
+	expected[2][2].SetUint64(5)
+	expected[2][3].SetUint64(4)
+
+	expected[3][0].SetUint64(3)
+	expected[3][1].SetUint64(1)
+	expected[3][2].SetUint64(7)
+	expected[3][3].SetUint64(6)
+
+	h := NewHash(4, 8, 56, "seed")
+	var tmp [4]fr.Element
+	for i := 0; i < 4; i++ {
+		for j := 0; j < 4; j++ {
+			tmp[j].SetUint64(0)
+			if i == j {
+				tmp[j].SetOne()
+			}
+		}
+		// h.Write(tmp[:])
+		h.matMulExternalInPlace(tmp[:])
+		for j := 0; j < 4; j++ {
+			if !tmp[j].Equal(&expected[i][j]) {
+				t.Fatal("error matMul4")
+			}
+		}
+	}
+
+}
+
+func BenchmarkPoseidon2(b *testing.B) {
+	h := NewHash(3, 8, 56, "seed")
+	var tmp [3]fr.Element
+	tmp[0].SetRandom()
+	tmp[1].SetRandom()
+	tmp[2].SetRandom()
+	b.ResetTimer()
+	for i := 0; i<b.N; i++ {
+		h.Permutation(tmp[:])
+	}
+}
\ No newline at end of file
diff --git a/internal/generator/main.go b/internal/generator/main.go
index a9fe8390ca..7d8cfbe212 100644
--- a/internal/generator/main.go
+++ b/internal/generator/main.go
@@ -12,6 +12,7 @@ import (
 	field "github.com/consensys/gnark-crypto/field/generator/config"
 	"github.com/consensys/gnark-crypto/internal/generator/config"
 	"github.com/consensys/gnark-crypto/internal/generator/crypto/hash/mimc"
+	"github.com/consensys/gnark-crypto/internal/generator/crypto/hash/poseidon2"
 	"github.com/consensys/gnark-crypto/internal/generator/ecc"
 	"github.com/consensys/gnark-crypto/internal/generator/ecdsa"
 	"github.com/consensys/gnark-crypto/internal/generator/edwards"
@@ -146,6 +147,9 @@ func main() {
 			// generate mimc on fr
 			assertNoError(mimc.Generate(conf, filepath.Join(curveDir, "fr", "mimc"), bgen))
 
+			// generate poseidon2 on fr
+			assertNoError(poseidon2.Generate(conf, filepath.Join(curveDir, "fr", "poseidon2"), bgen))
+
 			frInfo := config.FieldDependency{
 				FieldPackagePath: "github.com/consensys/gnark-crypto/ecc/" + conf.Name + "/fr",
 				FieldPackageName: "fr",

From c38a8aaddbe6987a6a2838e5fba7a23cf6aa37b2 Mon Sep 17 00:00:00 2001
From: Gautam Botrel <gautam.botrel@gmail.com>
Date: Fri, 6 Dec 2024 04:35:17 -0600
Subject: [PATCH 089/114] refactor: remove dependency on ecc Encoder in fft
 domain marshal (#565)

---
 ecc/bls12-377/fr/fft/domain.go                | 60 +++++++++++++++----
 ecc/bls12-381/fr/fft/domain.go                | 60 +++++++++++++++----
 ecc/bls24-315/fr/fft/domain.go                | 60 +++++++++++++++----
 ecc/bls24-317/fr/fft/domain.go                | 60 +++++++++++++++----
 ecc/bn254/fr/fft/domain.go                    | 60 +++++++++++++++----
 ecc/bw6-633/fr/fft/domain.go                  | 60 +++++++++++++++----
 ecc/bw6-761/fr/fft/domain.go                  | 60 +++++++++++++++----
 .../generator/fft/template/domain.go.tmpl     | 59 ++++++++++++++----
 8 files changed, 384 insertions(+), 95 deletions(-)

diff --git a/ecc/bls12-377/fr/fft/domain.go b/ecc/bls12-377/fr/fft/domain.go
index 74645ef46d..645b68f4e7 100644
--- a/ecc/bls12-377/fr/fft/domain.go
+++ b/ecc/bls12-377/fr/fft/domain.go
@@ -17,6 +17,7 @@
 package fft
 
 import (
+	"encoding/binary"
 	"errors"
 	"io"
 	"math/big"
@@ -26,8 +27,6 @@ import (
 
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
 
-	curve "github.com/consensys/gnark-crypto/ecc/bls12-377"
-
 	"github.com/consensys/gnark-crypto/ecc"
 )
 
@@ -257,36 +256,73 @@ func precomputeExpTableChunk(w fr.Element, power uint64, table []fr.Element) {
 // WriteTo writes a binary representation of the domain (without the precomputed twiddle factors)
 // to the provided writer
 func (d *Domain) WriteTo(w io.Writer) (int64, error) {
+	// note to stay retro compatible with previous version using ecc/encoder, we encode as:
+	// d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute
 
-	enc := curve.NewEncoder(w)
+	var written int64
+	var err error
 
-	toEncode := []interface{}{d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute}
+	err = binary.Write(w, binary.BigEndian, d.Cardinality)
+	if err != nil {
+		return written, err
+	}
+	written += 8
 
+	toEncode := []*fr.Element{&d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
 	for _, v := range toEncode {
-		if err := enc.Encode(v); err != nil {
-			return enc.BytesWritten(), err
+		buf := v.Bytes()
+		_, err = w.Write(buf[:])
+		if err != nil {
+			return written, err
 		}
+		written += fr.Bytes
 	}
 
-	return enc.BytesWritten(), nil
+	err = binary.Write(w, binary.BigEndian, d.withPrecompute)
+	if err != nil {
+		return written, err
+	}
+	written += 1
+
+	return written, nil
 }
 
 // ReadFrom attempts to decode a domain from Reader
 func (d *Domain) ReadFrom(r io.Reader) (int64, error) {
 
-	dec := curve.NewDecoder(r)
+	var read int64
+	var err error
 
-	toDecode := []interface{}{&d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute}
+	err = binary.Read(r, binary.BigEndian, &d.Cardinality)
+	if err != nil {
+		return read, err
+	}
+	read += 8
+
+	toDecode := []*fr.Element{&d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
 
 	for _, v := range toDecode {
-		if err := dec.Decode(v); err != nil {
-			return dec.BytesRead(), err
+		var buf [fr.Bytes]byte
+		_, err = r.Read(buf[:])
+		if err != nil {
+			return read, err
+		}
+		read += fr.Bytes
+		*v, err = fr.BigEndian.Element(&buf)
+		if err != nil {
+			return read, err
 		}
 	}
 
+	err = binary.Read(r, binary.BigEndian, &d.withPrecompute)
+	if err != nil {
+		return read, err
+	}
+	read += 1
+
 	if d.withPrecompute {
 		d.preComputeTwiddles()
 	}
 
-	return dec.BytesRead(), nil
+	return read, nil
 }
diff --git a/ecc/bls12-381/fr/fft/domain.go b/ecc/bls12-381/fr/fft/domain.go
index 3bc21d6f86..7913415e10 100644
--- a/ecc/bls12-381/fr/fft/domain.go
+++ b/ecc/bls12-381/fr/fft/domain.go
@@ -17,6 +17,7 @@
 package fft
 
 import (
+	"encoding/binary"
 	"errors"
 	"io"
 	"math/big"
@@ -26,8 +27,6 @@ import (
 
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
 
-	curve "github.com/consensys/gnark-crypto/ecc/bls12-381"
-
 	"github.com/consensys/gnark-crypto/ecc"
 )
 
@@ -257,36 +256,73 @@ func precomputeExpTableChunk(w fr.Element, power uint64, table []fr.Element) {
 // WriteTo writes a binary representation of the domain (without the precomputed twiddle factors)
 // to the provided writer
 func (d *Domain) WriteTo(w io.Writer) (int64, error) {
+	// note to stay retro compatible with previous version using ecc/encoder, we encode as:
+	// d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute
 
-	enc := curve.NewEncoder(w)
+	var written int64
+	var err error
 
-	toEncode := []interface{}{d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute}
+	err = binary.Write(w, binary.BigEndian, d.Cardinality)
+	if err != nil {
+		return written, err
+	}
+	written += 8
 
+	toEncode := []*fr.Element{&d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
 	for _, v := range toEncode {
-		if err := enc.Encode(v); err != nil {
-			return enc.BytesWritten(), err
+		buf := v.Bytes()
+		_, err = w.Write(buf[:])
+		if err != nil {
+			return written, err
 		}
+		written += fr.Bytes
 	}
 
-	return enc.BytesWritten(), nil
+	err = binary.Write(w, binary.BigEndian, d.withPrecompute)
+	if err != nil {
+		return written, err
+	}
+	written += 1
+
+	return written, nil
 }
 
 // ReadFrom attempts to decode a domain from Reader
 func (d *Domain) ReadFrom(r io.Reader) (int64, error) {
 
-	dec := curve.NewDecoder(r)
+	var read int64
+	var err error
 
-	toDecode := []interface{}{&d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute}
+	err = binary.Read(r, binary.BigEndian, &d.Cardinality)
+	if err != nil {
+		return read, err
+	}
+	read += 8
+
+	toDecode := []*fr.Element{&d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
 
 	for _, v := range toDecode {
-		if err := dec.Decode(v); err != nil {
-			return dec.BytesRead(), err
+		var buf [fr.Bytes]byte
+		_, err = r.Read(buf[:])
+		if err != nil {
+			return read, err
+		}
+		read += fr.Bytes
+		*v, err = fr.BigEndian.Element(&buf)
+		if err != nil {
+			return read, err
 		}
 	}
 
+	err = binary.Read(r, binary.BigEndian, &d.withPrecompute)
+	if err != nil {
+		return read, err
+	}
+	read += 1
+
 	if d.withPrecompute {
 		d.preComputeTwiddles()
 	}
 
-	return dec.BytesRead(), nil
+	return read, nil
 }
diff --git a/ecc/bls24-315/fr/fft/domain.go b/ecc/bls24-315/fr/fft/domain.go
index 765f4a8276..1226a1b856 100644
--- a/ecc/bls24-315/fr/fft/domain.go
+++ b/ecc/bls24-315/fr/fft/domain.go
@@ -17,6 +17,7 @@
 package fft
 
 import (
+	"encoding/binary"
 	"errors"
 	"io"
 	"math/big"
@@ -26,8 +27,6 @@ import (
 
 	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
 
-	curve "github.com/consensys/gnark-crypto/ecc/bls24-315"
-
 	"github.com/consensys/gnark-crypto/ecc"
 )
 
@@ -257,36 +256,73 @@ func precomputeExpTableChunk(w fr.Element, power uint64, table []fr.Element) {
 // WriteTo writes a binary representation of the domain (without the precomputed twiddle factors)
 // to the provided writer
 func (d *Domain) WriteTo(w io.Writer) (int64, error) {
+	// note to stay retro compatible with previous version using ecc/encoder, we encode as:
+	// d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute
 
-	enc := curve.NewEncoder(w)
+	var written int64
+	var err error
 
-	toEncode := []interface{}{d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute}
+	err = binary.Write(w, binary.BigEndian, d.Cardinality)
+	if err != nil {
+		return written, err
+	}
+	written += 8
 
+	toEncode := []*fr.Element{&d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
 	for _, v := range toEncode {
-		if err := enc.Encode(v); err != nil {
-			return enc.BytesWritten(), err
+		buf := v.Bytes()
+		_, err = w.Write(buf[:])
+		if err != nil {
+			return written, err
 		}
+		written += fr.Bytes
 	}
 
-	return enc.BytesWritten(), nil
+	err = binary.Write(w, binary.BigEndian, d.withPrecompute)
+	if err != nil {
+		return written, err
+	}
+	written += 1
+
+	return written, nil
 }
 
 // ReadFrom attempts to decode a domain from Reader
 func (d *Domain) ReadFrom(r io.Reader) (int64, error) {
 
-	dec := curve.NewDecoder(r)
+	var read int64
+	var err error
 
-	toDecode := []interface{}{&d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute}
+	err = binary.Read(r, binary.BigEndian, &d.Cardinality)
+	if err != nil {
+		return read, err
+	}
+	read += 8
+
+	toDecode := []*fr.Element{&d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
 
 	for _, v := range toDecode {
-		if err := dec.Decode(v); err != nil {
-			return dec.BytesRead(), err
+		var buf [fr.Bytes]byte
+		_, err = r.Read(buf[:])
+		if err != nil {
+			return read, err
+		}
+		read += fr.Bytes
+		*v, err = fr.BigEndian.Element(&buf)
+		if err != nil {
+			return read, err
 		}
 	}
 
+	err = binary.Read(r, binary.BigEndian, &d.withPrecompute)
+	if err != nil {
+		return read, err
+	}
+	read += 1
+
 	if d.withPrecompute {
 		d.preComputeTwiddles()
 	}
 
-	return dec.BytesRead(), nil
+	return read, nil
 }
diff --git a/ecc/bls24-317/fr/fft/domain.go b/ecc/bls24-317/fr/fft/domain.go
index 6fcdd4f337..e60bb48d9d 100644
--- a/ecc/bls24-317/fr/fft/domain.go
+++ b/ecc/bls24-317/fr/fft/domain.go
@@ -17,6 +17,7 @@
 package fft
 
 import (
+	"encoding/binary"
 	"errors"
 	"io"
 	"math/big"
@@ -26,8 +27,6 @@ import (
 
 	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
 
-	curve "github.com/consensys/gnark-crypto/ecc/bls24-317"
-
 	"github.com/consensys/gnark-crypto/ecc"
 )
 
@@ -257,36 +256,73 @@ func precomputeExpTableChunk(w fr.Element, power uint64, table []fr.Element) {
 // WriteTo writes a binary representation of the domain (without the precomputed twiddle factors)
 // to the provided writer
 func (d *Domain) WriteTo(w io.Writer) (int64, error) {
+	// note to stay retro compatible with previous version using ecc/encoder, we encode as:
+	// d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute
 
-	enc := curve.NewEncoder(w)
+	var written int64
+	var err error
 
-	toEncode := []interface{}{d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute}
+	err = binary.Write(w, binary.BigEndian, d.Cardinality)
+	if err != nil {
+		return written, err
+	}
+	written += 8
 
+	toEncode := []*fr.Element{&d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
 	for _, v := range toEncode {
-		if err := enc.Encode(v); err != nil {
-			return enc.BytesWritten(), err
+		buf := v.Bytes()
+		_, err = w.Write(buf[:])
+		if err != nil {
+			return written, err
 		}
+		written += fr.Bytes
 	}
 
-	return enc.BytesWritten(), nil
+	err = binary.Write(w, binary.BigEndian, d.withPrecompute)
+	if err != nil {
+		return written, err
+	}
+	written += 1
+
+	return written, nil
 }
 
 // ReadFrom attempts to decode a domain from Reader
 func (d *Domain) ReadFrom(r io.Reader) (int64, error) {
 
-	dec := curve.NewDecoder(r)
+	var read int64
+	var err error
 
-	toDecode := []interface{}{&d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute}
+	err = binary.Read(r, binary.BigEndian, &d.Cardinality)
+	if err != nil {
+		return read, err
+	}
+	read += 8
+
+	toDecode := []*fr.Element{&d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
 
 	for _, v := range toDecode {
-		if err := dec.Decode(v); err != nil {
-			return dec.BytesRead(), err
+		var buf [fr.Bytes]byte
+		_, err = r.Read(buf[:])
+		if err != nil {
+			return read, err
+		}
+		read += fr.Bytes
+		*v, err = fr.BigEndian.Element(&buf)
+		if err != nil {
+			return read, err
 		}
 	}
 
+	err = binary.Read(r, binary.BigEndian, &d.withPrecompute)
+	if err != nil {
+		return read, err
+	}
+	read += 1
+
 	if d.withPrecompute {
 		d.preComputeTwiddles()
 	}
 
-	return dec.BytesRead(), nil
+	return read, nil
 }
diff --git a/ecc/bn254/fr/fft/domain.go b/ecc/bn254/fr/fft/domain.go
index 409ff7e4ff..f80b4e95f8 100644
--- a/ecc/bn254/fr/fft/domain.go
+++ b/ecc/bn254/fr/fft/domain.go
@@ -17,6 +17,7 @@
 package fft
 
 import (
+	"encoding/binary"
 	"errors"
 	"io"
 	"math/big"
@@ -26,8 +27,6 @@ import (
 
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
 
-	curve "github.com/consensys/gnark-crypto/ecc/bn254"
-
 	"github.com/consensys/gnark-crypto/ecc"
 )
 
@@ -257,36 +256,73 @@ func precomputeExpTableChunk(w fr.Element, power uint64, table []fr.Element) {
 // WriteTo writes a binary representation of the domain (without the precomputed twiddle factors)
 // to the provided writer
 func (d *Domain) WriteTo(w io.Writer) (int64, error) {
+	// note to stay retro compatible with previous version using ecc/encoder, we encode as:
+	// d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute
 
-	enc := curve.NewEncoder(w)
+	var written int64
+	var err error
 
-	toEncode := []interface{}{d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute}
+	err = binary.Write(w, binary.BigEndian, d.Cardinality)
+	if err != nil {
+		return written, err
+	}
+	written += 8
 
+	toEncode := []*fr.Element{&d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
 	for _, v := range toEncode {
-		if err := enc.Encode(v); err != nil {
-			return enc.BytesWritten(), err
+		buf := v.Bytes()
+		_, err = w.Write(buf[:])
+		if err != nil {
+			return written, err
 		}
+		written += fr.Bytes
 	}
 
-	return enc.BytesWritten(), nil
+	err = binary.Write(w, binary.BigEndian, d.withPrecompute)
+	if err != nil {
+		return written, err
+	}
+	written += 1
+
+	return written, nil
 }
 
 // ReadFrom attempts to decode a domain from Reader
 func (d *Domain) ReadFrom(r io.Reader) (int64, error) {
 
-	dec := curve.NewDecoder(r)
+	var read int64
+	var err error
 
-	toDecode := []interface{}{&d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute}
+	err = binary.Read(r, binary.BigEndian, &d.Cardinality)
+	if err != nil {
+		return read, err
+	}
+	read += 8
+
+	toDecode := []*fr.Element{&d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
 
 	for _, v := range toDecode {
-		if err := dec.Decode(v); err != nil {
-			return dec.BytesRead(), err
+		var buf [fr.Bytes]byte
+		_, err = r.Read(buf[:])
+		if err != nil {
+			return read, err
+		}
+		read += fr.Bytes
+		*v, err = fr.BigEndian.Element(&buf)
+		if err != nil {
+			return read, err
 		}
 	}
 
+	err = binary.Read(r, binary.BigEndian, &d.withPrecompute)
+	if err != nil {
+		return read, err
+	}
+	read += 1
+
 	if d.withPrecompute {
 		d.preComputeTwiddles()
 	}
 
-	return dec.BytesRead(), nil
+	return read, nil
 }
diff --git a/ecc/bw6-633/fr/fft/domain.go b/ecc/bw6-633/fr/fft/domain.go
index c36dfe4a27..3174495684 100644
--- a/ecc/bw6-633/fr/fft/domain.go
+++ b/ecc/bw6-633/fr/fft/domain.go
@@ -17,6 +17,7 @@
 package fft
 
 import (
+	"encoding/binary"
 	"errors"
 	"io"
 	"math/big"
@@ -26,8 +27,6 @@ import (
 
 	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
 
-	curve "github.com/consensys/gnark-crypto/ecc/bw6-633"
-
 	"github.com/consensys/gnark-crypto/ecc"
 )
 
@@ -257,36 +256,73 @@ func precomputeExpTableChunk(w fr.Element, power uint64, table []fr.Element) {
 // WriteTo writes a binary representation of the domain (without the precomputed twiddle factors)
 // to the provided writer
 func (d *Domain) WriteTo(w io.Writer) (int64, error) {
+	// note to stay retro compatible with previous version using ecc/encoder, we encode as:
+	// d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute
 
-	enc := curve.NewEncoder(w)
+	var written int64
+	var err error
 
-	toEncode := []interface{}{d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute}
+	err = binary.Write(w, binary.BigEndian, d.Cardinality)
+	if err != nil {
+		return written, err
+	}
+	written += 8
 
+	toEncode := []*fr.Element{&d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
 	for _, v := range toEncode {
-		if err := enc.Encode(v); err != nil {
-			return enc.BytesWritten(), err
+		buf := v.Bytes()
+		_, err = w.Write(buf[:])
+		if err != nil {
+			return written, err
 		}
+		written += fr.Bytes
 	}
 
-	return enc.BytesWritten(), nil
+	err = binary.Write(w, binary.BigEndian, d.withPrecompute)
+	if err != nil {
+		return written, err
+	}
+	written += 1
+
+	return written, nil
 }
 
 // ReadFrom attempts to decode a domain from Reader
 func (d *Domain) ReadFrom(r io.Reader) (int64, error) {
 
-	dec := curve.NewDecoder(r)
+	var read int64
+	var err error
 
-	toDecode := []interface{}{&d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute}
+	err = binary.Read(r, binary.BigEndian, &d.Cardinality)
+	if err != nil {
+		return read, err
+	}
+	read += 8
+
+	toDecode := []*fr.Element{&d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
 
 	for _, v := range toDecode {
-		if err := dec.Decode(v); err != nil {
-			return dec.BytesRead(), err
+		var buf [fr.Bytes]byte
+		_, err = r.Read(buf[:])
+		if err != nil {
+			return read, err
+		}
+		read += fr.Bytes
+		*v, err = fr.BigEndian.Element(&buf)
+		if err != nil {
+			return read, err
 		}
 	}
 
+	err = binary.Read(r, binary.BigEndian, &d.withPrecompute)
+	if err != nil {
+		return read, err
+	}
+	read += 1
+
 	if d.withPrecompute {
 		d.preComputeTwiddles()
 	}
 
-	return dec.BytesRead(), nil
+	return read, nil
 }
diff --git a/ecc/bw6-761/fr/fft/domain.go b/ecc/bw6-761/fr/fft/domain.go
index 276f1467d5..ba2932fb9f 100644
--- a/ecc/bw6-761/fr/fft/domain.go
+++ b/ecc/bw6-761/fr/fft/domain.go
@@ -17,6 +17,7 @@
 package fft
 
 import (
+	"encoding/binary"
 	"errors"
 	"io"
 	"math/big"
@@ -26,8 +27,6 @@ import (
 
 	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
 
-	curve "github.com/consensys/gnark-crypto/ecc/bw6-761"
-
 	"github.com/consensys/gnark-crypto/ecc"
 )
 
@@ -257,36 +256,73 @@ func precomputeExpTableChunk(w fr.Element, power uint64, table []fr.Element) {
 // WriteTo writes a binary representation of the domain (without the precomputed twiddle factors)
 // to the provided writer
 func (d *Domain) WriteTo(w io.Writer) (int64, error) {
+	// note to stay retro compatible with previous version using ecc/encoder, we encode as:
+	// d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute
 
-	enc := curve.NewEncoder(w)
+	var written int64
+	var err error
 
-	toEncode := []interface{}{d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute}
+	err = binary.Write(w, binary.BigEndian, d.Cardinality)
+	if err != nil {
+		return written, err
+	}
+	written += 8
 
+	toEncode := []*fr.Element{&d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
 	for _, v := range toEncode {
-		if err := enc.Encode(v); err != nil {
-			return enc.BytesWritten(), err
+		buf := v.Bytes()
+		_, err = w.Write(buf[:])
+		if err != nil {
+			return written, err
 		}
+		written += fr.Bytes
 	}
 
-	return enc.BytesWritten(), nil
+	err = binary.Write(w, binary.BigEndian, d.withPrecompute)
+	if err != nil {
+		return written, err
+	}
+	written += 1
+
+	return written, nil
 }
 
 // ReadFrom attempts to decode a domain from Reader
 func (d *Domain) ReadFrom(r io.Reader) (int64, error) {
 
-	dec := curve.NewDecoder(r)
+	var read int64
+	var err error
 
-	toDecode := []interface{}{&d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute}
+	err = binary.Read(r, binary.BigEndian, &d.Cardinality)
+	if err != nil {
+		return read, err
+	}
+	read += 8
+
+	toDecode := []*fr.Element{&d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
 
 	for _, v := range toDecode {
-		if err := dec.Decode(v); err != nil {
-			return dec.BytesRead(), err
+		var buf [fr.Bytes]byte
+		_, err = r.Read(buf[:])
+		if err != nil {
+			return read, err
+		}
+		read += fr.Bytes
+		*v, err = fr.BigEndian.Element(&buf)
+		if err != nil {
+			return read, err
 		}
 	}
 
+	err = binary.Read(r, binary.BigEndian, &d.withPrecompute)
+	if err != nil {
+		return read, err
+	}
+	read += 1
+
 	if d.withPrecompute {
 		d.preComputeTwiddles()
 	}
 
-	return dec.BytesRead(), nil
+	return read, nil
 }
diff --git a/internal/generator/fft/template/domain.go.tmpl b/internal/generator/fft/template/domain.go.tmpl
index a6953a29f0..59a87a6c19 100644
--- a/internal/generator/fft/template/domain.go.tmpl
+++ b/internal/generator/fft/template/domain.go.tmpl
@@ -5,9 +5,9 @@ import (
 	"runtime"
 	"sync"
 	"errors"
+	"encoding/binary"
 
 	{{ template "import_fr" . }}
-	{{ template "import_curve" . }}
 
 	"github.com/consensys/gnark-crypto/ecc"
 )
@@ -252,36 +252,73 @@ func precomputeExpTableChunk(w fr.Element, power uint64, table []fr.Element) {
 // WriteTo writes a binary representation of the domain (without the precomputed twiddle factors)
 // to the provided writer
 func (d *Domain) WriteTo(w io.Writer) (int64, error) {
+	// note to stay retro compatible with previous version using ecc/encoder, we encode as:
+	// d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute
 
-	enc := curve.NewEncoder(w)
+	var written int64
+	var err error
 
-	toEncode := []interface{}{d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute}
+	err = binary.Write(w, binary.BigEndian, d.Cardinality)
+	if err != nil {
+		return written, err
+	}
+	written += 8
 
+	toEncode := []*fr.Element{ &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
 	for _, v := range toEncode {
-		if err := enc.Encode(v); err != nil {
-			return enc.BytesWritten(), err
+		buf := v.Bytes()
+		_, err = w.Write(buf[:])
+		if err != nil {
+			return written, err
 		}
+		written += fr.Bytes
 	}
 
-	return enc.BytesWritten(), nil
+	err = binary.Write(w, binary.BigEndian, d.withPrecompute)
+	if err != nil {
+		return written, err
+	}
+	written += 1
+
+	return written, nil
 }
 
 // ReadFrom attempts to decode a domain from Reader
 func (d *Domain) ReadFrom(r io.Reader) (int64, error) {
 
-	dec := curve.NewDecoder(r)
+	var read int64
+	var err error
+
+	err = binary.Read(r, binary.BigEndian, &d.Cardinality)
+	if err != nil {
+		return read, err
+	}
+	read += 8
 
-	toDecode := []interface{}{&d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute}
+	toDecode := []*fr.Element{&d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
 
 	for _, v := range toDecode {
-		if err := dec.Decode(v); err != nil {
-			return dec.BytesRead(), err
+		var buf [fr.Bytes]byte
+		_, err = r.Read(buf[:])
+		if err != nil {
+			return read, err
+		}
+		read += fr.Bytes
+		*v, err = fr.BigEndian.Element(&buf)
+		if err != nil {
+			return read, err
 		}
 	}
 
+	err = binary.Read(r, binary.BigEndian, &d.withPrecompute)
+	if err != nil {
+		return read, err
+	}
+	read += 1
+
 	if d.withPrecompute {
 		d.preComputeTwiddles()
 	}
 
-	return dec.BytesRead(), nil
+	return read, nil
 }

From 35d2a690ab8674e54ebcda1cbce3dff9c40eb3d6 Mon Sep 17 00:00:00 2001
From: Gautam Botrel <gautam.botrel@gmail.com>
Date: Tue, 10 Dec 2024 08:36:30 -0600
Subject: [PATCH 090/114] perf: adds (some) `arm64` assembly for 4 and 6 words
 modulus (#554)

Co-authored-by: Arya Tabaie <15056835+Tabaie@users.noreply.github.com>
---
 .gitignore                                    |   1 +
 ecc/bls12-377/fp/arith.go                     |  13 -
 ecc/bls12-377/fp/asm_adx.go                   |   1 -
 ecc/bls12-377/fp/asm_noadx.go                 |   1 -
 ...{element_ops_amd64.go => element_amd64.go} |   1 -
 ecc/bls12-377/fp/element_amd64.s              |  21 +
 ecc/bls12-377/fp/element_arm64.go             |  79 ++++
 ecc/bls12-377/fp/element_arm64.s              |  21 +
 ecc/bls12-377/fp/element_ops_amd64.s          |   6 -
 ...lement_ops_purego.go => element_purego.go} |  19 +-
 ecc/bls12-377/fp/vector.go                    |  37 --
 ecc/bls12-377/fp/vector_purego.go             |  54 +++
 ecc/bls12-377/fr/arith.go                     |  13 -
 ecc/bls12-377/fr/asm_adx.go                   |   1 -
 ecc/bls12-377/fr/asm_avx.go                   |   1 -
 ecc/bls12-377/fr/asm_noadx.go                 |   1 -
 ecc/bls12-377/fr/asm_noavx.go                 |   1 -
 .../fr/element_amd64.go}                      |   1 -
 ecc/bls12-377/fr/element_amd64.s              |  21 +
 ecc/bls12-377/fr/element_arm64.go             |  77 ++++
 ecc/bls12-377/fr/element_arm64.s              |  21 +
 ecc/bls12-377/fr/element_ops_amd64.s          |   6 -
 ...lement_ops_purego.go => element_purego.go} |  56 +--
 .../fr/vector_amd64.go}                       |  48 ---
 ecc/bls12-377/fr/vector_purego.go             |  56 +++
 ecc/bls12-377/internal/fptower/asm.go         |   1 -
 ecc/bls12-377/internal/fptower/asm_noadx.go   |   1 -
 ecc/bls12-377/internal/fptower/e2_fallback.go |   1 -
 ecc/bls12-381/fp/arith.go                     |  13 -
 ecc/bls12-381/fp/asm_adx.go                   |   1 -
 ecc/bls12-381/fp/asm_noadx.go                 |   1 -
 ...{element_ops_amd64.go => element_amd64.go} |   1 -
 ecc/bls12-381/fp/element_amd64.s              |  21 +
 ecc/bls12-381/fp/element_arm64.go             |  79 ++++
 ecc/bls12-381/fp/element_arm64.s              |  21 +
 ecc/bls12-381/fp/element_ops_amd64.s          |   6 -
 ...lement_ops_purego.go => element_purego.go} |  19 +-
 ecc/bls12-381/fp/vector.go                    |  37 --
 ecc/bls12-381/fp/vector_purego.go             |  54 +++
 ecc/bls12-381/fr/arith.go                     |  13 -
 ecc/bls12-381/fr/asm_adx.go                   |   1 -
 ecc/bls12-381/fr/asm_avx.go                   |   1 -
 ecc/bls12-381/fr/asm_noadx.go                 |   1 -
 ecc/bls12-381/fr/asm_noavx.go                 |   1 -
 .../fr/element_amd64.go}                      |   1 -
 ecc/bls12-381/fr/element_amd64.s              |  21 +
 ecc/bls12-381/fr/element_arm64.go             |  77 ++++
 ecc/bls12-381/fr/element_arm64.s              |  21 +
 ecc/bls12-381/fr/element_ops_amd64.s          |   6 -
 ...lement_ops_purego.go => element_purego.go} |  56 +--
 .../fr/vector_amd64.go}                       |  48 ---
 ecc/bls12-381/fr/vector_purego.go             |  56 +++
 ecc/bls12-381/internal/fptower/asm.go         |   1 -
 ecc/bls12-381/internal/fptower/asm_noadx.go   |   1 -
 ecc/bls12-381/internal/fptower/e2_fallback.go |   1 -
 ecc/bls24-315/fp/arith.go                     |  13 -
 ecc/bls24-315/fp/asm_adx.go                   |   1 -
 ecc/bls24-315/fp/asm_noadx.go                 |   1 -
 ...{element_ops_amd64.go => element_amd64.go} |   1 -
 ecc/bls24-315/fp/element_amd64.s              |  21 +
 ecc/bls24-315/fp/element_ops_amd64.s          |   6 -
 ...lement_ops_purego.go => element_purego.go} |  19 +-
 ecc/bls24-315/fp/vector.go                    |  37 --
 ecc/bls24-315/fp/vector_purego.go             |  54 +++
 ecc/bls24-315/fr/arith.go                     |  13 -
 ecc/bls24-315/fr/asm_adx.go                   |   1 -
 ecc/bls24-315/fr/asm_avx.go                   |   1 -
 ecc/bls24-315/fr/asm_noadx.go                 |   1 -
 ecc/bls24-315/fr/asm_noavx.go                 |   1 -
 ecc/bls24-315/fr/element_amd64.go             |  66 ++++
 ecc/bls24-315/fr/element_amd64.s              |  21 +
 ecc/bls24-315/fr/element_arm64.go             |  77 ++++
 ecc/bls24-315/fr/element_arm64.s              |  21 +
 ecc/bls24-315/fr/element_ops_amd64.s          |   6 -
 ...lement_ops_purego.go => element_purego.go} |  56 +--
 .../fr/vector_amd64.go}                       |  48 ---
 ecc/bls24-315/fr/vector_purego.go             |  56 +++
 ecc/bls24-317/fp/arith.go                     |  13 -
 ecc/bls24-317/fp/asm_adx.go                   |   1 -
 ecc/bls24-317/fp/asm_noadx.go                 |   1 -
 ...{element_ops_amd64.go => element_amd64.go} |   1 -
 ecc/bls24-317/fp/element_amd64.s              |  21 +
 ecc/bls24-317/fp/element_ops_amd64.s          |   6 -
 ...lement_ops_purego.go => element_purego.go} |  19 +-
 ecc/bls24-317/fp/vector.go                    |  37 --
 ecc/bls24-317/fp/vector_purego.go             |  54 +++
 ecc/bls24-317/fr/arith.go                     |  13 -
 ecc/bls24-317/fr/asm_adx.go                   |   1 -
 ecc/bls24-317/fr/asm_avx.go                   |   1 -
 ecc/bls24-317/fr/asm_noadx.go                 |   1 -
 ecc/bls24-317/fr/asm_noavx.go                 |   1 -
 ecc/bls24-317/fr/element_amd64.go             |  66 ++++
 ecc/bls24-317/fr/element_amd64.s              |  21 +
 ecc/bls24-317/fr/element_arm64.go             |  77 ++++
 ecc/bls24-317/fr/element_arm64.s              |  21 +
 ecc/bls24-317/fr/element_ops_amd64.s          |   6 -
 ...lement_ops_purego.go => element_purego.go} |  56 +--
 .../fr/vector_amd64.go}                       |  48 ---
 ecc/bls24-317/fr/vector_purego.go             |  56 +++
 ecc/bn254/fp/arith.go                         |  13 -
 ecc/bn254/fp/asm_adx.go                       |   1 -
 ecc/bn254/fp/asm_avx.go                       |   1 -
 ecc/bn254/fp/asm_noadx.go                     |   1 -
 ecc/bn254/fp/asm_noavx.go                     |   1 -
 ecc/bn254/fp/element_amd64.go                 |  66 ++++
 ecc/bn254/fp/element_amd64.s                  |  21 +
 ecc/bn254/fp/element_arm64.go                 |  77 ++++
 ecc/bn254/fp/element_arm64.s                  |  21 +
 ecc/bn254/fp/element_ops_amd64.s              |   6 -
 ...lement_ops_purego.go => element_purego.go} |  56 +--
 .../{element_ops_amd64.go => vector_amd64.go} |  48 ---
 ecc/bn254/fp/vector_purego.go                 |  56 +++
 ecc/bn254/fr/arith.go                         |  13 -
 ecc/bn254/fr/asm_adx.go                       |   1 -
 ecc/bn254/fr/asm_avx.go                       |   1 -
 ecc/bn254/fr/asm_noadx.go                     |   1 -
 ecc/bn254/fr/asm_noavx.go                     |   1 -
 ecc/bn254/fr/element_amd64.go                 |  66 ++++
 ecc/bn254/fr/element_amd64.s                  |  21 +
 ecc/bn254/fr/element_arm64.go                 |  77 ++++
 ecc/bn254/fr/element_arm64.s                  |  21 +
 ecc/bn254/fr/element_ops_amd64.go             | 208 ----------
 ecc/bn254/fr/element_ops_amd64.s              |   6 -
 ...lement_ops_purego.go => element_purego.go} |  56 +--
 ecc/bn254/fr/mimc/test_vectors/main.go        |   4 +-
 ecc/bn254/fr/vector_amd64.go                  | 160 ++++++++
 ecc/bn254/fr/vector_purego.go                 |  56 +++
 ecc/bn254/internal/fptower/asm.go             |   1 -
 ecc/bn254/internal/fptower/asm_noadx.go       |   1 -
 ecc/bn254/internal/fptower/e2_fallback.go     |   1 -
 ecc/bw6-633/fp/arith.go                       |  13 -
 ecc/bw6-633/fp/asm_adx.go                     |   1 -
 ecc/bw6-633/fp/asm_noadx.go                   |   1 -
 ecc/bw6-633/fp/element_amd64.go               |  66 ++++
 ecc/bw6-633/fp/element_amd64.s                |  21 +
 ecc/bw6-633/fp/element_arm64.go               |  83 ++++
 ecc/bw6-633/fp/element_arm64.s                |  21 +
 ecc/bw6-633/fp/element_ops_amd64.go           |  67 ----
 ecc/bw6-633/fp/element_ops_amd64.s            |   6 -
 ...lement_ops_purego.go => element_purego.go} |  19 +-
 ecc/bw6-633/fp/vector.go                      |  37 --
 ecc/bw6-633/fp/vector_purego.go               |  54 +++
 ecc/bw6-633/fr/arith.go                       |  13 -
 ecc/bw6-633/fr/asm_adx.go                     |   1 -
 ecc/bw6-633/fr/asm_noadx.go                   |   1 -
 ecc/bw6-633/fr/element_amd64.go               |  66 ++++
 ecc/bw6-633/fr/element_amd64.s                |  21 +
 ecc/bw6-633/fr/element_ops_amd64.s            |   6 -
 ...lement_ops_purego.go => element_purego.go} |  19 +-
 ecc/bw6-633/fr/vector.go                      |  37 --
 ecc/bw6-633/fr/vector_purego.go               |  54 +++
 ecc/bw6-761/fp/arith.go                       |  13 -
 ecc/bw6-761/fp/asm_adx.go                     |   1 -
 ecc/bw6-761/fp/asm_noadx.go                   |   1 -
 ecc/bw6-761/fp/element_amd64.go               |  66 ++++
 ecc/bw6-761/fp/element_amd64.s                |  21 +
 ecc/bw6-761/fp/element_arm64.go               |  85 ++++
 ecc/bw6-761/fp/element_arm64.s                |  21 +
 ecc/bw6-761/fp/element_ops_amd64.go           |  67 ----
 ecc/bw6-761/fp/element_ops_amd64.s            |   6 -
 ...lement_ops_purego.go => element_purego.go} |  19 +-
 ecc/bw6-761/fp/vector.go                      |  37 --
 ecc/bw6-761/fp/vector_purego.go               |  54 +++
 ecc/bw6-761/fr/arith.go                       |  13 -
 ecc/bw6-761/fr/asm_adx.go                     |   1 -
 ecc/bw6-761/fr/asm_noadx.go                   |   1 -
 ecc/bw6-761/fr/element_amd64.go               |  66 ++++
 ecc/bw6-761/fr/element_amd64.s                |  21 +
 ecc/bw6-761/fr/element_arm64.go               |  79 ++++
 ecc/bw6-761/fr/element_arm64.s                |  21 +
 ecc/bw6-761/fr/element_ops_amd64.s            |   6 -
 ...lement_ops_purego.go => element_purego.go} |  19 +-
 ecc/bw6-761/fr/vector.go                      |  37 --
 ecc/bw6-761/fr/vector_purego.go               |  54 +++
 ...lement_ops_purego.go => element_purego.go} |  16 +-
 ecc/secp256k1/fp/vector.go                    |  37 --
 ecc/secp256k1/fp/vector_purego.go             |  54 +++
 ...lement_ops_purego.go => element_purego.go} |  16 +-
 ecc/secp256k1/fr/vector.go                    |  37 --
 ecc/secp256k1/fr/vector_purego.go             |  54 +++
 ecc/stark-curve/fp/arith.go                   |  13 -
 ecc/stark-curve/fp/asm_adx.go                 |   1 -
 ecc/stark-curve/fp/asm_avx.go                 |   1 -
 ecc/stark-curve/fp/asm_noadx.go               |   1 -
 ecc/stark-curve/fp/asm_noavx.go               |   1 -
 ecc/stark-curve/fp/element_amd64.go           |  66 ++++
 ecc/stark-curve/fp/element_amd64.s            |  21 +
 ecc/stark-curve/fp/element_arm64.go           |  77 ++++
 ecc/stark-curve/fp/element_arm64.s            |  21 +
 ecc/stark-curve/fp/element_ops_amd64.s        |   6 -
 ...lement_ops_purego.go => element_purego.go} |  56 +--
 .../{element_ops_amd64.go => vector_amd64.go} |  48 ---
 ecc/stark-curve/fp/vector_purego.go           |  56 +++
 ecc/stark-curve/fr/arith.go                   |  13 -
 ecc/stark-curve/fr/asm_adx.go                 |   1 -
 ecc/stark-curve/fr/asm_avx.go                 |   1 -
 ecc/stark-curve/fr/asm_noadx.go               |   1 -
 ecc/stark-curve/fr/asm_noavx.go               |   1 -
 ecc/stark-curve/fr/element_amd64.go           |  66 ++++
 ecc/stark-curve/fr/element_amd64.s            |  21 +
 ecc/stark-curve/fr/element_arm64.go           |  77 ++++
 ecc/stark-curve/fr/element_arm64.s            |  21 +
 ecc/stark-curve/fr/element_ops_amd64.go       | 208 ----------
 ecc/stark-curve/fr/element_ops_amd64.s        |   6 -
 ...lement_ops_purego.go => element_purego.go} |  56 +--
 ecc/stark-curve/fr/vector_amd64.go            | 160 ++++++++
 ecc/stark-curve/fr/vector_purego.go           |  56 +++
 field/asm/.gitignore                          |   7 +-
 field/asm/element_10w_arm64.s                 | 266 +++++++++++++
 field/asm/element_12w_arm64.s                 | 312 +++++++++++++++
 field/asm/element_4w_arm64.s                  | 163 ++++++++
 field/asm/element_6w_arm64.s                  | 220 +++++++++++
 field/generator/asm/amd64/build.go            |   7 -
 field/generator/asm/arm64/build.go            | 258 ++++++++++++
 .../generator/asm/arm64/element_butterfly.go  |  47 +++
 field/generator/asm/arm64/element_mul.go      | 259 ++++++++++++
 field/generator/config/field_config.go        |  14 +-
 field/generator/generator.go                  | 371 +++++++++---------
 field/generator/generator_test.go             |  11 +-
 .../internal/templates/element/arith.go       |  16 -
 .../internal/templates/element/base.go        |   5 +
 .../internal/templates/element/ops_asm.go     | 208 ++++------
 .../internal/templates/element/ops_purego.go  |  55 +--
 .../internal/templates/element/tests.go       |   1 +
 .../internal/templates/element/vector.go      |  43 --
 .../templates/element/vector_ops_asm.go       | 147 +++++++
 .../templates/element/vector_ops_purego.go    |  40 ++
 field/goff/cmd/root.go                        |  14 +-
 ...lement_ops_purego.go => element_purego.go} |  16 +-
 field/goldilocks/vector.go                    |  37 --
 field/goldilocks/vector_purego.go             |  54 +++
 go.mod                                        |   2 +-
 go.sum                                        |   4 +-
 internal/generator/main.go                    |  44 +--
 234 files changed, 5865 insertions(+), 2566 deletions(-)
 rename ecc/bls12-377/fp/{element_ops_amd64.go => element_amd64.go} (98%)
 create mode 100644 ecc/bls12-377/fp/element_amd64.s
 create mode 100644 ecc/bls12-377/fp/element_arm64.go
 create mode 100644 ecc/bls12-377/fp/element_arm64.s
 delete mode 100644 ecc/bls12-377/fp/element_ops_amd64.s
 rename ecc/bls12-377/fp/{element_ops_purego.go => element_purego.go} (99%)
 create mode 100644 ecc/bls12-377/fp/vector_purego.go
 rename ecc/{bw6-633/fr/element_ops_amd64.go => bls12-377/fr/element_amd64.go} (98%)
 create mode 100644 ecc/bls12-377/fr/element_amd64.s
 create mode 100644 ecc/bls12-377/fr/element_arm64.go
 create mode 100644 ecc/bls12-377/fr/element_arm64.s
 delete mode 100644 ecc/bls12-377/fr/element_ops_amd64.s
 rename ecc/bls12-377/fr/{element_ops_purego.go => element_purego.go} (88%)
 rename ecc/{bls12-381/fr/element_ops_amd64.go => bls12-377/fr/vector_amd64.go} (84%)
 create mode 100644 ecc/bls12-377/fr/vector_purego.go
 rename ecc/bls12-381/fp/{element_ops_amd64.go => element_amd64.go} (98%)
 create mode 100644 ecc/bls12-381/fp/element_amd64.s
 create mode 100644 ecc/bls12-381/fp/element_arm64.go
 create mode 100644 ecc/bls12-381/fp/element_arm64.s
 delete mode 100644 ecc/bls12-381/fp/element_ops_amd64.s
 rename ecc/bls12-381/fp/{element_ops_purego.go => element_purego.go} (99%)
 create mode 100644 ecc/bls12-381/fp/vector_purego.go
 rename ecc/{bw6-761/fr/element_ops_amd64.go => bls12-381/fr/element_amd64.go} (98%)
 create mode 100644 ecc/bls12-381/fr/element_amd64.s
 create mode 100644 ecc/bls12-381/fr/element_arm64.go
 create mode 100644 ecc/bls12-381/fr/element_arm64.s
 delete mode 100644 ecc/bls12-381/fr/element_ops_amd64.s
 rename ecc/bls12-381/fr/{element_ops_purego.go => element_purego.go} (88%)
 rename ecc/{bls24-315/fr/element_ops_amd64.go => bls12-381/fr/vector_amd64.go} (84%)
 create mode 100644 ecc/bls12-381/fr/vector_purego.go
 rename ecc/bls24-315/fp/{element_ops_amd64.go => element_amd64.go} (98%)
 create mode 100644 ecc/bls24-315/fp/element_amd64.s
 delete mode 100644 ecc/bls24-315/fp/element_ops_amd64.s
 rename ecc/bls24-315/fp/{element_ops_purego.go => element_purego.go} (99%)
 create mode 100644 ecc/bls24-315/fp/vector_purego.go
 create mode 100644 ecc/bls24-315/fr/element_amd64.go
 create mode 100644 ecc/bls24-315/fr/element_amd64.s
 create mode 100644 ecc/bls24-315/fr/element_arm64.go
 create mode 100644 ecc/bls24-315/fr/element_arm64.s
 delete mode 100644 ecc/bls24-315/fr/element_ops_amd64.s
 rename ecc/bls24-315/fr/{element_ops_purego.go => element_purego.go} (88%)
 rename ecc/{bls24-317/fr/element_ops_amd64.go => bls24-315/fr/vector_amd64.go} (84%)
 create mode 100644 ecc/bls24-315/fr/vector_purego.go
 rename ecc/bls24-317/fp/{element_ops_amd64.go => element_amd64.go} (98%)
 create mode 100644 ecc/bls24-317/fp/element_amd64.s
 delete mode 100644 ecc/bls24-317/fp/element_ops_amd64.s
 rename ecc/bls24-317/fp/{element_ops_purego.go => element_purego.go} (99%)
 create mode 100644 ecc/bls24-317/fp/vector_purego.go
 create mode 100644 ecc/bls24-317/fr/element_amd64.go
 create mode 100644 ecc/bls24-317/fr/element_amd64.s
 create mode 100644 ecc/bls24-317/fr/element_arm64.go
 create mode 100644 ecc/bls24-317/fr/element_arm64.s
 delete mode 100644 ecc/bls24-317/fr/element_ops_amd64.s
 rename ecc/bls24-317/fr/{element_ops_purego.go => element_purego.go} (88%)
 rename ecc/{bls12-377/fr/element_ops_amd64.go => bls24-317/fr/vector_amd64.go} (84%)
 create mode 100644 ecc/bls24-317/fr/vector_purego.go
 create mode 100644 ecc/bn254/fp/element_amd64.go
 create mode 100644 ecc/bn254/fp/element_amd64.s
 create mode 100644 ecc/bn254/fp/element_arm64.go
 create mode 100644 ecc/bn254/fp/element_arm64.s
 delete mode 100644 ecc/bn254/fp/element_ops_amd64.s
 rename ecc/bn254/fp/{element_ops_purego.go => element_purego.go} (88%)
 rename ecc/bn254/fp/{element_ops_amd64.go => vector_amd64.go} (84%)
 create mode 100644 ecc/bn254/fp/vector_purego.go
 create mode 100644 ecc/bn254/fr/element_amd64.go
 create mode 100644 ecc/bn254/fr/element_amd64.s
 create mode 100644 ecc/bn254/fr/element_arm64.go
 create mode 100644 ecc/bn254/fr/element_arm64.s
 delete mode 100644 ecc/bn254/fr/element_ops_amd64.go
 delete mode 100644 ecc/bn254/fr/element_ops_amd64.s
 rename ecc/bn254/fr/{element_ops_purego.go => element_purego.go} (88%)
 create mode 100644 ecc/bn254/fr/vector_amd64.go
 create mode 100644 ecc/bn254/fr/vector_purego.go
 create mode 100644 ecc/bw6-633/fp/element_amd64.go
 create mode 100644 ecc/bw6-633/fp/element_amd64.s
 create mode 100644 ecc/bw6-633/fp/element_arm64.go
 create mode 100644 ecc/bw6-633/fp/element_arm64.s
 delete mode 100644 ecc/bw6-633/fp/element_ops_amd64.go
 delete mode 100644 ecc/bw6-633/fp/element_ops_amd64.s
 rename ecc/bw6-633/fp/{element_ops_purego.go => element_purego.go} (99%)
 create mode 100644 ecc/bw6-633/fp/vector_purego.go
 create mode 100644 ecc/bw6-633/fr/element_amd64.go
 create mode 100644 ecc/bw6-633/fr/element_amd64.s
 delete mode 100644 ecc/bw6-633/fr/element_ops_amd64.s
 rename ecc/bw6-633/fr/{element_ops_purego.go => element_purego.go} (99%)
 create mode 100644 ecc/bw6-633/fr/vector_purego.go
 create mode 100644 ecc/bw6-761/fp/element_amd64.go
 create mode 100644 ecc/bw6-761/fp/element_amd64.s
 create mode 100644 ecc/bw6-761/fp/element_arm64.go
 create mode 100644 ecc/bw6-761/fp/element_arm64.s
 delete mode 100644 ecc/bw6-761/fp/element_ops_amd64.go
 delete mode 100644 ecc/bw6-761/fp/element_ops_amd64.s
 rename ecc/bw6-761/fp/{element_ops_purego.go => element_purego.go} (99%)
 create mode 100644 ecc/bw6-761/fp/vector_purego.go
 create mode 100644 ecc/bw6-761/fr/element_amd64.go
 create mode 100644 ecc/bw6-761/fr/element_amd64.s
 create mode 100644 ecc/bw6-761/fr/element_arm64.go
 create mode 100644 ecc/bw6-761/fr/element_arm64.s
 delete mode 100644 ecc/bw6-761/fr/element_ops_amd64.s
 rename ecc/bw6-761/fr/{element_ops_purego.go => element_purego.go} (99%)
 create mode 100644 ecc/bw6-761/fr/vector_purego.go
 rename ecc/secp256k1/fp/{element_ops_purego.go => element_purego.go} (100%)
 create mode 100644 ecc/secp256k1/fp/vector_purego.go
 rename ecc/secp256k1/fr/{element_ops_purego.go => element_purego.go} (100%)
 create mode 100644 ecc/secp256k1/fr/vector_purego.go
 create mode 100644 ecc/stark-curve/fp/element_amd64.go
 create mode 100644 ecc/stark-curve/fp/element_amd64.s
 create mode 100644 ecc/stark-curve/fp/element_arm64.go
 create mode 100644 ecc/stark-curve/fp/element_arm64.s
 delete mode 100644 ecc/stark-curve/fp/element_ops_amd64.s
 rename ecc/stark-curve/fp/{element_ops_purego.go => element_purego.go} (88%)
 rename ecc/stark-curve/fp/{element_ops_amd64.go => vector_amd64.go} (84%)
 create mode 100644 ecc/stark-curve/fp/vector_purego.go
 create mode 100644 ecc/stark-curve/fr/element_amd64.go
 create mode 100644 ecc/stark-curve/fr/element_amd64.s
 create mode 100644 ecc/stark-curve/fr/element_arm64.go
 create mode 100644 ecc/stark-curve/fr/element_arm64.s
 delete mode 100644 ecc/stark-curve/fr/element_ops_amd64.go
 delete mode 100644 ecc/stark-curve/fr/element_ops_amd64.s
 rename ecc/stark-curve/fr/{element_ops_purego.go => element_purego.go} (88%)
 create mode 100644 ecc/stark-curve/fr/vector_amd64.go
 create mode 100644 ecc/stark-curve/fr/vector_purego.go
 create mode 100644 field/asm/element_10w_arm64.s
 create mode 100644 field/asm/element_12w_arm64.s
 create mode 100644 field/asm/element_4w_arm64.s
 create mode 100644 field/asm/element_6w_arm64.s
 create mode 100644 field/generator/asm/arm64/build.go
 create mode 100644 field/generator/asm/arm64/element_butterfly.go
 create mode 100644 field/generator/asm/arm64/element_mul.go
 create mode 100644 field/generator/internal/templates/element/vector_ops_asm.go
 create mode 100644 field/generator/internal/templates/element/vector_ops_purego.go
 rename field/goldilocks/{element_ops_purego.go => element_purego.go} (100%)
 create mode 100644 field/goldilocks/vector_purego.go

diff --git a/.gitignore b/.gitignore
index bb95194a5f..4d9d603f74 100644
--- a/.gitignore
+++ b/.gitignore
@@ -5,6 +5,7 @@
 *.so
 *.dylib
 *.txt
+**/.rbench.lock
 
 # Test binary, build with `go test -c`
 *.test
diff --git a/ecc/bls12-377/fp/arith.go b/ecc/bls12-377/fp/arith.go
index 6f281563b3..66fa667482 100644
--- a/ecc/bls12-377/fp/arith.go
+++ b/ecc/bls12-377/fp/arith.go
@@ -58,16 +58,3 @@ func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) {
 	hi, _ = bits.Add64(hi, e, carry)
 	return
 }
-func max(a int, b int) int {
-	if a > b {
-		return a
-	}
-	return b
-}
-
-func min(a int, b int) int {
-	if a < b {
-		return a
-	}
-	return b
-}
diff --git a/ecc/bls12-377/fp/asm_adx.go b/ecc/bls12-377/fp/asm_adx.go
index 0481989ec6..f8e29bd1a7 100644
--- a/ecc/bls12-377/fp/asm_adx.go
+++ b/ecc/bls12-377/fp/asm_adx.go
@@ -1,5 +1,4 @@
 //go:build !noadx
-// +build !noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls12-377/fp/asm_noadx.go b/ecc/bls12-377/fp/asm_noadx.go
index 92f8cc0f42..cb6cfa0f50 100644
--- a/ecc/bls12-377/fp/asm_noadx.go
+++ b/ecc/bls12-377/fp/asm_noadx.go
@@ -1,5 +1,4 @@
 //go:build noadx
-// +build noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls12-377/fp/element_ops_amd64.go b/ecc/bls12-377/fp/element_amd64.go
similarity index 98%
rename from ecc/bls12-377/fp/element_ops_amd64.go
rename to ecc/bls12-377/fp/element_amd64.go
index ed2803d717..77a51ee25e 100644
--- a/ecc/bls12-377/fp/element_ops_amd64.go
+++ b/ecc/bls12-377/fp/element_amd64.go
@@ -1,5 +1,4 @@
 //go:build !purego
-// +build !purego
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls12-377/fp/element_amd64.s b/ecc/bls12-377/fp/element_amd64.s
new file mode 100644
index 0000000000..872eddf5d6
--- /dev/null
+++ b/ecc/bls12-377/fp/element_amd64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 11124594824487954849
+#include "../../../field/asm/element_6w_amd64.s"
+
diff --git a/ecc/bls12-377/fp/element_arm64.go b/ecc/bls12-377/fp/element_arm64.go
new file mode 100644
index 0000000000..9793f7eb28
--- /dev/null
+++ b/ecc/bls12-377/fp/element_arm64.go
@@ -0,0 +1,79 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fp
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+//
+//go:noescape
+func Butterfly(a, b *Element)
+
+//go:noescape
+func mul(res, x, y *Element)
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+	mul(z, x, y)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for doc.
+	mul(z, x, x)
+	return z
+}
+
+// MulBy3 x *= 3 (mod q)
+func MulBy3(x *Element) {
+	_x := *x
+	x.Double(x).Add(x, &_x)
+}
+
+// MulBy5 x *= 5 (mod q)
+func MulBy5(x *Element) {
+	_x := *x
+	x.Double(x).Double(x).Add(x, &_x)
+}
+
+// MulBy13 x *= 13 (mod q)
+func MulBy13(x *Element) {
+	var y = Element{
+		1176283927673829444,
+		14130787773971430395,
+		11354866436980285261,
+		15740727779991009548,
+		14951814113394531041,
+		33013799364667434,
+	}
+	x.Mul(x, &y)
+}
+
+func fromMont(z *Element) {
+	_fromMontGeneric(z)
+}
+
+//go:noescape
+func reduce(res *Element)
diff --git a/ecc/bls12-377/fp/element_arm64.s b/ecc/bls12-377/fp/element_arm64.s
new file mode 100644
index 0000000000..2a3f7d0b2c
--- /dev/null
+++ b/ecc/bls12-377/fp/element_arm64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 15397482240260640864
+#include "../../../field/asm/element_6w_arm64.s"
+
diff --git a/ecc/bls12-377/fp/element_ops_amd64.s b/ecc/bls12-377/fp/element_ops_amd64.s
deleted file mode 100644
index cabff26f70..0000000000
--- a/ecc/bls12-377/fp/element_ops_amd64.s
+++ /dev/null
@@ -1,6 +0,0 @@
-// +build !purego
-
-// Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 11124594824487954849
-#include "../../../field/asm/element_6w_amd64.s"
-
diff --git a/ecc/bls12-377/fp/element_ops_purego.go b/ecc/bls12-377/fp/element_purego.go
similarity index 99%
rename from ecc/bls12-377/fp/element_ops_purego.go
rename to ecc/bls12-377/fp/element_purego.go
index 072fb87c01..93afd90757 100644
--- a/ecc/bls12-377/fp/element_ops_purego.go
+++ b/ecc/bls12-377/fp/element_purego.go
@@ -1,5 +1,4 @@
-//go:build !amd64 || purego
-// +build !amd64 purego
+//go:build purego || (!amd64 && !arm64)
 
 // Copyright 2020 ConsenSys Software Inc.
 //
@@ -46,14 +45,6 @@ func MulBy13(x *Element) {
 	x.Mul(x, &y)
 }
 
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-func Butterfly(a, b *Element) {
-	_butterflyGeneric(a, b)
-}
-
 func fromMont(z *Element) {
 	_fromMontGeneric(z)
 }
@@ -703,3 +694,11 @@ func (z *Element) Square(x *Element) *Element {
 	}
 	return z
 }
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
diff --git a/ecc/bls12-377/fp/vector.go b/ecc/bls12-377/fp/vector.go
index f1d659e767..64228605a8 100644
--- a/ecc/bls12-377/fp/vector.go
+++ b/ecc/bls12-377/fp/vector.go
@@ -201,43 +201,6 @@ func (vector Vector) Swap(i, j int) {
 	vector[i], vector[j] = vector[j], vector[i]
 }
 
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	addVecGeneric(*vector, a, b)
-}
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	subVecGeneric(*vector, a, b)
-}
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *Element) {
-	scalarMulVecGeneric(*vector, a, b)
-}
-
-// Sum computes the sum of all elements in the vector.
-func (vector *Vector) Sum() (res Element) {
-	sumVecGeneric(&res, *vector)
-	return
-}
-
-// InnerProduct computes the inner product of two vectors.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) InnerProduct(other Vector) (res Element) {
-	innerProductVecGeneric(&res, *vector, other)
-	return
-}
-
-// Mul multiplies two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Mul(a, b Vector) {
-	mulVecGeneric(*vector, a, b)
-}
-
 func addVecGeneric(res, a, b Vector) {
 	if len(a) != len(b) || len(a) != len(res) {
 		panic("vector.Add: vectors don't have the same length")
diff --git a/ecc/bls12-377/fp/vector_purego.go b/ecc/bls12-377/fp/vector_purego.go
new file mode 100644
index 0000000000..798b669887
--- /dev/null
+++ b/ecc/bls12-377/fp/vector_purego.go
@@ -0,0 +1,54 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fp
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	addVecGeneric(*vector, a, b)
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	subVecGeneric(*vector, a, b)
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
diff --git a/ecc/bls12-377/fr/arith.go b/ecc/bls12-377/fr/arith.go
index 7cfd55da19..83c9fd9ef9 100644
--- a/ecc/bls12-377/fr/arith.go
+++ b/ecc/bls12-377/fr/arith.go
@@ -58,16 +58,3 @@ func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) {
 	hi, _ = bits.Add64(hi, e, carry)
 	return
 }
-func max(a int, b int) int {
-	if a > b {
-		return a
-	}
-	return b
-}
-
-func min(a int, b int) int {
-	if a < b {
-		return a
-	}
-	return b
-}
diff --git a/ecc/bls12-377/fr/asm_adx.go b/ecc/bls12-377/fr/asm_adx.go
index da061913ba..9273ea23ab 100644
--- a/ecc/bls12-377/fr/asm_adx.go
+++ b/ecc/bls12-377/fr/asm_adx.go
@@ -1,5 +1,4 @@
 //go:build !noadx
-// +build !noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls12-377/fr/asm_avx.go b/ecc/bls12-377/fr/asm_avx.go
index 955f559799..1cc06c6e8d 100644
--- a/ecc/bls12-377/fr/asm_avx.go
+++ b/ecc/bls12-377/fr/asm_avx.go
@@ -1,5 +1,4 @@
 //go:build !noavx
-// +build !noavx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls12-377/fr/asm_noadx.go b/ecc/bls12-377/fr/asm_noadx.go
index 7f52ffa197..b784a24247 100644
--- a/ecc/bls12-377/fr/asm_noadx.go
+++ b/ecc/bls12-377/fr/asm_noadx.go
@@ -1,5 +1,4 @@
 //go:build noadx
-// +build noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls12-377/fr/asm_noavx.go b/ecc/bls12-377/fr/asm_noavx.go
index e5a5b1f2cc..66bfc00772 100644
--- a/ecc/bls12-377/fr/asm_noavx.go
+++ b/ecc/bls12-377/fr/asm_noavx.go
@@ -1,5 +1,4 @@
 //go:build noavx
-// +build noavx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bw6-633/fr/element_ops_amd64.go b/ecc/bls12-377/fr/element_amd64.go
similarity index 98%
rename from ecc/bw6-633/fr/element_ops_amd64.go
rename to ecc/bls12-377/fr/element_amd64.go
index 83d40c28c1..0ddb905f7b 100644
--- a/ecc/bw6-633/fr/element_ops_amd64.go
+++ b/ecc/bls12-377/fr/element_amd64.go
@@ -1,5 +1,4 @@
 //go:build !purego
-// +build !purego
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls12-377/fr/element_amd64.s b/ecc/bls12-377/fr/element_amd64.s
new file mode 100644
index 0000000000..fb00194d7e
--- /dev/null
+++ b/ecc/bls12-377/fr/element_amd64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 9425145785761608449
+#include "../../../field/asm/element_4w_amd64.s"
+
diff --git a/ecc/bls12-377/fr/element_arm64.go b/ecc/bls12-377/fr/element_arm64.go
new file mode 100644
index 0000000000..fce7cbcd94
--- /dev/null
+++ b/ecc/bls12-377/fr/element_arm64.go
@@ -0,0 +1,77 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+//
+//go:noescape
+func Butterfly(a, b *Element)
+
+//go:noescape
+func mul(res, x, y *Element)
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+	mul(z, x, y)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for doc.
+	mul(z, x, x)
+	return z
+}
+
+// MulBy3 x *= 3 (mod q)
+func MulBy3(x *Element) {
+	_x := *x
+	x.Double(x).Add(x, &_x)
+}
+
+// MulBy5 x *= 5 (mod q)
+func MulBy5(x *Element) {
+	_x := *x
+	x.Double(x).Double(x).Add(x, &_x)
+}
+
+// MulBy13 x *= 13 (mod q)
+func MulBy13(x *Element) {
+	var y = Element{
+		18434640649710993230,
+		12067750152132099910,
+		14024878721438555919,
+		347766975729306096,
+	}
+	x.Mul(x, &y)
+}
+
+func fromMont(z *Element) {
+	_fromMontGeneric(z)
+}
+
+//go:noescape
+func reduce(res *Element)
diff --git a/ecc/bls12-377/fr/element_arm64.s b/ecc/bls12-377/fr/element_arm64.s
new file mode 100644
index 0000000000..5d328815aa
--- /dev/null
+++ b/ecc/bls12-377/fr/element_arm64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 1501560133179981797
+#include "../../../field/asm/element_4w_arm64.s"
+
diff --git a/ecc/bls12-377/fr/element_ops_amd64.s b/ecc/bls12-377/fr/element_ops_amd64.s
deleted file mode 100644
index 6c42136a7a..0000000000
--- a/ecc/bls12-377/fr/element_ops_amd64.s
+++ /dev/null
@@ -1,6 +0,0 @@
-// +build !purego
-
-// Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 9425145785761608449
-#include "../../../field/asm/element_4w_amd64.s"
-
diff --git a/ecc/bls12-377/fr/element_ops_purego.go b/ecc/bls12-377/fr/element_purego.go
similarity index 88%
rename from ecc/bls12-377/fr/element_ops_purego.go
rename to ecc/bls12-377/fr/element_purego.go
index f107066c79..60de099977 100644
--- a/ecc/bls12-377/fr/element_ops_purego.go
+++ b/ecc/bls12-377/fr/element_purego.go
@@ -1,5 +1,4 @@
-//go:build !amd64 || purego
-// +build !amd64 purego
+//go:build purego || (!amd64 && !arm64)
 
 // Copyright 2020 ConsenSys Software Inc.
 //
@@ -44,14 +43,6 @@ func MulBy13(x *Element) {
 	x.Mul(x, &y)
 }
 
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-func Butterfly(a, b *Element) {
-	_butterflyGeneric(a, b)
-}
-
 func fromMont(z *Element) {
 	_fromMontGeneric(z)
 }
@@ -60,43 +51,6 @@ func reduce(z *Element) {
 	_reduceGeneric(z)
 }
 
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	addVecGeneric(*vector, a, b)
-}
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	subVecGeneric(*vector, a, b)
-}
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *Element) {
-	scalarMulVecGeneric(*vector, a, b)
-}
-
-// Sum computes the sum of all elements in the vector.
-func (vector *Vector) Sum() (res Element) {
-	sumVecGeneric(&res, *vector)
-	return
-}
-
-// InnerProduct computes the inner product of two vectors.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) InnerProduct(other Vector) (res Element) {
-	innerProductVecGeneric(&res, *vector, other)
-	return
-}
-
-// Mul multiplies two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Mul(a, b Vector) {
-	mulVecGeneric(*vector, a, b)
-}
-
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
@@ -438,3 +392,11 @@ func (z *Element) Square(x *Element) *Element {
 	}
 	return z
 }
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
diff --git a/ecc/bls12-381/fr/element_ops_amd64.go b/ecc/bls12-377/fr/vector_amd64.go
similarity index 84%
rename from ecc/bls12-381/fr/element_ops_amd64.go
rename to ecc/bls12-377/fr/vector_amd64.go
index b653e80069..0164ecb382 100644
--- a/ecc/bls12-381/fr/element_ops_amd64.go
+++ b/ecc/bls12-377/fr/vector_amd64.go
@@ -1,5 +1,4 @@
 //go:build !purego
-// +build !purego
 
 // Copyright 2020 ConsenSys Software Inc.
 //
@@ -19,32 +18,6 @@
 
 package fr
 
-//go:noescape
-func MulBy3(x *Element)
-
-//go:noescape
-func MulBy5(x *Element)
-
-//go:noescape
-func MulBy13(x *Element)
-
-//go:noescape
-func mul(res, x, y *Element)
-
-//go:noescape
-func fromMont(res *Element)
-
-//go:noescape
-func reduce(res *Element)
-
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-//
-//go:noescape
-func Butterfly(a, b *Element)
-
 // Add adds two vectors element-wise and stores the result in self.
 // It panics if the vectors don't have the same length.
 func (vector *Vector) Add(a, b Vector) {
@@ -185,24 +158,3 @@ var (
 
 //go:noescape
 func mulVec(res, a, b *Element, n uint64, qInvNeg uint64)
-
-// Mul z = x * y (mod q)
-//
-// x and y must be less than q
-func (z *Element) Mul(x, y *Element) *Element {
-
-	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
-	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
-
-	mul(z, x, y)
-	return z
-}
-
-// Square z = x * x (mod q)
-//
-// x must be less than q
-func (z *Element) Square(x *Element) *Element {
-	// see Mul for doc.
-	mul(z, x, x)
-	return z
-}
diff --git a/ecc/bls12-377/fr/vector_purego.go b/ecc/bls12-377/fr/vector_purego.go
new file mode 100644
index 0000000000..84f86a40b1
--- /dev/null
+++ b/ecc/bls12-377/fr/vector_purego.go
@@ -0,0 +1,56 @@
+//go:build purego || !amd64
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	addVecGeneric(*vector, a, b)
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	subVecGeneric(*vector, a, b)
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
diff --git a/ecc/bls12-377/internal/fptower/asm.go b/ecc/bls12-377/internal/fptower/asm.go
index 49751a9396..03b1160807 100644
--- a/ecc/bls12-377/internal/fptower/asm.go
+++ b/ecc/bls12-377/internal/fptower/asm.go
@@ -1,5 +1,4 @@
 //go:build !noadx
-// +build !noadx
 
 // Copyright 2020 Consensys Software Inc.
 //
diff --git a/ecc/bls12-377/internal/fptower/asm_noadx.go b/ecc/bls12-377/internal/fptower/asm_noadx.go
index c6a97081fc..ea7782392c 100644
--- a/ecc/bls12-377/internal/fptower/asm_noadx.go
+++ b/ecc/bls12-377/internal/fptower/asm_noadx.go
@@ -1,5 +1,4 @@
 //go:build noadx
-// +build noadx
 
 // Copyright 2020 Consensys Software Inc.
 //
diff --git a/ecc/bls12-377/internal/fptower/e2_fallback.go b/ecc/bls12-377/internal/fptower/e2_fallback.go
index 6fe47c4111..1b6011564f 100644
--- a/ecc/bls12-377/internal/fptower/e2_fallback.go
+++ b/ecc/bls12-377/internal/fptower/e2_fallback.go
@@ -1,5 +1,4 @@
 //go:build !amd64
-// +build !amd64
 
 // Copyright 2020 Consensys Software Inc.
 //
diff --git a/ecc/bls12-381/fp/arith.go b/ecc/bls12-381/fp/arith.go
index 6f281563b3..66fa667482 100644
--- a/ecc/bls12-381/fp/arith.go
+++ b/ecc/bls12-381/fp/arith.go
@@ -58,16 +58,3 @@ func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) {
 	hi, _ = bits.Add64(hi, e, carry)
 	return
 }
-func max(a int, b int) int {
-	if a > b {
-		return a
-	}
-	return b
-}
-
-func min(a int, b int) int {
-	if a < b {
-		return a
-	}
-	return b
-}
diff --git a/ecc/bls12-381/fp/asm_adx.go b/ecc/bls12-381/fp/asm_adx.go
index 0481989ec6..f8e29bd1a7 100644
--- a/ecc/bls12-381/fp/asm_adx.go
+++ b/ecc/bls12-381/fp/asm_adx.go
@@ -1,5 +1,4 @@
 //go:build !noadx
-// +build !noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls12-381/fp/asm_noadx.go b/ecc/bls12-381/fp/asm_noadx.go
index 92f8cc0f42..cb6cfa0f50 100644
--- a/ecc/bls12-381/fp/asm_noadx.go
+++ b/ecc/bls12-381/fp/asm_noadx.go
@@ -1,5 +1,4 @@
 //go:build noadx
-// +build noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls12-381/fp/element_ops_amd64.go b/ecc/bls12-381/fp/element_amd64.go
similarity index 98%
rename from ecc/bls12-381/fp/element_ops_amd64.go
rename to ecc/bls12-381/fp/element_amd64.go
index ed2803d717..77a51ee25e 100644
--- a/ecc/bls12-381/fp/element_ops_amd64.go
+++ b/ecc/bls12-381/fp/element_amd64.go
@@ -1,5 +1,4 @@
 //go:build !purego
-// +build !purego
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls12-381/fp/element_amd64.s b/ecc/bls12-381/fp/element_amd64.s
new file mode 100644
index 0000000000..872eddf5d6
--- /dev/null
+++ b/ecc/bls12-381/fp/element_amd64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 11124594824487954849
+#include "../../../field/asm/element_6w_amd64.s"
+
diff --git a/ecc/bls12-381/fp/element_arm64.go b/ecc/bls12-381/fp/element_arm64.go
new file mode 100644
index 0000000000..044b606293
--- /dev/null
+++ b/ecc/bls12-381/fp/element_arm64.go
@@ -0,0 +1,79 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fp
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+//
+//go:noescape
+func Butterfly(a, b *Element)
+
+//go:noescape
+func mul(res, x, y *Element)
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+	mul(z, x, y)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for doc.
+	mul(z, x, x)
+	return z
+}
+
+// MulBy3 x *= 3 (mod q)
+func MulBy3(x *Element) {
+	_x := *x
+	x.Double(x).Add(x, &_x)
+}
+
+// MulBy5 x *= 5 (mod q)
+func MulBy5(x *Element) {
+	_x := *x
+	x.Double(x).Double(x).Add(x, &_x)
+}
+
+// MulBy13 x *= 13 (mod q)
+func MulBy13(x *Element) {
+	var y = Element{
+		13438459813099623723,
+		14459933216667336738,
+		14900020990258308116,
+		2941282712809091851,
+		13639094935183769893,
+		1835248516986607988,
+	}
+	x.Mul(x, &y)
+}
+
+func fromMont(z *Element) {
+	_fromMontGeneric(z)
+}
+
+//go:noescape
+func reduce(res *Element)
diff --git a/ecc/bls12-381/fp/element_arm64.s b/ecc/bls12-381/fp/element_arm64.s
new file mode 100644
index 0000000000..2a3f7d0b2c
--- /dev/null
+++ b/ecc/bls12-381/fp/element_arm64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 15397482240260640864
+#include "../../../field/asm/element_6w_arm64.s"
+
diff --git a/ecc/bls12-381/fp/element_ops_amd64.s b/ecc/bls12-381/fp/element_ops_amd64.s
deleted file mode 100644
index cabff26f70..0000000000
--- a/ecc/bls12-381/fp/element_ops_amd64.s
+++ /dev/null
@@ -1,6 +0,0 @@
-// +build !purego
-
-// Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 11124594824487954849
-#include "../../../field/asm/element_6w_amd64.s"
-
diff --git a/ecc/bls12-381/fp/element_ops_purego.go b/ecc/bls12-381/fp/element_purego.go
similarity index 99%
rename from ecc/bls12-381/fp/element_ops_purego.go
rename to ecc/bls12-381/fp/element_purego.go
index ee3f7e7408..ac96223a0a 100644
--- a/ecc/bls12-381/fp/element_ops_purego.go
+++ b/ecc/bls12-381/fp/element_purego.go
@@ -1,5 +1,4 @@
-//go:build !amd64 || purego
-// +build !amd64 purego
+//go:build purego || (!amd64 && !arm64)
 
 // Copyright 2020 ConsenSys Software Inc.
 //
@@ -46,14 +45,6 @@ func MulBy13(x *Element) {
 	x.Mul(x, &y)
 }
 
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-func Butterfly(a, b *Element) {
-	_butterflyGeneric(a, b)
-}
-
 func fromMont(z *Element) {
 	_fromMontGeneric(z)
 }
@@ -703,3 +694,11 @@ func (z *Element) Square(x *Element) *Element {
 	}
 	return z
 }
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
diff --git a/ecc/bls12-381/fp/vector.go b/ecc/bls12-381/fp/vector.go
index f1d659e767..64228605a8 100644
--- a/ecc/bls12-381/fp/vector.go
+++ b/ecc/bls12-381/fp/vector.go
@@ -201,43 +201,6 @@ func (vector Vector) Swap(i, j int) {
 	vector[i], vector[j] = vector[j], vector[i]
 }
 
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	addVecGeneric(*vector, a, b)
-}
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	subVecGeneric(*vector, a, b)
-}
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *Element) {
-	scalarMulVecGeneric(*vector, a, b)
-}
-
-// Sum computes the sum of all elements in the vector.
-func (vector *Vector) Sum() (res Element) {
-	sumVecGeneric(&res, *vector)
-	return
-}
-
-// InnerProduct computes the inner product of two vectors.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) InnerProduct(other Vector) (res Element) {
-	innerProductVecGeneric(&res, *vector, other)
-	return
-}
-
-// Mul multiplies two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Mul(a, b Vector) {
-	mulVecGeneric(*vector, a, b)
-}
-
 func addVecGeneric(res, a, b Vector) {
 	if len(a) != len(b) || len(a) != len(res) {
 		panic("vector.Add: vectors don't have the same length")
diff --git a/ecc/bls12-381/fp/vector_purego.go b/ecc/bls12-381/fp/vector_purego.go
new file mode 100644
index 0000000000..798b669887
--- /dev/null
+++ b/ecc/bls12-381/fp/vector_purego.go
@@ -0,0 +1,54 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fp
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	addVecGeneric(*vector, a, b)
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	subVecGeneric(*vector, a, b)
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
diff --git a/ecc/bls12-381/fr/arith.go b/ecc/bls12-381/fr/arith.go
index 7cfd55da19..83c9fd9ef9 100644
--- a/ecc/bls12-381/fr/arith.go
+++ b/ecc/bls12-381/fr/arith.go
@@ -58,16 +58,3 @@ func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) {
 	hi, _ = bits.Add64(hi, e, carry)
 	return
 }
-func max(a int, b int) int {
-	if a > b {
-		return a
-	}
-	return b
-}
-
-func min(a int, b int) int {
-	if a < b {
-		return a
-	}
-	return b
-}
diff --git a/ecc/bls12-381/fr/asm_adx.go b/ecc/bls12-381/fr/asm_adx.go
index da061913ba..9273ea23ab 100644
--- a/ecc/bls12-381/fr/asm_adx.go
+++ b/ecc/bls12-381/fr/asm_adx.go
@@ -1,5 +1,4 @@
 //go:build !noadx
-// +build !noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls12-381/fr/asm_avx.go b/ecc/bls12-381/fr/asm_avx.go
index 955f559799..1cc06c6e8d 100644
--- a/ecc/bls12-381/fr/asm_avx.go
+++ b/ecc/bls12-381/fr/asm_avx.go
@@ -1,5 +1,4 @@
 //go:build !noavx
-// +build !noavx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls12-381/fr/asm_noadx.go b/ecc/bls12-381/fr/asm_noadx.go
index 7f52ffa197..b784a24247 100644
--- a/ecc/bls12-381/fr/asm_noadx.go
+++ b/ecc/bls12-381/fr/asm_noadx.go
@@ -1,5 +1,4 @@
 //go:build noadx
-// +build noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls12-381/fr/asm_noavx.go b/ecc/bls12-381/fr/asm_noavx.go
index e5a5b1f2cc..66bfc00772 100644
--- a/ecc/bls12-381/fr/asm_noavx.go
+++ b/ecc/bls12-381/fr/asm_noavx.go
@@ -1,5 +1,4 @@
 //go:build noavx
-// +build noavx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bw6-761/fr/element_ops_amd64.go b/ecc/bls12-381/fr/element_amd64.go
similarity index 98%
rename from ecc/bw6-761/fr/element_ops_amd64.go
rename to ecc/bls12-381/fr/element_amd64.go
index 83d40c28c1..0ddb905f7b 100644
--- a/ecc/bw6-761/fr/element_ops_amd64.go
+++ b/ecc/bls12-381/fr/element_amd64.go
@@ -1,5 +1,4 @@
 //go:build !purego
-// +build !purego
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls12-381/fr/element_amd64.s b/ecc/bls12-381/fr/element_amd64.s
new file mode 100644
index 0000000000..fb00194d7e
--- /dev/null
+++ b/ecc/bls12-381/fr/element_amd64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 9425145785761608449
+#include "../../../field/asm/element_4w_amd64.s"
+
diff --git a/ecc/bls12-381/fr/element_arm64.go b/ecc/bls12-381/fr/element_arm64.go
new file mode 100644
index 0000000000..e82da3dad7
--- /dev/null
+++ b/ecc/bls12-381/fr/element_arm64.go
@@ -0,0 +1,77 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+//
+//go:noescape
+func Butterfly(a, b *Element)
+
+//go:noescape
+func mul(res, x, y *Element)
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+	mul(z, x, y)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for doc.
+	mul(z, x, x)
+	return z
+}
+
+// MulBy3 x *= 3 (mod q)
+func MulBy3(x *Element) {
+	_x := *x
+	x.Double(x).Add(x, &_x)
+}
+
+// MulBy5 x *= 5 (mod q)
+func MulBy5(x *Element) {
+	_x := *x
+	x.Double(x).Double(x).Add(x, &_x)
+}
+
+// MulBy13 x *= 13 (mod q)
+func MulBy13(x *Element) {
+	var y = Element{
+		120259084260,
+		15510977298029211676,
+		7326335280343703402,
+		5909200893219589146,
+	}
+	x.Mul(x, &y)
+}
+
+func fromMont(z *Element) {
+	_fromMontGeneric(z)
+}
+
+//go:noescape
+func reduce(res *Element)
diff --git a/ecc/bls12-381/fr/element_arm64.s b/ecc/bls12-381/fr/element_arm64.s
new file mode 100644
index 0000000000..5d328815aa
--- /dev/null
+++ b/ecc/bls12-381/fr/element_arm64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 1501560133179981797
+#include "../../../field/asm/element_4w_arm64.s"
+
diff --git a/ecc/bls12-381/fr/element_ops_amd64.s b/ecc/bls12-381/fr/element_ops_amd64.s
deleted file mode 100644
index 6c42136a7a..0000000000
--- a/ecc/bls12-381/fr/element_ops_amd64.s
+++ /dev/null
@@ -1,6 +0,0 @@
-// +build !purego
-
-// Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 9425145785761608449
-#include "../../../field/asm/element_4w_amd64.s"
-
diff --git a/ecc/bls12-381/fr/element_ops_purego.go b/ecc/bls12-381/fr/element_purego.go
similarity index 88%
rename from ecc/bls12-381/fr/element_ops_purego.go
rename to ecc/bls12-381/fr/element_purego.go
index 8c10496433..193edfb5d2 100644
--- a/ecc/bls12-381/fr/element_ops_purego.go
+++ b/ecc/bls12-381/fr/element_purego.go
@@ -1,5 +1,4 @@
-//go:build !amd64 || purego
-// +build !amd64 purego
+//go:build purego || (!amd64 && !arm64)
 
 // Copyright 2020 ConsenSys Software Inc.
 //
@@ -44,14 +43,6 @@ func MulBy13(x *Element) {
 	x.Mul(x, &y)
 }
 
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-func Butterfly(a, b *Element) {
-	_butterflyGeneric(a, b)
-}
-
 func fromMont(z *Element) {
 	_fromMontGeneric(z)
 }
@@ -60,43 +51,6 @@ func reduce(z *Element) {
 	_reduceGeneric(z)
 }
 
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	addVecGeneric(*vector, a, b)
-}
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	subVecGeneric(*vector, a, b)
-}
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *Element) {
-	scalarMulVecGeneric(*vector, a, b)
-}
-
-// Sum computes the sum of all elements in the vector.
-func (vector *Vector) Sum() (res Element) {
-	sumVecGeneric(&res, *vector)
-	return
-}
-
-// InnerProduct computes the inner product of two vectors.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) InnerProduct(other Vector) (res Element) {
-	innerProductVecGeneric(&res, *vector, other)
-	return
-}
-
-// Mul multiplies two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Mul(a, b Vector) {
-	mulVecGeneric(*vector, a, b)
-}
-
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
@@ -438,3 +392,11 @@ func (z *Element) Square(x *Element) *Element {
 	}
 	return z
 }
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
diff --git a/ecc/bls24-315/fr/element_ops_amd64.go b/ecc/bls12-381/fr/vector_amd64.go
similarity index 84%
rename from ecc/bls24-315/fr/element_ops_amd64.go
rename to ecc/bls12-381/fr/vector_amd64.go
index b653e80069..0164ecb382 100644
--- a/ecc/bls24-315/fr/element_ops_amd64.go
+++ b/ecc/bls12-381/fr/vector_amd64.go
@@ -1,5 +1,4 @@
 //go:build !purego
-// +build !purego
 
 // Copyright 2020 ConsenSys Software Inc.
 //
@@ -19,32 +18,6 @@
 
 package fr
 
-//go:noescape
-func MulBy3(x *Element)
-
-//go:noescape
-func MulBy5(x *Element)
-
-//go:noescape
-func MulBy13(x *Element)
-
-//go:noescape
-func mul(res, x, y *Element)
-
-//go:noescape
-func fromMont(res *Element)
-
-//go:noescape
-func reduce(res *Element)
-
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-//
-//go:noescape
-func Butterfly(a, b *Element)
-
 // Add adds two vectors element-wise and stores the result in self.
 // It panics if the vectors don't have the same length.
 func (vector *Vector) Add(a, b Vector) {
@@ -185,24 +158,3 @@ var (
 
 //go:noescape
 func mulVec(res, a, b *Element, n uint64, qInvNeg uint64)
-
-// Mul z = x * y (mod q)
-//
-// x and y must be less than q
-func (z *Element) Mul(x, y *Element) *Element {
-
-	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
-	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
-
-	mul(z, x, y)
-	return z
-}
-
-// Square z = x * x (mod q)
-//
-// x must be less than q
-func (z *Element) Square(x *Element) *Element {
-	// see Mul for doc.
-	mul(z, x, x)
-	return z
-}
diff --git a/ecc/bls12-381/fr/vector_purego.go b/ecc/bls12-381/fr/vector_purego.go
new file mode 100644
index 0000000000..84f86a40b1
--- /dev/null
+++ b/ecc/bls12-381/fr/vector_purego.go
@@ -0,0 +1,56 @@
+//go:build purego || !amd64
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	addVecGeneric(*vector, a, b)
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	subVecGeneric(*vector, a, b)
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
diff --git a/ecc/bls12-381/internal/fptower/asm.go b/ecc/bls12-381/internal/fptower/asm.go
index 49751a9396..03b1160807 100644
--- a/ecc/bls12-381/internal/fptower/asm.go
+++ b/ecc/bls12-381/internal/fptower/asm.go
@@ -1,5 +1,4 @@
 //go:build !noadx
-// +build !noadx
 
 // Copyright 2020 Consensys Software Inc.
 //
diff --git a/ecc/bls12-381/internal/fptower/asm_noadx.go b/ecc/bls12-381/internal/fptower/asm_noadx.go
index c6a97081fc..ea7782392c 100644
--- a/ecc/bls12-381/internal/fptower/asm_noadx.go
+++ b/ecc/bls12-381/internal/fptower/asm_noadx.go
@@ -1,5 +1,4 @@
 //go:build noadx
-// +build noadx
 
 // Copyright 2020 Consensys Software Inc.
 //
diff --git a/ecc/bls12-381/internal/fptower/e2_fallback.go b/ecc/bls12-381/internal/fptower/e2_fallback.go
index 6fe47c4111..1b6011564f 100644
--- a/ecc/bls12-381/internal/fptower/e2_fallback.go
+++ b/ecc/bls12-381/internal/fptower/e2_fallback.go
@@ -1,5 +1,4 @@
 //go:build !amd64
-// +build !amd64
 
 // Copyright 2020 Consensys Software Inc.
 //
diff --git a/ecc/bls24-315/fp/arith.go b/ecc/bls24-315/fp/arith.go
index 6f281563b3..66fa667482 100644
--- a/ecc/bls24-315/fp/arith.go
+++ b/ecc/bls24-315/fp/arith.go
@@ -58,16 +58,3 @@ func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) {
 	hi, _ = bits.Add64(hi, e, carry)
 	return
 }
-func max(a int, b int) int {
-	if a > b {
-		return a
-	}
-	return b
-}
-
-func min(a int, b int) int {
-	if a < b {
-		return a
-	}
-	return b
-}
diff --git a/ecc/bls24-315/fp/asm_adx.go b/ecc/bls24-315/fp/asm_adx.go
index 0481989ec6..f8e29bd1a7 100644
--- a/ecc/bls24-315/fp/asm_adx.go
+++ b/ecc/bls24-315/fp/asm_adx.go
@@ -1,5 +1,4 @@
 //go:build !noadx
-// +build !noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls24-315/fp/asm_noadx.go b/ecc/bls24-315/fp/asm_noadx.go
index 92f8cc0f42..cb6cfa0f50 100644
--- a/ecc/bls24-315/fp/asm_noadx.go
+++ b/ecc/bls24-315/fp/asm_noadx.go
@@ -1,5 +1,4 @@
 //go:build noadx
-// +build noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls24-315/fp/element_ops_amd64.go b/ecc/bls24-315/fp/element_amd64.go
similarity index 98%
rename from ecc/bls24-315/fp/element_ops_amd64.go
rename to ecc/bls24-315/fp/element_amd64.go
index ed2803d717..77a51ee25e 100644
--- a/ecc/bls24-315/fp/element_ops_amd64.go
+++ b/ecc/bls24-315/fp/element_amd64.go
@@ -1,5 +1,4 @@
 //go:build !purego
-// +build !purego
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls24-315/fp/element_amd64.s b/ecc/bls24-315/fp/element_amd64.s
new file mode 100644
index 0000000000..00858d648e
--- /dev/null
+++ b/ecc/bls24-315/fp/element_amd64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 18184981773209750009
+#include "../../../field/asm/element_5w_amd64.s"
+
diff --git a/ecc/bls24-315/fp/element_ops_amd64.s b/ecc/bls24-315/fp/element_ops_amd64.s
deleted file mode 100644
index 29314843d7..0000000000
--- a/ecc/bls24-315/fp/element_ops_amd64.s
+++ /dev/null
@@ -1,6 +0,0 @@
-// +build !purego
-
-// Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 18184981773209750009
-#include "../../../field/asm/element_5w_amd64.s"
-
diff --git a/ecc/bls24-315/fp/element_ops_purego.go b/ecc/bls24-315/fp/element_purego.go
similarity index 99%
rename from ecc/bls24-315/fp/element_ops_purego.go
rename to ecc/bls24-315/fp/element_purego.go
index 4796fc3c5b..f5c6690f7e 100644
--- a/ecc/bls24-315/fp/element_ops_purego.go
+++ b/ecc/bls24-315/fp/element_purego.go
@@ -1,5 +1,4 @@
-//go:build !amd64 || purego
-// +build !amd64 purego
+//go:build purego || !amd64
 
 // Copyright 2020 ConsenSys Software Inc.
 //
@@ -45,14 +44,6 @@ func MulBy13(x *Element) {
 	x.Mul(x, &y)
 }
 
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-func Butterfly(a, b *Element) {
-	_butterflyGeneric(a, b)
-}
-
 func fromMont(z *Element) {
 	_fromMontGeneric(z)
 }
@@ -540,3 +531,11 @@ func (z *Element) Square(x *Element) *Element {
 	}
 	return z
 }
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
diff --git a/ecc/bls24-315/fp/vector.go b/ecc/bls24-315/fp/vector.go
index ce61e70ea0..5d7cd31fe6 100644
--- a/ecc/bls24-315/fp/vector.go
+++ b/ecc/bls24-315/fp/vector.go
@@ -200,43 +200,6 @@ func (vector Vector) Swap(i, j int) {
 	vector[i], vector[j] = vector[j], vector[i]
 }
 
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	addVecGeneric(*vector, a, b)
-}
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	subVecGeneric(*vector, a, b)
-}
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *Element) {
-	scalarMulVecGeneric(*vector, a, b)
-}
-
-// Sum computes the sum of all elements in the vector.
-func (vector *Vector) Sum() (res Element) {
-	sumVecGeneric(&res, *vector)
-	return
-}
-
-// InnerProduct computes the inner product of two vectors.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) InnerProduct(other Vector) (res Element) {
-	innerProductVecGeneric(&res, *vector, other)
-	return
-}
-
-// Mul multiplies two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Mul(a, b Vector) {
-	mulVecGeneric(*vector, a, b)
-}
-
 func addVecGeneric(res, a, b Vector) {
 	if len(a) != len(b) || len(a) != len(res) {
 		panic("vector.Add: vectors don't have the same length")
diff --git a/ecc/bls24-315/fp/vector_purego.go b/ecc/bls24-315/fp/vector_purego.go
new file mode 100644
index 0000000000..798b669887
--- /dev/null
+++ b/ecc/bls24-315/fp/vector_purego.go
@@ -0,0 +1,54 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fp
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	addVecGeneric(*vector, a, b)
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	subVecGeneric(*vector, a, b)
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
diff --git a/ecc/bls24-315/fr/arith.go b/ecc/bls24-315/fr/arith.go
index 7cfd55da19..83c9fd9ef9 100644
--- a/ecc/bls24-315/fr/arith.go
+++ b/ecc/bls24-315/fr/arith.go
@@ -58,16 +58,3 @@ func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) {
 	hi, _ = bits.Add64(hi, e, carry)
 	return
 }
-func max(a int, b int) int {
-	if a > b {
-		return a
-	}
-	return b
-}
-
-func min(a int, b int) int {
-	if a < b {
-		return a
-	}
-	return b
-}
diff --git a/ecc/bls24-315/fr/asm_adx.go b/ecc/bls24-315/fr/asm_adx.go
index da061913ba..9273ea23ab 100644
--- a/ecc/bls24-315/fr/asm_adx.go
+++ b/ecc/bls24-315/fr/asm_adx.go
@@ -1,5 +1,4 @@
 //go:build !noadx
-// +build !noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls24-315/fr/asm_avx.go b/ecc/bls24-315/fr/asm_avx.go
index 955f559799..1cc06c6e8d 100644
--- a/ecc/bls24-315/fr/asm_avx.go
+++ b/ecc/bls24-315/fr/asm_avx.go
@@ -1,5 +1,4 @@
 //go:build !noavx
-// +build !noavx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls24-315/fr/asm_noadx.go b/ecc/bls24-315/fr/asm_noadx.go
index 7f52ffa197..b784a24247 100644
--- a/ecc/bls24-315/fr/asm_noadx.go
+++ b/ecc/bls24-315/fr/asm_noadx.go
@@ -1,5 +1,4 @@
 //go:build noadx
-// +build noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls24-315/fr/asm_noavx.go b/ecc/bls24-315/fr/asm_noavx.go
index e5a5b1f2cc..66bfc00772 100644
--- a/ecc/bls24-315/fr/asm_noavx.go
+++ b/ecc/bls24-315/fr/asm_noavx.go
@@ -1,5 +1,4 @@
 //go:build noavx
-// +build noavx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls24-315/fr/element_amd64.go b/ecc/bls24-315/fr/element_amd64.go
new file mode 100644
index 0000000000..0ddb905f7b
--- /dev/null
+++ b/ecc/bls24-315/fr/element_amd64.go
@@ -0,0 +1,66 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+//go:noescape
+func MulBy3(x *Element)
+
+//go:noescape
+func MulBy5(x *Element)
+
+//go:noescape
+func MulBy13(x *Element)
+
+//go:noescape
+func mul(res, x, y *Element)
+
+//go:noescape
+func fromMont(res *Element)
+
+//go:noescape
+func reduce(res *Element)
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+//
+//go:noescape
+func Butterfly(a, b *Element)
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+
+	mul(z, x, y)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for doc.
+	mul(z, x, x)
+	return z
+}
diff --git a/ecc/bls24-315/fr/element_amd64.s b/ecc/bls24-315/fr/element_amd64.s
new file mode 100644
index 0000000000..fb00194d7e
--- /dev/null
+++ b/ecc/bls24-315/fr/element_amd64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 9425145785761608449
+#include "../../../field/asm/element_4w_amd64.s"
+
diff --git a/ecc/bls24-315/fr/element_arm64.go b/ecc/bls24-315/fr/element_arm64.go
new file mode 100644
index 0000000000..cdf726a8eb
--- /dev/null
+++ b/ecc/bls24-315/fr/element_arm64.go
@@ -0,0 +1,77 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+//
+//go:noescape
+func Butterfly(a, b *Element)
+
+//go:noescape
+func mul(res, x, y *Element)
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+	mul(z, x, y)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for doc.
+	mul(z, x, x)
+	return z
+}
+
+// MulBy3 x *= 3 (mod q)
+func MulBy3(x *Element) {
+	_x := *x
+	x.Double(x).Add(x, &_x)
+}
+
+// MulBy5 x *= 5 (mod q)
+func MulBy5(x *Element) {
+	_x := *x
+	x.Double(x).Double(x).Add(x, &_x)
+}
+
+// MulBy13 x *= 13 (mod q)
+func MulBy13(x *Element) {
+	var y = Element{
+		16427853282514304894,
+		880039980351915818,
+		13098611234035318378,
+		1598436289436461078,
+	}
+	x.Mul(x, &y)
+}
+
+func fromMont(z *Element) {
+	_fromMontGeneric(z)
+}
+
+//go:noescape
+func reduce(res *Element)
diff --git a/ecc/bls24-315/fr/element_arm64.s b/ecc/bls24-315/fr/element_arm64.s
new file mode 100644
index 0000000000..5d328815aa
--- /dev/null
+++ b/ecc/bls24-315/fr/element_arm64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 1501560133179981797
+#include "../../../field/asm/element_4w_arm64.s"
+
diff --git a/ecc/bls24-315/fr/element_ops_amd64.s b/ecc/bls24-315/fr/element_ops_amd64.s
deleted file mode 100644
index 6c42136a7a..0000000000
--- a/ecc/bls24-315/fr/element_ops_amd64.s
+++ /dev/null
@@ -1,6 +0,0 @@
-// +build !purego
-
-// Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 9425145785761608449
-#include "../../../field/asm/element_4w_amd64.s"
-
diff --git a/ecc/bls24-315/fr/element_ops_purego.go b/ecc/bls24-315/fr/element_purego.go
similarity index 88%
rename from ecc/bls24-315/fr/element_ops_purego.go
rename to ecc/bls24-315/fr/element_purego.go
index e7a8817f01..a93f64f06e 100644
--- a/ecc/bls24-315/fr/element_ops_purego.go
+++ b/ecc/bls24-315/fr/element_purego.go
@@ -1,5 +1,4 @@
-//go:build !amd64 || purego
-// +build !amd64 purego
+//go:build purego || (!amd64 && !arm64)
 
 // Copyright 2020 ConsenSys Software Inc.
 //
@@ -44,14 +43,6 @@ func MulBy13(x *Element) {
 	x.Mul(x, &y)
 }
 
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-func Butterfly(a, b *Element) {
-	_butterflyGeneric(a, b)
-}
-
 func fromMont(z *Element) {
 	_fromMontGeneric(z)
 }
@@ -60,43 +51,6 @@ func reduce(z *Element) {
 	_reduceGeneric(z)
 }
 
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	addVecGeneric(*vector, a, b)
-}
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	subVecGeneric(*vector, a, b)
-}
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *Element) {
-	scalarMulVecGeneric(*vector, a, b)
-}
-
-// Sum computes the sum of all elements in the vector.
-func (vector *Vector) Sum() (res Element) {
-	sumVecGeneric(&res, *vector)
-	return
-}
-
-// InnerProduct computes the inner product of two vectors.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) InnerProduct(other Vector) (res Element) {
-	innerProductVecGeneric(&res, *vector, other)
-	return
-}
-
-// Mul multiplies two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Mul(a, b Vector) {
-	mulVecGeneric(*vector, a, b)
-}
-
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
@@ -438,3 +392,11 @@ func (z *Element) Square(x *Element) *Element {
 	}
 	return z
 }
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
diff --git a/ecc/bls24-317/fr/element_ops_amd64.go b/ecc/bls24-315/fr/vector_amd64.go
similarity index 84%
rename from ecc/bls24-317/fr/element_ops_amd64.go
rename to ecc/bls24-315/fr/vector_amd64.go
index b653e80069..0164ecb382 100644
--- a/ecc/bls24-317/fr/element_ops_amd64.go
+++ b/ecc/bls24-315/fr/vector_amd64.go
@@ -1,5 +1,4 @@
 //go:build !purego
-// +build !purego
 
 // Copyright 2020 ConsenSys Software Inc.
 //
@@ -19,32 +18,6 @@
 
 package fr
 
-//go:noescape
-func MulBy3(x *Element)
-
-//go:noescape
-func MulBy5(x *Element)
-
-//go:noescape
-func MulBy13(x *Element)
-
-//go:noescape
-func mul(res, x, y *Element)
-
-//go:noescape
-func fromMont(res *Element)
-
-//go:noescape
-func reduce(res *Element)
-
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-//
-//go:noescape
-func Butterfly(a, b *Element)
-
 // Add adds two vectors element-wise and stores the result in self.
 // It panics if the vectors don't have the same length.
 func (vector *Vector) Add(a, b Vector) {
@@ -185,24 +158,3 @@ var (
 
 //go:noescape
 func mulVec(res, a, b *Element, n uint64, qInvNeg uint64)
-
-// Mul z = x * y (mod q)
-//
-// x and y must be less than q
-func (z *Element) Mul(x, y *Element) *Element {
-
-	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
-	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
-
-	mul(z, x, y)
-	return z
-}
-
-// Square z = x * x (mod q)
-//
-// x must be less than q
-func (z *Element) Square(x *Element) *Element {
-	// see Mul for doc.
-	mul(z, x, x)
-	return z
-}
diff --git a/ecc/bls24-315/fr/vector_purego.go b/ecc/bls24-315/fr/vector_purego.go
new file mode 100644
index 0000000000..84f86a40b1
--- /dev/null
+++ b/ecc/bls24-315/fr/vector_purego.go
@@ -0,0 +1,56 @@
+//go:build purego || !amd64
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	addVecGeneric(*vector, a, b)
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	subVecGeneric(*vector, a, b)
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
diff --git a/ecc/bls24-317/fp/arith.go b/ecc/bls24-317/fp/arith.go
index 6f281563b3..66fa667482 100644
--- a/ecc/bls24-317/fp/arith.go
+++ b/ecc/bls24-317/fp/arith.go
@@ -58,16 +58,3 @@ func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) {
 	hi, _ = bits.Add64(hi, e, carry)
 	return
 }
-func max(a int, b int) int {
-	if a > b {
-		return a
-	}
-	return b
-}
-
-func min(a int, b int) int {
-	if a < b {
-		return a
-	}
-	return b
-}
diff --git a/ecc/bls24-317/fp/asm_adx.go b/ecc/bls24-317/fp/asm_adx.go
index 0481989ec6..f8e29bd1a7 100644
--- a/ecc/bls24-317/fp/asm_adx.go
+++ b/ecc/bls24-317/fp/asm_adx.go
@@ -1,5 +1,4 @@
 //go:build !noadx
-// +build !noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls24-317/fp/asm_noadx.go b/ecc/bls24-317/fp/asm_noadx.go
index 92f8cc0f42..cb6cfa0f50 100644
--- a/ecc/bls24-317/fp/asm_noadx.go
+++ b/ecc/bls24-317/fp/asm_noadx.go
@@ -1,5 +1,4 @@
 //go:build noadx
-// +build noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls24-317/fp/element_ops_amd64.go b/ecc/bls24-317/fp/element_amd64.go
similarity index 98%
rename from ecc/bls24-317/fp/element_ops_amd64.go
rename to ecc/bls24-317/fp/element_amd64.go
index ed2803d717..77a51ee25e 100644
--- a/ecc/bls24-317/fp/element_ops_amd64.go
+++ b/ecc/bls24-317/fp/element_amd64.go
@@ -1,5 +1,4 @@
 //go:build !purego
-// +build !purego
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls24-317/fp/element_amd64.s b/ecc/bls24-317/fp/element_amd64.s
new file mode 100644
index 0000000000..00858d648e
--- /dev/null
+++ b/ecc/bls24-317/fp/element_amd64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 18184981773209750009
+#include "../../../field/asm/element_5w_amd64.s"
+
diff --git a/ecc/bls24-317/fp/element_ops_amd64.s b/ecc/bls24-317/fp/element_ops_amd64.s
deleted file mode 100644
index 29314843d7..0000000000
--- a/ecc/bls24-317/fp/element_ops_amd64.s
+++ /dev/null
@@ -1,6 +0,0 @@
-// +build !purego
-
-// Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 18184981773209750009
-#include "../../../field/asm/element_5w_amd64.s"
-
diff --git a/ecc/bls24-317/fp/element_ops_purego.go b/ecc/bls24-317/fp/element_purego.go
similarity index 99%
rename from ecc/bls24-317/fp/element_ops_purego.go
rename to ecc/bls24-317/fp/element_purego.go
index 9f72e6f84b..0f21692f40 100644
--- a/ecc/bls24-317/fp/element_ops_purego.go
+++ b/ecc/bls24-317/fp/element_purego.go
@@ -1,5 +1,4 @@
-//go:build !amd64 || purego
-// +build !amd64 purego
+//go:build purego || !amd64
 
 // Copyright 2020 ConsenSys Software Inc.
 //
@@ -45,14 +44,6 @@ func MulBy13(x *Element) {
 	x.Mul(x, &y)
 }
 
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-func Butterfly(a, b *Element) {
-	_butterflyGeneric(a, b)
-}
-
 func fromMont(z *Element) {
 	_fromMontGeneric(z)
 }
@@ -540,3 +531,11 @@ func (z *Element) Square(x *Element) *Element {
 	}
 	return z
 }
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
diff --git a/ecc/bls24-317/fp/vector.go b/ecc/bls24-317/fp/vector.go
index ce61e70ea0..5d7cd31fe6 100644
--- a/ecc/bls24-317/fp/vector.go
+++ b/ecc/bls24-317/fp/vector.go
@@ -200,43 +200,6 @@ func (vector Vector) Swap(i, j int) {
 	vector[i], vector[j] = vector[j], vector[i]
 }
 
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	addVecGeneric(*vector, a, b)
-}
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	subVecGeneric(*vector, a, b)
-}
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *Element) {
-	scalarMulVecGeneric(*vector, a, b)
-}
-
-// Sum computes the sum of all elements in the vector.
-func (vector *Vector) Sum() (res Element) {
-	sumVecGeneric(&res, *vector)
-	return
-}
-
-// InnerProduct computes the inner product of two vectors.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) InnerProduct(other Vector) (res Element) {
-	innerProductVecGeneric(&res, *vector, other)
-	return
-}
-
-// Mul multiplies two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Mul(a, b Vector) {
-	mulVecGeneric(*vector, a, b)
-}
-
 func addVecGeneric(res, a, b Vector) {
 	if len(a) != len(b) || len(a) != len(res) {
 		panic("vector.Add: vectors don't have the same length")
diff --git a/ecc/bls24-317/fp/vector_purego.go b/ecc/bls24-317/fp/vector_purego.go
new file mode 100644
index 0000000000..798b669887
--- /dev/null
+++ b/ecc/bls24-317/fp/vector_purego.go
@@ -0,0 +1,54 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fp
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	addVecGeneric(*vector, a, b)
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	subVecGeneric(*vector, a, b)
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
diff --git a/ecc/bls24-317/fr/arith.go b/ecc/bls24-317/fr/arith.go
index 7cfd55da19..83c9fd9ef9 100644
--- a/ecc/bls24-317/fr/arith.go
+++ b/ecc/bls24-317/fr/arith.go
@@ -58,16 +58,3 @@ func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) {
 	hi, _ = bits.Add64(hi, e, carry)
 	return
 }
-func max(a int, b int) int {
-	if a > b {
-		return a
-	}
-	return b
-}
-
-func min(a int, b int) int {
-	if a < b {
-		return a
-	}
-	return b
-}
diff --git a/ecc/bls24-317/fr/asm_adx.go b/ecc/bls24-317/fr/asm_adx.go
index da061913ba..9273ea23ab 100644
--- a/ecc/bls24-317/fr/asm_adx.go
+++ b/ecc/bls24-317/fr/asm_adx.go
@@ -1,5 +1,4 @@
 //go:build !noadx
-// +build !noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls24-317/fr/asm_avx.go b/ecc/bls24-317/fr/asm_avx.go
index 955f559799..1cc06c6e8d 100644
--- a/ecc/bls24-317/fr/asm_avx.go
+++ b/ecc/bls24-317/fr/asm_avx.go
@@ -1,5 +1,4 @@
 //go:build !noavx
-// +build !noavx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls24-317/fr/asm_noadx.go b/ecc/bls24-317/fr/asm_noadx.go
index 7f52ffa197..b784a24247 100644
--- a/ecc/bls24-317/fr/asm_noadx.go
+++ b/ecc/bls24-317/fr/asm_noadx.go
@@ -1,5 +1,4 @@
 //go:build noadx
-// +build noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls24-317/fr/asm_noavx.go b/ecc/bls24-317/fr/asm_noavx.go
index e5a5b1f2cc..66bfc00772 100644
--- a/ecc/bls24-317/fr/asm_noavx.go
+++ b/ecc/bls24-317/fr/asm_noavx.go
@@ -1,5 +1,4 @@
 //go:build noavx
-// +build noavx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bls24-317/fr/element_amd64.go b/ecc/bls24-317/fr/element_amd64.go
new file mode 100644
index 0000000000..0ddb905f7b
--- /dev/null
+++ b/ecc/bls24-317/fr/element_amd64.go
@@ -0,0 +1,66 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+//go:noescape
+func MulBy3(x *Element)
+
+//go:noescape
+func MulBy5(x *Element)
+
+//go:noescape
+func MulBy13(x *Element)
+
+//go:noescape
+func mul(res, x, y *Element)
+
+//go:noescape
+func fromMont(res *Element)
+
+//go:noescape
+func reduce(res *Element)
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+//
+//go:noescape
+func Butterfly(a, b *Element)
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+
+	mul(z, x, y)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for doc.
+	mul(z, x, x)
+	return z
+}
diff --git a/ecc/bls24-317/fr/element_amd64.s b/ecc/bls24-317/fr/element_amd64.s
new file mode 100644
index 0000000000..fb00194d7e
--- /dev/null
+++ b/ecc/bls24-317/fr/element_amd64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 9425145785761608449
+#include "../../../field/asm/element_4w_amd64.s"
+
diff --git a/ecc/bls24-317/fr/element_arm64.go b/ecc/bls24-317/fr/element_arm64.go
new file mode 100644
index 0000000000..7a483d1551
--- /dev/null
+++ b/ecc/bls24-317/fr/element_arm64.go
@@ -0,0 +1,77 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+//
+//go:noescape
+func Butterfly(a, b *Element)
+
+//go:noescape
+func mul(res, x, y *Element)
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+	mul(z, x, y)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for doc.
+	mul(z, x, x)
+	return z
+}
+
+// MulBy3 x *= 3 (mod q)
+func MulBy3(x *Element) {
+	_x := *x
+	x.Double(x).Add(x, &_x)
+}
+
+// MulBy5 x *= 5 (mod q)
+func MulBy5(x *Element) {
+	_x := *x
+	x.Double(x).Double(x).Add(x, &_x)
+}
+
+// MulBy13 x *= 13 (mod q)
+func MulBy13(x *Element) {
+	var y = Element{
+		18446744073709551568,
+		10999079689622735090,
+		16060824205876888138,
+		3752826977836272504,
+	}
+	x.Mul(x, &y)
+}
+
+func fromMont(z *Element) {
+	_fromMontGeneric(z)
+}
+
+//go:noescape
+func reduce(res *Element)
diff --git a/ecc/bls24-317/fr/element_arm64.s b/ecc/bls24-317/fr/element_arm64.s
new file mode 100644
index 0000000000..5d328815aa
--- /dev/null
+++ b/ecc/bls24-317/fr/element_arm64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 1501560133179981797
+#include "../../../field/asm/element_4w_arm64.s"
+
diff --git a/ecc/bls24-317/fr/element_ops_amd64.s b/ecc/bls24-317/fr/element_ops_amd64.s
deleted file mode 100644
index 6c42136a7a..0000000000
--- a/ecc/bls24-317/fr/element_ops_amd64.s
+++ /dev/null
@@ -1,6 +0,0 @@
-// +build !purego
-
-// Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 9425145785761608449
-#include "../../../field/asm/element_4w_amd64.s"
-
diff --git a/ecc/bls24-317/fr/element_ops_purego.go b/ecc/bls24-317/fr/element_purego.go
similarity index 88%
rename from ecc/bls24-317/fr/element_ops_purego.go
rename to ecc/bls24-317/fr/element_purego.go
index 7afd9cc8df..c9b8bd4616 100644
--- a/ecc/bls24-317/fr/element_ops_purego.go
+++ b/ecc/bls24-317/fr/element_purego.go
@@ -1,5 +1,4 @@
-//go:build !amd64 || purego
-// +build !amd64 purego
+//go:build purego || (!amd64 && !arm64)
 
 // Copyright 2020 ConsenSys Software Inc.
 //
@@ -44,14 +43,6 @@ func MulBy13(x *Element) {
 	x.Mul(x, &y)
 }
 
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-func Butterfly(a, b *Element) {
-	_butterflyGeneric(a, b)
-}
-
 func fromMont(z *Element) {
 	_fromMontGeneric(z)
 }
@@ -60,43 +51,6 @@ func reduce(z *Element) {
 	_reduceGeneric(z)
 }
 
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	addVecGeneric(*vector, a, b)
-}
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	subVecGeneric(*vector, a, b)
-}
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *Element) {
-	scalarMulVecGeneric(*vector, a, b)
-}
-
-// Sum computes the sum of all elements in the vector.
-func (vector *Vector) Sum() (res Element) {
-	sumVecGeneric(&res, *vector)
-	return
-}
-
-// InnerProduct computes the inner product of two vectors.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) InnerProduct(other Vector) (res Element) {
-	innerProductVecGeneric(&res, *vector, other)
-	return
-}
-
-// Mul multiplies two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Mul(a, b Vector) {
-	mulVecGeneric(*vector, a, b)
-}
-
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
@@ -438,3 +392,11 @@ func (z *Element) Square(x *Element) *Element {
 	}
 	return z
 }
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
diff --git a/ecc/bls12-377/fr/element_ops_amd64.go b/ecc/bls24-317/fr/vector_amd64.go
similarity index 84%
rename from ecc/bls12-377/fr/element_ops_amd64.go
rename to ecc/bls24-317/fr/vector_amd64.go
index b653e80069..0164ecb382 100644
--- a/ecc/bls12-377/fr/element_ops_amd64.go
+++ b/ecc/bls24-317/fr/vector_amd64.go
@@ -1,5 +1,4 @@
 //go:build !purego
-// +build !purego
 
 // Copyright 2020 ConsenSys Software Inc.
 //
@@ -19,32 +18,6 @@
 
 package fr
 
-//go:noescape
-func MulBy3(x *Element)
-
-//go:noescape
-func MulBy5(x *Element)
-
-//go:noescape
-func MulBy13(x *Element)
-
-//go:noescape
-func mul(res, x, y *Element)
-
-//go:noescape
-func fromMont(res *Element)
-
-//go:noescape
-func reduce(res *Element)
-
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-//
-//go:noescape
-func Butterfly(a, b *Element)
-
 // Add adds two vectors element-wise and stores the result in self.
 // It panics if the vectors don't have the same length.
 func (vector *Vector) Add(a, b Vector) {
@@ -185,24 +158,3 @@ var (
 
 //go:noescape
 func mulVec(res, a, b *Element, n uint64, qInvNeg uint64)
-
-// Mul z = x * y (mod q)
-//
-// x and y must be less than q
-func (z *Element) Mul(x, y *Element) *Element {
-
-	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
-	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
-
-	mul(z, x, y)
-	return z
-}
-
-// Square z = x * x (mod q)
-//
-// x must be less than q
-func (z *Element) Square(x *Element) *Element {
-	// see Mul for doc.
-	mul(z, x, x)
-	return z
-}
diff --git a/ecc/bls24-317/fr/vector_purego.go b/ecc/bls24-317/fr/vector_purego.go
new file mode 100644
index 0000000000..84f86a40b1
--- /dev/null
+++ b/ecc/bls24-317/fr/vector_purego.go
@@ -0,0 +1,56 @@
+//go:build purego || !amd64
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	addVecGeneric(*vector, a, b)
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	subVecGeneric(*vector, a, b)
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
diff --git a/ecc/bn254/fp/arith.go b/ecc/bn254/fp/arith.go
index 6f281563b3..66fa667482 100644
--- a/ecc/bn254/fp/arith.go
+++ b/ecc/bn254/fp/arith.go
@@ -58,16 +58,3 @@ func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) {
 	hi, _ = bits.Add64(hi, e, carry)
 	return
 }
-func max(a int, b int) int {
-	if a > b {
-		return a
-	}
-	return b
-}
-
-func min(a int, b int) int {
-	if a < b {
-		return a
-	}
-	return b
-}
diff --git a/ecc/bn254/fp/asm_adx.go b/ecc/bn254/fp/asm_adx.go
index 0481989ec6..f8e29bd1a7 100644
--- a/ecc/bn254/fp/asm_adx.go
+++ b/ecc/bn254/fp/asm_adx.go
@@ -1,5 +1,4 @@
 //go:build !noadx
-// +build !noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bn254/fp/asm_avx.go b/ecc/bn254/fp/asm_avx.go
index cea035ee84..52fc07a325 100644
--- a/ecc/bn254/fp/asm_avx.go
+++ b/ecc/bn254/fp/asm_avx.go
@@ -1,5 +1,4 @@
 //go:build !noavx
-// +build !noavx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bn254/fp/asm_noadx.go b/ecc/bn254/fp/asm_noadx.go
index 92f8cc0f42..cb6cfa0f50 100644
--- a/ecc/bn254/fp/asm_noadx.go
+++ b/ecc/bn254/fp/asm_noadx.go
@@ -1,5 +1,4 @@
 //go:build noadx
-// +build noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bn254/fp/asm_noavx.go b/ecc/bn254/fp/asm_noavx.go
index 9ca08a375a..12261b1f03 100644
--- a/ecc/bn254/fp/asm_noavx.go
+++ b/ecc/bn254/fp/asm_noavx.go
@@ -1,5 +1,4 @@
 //go:build noavx
-// +build noavx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bn254/fp/element_amd64.go b/ecc/bn254/fp/element_amd64.go
new file mode 100644
index 0000000000..77a51ee25e
--- /dev/null
+++ b/ecc/bn254/fp/element_amd64.go
@@ -0,0 +1,66 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fp
+
+//go:noescape
+func MulBy3(x *Element)
+
+//go:noescape
+func MulBy5(x *Element)
+
+//go:noescape
+func MulBy13(x *Element)
+
+//go:noescape
+func mul(res, x, y *Element)
+
+//go:noescape
+func fromMont(res *Element)
+
+//go:noescape
+func reduce(res *Element)
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+//
+//go:noescape
+func Butterfly(a, b *Element)
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+
+	mul(z, x, y)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for doc.
+	mul(z, x, x)
+	return z
+}
diff --git a/ecc/bn254/fp/element_amd64.s b/ecc/bn254/fp/element_amd64.s
new file mode 100644
index 0000000000..fb00194d7e
--- /dev/null
+++ b/ecc/bn254/fp/element_amd64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 9425145785761608449
+#include "../../../field/asm/element_4w_amd64.s"
+
diff --git a/ecc/bn254/fp/element_arm64.go b/ecc/bn254/fp/element_arm64.go
new file mode 100644
index 0000000000..dfb583df86
--- /dev/null
+++ b/ecc/bn254/fp/element_arm64.go
@@ -0,0 +1,77 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fp
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+//
+//go:noescape
+func Butterfly(a, b *Element)
+
+//go:noescape
+func mul(res, x, y *Element)
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+	mul(z, x, y)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for doc.
+	mul(z, x, x)
+	return z
+}
+
+// MulBy3 x *= 3 (mod q)
+func MulBy3(x *Element) {
+	_x := *x
+	x.Double(x).Add(x, &_x)
+}
+
+// MulBy5 x *= 5 (mod q)
+func MulBy5(x *Element) {
+	_x := *x
+	x.Double(x).Double(x).Add(x, &_x)
+}
+
+// MulBy13 x *= 13 (mod q)
+func MulBy13(x *Element) {
+	var y = Element{
+		529957932336199972,
+		13952065197595570812,
+		769406925088786211,
+		2691790815622165739,
+	}
+	x.Mul(x, &y)
+}
+
+func fromMont(z *Element) {
+	_fromMontGeneric(z)
+}
+
+//go:noescape
+func reduce(res *Element)
diff --git a/ecc/bn254/fp/element_arm64.s b/ecc/bn254/fp/element_arm64.s
new file mode 100644
index 0000000000..5d328815aa
--- /dev/null
+++ b/ecc/bn254/fp/element_arm64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 1501560133179981797
+#include "../../../field/asm/element_4w_arm64.s"
+
diff --git a/ecc/bn254/fp/element_ops_amd64.s b/ecc/bn254/fp/element_ops_amd64.s
deleted file mode 100644
index 6c42136a7a..0000000000
--- a/ecc/bn254/fp/element_ops_amd64.s
+++ /dev/null
@@ -1,6 +0,0 @@
-// +build !purego
-
-// Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 9425145785761608449
-#include "../../../field/asm/element_4w_amd64.s"
-
diff --git a/ecc/bn254/fp/element_ops_purego.go b/ecc/bn254/fp/element_purego.go
similarity index 88%
rename from ecc/bn254/fp/element_ops_purego.go
rename to ecc/bn254/fp/element_purego.go
index 454376da57..ded61b6088 100644
--- a/ecc/bn254/fp/element_ops_purego.go
+++ b/ecc/bn254/fp/element_purego.go
@@ -1,5 +1,4 @@
-//go:build !amd64 || purego
-// +build !amd64 purego
+//go:build purego || (!amd64 && !arm64)
 
 // Copyright 2020 ConsenSys Software Inc.
 //
@@ -44,14 +43,6 @@ func MulBy13(x *Element) {
 	x.Mul(x, &y)
 }
 
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-func Butterfly(a, b *Element) {
-	_butterflyGeneric(a, b)
-}
-
 func fromMont(z *Element) {
 	_fromMontGeneric(z)
 }
@@ -60,43 +51,6 @@ func reduce(z *Element) {
 	_reduceGeneric(z)
 }
 
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	addVecGeneric(*vector, a, b)
-}
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	subVecGeneric(*vector, a, b)
-}
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *Element) {
-	scalarMulVecGeneric(*vector, a, b)
-}
-
-// Sum computes the sum of all elements in the vector.
-func (vector *Vector) Sum() (res Element) {
-	sumVecGeneric(&res, *vector)
-	return
-}
-
-// InnerProduct computes the inner product of two vectors.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) InnerProduct(other Vector) (res Element) {
-	innerProductVecGeneric(&res, *vector, other)
-	return
-}
-
-// Mul multiplies two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Mul(a, b Vector) {
-	mulVecGeneric(*vector, a, b)
-}
-
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
@@ -438,3 +392,11 @@ func (z *Element) Square(x *Element) *Element {
 	}
 	return z
 }
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
diff --git a/ecc/bn254/fp/element_ops_amd64.go b/ecc/bn254/fp/vector_amd64.go
similarity index 84%
rename from ecc/bn254/fp/element_ops_amd64.go
rename to ecc/bn254/fp/vector_amd64.go
index 2ab1a98399..75719deedb 100644
--- a/ecc/bn254/fp/element_ops_amd64.go
+++ b/ecc/bn254/fp/vector_amd64.go
@@ -1,5 +1,4 @@
 //go:build !purego
-// +build !purego
 
 // Copyright 2020 ConsenSys Software Inc.
 //
@@ -19,32 +18,6 @@
 
 package fp
 
-//go:noescape
-func MulBy3(x *Element)
-
-//go:noescape
-func MulBy5(x *Element)
-
-//go:noescape
-func MulBy13(x *Element)
-
-//go:noescape
-func mul(res, x, y *Element)
-
-//go:noescape
-func fromMont(res *Element)
-
-//go:noescape
-func reduce(res *Element)
-
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-//
-//go:noescape
-func Butterfly(a, b *Element)
-
 // Add adds two vectors element-wise and stores the result in self.
 // It panics if the vectors don't have the same length.
 func (vector *Vector) Add(a, b Vector) {
@@ -185,24 +158,3 @@ var (
 
 //go:noescape
 func mulVec(res, a, b *Element, n uint64, qInvNeg uint64)
-
-// Mul z = x * y (mod q)
-//
-// x and y must be less than q
-func (z *Element) Mul(x, y *Element) *Element {
-
-	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
-	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
-
-	mul(z, x, y)
-	return z
-}
-
-// Square z = x * x (mod q)
-//
-// x must be less than q
-func (z *Element) Square(x *Element) *Element {
-	// see Mul for doc.
-	mul(z, x, x)
-	return z
-}
diff --git a/ecc/bn254/fp/vector_purego.go b/ecc/bn254/fp/vector_purego.go
new file mode 100644
index 0000000000..fc0f66e2a3
--- /dev/null
+++ b/ecc/bn254/fp/vector_purego.go
@@ -0,0 +1,56 @@
+//go:build purego || !amd64
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fp
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	addVecGeneric(*vector, a, b)
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	subVecGeneric(*vector, a, b)
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
diff --git a/ecc/bn254/fr/arith.go b/ecc/bn254/fr/arith.go
index 7cfd55da19..83c9fd9ef9 100644
--- a/ecc/bn254/fr/arith.go
+++ b/ecc/bn254/fr/arith.go
@@ -58,16 +58,3 @@ func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) {
 	hi, _ = bits.Add64(hi, e, carry)
 	return
 }
-func max(a int, b int) int {
-	if a > b {
-		return a
-	}
-	return b
-}
-
-func min(a int, b int) int {
-	if a < b {
-		return a
-	}
-	return b
-}
diff --git a/ecc/bn254/fr/asm_adx.go b/ecc/bn254/fr/asm_adx.go
index da061913ba..9273ea23ab 100644
--- a/ecc/bn254/fr/asm_adx.go
+++ b/ecc/bn254/fr/asm_adx.go
@@ -1,5 +1,4 @@
 //go:build !noadx
-// +build !noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bn254/fr/asm_avx.go b/ecc/bn254/fr/asm_avx.go
index 955f559799..1cc06c6e8d 100644
--- a/ecc/bn254/fr/asm_avx.go
+++ b/ecc/bn254/fr/asm_avx.go
@@ -1,5 +1,4 @@
 //go:build !noavx
-// +build !noavx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bn254/fr/asm_noadx.go b/ecc/bn254/fr/asm_noadx.go
index 7f52ffa197..b784a24247 100644
--- a/ecc/bn254/fr/asm_noadx.go
+++ b/ecc/bn254/fr/asm_noadx.go
@@ -1,5 +1,4 @@
 //go:build noadx
-// +build noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bn254/fr/asm_noavx.go b/ecc/bn254/fr/asm_noavx.go
index e5a5b1f2cc..66bfc00772 100644
--- a/ecc/bn254/fr/asm_noavx.go
+++ b/ecc/bn254/fr/asm_noavx.go
@@ -1,5 +1,4 @@
 //go:build noavx
-// +build noavx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bn254/fr/element_amd64.go b/ecc/bn254/fr/element_amd64.go
new file mode 100644
index 0000000000..0ddb905f7b
--- /dev/null
+++ b/ecc/bn254/fr/element_amd64.go
@@ -0,0 +1,66 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+//go:noescape
+func MulBy3(x *Element)
+
+//go:noescape
+func MulBy5(x *Element)
+
+//go:noescape
+func MulBy13(x *Element)
+
+//go:noescape
+func mul(res, x, y *Element)
+
+//go:noescape
+func fromMont(res *Element)
+
+//go:noescape
+func reduce(res *Element)
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+//
+//go:noescape
+func Butterfly(a, b *Element)
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+
+	mul(z, x, y)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for doc.
+	mul(z, x, x)
+	return z
+}
diff --git a/ecc/bn254/fr/element_amd64.s b/ecc/bn254/fr/element_amd64.s
new file mode 100644
index 0000000000..fb00194d7e
--- /dev/null
+++ b/ecc/bn254/fr/element_amd64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 9425145785761608449
+#include "../../../field/asm/element_4w_amd64.s"
+
diff --git a/ecc/bn254/fr/element_arm64.go b/ecc/bn254/fr/element_arm64.go
new file mode 100644
index 0000000000..8b28f5123b
--- /dev/null
+++ b/ecc/bn254/fr/element_arm64.go
@@ -0,0 +1,77 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+//
+//go:noescape
+func Butterfly(a, b *Element)
+
+//go:noescape
+func mul(res, x, y *Element)
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+	mul(z, x, y)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for doc.
+	mul(z, x, x)
+	return z
+}
+
+// MulBy3 x *= 3 (mod q)
+func MulBy3(x *Element) {
+	_x := *x
+	x.Double(x).Add(x, &_x)
+}
+
+// MulBy5 x *= 5 (mod q)
+func MulBy5(x *Element) {
+	_x := *x
+	x.Double(x).Double(x).Add(x, &_x)
+}
+
+// MulBy13 x *= 13 (mod q)
+func MulBy13(x *Element) {
+	var y = Element{
+		17868810749992763324,
+		5924006745939515753,
+		769406925088786241,
+		2691790815622165739,
+	}
+	x.Mul(x, &y)
+}
+
+func fromMont(z *Element) {
+	_fromMontGeneric(z)
+}
+
+//go:noescape
+func reduce(res *Element)
diff --git a/ecc/bn254/fr/element_arm64.s b/ecc/bn254/fr/element_arm64.s
new file mode 100644
index 0000000000..5d328815aa
--- /dev/null
+++ b/ecc/bn254/fr/element_arm64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 1501560133179981797
+#include "../../../field/asm/element_4w_arm64.s"
+
diff --git a/ecc/bn254/fr/element_ops_amd64.go b/ecc/bn254/fr/element_ops_amd64.go
deleted file mode 100644
index b653e80069..0000000000
--- a/ecc/bn254/fr/element_ops_amd64.go
+++ /dev/null
@@ -1,208 +0,0 @@
-//go:build !purego
-// +build !purego
-
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-// Code generated by consensys/gnark-crypto DO NOT EDIT
-
-package fr
-
-//go:noescape
-func MulBy3(x *Element)
-
-//go:noescape
-func MulBy5(x *Element)
-
-//go:noescape
-func MulBy13(x *Element)
-
-//go:noescape
-func mul(res, x, y *Element)
-
-//go:noescape
-func fromMont(res *Element)
-
-//go:noescape
-func reduce(res *Element)
-
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-//
-//go:noescape
-func Butterfly(a, b *Element)
-
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	if len(a) != len(b) || len(a) != len(*vector) {
-		panic("vector.Add: vectors don't have the same length")
-	}
-	n := uint64(len(a))
-	addVec(&(*vector)[0], &a[0], &b[0], n)
-}
-
-//go:noescape
-func addVec(res, a, b *Element, n uint64)
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	if len(a) != len(b) || len(a) != len(*vector) {
-		panic("vector.Sub: vectors don't have the same length")
-	}
-	subVec(&(*vector)[0], &a[0], &b[0], uint64(len(a)))
-}
-
-//go:noescape
-func subVec(res, a, b *Element, n uint64)
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *Element) {
-	if len(a) != len(*vector) {
-		panic("vector.ScalarMul: vectors don't have the same length")
-	}
-	const maxN = (1 << 32) - 1
-	if !supportAvx512 || uint64(len(a)) >= maxN {
-		// call scalarMulVecGeneric
-		scalarMulVecGeneric(*vector, a, b)
-		return
-	}
-	n := uint64(len(a))
-	if n == 0 {
-		return
-	}
-	// the code for scalarMul is identical to mulVec; and it expects at least
-	// 2 elements in the vector to fill the Z registers
-	var bb [2]Element
-	bb[0] = *b
-	bb[1] = *b
-	const blockSize = 16
-	scalarMulVec(&(*vector)[0], &a[0], &bb[0], n/blockSize, qInvNeg)
-	if n%blockSize != 0 {
-		// call scalarMulVecGeneric on the rest
-		start := n - n%blockSize
-		scalarMulVecGeneric((*vector)[start:], a[start:], b)
-	}
-}
-
-//go:noescape
-func scalarMulVec(res, a, b *Element, n uint64, qInvNeg uint64)
-
-// Sum computes the sum of all elements in the vector.
-func (vector *Vector) Sum() (res Element) {
-	n := uint64(len(*vector))
-	if n == 0 {
-		return
-	}
-	const minN = 16 * 7 // AVX512 slower than generic for small n
-	const maxN = (1 << 32) - 1
-	if !supportAvx512 || n <= minN || n >= maxN {
-		// call sumVecGeneric
-		sumVecGeneric(&res, *vector)
-		return
-	}
-	sumVec(&res, &(*vector)[0], uint64(len(*vector)))
-	return
-}
-
-//go:noescape
-func sumVec(res *Element, a *Element, n uint64)
-
-// InnerProduct computes the inner product of two vectors.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) InnerProduct(other Vector) (res Element) {
-	n := uint64(len(*vector))
-	if n == 0 {
-		return
-	}
-	if n != uint64(len(other)) {
-		panic("vector.InnerProduct: vectors don't have the same length")
-	}
-	const maxN = (1 << 32) - 1
-	if !supportAvx512 || n >= maxN {
-		// call innerProductVecGeneric
-		// note; we could split the vector into smaller chunks and call innerProductVec
-		innerProductVecGeneric(&res, *vector, other)
-		return
-	}
-	innerProdVec(&res[0], &(*vector)[0], &other[0], uint64(len(*vector)))
-
-	return
-}
-
-//go:noescape
-func innerProdVec(res *uint64, a, b *Element, n uint64)
-
-// Mul multiplies two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Mul(a, b Vector) {
-	if len(a) != len(b) || len(a) != len(*vector) {
-		panic("vector.Mul: vectors don't have the same length")
-	}
-	n := uint64(len(a))
-	if n == 0 {
-		return
-	}
-	const maxN = (1 << 32) - 1
-	if !supportAvx512 || n >= maxN {
-		// call mulVecGeneric
-		mulVecGeneric(*vector, a, b)
-		return
-	}
-
-	const blockSize = 16
-	mulVec(&(*vector)[0], &a[0], &b[0], n/blockSize, qInvNeg)
-	if n%blockSize != 0 {
-		// call mulVecGeneric on the rest
-		start := n - n%blockSize
-		mulVecGeneric((*vector)[start:], a[start:], b[start:])
-	}
-
-}
-
-// Patterns use for transposing the vectors in mulVec
-var (
-	pattern1 = [8]uint64{0, 8, 1, 9, 2, 10, 3, 11}
-	pattern2 = [8]uint64{12, 4, 13, 5, 14, 6, 15, 7}
-	pattern3 = [8]uint64{0, 1, 8, 9, 2, 3, 10, 11}
-	pattern4 = [8]uint64{12, 13, 4, 5, 14, 15, 6, 7}
-)
-
-//go:noescape
-func mulVec(res, a, b *Element, n uint64, qInvNeg uint64)
-
-// Mul z = x * y (mod q)
-//
-// x and y must be less than q
-func (z *Element) Mul(x, y *Element) *Element {
-
-	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
-	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
-
-	mul(z, x, y)
-	return z
-}
-
-// Square z = x * x (mod q)
-//
-// x must be less than q
-func (z *Element) Square(x *Element) *Element {
-	// see Mul for doc.
-	mul(z, x, x)
-	return z
-}
diff --git a/ecc/bn254/fr/element_ops_amd64.s b/ecc/bn254/fr/element_ops_amd64.s
deleted file mode 100644
index 6c42136a7a..0000000000
--- a/ecc/bn254/fr/element_ops_amd64.s
+++ /dev/null
@@ -1,6 +0,0 @@
-// +build !purego
-
-// Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 9425145785761608449
-#include "../../../field/asm/element_4w_amd64.s"
-
diff --git a/ecc/bn254/fr/element_ops_purego.go b/ecc/bn254/fr/element_purego.go
similarity index 88%
rename from ecc/bn254/fr/element_ops_purego.go
rename to ecc/bn254/fr/element_purego.go
index 4ea220c185..034ee75ffe 100644
--- a/ecc/bn254/fr/element_ops_purego.go
+++ b/ecc/bn254/fr/element_purego.go
@@ -1,5 +1,4 @@
-//go:build !amd64 || purego
-// +build !amd64 purego
+//go:build purego || (!amd64 && !arm64)
 
 // Copyright 2020 ConsenSys Software Inc.
 //
@@ -44,14 +43,6 @@ func MulBy13(x *Element) {
 	x.Mul(x, &y)
 }
 
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-func Butterfly(a, b *Element) {
-	_butterflyGeneric(a, b)
-}
-
 func fromMont(z *Element) {
 	_fromMontGeneric(z)
 }
@@ -60,43 +51,6 @@ func reduce(z *Element) {
 	_reduceGeneric(z)
 }
 
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	addVecGeneric(*vector, a, b)
-}
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	subVecGeneric(*vector, a, b)
-}
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *Element) {
-	scalarMulVecGeneric(*vector, a, b)
-}
-
-// Sum computes the sum of all elements in the vector.
-func (vector *Vector) Sum() (res Element) {
-	sumVecGeneric(&res, *vector)
-	return
-}
-
-// InnerProduct computes the inner product of two vectors.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) InnerProduct(other Vector) (res Element) {
-	innerProductVecGeneric(&res, *vector, other)
-	return
-}
-
-// Mul multiplies two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Mul(a, b Vector) {
-	mulVecGeneric(*vector, a, b)
-}
-
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
@@ -438,3 +392,11 @@ func (z *Element) Square(x *Element) *Element {
 	}
 	return z
 }
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
diff --git a/ecc/bn254/fr/mimc/test_vectors/main.go b/ecc/bn254/fr/mimc/test_vectors/main.go
index e5cdef6c1a..b2e306a590 100644
--- a/ecc/bn254/fr/mimc/test_vectors/main.go
+++ b/ecc/bn254/fr/mimc/test_vectors/main.go
@@ -3,9 +3,10 @@ package main
 import (
 	"encoding/json"
 	"fmt"
+	"os"
+
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr/mimc"
-	"os"
 )
 
 type numericalMiMCTestCase struct {
@@ -22,6 +23,7 @@ func assertNoError(err error) {
 
 //go:generate go run main.go
 func main() {
+	fmt.Println("generating test vectors for MiMC...")
 	var tests []numericalMiMCTestCase
 
 	bytes, err := os.ReadFile("./vectors.json")
diff --git a/ecc/bn254/fr/vector_amd64.go b/ecc/bn254/fr/vector_amd64.go
new file mode 100644
index 0000000000..0164ecb382
--- /dev/null
+++ b/ecc/bn254/fr/vector_amd64.go
@@ -0,0 +1,160 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Add: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	addVec(&(*vector)[0], &a[0], &b[0], n)
+}
+
+//go:noescape
+func addVec(res, a, b *Element, n uint64)
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Sub: vectors don't have the same length")
+	}
+	subVec(&(*vector)[0], &a[0], &b[0], uint64(len(a)))
+}
+
+//go:noescape
+func subVec(res, a, b *Element, n uint64)
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	if len(a) != len(*vector) {
+		panic("vector.ScalarMul: vectors don't have the same length")
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || uint64(len(a)) >= maxN {
+		// call scalarMulVecGeneric
+		scalarMulVecGeneric(*vector, a, b)
+		return
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	// the code for scalarMul is identical to mulVec; and it expects at least
+	// 2 elements in the vector to fill the Z registers
+	var bb [2]Element
+	bb[0] = *b
+	bb[1] = *b
+	const blockSize = 16
+	scalarMulVec(&(*vector)[0], &a[0], &bb[0], n/blockSize, qInvNeg)
+	if n%blockSize != 0 {
+		// call scalarMulVecGeneric on the rest
+		start := n - n%blockSize
+		scalarMulVecGeneric((*vector)[start:], a[start:], b)
+	}
+}
+
+//go:noescape
+func scalarMulVec(res, a, b *Element, n uint64, qInvNeg uint64)
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	const minN = 16 * 7 // AVX512 slower than generic for small n
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n <= minN || n >= maxN {
+		// call sumVecGeneric
+		sumVecGeneric(&res, *vector)
+		return
+	}
+	sumVec(&res, &(*vector)[0], uint64(len(*vector)))
+	return
+}
+
+//go:noescape
+func sumVec(res *Element, a *Element, n uint64)
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	if n != uint64(len(other)) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n >= maxN {
+		// call innerProductVecGeneric
+		// note; we could split the vector into smaller chunks and call innerProductVec
+		innerProductVecGeneric(&res, *vector, other)
+		return
+	}
+	innerProdVec(&res[0], &(*vector)[0], &other[0], uint64(len(*vector)))
+
+	return
+}
+
+//go:noescape
+func innerProdVec(res *uint64, a, b *Element, n uint64)
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n >= maxN {
+		// call mulVecGeneric
+		mulVecGeneric(*vector, a, b)
+		return
+	}
+
+	const blockSize = 16
+	mulVec(&(*vector)[0], &a[0], &b[0], n/blockSize, qInvNeg)
+	if n%blockSize != 0 {
+		// call mulVecGeneric on the rest
+		start := n - n%blockSize
+		mulVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+
+}
+
+// Patterns use for transposing the vectors in mulVec
+var (
+	pattern1 = [8]uint64{0, 8, 1, 9, 2, 10, 3, 11}
+	pattern2 = [8]uint64{12, 4, 13, 5, 14, 6, 15, 7}
+	pattern3 = [8]uint64{0, 1, 8, 9, 2, 3, 10, 11}
+	pattern4 = [8]uint64{12, 13, 4, 5, 14, 15, 6, 7}
+)
+
+//go:noescape
+func mulVec(res, a, b *Element, n uint64, qInvNeg uint64)
diff --git a/ecc/bn254/fr/vector_purego.go b/ecc/bn254/fr/vector_purego.go
new file mode 100644
index 0000000000..84f86a40b1
--- /dev/null
+++ b/ecc/bn254/fr/vector_purego.go
@@ -0,0 +1,56 @@
+//go:build purego || !amd64
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	addVecGeneric(*vector, a, b)
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	subVecGeneric(*vector, a, b)
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
diff --git a/ecc/bn254/internal/fptower/asm.go b/ecc/bn254/internal/fptower/asm.go
index 49751a9396..03b1160807 100644
--- a/ecc/bn254/internal/fptower/asm.go
+++ b/ecc/bn254/internal/fptower/asm.go
@@ -1,5 +1,4 @@
 //go:build !noadx
-// +build !noadx
 
 // Copyright 2020 Consensys Software Inc.
 //
diff --git a/ecc/bn254/internal/fptower/asm_noadx.go b/ecc/bn254/internal/fptower/asm_noadx.go
index c6a97081fc..ea7782392c 100644
--- a/ecc/bn254/internal/fptower/asm_noadx.go
+++ b/ecc/bn254/internal/fptower/asm_noadx.go
@@ -1,5 +1,4 @@
 //go:build noadx
-// +build noadx
 
 // Copyright 2020 Consensys Software Inc.
 //
diff --git a/ecc/bn254/internal/fptower/e2_fallback.go b/ecc/bn254/internal/fptower/e2_fallback.go
index 6fe47c4111..1b6011564f 100644
--- a/ecc/bn254/internal/fptower/e2_fallback.go
+++ b/ecc/bn254/internal/fptower/e2_fallback.go
@@ -1,5 +1,4 @@
 //go:build !amd64
-// +build !amd64
 
 // Copyright 2020 Consensys Software Inc.
 //
diff --git a/ecc/bw6-633/fp/arith.go b/ecc/bw6-633/fp/arith.go
index 6f281563b3..66fa667482 100644
--- a/ecc/bw6-633/fp/arith.go
+++ b/ecc/bw6-633/fp/arith.go
@@ -58,16 +58,3 @@ func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) {
 	hi, _ = bits.Add64(hi, e, carry)
 	return
 }
-func max(a int, b int) int {
-	if a > b {
-		return a
-	}
-	return b
-}
-
-func min(a int, b int) int {
-	if a < b {
-		return a
-	}
-	return b
-}
diff --git a/ecc/bw6-633/fp/asm_adx.go b/ecc/bw6-633/fp/asm_adx.go
index 0481989ec6..f8e29bd1a7 100644
--- a/ecc/bw6-633/fp/asm_adx.go
+++ b/ecc/bw6-633/fp/asm_adx.go
@@ -1,5 +1,4 @@
 //go:build !noadx
-// +build !noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bw6-633/fp/asm_noadx.go b/ecc/bw6-633/fp/asm_noadx.go
index 92f8cc0f42..cb6cfa0f50 100644
--- a/ecc/bw6-633/fp/asm_noadx.go
+++ b/ecc/bw6-633/fp/asm_noadx.go
@@ -1,5 +1,4 @@
 //go:build noadx
-// +build noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bw6-633/fp/element_amd64.go b/ecc/bw6-633/fp/element_amd64.go
new file mode 100644
index 0000000000..77a51ee25e
--- /dev/null
+++ b/ecc/bw6-633/fp/element_amd64.go
@@ -0,0 +1,66 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fp
+
+//go:noescape
+func MulBy3(x *Element)
+
+//go:noescape
+func MulBy5(x *Element)
+
+//go:noescape
+func MulBy13(x *Element)
+
+//go:noescape
+func mul(res, x, y *Element)
+
+//go:noescape
+func fromMont(res *Element)
+
+//go:noescape
+func reduce(res *Element)
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+//
+//go:noescape
+func Butterfly(a, b *Element)
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+
+	mul(z, x, y)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for doc.
+	mul(z, x, x)
+	return z
+}
diff --git a/ecc/bw6-633/fp/element_amd64.s b/ecc/bw6-633/fp/element_amd64.s
new file mode 100644
index 0000000000..4820949b69
--- /dev/null
+++ b/ecc/bw6-633/fp/element_amd64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 747913930085520082
+#include "../../../field/asm/element_10w_amd64.s"
+
diff --git a/ecc/bw6-633/fp/element_arm64.go b/ecc/bw6-633/fp/element_arm64.go
new file mode 100644
index 0000000000..aeabec816c
--- /dev/null
+++ b/ecc/bw6-633/fp/element_arm64.go
@@ -0,0 +1,83 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fp
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
+
+//go:noescape
+func mul(res, x, y *Element)
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+	mul(z, x, y)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for doc.
+	mul(z, x, x)
+	return z
+}
+
+// MulBy3 x *= 3 (mod q)
+func MulBy3(x *Element) {
+	_x := *x
+	x.Double(x).Add(x, &_x)
+}
+
+// MulBy5 x *= 5 (mod q)
+func MulBy5(x *Element) {
+	_x := *x
+	x.Double(x).Double(x).Add(x, &_x)
+}
+
+// MulBy13 x *= 13 (mod q)
+func MulBy13(x *Element) {
+	var y = Element{
+		4881606927653498122,
+		47978232019095094,
+		8555661377410121478,
+		17849732488791568215,
+		5227097555314997552,
+		839611732066804726,
+		5234648925333584632,
+		11936054402769696488,
+		1228498468693814883,
+		2857848702739380,
+	}
+	x.Mul(x, &y)
+}
+
+func fromMont(z *Element) {
+	_fromMontGeneric(z)
+}
+
+//go:noescape
+func reduce(res *Element)
diff --git a/ecc/bw6-633/fp/element_arm64.s b/ecc/bw6-633/fp/element_arm64.s
new file mode 100644
index 0000000000..19ca3bc382
--- /dev/null
+++ b/ecc/bw6-633/fp/element_arm64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 4283725514119985738
+#include "../../../field/asm/element_10w_arm64.s"
+
diff --git a/ecc/bw6-633/fp/element_ops_amd64.go b/ecc/bw6-633/fp/element_ops_amd64.go
deleted file mode 100644
index ed2803d717..0000000000
--- a/ecc/bw6-633/fp/element_ops_amd64.go
+++ /dev/null
@@ -1,67 +0,0 @@
-//go:build !purego
-// +build !purego
-
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-// Code generated by consensys/gnark-crypto DO NOT EDIT
-
-package fp
-
-//go:noescape
-func MulBy3(x *Element)
-
-//go:noescape
-func MulBy5(x *Element)
-
-//go:noescape
-func MulBy13(x *Element)
-
-//go:noescape
-func mul(res, x, y *Element)
-
-//go:noescape
-func fromMont(res *Element)
-
-//go:noescape
-func reduce(res *Element)
-
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-//
-//go:noescape
-func Butterfly(a, b *Element)
-
-// Mul z = x * y (mod q)
-//
-// x and y must be less than q
-func (z *Element) Mul(x, y *Element) *Element {
-
-	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
-	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
-
-	mul(z, x, y)
-	return z
-}
-
-// Square z = x * x (mod q)
-//
-// x must be less than q
-func (z *Element) Square(x *Element) *Element {
-	// see Mul for doc.
-	mul(z, x, x)
-	return z
-}
diff --git a/ecc/bw6-633/fp/element_ops_amd64.s b/ecc/bw6-633/fp/element_ops_amd64.s
deleted file mode 100644
index db6a61c53a..0000000000
--- a/ecc/bw6-633/fp/element_ops_amd64.s
+++ /dev/null
@@ -1,6 +0,0 @@
-// +build !purego
-
-// Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 747913930085520082
-#include "../../../field/asm/element_10w_amd64.s"
-
diff --git a/ecc/bw6-633/fp/element_ops_purego.go b/ecc/bw6-633/fp/element_purego.go
similarity index 99%
rename from ecc/bw6-633/fp/element_ops_purego.go
rename to ecc/bw6-633/fp/element_purego.go
index 3b5d489a30..637ecd9d67 100644
--- a/ecc/bw6-633/fp/element_ops_purego.go
+++ b/ecc/bw6-633/fp/element_purego.go
@@ -1,5 +1,4 @@
-//go:build !amd64 || purego
-// +build !amd64 purego
+//go:build purego || (!amd64 && !arm64)
 
 // Copyright 2020 ConsenSys Software Inc.
 //
@@ -50,14 +49,6 @@ func MulBy13(x *Element) {
 	x.Mul(x, &y)
 }
 
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-func Butterfly(a, b *Element) {
-	_butterflyGeneric(a, b)
-}
-
 func fromMont(z *Element) {
 	_fromMontGeneric(z)
 }
@@ -1595,3 +1586,11 @@ func (z *Element) Square(x *Element) *Element {
 	}
 	return z
 }
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
diff --git a/ecc/bw6-633/fp/vector.go b/ecc/bw6-633/fp/vector.go
index 90e2236c7e..9f86d6d8e7 100644
--- a/ecc/bw6-633/fp/vector.go
+++ b/ecc/bw6-633/fp/vector.go
@@ -205,43 +205,6 @@ func (vector Vector) Swap(i, j int) {
 	vector[i], vector[j] = vector[j], vector[i]
 }
 
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	addVecGeneric(*vector, a, b)
-}
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	subVecGeneric(*vector, a, b)
-}
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *Element) {
-	scalarMulVecGeneric(*vector, a, b)
-}
-
-// Sum computes the sum of all elements in the vector.
-func (vector *Vector) Sum() (res Element) {
-	sumVecGeneric(&res, *vector)
-	return
-}
-
-// InnerProduct computes the inner product of two vectors.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) InnerProduct(other Vector) (res Element) {
-	innerProductVecGeneric(&res, *vector, other)
-	return
-}
-
-// Mul multiplies two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Mul(a, b Vector) {
-	mulVecGeneric(*vector, a, b)
-}
-
 func addVecGeneric(res, a, b Vector) {
 	if len(a) != len(b) || len(a) != len(res) {
 		panic("vector.Add: vectors don't have the same length")
diff --git a/ecc/bw6-633/fp/vector_purego.go b/ecc/bw6-633/fp/vector_purego.go
new file mode 100644
index 0000000000..798b669887
--- /dev/null
+++ b/ecc/bw6-633/fp/vector_purego.go
@@ -0,0 +1,54 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fp
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	addVecGeneric(*vector, a, b)
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	subVecGeneric(*vector, a, b)
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
diff --git a/ecc/bw6-633/fr/arith.go b/ecc/bw6-633/fr/arith.go
index 7cfd55da19..83c9fd9ef9 100644
--- a/ecc/bw6-633/fr/arith.go
+++ b/ecc/bw6-633/fr/arith.go
@@ -58,16 +58,3 @@ func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) {
 	hi, _ = bits.Add64(hi, e, carry)
 	return
 }
-func max(a int, b int) int {
-	if a > b {
-		return a
-	}
-	return b
-}
-
-func min(a int, b int) int {
-	if a < b {
-		return a
-	}
-	return b
-}
diff --git a/ecc/bw6-633/fr/asm_adx.go b/ecc/bw6-633/fr/asm_adx.go
index da061913ba..9273ea23ab 100644
--- a/ecc/bw6-633/fr/asm_adx.go
+++ b/ecc/bw6-633/fr/asm_adx.go
@@ -1,5 +1,4 @@
 //go:build !noadx
-// +build !noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bw6-633/fr/asm_noadx.go b/ecc/bw6-633/fr/asm_noadx.go
index 7f52ffa197..b784a24247 100644
--- a/ecc/bw6-633/fr/asm_noadx.go
+++ b/ecc/bw6-633/fr/asm_noadx.go
@@ -1,5 +1,4 @@
 //go:build noadx
-// +build noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bw6-633/fr/element_amd64.go b/ecc/bw6-633/fr/element_amd64.go
new file mode 100644
index 0000000000..0ddb905f7b
--- /dev/null
+++ b/ecc/bw6-633/fr/element_amd64.go
@@ -0,0 +1,66 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+//go:noescape
+func MulBy3(x *Element)
+
+//go:noescape
+func MulBy5(x *Element)
+
+//go:noescape
+func MulBy13(x *Element)
+
+//go:noescape
+func mul(res, x, y *Element)
+
+//go:noescape
+func fromMont(res *Element)
+
+//go:noescape
+func reduce(res *Element)
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+//
+//go:noescape
+func Butterfly(a, b *Element)
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+
+	mul(z, x, y)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for doc.
+	mul(z, x, x)
+	return z
+}
diff --git a/ecc/bw6-633/fr/element_amd64.s b/ecc/bw6-633/fr/element_amd64.s
new file mode 100644
index 0000000000..00858d648e
--- /dev/null
+++ b/ecc/bw6-633/fr/element_amd64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 18184981773209750009
+#include "../../../field/asm/element_5w_amd64.s"
+
diff --git a/ecc/bw6-633/fr/element_ops_amd64.s b/ecc/bw6-633/fr/element_ops_amd64.s
deleted file mode 100644
index 29314843d7..0000000000
--- a/ecc/bw6-633/fr/element_ops_amd64.s
+++ /dev/null
@@ -1,6 +0,0 @@
-// +build !purego
-
-// Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 18184981773209750009
-#include "../../../field/asm/element_5w_amd64.s"
-
diff --git a/ecc/bw6-633/fr/element_ops_purego.go b/ecc/bw6-633/fr/element_purego.go
similarity index 99%
rename from ecc/bw6-633/fr/element_ops_purego.go
rename to ecc/bw6-633/fr/element_purego.go
index 4a7cdbfe46..93ea6339b3 100644
--- a/ecc/bw6-633/fr/element_ops_purego.go
+++ b/ecc/bw6-633/fr/element_purego.go
@@ -1,5 +1,4 @@
-//go:build !amd64 || purego
-// +build !amd64 purego
+//go:build purego || !amd64
 
 // Copyright 2020 ConsenSys Software Inc.
 //
@@ -45,14 +44,6 @@ func MulBy13(x *Element) {
 	x.Mul(x, &y)
 }
 
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-func Butterfly(a, b *Element) {
-	_butterflyGeneric(a, b)
-}
-
 func fromMont(z *Element) {
 	_fromMontGeneric(z)
 }
@@ -540,3 +531,11 @@ func (z *Element) Square(x *Element) *Element {
 	}
 	return z
 }
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
diff --git a/ecc/bw6-633/fr/vector.go b/ecc/bw6-633/fr/vector.go
index e3bee5fbd3..146828f9f7 100644
--- a/ecc/bw6-633/fr/vector.go
+++ b/ecc/bw6-633/fr/vector.go
@@ -200,43 +200,6 @@ func (vector Vector) Swap(i, j int) {
 	vector[i], vector[j] = vector[j], vector[i]
 }
 
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	addVecGeneric(*vector, a, b)
-}
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	subVecGeneric(*vector, a, b)
-}
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *Element) {
-	scalarMulVecGeneric(*vector, a, b)
-}
-
-// Sum computes the sum of all elements in the vector.
-func (vector *Vector) Sum() (res Element) {
-	sumVecGeneric(&res, *vector)
-	return
-}
-
-// InnerProduct computes the inner product of two vectors.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) InnerProduct(other Vector) (res Element) {
-	innerProductVecGeneric(&res, *vector, other)
-	return
-}
-
-// Mul multiplies two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Mul(a, b Vector) {
-	mulVecGeneric(*vector, a, b)
-}
-
 func addVecGeneric(res, a, b Vector) {
 	if len(a) != len(b) || len(a) != len(res) {
 		panic("vector.Add: vectors don't have the same length")
diff --git a/ecc/bw6-633/fr/vector_purego.go b/ecc/bw6-633/fr/vector_purego.go
new file mode 100644
index 0000000000..04662dde33
--- /dev/null
+++ b/ecc/bw6-633/fr/vector_purego.go
@@ -0,0 +1,54 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	addVecGeneric(*vector, a, b)
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	subVecGeneric(*vector, a, b)
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
diff --git a/ecc/bw6-761/fp/arith.go b/ecc/bw6-761/fp/arith.go
index 6f281563b3..66fa667482 100644
--- a/ecc/bw6-761/fp/arith.go
+++ b/ecc/bw6-761/fp/arith.go
@@ -58,16 +58,3 @@ func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) {
 	hi, _ = bits.Add64(hi, e, carry)
 	return
 }
-func max(a int, b int) int {
-	if a > b {
-		return a
-	}
-	return b
-}
-
-func min(a int, b int) int {
-	if a < b {
-		return a
-	}
-	return b
-}
diff --git a/ecc/bw6-761/fp/asm_adx.go b/ecc/bw6-761/fp/asm_adx.go
index 0481989ec6..f8e29bd1a7 100644
--- a/ecc/bw6-761/fp/asm_adx.go
+++ b/ecc/bw6-761/fp/asm_adx.go
@@ -1,5 +1,4 @@
 //go:build !noadx
-// +build !noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bw6-761/fp/asm_noadx.go b/ecc/bw6-761/fp/asm_noadx.go
index 92f8cc0f42..cb6cfa0f50 100644
--- a/ecc/bw6-761/fp/asm_noadx.go
+++ b/ecc/bw6-761/fp/asm_noadx.go
@@ -1,5 +1,4 @@
 //go:build noadx
-// +build noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bw6-761/fp/element_amd64.go b/ecc/bw6-761/fp/element_amd64.go
new file mode 100644
index 0000000000..77a51ee25e
--- /dev/null
+++ b/ecc/bw6-761/fp/element_amd64.go
@@ -0,0 +1,66 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fp
+
+//go:noescape
+func MulBy3(x *Element)
+
+//go:noescape
+func MulBy5(x *Element)
+
+//go:noescape
+func MulBy13(x *Element)
+
+//go:noescape
+func mul(res, x, y *Element)
+
+//go:noescape
+func fromMont(res *Element)
+
+//go:noescape
+func reduce(res *Element)
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+//
+//go:noescape
+func Butterfly(a, b *Element)
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+
+	mul(z, x, y)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for doc.
+	mul(z, x, x)
+	return z
+}
diff --git a/ecc/bw6-761/fp/element_amd64.s b/ecc/bw6-761/fp/element_amd64.s
new file mode 100644
index 0000000000..8bee44a5e7
--- /dev/null
+++ b/ecc/bw6-761/fp/element_amd64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 13892629867042773109
+#include "../../../field/asm/element_12w_amd64.s"
+
diff --git a/ecc/bw6-761/fp/element_arm64.go b/ecc/bw6-761/fp/element_arm64.go
new file mode 100644
index 0000000000..df5acdc99a
--- /dev/null
+++ b/ecc/bw6-761/fp/element_arm64.go
@@ -0,0 +1,85 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fp
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
+
+//go:noescape
+func mul(res, x, y *Element)
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+	mul(z, x, y)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for doc.
+	mul(z, x, x)
+	return z
+}
+
+// MulBy3 x *= 3 (mod q)
+func MulBy3(x *Element) {
+	_x := *x
+	x.Double(x).Add(x, &_x)
+}
+
+// MulBy5 x *= 5 (mod q)
+func MulBy5(x *Element) {
+	_x := *x
+	x.Double(x).Double(x).Add(x, &_x)
+}
+
+// MulBy13 x *= 13 (mod q)
+func MulBy13(x *Element) {
+	var y = Element{
+		4345973640412121648,
+		16340807117537158706,
+		14673764841507373218,
+		5587754667198343811,
+		12846753860245084942,
+		4041391838244625385,
+		8324122986343791677,
+		8773809490091176420,
+		5465994123296109449,
+		6649773564661156048,
+		9147430723089113754,
+		54281803719730243,
+	}
+	x.Mul(x, &y)
+}
+
+func fromMont(z *Element) {
+	_fromMontGeneric(z)
+}
+
+//go:noescape
+func reduce(res *Element)
diff --git a/ecc/bw6-761/fp/element_arm64.s b/ecc/bw6-761/fp/element_arm64.s
new file mode 100644
index 0000000000..9ed6049e69
--- /dev/null
+++ b/ecc/bw6-761/fp/element_arm64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 17465962485072383759
+#include "../../../field/asm/element_12w_arm64.s"
+
diff --git a/ecc/bw6-761/fp/element_ops_amd64.go b/ecc/bw6-761/fp/element_ops_amd64.go
deleted file mode 100644
index ed2803d717..0000000000
--- a/ecc/bw6-761/fp/element_ops_amd64.go
+++ /dev/null
@@ -1,67 +0,0 @@
-//go:build !purego
-// +build !purego
-
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-// Code generated by consensys/gnark-crypto DO NOT EDIT
-
-package fp
-
-//go:noescape
-func MulBy3(x *Element)
-
-//go:noescape
-func MulBy5(x *Element)
-
-//go:noescape
-func MulBy13(x *Element)
-
-//go:noescape
-func mul(res, x, y *Element)
-
-//go:noescape
-func fromMont(res *Element)
-
-//go:noescape
-func reduce(res *Element)
-
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-//
-//go:noescape
-func Butterfly(a, b *Element)
-
-// Mul z = x * y (mod q)
-//
-// x and y must be less than q
-func (z *Element) Mul(x, y *Element) *Element {
-
-	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
-	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
-
-	mul(z, x, y)
-	return z
-}
-
-// Square z = x * x (mod q)
-//
-// x must be less than q
-func (z *Element) Square(x *Element) *Element {
-	// see Mul for doc.
-	mul(z, x, x)
-	return z
-}
diff --git a/ecc/bw6-761/fp/element_ops_amd64.s b/ecc/bw6-761/fp/element_ops_amd64.s
deleted file mode 100644
index 3c8e045ed6..0000000000
--- a/ecc/bw6-761/fp/element_ops_amd64.s
+++ /dev/null
@@ -1,6 +0,0 @@
-// +build !purego
-
-// Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 13892629867042773109
-#include "../../../field/asm/element_12w_amd64.s"
-
diff --git a/ecc/bw6-761/fp/element_ops_purego.go b/ecc/bw6-761/fp/element_purego.go
similarity index 99%
rename from ecc/bw6-761/fp/element_ops_purego.go
rename to ecc/bw6-761/fp/element_purego.go
index 59d6d1d523..4338d90c2b 100644
--- a/ecc/bw6-761/fp/element_ops_purego.go
+++ b/ecc/bw6-761/fp/element_purego.go
@@ -1,5 +1,4 @@
-//go:build !amd64 || purego
-// +build !amd64 purego
+//go:build purego || (!amd64 && !arm64)
 
 // Copyright 2020 ConsenSys Software Inc.
 //
@@ -52,14 +51,6 @@ func MulBy13(x *Element) {
 	x.Mul(x, &y)
 }
 
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-func Butterfly(a, b *Element) {
-	_butterflyGeneric(a, b)
-}
-
 func fromMont(z *Element) {
 	_fromMontGeneric(z)
 }
@@ -2185,3 +2176,11 @@ func (z *Element) Square(x *Element) *Element {
 	}
 	return z
 }
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
diff --git a/ecc/bw6-761/fp/vector.go b/ecc/bw6-761/fp/vector.go
index 8b91076209..66d5027f64 100644
--- a/ecc/bw6-761/fp/vector.go
+++ b/ecc/bw6-761/fp/vector.go
@@ -207,43 +207,6 @@ func (vector Vector) Swap(i, j int) {
 	vector[i], vector[j] = vector[j], vector[i]
 }
 
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	addVecGeneric(*vector, a, b)
-}
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	subVecGeneric(*vector, a, b)
-}
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *Element) {
-	scalarMulVecGeneric(*vector, a, b)
-}
-
-// Sum computes the sum of all elements in the vector.
-func (vector *Vector) Sum() (res Element) {
-	sumVecGeneric(&res, *vector)
-	return
-}
-
-// InnerProduct computes the inner product of two vectors.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) InnerProduct(other Vector) (res Element) {
-	innerProductVecGeneric(&res, *vector, other)
-	return
-}
-
-// Mul multiplies two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Mul(a, b Vector) {
-	mulVecGeneric(*vector, a, b)
-}
-
 func addVecGeneric(res, a, b Vector) {
 	if len(a) != len(b) || len(a) != len(res) {
 		panic("vector.Add: vectors don't have the same length")
diff --git a/ecc/bw6-761/fp/vector_purego.go b/ecc/bw6-761/fp/vector_purego.go
new file mode 100644
index 0000000000..798b669887
--- /dev/null
+++ b/ecc/bw6-761/fp/vector_purego.go
@@ -0,0 +1,54 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fp
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	addVecGeneric(*vector, a, b)
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	subVecGeneric(*vector, a, b)
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
diff --git a/ecc/bw6-761/fr/arith.go b/ecc/bw6-761/fr/arith.go
index 7cfd55da19..83c9fd9ef9 100644
--- a/ecc/bw6-761/fr/arith.go
+++ b/ecc/bw6-761/fr/arith.go
@@ -58,16 +58,3 @@ func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) {
 	hi, _ = bits.Add64(hi, e, carry)
 	return
 }
-func max(a int, b int) int {
-	if a > b {
-		return a
-	}
-	return b
-}
-
-func min(a int, b int) int {
-	if a < b {
-		return a
-	}
-	return b
-}
diff --git a/ecc/bw6-761/fr/asm_adx.go b/ecc/bw6-761/fr/asm_adx.go
index da061913ba..9273ea23ab 100644
--- a/ecc/bw6-761/fr/asm_adx.go
+++ b/ecc/bw6-761/fr/asm_adx.go
@@ -1,5 +1,4 @@
 //go:build !noadx
-// +build !noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bw6-761/fr/asm_noadx.go b/ecc/bw6-761/fr/asm_noadx.go
index 7f52ffa197..b784a24247 100644
--- a/ecc/bw6-761/fr/asm_noadx.go
+++ b/ecc/bw6-761/fr/asm_noadx.go
@@ -1,5 +1,4 @@
 //go:build noadx
-// +build noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/bw6-761/fr/element_amd64.go b/ecc/bw6-761/fr/element_amd64.go
new file mode 100644
index 0000000000..0ddb905f7b
--- /dev/null
+++ b/ecc/bw6-761/fr/element_amd64.go
@@ -0,0 +1,66 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+//go:noescape
+func MulBy3(x *Element)
+
+//go:noescape
+func MulBy5(x *Element)
+
+//go:noescape
+func MulBy13(x *Element)
+
+//go:noescape
+func mul(res, x, y *Element)
+
+//go:noescape
+func fromMont(res *Element)
+
+//go:noescape
+func reduce(res *Element)
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+//
+//go:noescape
+func Butterfly(a, b *Element)
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+
+	mul(z, x, y)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for doc.
+	mul(z, x, x)
+	return z
+}
diff --git a/ecc/bw6-761/fr/element_amd64.s b/ecc/bw6-761/fr/element_amd64.s
new file mode 100644
index 0000000000..872eddf5d6
--- /dev/null
+++ b/ecc/bw6-761/fr/element_amd64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 11124594824487954849
+#include "../../../field/asm/element_6w_amd64.s"
+
diff --git a/ecc/bw6-761/fr/element_arm64.go b/ecc/bw6-761/fr/element_arm64.go
new file mode 100644
index 0000000000..7b389c515b
--- /dev/null
+++ b/ecc/bw6-761/fr/element_arm64.go
@@ -0,0 +1,79 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+//
+//go:noescape
+func Butterfly(a, b *Element)
+
+//go:noescape
+func mul(res, x, y *Element)
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+	mul(z, x, y)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for doc.
+	mul(z, x, x)
+	return z
+}
+
+// MulBy3 x *= 3 (mod q)
+func MulBy3(x *Element) {
+	_x := *x
+	x.Double(x).Add(x, &_x)
+}
+
+// MulBy5 x *= 5 (mod q)
+func MulBy5(x *Element) {
+	_x := *x
+	x.Double(x).Double(x).Add(x, &_x)
+}
+
+// MulBy13 x *= 13 (mod q)
+func MulBy13(x *Element) {
+	var y = Element{
+		1176283927673829444,
+		14130787773971430395,
+		11354866436980285261,
+		15740727779991009548,
+		14951814113394531041,
+		33013799364667434,
+	}
+	x.Mul(x, &y)
+}
+
+func fromMont(z *Element) {
+	_fromMontGeneric(z)
+}
+
+//go:noescape
+func reduce(res *Element)
diff --git a/ecc/bw6-761/fr/element_arm64.s b/ecc/bw6-761/fr/element_arm64.s
new file mode 100644
index 0000000000..2a3f7d0b2c
--- /dev/null
+++ b/ecc/bw6-761/fr/element_arm64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 15397482240260640864
+#include "../../../field/asm/element_6w_arm64.s"
+
diff --git a/ecc/bw6-761/fr/element_ops_amd64.s b/ecc/bw6-761/fr/element_ops_amd64.s
deleted file mode 100644
index cabff26f70..0000000000
--- a/ecc/bw6-761/fr/element_ops_amd64.s
+++ /dev/null
@@ -1,6 +0,0 @@
-// +build !purego
-
-// Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 11124594824487954849
-#include "../../../field/asm/element_6w_amd64.s"
-
diff --git a/ecc/bw6-761/fr/element_ops_purego.go b/ecc/bw6-761/fr/element_purego.go
similarity index 99%
rename from ecc/bw6-761/fr/element_ops_purego.go
rename to ecc/bw6-761/fr/element_purego.go
index bdf76428de..5d56b28300 100644
--- a/ecc/bw6-761/fr/element_ops_purego.go
+++ b/ecc/bw6-761/fr/element_purego.go
@@ -1,5 +1,4 @@
-//go:build !amd64 || purego
-// +build !amd64 purego
+//go:build purego || (!amd64 && !arm64)
 
 // Copyright 2020 ConsenSys Software Inc.
 //
@@ -46,14 +45,6 @@ func MulBy13(x *Element) {
 	x.Mul(x, &y)
 }
 
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-func Butterfly(a, b *Element) {
-	_butterflyGeneric(a, b)
-}
-
 func fromMont(z *Element) {
 	_fromMontGeneric(z)
 }
@@ -703,3 +694,11 @@ func (z *Element) Square(x *Element) *Element {
 	}
 	return z
 }
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
diff --git a/ecc/bw6-761/fr/vector.go b/ecc/bw6-761/fr/vector.go
index af400c4e47..47b20efbed 100644
--- a/ecc/bw6-761/fr/vector.go
+++ b/ecc/bw6-761/fr/vector.go
@@ -201,43 +201,6 @@ func (vector Vector) Swap(i, j int) {
 	vector[i], vector[j] = vector[j], vector[i]
 }
 
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	addVecGeneric(*vector, a, b)
-}
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	subVecGeneric(*vector, a, b)
-}
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *Element) {
-	scalarMulVecGeneric(*vector, a, b)
-}
-
-// Sum computes the sum of all elements in the vector.
-func (vector *Vector) Sum() (res Element) {
-	sumVecGeneric(&res, *vector)
-	return
-}
-
-// InnerProduct computes the inner product of two vectors.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) InnerProduct(other Vector) (res Element) {
-	innerProductVecGeneric(&res, *vector, other)
-	return
-}
-
-// Mul multiplies two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Mul(a, b Vector) {
-	mulVecGeneric(*vector, a, b)
-}
-
 func addVecGeneric(res, a, b Vector) {
 	if len(a) != len(b) || len(a) != len(res) {
 		panic("vector.Add: vectors don't have the same length")
diff --git a/ecc/bw6-761/fr/vector_purego.go b/ecc/bw6-761/fr/vector_purego.go
new file mode 100644
index 0000000000..04662dde33
--- /dev/null
+++ b/ecc/bw6-761/fr/vector_purego.go
@@ -0,0 +1,54 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	addVecGeneric(*vector, a, b)
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	subVecGeneric(*vector, a, b)
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
diff --git a/ecc/secp256k1/fp/element_ops_purego.go b/ecc/secp256k1/fp/element_purego.go
similarity index 100%
rename from ecc/secp256k1/fp/element_ops_purego.go
rename to ecc/secp256k1/fp/element_purego.go
index f53ffa325b..3be147f51a 100644
--- a/ecc/secp256k1/fp/element_ops_purego.go
+++ b/ecc/secp256k1/fp/element_purego.go
@@ -41,14 +41,6 @@ func MulBy13(x *Element) {
 	x.Mul(x, &y)
 }
 
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-func Butterfly(a, b *Element) {
-	_butterflyGeneric(a, b)
-}
-
 func fromMont(z *Element) {
 	_fromMontGeneric(z)
 }
@@ -304,3 +296,11 @@ func (z *Element) Square(x *Element) *Element {
 	}
 	return z
 }
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
diff --git a/ecc/secp256k1/fp/vector.go b/ecc/secp256k1/fp/vector.go
index fa22cb416a..c97b4283ce 100644
--- a/ecc/secp256k1/fp/vector.go
+++ b/ecc/secp256k1/fp/vector.go
@@ -199,43 +199,6 @@ func (vector Vector) Swap(i, j int) {
 	vector[i], vector[j] = vector[j], vector[i]
 }
 
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	addVecGeneric(*vector, a, b)
-}
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	subVecGeneric(*vector, a, b)
-}
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *Element) {
-	scalarMulVecGeneric(*vector, a, b)
-}
-
-// Sum computes the sum of all elements in the vector.
-func (vector *Vector) Sum() (res Element) {
-	sumVecGeneric(&res, *vector)
-	return
-}
-
-// InnerProduct computes the inner product of two vectors.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) InnerProduct(other Vector) (res Element) {
-	innerProductVecGeneric(&res, *vector, other)
-	return
-}
-
-// Mul multiplies two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Mul(a, b Vector) {
-	mulVecGeneric(*vector, a, b)
-}
-
 func addVecGeneric(res, a, b Vector) {
 	if len(a) != len(b) || len(a) != len(res) {
 		panic("vector.Add: vectors don't have the same length")
diff --git a/ecc/secp256k1/fp/vector_purego.go b/ecc/secp256k1/fp/vector_purego.go
new file mode 100644
index 0000000000..798b669887
--- /dev/null
+++ b/ecc/secp256k1/fp/vector_purego.go
@@ -0,0 +1,54 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fp
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	addVecGeneric(*vector, a, b)
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	subVecGeneric(*vector, a, b)
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
diff --git a/ecc/secp256k1/fr/element_ops_purego.go b/ecc/secp256k1/fr/element_purego.go
similarity index 100%
rename from ecc/secp256k1/fr/element_ops_purego.go
rename to ecc/secp256k1/fr/element_purego.go
index ef83ea20a5..80b3116256 100644
--- a/ecc/secp256k1/fr/element_ops_purego.go
+++ b/ecc/secp256k1/fr/element_purego.go
@@ -41,14 +41,6 @@ func MulBy13(x *Element) {
 	x.Mul(x, &y)
 }
 
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-func Butterfly(a, b *Element) {
-	_butterflyGeneric(a, b)
-}
-
 func fromMont(z *Element) {
 	_fromMontGeneric(z)
 }
@@ -304,3 +296,11 @@ func (z *Element) Square(x *Element) *Element {
 	}
 	return z
 }
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
diff --git a/ecc/secp256k1/fr/vector.go b/ecc/secp256k1/fr/vector.go
index bcc71efcd8..867cabbc3d 100644
--- a/ecc/secp256k1/fr/vector.go
+++ b/ecc/secp256k1/fr/vector.go
@@ -199,43 +199,6 @@ func (vector Vector) Swap(i, j int) {
 	vector[i], vector[j] = vector[j], vector[i]
 }
 
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	addVecGeneric(*vector, a, b)
-}
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	subVecGeneric(*vector, a, b)
-}
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *Element) {
-	scalarMulVecGeneric(*vector, a, b)
-}
-
-// Sum computes the sum of all elements in the vector.
-func (vector *Vector) Sum() (res Element) {
-	sumVecGeneric(&res, *vector)
-	return
-}
-
-// InnerProduct computes the inner product of two vectors.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) InnerProduct(other Vector) (res Element) {
-	innerProductVecGeneric(&res, *vector, other)
-	return
-}
-
-// Mul multiplies two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Mul(a, b Vector) {
-	mulVecGeneric(*vector, a, b)
-}
-
 func addVecGeneric(res, a, b Vector) {
 	if len(a) != len(b) || len(a) != len(res) {
 		panic("vector.Add: vectors don't have the same length")
diff --git a/ecc/secp256k1/fr/vector_purego.go b/ecc/secp256k1/fr/vector_purego.go
new file mode 100644
index 0000000000..04662dde33
--- /dev/null
+++ b/ecc/secp256k1/fr/vector_purego.go
@@ -0,0 +1,54 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	addVecGeneric(*vector, a, b)
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	subVecGeneric(*vector, a, b)
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
diff --git a/ecc/stark-curve/fp/arith.go b/ecc/stark-curve/fp/arith.go
index 6f281563b3..66fa667482 100644
--- a/ecc/stark-curve/fp/arith.go
+++ b/ecc/stark-curve/fp/arith.go
@@ -58,16 +58,3 @@ func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) {
 	hi, _ = bits.Add64(hi, e, carry)
 	return
 }
-func max(a int, b int) int {
-	if a > b {
-		return a
-	}
-	return b
-}
-
-func min(a int, b int) int {
-	if a < b {
-		return a
-	}
-	return b
-}
diff --git a/ecc/stark-curve/fp/asm_adx.go b/ecc/stark-curve/fp/asm_adx.go
index 0481989ec6..f8e29bd1a7 100644
--- a/ecc/stark-curve/fp/asm_adx.go
+++ b/ecc/stark-curve/fp/asm_adx.go
@@ -1,5 +1,4 @@
 //go:build !noadx
-// +build !noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/stark-curve/fp/asm_avx.go b/ecc/stark-curve/fp/asm_avx.go
index cea035ee84..52fc07a325 100644
--- a/ecc/stark-curve/fp/asm_avx.go
+++ b/ecc/stark-curve/fp/asm_avx.go
@@ -1,5 +1,4 @@
 //go:build !noavx
-// +build !noavx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/stark-curve/fp/asm_noadx.go b/ecc/stark-curve/fp/asm_noadx.go
index 92f8cc0f42..cb6cfa0f50 100644
--- a/ecc/stark-curve/fp/asm_noadx.go
+++ b/ecc/stark-curve/fp/asm_noadx.go
@@ -1,5 +1,4 @@
 //go:build noadx
-// +build noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/stark-curve/fp/asm_noavx.go b/ecc/stark-curve/fp/asm_noavx.go
index 9ca08a375a..12261b1f03 100644
--- a/ecc/stark-curve/fp/asm_noavx.go
+++ b/ecc/stark-curve/fp/asm_noavx.go
@@ -1,5 +1,4 @@
 //go:build noavx
-// +build noavx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/stark-curve/fp/element_amd64.go b/ecc/stark-curve/fp/element_amd64.go
new file mode 100644
index 0000000000..77a51ee25e
--- /dev/null
+++ b/ecc/stark-curve/fp/element_amd64.go
@@ -0,0 +1,66 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fp
+
+//go:noescape
+func MulBy3(x *Element)
+
+//go:noescape
+func MulBy5(x *Element)
+
+//go:noescape
+func MulBy13(x *Element)
+
+//go:noescape
+func mul(res, x, y *Element)
+
+//go:noescape
+func fromMont(res *Element)
+
+//go:noescape
+func reduce(res *Element)
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+//
+//go:noescape
+func Butterfly(a, b *Element)
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+
+	mul(z, x, y)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for doc.
+	mul(z, x, x)
+	return z
+}
diff --git a/ecc/stark-curve/fp/element_amd64.s b/ecc/stark-curve/fp/element_amd64.s
new file mode 100644
index 0000000000..fb00194d7e
--- /dev/null
+++ b/ecc/stark-curve/fp/element_amd64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 9425145785761608449
+#include "../../../field/asm/element_4w_amd64.s"
+
diff --git a/ecc/stark-curve/fp/element_arm64.go b/ecc/stark-curve/fp/element_arm64.go
new file mode 100644
index 0000000000..776a544644
--- /dev/null
+++ b/ecc/stark-curve/fp/element_arm64.go
@@ -0,0 +1,77 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fp
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+//
+//go:noescape
+func Butterfly(a, b *Element)
+
+//go:noescape
+func mul(res, x, y *Element)
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+	mul(z, x, y)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for doc.
+	mul(z, x, x)
+	return z
+}
+
+// MulBy3 x *= 3 (mod q)
+func MulBy3(x *Element) {
+	_x := *x
+	x.Double(x).Add(x, &_x)
+}
+
+// MulBy5 x *= 5 (mod q)
+func MulBy5(x *Element) {
+	_x := *x
+	x.Double(x).Double(x).Add(x, &_x)
+}
+
+// MulBy13 x *= 13 (mod q)
+func MulBy13(x *Element) {
+	var y = Element{
+		18446744073709551201,
+		18446744073709551615,
+		18446744073709551615,
+		576460752303416432,
+	}
+	x.Mul(x, &y)
+}
+
+func fromMont(z *Element) {
+	_fromMontGeneric(z)
+}
+
+//go:noescape
+func reduce(res *Element)
diff --git a/ecc/stark-curve/fp/element_arm64.s b/ecc/stark-curve/fp/element_arm64.s
new file mode 100644
index 0000000000..5d328815aa
--- /dev/null
+++ b/ecc/stark-curve/fp/element_arm64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 1501560133179981797
+#include "../../../field/asm/element_4w_arm64.s"
+
diff --git a/ecc/stark-curve/fp/element_ops_amd64.s b/ecc/stark-curve/fp/element_ops_amd64.s
deleted file mode 100644
index 6c42136a7a..0000000000
--- a/ecc/stark-curve/fp/element_ops_amd64.s
+++ /dev/null
@@ -1,6 +0,0 @@
-// +build !purego
-
-// Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 9425145785761608449
-#include "../../../field/asm/element_4w_amd64.s"
-
diff --git a/ecc/stark-curve/fp/element_ops_purego.go b/ecc/stark-curve/fp/element_purego.go
similarity index 88%
rename from ecc/stark-curve/fp/element_ops_purego.go
rename to ecc/stark-curve/fp/element_purego.go
index 19cb3649be..5308610f0b 100644
--- a/ecc/stark-curve/fp/element_ops_purego.go
+++ b/ecc/stark-curve/fp/element_purego.go
@@ -1,5 +1,4 @@
-//go:build !amd64 || purego
-// +build !amd64 purego
+//go:build purego || (!amd64 && !arm64)
 
 // Copyright 2020 ConsenSys Software Inc.
 //
@@ -44,14 +43,6 @@ func MulBy13(x *Element) {
 	x.Mul(x, &y)
 }
 
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-func Butterfly(a, b *Element) {
-	_butterflyGeneric(a, b)
-}
-
 func fromMont(z *Element) {
 	_fromMontGeneric(z)
 }
@@ -60,43 +51,6 @@ func reduce(z *Element) {
 	_reduceGeneric(z)
 }
 
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	addVecGeneric(*vector, a, b)
-}
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	subVecGeneric(*vector, a, b)
-}
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *Element) {
-	scalarMulVecGeneric(*vector, a, b)
-}
-
-// Sum computes the sum of all elements in the vector.
-func (vector *Vector) Sum() (res Element) {
-	sumVecGeneric(&res, *vector)
-	return
-}
-
-// InnerProduct computes the inner product of two vectors.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) InnerProduct(other Vector) (res Element) {
-	innerProductVecGeneric(&res, *vector, other)
-	return
-}
-
-// Mul multiplies two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Mul(a, b Vector) {
-	mulVecGeneric(*vector, a, b)
-}
-
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
@@ -438,3 +392,11 @@ func (z *Element) Square(x *Element) *Element {
 	}
 	return z
 }
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
diff --git a/ecc/stark-curve/fp/element_ops_amd64.go b/ecc/stark-curve/fp/vector_amd64.go
similarity index 84%
rename from ecc/stark-curve/fp/element_ops_amd64.go
rename to ecc/stark-curve/fp/vector_amd64.go
index 2ab1a98399..75719deedb 100644
--- a/ecc/stark-curve/fp/element_ops_amd64.go
+++ b/ecc/stark-curve/fp/vector_amd64.go
@@ -1,5 +1,4 @@
 //go:build !purego
-// +build !purego
 
 // Copyright 2020 ConsenSys Software Inc.
 //
@@ -19,32 +18,6 @@
 
 package fp
 
-//go:noescape
-func MulBy3(x *Element)
-
-//go:noescape
-func MulBy5(x *Element)
-
-//go:noescape
-func MulBy13(x *Element)
-
-//go:noescape
-func mul(res, x, y *Element)
-
-//go:noescape
-func fromMont(res *Element)
-
-//go:noescape
-func reduce(res *Element)
-
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-//
-//go:noescape
-func Butterfly(a, b *Element)
-
 // Add adds two vectors element-wise and stores the result in self.
 // It panics if the vectors don't have the same length.
 func (vector *Vector) Add(a, b Vector) {
@@ -185,24 +158,3 @@ var (
 
 //go:noescape
 func mulVec(res, a, b *Element, n uint64, qInvNeg uint64)
-
-// Mul z = x * y (mod q)
-//
-// x and y must be less than q
-func (z *Element) Mul(x, y *Element) *Element {
-
-	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
-	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
-
-	mul(z, x, y)
-	return z
-}
-
-// Square z = x * x (mod q)
-//
-// x must be less than q
-func (z *Element) Square(x *Element) *Element {
-	// see Mul for doc.
-	mul(z, x, x)
-	return z
-}
diff --git a/ecc/stark-curve/fp/vector_purego.go b/ecc/stark-curve/fp/vector_purego.go
new file mode 100644
index 0000000000..fc0f66e2a3
--- /dev/null
+++ b/ecc/stark-curve/fp/vector_purego.go
@@ -0,0 +1,56 @@
+//go:build purego || !amd64
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fp
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	addVecGeneric(*vector, a, b)
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	subVecGeneric(*vector, a, b)
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
diff --git a/ecc/stark-curve/fr/arith.go b/ecc/stark-curve/fr/arith.go
index 7cfd55da19..83c9fd9ef9 100644
--- a/ecc/stark-curve/fr/arith.go
+++ b/ecc/stark-curve/fr/arith.go
@@ -58,16 +58,3 @@ func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) {
 	hi, _ = bits.Add64(hi, e, carry)
 	return
 }
-func max(a int, b int) int {
-	if a > b {
-		return a
-	}
-	return b
-}
-
-func min(a int, b int) int {
-	if a < b {
-		return a
-	}
-	return b
-}
diff --git a/ecc/stark-curve/fr/asm_adx.go b/ecc/stark-curve/fr/asm_adx.go
index da061913ba..9273ea23ab 100644
--- a/ecc/stark-curve/fr/asm_adx.go
+++ b/ecc/stark-curve/fr/asm_adx.go
@@ -1,5 +1,4 @@
 //go:build !noadx
-// +build !noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/stark-curve/fr/asm_avx.go b/ecc/stark-curve/fr/asm_avx.go
index 955f559799..1cc06c6e8d 100644
--- a/ecc/stark-curve/fr/asm_avx.go
+++ b/ecc/stark-curve/fr/asm_avx.go
@@ -1,5 +1,4 @@
 //go:build !noavx
-// +build !noavx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/stark-curve/fr/asm_noadx.go b/ecc/stark-curve/fr/asm_noadx.go
index 7f52ffa197..b784a24247 100644
--- a/ecc/stark-curve/fr/asm_noadx.go
+++ b/ecc/stark-curve/fr/asm_noadx.go
@@ -1,5 +1,4 @@
 //go:build noadx
-// +build noadx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/stark-curve/fr/asm_noavx.go b/ecc/stark-curve/fr/asm_noavx.go
index e5a5b1f2cc..66bfc00772 100644
--- a/ecc/stark-curve/fr/asm_noavx.go
+++ b/ecc/stark-curve/fr/asm_noavx.go
@@ -1,5 +1,4 @@
 //go:build noavx
-// +build noavx
 
 // Copyright 2020 ConsenSys Software Inc.
 //
diff --git a/ecc/stark-curve/fr/element_amd64.go b/ecc/stark-curve/fr/element_amd64.go
new file mode 100644
index 0000000000..0ddb905f7b
--- /dev/null
+++ b/ecc/stark-curve/fr/element_amd64.go
@@ -0,0 +1,66 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+//go:noescape
+func MulBy3(x *Element)
+
+//go:noescape
+func MulBy5(x *Element)
+
+//go:noescape
+func MulBy13(x *Element)
+
+//go:noescape
+func mul(res, x, y *Element)
+
+//go:noescape
+func fromMont(res *Element)
+
+//go:noescape
+func reduce(res *Element)
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+//
+//go:noescape
+func Butterfly(a, b *Element)
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+
+	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
+	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+
+	mul(z, x, y)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for doc.
+	mul(z, x, x)
+	return z
+}
diff --git a/ecc/stark-curve/fr/element_amd64.s b/ecc/stark-curve/fr/element_amd64.s
new file mode 100644
index 0000000000..fb00194d7e
--- /dev/null
+++ b/ecc/stark-curve/fr/element_amd64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 9425145785761608449
+#include "../../../field/asm/element_4w_amd64.s"
+
diff --git a/ecc/stark-curve/fr/element_arm64.go b/ecc/stark-curve/fr/element_arm64.go
new file mode 100644
index 0000000000..69e7dd8b03
--- /dev/null
+++ b/ecc/stark-curve/fr/element_arm64.go
@@ -0,0 +1,77 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+//
+//go:noescape
+func Butterfly(a, b *Element)
+
+//go:noescape
+func mul(res, x, y *Element)
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+	mul(z, x, y)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for doc.
+	mul(z, x, x)
+	return z
+}
+
+// MulBy3 x *= 3 (mod q)
+func MulBy3(x *Element) {
+	_x := *x
+	x.Double(x).Add(x, &_x)
+}
+
+// MulBy5 x *= 5 (mod q)
+func MulBy5(x *Element) {
+	_x := *x
+	x.Double(x).Double(x).Add(x, &_x)
+}
+
+// MulBy13 x *= 13 (mod q)
+func MulBy13(x *Element) {
+	var y = Element{
+		13231284915721003215,
+		9638582829363634368,
+		117,
+		576460752303416433,
+	}
+	x.Mul(x, &y)
+}
+
+func fromMont(z *Element) {
+	_fromMontGeneric(z)
+}
+
+//go:noescape
+func reduce(res *Element)
diff --git a/ecc/stark-curve/fr/element_arm64.s b/ecc/stark-curve/fr/element_arm64.s
new file mode 100644
index 0000000000..5d328815aa
--- /dev/null
+++ b/ecc/stark-curve/fr/element_arm64.s
@@ -0,0 +1,21 @@
+//go:build  !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 1501560133179981797
+#include "../../../field/asm/element_4w_arm64.s"
+
diff --git a/ecc/stark-curve/fr/element_ops_amd64.go b/ecc/stark-curve/fr/element_ops_amd64.go
deleted file mode 100644
index b653e80069..0000000000
--- a/ecc/stark-curve/fr/element_ops_amd64.go
+++ /dev/null
@@ -1,208 +0,0 @@
-//go:build !purego
-// +build !purego
-
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-// Code generated by consensys/gnark-crypto DO NOT EDIT
-
-package fr
-
-//go:noescape
-func MulBy3(x *Element)
-
-//go:noescape
-func MulBy5(x *Element)
-
-//go:noescape
-func MulBy13(x *Element)
-
-//go:noescape
-func mul(res, x, y *Element)
-
-//go:noescape
-func fromMont(res *Element)
-
-//go:noescape
-func reduce(res *Element)
-
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-//
-//go:noescape
-func Butterfly(a, b *Element)
-
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	if len(a) != len(b) || len(a) != len(*vector) {
-		panic("vector.Add: vectors don't have the same length")
-	}
-	n := uint64(len(a))
-	addVec(&(*vector)[0], &a[0], &b[0], n)
-}
-
-//go:noescape
-func addVec(res, a, b *Element, n uint64)
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	if len(a) != len(b) || len(a) != len(*vector) {
-		panic("vector.Sub: vectors don't have the same length")
-	}
-	subVec(&(*vector)[0], &a[0], &b[0], uint64(len(a)))
-}
-
-//go:noescape
-func subVec(res, a, b *Element, n uint64)
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *Element) {
-	if len(a) != len(*vector) {
-		panic("vector.ScalarMul: vectors don't have the same length")
-	}
-	const maxN = (1 << 32) - 1
-	if !supportAvx512 || uint64(len(a)) >= maxN {
-		// call scalarMulVecGeneric
-		scalarMulVecGeneric(*vector, a, b)
-		return
-	}
-	n := uint64(len(a))
-	if n == 0 {
-		return
-	}
-	// the code for scalarMul is identical to mulVec; and it expects at least
-	// 2 elements in the vector to fill the Z registers
-	var bb [2]Element
-	bb[0] = *b
-	bb[1] = *b
-	const blockSize = 16
-	scalarMulVec(&(*vector)[0], &a[0], &bb[0], n/blockSize, qInvNeg)
-	if n%blockSize != 0 {
-		// call scalarMulVecGeneric on the rest
-		start := n - n%blockSize
-		scalarMulVecGeneric((*vector)[start:], a[start:], b)
-	}
-}
-
-//go:noescape
-func scalarMulVec(res, a, b *Element, n uint64, qInvNeg uint64)
-
-// Sum computes the sum of all elements in the vector.
-func (vector *Vector) Sum() (res Element) {
-	n := uint64(len(*vector))
-	if n == 0 {
-		return
-	}
-	const minN = 16 * 7 // AVX512 slower than generic for small n
-	const maxN = (1 << 32) - 1
-	if !supportAvx512 || n <= minN || n >= maxN {
-		// call sumVecGeneric
-		sumVecGeneric(&res, *vector)
-		return
-	}
-	sumVec(&res, &(*vector)[0], uint64(len(*vector)))
-	return
-}
-
-//go:noescape
-func sumVec(res *Element, a *Element, n uint64)
-
-// InnerProduct computes the inner product of two vectors.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) InnerProduct(other Vector) (res Element) {
-	n := uint64(len(*vector))
-	if n == 0 {
-		return
-	}
-	if n != uint64(len(other)) {
-		panic("vector.InnerProduct: vectors don't have the same length")
-	}
-	const maxN = (1 << 32) - 1
-	if !supportAvx512 || n >= maxN {
-		// call innerProductVecGeneric
-		// note; we could split the vector into smaller chunks and call innerProductVec
-		innerProductVecGeneric(&res, *vector, other)
-		return
-	}
-	innerProdVec(&res[0], &(*vector)[0], &other[0], uint64(len(*vector)))
-
-	return
-}
-
-//go:noescape
-func innerProdVec(res *uint64, a, b *Element, n uint64)
-
-// Mul multiplies two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Mul(a, b Vector) {
-	if len(a) != len(b) || len(a) != len(*vector) {
-		panic("vector.Mul: vectors don't have the same length")
-	}
-	n := uint64(len(a))
-	if n == 0 {
-		return
-	}
-	const maxN = (1 << 32) - 1
-	if !supportAvx512 || n >= maxN {
-		// call mulVecGeneric
-		mulVecGeneric(*vector, a, b)
-		return
-	}
-
-	const blockSize = 16
-	mulVec(&(*vector)[0], &a[0], &b[0], n/blockSize, qInvNeg)
-	if n%blockSize != 0 {
-		// call mulVecGeneric on the rest
-		start := n - n%blockSize
-		mulVecGeneric((*vector)[start:], a[start:], b[start:])
-	}
-
-}
-
-// Patterns use for transposing the vectors in mulVec
-var (
-	pattern1 = [8]uint64{0, 8, 1, 9, 2, 10, 3, 11}
-	pattern2 = [8]uint64{12, 4, 13, 5, 14, 6, 15, 7}
-	pattern3 = [8]uint64{0, 1, 8, 9, 2, 3, 10, 11}
-	pattern4 = [8]uint64{12, 13, 4, 5, 14, 15, 6, 7}
-)
-
-//go:noescape
-func mulVec(res, a, b *Element, n uint64, qInvNeg uint64)
-
-// Mul z = x * y (mod q)
-//
-// x and y must be less than q
-func (z *Element) Mul(x, y *Element) *Element {
-
-	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
-	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
-
-	mul(z, x, y)
-	return z
-}
-
-// Square z = x * x (mod q)
-//
-// x must be less than q
-func (z *Element) Square(x *Element) *Element {
-	// see Mul for doc.
-	mul(z, x, x)
-	return z
-}
diff --git a/ecc/stark-curve/fr/element_ops_amd64.s b/ecc/stark-curve/fr/element_ops_amd64.s
deleted file mode 100644
index 6c42136a7a..0000000000
--- a/ecc/stark-curve/fr/element_ops_amd64.s
+++ /dev/null
@@ -1,6 +0,0 @@
-// +build !purego
-
-// Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 9425145785761608449
-#include "../../../field/asm/element_4w_amd64.s"
-
diff --git a/ecc/stark-curve/fr/element_ops_purego.go b/ecc/stark-curve/fr/element_purego.go
similarity index 88%
rename from ecc/stark-curve/fr/element_ops_purego.go
rename to ecc/stark-curve/fr/element_purego.go
index 2d0db69153..ae05fe839b 100644
--- a/ecc/stark-curve/fr/element_ops_purego.go
+++ b/ecc/stark-curve/fr/element_purego.go
@@ -1,5 +1,4 @@
-//go:build !amd64 || purego
-// +build !amd64 purego
+//go:build purego || (!amd64 && !arm64)
 
 // Copyright 2020 ConsenSys Software Inc.
 //
@@ -44,14 +43,6 @@ func MulBy13(x *Element) {
 	x.Mul(x, &y)
 }
 
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-func Butterfly(a, b *Element) {
-	_butterflyGeneric(a, b)
-}
-
 func fromMont(z *Element) {
 	_fromMontGeneric(z)
 }
@@ -60,43 +51,6 @@ func reduce(z *Element) {
 	_reduceGeneric(z)
 }
 
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	addVecGeneric(*vector, a, b)
-}
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	subVecGeneric(*vector, a, b)
-}
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *Element) {
-	scalarMulVecGeneric(*vector, a, b)
-}
-
-// Sum computes the sum of all elements in the vector.
-func (vector *Vector) Sum() (res Element) {
-	sumVecGeneric(&res, *vector)
-	return
-}
-
-// InnerProduct computes the inner product of two vectors.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) InnerProduct(other Vector) (res Element) {
-	innerProductVecGeneric(&res, *vector, other)
-	return
-}
-
-// Mul multiplies two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Mul(a, b Vector) {
-	mulVecGeneric(*vector, a, b)
-}
-
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
@@ -438,3 +392,11 @@ func (z *Element) Square(x *Element) *Element {
 	}
 	return z
 }
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
diff --git a/ecc/stark-curve/fr/vector_amd64.go b/ecc/stark-curve/fr/vector_amd64.go
new file mode 100644
index 0000000000..0164ecb382
--- /dev/null
+++ b/ecc/stark-curve/fr/vector_amd64.go
@@ -0,0 +1,160 @@
+//go:build !purego
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Add: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	addVec(&(*vector)[0], &a[0], &b[0], n)
+}
+
+//go:noescape
+func addVec(res, a, b *Element, n uint64)
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Sub: vectors don't have the same length")
+	}
+	subVec(&(*vector)[0], &a[0], &b[0], uint64(len(a)))
+}
+
+//go:noescape
+func subVec(res, a, b *Element, n uint64)
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	if len(a) != len(*vector) {
+		panic("vector.ScalarMul: vectors don't have the same length")
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || uint64(len(a)) >= maxN {
+		// call scalarMulVecGeneric
+		scalarMulVecGeneric(*vector, a, b)
+		return
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	// the code for scalarMul is identical to mulVec; and it expects at least
+	// 2 elements in the vector to fill the Z registers
+	var bb [2]Element
+	bb[0] = *b
+	bb[1] = *b
+	const blockSize = 16
+	scalarMulVec(&(*vector)[0], &a[0], &bb[0], n/blockSize, qInvNeg)
+	if n%blockSize != 0 {
+		// call scalarMulVecGeneric on the rest
+		start := n - n%blockSize
+		scalarMulVecGeneric((*vector)[start:], a[start:], b)
+	}
+}
+
+//go:noescape
+func scalarMulVec(res, a, b *Element, n uint64, qInvNeg uint64)
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	const minN = 16 * 7 // AVX512 slower than generic for small n
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n <= minN || n >= maxN {
+		// call sumVecGeneric
+		sumVecGeneric(&res, *vector)
+		return
+	}
+	sumVec(&res, &(*vector)[0], uint64(len(*vector)))
+	return
+}
+
+//go:noescape
+func sumVec(res *Element, a *Element, n uint64)
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	if n != uint64(len(other)) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n >= maxN {
+		// call innerProductVecGeneric
+		// note; we could split the vector into smaller chunks and call innerProductVec
+		innerProductVecGeneric(&res, *vector, other)
+		return
+	}
+	innerProdVec(&res[0], &(*vector)[0], &other[0], uint64(len(*vector)))
+
+	return
+}
+
+//go:noescape
+func innerProdVec(res *uint64, a, b *Element, n uint64)
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n >= maxN {
+		// call mulVecGeneric
+		mulVecGeneric(*vector, a, b)
+		return
+	}
+
+	const blockSize = 16
+	mulVec(&(*vector)[0], &a[0], &b[0], n/blockSize, qInvNeg)
+	if n%blockSize != 0 {
+		// call mulVecGeneric on the rest
+		start := n - n%blockSize
+		mulVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+
+}
+
+// Patterns use for transposing the vectors in mulVec
+var (
+	pattern1 = [8]uint64{0, 8, 1, 9, 2, 10, 3, 11}
+	pattern2 = [8]uint64{12, 4, 13, 5, 14, 6, 15, 7}
+	pattern3 = [8]uint64{0, 1, 8, 9, 2, 3, 10, 11}
+	pattern4 = [8]uint64{12, 13, 4, 5, 14, 15, 6, 7}
+)
+
+//go:noescape
+func mulVec(res, a, b *Element, n uint64, qInvNeg uint64)
diff --git a/ecc/stark-curve/fr/vector_purego.go b/ecc/stark-curve/fr/vector_purego.go
new file mode 100644
index 0000000000..84f86a40b1
--- /dev/null
+++ b/ecc/stark-curve/fr/vector_purego.go
@@ -0,0 +1,56 @@
+//go:build purego || !amd64
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fr
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	addVecGeneric(*vector, a, b)
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	subVecGeneric(*vector, a, b)
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
diff --git a/field/asm/.gitignore b/field/asm/.gitignore
index 7c22f7f933..d534769fcb 100644
--- a/field/asm/.gitignore
+++ b/field/asm/.gitignore
@@ -3,4 +3,9 @@ element_2w_amd64.s
 element_3w_amd64.s
 element_7w_amd64.s
 element_8w_amd64.s
-*.h
\ No newline at end of file
+*.h
+
+element_2w_arm64.s
+element_3w_arm64.s
+element_7w_arm64.s
+element_8w_arm64.s
\ No newline at end of file
diff --git a/field/asm/element_10w_arm64.s b/field/asm/element_10w_arm64.s
new file mode 100644
index 0000000000..529fcae61d
--- /dev/null
+++ b/field/asm/element_10w_arm64.s
@@ -0,0 +1,266 @@
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+#include "textflag.h"
+#include "funcdata.h"
+#include "go_asm.h"
+
+// mul(res, x, y *Element)
+// Algorithm 2 of Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS
+// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+TEXT ·mul(SB), NOFRAME|NOSPLIT, $0-24
+#define DIVSHIFT() \
+	MOVD  $const_qInvNeg, R0   \
+	MUL   R12, R0, R1          \
+	MOVD  ·qElement+0(SB), R0  \
+	MUL   R0, R1, R0           \
+	ADDS  R0, R12, R12         \
+	MOVD  ·qElement+8(SB), R0  \
+	MUL   R0, R1, R0           \
+	ADCS  R0, R13, R13         \
+	MOVD  ·qElement+16(SB), R0 \
+	MUL   R0, R1, R0           \
+	ADCS  R0, R14, R14         \
+	MOVD  ·qElement+24(SB), R0 \
+	MUL   R0, R1, R0           \
+	ADCS  R0, R15, R15         \
+	MOVD  ·qElement+32(SB), R0 \
+	MUL   R0, R1, R0           \
+	ADCS  R0, R16, R16         \
+	MOVD  ·qElement+40(SB), R0 \
+	MUL   R0, R1, R0           \
+	ADCS  R0, R17, R17         \
+	MOVD  ·qElement+48(SB), R0 \
+	MUL   R0, R1, R0           \
+	ADCS  R0, R19, R19         \
+	MOVD  ·qElement+56(SB), R0 \
+	MUL   R0, R1, R0           \
+	ADCS  R0, R20, R20         \
+	MOVD  ·qElement+64(SB), R0 \
+	MUL   R0, R1, R0           \
+	ADCS  R0, R21, R21         \
+	MOVD  ·qElement+72(SB), R0 \
+	MUL   R0, R1, R0           \
+	ADCS  R0, R22, R22         \
+	ADC   R23, ZR, R23         \
+	MOVD  ·qElement+0(SB), R0  \
+	UMULH R0, R1, R0           \
+	ADDS  R0, R13, R12         \
+	MOVD  ·qElement+8(SB), R0  \
+	UMULH R0, R1, R0           \
+	ADCS  R0, R14, R13         \
+	MOVD  ·qElement+16(SB), R0 \
+	UMULH R0, R1, R0           \
+	ADCS  R0, R15, R14         \
+	MOVD  ·qElement+24(SB), R0 \
+	UMULH R0, R1, R0           \
+	ADCS  R0, R16, R15         \
+	MOVD  ·qElement+32(SB), R0 \
+	UMULH R0, R1, R0           \
+	ADCS  R0, R17, R16         \
+	MOVD  ·qElement+40(SB), R0 \
+	UMULH R0, R1, R0           \
+	ADCS  R0, R19, R17         \
+	MOVD  ·qElement+48(SB), R0 \
+	UMULH R0, R1, R0           \
+	ADCS  R0, R20, R19         \
+	MOVD  ·qElement+56(SB), R0 \
+	UMULH R0, R1, R0           \
+	ADCS  R0, R21, R20         \
+	MOVD  ·qElement+64(SB), R0 \
+	UMULH R0, R1, R0           \
+	ADCS  R0, R22, R21         \
+	MOVD  ·qElement+72(SB), R0 \
+	UMULH R0, R1, R0           \
+	ADCS  R0, R23, R22         \
+
+#define MUL_WORD_N() \
+	MUL   R2, R1, R0   \
+	ADDS  R0, R12, R12 \
+	MUL   R3, R1, R0   \
+	ADCS  R0, R13, R13 \
+	MUL   R4, R1, R0   \
+	ADCS  R0, R14, R14 \
+	MUL   R5, R1, R0   \
+	ADCS  R0, R15, R15 \
+	MUL   R6, R1, R0   \
+	ADCS  R0, R16, R16 \
+	MUL   R7, R1, R0   \
+	ADCS  R0, R17, R17 \
+	MUL   R8, R1, R0   \
+	ADCS  R0, R19, R19 \
+	MUL   R9, R1, R0   \
+	ADCS  R0, R20, R20 \
+	MUL   R10, R1, R0  \
+	ADCS  R0, R21, R21 \
+	MUL   R11, R1, R0  \
+	ADCS  R0, R22, R22 \
+	ADC   ZR, ZR, R23  \
+	UMULH R2, R1, R0   \
+	ADDS  R0, R13, R13 \
+	UMULH R3, R1, R0   \
+	ADCS  R0, R14, R14 \
+	UMULH R4, R1, R0   \
+	ADCS  R0, R15, R15 \
+	UMULH R5, R1, R0   \
+	ADCS  R0, R16, R16 \
+	UMULH R6, R1, R0   \
+	ADCS  R0, R17, R17 \
+	UMULH R7, R1, R0   \
+	ADCS  R0, R19, R19 \
+	UMULH R8, R1, R0   \
+	ADCS  R0, R20, R20 \
+	UMULH R9, R1, R0   \
+	ADCS  R0, R21, R21 \
+	UMULH R10, R1, R0  \
+	ADCS  R0, R22, R22 \
+	UMULH R11, R1, R0  \
+	ADC   R0, R23, R23 \
+	DIVSHIFT()         \
+
+#define MUL_WORD_0() \
+	MUL   R2, R1, R12  \
+	MUL   R3, R1, R13  \
+	MUL   R4, R1, R14  \
+	MUL   R5, R1, R15  \
+	MUL   R6, R1, R16  \
+	MUL   R7, R1, R17  \
+	MUL   R8, R1, R19  \
+	MUL   R9, R1, R20  \
+	MUL   R10, R1, R21 \
+	MUL   R11, R1, R22 \
+	UMULH R2, R1, R0   \
+	ADDS  R0, R13, R13 \
+	UMULH R3, R1, R0   \
+	ADCS  R0, R14, R14 \
+	UMULH R4, R1, R0   \
+	ADCS  R0, R15, R15 \
+	UMULH R5, R1, R0   \
+	ADCS  R0, R16, R16 \
+	UMULH R6, R1, R0   \
+	ADCS  R0, R17, R17 \
+	UMULH R7, R1, R0   \
+	ADCS  R0, R19, R19 \
+	UMULH R8, R1, R0   \
+	ADCS  R0, R20, R20 \
+	UMULH R9, R1, R0   \
+	ADCS  R0, R21, R21 \
+	UMULH R10, R1, R0  \
+	ADCS  R0, R22, R22 \
+	UMULH R11, R1, R0  \
+	ADC   R0, ZR, R23  \
+	DIVSHIFT()         \
+
+	MOVD y+16(FP), R1
+	MOVD x+8(FP), R0
+	LDP  0(R0), (R2, R3)
+	LDP  16(R0), (R4, R5)
+	LDP  32(R0), (R6, R7)
+	LDP  48(R0), (R8, R9)
+	LDP  64(R0), (R10, R11)
+	MOVD y+16(FP), R1
+	MOVD 0(R1), R1
+	MUL_WORD_0()
+	MOVD y+16(FP), R1
+	MOVD 8(R1), R1
+	MUL_WORD_N()
+	MOVD y+16(FP), R1
+	MOVD 16(R1), R1
+	MUL_WORD_N()
+	MOVD y+16(FP), R1
+	MOVD 24(R1), R1
+	MUL_WORD_N()
+	MOVD y+16(FP), R1
+	MOVD 32(R1), R1
+	MUL_WORD_N()
+	MOVD y+16(FP), R1
+	MOVD 40(R1), R1
+	MUL_WORD_N()
+	MOVD y+16(FP), R1
+	MOVD 48(R1), R1
+	MUL_WORD_N()
+	MOVD y+16(FP), R1
+	MOVD 56(R1), R1
+	MUL_WORD_N()
+	MOVD y+16(FP), R1
+	MOVD 64(R1), R1
+	MUL_WORD_N()
+	MOVD y+16(FP), R1
+	MOVD 72(R1), R1
+	MUL_WORD_N()
+	LDP  ·qElement+0(SB), (R2, R3)
+	LDP  ·qElement+16(SB), (R4, R5)
+	LDP  ·qElement+32(SB), (R6, R7)
+	LDP  ·qElement+48(SB), (R8, R9)
+	LDP  ·qElement+64(SB), (R10, R11)
+
+	// reduce if necessary
+	SUBS R2, R12, R2
+	SBCS R3, R13, R3
+	SBCS R4, R14, R4
+	SBCS R5, R15, R5
+	SBCS R6, R16, R6
+	SBCS R7, R17, R7
+	SBCS R8, R19, R8
+	SBCS R9, R20, R9
+	SBCS R10, R21, R10
+	SBCS R11, R22, R11
+	MOVD res+0(FP), R0
+	CSEL CS, R2, R12, R12
+	CSEL CS, R3, R13, R13
+	STP  (R12, R13), 0(R0)
+	CSEL CS, R4, R14, R14
+	CSEL CS, R5, R15, R15
+	STP  (R14, R15), 16(R0)
+	CSEL CS, R6, R16, R16
+	CSEL CS, R7, R17, R17
+	STP  (R16, R17), 32(R0)
+	CSEL CS, R8, R19, R19
+	CSEL CS, R9, R20, R20
+	STP  (R19, R20), 48(R0)
+	CSEL CS, R10, R21, R21
+	CSEL CS, R11, R22, R22
+	STP  (R21, R22), 64(R0)
+	RET
+
+// reduce(res *Element)
+TEXT ·reduce(SB), NOFRAME|NOSPLIT, $0-8
+	LDP  ·qElement+0(SB), (R10, R11)
+	LDP  ·qElement+16(SB), (R12, R13)
+	LDP  ·qElement+32(SB), (R14, R15)
+	LDP  ·qElement+48(SB), (R16, R17)
+	LDP  ·qElement+64(SB), (R19, R20)
+	MOVD res+0(FP), R21
+	LDP  0(R21), (R0, R1)
+	LDP  16(R21), (R2, R3)
+	LDP  32(R21), (R4, R5)
+	LDP  48(R21), (R6, R7)
+	LDP  64(R21), (R8, R9)
+
+	// q = t - q
+	SUBS R10, R0, R10
+	SBCS R11, R1, R11
+	SBCS R12, R2, R12
+	SBCS R13, R3, R13
+	SBCS R14, R4, R14
+	SBCS R15, R5, R15
+	SBCS R16, R6, R16
+	SBCS R17, R7, R17
+	SBCS R19, R8, R19
+	SBCS R20, R9, R20
+
+	// if no borrow, return q, else return t
+	CSEL CS, R10, R0, R0
+	CSEL CS, R11, R1, R1
+	STP  (R0, R1), 0(R21)
+	CSEL CS, R12, R2, R2
+	CSEL CS, R13, R3, R3
+	STP  (R2, R3), 16(R21)
+	CSEL CS, R14, R4, R4
+	CSEL CS, R15, R5, R5
+	STP  (R4, R5), 32(R21)
+	CSEL CS, R16, R6, R6
+	CSEL CS, R17, R7, R7
+	STP  (R6, R7), 48(R21)
+	CSEL CS, R19, R8, R8
+	CSEL CS, R20, R9, R9
+	STP  (R8, R9), 64(R21)
+	RET
diff --git a/field/asm/element_12w_arm64.s b/field/asm/element_12w_arm64.s
new file mode 100644
index 0000000000..a03e790ae6
--- /dev/null
+++ b/field/asm/element_12w_arm64.s
@@ -0,0 +1,312 @@
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+#include "textflag.h"
+#include "funcdata.h"
+#include "go_asm.h"
+
+// mul(res, x, y *Element)
+// Algorithm 2 of Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS
+// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+TEXT ·mul(SB), NOFRAME|NOSPLIT, $0-24
+#define DIVSHIFT() \
+	MOVD  $const_qInvNeg, R0   \
+	MUL   R14, R0, R1          \
+	MOVD  ·qElement+0(SB), R0  \
+	MUL   R0, R1, R0           \
+	ADDS  R0, R14, R14         \
+	MOVD  ·qElement+8(SB), R0  \
+	MUL   R0, R1, R0           \
+	ADCS  R0, R15, R15         \
+	MOVD  ·qElement+16(SB), R0 \
+	MUL   R0, R1, R0           \
+	ADCS  R0, R16, R16         \
+	MOVD  ·qElement+24(SB), R0 \
+	MUL   R0, R1, R0           \
+	ADCS  R0, R17, R17         \
+	MOVD  ·qElement+32(SB), R0 \
+	MUL   R0, R1, R0           \
+	ADCS  R0, R19, R19         \
+	MOVD  ·qElement+40(SB), R0 \
+	MUL   R0, R1, R0           \
+	ADCS  R0, R20, R20         \
+	MOVD  ·qElement+48(SB), R0 \
+	MUL   R0, R1, R0           \
+	ADCS  R0, R21, R21         \
+	MOVD  ·qElement+56(SB), R0 \
+	MUL   R0, R1, R0           \
+	ADCS  R0, R22, R22         \
+	MOVD  ·qElement+64(SB), R0 \
+	MUL   R0, R1, R0           \
+	ADCS  R0, R23, R23         \
+	MOVD  ·qElement+72(SB), R0 \
+	MUL   R0, R1, R0           \
+	ADCS  R0, R24, R24         \
+	MOVD  ·qElement+80(SB), R0 \
+	MUL   R0, R1, R0           \
+	ADCS  R0, R25, R25         \
+	MOVD  ·qElement+88(SB), R0 \
+	MUL   R0, R1, R0           \
+	ADCS  R0, R26, R26         \
+	ADC   R29, ZR, R29         \
+	MOVD  ·qElement+0(SB), R0  \
+	UMULH R0, R1, R0           \
+	ADDS  R0, R15, R14         \
+	MOVD  ·qElement+8(SB), R0  \
+	UMULH R0, R1, R0           \
+	ADCS  R0, R16, R15         \
+	MOVD  ·qElement+16(SB), R0 \
+	UMULH R0, R1, R0           \
+	ADCS  R0, R17, R16         \
+	MOVD  ·qElement+24(SB), R0 \
+	UMULH R0, R1, R0           \
+	ADCS  R0, R19, R17         \
+	MOVD  ·qElement+32(SB), R0 \
+	UMULH R0, R1, R0           \
+	ADCS  R0, R20, R19         \
+	MOVD  ·qElement+40(SB), R0 \
+	UMULH R0, R1, R0           \
+	ADCS  R0, R21, R20         \
+	MOVD  ·qElement+48(SB), R0 \
+	UMULH R0, R1, R0           \
+	ADCS  R0, R22, R21         \
+	MOVD  ·qElement+56(SB), R0 \
+	UMULH R0, R1, R0           \
+	ADCS  R0, R23, R22         \
+	MOVD  ·qElement+64(SB), R0 \
+	UMULH R0, R1, R0           \
+	ADCS  R0, R24, R23         \
+	MOVD  ·qElement+72(SB), R0 \
+	UMULH R0, R1, R0           \
+	ADCS  R0, R25, R24         \
+	MOVD  ·qElement+80(SB), R0 \
+	UMULH R0, R1, R0           \
+	ADCS  R0, R26, R25         \
+	MOVD  ·qElement+88(SB), R0 \
+	UMULH R0, R1, R0           \
+	ADCS  R0, R29, R26         \
+
+#define MUL_WORD_N() \
+	MUL   R2, R1, R0   \
+	ADDS  R0, R14, R14 \
+	MUL   R3, R1, R0   \
+	ADCS  R0, R15, R15 \
+	MUL   R4, R1, R0   \
+	ADCS  R0, R16, R16 \
+	MUL   R5, R1, R0   \
+	ADCS  R0, R17, R17 \
+	MUL   R6, R1, R0   \
+	ADCS  R0, R19, R19 \
+	MUL   R7, R1, R0   \
+	ADCS  R0, R20, R20 \
+	MUL   R8, R1, R0   \
+	ADCS  R0, R21, R21 \
+	MUL   R9, R1, R0   \
+	ADCS  R0, R22, R22 \
+	MUL   R10, R1, R0  \
+	ADCS  R0, R23, R23 \
+	MUL   R11, R1, R0  \
+	ADCS  R0, R24, R24 \
+	MUL   R12, R1, R0  \
+	ADCS  R0, R25, R25 \
+	MUL   R13, R1, R0  \
+	ADCS  R0, R26, R26 \
+	ADC   ZR, ZR, R29  \
+	UMULH R2, R1, R0   \
+	ADDS  R0, R15, R15 \
+	UMULH R3, R1, R0   \
+	ADCS  R0, R16, R16 \
+	UMULH R4, R1, R0   \
+	ADCS  R0, R17, R17 \
+	UMULH R5, R1, R0   \
+	ADCS  R0, R19, R19 \
+	UMULH R6, R1, R0   \
+	ADCS  R0, R20, R20 \
+	UMULH R7, R1, R0   \
+	ADCS  R0, R21, R21 \
+	UMULH R8, R1, R0   \
+	ADCS  R0, R22, R22 \
+	UMULH R9, R1, R0   \
+	ADCS  R0, R23, R23 \
+	UMULH R10, R1, R0  \
+	ADCS  R0, R24, R24 \
+	UMULH R11, R1, R0  \
+	ADCS  R0, R25, R25 \
+	UMULH R12, R1, R0  \
+	ADCS  R0, R26, R26 \
+	UMULH R13, R1, R0  \
+	ADC   R0, R29, R29 \
+	DIVSHIFT()         \
+
+#define MUL_WORD_0() \
+	MUL   R2, R1, R14  \
+	MUL   R3, R1, R15  \
+	MUL   R4, R1, R16  \
+	MUL   R5, R1, R17  \
+	MUL   R6, R1, R19  \
+	MUL   R7, R1, R20  \
+	MUL   R8, R1, R21  \
+	MUL   R9, R1, R22  \
+	MUL   R10, R1, R23 \
+	MUL   R11, R1, R24 \
+	MUL   R12, R1, R25 \
+	MUL   R13, R1, R26 \
+	UMULH R2, R1, R0   \
+	ADDS  R0, R15, R15 \
+	UMULH R3, R1, R0   \
+	ADCS  R0, R16, R16 \
+	UMULH R4, R1, R0   \
+	ADCS  R0, R17, R17 \
+	UMULH R5, R1, R0   \
+	ADCS  R0, R19, R19 \
+	UMULH R6, R1, R0   \
+	ADCS  R0, R20, R20 \
+	UMULH R7, R1, R0   \
+	ADCS  R0, R21, R21 \
+	UMULH R8, R1, R0   \
+	ADCS  R0, R22, R22 \
+	UMULH R9, R1, R0   \
+	ADCS  R0, R23, R23 \
+	UMULH R10, R1, R0  \
+	ADCS  R0, R24, R24 \
+	UMULH R11, R1, R0  \
+	ADCS  R0, R25, R25 \
+	UMULH R12, R1, R0  \
+	ADCS  R0, R26, R26 \
+	UMULH R13, R1, R0  \
+	ADC   R0, ZR, R29  \
+	DIVSHIFT()         \
+
+	MOVD y+16(FP), R1
+	MOVD x+8(FP), R0
+	LDP  0(R0), (R2, R3)
+	LDP  16(R0), (R4, R5)
+	LDP  32(R0), (R6, R7)
+	LDP  48(R0), (R8, R9)
+	LDP  64(R0), (R10, R11)
+	LDP  80(R0), (R12, R13)
+	MOVD y+16(FP), R1
+	MOVD 0(R1), R1
+	MUL_WORD_0()
+	MOVD y+16(FP), R1
+	MOVD 8(R1), R1
+	MUL_WORD_N()
+	MOVD y+16(FP), R1
+	MOVD 16(R1), R1
+	MUL_WORD_N()
+	MOVD y+16(FP), R1
+	MOVD 24(R1), R1
+	MUL_WORD_N()
+	MOVD y+16(FP), R1
+	MOVD 32(R1), R1
+	MUL_WORD_N()
+	MOVD y+16(FP), R1
+	MOVD 40(R1), R1
+	MUL_WORD_N()
+	MOVD y+16(FP), R1
+	MOVD 48(R1), R1
+	MUL_WORD_N()
+	MOVD y+16(FP), R1
+	MOVD 56(R1), R1
+	MUL_WORD_N()
+	MOVD y+16(FP), R1
+	MOVD 64(R1), R1
+	MUL_WORD_N()
+	MOVD y+16(FP), R1
+	MOVD 72(R1), R1
+	MUL_WORD_N()
+	MOVD y+16(FP), R1
+	MOVD 80(R1), R1
+	MUL_WORD_N()
+	MOVD y+16(FP), R1
+	MOVD 88(R1), R1
+	MUL_WORD_N()
+	LDP  ·qElement+0(SB), (R2, R3)
+	LDP  ·qElement+16(SB), (R4, R5)
+	LDP  ·qElement+32(SB), (R6, R7)
+	LDP  ·qElement+48(SB), (R8, R9)
+	LDP  ·qElement+64(SB), (R10, R11)
+	LDP  ·qElement+80(SB), (R12, R13)
+
+	// reduce if necessary
+	SUBS R2, R14, R2
+	SBCS R3, R15, R3
+	SBCS R4, R16, R4
+	SBCS R5, R17, R5
+	SBCS R6, R19, R6
+	SBCS R7, R20, R7
+	SBCS R8, R21, R8
+	SBCS R9, R22, R9
+	SBCS R10, R23, R10
+	SBCS R11, R24, R11
+	SBCS R12, R25, R12
+	SBCS R13, R26, R13
+	MOVD res+0(FP), R0
+	CSEL CS, R2, R14, R14
+	CSEL CS, R3, R15, R15
+	STP  (R14, R15), 0(R0)
+	CSEL CS, R4, R16, R16
+	CSEL CS, R5, R17, R17
+	STP  (R16, R17), 16(R0)
+	CSEL CS, R6, R19, R19
+	CSEL CS, R7, R20, R20
+	STP  (R19, R20), 32(R0)
+	CSEL CS, R8, R21, R21
+	CSEL CS, R9, R22, R22
+	STP  (R21, R22), 48(R0)
+	CSEL CS, R10, R23, R23
+	CSEL CS, R11, R24, R24
+	STP  (R23, R24), 64(R0)
+	CSEL CS, R12, R25, R25
+	CSEL CS, R13, R26, R26
+	STP  (R25, R26), 80(R0)
+	RET
+
+// reduce(res *Element)
+TEXT ·reduce(SB), NOFRAME|NOSPLIT, $0-8
+	LDP  ·qElement+0(SB), (R12, R13)
+	LDP  ·qElement+16(SB), (R14, R15)
+	LDP  ·qElement+32(SB), (R16, R17)
+	LDP  ·qElement+48(SB), (R19, R20)
+	LDP  ·qElement+64(SB), (R21, R22)
+	LDP  ·qElement+80(SB), (R23, R24)
+	MOVD res+0(FP), R25
+	LDP  0(R25), (R0, R1)
+	LDP  16(R25), (R2, R3)
+	LDP  32(R25), (R4, R5)
+	LDP  48(R25), (R6, R7)
+	LDP  64(R25), (R8, R9)
+	LDP  80(R25), (R10, R11)
+
+	// q = t - q
+	SUBS R12, R0, R12
+	SBCS R13, R1, R13
+	SBCS R14, R2, R14
+	SBCS R15, R3, R15
+	SBCS R16, R4, R16
+	SBCS R17, R5, R17
+	SBCS R19, R6, R19
+	SBCS R20, R7, R20
+	SBCS R21, R8, R21
+	SBCS R22, R9, R22
+	SBCS R23, R10, R23
+	SBCS R24, R11, R24
+
+	// if no borrow, return q, else return t
+	CSEL CS, R12, R0, R0
+	CSEL CS, R13, R1, R1
+	STP  (R0, R1), 0(R25)
+	CSEL CS, R14, R2, R2
+	CSEL CS, R15, R3, R3
+	STP  (R2, R3), 16(R25)
+	CSEL CS, R16, R4, R4
+	CSEL CS, R17, R5, R5
+	STP  (R4, R5), 32(R25)
+	CSEL CS, R19, R6, R6
+	CSEL CS, R20, R7, R7
+	STP  (R6, R7), 48(R25)
+	CSEL CS, R21, R8, R8
+	CSEL CS, R22, R9, R9
+	STP  (R8, R9), 64(R25)
+	CSEL CS, R23, R10, R10
+	CSEL CS, R24, R11, R11
+	STP  (R10, R11), 80(R25)
+	RET
diff --git a/field/asm/element_4w_arm64.s b/field/asm/element_4w_arm64.s
new file mode 100644
index 0000000000..fce96e3000
--- /dev/null
+++ b/field/asm/element_4w_arm64.s
@@ -0,0 +1,163 @@
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+#include "textflag.h"
+#include "funcdata.h"
+#include "go_asm.h"
+
+// butterfly(a, b *Element)
+// a, b = a+b, a-b
+TEXT ·Butterfly(SB), NOFRAME|NOSPLIT, $0-16
+	LDP  x+0(FP), (R16, R17)
+	LDP  0(R16), (R0, R1)
+	LDP  16(R16), (R2, R3)
+	LDP  0(R17), (R4, R5)
+	LDP  16(R17), (R6, R7)
+	ADDS R0, R4, R8
+	ADCS R1, R5, R9
+	ADCS R2, R6, R10
+	ADC  R3, R7, R11
+	SUBS R4, R0, R4
+	SBCS R5, R1, R5
+	SBCS R6, R2, R6
+	SBCS R7, R3, R7
+	LDP  ·qElement+0(SB), (R0, R1)
+	CSEL CS, ZR, R0, R12
+	CSEL CS, ZR, R1, R13
+	LDP  ·qElement+16(SB), (R2, R3)
+	CSEL CS, ZR, R2, R14
+	CSEL CS, ZR, R3, R15
+
+	// add q if underflow, 0 if not
+	ADDS R4, R12, R4
+	ADCS R5, R13, R5
+	STP  (R4, R5), 0(R17)
+	ADCS R6, R14, R6
+	ADC  R7, R15, R7
+	STP  (R6, R7), 16(R17)
+
+	// q = t - q
+	SUBS R0, R8, R0
+	SBCS R1, R9, R1
+	SBCS R2, R10, R2
+	SBCS R3, R11, R3
+
+	// if no borrow, return q, else return t
+	CSEL CS, R0, R8, R8
+	CSEL CS, R1, R9, R9
+	STP  (R8, R9), 0(R16)
+	CSEL CS, R2, R10, R10
+	CSEL CS, R3, R11, R11
+	STP  (R10, R11), 16(R16)
+	RET
+
+// mul(res, x, y *Element)
+// Algorithm 2 of Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS
+// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+TEXT ·mul(SB), NOFRAME|NOSPLIT, $0-24
+#define DIVSHIFT() \
+	MUL   R13, R12, R0 \
+	ADDS  R0, R6, R6   \
+	MUL   R14, R12, R0 \
+	ADCS  R0, R7, R7   \
+	MUL   R15, R12, R0 \
+	ADCS  R0, R8, R8   \
+	MUL   R16, R12, R0 \
+	ADCS  R0, R9, R9   \
+	ADC   R10, ZR, R10 \
+	UMULH R13, R12, R0 \
+	ADDS  R0, R7, R6   \
+	UMULH R14, R12, R0 \
+	ADCS  R0, R8, R7   \
+	UMULH R15, R12, R0 \
+	ADCS  R0, R9, R8   \
+	UMULH R16, R12, R0 \
+	ADCS  R0, R10, R9  \
+
+#define MUL_WORD_N() \
+	MUL   R2, R1, R0   \
+	ADDS  R0, R6, R6   \
+	MUL   R6, R11, R12 \
+	MUL   R3, R1, R0   \
+	ADCS  R0, R7, R7   \
+	MUL   R4, R1, R0   \
+	ADCS  R0, R8, R8   \
+	MUL   R5, R1, R0   \
+	ADCS  R0, R9, R9   \
+	ADC   ZR, ZR, R10  \
+	UMULH R2, R1, R0   \
+	ADDS  R0, R7, R7   \
+	UMULH R3, R1, R0   \
+	ADCS  R0, R8, R8   \
+	UMULH R4, R1, R0   \
+	ADCS  R0, R9, R9   \
+	UMULH R5, R1, R0   \
+	ADC   R0, R10, R10 \
+	DIVSHIFT()         \
+
+#define MUL_WORD_0() \
+	MUL   R2, R1, R6   \
+	MUL   R3, R1, R7   \
+	MUL   R4, R1, R8   \
+	MUL   R5, R1, R9   \
+	UMULH R2, R1, R0   \
+	ADDS  R0, R7, R7   \
+	UMULH R3, R1, R0   \
+	ADCS  R0, R8, R8   \
+	UMULH R4, R1, R0   \
+	ADCS  R0, R9, R9   \
+	UMULH R5, R1, R0   \
+	ADC   R0, ZR, R10  \
+	MUL   R6, R11, R12 \
+	DIVSHIFT()         \
+
+	MOVD y+16(FP), R17
+	MOVD x+8(FP), R0
+	LDP  0(R0), (R2, R3)
+	LDP  16(R0), (R4, R5)
+	MOVD 0(R17), R1
+	MOVD $const_qInvNeg, R11
+	LDP  ·qElement+0(SB), (R13, R14)
+	LDP  ·qElement+16(SB), (R15, R16)
+	MUL_WORD_0()
+	MOVD 8(R17), R1
+	MUL_WORD_N()
+	MOVD 16(R17), R1
+	MUL_WORD_N()
+	MOVD 24(R17), R1
+	MUL_WORD_N()
+
+	// reduce if necessary
+	SUBS R13, R6, R13
+	SBCS R14, R7, R14
+	SBCS R15, R8, R15
+	SBCS R16, R9, R16
+	MOVD res+0(FP), R0
+	CSEL CS, R13, R6, R6
+	CSEL CS, R14, R7, R7
+	STP  (R6, R7), 0(R0)
+	CSEL CS, R15, R8, R8
+	CSEL CS, R16, R9, R9
+	STP  (R8, R9), 16(R0)
+	RET
+
+// reduce(res *Element)
+TEXT ·reduce(SB), NOFRAME|NOSPLIT, $0-8
+	LDP  ·qElement+0(SB), (R4, R5)
+	LDP  ·qElement+16(SB), (R6, R7)
+	MOVD res+0(FP), R8
+	LDP  0(R8), (R0, R1)
+	LDP  16(R8), (R2, R3)
+
+	// q = t - q
+	SUBS R4, R0, R4
+	SBCS R5, R1, R5
+	SBCS R6, R2, R6
+	SBCS R7, R3, R7
+
+	// if no borrow, return q, else return t
+	CSEL CS, R4, R0, R0
+	CSEL CS, R5, R1, R1
+	STP  (R0, R1), 0(R8)
+	CSEL CS, R6, R2, R2
+	CSEL CS, R7, R3, R3
+	STP  (R2, R3), 16(R8)
+	RET
diff --git a/field/asm/element_6w_arm64.s b/field/asm/element_6w_arm64.s
new file mode 100644
index 0000000000..7dbd7ecaf3
--- /dev/null
+++ b/field/asm/element_6w_arm64.s
@@ -0,0 +1,220 @@
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+#include "textflag.h"
+#include "funcdata.h"
+#include "go_asm.h"
+
+// butterfly(a, b *Element)
+// a, b = a+b, a-b
+TEXT ·Butterfly(SB), NOFRAME|NOSPLIT, $0-16
+	LDP  x+0(FP), (R25, R26)
+	LDP  0(R25), (R0, R1)
+	LDP  16(R25), (R2, R3)
+	LDP  32(R25), (R4, R5)
+	LDP  0(R26), (R6, R7)
+	LDP  16(R26), (R8, R9)
+	LDP  32(R26), (R10, R11)
+	ADDS R0, R6, R12
+	ADCS R1, R7, R13
+	ADCS R2, R8, R14
+	ADCS R3, R9, R15
+	ADCS R4, R10, R16
+	ADC  R5, R11, R17
+	SUBS R6, R0, R6
+	SBCS R7, R1, R7
+	SBCS R8, R2, R8
+	SBCS R9, R3, R9
+	SBCS R10, R4, R10
+	SBCS R11, R5, R11
+	LDP  ·qElement+0(SB), (R0, R1)
+	CSEL CS, ZR, R0, R19
+	CSEL CS, ZR, R1, R20
+	LDP  ·qElement+16(SB), (R2, R3)
+	CSEL CS, ZR, R2, R21
+	CSEL CS, ZR, R3, R22
+	LDP  ·qElement+32(SB), (R4, R5)
+	CSEL CS, ZR, R4, R23
+	CSEL CS, ZR, R5, R24
+
+	// add q if underflow, 0 if not
+	ADDS R6, R19, R6
+	ADCS R7, R20, R7
+	STP  (R6, R7), 0(R26)
+	ADCS R8, R21, R8
+	ADCS R9, R22, R9
+	STP  (R8, R9), 16(R26)
+	ADCS R10, R23, R10
+	ADC  R11, R24, R11
+	STP  (R10, R11), 32(R26)
+
+	// q = t - q
+	SUBS R0, R12, R0
+	SBCS R1, R13, R1
+	SBCS R2, R14, R2
+	SBCS R3, R15, R3
+	SBCS R4, R16, R4
+	SBCS R5, R17, R5
+
+	// if no borrow, return q, else return t
+	CSEL CS, R0, R12, R12
+	CSEL CS, R1, R13, R13
+	STP  (R12, R13), 0(R25)
+	CSEL CS, R2, R14, R14
+	CSEL CS, R3, R15, R15
+	STP  (R14, R15), 16(R25)
+	CSEL CS, R4, R16, R16
+	CSEL CS, R5, R17, R17
+	STP  (R16, R17), 32(R25)
+	RET
+
+// mul(res, x, y *Element)
+// Algorithm 2 of Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS
+// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
+TEXT ·mul(SB), NOFRAME|NOSPLIT, $0-24
+#define DIVSHIFT() \
+	MUL   R17, R16, R0 \
+	ADDS  R0, R8, R8   \
+	MUL   R19, R16, R0 \
+	ADCS  R0, R9, R9   \
+	MUL   R20, R16, R0 \
+	ADCS  R0, R10, R10 \
+	MUL   R21, R16, R0 \
+	ADCS  R0, R11, R11 \
+	MUL   R22, R16, R0 \
+	ADCS  R0, R12, R12 \
+	MUL   R23, R16, R0 \
+	ADCS  R0, R13, R13 \
+	ADC   R14, ZR, R14 \
+	UMULH R17, R16, R0 \
+	ADDS  R0, R9, R8   \
+	UMULH R19, R16, R0 \
+	ADCS  R0, R10, R9  \
+	UMULH R20, R16, R0 \
+	ADCS  R0, R11, R10 \
+	UMULH R21, R16, R0 \
+	ADCS  R0, R12, R11 \
+	UMULH R22, R16, R0 \
+	ADCS  R0, R13, R12 \
+	UMULH R23, R16, R0 \
+	ADCS  R0, R14, R13 \
+
+#define MUL_WORD_N() \
+	MUL   R2, R1, R0   \
+	ADDS  R0, R8, R8   \
+	MUL   R8, R15, R16 \
+	MUL   R3, R1, R0   \
+	ADCS  R0, R9, R9   \
+	MUL   R4, R1, R0   \
+	ADCS  R0, R10, R10 \
+	MUL   R5, R1, R0   \
+	ADCS  R0, R11, R11 \
+	MUL   R6, R1, R0   \
+	ADCS  R0, R12, R12 \
+	MUL   R7, R1, R0   \
+	ADCS  R0, R13, R13 \
+	ADC   ZR, ZR, R14  \
+	UMULH R2, R1, R0   \
+	ADDS  R0, R9, R9   \
+	UMULH R3, R1, R0   \
+	ADCS  R0, R10, R10 \
+	UMULH R4, R1, R0   \
+	ADCS  R0, R11, R11 \
+	UMULH R5, R1, R0   \
+	ADCS  R0, R12, R12 \
+	UMULH R6, R1, R0   \
+	ADCS  R0, R13, R13 \
+	UMULH R7, R1, R0   \
+	ADC   R0, R14, R14 \
+	DIVSHIFT()         \
+
+#define MUL_WORD_0() \
+	MUL   R2, R1, R8   \
+	MUL   R3, R1, R9   \
+	MUL   R4, R1, R10  \
+	MUL   R5, R1, R11  \
+	MUL   R6, R1, R12  \
+	MUL   R7, R1, R13  \
+	UMULH R2, R1, R0   \
+	ADDS  R0, R9, R9   \
+	UMULH R3, R1, R0   \
+	ADCS  R0, R10, R10 \
+	UMULH R4, R1, R0   \
+	ADCS  R0, R11, R11 \
+	UMULH R5, R1, R0   \
+	ADCS  R0, R12, R12 \
+	UMULH R6, R1, R0   \
+	ADCS  R0, R13, R13 \
+	UMULH R7, R1, R0   \
+	ADC   R0, ZR, R14  \
+	MUL   R8, R15, R16 \
+	DIVSHIFT()         \
+
+	MOVD y+16(FP), R24
+	MOVD x+8(FP), R0
+	LDP  0(R0), (R2, R3)
+	LDP  16(R0), (R4, R5)
+	LDP  32(R0), (R6, R7)
+	MOVD 0(R24), R1
+	MOVD $const_qInvNeg, R15
+	LDP  ·qElement+0(SB), (R17, R19)
+	LDP  ·qElement+16(SB), (R20, R21)
+	LDP  ·qElement+32(SB), (R22, R23)
+	MUL_WORD_0()
+	MOVD 8(R24), R1
+	MUL_WORD_N()
+	MOVD 16(R24), R1
+	MUL_WORD_N()
+	MOVD 24(R24), R1
+	MUL_WORD_N()
+	MOVD 32(R24), R1
+	MUL_WORD_N()
+	MOVD 40(R24), R1
+	MUL_WORD_N()
+
+	// reduce if necessary
+	SUBS R17, R8, R17
+	SBCS R19, R9, R19
+	SBCS R20, R10, R20
+	SBCS R21, R11, R21
+	SBCS R22, R12, R22
+	SBCS R23, R13, R23
+	MOVD res+0(FP), R0
+	CSEL CS, R17, R8, R8
+	CSEL CS, R19, R9, R9
+	STP  (R8, R9), 0(R0)
+	CSEL CS, R20, R10, R10
+	CSEL CS, R21, R11, R11
+	STP  (R10, R11), 16(R0)
+	CSEL CS, R22, R12, R12
+	CSEL CS, R23, R13, R13
+	STP  (R12, R13), 32(R0)
+	RET
+
+// reduce(res *Element)
+TEXT ·reduce(SB), NOFRAME|NOSPLIT, $0-8
+	LDP  ·qElement+0(SB), (R6, R7)
+	LDP  ·qElement+16(SB), (R8, R9)
+	LDP  ·qElement+32(SB), (R10, R11)
+	MOVD res+0(FP), R12
+	LDP  0(R12), (R0, R1)
+	LDP  16(R12), (R2, R3)
+	LDP  32(R12), (R4, R5)
+
+	// q = t - q
+	SUBS R6, R0, R6
+	SBCS R7, R1, R7
+	SBCS R8, R2, R8
+	SBCS R9, R3, R9
+	SBCS R10, R4, R10
+	SBCS R11, R5, R11
+
+	// if no borrow, return q, else return t
+	CSEL CS, R6, R0, R0
+	CSEL CS, R7, R1, R1
+	STP  (R0, R1), 0(R12)
+	CSEL CS, R8, R2, R2
+	CSEL CS, R9, R3, R3
+	STP  (R2, R3), 16(R12)
+	CSEL CS, R10, R4, R4
+	CSEL CS, R11, R5, R5
+	STP  (R4, R5), 32(R12)
+	RET
diff --git a/field/generator/asm/amd64/build.go b/field/generator/asm/amd64/build.go
index 9f2e44bd1a..40edcfc366 100644
--- a/field/generator/asm/amd64/build.go
+++ b/field/generator/asm/amd64/build.go
@@ -137,13 +137,6 @@ startDefine:
 	return toReturn
 }
 
-func max(a, b int) int {
-	if a > b {
-		return a
-	}
-	return b
-}
-
 func (f *FFAmd64) AssertCleanStack(reservedStackSize, minStackSize int) {
 	if f.nbElementsOnStack != 0 {
 		panic("missing f.Push stack elements")
diff --git a/field/generator/asm/arm64/build.go b/field/generator/asm/arm64/build.go
new file mode 100644
index 0000000000..1752dae187
--- /dev/null
+++ b/field/generator/asm/arm64/build.go
@@ -0,0 +1,258 @@
+package arm64
+
+import (
+	"fmt"
+	"hash/fnv"
+	"io"
+	"os"
+	"path/filepath"
+	"strings"
+
+	"github.com/consensys/bavard/arm64"
+	"github.com/consensys/gnark-crypto/field/generator/config"
+)
+
+const (
+	ElementASMFileName = "element_%dw_arm64.s"
+)
+
+type defineFn func(args ...arm64.Register)
+
+func NewFFArm64(w io.Writer, nbWords int) *FFArm64 {
+	F := &FFArm64{
+		arm64.NewArm64(w),
+		0,
+		0,
+		nbWords,
+		nbWords - 1,
+		make([]int, nbWords),
+		make([]int, nbWords-1),
+		make(map[string]defineFn),
+	}
+
+	// indexes (template helpers)
+	for i := 0; i < F.NbWords; i++ {
+		F.NbWordsIndexesFull[i] = i
+		if i > 0 {
+			F.NbWordsIndexesNoZero[i-1] = i
+		}
+	}
+
+	return F
+}
+
+type FFArm64 struct {
+	*arm64.Arm64
+	nbElementsOnStack    int
+	maxOnStack           int
+	NbWords              int
+	NbWordsLastIndex     int
+	NbWordsIndexesFull   []int
+	NbWordsIndexesNoZero []int
+	mDefines             map[string]defineFn
+}
+
+func GenerateFieldWrapper(w io.Writer, F *config.FieldConfig, asmDirBuildPath, asmDirIncludePath string) error {
+	// for each field we generate the defines for the modulus and the montgomery constant
+	f := NewFFArm64(w, F.NbWords)
+
+	// we add the defines first, then the common asm, then the global variable section
+	// to enable correct compilations with #include in order.
+	f.WriteLn("")
+
+	hashAndInclude := func(fileName string) error {
+		// we hash the file content and include the hash in comment of the generated file
+		// to force the Go compiler to recompile the file if the content has changed
+		fData, err := os.ReadFile(filepath.Join(asmDirBuildPath, fileName))
+		if err != nil {
+			return err
+		}
+		// hash the file using FNV
+		hasher := fnv.New64()
+		hasher.Write(fData)
+		hash := hasher.Sum64()
+
+		f.WriteLn("// Code generated by gnark-crypto/generator. DO NOT EDIT.")
+		f.WriteLn(fmt.Sprintf("// We include the hash to force the Go compiler to recompile: %d", hash))
+		includePath := filepath.Join(asmDirIncludePath, fileName)
+		// on windows, we replace the "\" by "/"
+		if filepath.Separator == '\\' {
+			includePath = strings.ReplaceAll(includePath, "\\", "/")
+		}
+		f.WriteLn(fmt.Sprintf("#include \"%s\"\n", includePath))
+
+		return nil
+	}
+
+	toInclude := fmt.Sprintf(ElementASMFileName, F.NbWords)
+	if err := hashAndInclude(toInclude); err != nil {
+		return err
+	}
+
+	return nil
+}
+
+// GenerateCommonASM generates assembly code for the base field provided to goff
+// see internal/templates/ops*
+func GenerateCommonASM(w io.Writer, nbWords int, hasVector bool) error {
+	f := NewFFArm64(w, nbWords)
+	f.Comment("Code generated by gnark-crypto/generator. DO NOT EDIT.")
+
+	f.WriteLn("#include \"textflag.h\"")
+	f.WriteLn("#include \"funcdata.h\"")
+	f.WriteLn("#include \"go_asm.h\"")
+	f.WriteLn("")
+
+	if f.NbWords%2 != 0 {
+		panic("NbWords must be even")
+	}
+
+	if f.NbWords <= 6 {
+		f.generateButterfly()
+	}
+	f.generateMul()
+	f.generateReduce()
+
+	return nil
+}
+
+func (f *FFArm64) DefineFn(name string) (fn defineFn, err error) {
+	fn, ok := f.mDefines[name]
+	if !ok {
+		return nil, fmt.Errorf("function %s not defined", name)
+	}
+	return fn, nil
+}
+
+func (f *FFArm64) Define(name string, nbInputs int, fn defineFn) defineFn {
+
+	inputs := make([]string, nbInputs)
+	for i := 0; i < nbInputs; i++ {
+		inputs[i] = fmt.Sprintf("in%d", i)
+	}
+	name = strings.ToUpper(name)
+
+	for _, ok := f.mDefines[name]; ok; {
+		// name already exist, for code generation purpose we add a suffix
+		// should happen only with e2 deprecated functions
+		fmt.Println("WARNING: function name already defined, adding suffix")
+		i := 0
+		for {
+			newName := fmt.Sprintf("%s_%d", name, i)
+			if _, ok := f.mDefines[newName]; !ok {
+				name = newName
+				goto startDefine
+			}
+			i++
+		}
+	}
+startDefine:
+
+	f.StartDefine()
+	f.WriteLn("#define " + name + "(" + strings.Join(inputs, ", ") + ")")
+	inputsRegisters := make([]arm64.Register, nbInputs)
+	for i := 0; i < nbInputs; i++ {
+		inputsRegisters[i] = arm64.Register(inputs[i])
+	}
+	fn(inputsRegisters...)
+	f.EndDefine()
+	f.WriteLn("")
+
+	toReturn := func(args ...arm64.Register) {
+		if len(args) != nbInputs {
+			panic("invalid number of arguments")
+		}
+		inputsStr := make([]string, len(args))
+		for i := 0; i < len(args); i++ {
+			inputsStr[i] = string(args[i])
+		}
+		f.WriteLn(name + "(" + strings.Join(inputsStr, ", ") + ")")
+	}
+
+	f.mDefines[name] = toReturn
+
+	return toReturn
+}
+
+func (f *FFArm64) AssertCleanStack(reservedStackSize, minStackSize int) {
+	if f.nbElementsOnStack != 0 {
+		panic("missing f.Push stack elements")
+	}
+	if reservedStackSize < minStackSize {
+		panic("invalid minStackSize or reservedStackSize")
+	}
+	usedStackSize := f.maxOnStack * 8
+	if usedStackSize > reservedStackSize {
+		panic("using more stack size than reserved")
+	} else if max(usedStackSize, minStackSize) < reservedStackSize {
+		// this panic is for dev purposes as this may be by design for aligment
+		panic("reserved more stack size than needed")
+	}
+
+	f.maxOnStack = 0
+}
+
+func (f *FFArm64) Push(registers *arm64.Registers, rIn ...arm64.Register) {
+	for _, r := range rIn {
+		if strings.HasPrefix(string(r), "s") {
+			// it's on the stack, decrease the offset
+			f.nbElementsOnStack--
+			continue
+		}
+		registers.Push(r)
+	}
+}
+
+func (f *FFArm64) Pop(registers *arm64.Registers, forceStack ...bool) arm64.Register {
+	if registers.Available() >= 1 && !(len(forceStack) > 0 && forceStack[0]) {
+		return registers.Pop()
+	}
+	r := arm64.Register(fmt.Sprintf("s%d-%d(SP)", f.nbElementsOnStack, 8+f.nbElementsOnStack*8))
+	f.nbElementsOnStack++
+	if f.nbElementsOnStack > f.maxOnStack {
+		f.maxOnStack = f.nbElementsOnStack
+	}
+	return r
+}
+
+func (f *FFArm64) PopN(registers *arm64.Registers, forceStack ...bool) []arm64.Register {
+	if len(forceStack) > 0 && forceStack[0] {
+		nbStack := f.NbWords
+		var u []arm64.Register
+
+		for i := f.nbElementsOnStack; i < nbStack+f.nbElementsOnStack; i++ {
+			u = append(u, arm64.Register(fmt.Sprintf("s%d-%d(SP)", i, 8+i*8)))
+		}
+		f.nbElementsOnStack += nbStack
+		if f.nbElementsOnStack > f.maxOnStack {
+			f.maxOnStack = f.nbElementsOnStack
+		}
+		return u
+	}
+	if registers.Available() >= f.NbWords {
+		return registers.PopN(f.NbWords)
+	}
+	nbStack := f.NbWords - registers.Available()
+	u := registers.PopN(registers.Available())
+
+	for i := f.nbElementsOnStack; i < nbStack+f.nbElementsOnStack; i++ {
+		u = append(u, arm64.Register(fmt.Sprintf("s%d-%d(SP)", i, 8+i*8)))
+	}
+	f.nbElementsOnStack += nbStack
+	if f.nbElementsOnStack > f.maxOnStack {
+		f.maxOnStack = f.nbElementsOnStack
+	}
+	return u
+}
+
+func (f *FFArm64) qAt(index int) string {
+	return fmt.Sprintf("·qElement+%d(SB)", index*8)
+}
+
+func (f *FFArm64) qInv0() string {
+	return "$const_qInvNeg"
+}
+
+func (f *FFArm64) qi(i int) string {
+	return fmt.Sprintf("$const_q%d", i)
+}
diff --git a/field/generator/asm/arm64/element_butterfly.go b/field/generator/asm/arm64/element_butterfly.go
new file mode 100644
index 0000000000..064e3a2843
--- /dev/null
+++ b/field/generator/asm/arm64/element_butterfly.go
@@ -0,0 +1,47 @@
+package arm64
+
+func (f *FFArm64) generateButterfly() {
+	f.Comment("butterfly(a, b *Element)")
+	f.Comment("a, b = a+b, a-b")
+	registers := f.FnHeader("Butterfly", 0, 16)
+	defer f.AssertCleanStack(0, 0)
+
+	// registers
+	a := registers.PopN(f.NbWords)
+	b := registers.PopN(f.NbWords)
+	r := registers.PopN(f.NbWords)
+	t := registers.PopN(f.NbWords)
+	aPtr := registers.Pop()
+	bPtr := registers.Pop()
+
+	f.LDP("x+0(FP)", aPtr, bPtr)
+	f.load(aPtr, a)
+	f.load(bPtr, b)
+
+	for i := 0; i < f.NbWords; i++ {
+		f.add0n(i)(a[i], b[i], r[i])
+	}
+
+	f.SUBS(b[0], a[0], b[0])
+	for i := 1; i < f.NbWords; i++ {
+		f.SBCS(b[i], a[i], b[i])
+	}
+
+	for i := 0; i < f.NbWords; i++ {
+		if i%2 == 0 {
+			f.LDP(f.qAt(i), a[i], a[i+1])
+		}
+		f.CSEL("CS", "ZR", a[i], t[i])
+	}
+	f.Comment("add q if underflow, 0 if not")
+	for i := 0; i < f.NbWords; i++ {
+		f.add0n(i)(b[i], t[i], b[i])
+		if i%2 == 1 {
+			f.STP(b[i-1], b[i], bPtr.At(i-1))
+		}
+	}
+
+	f.reduceAndStore(r, a, aPtr)
+
+	f.RET()
+}
diff --git a/field/generator/asm/arm64/element_mul.go b/field/generator/asm/arm64/element_mul.go
new file mode 100644
index 0000000000..2a2de0ad0c
--- /dev/null
+++ b/field/generator/asm/arm64/element_mul.go
@@ -0,0 +1,259 @@
+// Copyright 2022 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package arm64
+
+import (
+	"github.com/consensys/bavard/arm64"
+)
+
+func (f *FFArm64) generateMul() {
+	f.Comment("mul(res, x, y *Element)")
+	f.Comment("Algorithm 2 of Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS")
+	f.Comment("by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521")
+	registers := f.FnHeader("mul", 0, 24)
+	defer f.AssertCleanStack(0, 0)
+
+	fatModulus := f.NbWords > 6
+
+	xPtr := registers.Pop()
+	// yPtr := registers.Pop()
+	bi := registers.Pop()
+	a := registers.PopN(f.NbWords)
+	t := registers.PopN(f.NbWords + 1)
+
+	var qInv0, m, yPtr arm64.Register
+	var q []arm64.Register
+	ax := xPtr
+	if fatModulus {
+		qInv0 = ax
+		m = bi
+		yPtr = bi
+	} else {
+		qInv0 = registers.Pop()
+		m = registers.Pop()
+		q = registers.PopN(f.NbWords)
+		yPtr = registers.Pop()
+	}
+
+	qAt := func(i int) arm64.Register {
+		if !fatModulus {
+			return q[i]
+		}
+		f.MOVD(f.qAt(i), ax)
+		return ax
+	}
+
+	divShift := f.Define("divShift", 0, func(args ...arm64.Register) {
+		if fatModulus {
+			f.MOVD(f.qInv0(), qInv0)
+			f.MUL(t[0], qInv0, m)
+		}
+		// for j=0 to N-1
+		//	(C,t[j-1]) := t[j] + m*q[j] + C
+
+		for j := 0; j < f.NbWords; j++ {
+			f.MUL(qAt(j), m, ax)
+			f.add0m(j)(ax, t[j], t[j])
+		}
+		f.add0m(f.NbWords)(t[f.NbWords], "ZR", t[f.NbWords])
+
+		// propagate high bits
+		f.UMULH(qAt(0), m, ax)
+		for j := 1; j <= f.NbWords; j++ {
+			f.add1m(j, true)(ax, t[j], t[j-1])
+			if j != f.NbWords {
+				f.UMULH(qAt(j), m, ax)
+			}
+		}
+	})
+
+	mulWordN := f.Define("MUL_WORD_N", 0, func(args ...arm64.Register) {
+		// for j=0 to N-1
+		//    (C,t[j])  := t[j] + a[j]*b[i] + C
+
+		// lo bits
+		for j := 0; j < f.NbWords; j++ {
+			f.MUL(a[j], bi, ax)
+			f.add0m(j)(ax, t[j], t[j])
+
+			if j == 0 && !fatModulus {
+				f.MUL(t[0], qInv0, m)
+			}
+		}
+		f.add0m(f.NbWords)("ZR", "ZR", t[f.NbWords])
+
+		// propagate high bits
+		f.UMULH(a[0], bi, ax)
+		for j := 1; j <= f.NbWords; j++ {
+			f.add1m(j)(ax, t[j], t[j])
+			if j != f.NbWords {
+				f.UMULH(a[j], bi, ax)
+			}
+		}
+		divShift()
+	})
+
+	mulWord0 := f.Define("MUL_WORD_0", 0, func(args ...arm64.Register) {
+		// for j=0 to N-1
+		//    (C,t[j])  := t[j] + a[j]*b[i] + C
+		// lo bits
+		for j := 0; j < f.NbWords; j++ {
+			f.MUL(a[j], bi, t[j])
+		}
+
+		// propagate high bits
+		f.UMULH(a[0], bi, ax)
+		for j := 1; j < f.NbWords; j++ {
+			f.add1m(j)(ax, t[j], t[j])
+			f.UMULH(a[j], bi, ax)
+		}
+		f.add1m(f.NbWords)(ax, "ZR", t[f.NbWords])
+		if !fatModulus {
+			f.MUL(t[0], qInv0, m)
+		}
+		divShift()
+	})
+
+	f.MOVD("y+16(FP)", yPtr)
+	f.MOVD("x+8(FP)", xPtr)
+	f.load(xPtr, a)
+
+	for i := 0; i < f.NbWords; i++ {
+		if fatModulus {
+			f.MOVD("y+16(FP)", yPtr)
+		}
+		f.MOVD(yPtr.At(i), bi)
+
+		if i == 0 {
+			// load qInv0 and q at first iteration.
+			if !fatModulus {
+				f.MOVD(f.qInv0(), qInv0)
+				for i := 0; i < f.NbWords; i += 2 {
+					f.LDP(f.qAt(i), q[i], q[i+1])
+				}
+			}
+			mulWord0()
+		} else {
+			mulWordN()
+		}
+	}
+
+	if fatModulus {
+		q = a
+		for i := 0; i < f.NbWords; i += 2 {
+			f.LDP(f.qAt(i), q[i], q[i+1])
+		}
+	}
+
+	f.Comment("reduce if necessary")
+	f.SUBS(q[0], t[0], q[0])
+	for i := 1; i < f.NbWords; i++ {
+		f.SBCS(q[i], t[i], q[i])
+	}
+
+	f.MOVD("res+0(FP)", ax)
+	for i := 0; i < f.NbWords; i++ {
+		f.CSEL("CS", q[i], t[i], t[i])
+		if i%2 == 1 {
+			f.STP(t[i-1], t[i], ax.At(i-1))
+		}
+	}
+
+	f.RET()
+}
+
+func (f *FFArm64) generateReduce() {
+	f.Comment("reduce(res *Element)")
+	registers := f.FnHeader("reduce", 0, 8)
+	defer f.AssertCleanStack(0, 0)
+
+	// registers
+	t := registers.PopN(f.NbWords)
+	q := registers.PopN(f.NbWords)
+	rPtr := registers.Pop()
+
+	for i := 0; i < f.NbWords; i += 2 {
+		f.LDP(f.qAt(i), q[i], q[i+1])
+	}
+
+	f.MOVD("res+0(FP)", rPtr)
+	f.load(rPtr, t)
+	f.reduceAndStore(t, q, rPtr)
+
+	f.RET()
+}
+
+func (f *FFArm64) load(zPtr arm64.Register, z []arm64.Register) {
+	for i := 0; i < f.NbWords; i += 2 {
+		f.LDP(zPtr.At(i), z[i], z[i+1])
+	}
+}
+
+// q must contain the modulus
+// q is modified
+// t = t mod q (t must be less than 2q)
+// t is stored in zPtr
+func (f *FFArm64) reduceAndStore(t, q []arm64.Register, zPtr arm64.Register) {
+	f.Comment("q = t - q")
+	f.SUBS(q[0], t[0], q[0])
+	for i := 1; i < f.NbWords; i++ {
+		f.SBCS(q[i], t[i], q[i])
+	}
+
+	f.Comment("if no borrow, return q, else return t")
+	for i := 0; i < f.NbWords; i++ {
+		f.CSEL("CS", q[i], t[i], t[i])
+		if i%2 == 1 {
+			f.STP(t[i-1], t[i], zPtr.At(i-1))
+		}
+	}
+}
+
+func (f *FFArm64) add0n(i int) func(op1, op2, dst interface{}, comment ...string) {
+	switch {
+	case i == 0:
+		return f.ADDS
+	case i == f.NbWordsLastIndex:
+		return f.ADC
+	default:
+		return f.ADCS
+	}
+}
+
+func (f *FFArm64) add0m(i int) func(op1, op2, dst interface{}, comment ...string) {
+	switch {
+	case i == 0:
+		return f.ADDS
+	case i == f.NbWordsLastIndex+1:
+		return f.ADC
+	default:
+		return f.ADCS
+	}
+}
+
+func (f *FFArm64) add1m(i int, dumb ...bool) func(op1, op2, dst interface{}, comment ...string) {
+	switch {
+	case i == 1:
+		return f.ADDS
+	case i == f.NbWordsLastIndex+1:
+		if len(dumb) == 1 && dumb[0] {
+			// odd, but it performs better on c8g instances.
+			return f.ADCS
+		}
+		return f.ADC
+	default:
+		return f.ADCS
+	}
+}
diff --git a/field/generator/config/field_config.go b/field/generator/config/field_config.go
index 6d24aab743..f6e5513b4c 100644
--- a/field/generator/config/field_config.go
+++ b/field/generator/config/field_config.go
@@ -52,8 +52,6 @@ type FieldConfig struct {
 	QInverse                  []uint64
 	QMinusOneHalvedP          []uint64 // ((q-1) / 2 ) + 1
 	Mu                        uint64   // mu = 2^288 / q for 4.5 word barrett reduction
-	ASM                       bool
-	ASMVector                 bool
 	RSquare                   []uint64
 	One, Thirteen             []uint64
 	LegendreExponent          string // big.Int to base16 string
@@ -74,6 +72,12 @@ type FieldConfig struct {
 	SqrtSMinusOneOver2Data    *addchain.AddChainData
 	SqrtQ3Mod4ExponentData    *addchain.AddChainData
 	UseAddChain               bool
+
+	// asm code generation
+	GenerateOpsAMD64       bool
+	GenerateOpsARM64       bool
+	GenerateVectorOpsAMD64 bool
+	GenerateVectorOpsARM64 bool
 }
 
 // NewFieldConfig returns a data structure with needed information to generate apis for field element
@@ -261,8 +265,10 @@ func NewFieldConfig(packageName, elementName, modulus string, useAddChain bool)
 	// note: to simplify output files generated, we generated ASM code only for
 	// moduli that meet the condition F.NoCarry
 	// asm code generation for moduli with more than 6 words can be optimized further
-	F.ASM = F.NoCarry && F.NbWords <= 12 && F.NbWords > 1
-	F.ASMVector = F.ASM && F.NbWords == 4 && F.NbBits > 225
+	F.GenerateOpsAMD64 = F.NoCarry && F.NbWords <= 12 && F.NbWords > 1
+	F.GenerateVectorOpsAMD64 = F.GenerateOpsAMD64 && F.NbWords == 4 && F.NbBits > 225
+	F.GenerateOpsARM64 = F.GenerateOpsAMD64 && (F.NbWords%2 == 0)
+	F.GenerateVectorOpsARM64 = false
 
 	// setting Mu 2^288 / q
 	if F.NbWords == 4 {
diff --git a/field/generator/generator.go b/field/generator/generator.go
index 0150897677..98f9015546 100644
--- a/field/generator/generator.go
+++ b/field/generator/generator.go
@@ -2,7 +2,7 @@ package generator
 
 import (
 	"fmt"
-	"io"
+	"hash/fnv"
 	"os"
 	"os/exec"
 	"path/filepath"
@@ -11,9 +11,11 @@ import (
 
 	"github.com/consensys/bavard"
 	"github.com/consensys/gnark-crypto/field/generator/asm/amd64"
+	"github.com/consensys/gnark-crypto/field/generator/asm/arm64"
 	"github.com/consensys/gnark-crypto/field/generator/config"
 	"github.com/consensys/gnark-crypto/field/generator/internal/addchain"
 	"github.com/consensys/gnark-crypto/field/generator/internal/templates/element"
+	"golang.org/x/sync/errgroup"
 )
 
 // GenerateFF will generate go (and .s) files in outputDir for modulus (in base 10)
@@ -45,37 +47,6 @@ func GenerateFF(F *config.FieldConfig, outputDir, asmDirBuildPath, asmDirInclude
 		element.Test,
 		element.InverseTests,
 	}
-	// output files
-	eName := strings.ToLower(F.ElementName)
-
-	pathSrc := filepath.Join(outputDir, eName+".go")
-	pathSrcVector := filepath.Join(outputDir, "vector.go")
-	pathSrcFixedExp := filepath.Join(outputDir, eName+"_exp.go")
-	pathSrcArith := filepath.Join(outputDir, "arith.go")
-	pathTest := filepath.Join(outputDir, eName+"_test.go")
-	pathTestVector := filepath.Join(outputDir, "vector_test.go")
-
-	// remove old format generated files
-	oldFiles := []string{"_mul.go", "_mul_amd64.go",
-		"_square.go", "_square_amd64.go", "_ops_decl.go", "_square_amd64.s",
-		"_mul_amd64.s",
-		"_mul_arm64.s",
-		"_mul_arm64.go",
-		"_ops_amd64.s",
-		"_ops_noasm.go",
-		"_mul_adx_amd64.s",
-		"_ops_amd64.go",
-		"_fuzz.go",
-	}
-
-	for _, of := range oldFiles {
-		_ = os.Remove(filepath.Join(outputDir, eName+of))
-	}
-	_ = os.Remove(filepath.Join(outputDir, "asm.go"))
-	_ = os.Remove(filepath.Join(outputDir, "asm_noadx.go"))
-	_ = os.Remove(filepath.Join(outputDir, "avx.go"))
-	_ = os.Remove(filepath.Join(outputDir, "noavx.go"))
-
 	funcs := template.FuncMap{}
 	if F.UseAddChain {
 		for _, f := range addchain.Functions {
@@ -88,180 +59,199 @@ func GenerateFF(F *config.FieldConfig, outputDir, asmDirBuildPath, asmDirInclude
 		return a < b
 	}
 
-	bavardOpts := []func(*bavard.Bavard) error{
-		bavard.Apache2("ConsenSys Software Inc.", 2020),
-		bavard.Package(F.PackageName),
-		bavard.GeneratedBy("consensys/gnark-crypto"),
-		bavard.Funcs(funcs),
-	}
+	generate := func(suffix string, templates []string, opts ...option) func() error {
+		opt := generateOptions(opts...)
+		if opt.skip {
+			return func() error { return nil }
+		}
+		return func() error {
+			bavardOpts := []func(*bavard.Bavard) error{
+				bavard.Apache2("ConsenSys Software Inc.", 2020),
+				bavard.GeneratedBy("consensys/gnark-crypto"),
+				bavard.Funcs(funcs),
+			}
+			if !strings.HasSuffix(suffix, ".s") {
+				bavardOpts = append(bavardOpts, bavard.Package(F.PackageName))
+			}
+			if opt.buildTag != "" {
+				bavardOpts = append(bavardOpts, bavard.BuildTag(opt.buildTag))
+			}
+			if suffix == ".go" {
+				suffix = filepath.Join(outputDir, suffix)
+			} else {
+				suffix = filepath.Join(outputDir, suffix)
+			}
 
-	// generate source file
-	if err := bavard.GenerateFromString(pathSrc, sourceFiles, F, bavardOpts...); err != nil {
-		return err
-	}
+			tmplData := any(F)
+			if opt.tmplData != nil {
+				tmplData = opt.tmplData
+			}
 
-	// generate vector
-	if err := bavard.GenerateFromString(pathSrcVector, []string{element.Vector}, F, bavardOpts...); err != nil {
-		return err
+			return bavard.GenerateFromString(suffix, templates, tmplData, bavardOpts...)
+		}
 	}
 
-	// generate arithmetics source file
-	if err := bavard.GenerateFromString(pathSrcArith, []string{element.Arith}, F, bavardOpts...); err != nil {
-		return err
+	// generate asm files;
+	// couple of cases;
+	// 1. we generate arm64 and amd64
+	// 2. we generate only amd64
+	// 3. we generate only purego
+
+	// sanity check
+	if (F.GenerateOpsARM64 && !F.GenerateOpsAMD64) ||
+		(F.GenerateVectorOpsAMD64 && !F.GenerateOpsAMD64) ||
+		(F.GenerateVectorOpsARM64 && !F.GenerateOpsARM64) {
+		panic("not implemented.")
 	}
 
-	// generate fixed exp source file
-	if F.UseAddChain {
-		if err := bavard.GenerateFromString(pathSrcFixedExp, []string{element.FixedExp}, F, bavardOpts...); err != nil {
+	// get hash of the common asm files to force compiler to recompile in case of changes.
+	var amd64d, arm64d ASMWrapperData
+	var err error
+
+	if F.GenerateOpsAMD64 {
+		amd64d, err = hashAndInclude(asmDirBuildPath, asmDirIncludePath, amd64.ElementASMFileName, F.NbWords)
+		if err != nil {
 			return err
 		}
 	}
 
-	// generate test file
-	if err := bavard.GenerateFromString(pathTest, testFiles, F, bavardOpts...); err != nil {
-		return err
+	if F.GenerateOpsARM64 {
+		arm64d, err = hashAndInclude(asmDirBuildPath, asmDirIncludePath, arm64.ElementASMFileName, F.NbWords)
+		if err != nil {
+			return err
+		}
 	}
 
-	if err := bavard.GenerateFromString(pathTestVector, []string{element.TestVector}, F, bavardOpts...); err != nil {
-		return err
+	// purego files have no build tags if we don't generate asm
+	pureGoBuildTag := "purego || (!amd64 && !arm64)"
+	if !F.GenerateOpsAMD64 && !F.GenerateOpsARM64 {
+		pureGoBuildTag = ""
+	} else if !F.GenerateOpsARM64 {
+		pureGoBuildTag = "purego || (!amd64)"
+	}
+	pureGoVectorBuildTag := "purego || (!amd64 && !arm64)"
+	if !F.GenerateVectorOpsAMD64 && !F.GenerateVectorOpsARM64 {
+		pureGoVectorBuildTag = ""
+	} else if !F.GenerateVectorOpsARM64 {
+		pureGoVectorBuildTag = "purego || (!amd64)"
 	}
 
-	// if we generate assembly code
-	if F.ASM {
-		// generate ops.s
-		{
-			pathSrc := filepath.Join(outputDir, eName+"_ops_amd64.s")
-			fmt.Println("generating", pathSrc)
-			f, err := os.Create(pathSrc)
-			if err != nil {
-				return err
-			}
+	var g errgroup.Group
 
-			_, _ = io.WriteString(f, "// +build !purego\n")
+	g.Go(generate("element.go", sourceFiles))
+	g.Go(generate("doc.go", []string{element.Doc}))
+	g.Go(generate("vector.go", []string{element.Vector}))
+	g.Go(generate("arith.go", []string{element.Arith}))
+	g.Go(generate("element_test.go", testFiles))
+	g.Go(generate("vector_test.go", []string{element.TestVector}))
 
-			if err := amd64.GenerateFieldWrapper(f, F, asmDirBuildPath, asmDirIncludePath); err != nil {
-				_ = f.Close()
-				return err
-			}
-			_ = f.Close()
-
-			// run asmfmt
-			// run go fmt on whole directory
-			cmd := exec.Command("asmfmt", "-w", pathSrc)
-			cmd.Stdout = os.Stdout
-			cmd.Stderr = os.Stderr
-			if err := cmd.Run(); err != nil {
-				return err
-			}
-		}
+	g.Go(generate("element_amd64.s", []string{element.IncludeASM}, Only(F.GenerateOpsAMD64), WithBuildTag("!purego"), WithData(amd64d)))
+	g.Go(generate("element_arm64.s", []string{element.IncludeASM}, Only(F.GenerateOpsARM64), WithBuildTag("!purego"), WithData(arm64d)))
+
+	g.Go(generate("element_amd64.go", []string{element.OpsAMD64, element.MulDoc}, Only(F.GenerateOpsAMD64), WithBuildTag("!purego")))
+	g.Go(generate("element_arm64.go", []string{element.OpsARM64, element.MulNoCarry, element.Reduce}, Only(F.GenerateOpsARM64), WithBuildTag("!purego")))
+
+	g.Go(generate("element_purego.go", []string{element.OpsNoAsm, element.MulCIOS, element.MulNoCarry, element.Reduce, element.MulDoc}, WithBuildTag(pureGoBuildTag)))
+
+	g.Go(generate("vector_amd64.go", []string{element.VectorOpsAmd64}, Only(F.GenerateVectorOpsAMD64), WithBuildTag("!purego")))
+	g.Go(generate("vector_arm64.go", []string{element.VectorOpsArm64}, Only(F.GenerateVectorOpsARM64), WithBuildTag("!purego")))
 
+	g.Go(generate("vector_purego.go", []string{element.VectorOpsPureGo}, WithBuildTag(pureGoVectorBuildTag)))
+
+	g.Go(generate("asm_adx.go", []string{element.Asm}, Only(F.GenerateOpsAMD64), WithBuildTag("!noadx")))
+	g.Go(generate("asm_noadx.go", []string{element.AsmNoAdx}, Only(F.GenerateOpsAMD64), WithBuildTag("noadx")))
+	g.Go(generate("asm_avx.go", []string{element.Avx}, Only(F.GenerateVectorOpsAMD64), WithBuildTag("!noavx")))
+	g.Go(generate("asm_noavx.go", []string{element.NoAvx}, Only(F.GenerateVectorOpsAMD64), WithBuildTag("noavx")))
+
+	if F.UseAddChain {
+		g.Go(generate("element_exp.go", []string{element.FixedExp}))
 	}
 
-	if F.ASM {
-		// generate ops_amd64.go
-		src := []string{
-			element.MulDoc,
-			element.OpsAMD64,
-		}
-		pathSrc := filepath.Join(outputDir, eName+"_ops_amd64.go")
-		bavardOptsCpy := make([]func(*bavard.Bavard) error, len(bavardOpts))
-		copy(bavardOptsCpy, bavardOpts)
-		if F.ASM {
-			bavardOptsCpy = append(bavardOptsCpy, bavard.BuildTag("!purego"))
-		}
-		if err := bavard.GenerateFromString(pathSrc, src, F, bavardOptsCpy...); err != nil {
-			return err
-		}
+	if err := g.Wait(); err != nil {
+		return err
 	}
 
 	{
-		// generate ops.go
-		src := []string{
-			element.OpsNoAsm,
-			element.MulCIOS,
-			element.MulNoCarry,
-			element.Reduce,
-			element.MulDoc,
-		}
-		pathSrc := filepath.Join(outputDir, eName+"_ops_purego.go")
-		bavardOptsCpy := make([]func(*bavard.Bavard) error, len(bavardOpts))
-		copy(bavardOptsCpy, bavardOpts)
-		if F.ASM {
-			bavardOptsCpy = append(bavardOptsCpy, bavard.BuildTag("!amd64 purego"))
-		}
-		if err := bavard.GenerateFromString(pathSrc, src, F, bavardOptsCpy...); err != nil {
+		// run go fmt on whole directory
+		cmd := exec.Command("gofmt", "-s", "-w", outputDir)
+		cmd.Stdout = os.Stdout
+		cmd.Stderr = os.Stderr
+		if err := cmd.Run(); err != nil {
 			return err
 		}
 	}
-
 	{
-		// generate doc.go
-		src := []string{
-			element.Doc,
-		}
-		pathSrc := filepath.Join(outputDir, "doc.go")
-		if err := bavard.GenerateFromString(pathSrc, src, F, bavardOpts...); err != nil {
+		// run asmfmt on whole directory
+		cmd := exec.Command("asmfmt", "-w", outputDir)
+		cmd.Stdout = os.Stdout
+		cmd.Stderr = os.Stderr
+		if err := cmd.Run(); err != nil {
 			return err
 		}
 	}
 
-	if F.ASM {
-		// generate asm.go and asm_noadx.go
-		src := []string{
-			element.Asm,
-		}
-		pathSrc := filepath.Join(outputDir, "asm_adx.go")
-		bavardOptsCpy := make([]func(*bavard.Bavard) error, len(bavardOpts))
-		copy(bavardOptsCpy, bavardOpts)
-		bavardOptsCpy = append(bavardOptsCpy, bavard.BuildTag("!noadx"))
-		if err := bavard.GenerateFromString(pathSrc, src, F, bavardOptsCpy...); err != nil {
-			return err
-		}
+	return nil
+}
+
+type ASMWrapperData struct {
+	IncludePath string
+	Hash        string
+}
+
+func hashAndInclude(asmDirBuildPath, asmDirIncludePath, fileName string, nbWords int) (data ASMWrapperData, err error) {
+	fileName = fmt.Sprintf(fileName, nbWords)
+	// we hash the file content and include the hash in comment of the generated file
+	// to force the Go compiler to recompile the file if the content has changed
+	fData, err := os.ReadFile(filepath.Join(asmDirBuildPath, fileName))
+	if err != nil {
+		return ASMWrapperData{}, err
 	}
-	if F.ASM {
-		// generate asm.go and asm_noadx.go
-		src := []string{
-			element.AsmNoAdx,
-		}
-		pathSrc := filepath.Join(outputDir, "asm_noadx.go")
-		bavardOptsCpy := make([]func(*bavard.Bavard) error, len(bavardOpts))
-		copy(bavardOptsCpy, bavardOpts)
-		bavardOptsCpy = append(bavardOptsCpy, bavard.BuildTag("noadx"))
-		if err := bavard.GenerateFromString(pathSrc, src, F, bavardOptsCpy...); err != nil {
-			return err
-		}
+	// hash the file using FNV
+	hasher := fnv.New64()
+	hasher.Write(fData)
+	hash64 := hasher.Sum64()
+
+	hash := fmt.Sprintf("%d", hash64)
+	includePath := filepath.Join(asmDirIncludePath, fileName)
+	// on windows, we replace the "\" by "/"
+	if filepath.Separator == '\\' {
+		includePath = strings.ReplaceAll(includePath, "\\", "/")
 	}
 
-	if F.ASMVector {
-		// generate asm.go and asm_noadx.go
-		src := []string{
-			element.Avx,
-		}
-		pathSrc := filepath.Join(outputDir, "asm_avx.go")
-		bavardOptsCpy := make([]func(*bavard.Bavard) error, len(bavardOpts))
-		copy(bavardOptsCpy, bavardOpts)
-		bavardOptsCpy = append(bavardOptsCpy, bavard.BuildTag("!noavx"))
-		if err := bavard.GenerateFromString(pathSrc, src, F, bavardOptsCpy...); err != nil {
-			return err
-		}
+	return ASMWrapperData{
+		IncludePath: includePath,
+		Hash:        hash,
+	}, nil
+
+}
+
+func shorten(input string) string {
+	const maxLen = 15
+	if len(input) > maxLen {
+		return input[:6] + "..." + input[len(input)-6:]
+	}
+	return input
+}
+
+func GenerateARM64(nbWords int, asmDir string, hasVector bool) error {
+	os.MkdirAll(asmDir, 0755)
+	pathSrc := filepath.Join(asmDir, fmt.Sprintf(arm64.ElementASMFileName, nbWords))
+
+	fmt.Println("generating", pathSrc)
+	f, err := os.Create(pathSrc)
+	if err != nil {
+		return err
 	}
 
-	if F.ASMVector {
-		// generate asm.go and asm_noadx.go
-		src := []string{
-			element.NoAvx,
-		}
-		pathSrc := filepath.Join(outputDir, "asm_noavx.go")
-		bavardOptsCpy := make([]func(*bavard.Bavard) error, len(bavardOpts))
-		copy(bavardOptsCpy, bavardOpts)
-		bavardOptsCpy = append(bavardOptsCpy, bavard.BuildTag("noavx"))
-		if err := bavard.GenerateFromString(pathSrc, src, F, bavardOptsCpy...); err != nil {
-			return err
-		}
+	if err := arm64.GenerateCommonASM(f, nbWords, hasVector); err != nil {
+		_ = f.Close()
+		return err
 	}
+	_ = f.Close()
 
+	// run asmfmt
 	// run go fmt on whole directory
-	cmd := exec.Command("gofmt", "-s", "-w", outputDir)
+	cmd := exec.Command("asmfmt", "-w", pathSrc)
 	cmd.Stdout = os.Stdout
 	cmd.Stderr = os.Stderr
 	if err := cmd.Run(); err != nil {
@@ -271,15 +261,7 @@ func GenerateFF(F *config.FieldConfig, outputDir, asmDirBuildPath, asmDirInclude
 	return nil
 }
 
-func shorten(input string) string {
-	const maxLen = 15
-	if len(input) > maxLen {
-		return input[:6] + "..." + input[len(input)-6:]
-	}
-	return input
-}
-
-func GenerateCommonASM(nbWords int, asmDir string, hasVector bool) error {
+func GenerateAMD64(nbWords int, asmDir string, hasVector bool) error {
 	os.MkdirAll(asmDir, 0755)
 	pathSrc := filepath.Join(asmDir, fmt.Sprintf(amd64.ElementASMFileName, nbWords))
 
@@ -306,3 +288,38 @@ func GenerateCommonASM(nbWords int, asmDir string, hasVector bool) error {
 
 	return nil
 }
+
+type option func(*generateConfig)
+type generateConfig struct {
+	buildTag string
+	skip     bool
+	tmplData any
+}
+
+func WithBuildTag(buildTag string) option {
+	return func(opt *generateConfig) {
+		opt.buildTag = buildTag
+	}
+}
+
+func Only(condition bool) option {
+	return func(opt *generateConfig) {
+		opt.skip = !condition
+	}
+}
+
+func WithData(data any) option {
+	return func(opt *generateConfig) {
+		opt.tmplData = data
+	}
+}
+
+// default options
+func generateOptions(opts ...option) generateConfig {
+	// apply options
+	opt := generateConfig{}
+	for _, option := range opts {
+		option(&opt)
+	}
+	return opt
+}
diff --git a/field/generator/generator_test.go b/field/generator/generator_test.go
index 2c4b055f65..ee5b5fafc0 100644
--- a/field/generator/generator_test.go
+++ b/field/generator/generator_test.go
@@ -79,10 +79,13 @@ func TestIntegration(t *testing.T) {
 	moduli["e_nocarry_edge_0127"] = "170141183460469231731687303715884105727"
 	moduli["e_nocarry_edge_1279"] = "10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729087"
 
-	assert.NoError(GenerateCommonASM(2, asmDir, false))
-	assert.NoError(GenerateCommonASM(3, asmDir, false))
-	assert.NoError(GenerateCommonASM(7, asmDir, false))
-	assert.NoError(GenerateCommonASM(8, asmDir, false))
+	assert.NoError(GenerateAMD64(2, asmDir, false))
+	assert.NoError(GenerateAMD64(3, asmDir, false))
+	assert.NoError(GenerateAMD64(7, asmDir, false))
+	assert.NoError(GenerateAMD64(8, asmDir, false))
+
+	assert.NoError(GenerateARM64(2, asmDir, false))
+	assert.NoError(GenerateARM64(8, asmDir, false))
 
 	for elementName, modulus := range moduli {
 		var fIntegration *field.FieldConfig
diff --git a/field/generator/internal/templates/element/arith.go b/field/generator/internal/templates/element/arith.go
index 7bf8086487..06a7805588 100644
--- a/field/generator/internal/templates/element/arith.go
+++ b/field/generator/internal/templates/element/arith.go
@@ -45,21 +45,5 @@ func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) {
 	return
 }
 
-{{- if $.UsingP20Inverse}}
-	func max(a int, b int) int {
-		if a > b {
-			return a
-		}
-		return b
-	}
-
-	func min(a int, b int) int {
-		if a < b {
-			return a
-		}
-		return b
-	}
-
-{{- end}}
 
 `
diff --git a/field/generator/internal/templates/element/base.go b/field/generator/internal/templates/element/base.go
index 7dc8bffc4e..dd05519baf 100644
--- a/field/generator/internal/templates/element/base.go
+++ b/field/generator/internal/templates/element/base.go
@@ -431,6 +431,8 @@ func (z *{{.ElementName}}) Add( x, y *{{.ElementName}}) *{{.ElementName}} {
 	return z
 }
 
+
+
 // Double z = x + x (mod q), aka Lsh 1
 func (z *{{.ElementName}}) Double( x *{{.ElementName}}) *{{.ElementName}} {
 	{{- if eq .NbWords 1}}
@@ -473,6 +475,7 @@ func (z *{{.ElementName}}) Double( x *{{.ElementName}}) *{{.ElementName}} {
 }
 
 
+
 // Sub z = x - y (mod q)
 func (z *{{.ElementName}}) Sub( x, y *{{.ElementName}}) *{{.ElementName}} {
 	var b uint64
@@ -498,6 +501,7 @@ func (z *{{.ElementName}}) Sub( x, y *{{.ElementName}}) *{{.ElementName}} {
 	return z
 }
 
+
 // Neg z = q - x
 func (z *{{.ElementName}}) Neg( x *{{.ElementName}}) *{{.ElementName}} {
 	if x.IsZero() {
@@ -520,6 +524,7 @@ func (z *{{.ElementName}}) Neg( x *{{.ElementName}}) *{{.ElementName}} {
 	return z
 }
 
+
 // Select is a constant-time conditional move.
 // If c=0, z = x0. Else z = x1
 func (z *{{.ElementName}}) Select(c int, x0 *{{.ElementName}}, x1 *{{.ElementName}}) *{{.ElementName}} {
diff --git a/field/generator/internal/templates/element/ops_asm.go b/field/generator/internal/templates/element/ops_asm.go
index 1d1408e264..52b2c0b2b7 100644
--- a/field/generator/internal/templates/element/ops_asm.go
+++ b/field/generator/internal/templates/element/ops_asm.go
@@ -2,9 +2,6 @@ package element
 
 // OpsAMD64 is included with AMD64 builds (regardless of architecture or if F.ASM is set)
 const OpsAMD64 = `
-
-{{if .ASM}}
-
 //go:noescape
 func MulBy3(x *{{.ElementName}})
 
@@ -29,156 +26,47 @@ func reduce(res *{{.ElementName}})
 //go:noescape
 func Butterfly(a, b *{{.ElementName}})
 
-{{- if .ASMVector}}
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	if len(a) != len(b) || len(a) != len(*vector) {
-		panic("vector.Add: vectors don't have the same length")
-	}
-		n := uint64(len(a))
-	addVec(&(*vector)[0], &a[0], &b[0], n)
-}
-
-//go:noescape
-func addVec(res, a, b *{{.ElementName}}, n uint64)
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	if len(a) != len(b) || len(a) != len(*vector) {
-		panic("vector.Sub: vectors don't have the same length")
-	}
-	subVec(&(*vector)[0], &a[0], &b[0], uint64(len(a)))
-}
-
-//go:noescape
-func subVec(res, a, b *{{.ElementName}}, n uint64)
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *{{.ElementName}}) {
-	if len(a) != len(*vector) {
-		panic("vector.ScalarMul: vectors don't have the same length")
-	}
-	const maxN = (1 << 32) - 1
-	if !supportAvx512 || uint64(len(a)) >= maxN {
-		// call scalarMulVecGeneric
-		scalarMulVecGeneric(*vector, a, b)
-		return
-	}
-	n := uint64(len(a))
-	if n == 0 {
-		return
-	}
-	// the code for scalarMul is identical to mulVec; and it expects at least 
-	// 2 elements in the vector to fill the Z registers
-	var bb  [2]{{.ElementName}}
-	bb[0] = *b
-	bb[1] = *b
-	const blockSize = 16
-	scalarMulVec(&(*vector)[0], &a[0], &bb[0], n/blockSize, qInvNeg)
-	if n % blockSize != 0 {
-		// call scalarMulVecGeneric on the rest
-		start := n - n % blockSize
-		scalarMulVecGeneric((*vector)[start:], a[start:], b)
-	}
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *{{.ElementName}}) Mul(x, y *{{.ElementName}}) *{{.ElementName}} {
+	{{ mul_doc $.NoCarry }}
+	mul(z, x, y)
+	return z
 }
 
-//go:noescape
-func scalarMulVec(res, a, b *{{.ElementName}}, n uint64, qInvNeg uint64)
-
-// Sum computes the sum of all elements in the vector.
-func (vector *Vector) Sum() (res {{.ElementName}}) {
-	n := uint64(len(*vector))
-	if n == 0 {
-		return
-	}
-	const minN = 16*7 // AVX512 slower than generic for small n
-	const maxN = (1 << 32) - 1
-	if !supportAvx512 || n <= minN || n >= maxN {
-		// call sumVecGeneric
-		sumVecGeneric(&res, *vector)
-		return
-	}
-	sumVec(&res, &(*vector)[0], uint64(len(*vector)))
-	return
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *{{.ElementName}}) Square(x *{{.ElementName}}) *{{.ElementName}} {
+	// see Mul for doc.
+	mul(z, x, x)
+	return z
 }
 
-//go:noescape
-func sumVec(res *{{.ElementName}}, a *{{.ElementName}}, n uint64)
-
-// InnerProduct computes the inner product of two vectors.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) InnerProduct(other Vector) (res {{.ElementName}}) {
-	n := uint64(len(*vector))
-	if n == 0 {
-		return
-	}
-	if n != uint64(len(other)) {
-		panic("vector.InnerProduct: vectors don't have the same length")
-	}
-	const maxN = (1 << 32) - 1
-	if !supportAvx512 || n >= maxN {
-		// call innerProductVecGeneric
-		// note; we could split the vector into smaller chunks and call innerProductVec
-		innerProductVecGeneric(&res, *vector, other)
-		return
-	}
-	innerProdVec(&res[0], &(*vector)[0], &other[0], uint64(len(*vector)))
-
-	return
-}
+`
 
+const OpsARM64 = `
+// Butterfly sets
+//  a = a + b (mod q)
+//  b = a - b (mod q)
+{{- if le .NbWords 6}}
 //go:noescape
-func innerProdVec(res *uint64, a,b *{{.ElementName}}, n uint64)
-
-// Mul multiplies two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Mul(a, b Vector) {
-	if len(a) != len(b) || len(a) != len(*vector) {
-		panic("vector.Mul: vectors don't have the same length")
-	}
-	n := uint64(len(a))
-	if n == 0 {
-		return
-	}
-	const maxN = (1 << 32) - 1
-	if !supportAvx512 || n >= maxN {
-		// call mulVecGeneric
-		mulVecGeneric(*vector, a, b)
-		return
-	}
-
-	const blockSize = 16
-	mulVec(&(*vector)[0], &a[0], &b[0], n/blockSize, qInvNeg)
-	if n % blockSize != 0 {
-		// call mulVecGeneric on the rest
-		start := n - n % blockSize
-		mulVecGeneric((*vector)[start:], a[start:], b[start:])
-	}
-	
+func Butterfly(a, b *{{.ElementName}})
+{{- else}}
+func Butterfly(a, b *{{.ElementName}}) {
+	_butterflyGeneric(a, b)
 }
-
-// Patterns use for transposing the vectors in mulVec
-var (
-	pattern1 = [8]uint64{0, 8, 1, 9, 2, 10, 3, 11}
-	pattern2 = [8]uint64{12, 4, 13, 5, 14, 6, 15, 7}
-	pattern3 = [8]uint64{0, 1, 8, 9, 2, 3, 10, 11}
-	pattern4 = [8]uint64{12, 13, 4, 5, 14, 15, 6, 7}
-)
+{{- end}}
 
 //go:noescape
-func mulVec(res, a, b *{{.ElementName}}, n uint64, qInvNeg uint64)
-
-{{- end}}
+func mul(res,x,y *{{.ElementName}})
 
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
 func (z *{{.ElementName}}) Mul(x, y *{{.ElementName}}) *{{.ElementName}} {
-	{{ mul_doc $.NoCarry }}
-	mul(z, x, y)
+	mul(z,x,y)
 	return z
 }
 
@@ -191,8 +79,48 @@ func (z *{{.ElementName}}) Square(x *{{.ElementName}}) *{{.ElementName}} {
 	return z
 }
 
-{{end}}
 
+{{ $mulConsts := list 3 5 13 }}
+{{- range $i := $mulConsts }}
+
+// MulBy{{$i}} x *= {{$i}} (mod q)
+func MulBy{{$i}}(x *{{$.ElementName}}) {
+	{{- if eq 1 $.NbWords}}
+	var y {{$.ElementName}}
+	y.SetUint64({{$i}})
+	x.Mul(x, &y)
+	{{- else}}
+		{{- if eq $i 3}}
+			_x := *x
+			x.Double(x).Add(x, &_x)
+		{{- else if eq $i 5}}
+			_x := *x
+			x.Double(x).Double(x).Add(x, &_x)
+		{{- else if eq $i 13}}
+			var y = {{$.ElementName}}{
+				{{- range $i := $.Thirteen}}
+				{{$i}},{{end}}
+			}
+			x.Mul(x, &y)
+		{{- else }}
+			NOT IMPLEMENTED
+		{{- end}}
+	{{- end}}
+}
+
+{{- end}}
+
+func fromMont(z *{{.ElementName}} ) {
+	_fromMontGeneric(z)
+}
+
+//go:noescape
+func reduce(res *{{.ElementName}})
+`
+
+const IncludeASM = `
 
+// We include the hash to force the Go compiler to recompile: {{.Hash}}
+#include "{{.IncludePath}}"
 
 `
diff --git a/field/generator/internal/templates/element/ops_purego.go b/field/generator/internal/templates/element/ops_purego.go
index fe3cead3c4..498b7e1ae6 100644
--- a/field/generator/internal/templates/element/ops_purego.go
+++ b/field/generator/internal/templates/element/ops_purego.go
@@ -34,14 +34,6 @@ func MulBy{{$i}}(x *{{$.ElementName}}) {
 
 {{- end}}
 
-// Butterfly sets
-//  a = a + b (mod q)
-//  b = a - b (mod q)
-func Butterfly(a, b *{{.ElementName}}) {
-	_butterflyGeneric(a, b)
-}
-
-
 func fromMont(z *{{.ElementName}} ) {
 	_fromMontGeneric(z)
 }
@@ -50,46 +42,6 @@ func reduce(z *{{.ElementName}})  {
 	_reduceGeneric(z)
 }
 
-{{- if .ASMVector}}
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	addVecGeneric(*vector, a, b)
-}
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	subVecGeneric(*vector, a, b)
-}
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *{{.ElementName}}) {
-	scalarMulVecGeneric(*vector, a, b)
-}
-
-// Sum computes the sum of all elements in the vector.
-func (vector *Vector) Sum() (res {{.ElementName}}) {
-	sumVecGeneric(&res, *vector)
-	return
-}
-
-// InnerProduct computes the inner product of two vectors.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) InnerProduct(other Vector) (res {{.ElementName}}) {
-	innerProductVecGeneric(&res, *vector, other)
-	return
-}
-
-// Mul multiplies two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Mul(a, b Vector) {
-	mulVecGeneric(*vector, a, b)
-}
-
-{{- end}}
-
 // Mul z = x * y (mod q)
 {{- if $.NoCarry}}
 //
@@ -130,4 +82,11 @@ func (z *{{.ElementName}}) Square(x *{{.ElementName}}) *{{.ElementName}} {
 	return z
 }
 
+// Butterfly sets
+//  a = a + b (mod q)
+//  b = a - b (mod q)
+func Butterfly(a, b *{{.ElementName}}) {
+	_butterflyGeneric(a, b)
+}
+
 `
diff --git a/field/generator/internal/templates/element/tests.go b/field/generator/internal/templates/element/tests.go
index d09dbeb7e5..35d777e493 100644
--- a/field/generator/internal/templates/element/tests.go
+++ b/field/generator/internal/templates/element/tests.go
@@ -207,6 +207,7 @@ func Benchmark{{toTitle .ElementName}}Mul(b *testing.B) {
 	}
 }
 
+
 func Benchmark{{toTitle .ElementName}}Cmp(b *testing.B) {
 	x := {{.ElementName}}{
 		{{- range $i := .RSquare}}
diff --git a/field/generator/internal/templates/element/vector.go b/field/generator/internal/templates/element/vector.go
index 6407a024d5..447b429556 100644
--- a/field/generator/internal/templates/element/vector.go
+++ b/field/generator/internal/templates/element/vector.go
@@ -191,49 +191,6 @@ func (vector Vector) Swap(i, j int) {
 }
 
 
-{{/* For 4 elements, we have a special assembly path and copy this in ops_pure.go */}}
-{{- if not .ASMVector}}
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	addVecGeneric(*vector, a, b)
-}
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	subVecGeneric(*vector, a, b)
-}
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *{{.ElementName}}) {
-	scalarMulVecGeneric(*vector, a, b)
-}
-
-// Sum computes the sum of all elements in the vector.
-func (vector *Vector) Sum() (res {{.ElementName}}) {
-	sumVecGeneric(&res, *vector)
-	return
-}
-
-// InnerProduct computes the inner product of two vectors.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) InnerProduct(other Vector) (res {{.ElementName}}) {
-	innerProductVecGeneric(&res, *vector, other)
-	return
-}
-
-// Mul multiplies two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Mul(a, b Vector) {
-	mulVecGeneric(*vector, a, b)
-}
-
-{{- end}}
-
-
-
 func addVecGeneric(res, a, b Vector) {
 	if len(a) != len(b) || len(a) != len(res) {
 		panic("vector.Add: vectors don't have the same length")
diff --git a/field/generator/internal/templates/element/vector_ops_asm.go b/field/generator/internal/templates/element/vector_ops_asm.go
new file mode 100644
index 0000000000..e4de4f1b27
--- /dev/null
+++ b/field/generator/internal/templates/element/vector_ops_asm.go
@@ -0,0 +1,147 @@
+package element
+
+const VectorOpsAmd64 = `
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Add: vectors don't have the same length")
+	}
+		n := uint64(len(a))
+	addVec(&(*vector)[0], &a[0], &b[0], n)
+}
+
+//go:noescape
+func addVec(res, a, b *{{.ElementName}}, n uint64)
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Sub: vectors don't have the same length")
+	}
+	subVec(&(*vector)[0], &a[0], &b[0], uint64(len(a)))
+}
+
+//go:noescape
+func subVec(res, a, b *{{.ElementName}}, n uint64)
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *{{.ElementName}}) {
+	if len(a) != len(*vector) {
+		panic("vector.ScalarMul: vectors don't have the same length")
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || uint64(len(a)) >= maxN {
+		// call scalarMulVecGeneric
+		scalarMulVecGeneric(*vector, a, b)
+		return
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	// the code for scalarMul is identical to mulVec; and it expects at least 
+	// 2 elements in the vector to fill the Z registers
+	var bb  [2]{{.ElementName}}
+	bb[0] = *b
+	bb[1] = *b
+	const blockSize = 16
+	scalarMulVec(&(*vector)[0], &a[0], &bb[0], n/blockSize, qInvNeg)
+	if n % blockSize != 0 {
+		// call scalarMulVecGeneric on the rest
+		start := n - n % blockSize
+		scalarMulVecGeneric((*vector)[start:], a[start:], b)
+	}
+}
+
+//go:noescape
+func scalarMulVec(res, a, b *{{.ElementName}}, n uint64, qInvNeg uint64)
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res {{.ElementName}}) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	const minN = 16*7 // AVX512 slower than generic for small n
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n <= minN || n >= maxN {
+		// call sumVecGeneric
+		sumVecGeneric(&res, *vector)
+		return
+	}
+	sumVec(&res, &(*vector)[0], uint64(len(*vector)))
+	return
+}
+
+//go:noescape
+func sumVec(res *{{.ElementName}}, a *{{.ElementName}}, n uint64)
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res {{.ElementName}}) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	if n != uint64(len(other)) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n >= maxN {
+		// call innerProductVecGeneric
+		// note; we could split the vector into smaller chunks and call innerProductVec
+		innerProductVecGeneric(&res, *vector, other)
+		return
+	}
+	innerProdVec(&res[0], &(*vector)[0], &other[0], uint64(len(*vector)))
+
+	return
+}
+
+//go:noescape
+func innerProdVec(res *uint64, a,b *{{.ElementName}}, n uint64)
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	const maxN = (1 << 32) - 1
+	if !supportAvx512 || n >= maxN {
+		// call mulVecGeneric
+		mulVecGeneric(*vector, a, b)
+		return
+	}
+
+	const blockSize = 16
+	mulVec(&(*vector)[0], &a[0], &b[0], n/blockSize, qInvNeg)
+	if n % blockSize != 0 {
+		// call mulVecGeneric on the rest
+		start := n - n % blockSize
+		mulVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+	
+}
+
+// Patterns use for transposing the vectors in mulVec
+var (
+	pattern1 = [8]uint64{0, 8, 1, 9, 2, 10, 3, 11}
+	pattern2 = [8]uint64{12, 4, 13, 5, 14, 6, 15, 7}
+	pattern3 = [8]uint64{0, 1, 8, 9, 2, 3, 10, 11}
+	pattern4 = [8]uint64{12, 13, 4, 5, 14, 15, 6, 7}
+)
+
+//go:noescape
+func mulVec(res, a, b *{{.ElementName}}, n uint64, qInvNeg uint64)
+
+`
+
+const VectorOpsArm64 = VectorOpsPureGo
diff --git a/field/generator/internal/templates/element/vector_ops_purego.go b/field/generator/internal/templates/element/vector_ops_purego.go
new file mode 100644
index 0000000000..071b710587
--- /dev/null
+++ b/field/generator/internal/templates/element/vector_ops_purego.go
@@ -0,0 +1,40 @@
+package element
+
+const VectorOpsPureGo = `
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	addVecGeneric(*vector, a, b)
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	subVecGeneric(*vector, a, b)
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *{{.ElementName}}) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res {{.ElementName}}) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res {{.ElementName}}) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
+`
diff --git a/field/goff/cmd/root.go b/field/goff/cmd/root.go
index 58d36dbdee..c2ae86809e 100644
--- a/field/goff/cmd/root.go
+++ b/field/goff/cmd/root.go
@@ -73,9 +73,17 @@ func cmdGenerate(cmd *cobra.Command, args []string) {
 	}
 
 	asmDir := filepath.Join(fOutputDir, "asm")
-	if err := generator.GenerateCommonASM(F.NbWords, asmDir, F.ASMVector); err != nil {
-		fmt.Printf("\n%s\n", err.Error())
-		os.Exit(-1)
+	if F.GenerateOpsAMD64 {
+		if err := generator.GenerateAMD64(F.NbWords, asmDir, F.GenerateVectorOpsAMD64); err != nil {
+			fmt.Printf("\n%s\n", err.Error())
+			os.Exit(-1)
+		}
+	}
+	if F.GenerateOpsARM64 {
+		if err := generator.GenerateARM64(F.NbWords, asmDir, F.GenerateVectorOpsARM64); err != nil {
+			fmt.Printf("\n%s\n", err.Error())
+			os.Exit(-1)
+		}
 	}
 
 	if err := generator.GenerateFF(F, fOutputDir, asmDir, "asm"); err != nil {
diff --git a/field/goldilocks/element_ops_purego.go b/field/goldilocks/element_purego.go
similarity index 100%
rename from field/goldilocks/element_ops_purego.go
rename to field/goldilocks/element_purego.go
index 5dc51ea242..f1090ab75f 100644
--- a/field/goldilocks/element_ops_purego.go
+++ b/field/goldilocks/element_purego.go
@@ -39,14 +39,6 @@ func MulBy13(x *Element) {
 	x.Mul(x, &y)
 }
 
-// Butterfly sets
-//
-//	a = a + b (mod q)
-//	b = a - b (mod q)
-func Butterfly(a, b *Element) {
-	_butterflyGeneric(a, b)
-}
-
 func fromMont(z *Element) {
 	_fromMontGeneric(z)
 }
@@ -121,3 +113,11 @@ func (z *Element) Square(x *Element) *Element {
 
 	return z
 }
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
diff --git a/field/goldilocks/vector.go b/field/goldilocks/vector.go
index 7411cb7bf7..47b0664aa3 100644
--- a/field/goldilocks/vector.go
+++ b/field/goldilocks/vector.go
@@ -196,43 +196,6 @@ func (vector Vector) Swap(i, j int) {
 	vector[i], vector[j] = vector[j], vector[i]
 }
 
-// Add adds two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Add(a, b Vector) {
-	addVecGeneric(*vector, a, b)
-}
-
-// Sub subtracts two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Sub(a, b Vector) {
-	subVecGeneric(*vector, a, b)
-}
-
-// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) ScalarMul(a Vector, b *Element) {
-	scalarMulVecGeneric(*vector, a, b)
-}
-
-// Sum computes the sum of all elements in the vector.
-func (vector *Vector) Sum() (res Element) {
-	sumVecGeneric(&res, *vector)
-	return
-}
-
-// InnerProduct computes the inner product of two vectors.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) InnerProduct(other Vector) (res Element) {
-	innerProductVecGeneric(&res, *vector, other)
-	return
-}
-
-// Mul multiplies two vectors element-wise and stores the result in self.
-// It panics if the vectors don't have the same length.
-func (vector *Vector) Mul(a, b Vector) {
-	mulVecGeneric(*vector, a, b)
-}
-
 func addVecGeneric(res, a, b Vector) {
 	if len(a) != len(b) || len(a) != len(res) {
 		panic("vector.Add: vectors don't have the same length")
diff --git a/field/goldilocks/vector_purego.go b/field/goldilocks/vector_purego.go
new file mode 100644
index 0000000000..857d3e9f4c
--- /dev/null
+++ b/field/goldilocks/vector_purego.go
@@ -0,0 +1,54 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package goldilocks
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	addVecGeneric(*vector, a, b)
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	subVecGeneric(*vector, a, b)
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
diff --git a/go.mod b/go.mod
index b5486971f2..c4dbc8bc84 100644
--- a/go.mod
+++ b/go.mod
@@ -4,7 +4,7 @@ go 1.22
 
 require (
 	github.com/bits-and-blooms/bitset v1.14.2
-	github.com/consensys/bavard v0.1.22
+	github.com/consensys/bavard v0.1.23-0.20241022191302-a6fdcdb6e8f3
 	github.com/leanovate/gopter v0.2.11
 	github.com/mmcloughlin/addchain v0.4.0
 	github.com/spf13/cobra v1.8.1
diff --git a/go.sum b/go.sum
index 26af63d69f..54ef0689c1 100644
--- a/go.sum
+++ b/go.sum
@@ -55,8 +55,8 @@ github.com/client9/misspell v0.3.4/go.mod h1:qj6jICC3Q7zFZvVWo7KLAzC3yx5G7kyvSDk
 github.com/cncf/udpa/go v0.0.0-20191209042840-269d4d468f6f/go.mod h1:M8M6+tZqaGXZJjfX53e64911xZQV5JYwmTeXPW+k8Sc=
 github.com/cncf/udpa/go v0.0.0-20200629203442-efcf912fb354/go.mod h1:WmhPx2Nbnhtbo57+VJT5O0JRkEi1Wbu0z5j0R8u5Hbk=
 github.com/cncf/udpa/go v0.0.0-20201120205902-5459f2c99403/go.mod h1:WmhPx2Nbnhtbo57+VJT5O0JRkEi1Wbu0z5j0R8u5Hbk=
-github.com/consensys/bavard v0.1.22 h1:Uw2CGvbXSZWhqK59X0VG/zOjpTFuOMcPLStrp1ihI0A=
-github.com/consensys/bavard v0.1.22/go.mod h1:k/zVjHHC4B+PQy1Pg7fgvG3ALicQw540Crag8qx+dZs=
+github.com/consensys/bavard v0.1.23-0.20241022191302-a6fdcdb6e8f3 h1:8gPxbjhwhxXTakOXII32eLlAFLlYImoENa3uQ6iP+go=
+github.com/consensys/bavard v0.1.23-0.20241022191302-a6fdcdb6e8f3/go.mod h1:k/zVjHHC4B+PQy1Pg7fgvG3ALicQw540Crag8qx+dZs=
 github.com/coreos/go-semver v0.3.0/go.mod h1:nnelYz7RCh+5ahJtPPxZlU+153eP4D4r3EedlOD2RNk=
 github.com/coreos/go-systemd/v22 v22.3.2/go.mod h1:Y58oyj3AT4RCenI/lSvhwexgC+NSVTIJ3seZv2GcEnc=
 github.com/cpuguy83/go-md2man/v2 v2.0.0/go.mod h1:maD7wRr/U5Z6m/iR4s+kqSMx2CaBsrgA7czyZG/E6dU=
diff --git a/internal/generator/main.go b/internal/generator/main.go
index 7d8cfbe212..76467b4d7e 100644
--- a/internal/generator/main.go
+++ b/internal/generator/main.go
@@ -53,34 +53,16 @@ func main() {
 	asmDirIncludePath := filepath.Join(baseDir, "..", "field", "asm")
 
 	// generate common assembly files depending on field number of words
-	mCommon := make(map[int]bool)
-	mVec := make(map[int]bool)
+	assertNoError(generator.GenerateAMD64(4, asmDirBuildPath, true))
+	assertNoError(generator.GenerateAMD64(5, asmDirBuildPath, false))
+	assertNoError(generator.GenerateAMD64(6, asmDirBuildPath, false))
+	assertNoError(generator.GenerateAMD64(10, asmDirBuildPath, false))
+	assertNoError(generator.GenerateAMD64(12, asmDirBuildPath, false))
 
-	for i, conf := range config.Curves {
-		var err error
-		// generate base field
-		conf.Fp, err = field.NewFieldConfig("fp", "Element", conf.FpModulus, true)
-		assertNoError(err)
-
-		conf.Fr, err = field.NewFieldConfig("fr", "Element", conf.FrModulus, !conf.Equal(config.STARK_CURVE))
-		assertNoError(err)
-
-		mCommon[conf.Fr.NbWords] = true
-		mCommon[conf.Fp.NbWords] = true
-
-		if conf.Fr.ASMVector {
-			mVec[conf.Fr.NbWords] = true
-		}
-		if conf.Fp.ASMVector {
-			mVec[conf.Fp.NbWords] = true
-		}
-
-		config.Curves[i] = conf
-	}
-
-	for nbWords := range mCommon {
-		assertNoError(generator.GenerateCommonASM(nbWords, asmDirBuildPath, mVec[nbWords]))
-	}
+	assertNoError(generator.GenerateARM64(4, asmDirBuildPath, false))
+	assertNoError(generator.GenerateARM64(6, asmDirBuildPath, false))
+	assertNoError(generator.GenerateARM64(10, asmDirBuildPath, false))
+	assertNoError(generator.GenerateARM64(12, asmDirBuildPath, false))
 
 	var wg sync.WaitGroup
 	for _, conf := range config.Curves {
@@ -89,6 +71,14 @@ func main() {
 		go func(conf config.Curve) {
 			defer wg.Done()
 
+			var err error
+
+			conf.Fp, err = field.NewFieldConfig("fp", "Element", conf.FpModulus, true)
+			assertNoError(err)
+
+			conf.Fr, err = field.NewFieldConfig("fr", "Element", conf.FrModulus, !conf.Equal(config.STARK_CURVE))
+			assertNoError(err)
+
 			curveDir := filepath.Join(baseDir, "ecc", conf.Name)
 
 			conf.FpUnusedBits = 64 - (conf.Fp.NbBits % 64)

From 77d62f9fa9d0a650781c69fc2fcdc6a1d2f02a1f Mon Sep 17 00:00:00 2001
From: Gautam Botrel <gautam.botrel@gmail.com>
Date: Tue, 10 Dec 2024 13:00:33 -0600
Subject: [PATCH 091/114] feat: add `BabyBear` and `KoalaBear` 31bits fields
 vanilla Go impl (#558)

---
 .github/workflows/pr.yml                      |    5 +-
 .github/workflows/push.yml                    |    3 +
 ecc/bls12-377/fp/element.go                   |   14 +-
 ecc/bls12-377/fr/element.go                   |   10 +-
 ecc/bls12-381/fp/element.go                   |   14 +-
 ecc/bls12-381/fr/element.go                   |   10 +-
 ecc/bls24-315/fp/element.go                   |   12 +-
 ecc/bls24-315/fr/element.go                   |   10 +-
 ecc/bls24-317/fp/element.go                   |   12 +-
 ecc/bls24-317/fr/element.go                   |   10 +-
 ecc/bn254/fp/element.go                       |   10 +-
 ecc/bn254/fr/element.go                       |   10 +-
 ecc/bw6-633/fp/element.go                     |   22 +-
 ecc/bw6-633/fr/element.go                     |   12 +-
 ecc/bw6-761/fp/element.go                     |   26 +-
 ecc/bw6-761/fr/element.go                     |   14 +-
 ecc/secp256k1/fp/element.go                   |   10 +-
 ecc/secp256k1/fr/element.go                   |   10 +-
 ecc/stark-curve/fp/element.go                 |   10 +-
 ecc/stark-curve/fr/element.go                 |   10 +-
 field/babybear/arith.go                       |   60 +
 field/babybear/doc.go                         |   53 +
 field/babybear/element.go                     |  980 ++++++++
 field/babybear/element_exp.go                 |   92 +
 field/babybear/element_purego.go              |   81 +
 field/babybear/element_test.go                | 2230 +++++++++++++++++
 field/babybear/vector.go                      |  303 +++
 field/babybear/vector_purego.go               |   54 +
 field/babybear/vector_test.go                 |  365 +++
 field/generator/config/field_config.go        |   58 +-
 field/generator/config/field_test.go          |   11 +-
 field/generator/generator.go                  |    5 +-
 .../internal/templates/element/base.go        |  208 +-
 .../internal/templates/element/conv.go        |   72 +-
 .../internal/templates/element/inverse.go     |   20 +-
 .../internal/templates/element/mul_cios.go    |    6 +-
 .../internal/templates/element/ops_purego.go  |   27 +-
 .../internal/templates/element/tests.go       |   30 +-
 .../templates/element/tests_vector.go         |   13 +-
 .../internal/templates/element/vector.go      |    6 +-
 field/goldilocks/element.go                   |   53 +-
 field/goldilocks/element_purego.go            |    4 -
 field/goldilocks/element_test.go              |   26 -
 field/goldilocks/internal/main.go             |   21 -
 field/internal/addchain/3c000000              |  Bin 0 -> 206 bytes
 field/internal/addchain/3f                    |  Bin 0 -> 90 bytes
 field/internal/addchain/3f800000              |  Bin 0 -> 212 bytes
 field/internal/addchain/7                     |  Bin 0 -> 68 bytes
 .../internal/addchain/7fffffff                |  Bin 233 -> 232 bytes
 .../internal/addchain/7fffffff80000000        |  Bin 394 -> 393 bytes
 field/internal/main.go                        |   36 +
 field/koalabear/arith.go                      |   60 +
 field/koalabear/doc.go                        |   53 +
 field/koalabear/element.go                    |  980 ++++++++
 field/koalabear/element_exp.go                |  122 +
 field/koalabear/element_purego.go             |   81 +
 field/koalabear/element_test.go               | 2230 +++++++++++++++++
 field/koalabear/vector.go                     |  303 +++
 field/koalabear/vector_purego.go              |   54 +
 field/koalabear/vector_test.go                |  365 +++
 60 files changed, 8924 insertions(+), 372 deletions(-)
 create mode 100644 field/babybear/arith.go
 create mode 100644 field/babybear/doc.go
 create mode 100644 field/babybear/element.go
 create mode 100644 field/babybear/element_exp.go
 create mode 100644 field/babybear/element_purego.go
 create mode 100644 field/babybear/element_test.go
 create mode 100644 field/babybear/vector.go
 create mode 100644 field/babybear/vector_purego.go
 create mode 100644 field/babybear/vector_test.go
 delete mode 100644 field/goldilocks/internal/main.go
 create mode 100644 field/internal/addchain/3c000000
 create mode 100644 field/internal/addchain/3f
 create mode 100644 field/internal/addchain/3f800000
 create mode 100644 field/internal/addchain/7
 rename field/{goldilocks => }/internal/addchain/7fffffff (66%)
 rename field/{goldilocks => }/internal/addchain/7fffffff80000000 (79%)
 create mode 100644 field/internal/main.go
 create mode 100644 field/koalabear/arith.go
 create mode 100644 field/koalabear/doc.go
 create mode 100644 field/koalabear/element.go
 create mode 100644 field/koalabear/element_exp.go
 create mode 100644 field/koalabear/element_purego.go
 create mode 100644 field/koalabear/element_test.go
 create mode 100644 field/koalabear/vector.go
 create mode 100644 field/koalabear/vector_purego.go
 create mode 100644 field/koalabear/vector_test.go

diff --git a/.github/workflows/pr.yml b/.github/workflows/pr.yml
index 6da517779b..a6e3b4607e 100644
--- a/.github/workflows/pr.yml
+++ b/.github/workflows/pr.yml
@@ -61,7 +61,10 @@ jobs:
         go test -json -v -short -timeout=30m ./... 2>&1 | gotestfmt -hide=all |  tee /tmp/gotest.log 
         go test -json -v -tags=purego -timeout=30m ./... 2>&1 | gotestfmt -hide=all | tee -a /tmp/gotest.log 
         go test -json -v -race -timeout=30m ./ecc/bn254/... 2>&1 | gotestfmt -hide=all | tee -a /tmp/gotest.log 
-        GOARCH=386 go test -json -short -v -timeout=30m ./ecc/bn254/... 2>&1 | gotestfmt -hide=all | tee -a /tmp/gotest.log 
+        GOARCH=386 go test -json -short -v -timeout=30m ./ecc/bn254/... 2>&1 | gotestfmt -hide=all | tee -a /tmp/gotest.log
+        GOARCH=386 go test -json -short -v -timeout=30m ./field/goldilocks 2>&1 | gotestfmt -hide=all | tee -a /tmp/gotest.log 
+        GOARCH=386 go test -json -short -v -timeout=30m ./field/koalabear 2>&1 | gotestfmt -hide=all | tee -a /tmp/gotest.log 
+        GOARCH=386 go test -json -short -v -timeout=30m ./field/babybear 2>&1 | gotestfmt -hide=all | tee -a /tmp/gotest.log 
 
 
   slack-notifications:
diff --git a/.github/workflows/push.yml b/.github/workflows/push.yml
index 1ed9bfa9bc..a762da4cb4 100644
--- a/.github/workflows/push.yml
+++ b/.github/workflows/push.yml
@@ -73,6 +73,9 @@ jobs:
         go test -json -v -tags=purego -timeout=30m ./... 2>&1 | gotestfmt -hide=all | tee -a /tmp/gotest.log
         go test -json -v -race -timeout=30m ./ecc/bn254/... 2>&1 | gotestfmt -hide=all | tee -a /tmp/gotest.log
         GOARCH=386 go test -json -short -v -timeout=30m ./ecc/bn254/... 2>&1 | gotestfmt -hide=all | tee -a /tmp/gotest.log
+        GOARCH=386 go test -json -short -v -timeout=30m ./field/goldilocks 2>&1 | gotestfmt -hide=all | tee -a /tmp/gotest.log
+        GOARCH=386 go test -json -short -v -timeout=30m ./field/koalabear 2>&1 | gotestfmt -hide=all | tee -a /tmp/gotest.log
+        GOARCH=386 go test -json -short -v -timeout=30m ./field/babybear 2>&1 | gotestfmt -hide=all | tee -a /tmp/gotest.log
     
   
   slack-notifications:
diff --git a/ecc/bls12-377/fp/element.go b/ecc/bls12-377/fp/element.go
index 393f45744d..1c135e16f9 100644
--- a/ecc/bls12-377/fp/element.go
+++ b/ecc/bls12-377/fp/element.go
@@ -54,12 +54,12 @@ const (
 
 // Field modulus q
 const (
-	q0 uint64 = 9586122913090633729
-	q1 uint64 = 1660523435060625408
-	q2 uint64 = 2230234197602682880
-	q3 uint64 = 1883307231910630287
-	q4 uint64 = 14284016967150029115
-	q5 uint64 = 121098312706494698
+	q0 = 9586122913090633729
+	q1 = 1660523435060625408
+	q2 = 2230234197602682880
+	q3 = 1883307231910630287
+	q4 = 14284016967150029115
+	q5 = 121098312706494698
 )
 
 var qElement = Element{
@@ -83,7 +83,7 @@ func Modulus() *big.Int {
 
 // q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
 // used for Montgomery reduction
-const qInvNeg uint64 = 9586122913090633727
+const qInvNeg = 9586122913090633727
 
 func init() {
 	_modulus.SetString("1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d44300000008508c00000000001", 16)
diff --git a/ecc/bls12-377/fr/element.go b/ecc/bls12-377/fr/element.go
index af277e8bb1..93c0d1cc7d 100644
--- a/ecc/bls12-377/fr/element.go
+++ b/ecc/bls12-377/fr/element.go
@@ -54,10 +54,10 @@ const (
 
 // Field modulus q
 const (
-	q0 uint64 = 725501752471715841
-	q1 uint64 = 6461107452199829505
-	q2 uint64 = 6968279316240510977
-	q3 uint64 = 1345280370688173398
+	q0 = 725501752471715841
+	q1 = 6461107452199829505
+	q2 = 6968279316240510977
+	q3 = 1345280370688173398
 )
 
 var qElement = Element{
@@ -79,7 +79,7 @@ func Modulus() *big.Int {
 
 // q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
 // used for Montgomery reduction
-const qInvNeg uint64 = 725501752471715839
+const qInvNeg = 725501752471715839
 
 // mu = 2^288 / q needed for partial Barrett reduction
 const mu uint64 = 58893420465
diff --git a/ecc/bls12-381/fp/element.go b/ecc/bls12-381/fp/element.go
index f0bcfe51bc..d5c6cefb2a 100644
--- a/ecc/bls12-381/fp/element.go
+++ b/ecc/bls12-381/fp/element.go
@@ -54,12 +54,12 @@ const (
 
 // Field modulus q
 const (
-	q0 uint64 = 13402431016077863595
-	q1 uint64 = 2210141511517208575
-	q2 uint64 = 7435674573564081700
-	q3 uint64 = 7239337960414712511
-	q4 uint64 = 5412103778470702295
-	q5 uint64 = 1873798617647539866
+	q0 = 13402431016077863595
+	q1 = 2210141511517208575
+	q2 = 7435674573564081700
+	q3 = 7239337960414712511
+	q4 = 5412103778470702295
+	q5 = 1873798617647539866
 )
 
 var qElement = Element{
@@ -83,7 +83,7 @@ func Modulus() *big.Int {
 
 // q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
 // used for Montgomery reduction
-const qInvNeg uint64 = 9940570264628428797
+const qInvNeg = 9940570264628428797
 
 func init() {
 	_modulus.SetString("1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab", 16)
diff --git a/ecc/bls12-381/fr/element.go b/ecc/bls12-381/fr/element.go
index dc38f08cd3..5d218be808 100644
--- a/ecc/bls12-381/fr/element.go
+++ b/ecc/bls12-381/fr/element.go
@@ -54,10 +54,10 @@ const (
 
 // Field modulus q
 const (
-	q0 uint64 = 18446744069414584321
-	q1 uint64 = 6034159408538082302
-	q2 uint64 = 3691218898639771653
-	q3 uint64 = 8353516859464449352
+	q0 = 18446744069414584321
+	q1 = 6034159408538082302
+	q2 = 3691218898639771653
+	q3 = 8353516859464449352
 )
 
 var qElement = Element{
@@ -79,7 +79,7 @@ func Modulus() *big.Int {
 
 // q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
 // used for Montgomery reduction
-const qInvNeg uint64 = 18446744069414584319
+const qInvNeg = 18446744069414584319
 
 // mu = 2^288 / q needed for partial Barrett reduction
 const mu uint64 = 9484408045
diff --git a/ecc/bls24-315/fp/element.go b/ecc/bls24-315/fp/element.go
index 4ab67695e3..361e0482c6 100644
--- a/ecc/bls24-315/fp/element.go
+++ b/ecc/bls24-315/fp/element.go
@@ -54,11 +54,11 @@ const (
 
 // Field modulus q
 const (
-	q0 uint64 = 8063698428123676673
-	q1 uint64 = 4764498181658371330
-	q2 uint64 = 16051339359738796768
-	q3 uint64 = 15273757526516850351
-	q4 uint64 = 342900304943437392
+	q0 = 8063698428123676673
+	q1 = 4764498181658371330
+	q2 = 16051339359738796768
+	q3 = 15273757526516850351
+	q4 = 342900304943437392
 )
 
 var qElement = Element{
@@ -81,7 +81,7 @@ func Modulus() *big.Int {
 
 // q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
 // used for Montgomery reduction
-const qInvNeg uint64 = 8083954730842193919
+const qInvNeg = 8083954730842193919
 
 func init() {
 	_modulus.SetString("4c23a02b586d650d3f7498be97c5eafdec1d01aa27a1ae0421ee5da52bde5026fe802ff40300001", 16)
diff --git a/ecc/bls24-315/fr/element.go b/ecc/bls24-315/fr/element.go
index abdb822acf..2fe6f12cdc 100644
--- a/ecc/bls24-315/fr/element.go
+++ b/ecc/bls24-315/fr/element.go
@@ -54,10 +54,10 @@ const (
 
 // Field modulus q
 const (
-	q0 uint64 = 1860204336533995521
-	q1 uint64 = 14466829657984787300
-	q2 uint64 = 2737202078770428568
-	q3 uint64 = 1832378743606059307
+	q0 = 1860204336533995521
+	q1 = 14466829657984787300
+	q2 = 2737202078770428568
+	q3 = 1832378743606059307
 )
 
 var qElement = Element{
@@ -79,7 +79,7 @@ func Modulus() *big.Int {
 
 // q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
 // used for Montgomery reduction
-const qInvNeg uint64 = 2184305180030271487
+const qInvNeg = 2184305180030271487
 
 // mu = 2^288 / q needed for partial Barrett reduction
 const mu uint64 = 43237874697
diff --git a/ecc/bls24-317/fp/element.go b/ecc/bls24-317/fp/element.go
index 77818de479..80bab83a71 100644
--- a/ecc/bls24-317/fp/element.go
+++ b/ecc/bls24-317/fp/element.go
@@ -54,11 +54,11 @@ const (
 
 // Field modulus q
 const (
-	q0 uint64 = 10182971180934965931
-	q1 uint64 = 15488787195747417982
-	q2 uint64 = 1628721857945875526
-	q3 uint64 = 17478405972920225849
-	q4 uint64 = 1177913551803681068
+	q0 = 10182971180934965931
+	q1 = 15488787195747417982
+	q2 = 1628721857945875526
+	q3 = 17478405972920225849
+	q4 = 1177913551803681068
 )
 
 var qElement = Element{
@@ -81,7 +81,7 @@ func Modulus() *big.Int {
 
 // q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
 // used for Montgomery reduction
-const qInvNeg uint64 = 6176088765535387645
+const qInvNeg = 6176088765535387645
 
 func init() {
 	_modulus.SetString("1058ca226f60892cf28fc5a0b7f9d039169a61e684c73446d6f339e43424bf7e8d512e565dab2aab", 16)
diff --git a/ecc/bls24-317/fr/element.go b/ecc/bls24-317/fr/element.go
index 3aefaebe62..df5f9dc4cf 100644
--- a/ecc/bls24-317/fr/element.go
+++ b/ecc/bls24-317/fr/element.go
@@ -54,10 +54,10 @@ const (
 
 // Field modulus q
 const (
-	q0 uint64 = 17293822569102704641
-	q1 uint64 = 2076695515679886970
-	q2 uint64 = 15037686223802191177
-	q3 uint64 = 4917809291258081218
+	q0 = 17293822569102704641
+	q1 = 2076695515679886970
+	q2 = 15037686223802191177
+	q3 = 4917809291258081218
 )
 
 var qElement = Element{
@@ -79,7 +79,7 @@ func Modulus() *big.Int {
 
 // q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
 // used for Montgomery reduction
-const qInvNeg uint64 = 17293822569102704639
+const qInvNeg = 17293822569102704639
 
 // mu = 2^288 / q needed for partial Barrett reduction
 const mu uint64 = 16110458503
diff --git a/ecc/bn254/fp/element.go b/ecc/bn254/fp/element.go
index 25fcdb67cc..395030094f 100644
--- a/ecc/bn254/fp/element.go
+++ b/ecc/bn254/fp/element.go
@@ -54,10 +54,10 @@ const (
 
 // Field modulus q
 const (
-	q0 uint64 = 4332616871279656263
-	q1 uint64 = 10917124144477883021
-	q2 uint64 = 13281191951274694749
-	q3 uint64 = 3486998266802970665
+	q0 = 4332616871279656263
+	q1 = 10917124144477883021
+	q2 = 13281191951274694749
+	q3 = 3486998266802970665
 )
 
 var qElement = Element{
@@ -79,7 +79,7 @@ func Modulus() *big.Int {
 
 // q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
 // used for Montgomery reduction
-const qInvNeg uint64 = 9786893198990664585
+const qInvNeg = 9786893198990664585
 
 // mu = 2^288 / q needed for partial Barrett reduction
 const mu uint64 = 22721021478
diff --git a/ecc/bn254/fr/element.go b/ecc/bn254/fr/element.go
index 3650c954c5..f8b6c10840 100644
--- a/ecc/bn254/fr/element.go
+++ b/ecc/bn254/fr/element.go
@@ -54,10 +54,10 @@ const (
 
 // Field modulus q
 const (
-	q0 uint64 = 4891460686036598785
-	q1 uint64 = 2896914383306846353
-	q2 uint64 = 13281191951274694749
-	q3 uint64 = 3486998266802970665
+	q0 = 4891460686036598785
+	q1 = 2896914383306846353
+	q2 = 13281191951274694749
+	q3 = 3486998266802970665
 )
 
 var qElement = Element{
@@ -79,7 +79,7 @@ func Modulus() *big.Int {
 
 // q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
 // used for Montgomery reduction
-const qInvNeg uint64 = 14042775128853446655
+const qInvNeg = 14042775128853446655
 
 // mu = 2^288 / q needed for partial Barrett reduction
 const mu uint64 = 22721021478
diff --git a/ecc/bw6-633/fp/element.go b/ecc/bw6-633/fp/element.go
index 7656002f47..6f2565eaf7 100644
--- a/ecc/bw6-633/fp/element.go
+++ b/ecc/bw6-633/fp/element.go
@@ -54,16 +54,16 @@ const (
 
 // Field modulus q
 const (
-	q0 uint64 = 15512955586897510413
-	q1 uint64 = 4410884215886313276
-	q2 uint64 = 15543556715411259941
-	q3 uint64 = 9083347379620258823
-	q4 uint64 = 13320134076191308873
-	q5 uint64 = 9318693926755804304
-	q6 uint64 = 5645674015335635503
-	q7 uint64 = 12176845843281334983
-	q8 uint64 = 18165857675053050549
-	q9 uint64 = 82862755739295587
+	q0 = 15512955586897510413
+	q1 = 4410884215886313276
+	q2 = 15543556715411259941
+	q3 = 9083347379620258823
+	q4 = 13320134076191308873
+	q5 = 9318693926755804304
+	q6 = 5645674015335635503
+	q7 = 12176845843281334983
+	q8 = 18165857675053050549
+	q9 = 82862755739295587
 )
 
 var qElement = Element{
@@ -91,7 +91,7 @@ func Modulus() *big.Int {
 
 // q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
 // used for Montgomery reduction
-const qInvNeg uint64 = 13046692460116554043
+const qInvNeg = 13046692460116554043
 
 func init() {
 	_modulus.SetString("126633cc0f35f63fc1a174f01d72ab5a8fcd8c75d79d2c74e59769ad9bbda2f8152a6c0fadea490b8da9f5e83f57c497e0e8850edbda407d7b5ce7ab839c2253d369bd31147f73cd74916ea4570000d", 16)
diff --git a/ecc/bw6-633/fr/element.go b/ecc/bw6-633/fr/element.go
index 8841cd342c..b9cff65b7a 100644
--- a/ecc/bw6-633/fr/element.go
+++ b/ecc/bw6-633/fr/element.go
@@ -54,11 +54,11 @@ const (
 
 // Field modulus q
 const (
-	q0 uint64 = 8063698428123676673
-	q1 uint64 = 4764498181658371330
-	q2 uint64 = 16051339359738796768
-	q3 uint64 = 15273757526516850351
-	q4 uint64 = 342900304943437392
+	q0 = 8063698428123676673
+	q1 = 4764498181658371330
+	q2 = 16051339359738796768
+	q3 = 15273757526516850351
+	q4 = 342900304943437392
 )
 
 var qElement = Element{
@@ -81,7 +81,7 @@ func Modulus() *big.Int {
 
 // q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
 // used for Montgomery reduction
-const qInvNeg uint64 = 8083954730842193919
+const qInvNeg = 8083954730842193919
 
 func init() {
 	_modulus.SetString("4c23a02b586d650d3f7498be97c5eafdec1d01aa27a1ae0421ee5da52bde5026fe802ff40300001", 16)
diff --git a/ecc/bw6-761/fp/element.go b/ecc/bw6-761/fp/element.go
index 8cdd31218e..a266ee9014 100644
--- a/ecc/bw6-761/fp/element.go
+++ b/ecc/bw6-761/fp/element.go
@@ -54,18 +54,18 @@ const (
 
 // Field modulus q
 const (
-	q0  uint64 = 17626244516597989515
-	q1  uint64 = 16614129118623039618
-	q2  uint64 = 1588918198704579639
-	q3  uint64 = 10998096788944562424
-	q4  uint64 = 8204665564953313070
-	q5  uint64 = 9694500593442880912
-	q6  uint64 = 274362232328168196
-	q7  uint64 = 8105254717682411801
-	q8  uint64 = 5945444129596489281
-	q9  uint64 = 13341377791855249032
-	q10 uint64 = 15098257552581525310
-	q11 uint64 = 81882988782276106
+	q0  = 17626244516597989515
+	q1  = 16614129118623039618
+	q2  = 1588918198704579639
+	q3  = 10998096788944562424
+	q4  = 8204665564953313070
+	q5  = 9694500593442880912
+	q6  = 274362232328168196
+	q7  = 8105254717682411801
+	q8  = 5945444129596489281
+	q9  = 13341377791855249032
+	q10 = 15098257552581525310
+	q11 = 81882988782276106
 )
 
 var qElement = Element{
@@ -95,7 +95,7 @@ func Modulus() *big.Int {
 
 // q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
 // used for Montgomery reduction
-const qInvNeg uint64 = 744663313386281181
+const qInvNeg = 744663313386281181
 
 func init() {
 	_modulus.SetString("122e824fb83ce0ad187c94004faff3eb926186a81d14688528275ef8087be41707ba638e584e91903cebaff25b423048689c8ed12f9fd9071dcd3dc73ebff2e98a116c25667a8f8160cf8aeeaf0a437e6913e6870000082f49d00000000008b", 16)
diff --git a/ecc/bw6-761/fr/element.go b/ecc/bw6-761/fr/element.go
index 6784bc911f..dad9bbec1c 100644
--- a/ecc/bw6-761/fr/element.go
+++ b/ecc/bw6-761/fr/element.go
@@ -54,12 +54,12 @@ const (
 
 // Field modulus q
 const (
-	q0 uint64 = 9586122913090633729
-	q1 uint64 = 1660523435060625408
-	q2 uint64 = 2230234197602682880
-	q3 uint64 = 1883307231910630287
-	q4 uint64 = 14284016967150029115
-	q5 uint64 = 121098312706494698
+	q0 = 9586122913090633729
+	q1 = 1660523435060625408
+	q2 = 2230234197602682880
+	q3 = 1883307231910630287
+	q4 = 14284016967150029115
+	q5 = 121098312706494698
 )
 
 var qElement = Element{
@@ -83,7 +83,7 @@ func Modulus() *big.Int {
 
 // q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
 // used for Montgomery reduction
-const qInvNeg uint64 = 9586122913090633727
+const qInvNeg = 9586122913090633727
 
 func init() {
 	_modulus.SetString("1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d44300000008508c00000000001", 16)
diff --git a/ecc/secp256k1/fp/element.go b/ecc/secp256k1/fp/element.go
index 73045a133c..cb1b02995e 100644
--- a/ecc/secp256k1/fp/element.go
+++ b/ecc/secp256k1/fp/element.go
@@ -54,10 +54,10 @@ const (
 
 // Field modulus q
 const (
-	q0 uint64 = 18446744069414583343
-	q1 uint64 = 18446744073709551615
-	q2 uint64 = 18446744073709551615
-	q3 uint64 = 18446744073709551615
+	q0 = 18446744069414583343
+	q1 = 18446744073709551615
+	q2 = 18446744073709551615
+	q3 = 18446744073709551615
 )
 
 var qElement = Element{
@@ -79,7 +79,7 @@ func Modulus() *big.Int {
 
 // q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
 // used for Montgomery reduction
-const qInvNeg uint64 = 15580212934572586289
+const qInvNeg = 15580212934572586289
 
 // mu = 2^288 / q needed for partial Barrett reduction
 const mu uint64 = 4294967296
diff --git a/ecc/secp256k1/fr/element.go b/ecc/secp256k1/fr/element.go
index e2f81b66b3..d0684c6cc1 100644
--- a/ecc/secp256k1/fr/element.go
+++ b/ecc/secp256k1/fr/element.go
@@ -54,10 +54,10 @@ const (
 
 // Field modulus q
 const (
-	q0 uint64 = 13822214165235122497
-	q1 uint64 = 13451932020343611451
-	q2 uint64 = 18446744073709551614
-	q3 uint64 = 18446744073709551615
+	q0 = 13822214165235122497
+	q1 = 13451932020343611451
+	q2 = 18446744073709551614
+	q3 = 18446744073709551615
 )
 
 var qElement = Element{
@@ -79,7 +79,7 @@ func Modulus() *big.Int {
 
 // q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
 // used for Montgomery reduction
-const qInvNeg uint64 = 5408259542528602431
+const qInvNeg = 5408259542528602431
 
 // mu = 2^288 / q needed for partial Barrett reduction
 const mu uint64 = 4294967296
diff --git a/ecc/stark-curve/fp/element.go b/ecc/stark-curve/fp/element.go
index 1c53dcb090..4b14ff1149 100644
--- a/ecc/stark-curve/fp/element.go
+++ b/ecc/stark-curve/fp/element.go
@@ -54,10 +54,10 @@ const (
 
 // Field modulus q
 const (
-	q0 uint64 = 1
-	q1 uint64 = 0
-	q2 uint64 = 0
-	q3 uint64 = 576460752303423505
+	q0 = 1
+	q1 = 0
+	q2 = 0
+	q3 = 576460752303423505
 )
 
 var qElement = Element{
@@ -79,7 +79,7 @@ func Modulus() *big.Int {
 
 // q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
 // used for Montgomery reduction
-const qInvNeg uint64 = 18446744073709551615
+const qInvNeg = 18446744073709551615
 
 // mu = 2^288 / q needed for partial Barrett reduction
 const mu uint64 = 137438953471
diff --git a/ecc/stark-curve/fr/element.go b/ecc/stark-curve/fr/element.go
index 216e287ebb..2acb6e46b7 100644
--- a/ecc/stark-curve/fr/element.go
+++ b/ecc/stark-curve/fr/element.go
@@ -54,10 +54,10 @@ const (
 
 // Field modulus q
 const (
-	q0 uint64 = 2190616671734353199
-	q1 uint64 = 13222870243701404210
-	q2 uint64 = 18446744073709551615
-	q3 uint64 = 576460752303423504
+	q0 = 2190616671734353199
+	q1 = 13222870243701404210
+	q2 = 18446744073709551615
+	q3 = 576460752303423504
 )
 
 var qElement = Element{
@@ -79,7 +79,7 @@ func Modulus() *big.Int {
 
 // q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
 // used for Montgomery reduction
-const qInvNeg uint64 = 13504954208620504625
+const qInvNeg = 13504954208620504625
 
 // mu = 2^288 / q needed for partial Barrett reduction
 const mu uint64 = 137438953471
diff --git a/field/babybear/arith.go b/field/babybear/arith.go
new file mode 100644
index 0000000000..3dfd7e5ffe
--- /dev/null
+++ b/field/babybear/arith.go
@@ -0,0 +1,60 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package babybear
+
+import (
+	"math/bits"
+)
+
+// madd0 hi = a*b + c (discards lo bits)
+func madd0(a, b, c uint64) (hi uint64) {
+	var carry, lo uint64
+	hi, lo = bits.Mul64(a, b)
+	_, carry = bits.Add64(lo, c, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	return
+}
+
+// madd1 hi, lo = a*b + c
+func madd1(a, b, c uint64) (hi uint64, lo uint64) {
+	var carry uint64
+	hi, lo = bits.Mul64(a, b)
+	lo, carry = bits.Add64(lo, c, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	return
+}
+
+// madd2 hi, lo = a*b + c + d
+func madd2(a, b, c, d uint64) (hi uint64, lo uint64) {
+	var carry uint64
+	hi, lo = bits.Mul64(a, b)
+	c, carry = bits.Add64(c, d, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	lo, carry = bits.Add64(lo, c, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	return
+}
+
+func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) {
+	var carry uint64
+	hi, lo = bits.Mul64(a, b)
+	c, carry = bits.Add64(c, d, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	lo, carry = bits.Add64(lo, c, 0)
+	hi, _ = bits.Add64(hi, e, carry)
+	return
+}
diff --git a/field/babybear/doc.go b/field/babybear/doc.go
new file mode 100644
index 0000000000..65011bef3f
--- /dev/null
+++ b/field/babybear/doc.go
@@ -0,0 +1,53 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// Package babybear contains field arithmetic operations for modulus = 0x78000001.
+//
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@gnark/modular_multiplication)
+//
+// The modulus is hardcoded in all the operations.
+//
+// Field elements are represented as an array, and assumed to be in Montgomery form in all methods:
+//
+//	type Element [1]uint64
+//
+// # Usage
+//
+// Example API signature:
+//
+//	// Mul z = x * y (mod q)
+//	func (z *Element) Mul(x, y *Element) *Element
+//
+// and can be used like so:
+//
+//	var a, b Element
+//	a.SetUint64(2)
+//	b.SetString("984896738")
+//	a.Mul(a, b)
+//	a.Sub(a, a)
+//	 .Add(a, b)
+//	 .Inv(a)
+//	b.Exp(b, new(big.Int).SetUint64(42))
+//
+// Modulus q =
+//
+//	q[base10] = 2013265921
+//	q[base16] = 0x78000001
+//
+// # Warning
+//
+// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+package babybear
diff --git a/field/babybear/element.go b/field/babybear/element.go
new file mode 100644
index 0000000000..a9f524fa84
--- /dev/null
+++ b/field/babybear/element.go
@@ -0,0 +1,980 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package babybear
+
+import (
+	"crypto/rand"
+	"encoding/binary"
+	"errors"
+	"io"
+	"math/big"
+	"math/bits"
+	"reflect"
+	"strconv"
+	"strings"
+
+	"github.com/bits-and-blooms/bitset"
+	"github.com/consensys/gnark-crypto/field/hash"
+	"github.com/consensys/gnark-crypto/field/pool"
+)
+
+// Element represents a field element stored on 1 words (uint32)
+//
+// Element are assumed to be in Montgomery form in all methods.
+//
+// Modulus q =
+//
+//	q[base10] = 2013265921
+//	q[base16] = 0x78000001
+//
+// # Warning
+//
+// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+type Element [1]uint32
+
+const (
+	Limbs = 1  // number of 32 bits words needed to represent a Element
+	Bits  = 31 // number of bits needed to represent a Element
+	Bytes = 4  // number of bytes needed to represent a Element
+)
+
+// Field modulus q
+const (
+	q0 = 2013265921
+	q  = q0
+)
+
+var qElement = Element{
+	q0,
+}
+
+var _modulus big.Int // q stored as big.Int
+
+// Modulus returns q as a big.Int
+//
+//	q[base10] = 2013265921
+//	q[base16] = 0x78000001
+func Modulus() *big.Int {
+	return new(big.Int).Set(&_modulus)
+}
+
+// q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
+// used for Montgomery reduction
+const qInvNeg = 2013265919
+
+func init() {
+	_modulus.SetString("78000001", 16)
+}
+
+// NewElement returns a new Element from a uint64 value
+//
+// it is equivalent to
+//
+//	var v Element
+//	v.SetUint64(...)
+func NewElement(v uint64) Element {
+	z := Element{uint32(v % uint64(q0))}
+	z.toMont()
+	return z
+}
+
+// SetUint64 sets z to v and returns z
+func (z *Element) SetUint64(v uint64) *Element {
+	//  sets z LSB to v (non-Montgomery form) and convert z to Montgomery form
+	*z = Element{uint32(v % uint64(q0))}
+	return z.toMont()
+}
+
+// SetInt64 sets z to v and returns z
+func (z *Element) SetInt64(v int64) *Element {
+
+	// absolute value of v
+	m := v >> 63
+	z.SetUint64(uint64((v ^ m) - m))
+
+	if m != 0 {
+		// v is negative
+		z.Neg(z)
+	}
+
+	return z
+}
+
+// Set z = x and returns z
+func (z *Element) Set(x *Element) *Element {
+	z[0] = x[0]
+	return z
+}
+
+// SetInterface converts provided interface into Element
+// returns an error if provided type is not supported
+// supported types:
+//
+//	Element
+//	*Element
+//	uint64
+//	int
+//	string (see SetString for valid formats)
+//	*big.Int
+//	big.Int
+//	[]byte
+func (z *Element) SetInterface(i1 interface{}) (*Element, error) {
+	if i1 == nil {
+		return nil, errors.New("can't set babybear.Element with <nil>")
+	}
+
+	switch c1 := i1.(type) {
+	case Element:
+		return z.Set(&c1), nil
+	case *Element:
+		if c1 == nil {
+			return nil, errors.New("can't set babybear.Element with <nil>")
+		}
+		return z.Set(c1), nil
+	case uint8:
+		return z.SetUint64(uint64(c1)), nil
+	case uint16:
+		return z.SetUint64(uint64(c1)), nil
+	case uint32:
+		return z.SetUint64(uint64(c1)), nil
+	case uint:
+		return z.SetUint64(uint64(c1)), nil
+	case uint64:
+		return z.SetUint64(c1), nil
+	case int8:
+		return z.SetInt64(int64(c1)), nil
+	case int16:
+		return z.SetInt64(int64(c1)), nil
+	case int32:
+		return z.SetInt64(int64(c1)), nil
+	case int64:
+		return z.SetInt64(c1), nil
+	case int:
+		return z.SetInt64(int64(c1)), nil
+	case string:
+		return z.SetString(c1)
+	case *big.Int:
+		if c1 == nil {
+			return nil, errors.New("can't set babybear.Element with <nil>")
+		}
+		return z.SetBigInt(c1), nil
+	case big.Int:
+		return z.SetBigInt(&c1), nil
+	case []byte:
+		return z.SetBytes(c1), nil
+	default:
+		return nil, errors.New("can't set babybear.Element from type " + reflect.TypeOf(i1).String())
+	}
+}
+
+// SetZero z = 0
+func (z *Element) SetZero() *Element {
+	z[0] = 0
+	return z
+}
+
+// SetOne z = 1 (in Montgomery form)
+func (z *Element) SetOne() *Element {
+	z[0] = 268435454
+	return z
+}
+
+// Div z = x*y⁻¹ (mod q)
+func (z *Element) Div(x, y *Element) *Element {
+	var yInv Element
+	yInv.Inverse(y)
+	z.Mul(x, &yInv)
+	return z
+}
+
+// Equal returns z == x; constant-time
+func (z *Element) Equal(x *Element) bool {
+	return z.NotEqual(x) == 0
+}
+
+// NotEqual returns 0 if and only if z == x; constant-time
+func (z *Element) NotEqual(x *Element) uint32 {
+	return (z[0] ^ x[0])
+}
+
+// IsZero returns z == 0
+func (z *Element) IsZero() bool {
+	return (z[0]) == 0
+}
+
+// IsOne returns z == 1
+func (z *Element) IsOne() bool {
+	return z[0] == 268435454
+}
+
+// IsUint64 reports whether z can be represented as an uint64.
+func (z *Element) IsUint64() bool {
+	return true
+}
+
+// Uint64 returns the uint64 representation of x. If x cannot be represented in a uint64, the result is undefined.
+func (z *Element) Uint64() uint64 {
+	return uint64(z.Bits()[0])
+}
+
+// FitsOnOneWord reports whether z words (except the least significant word) are 0
+//
+// It is the responsibility of the caller to convert from Montgomery to Regular form if needed.
+func (z *Element) FitsOnOneWord() bool {
+	return true
+}
+
+// Cmp compares (lexicographic order) z and x and returns:
+//
+//	-1 if z <  x
+//	 0 if z == x
+//	+1 if z >  x
+func (z *Element) Cmp(x *Element) int {
+	_z := z.Bits()
+	_x := x.Bits()
+	if _z[0] > _x[0] {
+		return 1
+	} else if _z[0] < _x[0] {
+		return -1
+	}
+	return 0
+}
+
+// LexicographicallyLargest returns true if this element is strictly lexicographically
+// larger than its negation, false otherwise
+func (z *Element) LexicographicallyLargest() bool {
+	// adapted from github.com/zkcrypto/bls12_381
+	// we check if the element is larger than (q-1) / 2
+	// if z - (((q -1) / 2) + 1) have no underflow, then z > (q-1) / 2
+
+	_z := z.Bits()
+
+	var b uint32
+	_, b = bits.Sub32(_z[0], 1006632961, 0)
+
+	return b == 0
+}
+
+// SetRandom sets z to a uniform random value in [0, q).
+//
+// This might error only if reading from crypto/rand.Reader errors,
+// in which case, value of z is undefined.
+func (z *Element) SetRandom() (*Element, error) {
+	// this code is generated for all modulus
+	// and derived from go/src/crypto/rand/util.go
+
+	// l is number of limbs * 8; the number of bytes needed to reconstruct 1 uint64
+	const l = 8
+
+	// bitLen is the maximum bit length needed to encode a value < q.
+	const bitLen = 31
+
+	// k is the maximum byte length needed to encode a value < q.
+	const k = (bitLen + 7) / 8
+
+	// b is the number of bits in the most significant byte of q-1.
+	b := uint(bitLen % 8)
+	if b == 0 {
+		b = 8
+	}
+
+	var bytes [l]byte
+
+	for {
+		// note that bytes[k:l] is always 0
+		if _, err := io.ReadFull(rand.Reader, bytes[:k]); err != nil {
+			return nil, err
+		}
+
+		// Clear unused bits in in the most significant byte to increase probability
+		// that the candidate is < q.
+		bytes[k-1] &= uint8(int(1<<b) - 1)
+		z[0] = binary.LittleEndian.Uint32(bytes[0:4])
+
+		if !z.smallerThanModulus() {
+			continue // ignore the candidate and re-sample
+		}
+
+		return z, nil
+	}
+}
+
+// smallerThanModulus returns true if z < q
+// This is not constant time
+func (z *Element) smallerThanModulus() bool {
+	return z[0] < q
+}
+
+// One returns 1
+func One() Element {
+	var one Element
+	one.SetOne()
+	return one
+}
+
+// Halve sets z to z / 2 (mod q)
+func (z *Element) Halve() {
+
+	if z[0]&1 == 1 {
+		// z = z + q
+		z[0], _ = bits.Add32(z[0], q0, 0)
+
+	}
+	// z = z >> 1
+	z[0] >>= 1
+
+}
+
+// fromMont converts z in place (i.e. mutates) from Montgomery to regular representation
+// sets and returns z = z * 1
+func (z *Element) fromMont() *Element {
+	fromMont(z)
+	return z
+}
+
+// Add z = x + y (mod q)
+func (z *Element) Add(x, y *Element) *Element {
+
+	t := x[0] + y[0]
+	if t >= q {
+		t -= q
+	}
+	z[0] = t
+	return z
+}
+
+// Double z = x + x (mod q), aka Lsh 1
+func (z *Element) Double(x *Element) *Element {
+	t := x[0] << 1
+	if t >= q {
+		t -= q
+	}
+	z[0] = t
+	return z
+}
+
+// Sub z = x - y (mod q)
+func (z *Element) Sub(x, y *Element) *Element {
+	t, b := bits.Sub32(x[0], y[0], 0)
+	if b != 0 {
+		t += q
+	}
+	z[0] = t
+	return z
+}
+
+// Neg z = q - x
+func (z *Element) Neg(x *Element) *Element {
+	if x.IsZero() {
+		z.SetZero()
+		return z
+	}
+	z[0] = q - x[0]
+	return z
+}
+
+// Select is a constant-time conditional move.
+// If c=0, z = x0. Else z = x1
+func (z *Element) Select(c int, x0 *Element, x1 *Element) *Element {
+	cC := uint32((int64(c) | -int64(c)) >> 63) // "canonicized" into: 0 if c=0, -1 otherwise
+	z[0] = x0[0] ^ cC&(x0[0]^x1[0])
+	return z
+}
+
+func _fromMontGeneric(z *Element) {
+	z[0] = montReduce(uint64(z[0]))
+}
+
+func _reduceGeneric(z *Element) {
+
+	// if z ⩾ q → z -= q
+	if !z.smallerThanModulus() {
+		z[0] -= q
+	}
+}
+
+// BatchInvert returns a new slice with every element inverted.
+// Uses Montgomery batch inversion trick
+func BatchInvert(a []Element) []Element {
+	res := make([]Element, len(a))
+	if len(a) == 0 {
+		return res
+	}
+
+	zeroes := bitset.New(uint(len(a)))
+	accumulator := One()
+
+	for i := 0; i < len(a); i++ {
+		if a[i].IsZero() {
+			zeroes.Set(uint(i))
+			continue
+		}
+		res[i] = accumulator
+		accumulator.Mul(&accumulator, &a[i])
+	}
+
+	accumulator.Inverse(&accumulator)
+
+	for i := len(a) - 1; i >= 0; i-- {
+		if zeroes.Test(uint(i)) {
+			continue
+		}
+		res[i].Mul(&res[i], &accumulator)
+		accumulator.Mul(&accumulator, &a[i])
+	}
+
+	return res
+}
+
+func _butterflyGeneric(a, b *Element) {
+	t := *a
+	a.Add(a, b)
+	b.Sub(&t, b)
+}
+
+// BitLen returns the minimum number of bits needed to represent z
+// returns 0 if z == 0
+func (z *Element) BitLen() int {
+	return bits.Len32(z[0])
+}
+
+// Hash msg to count prime field elements.
+// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06#section-5.2
+func Hash(msg, dst []byte, count int) ([]Element, error) {
+	// 128 bits of security
+	// L = ceil((ceil(log2(p)) + k) / 8), where k is the security parameter = 128
+	const Bytes = 1 + (Bits-1)/8
+	const L = 16 + Bytes
+
+	lenInBytes := count * L
+	pseudoRandomBytes, err := hash.ExpandMsgXmd(msg, dst, lenInBytes)
+	if err != nil {
+		return nil, err
+	}
+
+	// get temporary big int from the pool
+	vv := pool.BigInt.Get()
+
+	res := make([]Element, count)
+	for i := 0; i < count; i++ {
+		vv.SetBytes(pseudoRandomBytes[i*L : (i+1)*L])
+		res[i].SetBigInt(vv)
+	}
+
+	// release object into pool
+	pool.BigInt.Put(vv)
+
+	return res, nil
+}
+
+// Exp z = xᵏ (mod q)
+func (z *Element) Exp(x Element, k *big.Int) *Element {
+	if k.IsUint64() && k.Uint64() == 0 {
+		return z.SetOne()
+	}
+
+	e := k
+	if k.Sign() == -1 {
+		// negative k, we invert
+		// if k < 0: xᵏ (mod q) == (x⁻¹)ᵏ (mod q)
+		x.Inverse(&x)
+
+		// we negate k in a temp big.Int since
+		// Int.Bit(_) of k and -k is different
+		e = pool.BigInt.Get()
+		defer pool.BigInt.Put(e)
+		e.Neg(k)
+	}
+
+	z.Set(&x)
+
+	for i := e.BitLen() - 2; i >= 0; i-- {
+		z.Square(z)
+		if e.Bit(i) == 1 {
+			z.Mul(z, &x)
+		}
+	}
+
+	return z
+}
+
+// rSquare where r is the Montgommery constant
+// see section 2.3.2 of Tolga Acar's thesis
+// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
+var rSquare = Element{
+	1172168163,
+}
+
+// toMont converts z to Montgomery form
+// sets and returns z = z * r²
+func (z *Element) toMont() *Element {
+	const rBits = 32
+	z[0] = uint32((uint64(z[0]) << rBits) % q)
+	return z
+}
+
+// String returns the decimal representation of z as generated by
+// z.Text(10).
+func (z *Element) String() string {
+	return z.Text(10)
+}
+
+// toBigInt returns z as a big.Int in Montgomery form
+func (z *Element) toBigInt(res *big.Int) *big.Int {
+	var b [Bytes]byte
+	binary.BigEndian.PutUint32(b[0:4], z[0])
+
+	return res.SetBytes(b[:])
+}
+
+// Text returns the string representation of z in the given base.
+// Base must be between 2 and 36, inclusive. The result uses the
+// lower-case letters 'a' to 'z' for digit values 10 to 35.
+// No prefix (such as "0x") is added to the string. If z is a nil
+// pointer it returns "<nil>".
+// If base == 10 and -z fits in a uint16 prefix "-" is added to the string.
+func (z *Element) Text(base int) string {
+	if base < 2 || base > 36 {
+		panic("invalid base")
+	}
+	if z == nil {
+		return "<nil>"
+	}
+
+	const maxUint16 = 65535
+	if base == 10 {
+		var zzNeg Element
+		zzNeg.Neg(z)
+		zzNeg.fromMont()
+		if zzNeg[0] <= maxUint16 && zzNeg[0] != 0 {
+			return "-" + strconv.FormatUint(uint64(zzNeg[0]), base)
+		}
+	}
+	zz := z.Bits()
+	return strconv.FormatUint(uint64(zz[0]), base)
+}
+
+// BigInt sets and return z as a *big.Int
+func (z *Element) BigInt(res *big.Int) *big.Int {
+	_z := *z
+	_z.fromMont()
+	return _z.toBigInt(res)
+}
+
+// ToBigIntRegular returns z as a big.Int in regular form
+//
+// Deprecated: use BigInt(*big.Int) instead
+func (z Element) ToBigIntRegular(res *big.Int) *big.Int {
+	z.fromMont()
+	return z.toBigInt(res)
+}
+
+// Bits provides access to z by returning its value as a little-endian [1]uint32 array.
+// Bits is intended to support implementation of missing low-level Element
+// functionality outside this package; it should be avoided otherwise.
+func (z *Element) Bits() [1]uint32 {
+	_z := *z
+	fromMont(&_z)
+	return _z
+}
+
+// Bytes returns the value of z as a big-endian byte array
+func (z *Element) Bytes() (res [Bytes]byte) {
+	BigEndian.PutElement(&res, *z)
+	return
+}
+
+// Marshal returns the value of z as a big-endian byte slice
+func (z *Element) Marshal() []byte {
+	b := z.Bytes()
+	return b[:]
+}
+
+// Unmarshal is an alias for SetBytes, it sets z to the value of e.
+func (z *Element) Unmarshal(e []byte) {
+	z.SetBytes(e)
+}
+
+// SetBytes interprets e as the bytes of a big-endian unsigned integer,
+// sets z to that value, and returns z.
+func (z *Element) SetBytes(e []byte) *Element {
+	if len(e) == Bytes {
+		// fast path
+		v, err := BigEndian.Element((*[Bytes]byte)(e))
+		if err == nil {
+			*z = v
+			return z
+		}
+	}
+
+	// slow path.
+	// get a big int from our pool
+	vv := pool.BigInt.Get()
+	vv.SetBytes(e)
+
+	// set big int
+	z.SetBigInt(vv)
+
+	// put temporary object back in pool
+	pool.BigInt.Put(vv)
+
+	return z
+}
+
+// SetBytesCanonical interprets e as the bytes of a big-endian 4-byte integer.
+// If e is not a 4-byte slice or encodes a value higher than q,
+// SetBytesCanonical returns an error.
+func (z *Element) SetBytesCanonical(e []byte) error {
+	if len(e) != Bytes {
+		return errors.New("invalid babybear.Element encoding")
+	}
+	v, err := BigEndian.Element((*[Bytes]byte)(e))
+	if err != nil {
+		return err
+	}
+	*z = v
+	return nil
+}
+
+// SetBigInt sets z to v and returns z
+func (z *Element) SetBigInt(v *big.Int) *Element {
+	z.SetZero()
+
+	var zero big.Int
+
+	// fast path
+	c := v.Cmp(&_modulus)
+	if c == 0 {
+		// v == 0
+		return z
+	} else if c != 1 && v.Cmp(&zero) != -1 {
+		// 0 < v < q
+		return z.setBigInt(v)
+	}
+
+	// get temporary big int from the pool
+	vv := pool.BigInt.Get()
+
+	// copy input + modular reduction
+	vv.Mod(v, &_modulus)
+
+	// set big int byte value
+	z.setBigInt(vv)
+
+	// release object into pool
+	pool.BigInt.Put(vv)
+	return z
+}
+
+// setBigInt assumes 0 ⩽ v < q
+func (z *Element) setBigInt(v *big.Int) *Element {
+	vBits := v.Bits()
+	// we assume v < q, so even if big.Int words are on 64bits, we can safely cast them to 32bits
+	for i := 0; i < len(vBits); i++ {
+		z[i] = uint32(vBits[i])
+	}
+
+	return z.toMont()
+}
+
+// SetString creates a big.Int with number and calls SetBigInt on z
+//
+// The number prefix determines the actual base: A prefix of
+// ”0b” or ”0B” selects base 2, ”0”, ”0o” or ”0O” selects base 8,
+// and ”0x” or ”0X” selects base 16. Otherwise, the selected base is 10
+// and no prefix is accepted.
+//
+// For base 16, lower and upper case letters are considered the same:
+// The letters 'a' to 'f' and 'A' to 'F' represent digit values 10 to 15.
+//
+// An underscore character ”_” may appear between a base
+// prefix and an adjacent digit, and between successive digits; such
+// underscores do not change the value of the number.
+// Incorrect placement of underscores is reported as a panic if there
+// are no other errors.
+//
+// If the number is invalid this method leaves z unchanged and returns nil, error.
+func (z *Element) SetString(number string) (*Element, error) {
+	// get temporary big int from the pool
+	vv := pool.BigInt.Get()
+
+	if _, ok := vv.SetString(number, 0); !ok {
+		return nil, errors.New("Element.SetString failed -> can't parse number into a big.Int " + number)
+	}
+
+	z.SetBigInt(vv)
+
+	// release object into pool
+	pool.BigInt.Put(vv)
+
+	return z, nil
+}
+
+// MarshalJSON returns json encoding of z (z.Text(10))
+// If z == nil, returns null
+func (z *Element) MarshalJSON() ([]byte, error) {
+	if z == nil {
+		return []byte("null"), nil
+	}
+	const maxSafeBound = 15 // we encode it as number if it's small
+	s := z.Text(10)
+	if len(s) <= maxSafeBound {
+		return []byte(s), nil
+	}
+	var sbb strings.Builder
+	sbb.WriteByte('"')
+	sbb.WriteString(s)
+	sbb.WriteByte('"')
+	return []byte(sbb.String()), nil
+}
+
+// UnmarshalJSON accepts numbers and strings as input
+// See Element.SetString for valid prefixes (0x, 0b, ...)
+func (z *Element) UnmarshalJSON(data []byte) error {
+	s := string(data)
+	if len(s) > Bits*3 {
+		return errors.New("value too large (max = Element.Bits * 3)")
+	}
+
+	// we accept numbers and strings, remove leading and trailing quotes if any
+	if len(s) > 0 && s[0] == '"' {
+		s = s[1:]
+	}
+	if len(s) > 0 && s[len(s)-1] == '"' {
+		s = s[:len(s)-1]
+	}
+
+	// get temporary big int from the pool
+	vv := pool.BigInt.Get()
+
+	if _, ok := vv.SetString(s, 0); !ok {
+		return errors.New("can't parse into a big.Int: " + s)
+	}
+
+	z.SetBigInt(vv)
+
+	// release object into pool
+	pool.BigInt.Put(vv)
+	return nil
+}
+
+// A ByteOrder specifies how to convert byte slices into a Element
+type ByteOrder interface {
+	Element(*[Bytes]byte) (Element, error)
+	PutElement(*[Bytes]byte, Element)
+	String() string
+}
+
+// BigEndian is the big-endian implementation of ByteOrder and AppendByteOrder.
+var BigEndian bigEndian
+
+type bigEndian struct{}
+
+// Element interpret b is a big-endian 4-byte slice.
+// If b encodes a value higher than q, Element returns error.
+func (bigEndian) Element(b *[Bytes]byte) (Element, error) {
+	var z Element
+	z[0] = binary.BigEndian.Uint32((*b)[0:4])
+
+	if !z.smallerThanModulus() {
+		return Element{}, errors.New("invalid babybear.Element encoding")
+	}
+
+	z.toMont()
+	return z, nil
+}
+
+func (bigEndian) PutElement(b *[Bytes]byte, e Element) {
+	e.fromMont()
+	binary.BigEndian.PutUint32((*b)[0:4], e[0])
+}
+
+func (bigEndian) String() string { return "BigEndian" }
+
+// LittleEndian is the little-endian implementation of ByteOrder and AppendByteOrder.
+var LittleEndian littleEndian
+
+type littleEndian struct{}
+
+func (littleEndian) Element(b *[Bytes]byte) (Element, error) {
+	var z Element
+	z[0] = binary.LittleEndian.Uint32((*b)[0:4])
+
+	if !z.smallerThanModulus() {
+		return Element{}, errors.New("invalid babybear.Element encoding")
+	}
+
+	z.toMont()
+	return z, nil
+}
+
+func (littleEndian) PutElement(b *[Bytes]byte, e Element) {
+	e.fromMont()
+	binary.LittleEndian.PutUint32((*b)[0:4], e[0])
+}
+
+func (littleEndian) String() string { return "LittleEndian" }
+
+// Legendre returns the Legendre symbol of z (either +1, -1, or 0.)
+func (z *Element) Legendre() int {
+	var l Element
+	// z^((q-1)/2)
+	l.expByLegendreExp(*z)
+
+	if l.IsZero() {
+		return 0
+	}
+
+	// if l == 1
+	if l.IsOne() {
+		return 1
+	}
+	return -1
+}
+
+// Sqrt z = √x (mod q)
+// if the square root doesn't exist (x is not a square mod q)
+// Sqrt leaves z unchanged and returns nil
+func (z *Element) Sqrt(x *Element) *Element {
+	// q ≡ 1 (mod 4)
+	// see modSqrtTonelliShanks in math/big/int.go
+	// using https://www.maa.org/sites/default/files/pdf/upload_library/22/Polya/07468342.di020786.02p0470a.pdf
+
+	var y, b, t, w Element
+	// w = x^((s-1)/2))
+	w.expBySqrtExp(*x)
+
+	// y = x^((s+1)/2)) = w * x
+	y.Mul(x, &w)
+
+	// b = xˢ = w * w * x = y * x
+	b.Mul(&w, &y)
+
+	// g = nonResidue ^ s
+	var g = Element{
+		66106732,
+	}
+	r := uint64(27)
+
+	// compute legendre symbol
+	// t = x^((q-1)/2) = r-1 squaring of xˢ
+	t = b
+	for i := uint64(0); i < r-1; i++ {
+		t.Square(&t)
+	}
+	if t.IsZero() {
+		return z.SetZero()
+	}
+	if !t.IsOne() {
+		// t != 1, we don't have a square root
+		return nil
+	}
+	for {
+		var m uint64
+		t = b
+
+		// for t != 1
+		for !t.IsOne() {
+			t.Square(&t)
+			m++
+		}
+
+		if m == 0 {
+			return z.Set(&y)
+		}
+		// t = g^(2^(r-m-1)) (mod q)
+		ge := int(r - m - 1)
+		t = g
+		for ge > 0 {
+			t.Square(&t)
+			ge--
+		}
+
+		g.Square(&t)
+		y.Mul(&y, &t)
+		b.Mul(&b, &g)
+		r = m
+	}
+}
+
+// Inverse z = x⁻¹ (mod q)
+//
+// if x == 0, sets and returns z = x
+func (z *Element) Inverse(x *Element) *Element {
+	// Algorithm 16 in "Efficient Software-Implementation of Finite Fields with Applications to Cryptography"
+	const q uint32 = q0
+	if x.IsZero() {
+		z.SetZero()
+		return z
+	}
+
+	var r, s, u, v uint32
+	u = q
+	s = 1172168163 // s = r²
+	r = 0
+	v = x[0]
+
+	var carry, borrow uint32
+
+	for (u != 1) && (v != 1) {
+		for v&1 == 0 {
+			v >>= 1
+			if s&1 == 0 {
+				s >>= 1
+			} else {
+				s, carry = bits.Add32(s, q, 0)
+				s >>= 1
+				if carry != 0 {
+					s |= (1 << 31)
+				}
+			}
+		}
+		for u&1 == 0 {
+			u >>= 1
+			if r&1 == 0 {
+				r >>= 1
+			} else {
+				r, carry = bits.Add32(r, q, 0)
+				r >>= 1
+				if carry != 0 {
+					r |= (1 << 31)
+				}
+			}
+		}
+		if v >= u {
+			v -= u
+			s, borrow = bits.Sub32(s, r, 0)
+			if borrow == 1 {
+				s += q
+			}
+		} else {
+			u -= v
+			r, borrow = bits.Sub32(r, s, 0)
+			if borrow == 1 {
+				r += q
+			}
+		}
+	}
+
+	if u == 1 {
+		z[0] = r
+	} else {
+		z[0] = s
+	}
+
+	return z
+}
diff --git a/field/babybear/element_exp.go b/field/babybear/element_exp.go
new file mode 100644
index 0000000000..44675979e6
--- /dev/null
+++ b/field/babybear/element_exp.go
@@ -0,0 +1,92 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package babybear
+
+// expBySqrtExp is equivalent to z.Exp(x, 7)
+//
+// uses github.com/mmcloughlin/addchain v0.4.0 to generate a shorter addition chain
+func (z *Element) expBySqrtExp(x Element) *Element {
+	// addition chain:
+	//
+	//	_10    = 2*1
+	//	_11    = 1 + _10
+	//	_110   = 2*_11
+	//	return   1 + _110
+	//
+	// Operations: 2 squares 2 multiplies
+
+	// Allocate Temporaries.
+	var ()
+
+	// var
+	// Step 1: z = x^0x2
+	z.Square(&x)
+
+	// Step 2: z = x^0x3
+	z.Mul(&x, z)
+
+	// Step 3: z = x^0x6
+	z.Square(z)
+
+	// Step 4: z = x^0x7
+	z.Mul(&x, z)
+
+	return z
+}
+
+// expByLegendreExp is equivalent to z.Exp(x, 3c000000)
+//
+// uses github.com/mmcloughlin/addchain v0.4.0 to generate a shorter addition chain
+func (z *Element) expByLegendreExp(x Element) *Element {
+	// addition chain:
+	//
+	//	_10    = 2*1
+	//	_11    = 1 + _10
+	//	_1100  = _11 << 2
+	//	_1111  = _11 + _1100
+	//	return   _1111 << 26
+	//
+	// Operations: 29 squares 2 multiplies
+
+	// Allocate Temporaries.
+	var (
+		t0 = new(Element)
+	)
+
+	// var t0 Element
+	// Step 1: z = x^0x2
+	z.Square(&x)
+
+	// Step 2: z = x^0x3
+	z.Mul(&x, z)
+
+	// Step 4: t0 = x^0xc
+	t0.Square(z)
+	for s := 1; s < 2; s++ {
+		t0.Square(t0)
+	}
+
+	// Step 5: z = x^0xf
+	z.Mul(z, t0)
+
+	// Step 31: z = x^0x3c000000
+	for s := 0; s < 26; s++ {
+		z.Square(z)
+	}
+
+	return z
+}
diff --git a/field/babybear/element_purego.go b/field/babybear/element_purego.go
new file mode 100644
index 0000000000..e618e83fd8
--- /dev/null
+++ b/field/babybear/element_purego.go
@@ -0,0 +1,81 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package babybear
+
+// MulBy3 x *= 3 (mod q)
+func MulBy3(x *Element) {
+	var y Element
+	y.SetUint64(3)
+	x.Mul(x, &y)
+}
+
+// MulBy5 x *= 5 (mod q)
+func MulBy5(x *Element) {
+	var y Element
+	y.SetUint64(5)
+	x.Mul(x, &y)
+}
+
+// MulBy13 x *= 13 (mod q)
+func MulBy13(x *Element) {
+	var y Element
+	y.SetUint64(13)
+	x.Mul(x, &y)
+}
+
+func fromMont(z *Element) {
+	_fromMontGeneric(z)
+}
+
+func reduce(z *Element) {
+	_reduceGeneric(z)
+}
+func montReduce(v uint64) uint32 {
+	m := uint32(v) * qInvNeg
+	t := uint32((v + uint64(m)*q) >> 32)
+	if t >= q {
+		t -= q
+	}
+	return t
+}
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+	v := uint64(x[0]) * uint64(y[0])
+	z[0] = montReduce(v)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for algorithm documentation
+	v := uint64(x[0]) * uint64(x[0])
+	z[0] = montReduce(v)
+	return z
+}
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
diff --git a/field/babybear/element_test.go b/field/babybear/element_test.go
new file mode 100644
index 0000000000..161c977b72
--- /dev/null
+++ b/field/babybear/element_test.go
@@ -0,0 +1,2230 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package babybear
+
+import (
+	"crypto/rand"
+	"encoding/json"
+	"fmt"
+	"math/big"
+	"math/bits"
+
+	"testing"
+
+	"github.com/leanovate/gopter"
+	ggen "github.com/leanovate/gopter/gen"
+	"github.com/leanovate/gopter/prop"
+
+	"github.com/stretchr/testify/require"
+)
+
+// -------------------------------------------------------------------------------------------------
+// benchmarks
+// most benchmarks are rudimentary and should sample a large number of random inputs
+// or be run multiple times to ensure it didn't measure the fastest path of the function
+
+var benchResElement Element
+
+func BenchmarkElementSelect(b *testing.B) {
+	var x, y Element
+	x.SetRandom()
+	y.SetRandom()
+
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Select(i%3, &x, &y)
+	}
+}
+
+func BenchmarkElementSetRandom(b *testing.B) {
+	var x Element
+	x.SetRandom()
+
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		_, _ = x.SetRandom()
+	}
+}
+
+func BenchmarkElementSetBytes(b *testing.B) {
+	var x Element
+	x.SetRandom()
+	bb := x.Bytes()
+	b.ResetTimer()
+
+	for i := 0; i < b.N; i++ {
+		benchResElement.SetBytes(bb[:])
+	}
+
+}
+
+func BenchmarkElementMulByConstants(b *testing.B) {
+	b.Run("mulBy3", func(b *testing.B) {
+		benchResElement.SetRandom()
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			MulBy3(&benchResElement)
+		}
+	})
+	b.Run("mulBy5", func(b *testing.B) {
+		benchResElement.SetRandom()
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			MulBy5(&benchResElement)
+		}
+	})
+	b.Run("mulBy13", func(b *testing.B) {
+		benchResElement.SetRandom()
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			MulBy13(&benchResElement)
+		}
+	})
+}
+
+func BenchmarkElementInverse(b *testing.B) {
+	var x Element
+	x.SetRandom()
+	benchResElement.SetRandom()
+	b.ResetTimer()
+
+	for i := 0; i < b.N; i++ {
+		benchResElement.Inverse(&x)
+	}
+
+}
+
+func BenchmarkElementButterfly(b *testing.B) {
+	var x Element
+	x.SetRandom()
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		Butterfly(&x, &benchResElement)
+	}
+}
+
+func BenchmarkElementExp(b *testing.B) {
+	var x Element
+	x.SetRandom()
+	benchResElement.SetRandom()
+	b1, _ := rand.Int(rand.Reader, Modulus())
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Exp(x, b1)
+	}
+}
+
+func BenchmarkElementDouble(b *testing.B) {
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Double(&benchResElement)
+	}
+}
+
+func BenchmarkElementAdd(b *testing.B) {
+	var x Element
+	x.SetRandom()
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Add(&x, &benchResElement)
+	}
+}
+
+func BenchmarkElementSub(b *testing.B) {
+	var x Element
+	x.SetRandom()
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Sub(&x, &benchResElement)
+	}
+}
+
+func BenchmarkElementNeg(b *testing.B) {
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Neg(&benchResElement)
+	}
+}
+
+func BenchmarkElementDiv(b *testing.B) {
+	var x Element
+	x.SetRandom()
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Div(&x, &benchResElement)
+	}
+}
+
+func BenchmarkElementFromMont(b *testing.B) {
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.fromMont()
+	}
+}
+
+func BenchmarkElementSquare(b *testing.B) {
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Square(&benchResElement)
+	}
+}
+
+func BenchmarkElementSqrt(b *testing.B) {
+	var a Element
+	a.SetUint64(4)
+	a.Neg(&a)
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Sqrt(&a)
+	}
+}
+
+func BenchmarkElementMul(b *testing.B) {
+	x := Element{
+		1172168163,
+	}
+	benchResElement.SetOne()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Mul(&benchResElement, &x)
+	}
+}
+
+func BenchmarkElementCmp(b *testing.B) {
+	x := Element{
+		1172168163,
+	}
+	benchResElement = x
+	benchResElement[0] = 0
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Cmp(&x)
+	}
+}
+
+func TestElementCmp(t *testing.T) {
+	var x, y Element
+
+	if x.Cmp(&y) != 0 {
+		t.Fatal("x == y")
+	}
+
+	one := One()
+	y.Sub(&y, &one)
+
+	if x.Cmp(&y) != -1 {
+		t.Fatal("x < y")
+	}
+	if y.Cmp(&x) != 1 {
+		t.Fatal("x < y")
+	}
+
+	x = y
+	if x.Cmp(&y) != 0 {
+		t.Fatal("x == y")
+	}
+
+	x.Sub(&x, &one)
+	if x.Cmp(&y) != -1 {
+		t.Fatal("x < y")
+	}
+	if y.Cmp(&x) != 1 {
+		t.Fatal("x < y")
+	}
+}
+
+func TestElementNegZero(t *testing.T) {
+	var a, b Element
+	b.SetZero()
+	for a.IsZero() {
+		a.SetRandom()
+	}
+	a.Neg(&b)
+	if !a.IsZero() {
+		t.Fatal("neg(0) != 0")
+	}
+}
+
+// -------------------------------------------------------------------------------------------------
+// Gopter tests
+// most of them are generated with a template
+
+const (
+	nbFuzzShort = 200
+	nbFuzz      = 1000
+)
+
+// special values to be used in tests
+var staticTestValues []Element
+
+func init() {
+	staticTestValues = append(staticTestValues, Element{}) // zero
+	staticTestValues = append(staticTestValues, One())     // one
+	staticTestValues = append(staticTestValues, rSquare)   // r²
+	var e, one Element
+	one.SetOne()
+	e.Sub(&qElement, &one)
+	staticTestValues = append(staticTestValues, e) // q - 1
+	e.Double(&one)
+	staticTestValues = append(staticTestValues, e) // 2
+
+	{
+		a := qElement
+		a[0]--
+		staticTestValues = append(staticTestValues, a)
+	}
+	staticTestValues = append(staticTestValues, Element{0})
+	staticTestValues = append(staticTestValues, Element{1})
+	staticTestValues = append(staticTestValues, Element{2})
+
+	{
+		a := qElement
+		a[0]--
+		staticTestValues = append(staticTestValues, a)
+	}
+
+	{
+		a := qElement
+		a[0] = 0
+		staticTestValues = append(staticTestValues, a)
+	}
+
+}
+
+func TestElementReduce(t *testing.T) {
+	testValues := make([]Element, len(staticTestValues))
+	copy(testValues, staticTestValues)
+
+	for i := range testValues {
+		s := testValues[i]
+		expected := s
+		reduce(&s)
+		_reduceGeneric(&expected)
+		if !s.Equal(&expected) {
+			t.Fatal("reduce failed: asm and generic impl don't match")
+		}
+	}
+
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := genFull()
+
+	properties.Property("reduce should output a result smaller than modulus", prop.ForAll(
+		func(a Element) bool {
+			b := a
+			reduce(&a)
+			_reduceGeneric(&b)
+			return a.smallerThanModulus() && a.Equal(&b)
+		},
+		genA,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+
+}
+
+func TestElementEqual(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+	genB := gen()
+
+	properties.Property("x.Equal(&y) iff x == y; likely false for random pairs", prop.ForAll(
+		func(a testPairElement, b testPairElement) bool {
+			return a.element.Equal(&b.element) == (a.element == b.element)
+		},
+		genA,
+		genB,
+	))
+
+	properties.Property("x.Equal(&y) if x == y", prop.ForAll(
+		func(a testPairElement) bool {
+			b := a.element
+			return a.element.Equal(&b)
+		},
+		genA,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+}
+
+func TestElementBytes(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("SetBytes(Bytes()) should stay constant", prop.ForAll(
+		func(a testPairElement) bool {
+			var b Element
+			bytes := a.element.Bytes()
+			b.SetBytes(bytes[:])
+			return a.element.Equal(&b)
+		},
+		genA,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+}
+
+func TestElementInverseExp(t *testing.T) {
+	// inverse must be equal to exp^-2
+	exp := Modulus()
+	exp.Sub(exp, new(big.Int).SetUint64(2))
+
+	invMatchExp := func(a testPairElement) bool {
+		var b Element
+		b.Set(&a.element)
+		a.element.Inverse(&a.element)
+		b.Exp(b, exp)
+
+		return a.element.Equal(&b)
+	}
+
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+	properties := gopter.NewProperties(parameters)
+	genA := gen()
+	properties.Property("inv == exp^-2", prop.ForAll(invMatchExp, genA))
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+
+	parameters.MinSuccessfulTests = 1
+	properties = gopter.NewProperties(parameters)
+	properties.Property("inv(0) == 0", prop.ForAll(invMatchExp, ggen.OneConstOf(testPairElement{})))
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+
+}
+
+func mulByConstant(z *Element, c uint8) {
+	var y Element
+	y.SetUint64(uint64(c))
+	z.Mul(z, &y)
+}
+
+func TestElementMulByConstants(t *testing.T) {
+
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	implemented := []uint8{0, 1, 2, 3, 5, 13}
+	properties.Property("mulByConstant", prop.ForAll(
+		func(a testPairElement) bool {
+			for _, c := range implemented {
+				var constant Element
+				constant.SetUint64(uint64(c))
+
+				b := a.element
+				b.Mul(&b, &constant)
+
+				aa := a.element
+				mulByConstant(&aa, c)
+
+				if !aa.Equal(&b) {
+					return false
+				}
+			}
+
+			return true
+		},
+		genA,
+	))
+
+	properties.Property("MulBy3(x) == Mul(x, 3)", prop.ForAll(
+		func(a testPairElement) bool {
+			var constant Element
+			constant.SetUint64(3)
+
+			b := a.element
+			b.Mul(&b, &constant)
+
+			MulBy3(&a.element)
+
+			return a.element.Equal(&b)
+		},
+		genA,
+	))
+
+	properties.Property("MulBy5(x) == Mul(x, 5)", prop.ForAll(
+		func(a testPairElement) bool {
+			var constant Element
+			constant.SetUint64(5)
+
+			b := a.element
+			b.Mul(&b, &constant)
+
+			MulBy5(&a.element)
+
+			return a.element.Equal(&b)
+		},
+		genA,
+	))
+
+	properties.Property("MulBy13(x) == Mul(x, 13)", prop.ForAll(
+		func(a testPairElement) bool {
+			var constant Element
+			constant.SetUint64(13)
+
+			b := a.element
+			b.Mul(&b, &constant)
+
+			MulBy13(&a.element)
+
+			return a.element.Equal(&b)
+		},
+		genA,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+
+}
+
+func TestElementLegendre(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("legendre should output same result than big.Int.Jacobi", prop.ForAll(
+		func(a testPairElement) bool {
+			return a.element.Legendre() == big.Jacobi(&a.bigint, Modulus())
+		},
+		genA,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+
+}
+
+func TestElementBitLen(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("BitLen should output same result than big.Int.BitLen", prop.ForAll(
+		func(a testPairElement) bool {
+			return a.element.fromMont().BitLen() == a.bigint.BitLen()
+		},
+		genA,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+}
+
+func TestElementButterflies(t *testing.T) {
+
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("butterfly0 == a -b; a +b", prop.ForAll(
+		func(a, b testPairElement) bool {
+			a0, b0 := a.element, b.element
+
+			_butterflyGeneric(&a.element, &b.element)
+			Butterfly(&a0, &b0)
+
+			return a.element.Equal(&a0) && b.element.Equal(&b0)
+		},
+		genA,
+		genA,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+
+}
+
+func TestElementLexicographicallyLargest(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("element.Cmp should match LexicographicallyLargest output", prop.ForAll(
+		func(a testPairElement) bool {
+			var negA Element
+			negA.Neg(&a.element)
+
+			cmpResult := a.element.Cmp(&negA)
+			lResult := a.element.LexicographicallyLargest()
+
+			if lResult && cmpResult == 1 {
+				return true
+			}
+			if !lResult && cmpResult != 1 {
+				return true
+			}
+			return false
+		},
+		genA,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+
+}
+
+func TestElementAdd(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+	genB := gen()
+
+	properties.Property("Add: having the receiver as operand should output the same result", prop.ForAll(
+		func(a, b testPairElement) bool {
+			var c, d Element
+			d.Set(&a.element)
+
+			c.Add(&a.element, &b.element)
+			a.element.Add(&a.element, &b.element)
+			b.element.Add(&d, &b.element)
+
+			return a.element.Equal(&b.element) && a.element.Equal(&c) && b.element.Equal(&c)
+		},
+		genA,
+		genB,
+	))
+
+	properties.Property("Add: operation result must match big.Int result", prop.ForAll(
+		func(a, b testPairElement) bool {
+			{
+				var c Element
+
+				c.Add(&a.element, &b.element)
+
+				var d, e big.Int
+				d.Add(&a.bigint, &b.bigint).Mod(&d, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					return false
+				}
+			}
+
+			// fixed elements
+			// a is random
+			// r takes special values
+			testValues := make([]Element, len(staticTestValues))
+			copy(testValues, staticTestValues)
+
+			for i := range testValues {
+				r := testValues[i]
+				var d, e, rb big.Int
+				r.BigInt(&rb)
+
+				var c Element
+				c.Add(&a.element, &r)
+				d.Add(&a.bigint, &rb).Mod(&d, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					return false
+				}
+			}
+			return true
+		},
+		genA,
+		genB,
+	))
+
+	properties.Property("Add: operation result must be smaller than modulus", prop.ForAll(
+		func(a, b testPairElement) bool {
+			var c Element
+
+			c.Add(&a.element, &b.element)
+
+			return c.smallerThanModulus()
+		},
+		genA,
+		genB,
+	))
+
+	specialValueTest := func() {
+		// test special values against special values
+		testValues := make([]Element, len(staticTestValues))
+		copy(testValues, staticTestValues)
+
+		for i := range testValues {
+			a := testValues[i]
+			var aBig big.Int
+			a.BigInt(&aBig)
+			for j := range testValues {
+				b := testValues[j]
+				var bBig, d, e big.Int
+				b.BigInt(&bBig)
+
+				var c Element
+				c.Add(&a, &b)
+				d.Add(&aBig, &bBig).Mod(&d, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					t.Fatal("Add failed special test values")
+				}
+			}
+		}
+	}
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+	specialValueTest()
+
+}
+
+func TestElementSub(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+	genB := gen()
+
+	properties.Property("Sub: having the receiver as operand should output the same result", prop.ForAll(
+		func(a, b testPairElement) bool {
+			var c, d Element
+			d.Set(&a.element)
+
+			c.Sub(&a.element, &b.element)
+			a.element.Sub(&a.element, &b.element)
+			b.element.Sub(&d, &b.element)
+
+			return a.element.Equal(&b.element) && a.element.Equal(&c) && b.element.Equal(&c)
+		},
+		genA,
+		genB,
+	))
+
+	properties.Property("Sub: operation result must match big.Int result", prop.ForAll(
+		func(a, b testPairElement) bool {
+			{
+				var c Element
+
+				c.Sub(&a.element, &b.element)
+
+				var d, e big.Int
+				d.Sub(&a.bigint, &b.bigint).Mod(&d, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					return false
+				}
+			}
+
+			// fixed elements
+			// a is random
+			// r takes special values
+			testValues := make([]Element, len(staticTestValues))
+			copy(testValues, staticTestValues)
+
+			for i := range testValues {
+				r := testValues[i]
+				var d, e, rb big.Int
+				r.BigInt(&rb)
+
+				var c Element
+				c.Sub(&a.element, &r)
+				d.Sub(&a.bigint, &rb).Mod(&d, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					return false
+				}
+			}
+			return true
+		},
+		genA,
+		genB,
+	))
+
+	properties.Property("Sub: operation result must be smaller than modulus", prop.ForAll(
+		func(a, b testPairElement) bool {
+			var c Element
+
+			c.Sub(&a.element, &b.element)
+
+			return c.smallerThanModulus()
+		},
+		genA,
+		genB,
+	))
+
+	specialValueTest := func() {
+		// test special values against special values
+		testValues := make([]Element, len(staticTestValues))
+		copy(testValues, staticTestValues)
+
+		for i := range testValues {
+			a := testValues[i]
+			var aBig big.Int
+			a.BigInt(&aBig)
+			for j := range testValues {
+				b := testValues[j]
+				var bBig, d, e big.Int
+				b.BigInt(&bBig)
+
+				var c Element
+				c.Sub(&a, &b)
+				d.Sub(&aBig, &bBig).Mod(&d, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					t.Fatal("Sub failed special test values")
+				}
+			}
+		}
+	}
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+	specialValueTest()
+
+}
+
+func TestElementMul(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+	genB := gen()
+
+	properties.Property("Mul: having the receiver as operand should output the same result", prop.ForAll(
+		func(a, b testPairElement) bool {
+			var c, d Element
+			d.Set(&a.element)
+
+			c.Mul(&a.element, &b.element)
+			a.element.Mul(&a.element, &b.element)
+			b.element.Mul(&d, &b.element)
+
+			return a.element.Equal(&b.element) && a.element.Equal(&c) && b.element.Equal(&c)
+		},
+		genA,
+		genB,
+	))
+
+	properties.Property("Mul: operation result must match big.Int result", prop.ForAll(
+		func(a, b testPairElement) bool {
+			{
+				var c Element
+
+				c.Mul(&a.element, &b.element)
+
+				var d, e big.Int
+				d.Mul(&a.bigint, &b.bigint).Mod(&d, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					return false
+				}
+			}
+
+			// fixed elements
+			// a is random
+			// r takes special values
+			testValues := make([]Element, len(staticTestValues))
+			copy(testValues, staticTestValues)
+
+			for i := range testValues {
+				r := testValues[i]
+				var d, e, rb big.Int
+				r.BigInt(&rb)
+
+				var c Element
+				c.Mul(&a.element, &r)
+				d.Mul(&a.bigint, &rb).Mod(&d, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					return false
+				}
+			}
+			return true
+		},
+		genA,
+		genB,
+	))
+
+	properties.Property("Mul: operation result must be smaller than modulus", prop.ForAll(
+		func(a, b testPairElement) bool {
+			var c Element
+
+			c.Mul(&a.element, &b.element)
+
+			return c.smallerThanModulus()
+		},
+		genA,
+		genB,
+	))
+
+	specialValueTest := func() {
+		// test special values against special values
+		testValues := make([]Element, len(staticTestValues))
+		copy(testValues, staticTestValues)
+
+		for i := range testValues {
+			a := testValues[i]
+			var aBig big.Int
+			a.BigInt(&aBig)
+			for j := range testValues {
+				b := testValues[j]
+				var bBig, d, e big.Int
+				b.BigInt(&bBig)
+
+				var c Element
+				c.Mul(&a, &b)
+				d.Mul(&aBig, &bBig).Mod(&d, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					t.Fatal("Mul failed special test values")
+				}
+			}
+		}
+	}
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+	specialValueTest()
+
+}
+
+func TestElementDiv(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+	genB := gen()
+
+	properties.Property("Div: having the receiver as operand should output the same result", prop.ForAll(
+		func(a, b testPairElement) bool {
+			var c, d Element
+			d.Set(&a.element)
+
+			c.Div(&a.element, &b.element)
+			a.element.Div(&a.element, &b.element)
+			b.element.Div(&d, &b.element)
+
+			return a.element.Equal(&b.element) && a.element.Equal(&c) && b.element.Equal(&c)
+		},
+		genA,
+		genB,
+	))
+
+	properties.Property("Div: operation result must match big.Int result", prop.ForAll(
+		func(a, b testPairElement) bool {
+			{
+				var c Element
+
+				c.Div(&a.element, &b.element)
+
+				var d, e big.Int
+				d.ModInverse(&b.bigint, Modulus())
+				d.Mul(&d, &a.bigint).Mod(&d, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					return false
+				}
+			}
+
+			// fixed elements
+			// a is random
+			// r takes special values
+			testValues := make([]Element, len(staticTestValues))
+			copy(testValues, staticTestValues)
+
+			for i := range testValues {
+				r := testValues[i]
+				var d, e, rb big.Int
+				r.BigInt(&rb)
+
+				var c Element
+				c.Div(&a.element, &r)
+				d.ModInverse(&rb, Modulus())
+				d.Mul(&d, &a.bigint).Mod(&d, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					return false
+				}
+			}
+			return true
+		},
+		genA,
+		genB,
+	))
+
+	properties.Property("Div: operation result must be smaller than modulus", prop.ForAll(
+		func(a, b testPairElement) bool {
+			var c Element
+
+			c.Div(&a.element, &b.element)
+
+			return c.smallerThanModulus()
+		},
+		genA,
+		genB,
+	))
+
+	specialValueTest := func() {
+		// test special values against special values
+		testValues := make([]Element, len(staticTestValues))
+		copy(testValues, staticTestValues)
+
+		for i := range testValues {
+			a := testValues[i]
+			var aBig big.Int
+			a.BigInt(&aBig)
+			for j := range testValues {
+				b := testValues[j]
+				var bBig, d, e big.Int
+				b.BigInt(&bBig)
+
+				var c Element
+				c.Div(&a, &b)
+				d.ModInverse(&bBig, Modulus())
+				d.Mul(&d, &aBig).Mod(&d, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					t.Fatal("Div failed special test values")
+				}
+			}
+		}
+	}
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+	specialValueTest()
+
+}
+
+func TestElementExp(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+	genB := gen()
+
+	properties.Property("Exp: having the receiver as operand should output the same result", prop.ForAll(
+		func(a, b testPairElement) bool {
+			var c, d Element
+			d.Set(&a.element)
+
+			c.Exp(a.element, &b.bigint)
+			a.element.Exp(a.element, &b.bigint)
+			b.element.Exp(d, &b.bigint)
+
+			return a.element.Equal(&b.element) && a.element.Equal(&c) && b.element.Equal(&c)
+		},
+		genA,
+		genB,
+	))
+
+	properties.Property("Exp: operation result must match big.Int result", prop.ForAll(
+		func(a, b testPairElement) bool {
+			{
+				var c Element
+
+				c.Exp(a.element, &b.bigint)
+
+				var d, e big.Int
+				d.Exp(&a.bigint, &b.bigint, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					return false
+				}
+			}
+
+			// fixed elements
+			// a is random
+			// r takes special values
+			testValues := make([]Element, len(staticTestValues))
+			copy(testValues, staticTestValues)
+
+			for i := range testValues {
+				r := testValues[i]
+				var d, e, rb big.Int
+				r.BigInt(&rb)
+
+				var c Element
+				c.Exp(a.element, &rb)
+				d.Exp(&a.bigint, &rb, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					return false
+				}
+			}
+			return true
+		},
+		genA,
+		genB,
+	))
+
+	properties.Property("Exp: operation result must be smaller than modulus", prop.ForAll(
+		func(a, b testPairElement) bool {
+			var c Element
+
+			c.Exp(a.element, &b.bigint)
+
+			return c.smallerThanModulus()
+		},
+		genA,
+		genB,
+	))
+
+	specialValueTest := func() {
+		// test special values against special values
+		testValues := make([]Element, len(staticTestValues))
+		copy(testValues, staticTestValues)
+
+		for i := range testValues {
+			a := testValues[i]
+			var aBig big.Int
+			a.BigInt(&aBig)
+			for j := range testValues {
+				b := testValues[j]
+				var bBig, d, e big.Int
+				b.BigInt(&bBig)
+
+				var c Element
+				c.Exp(a, &bBig)
+				d.Exp(&aBig, &bBig, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					t.Fatal("Exp failed special test values")
+				}
+			}
+		}
+	}
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+	specialValueTest()
+
+}
+
+func TestElementSquare(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("Square: having the receiver as operand should output the same result", prop.ForAll(
+		func(a testPairElement) bool {
+
+			var b Element
+
+			b.Square(&a.element)
+			a.element.Square(&a.element)
+			return a.element.Equal(&b)
+		},
+		genA,
+	))
+
+	properties.Property("Square: operation result must match big.Int result", prop.ForAll(
+		func(a testPairElement) bool {
+			var c Element
+			c.Square(&a.element)
+
+			var d, e big.Int
+			d.Mul(&a.bigint, &a.bigint).Mod(&d, Modulus())
+
+			return c.BigInt(&e).Cmp(&d) == 0
+		},
+		genA,
+	))
+
+	properties.Property("Square: operation result must be smaller than modulus", prop.ForAll(
+		func(a testPairElement) bool {
+			var c Element
+			c.Square(&a.element)
+			return c.smallerThanModulus()
+		},
+		genA,
+	))
+
+	specialValueTest := func() {
+		// test special values
+		testValues := make([]Element, len(staticTestValues))
+		copy(testValues, staticTestValues)
+
+		for i := range testValues {
+			a := testValues[i]
+			var aBig big.Int
+			a.BigInt(&aBig)
+			var c Element
+			c.Square(&a)
+
+			var d, e big.Int
+			d.Mul(&aBig, &aBig).Mod(&d, Modulus())
+
+			if c.BigInt(&e).Cmp(&d) != 0 {
+				t.Fatal("Square failed special test values")
+			}
+		}
+	}
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+	specialValueTest()
+
+}
+
+func TestElementInverse(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("Inverse: having the receiver as operand should output the same result", prop.ForAll(
+		func(a testPairElement) bool {
+
+			var b Element
+
+			b.Inverse(&a.element)
+			a.element.Inverse(&a.element)
+			return a.element.Equal(&b)
+		},
+		genA,
+	))
+
+	properties.Property("Inverse: operation result must match big.Int result", prop.ForAll(
+		func(a testPairElement) bool {
+			var c Element
+			c.Inverse(&a.element)
+
+			var d, e big.Int
+			d.ModInverse(&a.bigint, Modulus())
+
+			return c.BigInt(&e).Cmp(&d) == 0
+		},
+		genA,
+	))
+
+	properties.Property("Inverse: operation result must be smaller than modulus", prop.ForAll(
+		func(a testPairElement) bool {
+			var c Element
+			c.Inverse(&a.element)
+			return c.smallerThanModulus()
+		},
+		genA,
+	))
+
+	specialValueTest := func() {
+		// test special values
+		testValues := make([]Element, len(staticTestValues))
+		copy(testValues, staticTestValues)
+
+		for i := range testValues {
+			a := testValues[i]
+			var aBig big.Int
+			a.BigInt(&aBig)
+			var c Element
+			c.Inverse(&a)
+
+			var d, e big.Int
+			d.ModInverse(&aBig, Modulus())
+
+			if c.BigInt(&e).Cmp(&d) != 0 {
+				t.Fatal("Inverse failed special test values")
+			}
+		}
+	}
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+	specialValueTest()
+
+}
+
+func TestElementSqrt(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("Sqrt: having the receiver as operand should output the same result", prop.ForAll(
+		func(a testPairElement) bool {
+
+			b := a.element
+
+			b.Sqrt(&a.element)
+			a.element.Sqrt(&a.element)
+			return a.element.Equal(&b)
+		},
+		genA,
+	))
+
+	properties.Property("Sqrt: operation result must match big.Int result", prop.ForAll(
+		func(a testPairElement) bool {
+			var c Element
+			c.Sqrt(&a.element)
+
+			var d, e big.Int
+			d.ModSqrt(&a.bigint, Modulus())
+
+			return c.BigInt(&e).Cmp(&d) == 0
+		},
+		genA,
+	))
+
+	properties.Property("Sqrt: operation result must be smaller than modulus", prop.ForAll(
+		func(a testPairElement) bool {
+			var c Element
+			c.Sqrt(&a.element)
+			return c.smallerThanModulus()
+		},
+		genA,
+	))
+
+	specialValueTest := func() {
+		// test special values
+		testValues := make([]Element, len(staticTestValues))
+		copy(testValues, staticTestValues)
+
+		for i := range testValues {
+			a := testValues[i]
+			var aBig big.Int
+			a.BigInt(&aBig)
+			var c Element
+			c.Sqrt(&a)
+
+			var d, e big.Int
+			d.ModSqrt(&aBig, Modulus())
+
+			if c.BigInt(&e).Cmp(&d) != 0 {
+				t.Fatal("Sqrt failed special test values")
+			}
+		}
+	}
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+	specialValueTest()
+
+}
+
+func TestElementDouble(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("Double: having the receiver as operand should output the same result", prop.ForAll(
+		func(a testPairElement) bool {
+
+			var b Element
+
+			b.Double(&a.element)
+			a.element.Double(&a.element)
+			return a.element.Equal(&b)
+		},
+		genA,
+	))
+
+	properties.Property("Double: operation result must match big.Int result", prop.ForAll(
+		func(a testPairElement) bool {
+			var c Element
+			c.Double(&a.element)
+
+			var d, e big.Int
+			d.Lsh(&a.bigint, 1).Mod(&d, Modulus())
+
+			return c.BigInt(&e).Cmp(&d) == 0
+		},
+		genA,
+	))
+
+	properties.Property("Double: operation result must be smaller than modulus", prop.ForAll(
+		func(a testPairElement) bool {
+			var c Element
+			c.Double(&a.element)
+			return c.smallerThanModulus()
+		},
+		genA,
+	))
+
+	specialValueTest := func() {
+		// test special values
+		testValues := make([]Element, len(staticTestValues))
+		copy(testValues, staticTestValues)
+
+		for i := range testValues {
+			a := testValues[i]
+			var aBig big.Int
+			a.BigInt(&aBig)
+			var c Element
+			c.Double(&a)
+
+			var d, e big.Int
+			d.Lsh(&aBig, 1).Mod(&d, Modulus())
+
+			if c.BigInt(&e).Cmp(&d) != 0 {
+				t.Fatal("Double failed special test values")
+			}
+		}
+	}
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+	specialValueTest()
+
+}
+
+func TestElementNeg(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("Neg: having the receiver as operand should output the same result", prop.ForAll(
+		func(a testPairElement) bool {
+
+			var b Element
+
+			b.Neg(&a.element)
+			a.element.Neg(&a.element)
+			return a.element.Equal(&b)
+		},
+		genA,
+	))
+
+	properties.Property("Neg: operation result must match big.Int result", prop.ForAll(
+		func(a testPairElement) bool {
+			var c Element
+			c.Neg(&a.element)
+
+			var d, e big.Int
+			d.Neg(&a.bigint).Mod(&d, Modulus())
+
+			return c.BigInt(&e).Cmp(&d) == 0
+		},
+		genA,
+	))
+
+	properties.Property("Neg: operation result must be smaller than modulus", prop.ForAll(
+		func(a testPairElement) bool {
+			var c Element
+			c.Neg(&a.element)
+			return c.smallerThanModulus()
+		},
+		genA,
+	))
+
+	specialValueTest := func() {
+		// test special values
+		testValues := make([]Element, len(staticTestValues))
+		copy(testValues, staticTestValues)
+
+		for i := range testValues {
+			a := testValues[i]
+			var aBig big.Int
+			a.BigInt(&aBig)
+			var c Element
+			c.Neg(&a)
+
+			var d, e big.Int
+			d.Neg(&aBig).Mod(&d, Modulus())
+
+			if c.BigInt(&e).Cmp(&d) != 0 {
+				t.Fatal("Neg failed special test values")
+			}
+		}
+	}
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+	specialValueTest()
+
+}
+
+func TestElementFixedExp(t *testing.T) {
+
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	var (
+		_bLegendreExponentElement *big.Int
+		_bSqrtExponentElement     *big.Int
+	)
+
+	_bLegendreExponentElement, _ = new(big.Int).SetString("3c000000", 16)
+	const sqrtExponentElement = "7"
+	_bSqrtExponentElement, _ = new(big.Int).SetString(sqrtExponentElement, 16)
+
+	genA := gen()
+
+	properties.Property(fmt.Sprintf("expBySqrtExp must match Exp(%s)", sqrtExponentElement), prop.ForAll(
+		func(a testPairElement) bool {
+			c := a.element
+			d := a.element
+			c.expBySqrtExp(c)
+			d.Exp(d, _bSqrtExponentElement)
+			return c.Equal(&d)
+		},
+		genA,
+	))
+
+	properties.Property("expByLegendreExp must match Exp(3c000000)", prop.ForAll(
+		func(a testPairElement) bool {
+			c := a.element
+			d := a.element
+			c.expByLegendreExp(c)
+			d.Exp(d, _bLegendreExponentElement)
+			return c.Equal(&d)
+		},
+		genA,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+}
+
+func TestElementHalve(t *testing.T) {
+
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+	var twoInv Element
+	twoInv.SetUint64(2)
+	twoInv.Inverse(&twoInv)
+
+	properties.Property("z.Halve must match z / 2", prop.ForAll(
+		func(a testPairElement) bool {
+			c := a.element
+			d := a.element
+			c.Halve()
+			d.Mul(&d, &twoInv)
+			return c.Equal(&d)
+		},
+		genA,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+}
+
+func combineSelectionArguments(c int64, z int8) int {
+	if z%3 == 0 {
+		return 0
+	}
+	return int(c)
+}
+
+func TestElementSelect(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := genFull()
+	genB := genFull()
+	genC := ggen.Int64() //the condition
+	genZ := ggen.Int8()  //to make zeros artificially more likely
+
+	properties.Property("Select: must select correctly", prop.ForAll(
+		func(a, b Element, cond int64, z int8) bool {
+			condC := combineSelectionArguments(cond, z)
+
+			var c Element
+			c.Select(condC, &a, &b)
+
+			if condC == 0 {
+				return c.Equal(&a)
+			}
+			return c.Equal(&b)
+		},
+		genA,
+		genB,
+		genC,
+		genZ,
+	))
+
+	properties.Property("Select: having the receiver as operand should output the same result", prop.ForAll(
+		func(a, b Element, cond int64, z int8) bool {
+			condC := combineSelectionArguments(cond, z)
+
+			var c, d Element
+			d.Set(&a)
+			c.Select(condC, &a, &b)
+			a.Select(condC, &a, &b)
+			b.Select(condC, &d, &b)
+			return a.Equal(&b) && a.Equal(&c) && b.Equal(&c)
+		},
+		genA,
+		genB,
+		genC,
+		genZ,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+}
+
+func TestElementSetInt64(t *testing.T) {
+
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("z.SetInt64 must match z.SetString", prop.ForAll(
+		func(a testPairElement, v int64) bool {
+			c := a.element
+			d := a.element
+
+			c.SetInt64(v)
+			d.SetString(fmt.Sprintf("%v", v))
+
+			return c.Equal(&d)
+		},
+		genA, ggen.Int64(),
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+}
+
+func TestElementSetInterface(t *testing.T) {
+
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+	genInt := ggen.Int
+	genInt8 := ggen.Int8
+	genInt16 := ggen.Int16
+	genInt32 := ggen.Int32
+	genInt64 := ggen.Int64
+
+	genUint := ggen.UInt
+	genUint8 := ggen.UInt8
+	genUint16 := ggen.UInt16
+	genUint32 := ggen.UInt32
+	genUint64 := ggen.UInt64
+
+	properties.Property("z.SetInterface must match z.SetString with int8", prop.ForAll(
+		func(a testPairElement, v int8) bool {
+			c := a.element
+			d := a.element
+
+			c.SetInterface(v)
+			d.SetString(fmt.Sprintf("%v", v))
+
+			return c.Equal(&d)
+		},
+		genA, genInt8(),
+	))
+
+	properties.Property("z.SetInterface must match z.SetString with int16", prop.ForAll(
+		func(a testPairElement, v int16) bool {
+			c := a.element
+			d := a.element
+
+			c.SetInterface(v)
+			d.SetString(fmt.Sprintf("%v", v))
+
+			return c.Equal(&d)
+		},
+		genA, genInt16(),
+	))
+
+	properties.Property("z.SetInterface must match z.SetString with int32", prop.ForAll(
+		func(a testPairElement, v int32) bool {
+			c := a.element
+			d := a.element
+
+			c.SetInterface(v)
+			d.SetString(fmt.Sprintf("%v", v))
+
+			return c.Equal(&d)
+		},
+		genA, genInt32(),
+	))
+
+	properties.Property("z.SetInterface must match z.SetString with int64", prop.ForAll(
+		func(a testPairElement, v int64) bool {
+			c := a.element
+			d := a.element
+
+			c.SetInterface(v)
+			d.SetString(fmt.Sprintf("%v", v))
+
+			return c.Equal(&d)
+		},
+		genA, genInt64(),
+	))
+
+	properties.Property("z.SetInterface must match z.SetString with int", prop.ForAll(
+		func(a testPairElement, v int) bool {
+			c := a.element
+			d := a.element
+
+			c.SetInterface(v)
+			d.SetString(fmt.Sprintf("%v", v))
+
+			return c.Equal(&d)
+		},
+		genA, genInt(),
+	))
+
+	properties.Property("z.SetInterface must match z.SetString with uint8", prop.ForAll(
+		func(a testPairElement, v uint8) bool {
+			c := a.element
+			d := a.element
+
+			c.SetInterface(v)
+			d.SetString(fmt.Sprintf("%v", v))
+
+			return c.Equal(&d)
+		},
+		genA, genUint8(),
+	))
+
+	properties.Property("z.SetInterface must match z.SetString with uint16", prop.ForAll(
+		func(a testPairElement, v uint16) bool {
+			c := a.element
+			d := a.element
+
+			c.SetInterface(v)
+			d.SetString(fmt.Sprintf("%v", v))
+
+			return c.Equal(&d)
+		},
+		genA, genUint16(),
+	))
+
+	properties.Property("z.SetInterface must match z.SetString with uint32", prop.ForAll(
+		func(a testPairElement, v uint32) bool {
+			c := a.element
+			d := a.element
+
+			c.SetInterface(v)
+			d.SetString(fmt.Sprintf("%v", v))
+
+			return c.Equal(&d)
+		},
+		genA, genUint32(),
+	))
+
+	properties.Property("z.SetInterface must match z.SetString with uint64", prop.ForAll(
+		func(a testPairElement, v uint64) bool {
+			c := a.element
+			d := a.element
+
+			c.SetInterface(v)
+			d.SetString(fmt.Sprintf("%v", v))
+
+			return c.Equal(&d)
+		},
+		genA, genUint64(),
+	))
+
+	properties.Property("z.SetInterface must match z.SetString with uint", prop.ForAll(
+		func(a testPairElement, v uint) bool {
+			c := a.element
+			d := a.element
+
+			c.SetInterface(v)
+			d.SetString(fmt.Sprintf("%v", v))
+
+			return c.Equal(&d)
+		},
+		genA, genUint(),
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+
+	{
+		assert := require.New(t)
+		var e Element
+		r, err := e.SetInterface(nil)
+		assert.Nil(r)
+		assert.Error(err)
+
+		var ptE *Element
+		var ptB *big.Int
+
+		r, err = e.SetInterface(ptE)
+		assert.Nil(r)
+		assert.Error(err)
+		ptE = new(Element).SetOne()
+		r, err = e.SetInterface(ptE)
+		assert.NoError(err)
+		assert.True(r.IsOne())
+
+		r, err = e.SetInterface(ptB)
+		assert.Nil(r)
+		assert.Error(err)
+
+	}
+}
+
+func TestElementNegativeExp(t *testing.T) {
+	t.Parallel()
+
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("x⁻ᵏ == 1/xᵏ", prop.ForAll(
+		func(a, b testPairElement) bool {
+
+			var nb, d, e big.Int
+			nb.Neg(&b.bigint)
+
+			var c Element
+			c.Exp(a.element, &nb)
+
+			d.Exp(&a.bigint, &nb, Modulus())
+
+			return c.BigInt(&e).Cmp(&d) == 0
+		},
+		genA, genA,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+}
+
+func TestElementNewElement(t *testing.T) {
+	assert := require.New(t)
+
+	t.Parallel()
+
+	e := NewElement(1)
+	assert.True(e.IsOne())
+
+	e = NewElement(0)
+	assert.True(e.IsZero())
+}
+
+func TestElementBatchInvert(t *testing.T) {
+	assert := require.New(t)
+
+	t.Parallel()
+
+	// ensure batchInvert([x]) == invert(x)
+	for i := int64(-1); i <= 2; i++ {
+		var e, eInv Element
+		e.SetInt64(i)
+		eInv.Inverse(&e)
+
+		a := []Element{e}
+		aInv := BatchInvert(a)
+
+		assert.True(aInv[0].Equal(&eInv), "batchInvert != invert")
+
+	}
+
+	// test x * x⁻¹ == 1
+	tData := [][]int64{
+		{-1, 1, 2, 3},
+		{0, -1, 1, 2, 3, 0},
+		{0, -1, 1, 0, 2, 3, 0},
+		{-1, 1, 0, 2, 3},
+		{0, 0, 1},
+		{1, 0, 0},
+		{0, 0, 0},
+	}
+
+	for _, t := range tData {
+		a := make([]Element, len(t))
+		for i := 0; i < len(a); i++ {
+			a[i].SetInt64(t[i])
+		}
+
+		aInv := BatchInvert(a)
+
+		assert.True(len(aInv) == len(a))
+
+		for i := 0; i < len(a); i++ {
+			if a[i].IsZero() {
+				assert.True(aInv[i].IsZero(), "0⁻¹ != 0")
+			} else {
+				assert.True(a[i].Mul(&a[i], &aInv[i]).IsOne(), "x * x⁻¹ != 1")
+			}
+		}
+	}
+
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("batchInvert --> x * x⁻¹ == 1", prop.ForAll(
+		func(tp testPairElement, r uint8) bool {
+
+			a := make([]Element, r)
+			if r != 0 {
+				a[0] = tp.element
+
+			}
+			one := One()
+			for i := 1; i < len(a); i++ {
+				a[i].Add(&a[i-1], &one)
+			}
+
+			aInv := BatchInvert(a)
+
+			assert.True(len(aInv) == len(a))
+
+			for i := 0; i < len(a); i++ {
+				if a[i].IsZero() {
+					if !aInv[i].IsZero() {
+						return false
+					}
+				} else {
+					if !a[i].Mul(&a[i], &aInv[i]).IsOne() {
+						return false
+					}
+				}
+			}
+			return true
+		},
+		genA, ggen.UInt8(),
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+}
+
+func TestElementFromMont(t *testing.T) {
+
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("Assembly implementation must be consistent with generic one", prop.ForAll(
+		func(a testPairElement) bool {
+			c := a.element
+			d := a.element
+			c.fromMont()
+			_fromMontGeneric(&d)
+			return c.Equal(&d)
+		},
+		genA,
+	))
+
+	properties.Property("x.fromMont().toMont() == x", prop.ForAll(
+		func(a testPairElement) bool {
+			c := a.element
+			c.fromMont().toMont()
+			return c.Equal(&a.element)
+		},
+		genA,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+}
+
+func TestElementJSON(t *testing.T) {
+	assert := require.New(t)
+
+	type S struct {
+		A Element
+		B [3]Element
+		C *Element
+		D *Element
+	}
+
+	// encode to JSON
+	var s S
+	s.A.SetString("-1")
+	s.B[2].SetUint64(42)
+	s.D = new(Element).SetUint64(8000)
+
+	encoded, err := json.Marshal(&s)
+	assert.NoError(err)
+	// we may need to adjust "42" and "8000" values for some moduli; see Text() method for more details.
+	formatValue := func(v int64) string {
+		var a big.Int
+		a.SetInt64(v)
+		a.Mod(&a, Modulus())
+		const maxUint16 = 65535
+		var aNeg big.Int
+		aNeg.Neg(&a).Mod(&aNeg, Modulus())
+		if aNeg.Uint64() != 0 && aNeg.Uint64() <= maxUint16 {
+			return "-" + aNeg.Text(10)
+		}
+		return a.Text(10)
+	}
+	expected := fmt.Sprintf("{\"A\":%s,\"B\":[0,0,%s],\"C\":null,\"D\":%s}", formatValue(-1), formatValue(42), formatValue(8000))
+	assert.Equal(expected, string(encoded))
+
+	// decode valid
+	var decoded S
+	err = json.Unmarshal([]byte(expected), &decoded)
+	assert.NoError(err)
+
+	assert.Equal(s, decoded, "element -> json -> element round trip failed")
+
+	// decode hex and string values
+	withHexValues := "{\"A\":\"-1\",\"B\":[0,\"0x00000\",\"0x2A\"],\"C\":null,\"D\":\"8000\"}"
+
+	var decodedS S
+	err = json.Unmarshal([]byte(withHexValues), &decodedS)
+	assert.NoError(err)
+
+	assert.Equal(s, decodedS, " json with strings  -> element  failed")
+
+}
+
+type testPairElement struct {
+	element Element
+	bigint  big.Int
+}
+
+func gen() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		var g testPairElement
+
+		g.element = Element{
+			uint32(genParams.NextUint64()),
+		}
+		if qElement[0] != ^uint32(0) {
+			g.element[0] %= (qElement[0] + 1)
+		}
+
+		for !g.element.smallerThanModulus() {
+			g.element = Element{
+				uint32(genParams.NextUint64()),
+			}
+			if qElement[0] != ^uint32(0) {
+				g.element[0] %= (qElement[0] + 1)
+			}
+		}
+
+		g.element.BigInt(&g.bigint)
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genRandomFq(genParams *gopter.GenParameters) Element {
+	var g Element
+
+	g = Element{
+		uint32(genParams.NextUint64()),
+	}
+
+	if qElement[0] != ^uint32(0) {
+		g[0] %= (qElement[0] + 1)
+	}
+
+	for !g.smallerThanModulus() {
+		g = Element{
+			uint32(genParams.NextUint64()),
+		}
+		if qElement[0] != ^uint32(0) {
+			g[0] %= (qElement[0] + 1)
+		}
+	}
+
+	return g
+}
+
+func genFull() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
+
+		var carry uint32
+		a[0], _ = bits.Add32(a[0], qElement[0], carry)
+
+		genResult := gopter.NewGenResult(a, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genElement() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
+		genResult := gopter.NewGenResult(a, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/field/babybear/vector.go b/field/babybear/vector.go
new file mode 100644
index 0000000000..19a57ac10d
--- /dev/null
+++ b/field/babybear/vector.go
@@ -0,0 +1,303 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package babybear
+
+import (
+	"bytes"
+	"encoding/binary"
+	"fmt"
+	"io"
+	"runtime"
+	"strings"
+	"sync"
+	"sync/atomic"
+	"unsafe"
+)
+
+// Vector represents a slice of Element.
+//
+// It implements the following interfaces:
+//   - Stringer
+//   - io.WriterTo
+//   - io.ReaderFrom
+//   - encoding.BinaryMarshaler
+//   - encoding.BinaryUnmarshaler
+//   - sort.Interface
+type Vector []Element
+
+// MarshalBinary implements encoding.BinaryMarshaler
+func (vector *Vector) MarshalBinary() (data []byte, err error) {
+	var buf bytes.Buffer
+
+	if _, err = vector.WriteTo(&buf); err != nil {
+		return
+	}
+	return buf.Bytes(), nil
+}
+
+// UnmarshalBinary implements encoding.BinaryUnmarshaler
+func (vector *Vector) UnmarshalBinary(data []byte) error {
+	r := bytes.NewReader(data)
+	_, err := vector.ReadFrom(r)
+	return err
+}
+
+// WriteTo implements io.WriterTo and writes a vector of big endian encoded Element.
+// Length of the vector is encoded as a uint32 on the first 4 bytes.
+func (vector *Vector) WriteTo(w io.Writer) (int64, error) {
+	// encode slice length
+	if err := binary.Write(w, binary.BigEndian, uint32(len(*vector))); err != nil {
+		return 0, err
+	}
+
+	n := int64(4)
+
+	var buf [Bytes]byte
+	for i := 0; i < len(*vector); i++ {
+		BigEndian.PutElement(&buf, (*vector)[i])
+		m, err := w.Write(buf[:])
+		n += int64(m)
+		if err != nil {
+			return n, err
+		}
+	}
+	return n, nil
+}
+
+// AsyncReadFrom reads a vector of big endian encoded Element.
+// Length of the vector must be encoded as a uint32 on the first 4 bytes.
+// It consumes the needed bytes from the reader and returns the number of bytes read and an error if any.
+// It also returns a channel that will be closed when the validation is done.
+// The validation consist of checking that the elements are smaller than the modulus, and
+// converting them to montgomery form.
+func (vector *Vector) AsyncReadFrom(r io.Reader) (int64, error, chan error) {
+	chErr := make(chan error, 1)
+	var buf [Bytes]byte
+	if read, err := io.ReadFull(r, buf[:4]); err != nil {
+		close(chErr)
+		return int64(read), err, chErr
+	}
+	sliceLen := binary.BigEndian.Uint32(buf[:4])
+
+	n := int64(4)
+	(*vector) = make(Vector, sliceLen)
+	if sliceLen == 0 {
+		close(chErr)
+		return n, nil, chErr
+	}
+
+	bSlice := unsafe.Slice((*byte)(unsafe.Pointer(&(*vector)[0])), sliceLen*Bytes)
+	read, err := io.ReadFull(r, bSlice)
+	n += int64(read)
+	if err != nil {
+		close(chErr)
+		return n, err, chErr
+	}
+
+	go func() {
+		var cptErrors uint64
+		// process the elements in parallel
+		execute(int(sliceLen), func(start, end int) {
+
+			var z Element
+			for i := start; i < end; i++ {
+				// we have to set vector[i]
+				bstart := i * Bytes
+				bend := bstart + Bytes
+				b := bSlice[bstart:bend]
+				z[0] = binary.BigEndian.Uint32(b[0:4])
+
+				if !z.smallerThanModulus() {
+					atomic.AddUint64(&cptErrors, 1)
+					return
+				}
+				z.toMont()
+				(*vector)[i] = z
+			}
+		})
+
+		if cptErrors > 0 {
+			chErr <- fmt.Errorf("async read: %d elements failed validation", cptErrors)
+		}
+		close(chErr)
+	}()
+	return n, nil, chErr
+}
+
+// ReadFrom implements io.ReaderFrom and reads a vector of big endian encoded Element.
+// Length of the vector must be encoded as a uint32 on the first 4 bytes.
+func (vector *Vector) ReadFrom(r io.Reader) (int64, error) {
+
+	var buf [Bytes]byte
+	if read, err := io.ReadFull(r, buf[:4]); err != nil {
+		return int64(read), err
+	}
+	sliceLen := binary.BigEndian.Uint32(buf[:4])
+
+	n := int64(4)
+	(*vector) = make(Vector, sliceLen)
+
+	for i := 0; i < int(sliceLen); i++ {
+		read, err := io.ReadFull(r, buf[:])
+		n += int64(read)
+		if err != nil {
+			return n, err
+		}
+		(*vector)[i], err = BigEndian.Element(&buf)
+		if err != nil {
+			return n, err
+		}
+	}
+
+	return n, nil
+}
+
+// String implements fmt.Stringer interface
+func (vector Vector) String() string {
+	var sbb strings.Builder
+	sbb.WriteByte('[')
+	for i := 0; i < len(vector); i++ {
+		sbb.WriteString(vector[i].String())
+		if i != len(vector)-1 {
+			sbb.WriteByte(',')
+		}
+	}
+	sbb.WriteByte(']')
+	return sbb.String()
+}
+
+// Len is the number of elements in the collection.
+func (vector Vector) Len() int {
+	return len(vector)
+}
+
+// Less reports whether the element with
+// index i should sort before the element with index j.
+func (vector Vector) Less(i, j int) bool {
+	return vector[i].Cmp(&vector[j]) == -1
+}
+
+// Swap swaps the elements with indexes i and j.
+func (vector Vector) Swap(i, j int) {
+	vector[i], vector[j] = vector[j], vector[i]
+}
+
+func addVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Add: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Add(&a[i], &b[i])
+	}
+}
+
+func subVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Sub: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Sub(&a[i], &b[i])
+	}
+}
+
+func scalarMulVecGeneric(res, a Vector, b *Element) {
+	if len(a) != len(res) {
+		panic("vector.ScalarMul: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Mul(&a[i], b)
+	}
+}
+
+func sumVecGeneric(res *Element, a Vector) {
+	for i := 0; i < len(a); i++ {
+		res.Add(res, &a[i])
+	}
+}
+
+func innerProductVecGeneric(res *Element, a, b Vector) {
+	if len(a) != len(b) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	var tmp Element
+	for i := 0; i < len(a); i++ {
+		tmp.Mul(&a[i], &b[i])
+		res.Add(res, &tmp)
+	}
+}
+
+func mulVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Mul(&a[i], &b[i])
+	}
+}
+
+// TODO @gbotrel make a public package out of that.
+// execute executes the work function in parallel.
+// this is copy paste from internal/parallel/parallel.go
+// as we don't want to generate code importing internal/
+func execute(nbIterations int, work func(int, int), maxCpus ...int) {
+
+	nbTasks := runtime.NumCPU()
+	if len(maxCpus) == 1 {
+		nbTasks = maxCpus[0]
+		if nbTasks < 1 {
+			nbTasks = 1
+		} else if nbTasks > 512 {
+			nbTasks = 512
+		}
+	}
+
+	if nbTasks == 1 {
+		// no go routines
+		work(0, nbIterations)
+		return
+	}
+
+	nbIterationsPerCpus := nbIterations / nbTasks
+
+	// more CPUs than tasks: a CPU will work on exactly one iteration
+	if nbIterationsPerCpus < 1 {
+		nbIterationsPerCpus = 1
+		nbTasks = nbIterations
+	}
+
+	var wg sync.WaitGroup
+
+	extraTasks := nbIterations - (nbTasks * nbIterationsPerCpus)
+	extraTasksOffset := 0
+
+	for i := 0; i < nbTasks; i++ {
+		wg.Add(1)
+		_start := i*nbIterationsPerCpus + extraTasksOffset
+		_end := _start + nbIterationsPerCpus
+		if extraTasks > 0 {
+			_end++
+			extraTasks--
+			extraTasksOffset++
+		}
+		go func() {
+			work(_start, _end)
+			wg.Done()
+		}()
+	}
+
+	wg.Wait()
+}
diff --git a/field/babybear/vector_purego.go b/field/babybear/vector_purego.go
new file mode 100644
index 0000000000..8843280543
--- /dev/null
+++ b/field/babybear/vector_purego.go
@@ -0,0 +1,54 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package babybear
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	addVecGeneric(*vector, a, b)
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	subVecGeneric(*vector, a, b)
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
diff --git a/field/babybear/vector_test.go b/field/babybear/vector_test.go
new file mode 100644
index 0000000000..5d35c3e7bb
--- /dev/null
+++ b/field/babybear/vector_test.go
@@ -0,0 +1,365 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package babybear
+
+import (
+	"bytes"
+	"fmt"
+	"github.com/stretchr/testify/require"
+	"os"
+	"reflect"
+	"sort"
+	"testing"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/prop"
+)
+
+func TestVectorSort(t *testing.T) {
+	assert := require.New(t)
+
+	v := make(Vector, 3)
+	v[0].SetUint64(2)
+	v[1].SetUint64(3)
+	v[2].SetUint64(1)
+
+	sort.Sort(v)
+
+	assert.Equal("[1,2,3]", v.String())
+}
+
+func TestVectorRoundTrip(t *testing.T) {
+	assert := require.New(t)
+
+	v1 := make(Vector, 3)
+	v1[0].SetUint64(2)
+	v1[1].SetUint64(3)
+	v1[2].SetUint64(1)
+
+	b, err := v1.MarshalBinary()
+	assert.NoError(err)
+
+	var v2, v3 Vector
+
+	err = v2.UnmarshalBinary(b)
+	assert.NoError(err)
+
+	err = v3.unmarshalBinaryAsync(b)
+	assert.NoError(err)
+
+	assert.True(reflect.DeepEqual(v1, v2))
+	assert.True(reflect.DeepEqual(v3, v2))
+}
+
+func TestVectorEmptyRoundTrip(t *testing.T) {
+	assert := require.New(t)
+
+	v1 := make(Vector, 0)
+
+	b, err := v1.MarshalBinary()
+	assert.NoError(err)
+
+	var v2, v3 Vector
+
+	err = v2.UnmarshalBinary(b)
+	assert.NoError(err)
+
+	err = v3.unmarshalBinaryAsync(b)
+	assert.NoError(err)
+
+	assert.True(reflect.DeepEqual(v1, v2))
+	assert.True(reflect.DeepEqual(v3, v2))
+}
+
+func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
+	r := bytes.NewReader(data)
+	_, err, chErr := vector.AsyncReadFrom(r)
+	if err != nil {
+		return err
+	}
+	return <-chErr
+}
+
+func TestVectorOps(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = 2
+	} else {
+		parameters.MinSuccessfulTests = 10
+	}
+	properties := gopter.NewProperties(parameters)
+
+	addVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Add(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Add(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	subVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Sub(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Sub(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	scalarMulVector := func(a Vector, b Element) bool {
+		c := make(Vector, len(a))
+		c.ScalarMul(a, &b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b)
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sumVector := func(a Vector) bool {
+		var sum Element
+		computed := a.Sum()
+		for i := 0; i < len(a); i++ {
+			sum.Add(&sum, &a[i])
+		}
+
+		return sum.Equal(&computed)
+	}
+
+	innerProductVector := func(a, b Vector) bool {
+		computed := a.InnerProduct(b)
+		var innerProduct Element
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			innerProduct.Add(&innerProduct, &tmp)
+		}
+
+		return innerProduct.Equal(&computed)
+	}
+
+	mulVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		a[0].SetUint64(0x24)
+		b[0].SetUint64(0x42)
+		c.Mul(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sizes := []int{1, 2, 3, 4, 8, 9, 15, 16, 509, 510, 511, 512, 513, 514}
+	type genPair struct {
+		g1, g2 gopter.Gen
+		label  string
+	}
+
+	for _, size := range sizes {
+		generators := []genPair{
+			{genZeroVector(size), genZeroVector(size), "zero vectors"},
+			{genMaxVector(size), genMaxVector(size), "max vectors"},
+			{genVector(size), genVector(size), "random vectors"},
+			{genVector(size), genZeroVector(size), "random and zero vectors"},
+		}
+		for _, gp := range generators {
+			properties.Property(fmt.Sprintf("vector addition %d - %s", size, gp.label), prop.ForAll(
+				addVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector subtraction %d - %s", size, gp.label), prop.ForAll(
+				subVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector scalar multiplication %d - %s", size, gp.label), prop.ForAll(
+				scalarMulVector,
+				gp.g1,
+				genElement(),
+			))
+
+			properties.Property(fmt.Sprintf("vector sum %d - %s", size, gp.label), prop.ForAll(
+				sumVector,
+				gp.g1,
+			))
+
+			properties.Property(fmt.Sprintf("vector inner product %d - %s", size, gp.label), prop.ForAll(
+				innerProductVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector multiplication %d - %s", size, gp.label), prop.ForAll(
+				mulVector,
+				gp.g1,
+				gp.g2,
+			))
+		}
+	}
+
+	properties.TestingRun(t, gopter.NewFormatedReporter(false, 260, os.Stdout))
+}
+
+func BenchmarkVectorOps(b *testing.B) {
+	// note; to benchmark against "no asm" version, use the following
+	// build tag: -tags purego
+	const N = 1 << 24
+	a1 := make(Vector, N)
+	b1 := make(Vector, N)
+	c1 := make(Vector, N)
+	var mixer Element
+	mixer.SetRandom()
+	for i := 1; i < N; i++ {
+		a1[i-1].SetUint64(uint64(i)).
+			Mul(&a1[i-1], &mixer)
+		b1[i-1].SetUint64(^uint64(i)).
+			Mul(&b1[i-1], &mixer)
+	}
+
+	for n := 1 << 4; n <= N; n <<= 1 {
+		b.Run(fmt.Sprintf("add %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Add(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sub %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Sub(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("scalarMul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.ScalarMul(_a, &mixer)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sum %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.Sum()
+			}
+		})
+
+		b.Run(fmt.Sprintf("innerProduct %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.InnerProduct(_b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("mul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Mul(_a, _b)
+			}
+		})
+	}
+}
+
+func genZeroVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genMaxVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+
+		qMinusOne := qElement
+		qMinusOne[0]--
+
+		for i := 0; i < size; i++ {
+			g[i] = qMinusOne
+		}
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		mixer := Element{
+			uint32(genParams.NextUint64()),
+		}
+		if qElement[0] != ^uint32(0) {
+			mixer[0] %= (qElement[0] + 1)
+		}
+
+		for !mixer.smallerThanModulus() {
+			mixer = Element{
+				uint32(genParams.NextUint64()),
+			}
+			if qElement[0] != ^uint32(0) {
+				mixer[0] %= (qElement[0] + 1)
+			}
+		}
+
+		for i := 1; i <= size; i++ {
+			g[i-1].SetUint64(uint64(i)).
+				Mul(&g[i-1], &mixer)
+		}
+
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/field/generator/config/field_config.go b/field/generator/config/field_config.go
index f6e5513b4c..2d992db463 100644
--- a/field/generator/config/field_config.go
+++ b/field/generator/config/field_config.go
@@ -73,6 +73,9 @@ type FieldConfig struct {
 	SqrtQ3Mod4ExponentData    *addchain.AddChainData
 	UseAddChain               bool
 
+	Word Word // 32 iff Q < 2^32, else 64
+	F31  bool // 31 bits field
+
 	// asm code generation
 	GenerateOpsAMD64       bool
 	GenerateOpsARM64       bool
@@ -80,6 +83,16 @@ type FieldConfig struct {
 	GenerateVectorOpsARM64 bool
 }
 
+type Word struct {
+	BitSize   int    // 32 or 64
+	ByteSize  int    // 4 or 8
+	TypeLower string // uint32 or uint64
+	TypeUpper string // Uint32 or Uint64
+	Add       string // Add64 or Add32
+	Sub       string // Sub64 or Sub32
+	Len       string // Len64 or Len32
+}
+
 // NewFieldConfig returns a data structure with needed information to generate apis for field element
 //
 // See field/generator package
@@ -101,9 +114,8 @@ func NewFieldConfig(packageName, elementName, modulus string, useAddChain bool)
 	}
 	// pre compute field constants
 	F.NbBits = bModulus.BitLen()
+	F.F31 = F.NbBits <= 31
 	F.NbWords = len(bModulus.Bits())
-	F.NbBytes = F.NbWords * 8 // (F.NbBits + 7) / 8
-
 	F.NbWordsLastIndex = F.NbWords - 1
 
 	// set q from big int repr
@@ -114,9 +126,31 @@ func NewFieldConfig(packageName, elementName, modulus string, useAddChain bool)
 	_qHalved.Sub(&bModulus, bOne).Rsh(_qHalved, 1).Add(_qHalved, bOne)
 	F.QMinusOneHalvedP = toUint64Slice(_qHalved, F.NbWords)
 
+	// Word size; we pick uint32 only if the modulus is less than 2^32
+	F.Word.BitSize = 64
+	F.Word.ByteSize = 8
+	F.Word.TypeLower = "uint64"
+	F.Word.TypeUpper = "Uint64"
+	F.Word.Add = "Add64"
+	F.Word.Sub = "Sub64"
+	F.Word.Len = "Len64"
+	if F.F31 {
+		F.Word.BitSize = 32
+		F.Word.ByteSize = 4
+		F.Word.TypeLower = "uint32"
+		F.Word.TypeUpper = "Uint32"
+		F.Word.Add = "Add32"
+		F.Word.Sub = "Sub32"
+		F.Word.Len = "Len32"
+	}
+
+	F.NbBytes = F.NbWords * F.Word.ByteSize
+
 	//  setting qInverse
+	radix := uint(F.Word.BitSize)
+
 	_r := big.NewInt(1)
-	_r.Lsh(_r, uint(F.NbWords)*64)
+	_r.Lsh(_r, uint(F.NbWords)*radix)
 	_rInv := big.NewInt(1)
 	_qInv := big.NewInt(0)
 	extendedEuclideanAlgo(_r, &bModulus, _rInv, _qInv)
@@ -140,24 +174,24 @@ func NewFieldConfig(packageName, elementName, modulus string, useAddChain bool)
 
 	{
 		c := F.NbWords * 64
-		F.UsingP20Inverse = F.NbWords > 1 && F.NbBits < c
+		// TODO @gbotrel check inverse performance for 32 bits
+		F.UsingP20Inverse = F.NbWords > 1 && F.NbBits < c && F.Word.BitSize == 64
 	}
 
 	// rsquare
-	_rSquare := big.NewInt(2)
-	exponent := big.NewInt(int64(F.NbWords) * 64 * 2)
-	_rSquare.Exp(_rSquare, exponent, &bModulus)
+	_rSquare := big.NewInt(1)
+	_rSquare.Lsh(_rSquare, uint(F.NbWords)*radix*2).Mod(_rSquare, &bModulus)
 	F.RSquare = toUint64Slice(_rSquare, F.NbWords)
 
 	var one big.Int
 	one.SetUint64(1)
-	one.Lsh(&one, uint(F.NbWords)*64).Mod(&one, &bModulus)
+	one.Lsh(&one, uint(F.NbWords)*radix).Mod(&one, &bModulus)
 	F.One = toUint64Slice(&one, F.NbWords)
 
 	{
 		var n big.Int
 		n.SetUint64(13)
-		n.Lsh(&n, uint(F.NbWords)*64).Mod(&n, &bModulus)
+		n.Lsh(&n, uint(F.NbWords)*radix).Mod(&n, &bModulus)
 		F.Thirteen = toUint64Slice(&n, F.NbWords)
 	}
 
@@ -246,7 +280,7 @@ func NewFieldConfig(packageName, elementName, modulus string, useAddChain bool)
 			var g big.Int
 			g.Exp(&nonResidue, &s, &bModulus)
 			// store g in montgomery form
-			g.Lsh(&g, uint(F.NbWords)*64).Mod(&g, &bModulus)
+			g.Lsh(&g, uint(F.NbWords)*radix).Mod(&g, &bModulus)
 			F.SqrtG = toUint64Slice(&g, F.NbWords)
 
 			// store non residue in montgomery form
@@ -342,7 +376,7 @@ func (f *FieldConfig) StringToMont(str string) big.Int {
 
 func (f *FieldConfig) ToMont(nonMont big.Int) big.Int {
 	var mont big.Int
-	mont.Lsh(&nonMont, uint(f.NbWords)*64)
+	mont.Lsh(&nonMont, uint(f.NbWords)*uint(f.Word.BitSize))
 	mont.Mod(&mont, f.ModulusBig)
 	return mont
 }
@@ -354,7 +388,7 @@ func (f *FieldConfig) FromMont(nonMont *big.Int, mont *big.Int) *FieldConfig {
 		return f
 	}
 	f.halve(nonMont, mont)
-	for i := 1; i < f.NbWords*64; i++ {
+	for i := 1; i < f.NbWords*f.Word.BitSize; i++ {
 		f.halve(nonMont, nonMont)
 	}
 
diff --git a/field/generator/config/field_test.go b/field/generator/config/field_test.go
index a15370f728..6b668b60cd 100644
--- a/field/generator/config/field_test.go
+++ b/field/generator/config/field_test.go
@@ -20,7 +20,7 @@ func TestIntToMont(t *testing.T) {
 	t.Parallel()
 
 	parameters := gopter.DefaultTestParameters()
-	parameters.MinSuccessfulTests = 10
+	parameters.MinSuccessfulTests = 20
 	properties := gopter.NewProperties(parameters)
 	genF := genField(t)
 
@@ -42,11 +42,12 @@ func TestIntToMont(t *testing.T) {
 	properties.Property("turning R into montgomery form must match the R value from field", prop.ForAll(
 		func(f *FieldConfig) (bool, error) {
 			// test if using the same R
-			i := big.NewInt(1)
-			i.Lsh(i, 64*uint(f.NbWords))
-			*i = f.ToMont(*i)
+			r := big.NewInt(1)
+			r.Lsh(r, uint(f.Word.BitSize)*uint(f.NbWords))
+
+			*r = f.ToMont(*r)
 
-			err := bigIntMatchUint64Slice(i, f.RSquare)
+			err := bigIntMatchUint64Slice(r, f.RSquare)
 			return err == nil, err
 		}, genF),
 	)
diff --git a/field/generator/generator.go b/field/generator/generator.go
index 98f9015546..7547db305a 100644
--- a/field/generator/generator.go
+++ b/field/generator/generator.go
@@ -54,6 +54,9 @@ func GenerateFF(F *config.FieldConfig, outputDir, asmDirBuildPath, asmDirInclude
 		}
 	}
 
+	os.Remove(filepath.Join(outputDir, "vector_arm64.go"))
+	os.Remove(filepath.Join(outputDir, "exp.go"))
+
 	funcs["shorten"] = shorten
 	funcs["ltu64"] = func(a, b uint64) bool {
 		return a < b
@@ -141,7 +144,7 @@ func GenerateFF(F *config.FieldConfig, outputDir, asmDirBuildPath, asmDirInclude
 	g.Go(generate("element.go", sourceFiles))
 	g.Go(generate("doc.go", []string{element.Doc}))
 	g.Go(generate("vector.go", []string{element.Vector}))
-	g.Go(generate("arith.go", []string{element.Arith}))
+	g.Go(generate("arith.go", []string{element.Arith}, Only(!F.F31)))
 	g.Go(generate("element_test.go", testFiles))
 	g.Go(generate("vector_test.go", []string{element.TestVector}))
 
diff --git a/field/generator/internal/templates/element/base.go b/field/generator/internal/templates/element/base.go
index dd05519baf..9965edbd52 100644
--- a/field/generator/internal/templates/element/base.go
+++ b/field/generator/internal/templates/element/base.go
@@ -18,7 +18,7 @@ import (
 	"github.com/bits-and-blooms/bitset"
 )
 
-// {{.ElementName}} represents a field element stored on {{.NbWords}} words (uint64)
+// {{.ElementName}} represents a field element stored on {{.NbWords}} words ({{$.Word.TypeLower}})
 //
 // {{.ElementName}} are assumed to be in Montgomery form in all methods.
 //
@@ -30,10 +30,10 @@ import (
 // Warning
 //
 // This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
-type {{.ElementName}} [{{.NbWords}}]uint64
+type {{.ElementName}} [{{.NbWords}}]{{$.Word.TypeLower}}
 
 const (
-	Limbs = {{.NbWords}} 	// number of 64 bits words needed to represent a {{.ElementName}}
+	Limbs = {{.NbWords}} 	// number of {{$.Word.BitSize}} bits words needed to represent a {{.ElementName}}
 	Bits = {{.NbBits}} 		// number of bits needed to represent a {{.ElementName}}
 	Bytes = {{.NbBytes}} 	// number of bytes needed to represent a {{.ElementName}}
 )
@@ -42,9 +42,9 @@ const (
 // Field modulus q
 const (
 {{- range $i := $.NbWordsIndexesFull}}
-	q{{$i}} uint64 = {{index $.Q $i}}
+	q{{$i}} = {{index $.Q $i}}
 	{{- if eq $.NbWords 1}}
-		q uint64 = q0
+		q  = q0
 	{{- end}}
 {{- end}}
 )
@@ -66,7 +66,7 @@ func Modulus() *big.Int {
 
 // q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
 // used for Montgomery reduction
-const qInvNeg uint64 = {{index .QInverse 0}}
+const qInvNeg = {{index .QInverse 0}}
 
 {{- if eq .NbWords 4}}
 // mu = 2^288 / q needed for partial Barrett reduction
@@ -84,16 +84,27 @@ func init() {
 // 		var v {{.ElementName}}
 // 		v.SetUint64(...)
 func New{{.ElementName}}(v uint64) {{.ElementName}} {
-	z := {{.ElementName}}{v}
-	z.Mul(&z, &rSquare)
-	return z
+	{{- if .F31}}
+		z := {{.ElementName}}{ uint32(v % uint64(q0)) }
+		z.toMont()
+		return z
+	{{- else }}
+		z := {{.ElementName}}{ v }
+		z.Mul(&z, &rSquare)
+		return z
+	{{- end}}
 }
 
 // SetUint64 sets z to v and returns z
 func (z *{{.ElementName}}) SetUint64(v uint64) *{{.ElementName}} {
 	//  sets z LSB to v (non-Montgomery form) and convert z to Montgomery form
-	*z = {{.ElementName}}{v}
-	return z.Mul(z, &rSquare) // z.toMont()
+	{{- if .F31}}
+		*z = {{.ElementName}}{ uint32(v % uint64(q0)) }
+		return z.toMont()
+	{{- else }}
+		*z = {{.ElementName}}{ v }
+		return z.Mul(z, &rSquare) // z.toMont()
+	{{- end}}
 }
 
 // SetInt64 sets z to v and returns z
@@ -210,7 +221,7 @@ func (z *{{.ElementName}}) Equal(x *{{.ElementName}}) bool {
 }
 
 // NotEqual returns 0 if and only if z == x; constant-time
-func (z *{{.ElementName}}) NotEqual(x *{{.ElementName}}) uint64 {
+func (z *{{.ElementName}}) NotEqual(x *{{.ElementName}}) {{.Word.TypeLower}} {
 return {{- range $i :=  reverse .NbWordsIndexesNoZero}}(z[{{$i}}] ^ x[{{$i}}]) | {{end}}(z[0] ^ x[0])
 }
 
@@ -241,7 +252,11 @@ func (z *{{.ElementName}}) IsUint64() bool {
 
 // Uint64 returns the uint64 representation of x. If x cannot be represented in a uint64, the result is undefined.
 func (z *{{.ElementName}}) Uint64() uint64 {
-	return z.Bits()[0]
+	{{- if eq .Word.BitSize 32}}
+		return uint64(z.Bits()[0])
+	{{- else}}
+		return z.Bits()[0]
+	{{- end}}
 }
 
 // FitsOnOneWord reports whether z words (except the least significant word) are 0
@@ -283,10 +298,10 @@ func (z *{{.ElementName}}) LexicographicallyLargest() bool {
 
 	_z := z.Bits()
 
-	var b uint64
-	_, b = bits.Sub64(_z[0], {{index .QMinusOneHalvedP 0}}, 0)
+	var b {{$.Word.TypeLower}}
+	_, b = bits.{{$.Word.Sub}}(_z[0], {{index .QMinusOneHalvedP 0}}, 0)
 	{{- range $i := .NbWordsIndexesNoZero}}
-		_, b = bits.Sub64(_z[{{$i}}], {{index $.QMinusOneHalvedP $i}}, b)
+		_, b = bits.{{$.Word.Sub}}(_z[{{$i}}], {{index $.QMinusOneHalvedP $i}}, b)
 	{{- end}}
 
 	return b == 0
@@ -329,7 +344,7 @@ func (z *{{.ElementName}}) SetRandom() (*{{.ElementName}}, error) {
 
 		{{- range $i :=  .NbWordsIndexesFull}}
 			{{- $k := add $i 1}}
-			z[{{$i}}] = binary.LittleEndian.Uint64(bytes[{{mul $i 8}}:{{mul $k 8}}])
+			z[{{$i}}] = binary.LittleEndian.{{$.Word.TypeUpper}}(bytes[{{mul $i $.Word.ByteSize}}:{{mul $k $.Word.ByteSize}}])
 		{{- end}}
 
 		if !z.smallerThanModulus() {
@@ -383,7 +398,7 @@ func (z *{{.ElementName}}) Halve()  {
 	{{- range $i := $.all.NbWordsIndexesFull }}
 		{{- $carryIn := ne $i 0}}
 		{{- $carryOut := or (ne $i $.all.NbWordsLastIndex) (and (eq $i $.all.NbWordsLastIndex) (not $.all.NoCarry))}}
-		{{$.V1}}[{{$i}}], {{- if $carryOut}}carry{{- else}}_{{- end}} = bits.Add64({{$.V1}}[{{$i}}], q{{$i}}, {{- if $carryIn}}carry{{- else}}0{{- end}})
+		{{$.V1}}[{{$i}}], {{- if $carryOut}}carry{{- else}}_{{- end}} = bits.{{$.all.Word.Add}}({{$.V1}}[{{$i}}], q{{$i}}, {{- if $carryIn}}carry{{- else}}0{{- end}})
 	{{- end}}
 {{ end }}
 
@@ -398,20 +413,31 @@ func (z *{{.ElementName}}) fromMont() *{{.ElementName}} {
 
 // Add z = x + y (mod q)
 func (z *{{.ElementName}}) Add( x, y *{{.ElementName}}) *{{.ElementName}} {
-	{{ $hasCarry := or (not $.NoCarry) (gt $.NbWords 1)}}
-	{{- if $hasCarry}}
+	{{- if eq .NbWords 1}}
+		{{ $hasCarry := (not $.NoCarry)}}
+		{{- if $hasCarry}}
+			var carry uint64
+			z[0], carry = bits.Add64(x[0], y[0], 0)
+			if carry != 0 || z[0] >= q {
+				z[0] -= q
+			}
+			return z
+		{{- else}}
+			t := x[0] + y[0]
+			if t >= q {
+				t -= q
+			}
+			z[0] = t
+			return z
+		{{- end}}
+	{{- else}}
+	
 		var carry uint64
-	{{- end}}
-	{{- range $i := iterate 0 $.NbWords}}
-		{{- $hasCarry := or (not $.NoCarry) (lt $i $.NbWordsLastIndex)}}
-		z[{{$i}}], {{- if $hasCarry}}carry{{- else}}_{{- end}} = bits.Add64(x[{{$i}}], y[{{$i}}], {{- if eq $i 0}}0{{- else}}carry{{- end}})
-	{{- end}}
+		{{- range $i := iterate 0 $.NbWords}}
+			{{- $hasCarry := or (not $.NoCarry) (lt $i $.NbWordsLastIndex)}}
+			z[{{$i}}], {{- if $hasCarry}}carry{{- else}}_{{- end}} = bits.Add64(x[{{$i}}], y[{{$i}}], {{- if eq $i 0}}0{{- else}}carry{{- end}})
+		{{- end}}
 
-	{{- if eq $.NbWords 1}}
-		if {{- if not .NoCarry}} carry != 0 ||{{- end }} z[0] >= q {
-			z[0] -= q
-		}
-	{{- else}}
 		{{- if not .NoCarry}}
 			// if we overflowed the last addition, z >= q
 			// if z >= q, z = z - q
@@ -425,10 +451,9 @@ func (z *{{.ElementName}}) Add( x, y *{{.ElementName}}) *{{.ElementName}} {
 				return z
 			}
 		{{- end}}
-
 		{{ template "reduce" .}}
+		 return z
 	{{- end}}
-	return z
 }
 
 
@@ -436,16 +461,26 @@ func (z *{{.ElementName}}) Add( x, y *{{.ElementName}}) *{{.ElementName}} {
 // Double z = x + x (mod q), aka Lsh 1
 func (z *{{.ElementName}}) Double( x *{{.ElementName}}) *{{.ElementName}} {
 	{{- if eq .NbWords 1}}
-	if x[0] & (1 << 63) == (1 << 63) {
-		// if highest bit is set, then we have a carry to x + x, we shift and subtract q
-		z[0] = (x[0] << 1) - q
-	} else {
-		// highest bit is not set, but x + x can still be >= q
-		z[0] = (x[0] << 1)
-		if z[0] >= q {
-			z[0] -= q
-		}
-	}
+		{{- if .F31}}
+			t := x[0] << 1
+			if t >= q {
+					t -= q
+			}
+			z[0] = t
+			return z
+		{{- else}}
+			if x[0]&(1<<63) == (1 << 63) {
+				// if highest bit is set, then we have a carry to x + x, we shift and subtract q
+				z[0] = (x[0] << 1) - q
+			} else {
+				// highest bit is not set, but x + x can still be >= q
+				z[0] = (x[0] << 1)
+				if z[0] >= q {
+						z[0] -= q
+				}
+			}
+			return z
+		{{- end}}
 	{{- else}}
 	{{ $hasCarry := or (not $.NoCarry) (gt $.NbWords 1)}}
 	{{- if $hasCarry}}
@@ -470,35 +505,44 @@ func (z *{{.ElementName}}) Double( x *{{.ElementName}}) *{{.ElementName}} {
 	{{- end}}
 
 	{{ template "reduce" .}}
-	{{- end}}
 	return z
+	{{- end}}
 }
 
 
 
 // Sub z = x - y (mod q)
 func (z *{{.ElementName}}) Sub( x, y *{{.ElementName}}) *{{.ElementName}} {
-	var b uint64
-	z[0], b = bits.Sub64(x[0], y[0], 0)
-	{{- range $i := .NbWordsIndexesNoZero}}
-		z[{{$i}}], b = bits.Sub64(x[{{$i}}], y[{{$i}}], b)
-	{{- end}}
-	if b != 0 {
-		{{- if eq .NbWords 1}}
-			z[0] += q
-		{{- else}}
-			var c uint64
-			z[0], c = bits.Add64(z[0], q0, 0)
-			{{- range $i := .NbWordsIndexesNoZero}}
-				{{- if eq $i $.NbWordsLastIndex}}
-					z[{{$i}}], _ = bits.Add64(z[{{$i}}], q{{$i}}, c)
-				{{- else}}
-					z[{{$i}}], c = bits.Add64(z[{{$i}}], q{{$i}}, c)
+	{{- if $.F31}}
+		t, b := bits.Sub32(x[0], y[0], 0)
+		if b != 0 {
+			t += q
+		}
+		z[0] = t
+		return z
+	{{- else}}
+		var b uint64
+		z[0], b = bits.Sub64(x[0], y[0], 0)
+		{{- range $i := .NbWordsIndexesNoZero}}
+			z[{{$i}}], b = bits.Sub64(x[{{$i}}], y[{{$i}}], b)
+		{{- end}}
+		if b != 0 {
+			{{- if eq .NbWords 1}}
+				z[0] += q
+			{{- else}}
+				var c uint64
+				z[0], c = bits.Add64(z[0], q0, 0)
+				{{- range $i := .NbWordsIndexesNoZero}}
+					{{- if eq $i $.NbWordsLastIndex}}
+						z[{{$i}}], _ = bits.Add64(z[{{$i}}], q{{$i}}, c)
+					{{- else}}
+						z[{{$i}}], c = bits.Add64(z[{{$i}}], q{{$i}}, c)
+					{{- end}}
 				{{- end}}
 			{{- end}}
-		{{- end}}
-	}
-	return z
+		}
+		return z
+	{{- end}}
 }
 
 
@@ -528,13 +572,14 @@ func (z *{{.ElementName}}) Neg( x *{{.ElementName}}) *{{.ElementName}} {
 // Select is a constant-time conditional move.
 // If c=0, z = x0. Else z = x1
 func (z *{{.ElementName}}) Select(c int, x0 *{{.ElementName}}, x1 *{{.ElementName}}) *{{.ElementName}} {
-	cC := uint64( (int64(c) | -int64(c)) >> 63 )	// "canonicized" into: 0 if c=0, -1 otherwise
+	cC := {{$.Word.TypeLower}}( (int64(c) | -int64(c)) >> 63 )	// "canonicized" into: 0 if c=0, -1 otherwise
 	{{- range $i := .NbWordsIndexesFull }}
 	z[{{$i}}] = x0[{{$i}}] ^ cC & (x0[{{$i}}] ^ x1[{{$i}}])
 	{{- end}}
 	return z
 }
 
+{{- if ne .NbWords 1}}
 // _mulGeneric is unoptimized textbook CIOS
 // it is a fallback solution on x86 when ADX instruction set is not available
 // and is used for testing purposes.
@@ -543,25 +588,30 @@ func _mulGeneric(z,x,y *{{.ElementName}}) {
 	{{ template "mul_cios" dict "all" . "V1" "x" "V2" "y"}}
 	{{ template "reduce"  . }}
 }
+{{- end}}
 
 
 func _fromMontGeneric(z *{{.ElementName}}) {
-	// the following lines implement z = z * 1
-	// with a modified CIOS montgomery multiplication
-	// see Mul for algorithm documentation
-	{{- range $j := .NbWordsIndexesFull}}
-	{
-		// m = z[0]n'[0] mod W
-		m := z[0] * qInvNeg
-		C := madd0(m, q0, z[0])
-		{{- range $i := $.NbWordsIndexesNoZero}}
-			C, z[{{sub $i 1}}] = madd2(m, q{{$i}}, z[{{$i}}], C)
+	{{- if .F31}}
+		z[0] = montReduce(uint64(z[0]))
+	{{- else}}
+		// the following lines implement z = z * 1
+		// with a modified CIOS montgomery multiplication
+		// see Mul for algorithm documentation
+		{{- range $j := .NbWordsIndexesFull}}
+		{
+			// m = z[0]n'[0] mod W
+			m := z[0] * qInvNeg
+			C := madd0(m, q0, z[0])
+			{{- range $i := $.NbWordsIndexesNoZero}}
+				C, z[{{sub $i 1}}] = madd2(m, q{{$i}}, z[{{$i}}], C)
+			{{- end}}
+			z[{{sub $.NbWords 1}}] = C
+		}
 		{{- end}}
-		z[{{sub $.NbWords 1}}] = C
-	}
-	{{- end}}
 
-	{{ template "reduce" .}}
+		{{ template "reduce" .}}
+	{{- end}}
 }
 
 func _reduceGeneric(z *{{.ElementName}})  {
@@ -612,10 +662,10 @@ func _butterflyGeneric(a, b *{{.ElementName}}) {
 func (z *{{.ElementName}}) BitLen() int {
 	{{- range $i := reverse .NbWordsIndexesNoZero}}
 	if z[{{$i}}] != 0 {
-		return {{mul $i 64}} + bits.Len64(z[{{$i}}])
+		return {{mul $i 64}} + bits.{{$.Word.Len}}(z[{{$i}}])
 	}
 	{{- end}}
-	return bits.Len64(z[0])
+	return bits.{{$.Word.Len}}(z[0])
 }
 
 // Hash msg to count prime field elements.
diff --git a/field/generator/internal/templates/element/conv.go b/field/generator/internal/templates/element/conv.go
index 9c40ffec79..1587bdb7fb 100644
--- a/field/generator/internal/templates/element/conv.go
+++ b/field/generator/internal/templates/element/conv.go
@@ -13,7 +13,13 @@ var rSquare = {{.ElementName}}{
 // toMont converts z to Montgomery form
 // sets and returns z = z * r²
 func (z *{{.ElementName}}) toMont() *{{.ElementName}} {
-	return z.Mul(z, &rSquare)
+	{{- if .F31}}
+		const rBits = 32
+		z[0] = uint32((uint64(z[0]) << rBits) % q)
+		return z
+	{{- else}}
+		return z.Mul(z, &rSquare)
+	{{- end}}
 }
 
 // String returns the decimal representation of z as generated by
@@ -26,11 +32,11 @@ func (z *{{.ElementName}}) String() string {
 func (z *{{.ElementName}}) toBigInt(res *big.Int) *big.Int {
        var b [Bytes]byte
        {{- range $i := reverse .NbWordsIndexesFull}}
-               {{- $j := mul $i 8}}
+               {{- $j := mul $i $.Word.ByteSize}}
                {{- $k := sub $.NbWords 1}}
                {{- $k := sub $k $i}}
-               {{- $jj := add $j 8}}
-               binary.BigEndian.PutUint64(b[{{$j}}:{{$jj}}], z[{{$k}}])
+               {{- $jj := add $j $.Word.ByteSize}}
+               binary.BigEndian.Put{{$.Word.TypeUpper}}(b[{{$j}}:{{$jj}}], z[{{$k}}])
        {{- end}}
 
        return res.SetBytes(b[:])
@@ -61,12 +67,12 @@ func (z *{{.ElementName}}) Text(base int) string {
 			zzNeg.Neg(z)
 			zzNeg.fromMont()
 			if zzNeg[0] <= maxUint16 && zzNeg[0] != 0 {
-				return "-" + strconv.FormatUint(zzNeg[0], base)
+				return "-" + strconv.FormatUint(uint64(zzNeg[0]), base)
 			}
 		}
 		{{- end}}
 		zz := z.Bits()
-		return strconv.FormatUint(zz[0], base)
+		return strconv.FormatUint(uint64(zz[0]), base)
 	{{- else }}
 		if base == 10 {
 			var zzNeg {{.ElementName}}
@@ -103,10 +109,10 @@ func (z {{.ElementName}}) ToBigIntRegular(res *big.Int) *big.Int {
 	return z.toBigInt(res)
 }
 
-// Bits provides access to z by returning its value as a little-endian [{{.NbWords}}]uint64 array. 
+// Bits provides access to z by returning its value as a little-endian [{{.NbWords}}]{{.Word.TypeLower}} array. 
 // Bits is intended to support implementation of missing low-level {{.ElementName}}
 // functionality outside this package; it should be avoided otherwise.
-func (z *{{.ElementName}}) Bits() [{{.NbWords}}]uint64 {
+func (z *{{.ElementName}}) Bits() [{{.NbWords}}]{{.Word.TypeLower}} {
 	_z := *z
 	fromMont(&_z)
 	return _z
@@ -205,19 +211,27 @@ func (z *{{.ElementName}}) SetBigInt(v *big.Int) *{{.ElementName}} {
 func (z *{{.ElementName}}) setBigInt(v *big.Int) *{{.ElementName}} {
 	vBits := v.Bits()
 
-	if bits.UintSize == 64 {
+	{{- if .F31}}
+		// we assume v < q, so even if big.Int words are on 64bits, we can safely cast them to 32bits
 		for i := 0; i < len(vBits); i++ {
-			z[i] = uint64(vBits[i])
+			z[i] = uint32(vBits[i])
 		}
-	} else {
-		for i := 0; i < len(vBits); i++ {
-			if i%2 == 0 {
-				z[i/2] = uint64(vBits[i])
-			} else {
-				z[i/2] |= uint64(vBits[i]) << 32
+	{{- else}}
+	
+		if bits.UintSize == 64 {
+			for i := 0; i < len(vBits); i++ {
+				z[i] = uint64(vBits[i])
+			}
+		} else {
+			for i := 0; i < len(vBits); i++ {
+				if i%2 == 0 {
+					z[i/2] = uint64(vBits[i])
+				} else {
+					z[i/2] |= uint64(vBits[i]) << 32
+				}
 			}
 		}
-	}
+	{{- end}}
 
 	return z.toMont()
 }
@@ -323,11 +337,11 @@ type bigEndian struct{}
 func (bigEndian) Element(b *[Bytes]byte) ({{.ElementName}}, error) {
 	var z {{.ElementName}}
 	{{- range $i := reverse .NbWordsIndexesFull}}
-		{{- $j := mul $i 8}}
+		{{- $j := mul $i $.Word.ByteSize}}
 		{{- $k := sub $.NbWords 1}}
 		{{- $k := sub $k $i}}
-		{{- $jj := add $j 8}}
-		z[{{$k}}] = binary.BigEndian.Uint64((*b)[{{$j}}:{{$jj}}])
+		{{- $jj := add $j $.Word.ByteSize}}
+		z[{{$k}}] = binary.BigEndian.{{$.Word.TypeUpper}}((*b)[{{$j}}:{{$jj}}])
 	{{- end}}
 
 	if !z.smallerThanModulus() {
@@ -342,11 +356,11 @@ func (bigEndian) PutElement(b *[Bytes]byte, e {{.ElementName}})  {
 	e.fromMont()
 
 	{{- range $i := reverse .NbWordsIndexesFull}}
-		{{- $j := mul $i 8}}
+		{{- $j := mul $i $.Word.ByteSize}}
 		{{- $k := sub $.NbWords 1}}
 		{{- $k := sub $k $i}}
-		{{- $jj := add $j 8}}
-		binary.BigEndian.PutUint64((*b)[{{$j}}:{{$jj}}], e[{{$k}}])
+		{{- $jj := add $j $.Word.ByteSize}}
+		binary.BigEndian.Put{{$.Word.TypeUpper}}((*b)[{{$j}}:{{$jj}}], e[{{$k}}])
 	{{- end}}
 }
 
@@ -362,9 +376,9 @@ type littleEndian struct{}
 func (littleEndian) Element(b *[Bytes]byte) ({{.ElementName}}, error) {
 	var z {{.ElementName}}
 	{{- range $i := .NbWordsIndexesFull}}
-		{{- $j := mul $i 8}}
-		{{- $jj := add $j 8}}
-		z[{{$i}}] = binary.LittleEndian.Uint64((*b)[{{$j}}:{{$jj}}])
+		{{- $j := mul $i $.Word.ByteSize}}
+		{{- $jj := add $j $.Word.ByteSize}}
+		z[{{$i}}] = binary.LittleEndian.{{$.Word.TypeUpper}}((*b)[{{$j}}:{{$jj}}])
 	{{- end}}
 
 	if !z.smallerThanModulus() {
@@ -379,9 +393,9 @@ func (littleEndian) PutElement(b *[Bytes]byte, e {{.ElementName}})  {
 	e.fromMont()
 
 	{{- range $i := .NbWordsIndexesFull}}
-		{{- $j := mul $i 8}}
-		{{- $jj := add $j 8}}
-		binary.LittleEndian.PutUint64((*b)[{{$j}}:{{$jj}}], e[{{$i}}])
+		{{- $j := mul $i $.Word.ByteSize}}
+		{{- $jj := add $j $.Word.ByteSize}}
+		binary.LittleEndian.Put{{$.Word.TypeUpper}}((*b)[{{$j}}:{{$jj}}], e[{{$i}}])
 	{{- end}}
 }
 
diff --git a/field/generator/internal/templates/element/inverse.go b/field/generator/internal/templates/element/inverse.go
index 6adaedc557..317f044b0b 100644
--- a/field/generator/internal/templates/element/inverse.go
+++ b/field/generator/internal/templates/element/inverse.go
@@ -26,19 +26,21 @@ if b != 0 {
 // if x == 0, sets and returns z = x 
 func (z *{{.ElementName}}) Inverse( x *{{.ElementName}}) *{{.ElementName}} {
 	// Algorithm 16 in "Efficient Software-Implementation of Finite Fields with Applications to Cryptography"
-	const q uint64 = q0
+	const q {{.Word.TypeLower}} = q0
 	if x.IsZero() {
 		z.SetZero()
 		return z
 	}
 
-	var r,s,u,v uint64
+	var r,s,u,v {{.Word.TypeLower}}
 	u = q
 	s = {{index .RSquare 0}} // s = r²
 	r = 0
 	v = x[0]
 
-	var carry, borrow uint64
+	var carry, borrow {{.Word.TypeLower}}
+
+	{{- $bitSizeMinus1 := sub .Word.BitSize 1}}
 
 	for  (u != 1) && (v != 1){
 		for v&1 == 0 {
@@ -46,10 +48,10 @@ func (z *{{.ElementName}}) Inverse( x *{{.ElementName}}) *{{.ElementName}} {
 			if s&1 == 0 {
 				s >>= 1
 			} else {
-				s, carry = bits.Add64(s, q, 0)
+				s, carry = bits.{{.Word.Add}}(s, q, 0)
 				s >>= 1
 				if carry != 0 {
-					s |= (1 << 63)
+					s |= (1 << {{$bitSizeMinus1}})
 				}
 			}
 		} 
@@ -58,22 +60,22 @@ func (z *{{.ElementName}}) Inverse( x *{{.ElementName}}) *{{.ElementName}} {
 			if r&1 == 0 {
 				r >>= 1
 			} else {
-				r, carry = bits.Add64(r, q, 0)
+				r, carry = bits.{{.Word.Add}}(r, q, 0)
 				r >>= 1
 				if carry != 0 {
-					r |= (1 << 63)
+					r |= (1 << {{$bitSizeMinus1}})
 				}
 			}
 		} 
 		if v >= u  {
 			v -= u
-			s, borrow = bits.Sub64(s, r, 0)
+			s, borrow = bits.{{.Word.Sub}}(s, r, 0)
 			if borrow == 1 {
 				s += q
 			}
 		} else {
 			u -= v
-			r, borrow = bits.Sub64(r, s, 0)
+			r, borrow = bits.{{.Word.Sub}}(r, s, 0)
 			if borrow == 1 {
 				r += q
 			}
diff --git a/field/generator/internal/templates/element/mul_cios.go b/field/generator/internal/templates/element/mul_cios.go
index 6fb554c3bd..e68992da0f 100644
--- a/field/generator/internal/templates/element/mul_cios.go
+++ b/field/generator/internal/templates/element/mul_cios.go
@@ -110,7 +110,6 @@ const MulCIOS = `
 	// Which finally gives (lo + m * q) / R = (lo + lo2 + R hi2) / R = hi2 + (lo+lo2) / R = hi2 + (lo != 0)
 	// This "optimization" lets us do away with one MUL instruction on ARM architectures and is available for all q < R.
 
-	var r uint64
 	hi, lo := bits.Mul64({{$.V1}}[0], {{$.V2}}[0])
 	if lo != 0 {
 		hi++ // x[0] * y[0] ≤ 2¹²⁸ - 2⁶⁵ + 1, meaning hi ≤ 2⁶⁴ - 2 so no need to worry about overflow
@@ -118,12 +117,11 @@ const MulCIOS = `
 	m := lo * qInvNeg
 	hi2, _ := bits.Mul64(m, q)
 	r, carry := bits.Add64(hi2, hi, 0)
-
 	if carry != 0 || r >= q  {
 		// we need to reduce
-		r -= q 
+		r -= q
 	}
-	z[0] = r 
+	z[0] = r
 {{ end }}
 `
 
diff --git a/field/generator/internal/templates/element/ops_purego.go b/field/generator/internal/templates/element/ops_purego.go
index 498b7e1ae6..53f257a089 100644
--- a/field/generator/internal/templates/element/ops_purego.go
+++ b/field/generator/internal/templates/element/ops_purego.go
@@ -2,7 +2,9 @@ package element
 
 const OpsNoAsm = `
 
+{{- if not .F31}}
 import "math/bits"
+{{- end}}
 
 {{ $mulConsts := list 3 5 13 }}
 {{- range $i := $mulConsts }}
@@ -42,6 +44,17 @@ func reduce(z *{{.ElementName}})  {
 	_reduceGeneric(z)
 }
 
+{{- if $.F31}}
+func montReduce(v uint64) uint32 {
+	m := uint32(v) * qInvNeg
+	t := uint32((v + uint64(m) * q) >> 32)
+	if t >= q {
+		t -= q
+	}
+	return t
+}
+{{- end}}
+
 // Mul z = x * y (mod q)
 {{- if $.NoCarry}}
 //
@@ -49,7 +62,12 @@ func reduce(z *{{.ElementName}})  {
 {{- end }}
 func (z *{{.ElementName}}) Mul(x, y *{{.ElementName}}) *{{.ElementName}} {
 	{{- if eq $.NbWords 1}}
-		{{ template "mul_cios_one_limb" dict "all" . "V1" "x" "V2" "y" }}
+		{{- if $.F31}}
+			v := uint64(x[0]) * uint64(y[0])
+			z[0] = montReduce(v)
+		{{- else}}
+			{{ template "mul_cios_one_limb" dict "all" . "V1" "x" "V2" "y" }}
+		{{- end}}
 	{{- else }}
 		{{ mul_doc $.NoCarry }}
 		{{- if $.NoCarry}}
@@ -70,7 +88,12 @@ func (z *{{.ElementName}}) Mul(x, y *{{.ElementName}}) *{{.ElementName}} {
 func (z *{{.ElementName}}) Square(x *{{.ElementName}}) *{{.ElementName}} {
 	// see Mul for algorithm documentation
 	{{- if eq $.NbWords 1}}
-		{{ template "mul_cios_one_limb" dict "all" . "V1" "x" "V2" "x" }}
+		{{- if $.F31}}
+			v := uint64(x[0]) * uint64(x[0])
+			z[0] = montReduce(v)
+		{{- else}}
+			{{ template "mul_cios_one_limb" dict "all" . "V1" "x" "V2" "x" }}
+		{{- end}}
 	{{- else }}
 		{{- if $.NoCarry}}
 			{{ template "mul_nocarry" dict "all" . "V1" "x" "V2" "x"}}
diff --git a/field/generator/internal/templates/element/tests.go b/field/generator/internal/templates/element/tests.go
index 35d777e493..bdcc83956c 100644
--- a/field/generator/internal/templates/element/tests.go
+++ b/field/generator/internal/templates/element/tests.go
@@ -730,7 +730,11 @@ func Test{{toTitle .ElementName}}LexicographicallyLargest(t *testing.T) {
 
 {{template "testBinaryOp" dict "all" . "Op" "Add"}}
 {{template "testBinaryOp" dict "all" . "Op" "Sub"}}
+{{- if ne .NbWords 1}}
 {{template "testBinaryOp" dict "all" . "Op" "Mul" "GenericOp" "_mulGeneric"}}
+{{- else}}
+{{template "testBinaryOp" dict "all" . "Op" "Mul"}}
+{{- end}}
 {{template "testBinaryOp" dict "all" . "Op" "Div"}}
 {{template "testBinaryOp" dict "all" . "Op" "Exp"}}
 
@@ -1569,6 +1573,10 @@ type testPair{{.ElementName}} struct {
 	bigint       big.Int
 }
 
+{{- $gen64 := "genParams.NextUint64()"}}
+{{- if eq .Word.BitSize 32}}
+{{- $gen64 = "uint32(genParams.NextUint64())"}}
+{{- end}}
 
 func gen() gopter.Gen {
 	return func(genParams *gopter.GenParameters) *gopter.GenResult {
@@ -1576,9 +1584,9 @@ func gen() gopter.Gen {
 
 		g.element = {{.ElementName}}{
 			{{- range $i := .NbWordsIndexesFull}}
-			genParams.NextUint64(),{{end}}
+			{{$gen64}},{{end}}
 		}
-		if qElement[{{.NbWordsLastIndex}}] != ^uint64(0) {
+		if qElement[{{.NbWordsLastIndex}}] != ^{{$.Word.TypeLower}}(0) {
 			g.element[{{.NbWordsLastIndex}}] %= (qElement[{{.NbWordsLastIndex}}] +1 )
 		}
 		
@@ -1586,9 +1594,9 @@ func gen() gopter.Gen {
 		for !g.element.smallerThanModulus() {
 			g.element = {{.ElementName}}{
 				{{- range $i := .NbWordsIndexesFull}}
-				genParams.NextUint64(),{{end}}
+				{{$gen64}},{{end}}
 			}
-			if qElement[{{.NbWordsLastIndex}}] != ^uint64(0) {
+			if qElement[{{.NbWordsLastIndex}}] != ^{{$.Word.TypeLower}}(0) {
 				g.element[{{.NbWordsLastIndex}}] %= (qElement[{{.NbWordsLastIndex}}] +1 )
 			}
 		}
@@ -1604,19 +1612,19 @@ func genRandomFq(genParams *gopter.GenParameters) {{.ElementName}} {
 
 	g = {{.ElementName}}{
 		{{- range $i := .NbWordsIndexesFull}}
-		genParams.NextUint64(),{{end}}
+		{{$gen64}},{{end}}
 	}
 
-	if qElement[{{.NbWordsLastIndex}}] != ^uint64(0) {
+	if qElement[{{.NbWordsLastIndex}}] != ^{{$.Word.TypeLower}}(0) {
 		g[{{.NbWordsLastIndex}}] %= (qElement[{{.NbWordsLastIndex}}] +1 )
 	}
 
 	for !g.smallerThanModulus() {
 		g = {{.ElementName}}{
 			{{- range $i := .NbWordsIndexesFull}}
-			genParams.NextUint64(),{{end}}
+			{{$gen64}},{{end}}
 		}
-		if qElement[{{.NbWordsLastIndex}}] != ^uint64(0) {
+		if qElement[{{.NbWordsLastIndex}}] != ^{{$.Word.TypeLower}}(0) {
 			g[{{.NbWordsLastIndex}}] %= (qElement[{{.NbWordsLastIndex}}] +1 )
 		}
 	}
@@ -1629,12 +1637,12 @@ func genFull() gopter.Gen {
 	return func(genParams *gopter.GenParameters) *gopter.GenResult {
 		a := genRandomFq(genParams)
 
-		var carry uint64
+		var carry {{$.Word.TypeLower}}
 		{{- range $i := .NbWordsIndexesFull}}
 			{{- if eq $i $.NbWordsLastIndex}}
-			a[{{$i}}], _ = bits.Add64(a[{{$i}}], qElement[{{$i}}], carry)
+			a[{{$i}}], _ = bits.{{$.Word.Add}}(a[{{$i}}], qElement[{{$i}}], carry)
 			{{- else}}
-			a[{{$i}}], carry = bits.Add64(a[{{$i}}], qElement[{{$i}}], carry)
+			a[{{$i}}], carry = bits.{{$.Word.Add}}(a[{{$i}}], qElement[{{$i}}], carry)
 			{{- end}}
 		{{- end}}
 		
diff --git a/field/generator/internal/templates/element/tests_vector.go b/field/generator/internal/templates/element/tests_vector.go
index 41187a2caa..3da4c94080 100644
--- a/field/generator/internal/templates/element/tests_vector.go
+++ b/field/generator/internal/templates/element/tests_vector.go
@@ -325,14 +325,19 @@ func genMaxVector(size int) gopter.Gen {
 	}
 }
 
+{{- $gen64 := "genParams.NextUint64()"}}
+{{- if eq .Word.BitSize 32}}
+{{- $gen64 = "uint32(genParams.NextUint64())"}}
+{{- end}}
+
 func genVector(size int) gopter.Gen {
 	return func(genParams *gopter.GenParameters) *gopter.GenResult {
 		g := make(Vector, size)
 		mixer := {{.ElementName}}{
 			{{- range $i := .NbWordsIndexesFull}}
-			genParams.NextUint64(),{{end}}
+			{{$gen64}},{{end}}
 		}
-		if qElement[{{.NbWordsLastIndex}}] != ^uint64(0) {
+		if qElement[{{.NbWordsLastIndex}}] != ^{{$.Word.TypeLower}}(0) {
 			mixer[{{.NbWordsLastIndex}}] %= (qElement[{{.NbWordsLastIndex}}] +1 )
 		}
 		
@@ -340,9 +345,9 @@ func genVector(size int) gopter.Gen {
 		for !mixer.smallerThanModulus() {
 			mixer = {{.ElementName}}{
 				{{- range $i := .NbWordsIndexesFull}}
-				genParams.NextUint64(),{{end}}
+				{{$gen64}},{{end}}
 			}
-			if qElement[{{.NbWordsLastIndex}}] != ^uint64(0) {
+			if qElement[{{.NbWordsLastIndex}}] != ^{{$.Word.TypeLower}}(0) {
 				mixer[{{.NbWordsLastIndex}}] %= (qElement[{{.NbWordsLastIndex}}] +1 )
 			}
 		}
diff --git a/field/generator/internal/templates/element/vector.go b/field/generator/internal/templates/element/vector.go
index 447b429556..f3120eb73a 100644
--- a/field/generator/internal/templates/element/vector.go
+++ b/field/generator/internal/templates/element/vector.go
@@ -107,11 +107,11 @@ func (vector *Vector) AsyncReadFrom(r io.Reader) (int64, error, chan error) {
 				bend := bstart + Bytes
 				b := bSlice[bstart:bend]
 				{{- range $i := reverse .NbWordsIndexesFull}}
-					{{- $j := mul $i 8}}
+					{{- $j := mul $i $.Word.ByteSize}}
 					{{- $k := sub $.NbWords 1}}
 					{{- $k := sub $k $i}}
-					{{- $jj := add $j 8}}
-					z[{{$k}}] = binary.BigEndian.Uint64(b[{{$j}}:{{$jj}}])
+					{{- $jj := add $j $.Word.ByteSize}}
+					z[{{$k}}] = binary.BigEndian.{{$.Word.TypeUpper}}(b[{{$j}}:{{$jj}}])
 				{{- end}}
 
 				if !z.smallerThanModulus() {
diff --git a/field/goldilocks/element.go b/field/goldilocks/element.go
index 8dd4d69919..207ee7fbb5 100644
--- a/field/goldilocks/element.go
+++ b/field/goldilocks/element.go
@@ -54,8 +54,8 @@ const (
 
 // Field modulus q
 const (
-	q0 uint64 = 18446744069414584321
-	q  uint64 = q0
+	q0 = 18446744069414584321
+	q  = q0
 )
 
 var qElement = Element{
@@ -74,7 +74,7 @@ func Modulus() *big.Int {
 
 // q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
 // used for Montgomery reduction
-const qInvNeg uint64 = 18446744069414584319
+const qInvNeg = 18446744069414584319
 
 func init() {
 	_modulus.SetString("ffffffff00000001", 16)
@@ -407,49 +407,6 @@ func (z *Element) Select(c int, x0 *Element, x1 *Element) *Element {
 	return z
 }
 
-// _mulGeneric is unoptimized textbook CIOS
-// it is a fallback solution on x86 when ADX instruction set is not available
-// and is used for testing purposes.
-func _mulGeneric(z, x, y *Element) {
-
-	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
-	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
-
-	var t [2]uint64
-	var D uint64
-	var m, C uint64
-	// -----------------------------------
-	// First loop
-
-	C, t[0] = bits.Mul64(y[0], x[0])
-
-	t[1], D = bits.Add64(t[1], C, 0)
-
-	// m = t[0]n'[0] mod W
-	m = t[0] * qInvNeg
-
-	// -----------------------------------
-	// Second loop
-	C = madd0(m, q0, t[0])
-
-	t[0], C = bits.Add64(t[1], C, 0)
-	t[1], _ = bits.Add64(0, D, C)
-
-	if t[1] != 0 {
-		// we need to reduce, we have a result on 2 words
-		z[0], _ = bits.Sub64(t[0], q0, 0)
-		return
-	}
-
-	// copy t into z
-	z[0] = t[0]
-
-	// if z ⩾ q → z -= q
-	if !z.smallerThanModulus() {
-		z[0] -= q
-	}
-}
-
 func _fromMontGeneric(z *Element) {
 	// the following lines implement z = z * 1
 	// with a modified CIOS montgomery multiplication
@@ -627,11 +584,11 @@ func (z *Element) Text(base int) string {
 		zzNeg.Neg(z)
 		zzNeg.fromMont()
 		if zzNeg[0] <= maxUint16 && zzNeg[0] != 0 {
-			return "-" + strconv.FormatUint(zzNeg[0], base)
+			return "-" + strconv.FormatUint(uint64(zzNeg[0]), base)
 		}
 	}
 	zz := z.Bits()
-	return strconv.FormatUint(zz[0], base)
+	return strconv.FormatUint(uint64(zz[0]), base)
 }
 
 // BigInt sets and return z as a *big.Int
diff --git a/field/goldilocks/element_purego.go b/field/goldilocks/element_purego.go
index f1090ab75f..2dfbd7dbd3 100644
--- a/field/goldilocks/element_purego.go
+++ b/field/goldilocks/element_purego.go
@@ -62,7 +62,6 @@ func (z *Element) Mul(x, y *Element) *Element {
 	// Which finally gives (lo + m * q) / R = (lo + lo2 + R hi2) / R = hi2 + (lo+lo2) / R = hi2 + (lo != 0)
 	// This "optimization" lets us do away with one MUL instruction on ARM architectures and is available for all q < R.
 
-	var r uint64
 	hi, lo := bits.Mul64(x[0], y[0])
 	if lo != 0 {
 		hi++ // x[0] * y[0] ≤ 2¹²⁸ - 2⁶⁵ + 1, meaning hi ≤ 2⁶⁴ - 2 so no need to worry about overflow
@@ -70,7 +69,6 @@ func (z *Element) Mul(x, y *Element) *Element {
 	m := lo * qInvNeg
 	hi2, _ := bits.Mul64(m, q)
 	r, carry := bits.Add64(hi2, hi, 0)
-
 	if carry != 0 || r >= q {
 		// we need to reduce
 		r -= q
@@ -96,7 +94,6 @@ func (z *Element) Square(x *Element) *Element {
 	// Which finally gives (lo + m * q) / R = (lo + lo2 + R hi2) / R = hi2 + (lo+lo2) / R = hi2 + (lo != 0)
 	// This "optimization" lets us do away with one MUL instruction on ARM architectures and is available for all q < R.
 
-	var r uint64
 	hi, lo := bits.Mul64(x[0], x[0])
 	if lo != 0 {
 		hi++ // x[0] * y[0] ≤ 2¹²⁸ - 2⁶⁵ + 1, meaning hi ≤ 2⁶⁴ - 2 so no need to worry about overflow
@@ -104,7 +101,6 @@ func (z *Element) Square(x *Element) *Element {
 	m := lo * qInvNeg
 	hi2, _ := bits.Mul64(m, q)
 	r, carry := bits.Add64(hi2, hi, 0)
-
 	if carry != 0 || r >= q {
 		// we need to reduce
 		r -= q
diff --git a/field/goldilocks/element_test.go b/field/goldilocks/element_test.go
index 454d057dbf..52fa5e2691 100644
--- a/field/goldilocks/element_test.go
+++ b/field/goldilocks/element_test.go
@@ -932,14 +932,6 @@ func TestElementMul(t *testing.T) {
 				c.Mul(&a.element, &r)
 				d.Mul(&a.bigint, &rb).Mod(&d, Modulus())
 
-				// checking generic impl against asm path
-				var cGeneric Element
-				_mulGeneric(&cGeneric, &a.element, &r)
-				if !cGeneric.Equal(&c) {
-					// need to give context to failing error.
-					return false
-				}
-
 				if c.BigInt(&e).Cmp(&d) != 0 {
 					return false
 				}
@@ -962,17 +954,6 @@ func TestElementMul(t *testing.T) {
 		genB,
 	))
 
-	properties.Property("Mul: assembly implementation must be consistent with generic one", prop.ForAll(
-		func(a, b testPairElement) bool {
-			var c, d Element
-			c.Mul(&a.element, &b.element)
-			_mulGeneric(&d, &a.element, &b.element)
-			return c.Equal(&d)
-		},
-		genA,
-		genB,
-	))
-
 	specialValueTest := func() {
 		// test special values against special values
 		testValues := make([]Element, len(staticTestValues))
@@ -991,13 +972,6 @@ func TestElementMul(t *testing.T) {
 				c.Mul(&a, &b)
 				d.Mul(&aBig, &bBig).Mod(&d, Modulus())
 
-				// checking asm against generic impl
-				var cGeneric Element
-				_mulGeneric(&cGeneric, &a, &b)
-				if !cGeneric.Equal(&c) {
-					t.Fatal("Mul failed special test values: asm and generic impl don't match")
-				}
-
 				if c.BigInt(&e).Cmp(&d) != 0 {
 					t.Fatal("Mul failed special test values")
 				}
diff --git a/field/goldilocks/internal/main.go b/field/goldilocks/internal/main.go
deleted file mode 100644
index 04d5d75305..0000000000
--- a/field/goldilocks/internal/main.go
+++ /dev/null
@@ -1,21 +0,0 @@
-package main
-
-import (
-	"fmt"
-
-	"github.com/consensys/gnark-crypto/field/generator"
-	"github.com/consensys/gnark-crypto/field/generator/config"
-)
-
-//go:generate go run main.go
-func main() {
-	const modulus = "0xFFFFFFFF00000001"
-	goldilocks, err := config.NewFieldConfig("goldilocks", "Element", modulus, true)
-	if err != nil {
-		panic(err)
-	}
-	if err := generator.GenerateFF(goldilocks, "..", "", ""); err != nil {
-		panic(err)
-	}
-	fmt.Println("successfully generated goldilocks field")
-}
diff --git a/field/internal/addchain/3c000000 b/field/internal/addchain/3c000000
new file mode 100644
index 0000000000000000000000000000000000000000..7ff1a13c6446abe67f721ba6b266f802910a054a
GIT binary patch
literal 206
zcmWlP-3q|~07lOlAuUN-Ys8WyNs_dd7vP3haOFzm1^m2)r=9KQ^qsF06`w$x=jZ+U
zyxc6lSiE8Is%da~RALz%tfR-0Q2fejOb}qbx*ImC)xx%I3=Oek2fKE$XAk@KF*3r~
x7!wm5I>eD9Oigj(1gB1M<_zb~ap3}&E^*}w*RFBn2Dff;=MFP7%*}D{o<E566|w*T

literal 0
HcmV?d00001

diff --git a/field/internal/addchain/3f b/field/internal/addchain/3f
new file mode 100644
index 0000000000000000000000000000000000000000..db4d062eb3428f2f32be62bc818f17072bee7103
GIT binary patch
literal 90
zcmWlPISzmz00eiCAR)xk#@@eZqhGMHG8#VM@o|J^voo1KzXsYhoqO62@+a~m4R-@(
exhhbC2`iY(N@Iz<j1jh4hpW$vKoF5wvC|J=Fby35

literal 0
HcmV?d00001

diff --git a/field/internal/addchain/3f800000 b/field/internal/addchain/3f800000
new file mode 100644
index 0000000000000000000000000000000000000000..09a0ef7a2be12c8b8f7cdfd572c98919e496e838
GIT binary patch
literal 212
zcmWlP%?bfw003t`LfRy06Vj3-Nzx`sa^=D+I5~;DfS(ufsB2xOW|}yA2Q8l-x69*v
zHTz)pg3hy`;duXx`LMT$9&$qV&96QoU@;G&gcU1<Dn>?Fvxar+|J=Z)O^l7PWeeN3
zv1=E5_AoKQfdd>m#E~N$JI09<oI1ssGn_leg$qngap@9Qu5j%dH*Rq27I*IW0Vl^6
AqyPW_

literal 0
HcmV?d00001

diff --git a/field/internal/addchain/7 b/field/internal/addchain/7
new file mode 100644
index 0000000000000000000000000000000000000000..c1410c6d13353d0351fa753eb3fe120b9d7c4f57
GIT binary patch
literal 68
zcmWgp-^j$s$R1FXpI(%h%lN;Ef$@I>1A}xuGb1CDe*uWY2vp$7$il$L=mjJh7zBWd
QSQwa?7#LZAd?q#q072&rs{jB1

literal 0
HcmV?d00001

diff --git a/field/goldilocks/internal/addchain/7fffffff b/field/internal/addchain/7fffffff
similarity index 66%
rename from field/goldilocks/internal/addchain/7fffffff
rename to field/internal/addchain/7fffffff
index b281f667616cfe8d6232c88a89b25860bf2916a7..2702c2bd601e9bdec1d5ecace2b67f582b0c5adf 100644
GIT binary patch
delta 63
zcmaFK_=3?~?0+K@BO`l2QGR++VlLzVCI-g;4Gav@^~{WnO#THR4kJ*3CnF03Bcm6P
OWMKHe`G3<yi;VzHXc4yn

delta 64
zcmaFC_>$2=?0+*8BO`l2QGR++VlLzV76!)uO$-b&{~MVZ8JYYGKs-jE3QtBB21Z6N
PAj!b+fAjyAiRK#td)5-e

diff --git a/field/goldilocks/internal/addchain/7fffffff80000000 b/field/internal/addchain/7fffffff80000000
similarity index 79%
rename from field/goldilocks/internal/addchain/7fffffff80000000
rename to field/internal/addchain/7fffffff80000000
index c1d158b8e6f129a758c61a95ae1c26ed84b13c1e..3f6891cde4118c5c70424386a705be833d3be08c 100644
GIT binary patch
delta 65
zcmeBT?qs$Q``^gK$jBa0l%HOdn9KOTiGlHd0|SF}Ju@RClYaq-!w6L1$;iUM$mj(m
Q85sUC2LEr`Xc@=|06YW`U;qFB

delta 66
zcmeBV?qaqS``^sO$jBa0l%HOdn9KOTg@N&Z69a?H|3+p;MkfCP5RVb4!jqAOfsxS*
RNHQ?|V+{V^ve6=t5ddq@5o`be

diff --git a/field/internal/main.go b/field/internal/main.go
new file mode 100644
index 0000000000..b495d394e5
--- /dev/null
+++ b/field/internal/main.go
@@ -0,0 +1,36 @@
+package main
+
+import (
+	"fmt"
+	"path/filepath"
+
+	"github.com/consensys/gnark-crypto/field/generator"
+	"github.com/consensys/gnark-crypto/field/generator/config"
+)
+
+//go:generate go run main.go
+func main() {
+	// generate the following fields
+
+	type field struct {
+		name    string
+		modulus string
+	}
+
+	fields := []field{
+		{"goldilocks", "0xFFFFFFFF00000001"},
+		{"koalabear", "0x7f000001"}, // 2^31 - 2^24 + 1 ==> the cube map (x -> x^3) is an automorphism of the multiplicative group
+		{"babybear", "0x78000001"},  // 2^31 - 2^27 + 1 ==> 2-adicity 27
+	}
+
+	for _, f := range fields {
+		fc, err := config.NewFieldConfig(f.name, "Element", f.modulus, true)
+		if err != nil {
+			panic(err)
+		}
+		if err := generator.GenerateFF(fc, filepath.Join("..", f.name), "", ""); err != nil {
+			panic(err)
+		}
+		fmt.Println("successfully generated", f.name, "field")
+	}
+}
diff --git a/field/koalabear/arith.go b/field/koalabear/arith.go
new file mode 100644
index 0000000000..0252a5bd1e
--- /dev/null
+++ b/field/koalabear/arith.go
@@ -0,0 +1,60 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package koalabear
+
+import (
+	"math/bits"
+)
+
+// madd0 hi = a*b + c (discards lo bits)
+func madd0(a, b, c uint64) (hi uint64) {
+	var carry, lo uint64
+	hi, lo = bits.Mul64(a, b)
+	_, carry = bits.Add64(lo, c, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	return
+}
+
+// madd1 hi, lo = a*b + c
+func madd1(a, b, c uint64) (hi uint64, lo uint64) {
+	var carry uint64
+	hi, lo = bits.Mul64(a, b)
+	lo, carry = bits.Add64(lo, c, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	return
+}
+
+// madd2 hi, lo = a*b + c + d
+func madd2(a, b, c, d uint64) (hi uint64, lo uint64) {
+	var carry uint64
+	hi, lo = bits.Mul64(a, b)
+	c, carry = bits.Add64(c, d, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	lo, carry = bits.Add64(lo, c, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	return
+}
+
+func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) {
+	var carry uint64
+	hi, lo = bits.Mul64(a, b)
+	c, carry = bits.Add64(c, d, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	lo, carry = bits.Add64(lo, c, 0)
+	hi, _ = bits.Add64(hi, e, carry)
+	return
+}
diff --git a/field/koalabear/doc.go b/field/koalabear/doc.go
new file mode 100644
index 0000000000..6c49ce3be1
--- /dev/null
+++ b/field/koalabear/doc.go
@@ -0,0 +1,53 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// Package koalabear contains field arithmetic operations for modulus = 0x7f000001.
+//
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@gnark/modular_multiplication)
+//
+// The modulus is hardcoded in all the operations.
+//
+// Field elements are represented as an array, and assumed to be in Montgomery form in all methods:
+//
+//	type Element [1]uint64
+//
+// # Usage
+//
+// Example API signature:
+//
+//	// Mul z = x * y (mod q)
+//	func (z *Element) Mul(x, y *Element) *Element
+//
+// and can be used like so:
+//
+//	var a, b Element
+//	a.SetUint64(2)
+//	b.SetString("984896738")
+//	a.Mul(a, b)
+//	a.Sub(a, a)
+//	 .Add(a, b)
+//	 .Inv(a)
+//	b.Exp(b, new(big.Int).SetUint64(42))
+//
+// Modulus q =
+//
+//	q[base10] = 2130706433
+//	q[base16] = 0x7f000001
+//
+// # Warning
+//
+// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+package koalabear
diff --git a/field/koalabear/element.go b/field/koalabear/element.go
new file mode 100644
index 0000000000..280a57d50f
--- /dev/null
+++ b/field/koalabear/element.go
@@ -0,0 +1,980 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package koalabear
+
+import (
+	"crypto/rand"
+	"encoding/binary"
+	"errors"
+	"io"
+	"math/big"
+	"math/bits"
+	"reflect"
+	"strconv"
+	"strings"
+
+	"github.com/bits-and-blooms/bitset"
+	"github.com/consensys/gnark-crypto/field/hash"
+	"github.com/consensys/gnark-crypto/field/pool"
+)
+
+// Element represents a field element stored on 1 words (uint32)
+//
+// Element are assumed to be in Montgomery form in all methods.
+//
+// Modulus q =
+//
+//	q[base10] = 2130706433
+//	q[base16] = 0x7f000001
+//
+// # Warning
+//
+// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+type Element [1]uint32
+
+const (
+	Limbs = 1  // number of 32 bits words needed to represent a Element
+	Bits  = 31 // number of bits needed to represent a Element
+	Bytes = 4  // number of bytes needed to represent a Element
+)
+
+// Field modulus q
+const (
+	q0 = 2130706433
+	q  = q0
+)
+
+var qElement = Element{
+	q0,
+}
+
+var _modulus big.Int // q stored as big.Int
+
+// Modulus returns q as a big.Int
+//
+//	q[base10] = 2130706433
+//	q[base16] = 0x7f000001
+func Modulus() *big.Int {
+	return new(big.Int).Set(&_modulus)
+}
+
+// q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
+// used for Montgomery reduction
+const qInvNeg = 2130706431
+
+func init() {
+	_modulus.SetString("7f000001", 16)
+}
+
+// NewElement returns a new Element from a uint64 value
+//
+// it is equivalent to
+//
+//	var v Element
+//	v.SetUint64(...)
+func NewElement(v uint64) Element {
+	z := Element{uint32(v % uint64(q0))}
+	z.toMont()
+	return z
+}
+
+// SetUint64 sets z to v and returns z
+func (z *Element) SetUint64(v uint64) *Element {
+	//  sets z LSB to v (non-Montgomery form) and convert z to Montgomery form
+	*z = Element{uint32(v % uint64(q0))}
+	return z.toMont()
+}
+
+// SetInt64 sets z to v and returns z
+func (z *Element) SetInt64(v int64) *Element {
+
+	// absolute value of v
+	m := v >> 63
+	z.SetUint64(uint64((v ^ m) - m))
+
+	if m != 0 {
+		// v is negative
+		z.Neg(z)
+	}
+
+	return z
+}
+
+// Set z = x and returns z
+func (z *Element) Set(x *Element) *Element {
+	z[0] = x[0]
+	return z
+}
+
+// SetInterface converts provided interface into Element
+// returns an error if provided type is not supported
+// supported types:
+//
+//	Element
+//	*Element
+//	uint64
+//	int
+//	string (see SetString for valid formats)
+//	*big.Int
+//	big.Int
+//	[]byte
+func (z *Element) SetInterface(i1 interface{}) (*Element, error) {
+	if i1 == nil {
+		return nil, errors.New("can't set koalabear.Element with <nil>")
+	}
+
+	switch c1 := i1.(type) {
+	case Element:
+		return z.Set(&c1), nil
+	case *Element:
+		if c1 == nil {
+			return nil, errors.New("can't set koalabear.Element with <nil>")
+		}
+		return z.Set(c1), nil
+	case uint8:
+		return z.SetUint64(uint64(c1)), nil
+	case uint16:
+		return z.SetUint64(uint64(c1)), nil
+	case uint32:
+		return z.SetUint64(uint64(c1)), nil
+	case uint:
+		return z.SetUint64(uint64(c1)), nil
+	case uint64:
+		return z.SetUint64(c1), nil
+	case int8:
+		return z.SetInt64(int64(c1)), nil
+	case int16:
+		return z.SetInt64(int64(c1)), nil
+	case int32:
+		return z.SetInt64(int64(c1)), nil
+	case int64:
+		return z.SetInt64(c1), nil
+	case int:
+		return z.SetInt64(int64(c1)), nil
+	case string:
+		return z.SetString(c1)
+	case *big.Int:
+		if c1 == nil {
+			return nil, errors.New("can't set koalabear.Element with <nil>")
+		}
+		return z.SetBigInt(c1), nil
+	case big.Int:
+		return z.SetBigInt(&c1), nil
+	case []byte:
+		return z.SetBytes(c1), nil
+	default:
+		return nil, errors.New("can't set koalabear.Element from type " + reflect.TypeOf(i1).String())
+	}
+}
+
+// SetZero z = 0
+func (z *Element) SetZero() *Element {
+	z[0] = 0
+	return z
+}
+
+// SetOne z = 1 (in Montgomery form)
+func (z *Element) SetOne() *Element {
+	z[0] = 33554430
+	return z
+}
+
+// Div z = x*y⁻¹ (mod q)
+func (z *Element) Div(x, y *Element) *Element {
+	var yInv Element
+	yInv.Inverse(y)
+	z.Mul(x, &yInv)
+	return z
+}
+
+// Equal returns z == x; constant-time
+func (z *Element) Equal(x *Element) bool {
+	return z.NotEqual(x) == 0
+}
+
+// NotEqual returns 0 if and only if z == x; constant-time
+func (z *Element) NotEqual(x *Element) uint32 {
+	return (z[0] ^ x[0])
+}
+
+// IsZero returns z == 0
+func (z *Element) IsZero() bool {
+	return (z[0]) == 0
+}
+
+// IsOne returns z == 1
+func (z *Element) IsOne() bool {
+	return z[0] == 33554430
+}
+
+// IsUint64 reports whether z can be represented as an uint64.
+func (z *Element) IsUint64() bool {
+	return true
+}
+
+// Uint64 returns the uint64 representation of x. If x cannot be represented in a uint64, the result is undefined.
+func (z *Element) Uint64() uint64 {
+	return uint64(z.Bits()[0])
+}
+
+// FitsOnOneWord reports whether z words (except the least significant word) are 0
+//
+// It is the responsibility of the caller to convert from Montgomery to Regular form if needed.
+func (z *Element) FitsOnOneWord() bool {
+	return true
+}
+
+// Cmp compares (lexicographic order) z and x and returns:
+//
+//	-1 if z <  x
+//	 0 if z == x
+//	+1 if z >  x
+func (z *Element) Cmp(x *Element) int {
+	_z := z.Bits()
+	_x := x.Bits()
+	if _z[0] > _x[0] {
+		return 1
+	} else if _z[0] < _x[0] {
+		return -1
+	}
+	return 0
+}
+
+// LexicographicallyLargest returns true if this element is strictly lexicographically
+// larger than its negation, false otherwise
+func (z *Element) LexicographicallyLargest() bool {
+	// adapted from github.com/zkcrypto/bls12_381
+	// we check if the element is larger than (q-1) / 2
+	// if z - (((q -1) / 2) + 1) have no underflow, then z > (q-1) / 2
+
+	_z := z.Bits()
+
+	var b uint32
+	_, b = bits.Sub32(_z[0], 1065353217, 0)
+
+	return b == 0
+}
+
+// SetRandom sets z to a uniform random value in [0, q).
+//
+// This might error only if reading from crypto/rand.Reader errors,
+// in which case, value of z is undefined.
+func (z *Element) SetRandom() (*Element, error) {
+	// this code is generated for all modulus
+	// and derived from go/src/crypto/rand/util.go
+
+	// l is number of limbs * 8; the number of bytes needed to reconstruct 1 uint64
+	const l = 8
+
+	// bitLen is the maximum bit length needed to encode a value < q.
+	const bitLen = 31
+
+	// k is the maximum byte length needed to encode a value < q.
+	const k = (bitLen + 7) / 8
+
+	// b is the number of bits in the most significant byte of q-1.
+	b := uint(bitLen % 8)
+	if b == 0 {
+		b = 8
+	}
+
+	var bytes [l]byte
+
+	for {
+		// note that bytes[k:l] is always 0
+		if _, err := io.ReadFull(rand.Reader, bytes[:k]); err != nil {
+			return nil, err
+		}
+
+		// Clear unused bits in in the most significant byte to increase probability
+		// that the candidate is < q.
+		bytes[k-1] &= uint8(int(1<<b) - 1)
+		z[0] = binary.LittleEndian.Uint32(bytes[0:4])
+
+		if !z.smallerThanModulus() {
+			continue // ignore the candidate and re-sample
+		}
+
+		return z, nil
+	}
+}
+
+// smallerThanModulus returns true if z < q
+// This is not constant time
+func (z *Element) smallerThanModulus() bool {
+	return z[0] < q
+}
+
+// One returns 1
+func One() Element {
+	var one Element
+	one.SetOne()
+	return one
+}
+
+// Halve sets z to z / 2 (mod q)
+func (z *Element) Halve() {
+
+	if z[0]&1 == 1 {
+		// z = z + q
+		z[0], _ = bits.Add32(z[0], q0, 0)
+
+	}
+	// z = z >> 1
+	z[0] >>= 1
+
+}
+
+// fromMont converts z in place (i.e. mutates) from Montgomery to regular representation
+// sets and returns z = z * 1
+func (z *Element) fromMont() *Element {
+	fromMont(z)
+	return z
+}
+
+// Add z = x + y (mod q)
+func (z *Element) Add(x, y *Element) *Element {
+
+	t := x[0] + y[0]
+	if t >= q {
+		t -= q
+	}
+	z[0] = t
+	return z
+}
+
+// Double z = x + x (mod q), aka Lsh 1
+func (z *Element) Double(x *Element) *Element {
+	t := x[0] << 1
+	if t >= q {
+		t -= q
+	}
+	z[0] = t
+	return z
+}
+
+// Sub z = x - y (mod q)
+func (z *Element) Sub(x, y *Element) *Element {
+	t, b := bits.Sub32(x[0], y[0], 0)
+	if b != 0 {
+		t += q
+	}
+	z[0] = t
+	return z
+}
+
+// Neg z = q - x
+func (z *Element) Neg(x *Element) *Element {
+	if x.IsZero() {
+		z.SetZero()
+		return z
+	}
+	z[0] = q - x[0]
+	return z
+}
+
+// Select is a constant-time conditional move.
+// If c=0, z = x0. Else z = x1
+func (z *Element) Select(c int, x0 *Element, x1 *Element) *Element {
+	cC := uint32((int64(c) | -int64(c)) >> 63) // "canonicized" into: 0 if c=0, -1 otherwise
+	z[0] = x0[0] ^ cC&(x0[0]^x1[0])
+	return z
+}
+
+func _fromMontGeneric(z *Element) {
+	z[0] = montReduce(uint64(z[0]))
+}
+
+func _reduceGeneric(z *Element) {
+
+	// if z ⩾ q → z -= q
+	if !z.smallerThanModulus() {
+		z[0] -= q
+	}
+}
+
+// BatchInvert returns a new slice with every element inverted.
+// Uses Montgomery batch inversion trick
+func BatchInvert(a []Element) []Element {
+	res := make([]Element, len(a))
+	if len(a) == 0 {
+		return res
+	}
+
+	zeroes := bitset.New(uint(len(a)))
+	accumulator := One()
+
+	for i := 0; i < len(a); i++ {
+		if a[i].IsZero() {
+			zeroes.Set(uint(i))
+			continue
+		}
+		res[i] = accumulator
+		accumulator.Mul(&accumulator, &a[i])
+	}
+
+	accumulator.Inverse(&accumulator)
+
+	for i := len(a) - 1; i >= 0; i-- {
+		if zeroes.Test(uint(i)) {
+			continue
+		}
+		res[i].Mul(&res[i], &accumulator)
+		accumulator.Mul(&accumulator, &a[i])
+	}
+
+	return res
+}
+
+func _butterflyGeneric(a, b *Element) {
+	t := *a
+	a.Add(a, b)
+	b.Sub(&t, b)
+}
+
+// BitLen returns the minimum number of bits needed to represent z
+// returns 0 if z == 0
+func (z *Element) BitLen() int {
+	return bits.Len32(z[0])
+}
+
+// Hash msg to count prime field elements.
+// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06#section-5.2
+func Hash(msg, dst []byte, count int) ([]Element, error) {
+	// 128 bits of security
+	// L = ceil((ceil(log2(p)) + k) / 8), where k is the security parameter = 128
+	const Bytes = 1 + (Bits-1)/8
+	const L = 16 + Bytes
+
+	lenInBytes := count * L
+	pseudoRandomBytes, err := hash.ExpandMsgXmd(msg, dst, lenInBytes)
+	if err != nil {
+		return nil, err
+	}
+
+	// get temporary big int from the pool
+	vv := pool.BigInt.Get()
+
+	res := make([]Element, count)
+	for i := 0; i < count; i++ {
+		vv.SetBytes(pseudoRandomBytes[i*L : (i+1)*L])
+		res[i].SetBigInt(vv)
+	}
+
+	// release object into pool
+	pool.BigInt.Put(vv)
+
+	return res, nil
+}
+
+// Exp z = xᵏ (mod q)
+func (z *Element) Exp(x Element, k *big.Int) *Element {
+	if k.IsUint64() && k.Uint64() == 0 {
+		return z.SetOne()
+	}
+
+	e := k
+	if k.Sign() == -1 {
+		// negative k, we invert
+		// if k < 0: xᵏ (mod q) == (x⁻¹)ᵏ (mod q)
+		x.Inverse(&x)
+
+		// we negate k in a temp big.Int since
+		// Int.Bit(_) of k and -k is different
+		e = pool.BigInt.Get()
+		defer pool.BigInt.Put(e)
+		e.Neg(k)
+	}
+
+	z.Set(&x)
+
+	for i := e.BitLen() - 2; i >= 0; i-- {
+		z.Square(z)
+		if e.Bit(i) == 1 {
+			z.Mul(z, &x)
+		}
+	}
+
+	return z
+}
+
+// rSquare where r is the Montgommery constant
+// see section 2.3.2 of Tolga Acar's thesis
+// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
+var rSquare = Element{
+	402124772,
+}
+
+// toMont converts z to Montgomery form
+// sets and returns z = z * r²
+func (z *Element) toMont() *Element {
+	const rBits = 32
+	z[0] = uint32((uint64(z[0]) << rBits) % q)
+	return z
+}
+
+// String returns the decimal representation of z as generated by
+// z.Text(10).
+func (z *Element) String() string {
+	return z.Text(10)
+}
+
+// toBigInt returns z as a big.Int in Montgomery form
+func (z *Element) toBigInt(res *big.Int) *big.Int {
+	var b [Bytes]byte
+	binary.BigEndian.PutUint32(b[0:4], z[0])
+
+	return res.SetBytes(b[:])
+}
+
+// Text returns the string representation of z in the given base.
+// Base must be between 2 and 36, inclusive. The result uses the
+// lower-case letters 'a' to 'z' for digit values 10 to 35.
+// No prefix (such as "0x") is added to the string. If z is a nil
+// pointer it returns "<nil>".
+// If base == 10 and -z fits in a uint16 prefix "-" is added to the string.
+func (z *Element) Text(base int) string {
+	if base < 2 || base > 36 {
+		panic("invalid base")
+	}
+	if z == nil {
+		return "<nil>"
+	}
+
+	const maxUint16 = 65535
+	if base == 10 {
+		var zzNeg Element
+		zzNeg.Neg(z)
+		zzNeg.fromMont()
+		if zzNeg[0] <= maxUint16 && zzNeg[0] != 0 {
+			return "-" + strconv.FormatUint(uint64(zzNeg[0]), base)
+		}
+	}
+	zz := z.Bits()
+	return strconv.FormatUint(uint64(zz[0]), base)
+}
+
+// BigInt sets and return z as a *big.Int
+func (z *Element) BigInt(res *big.Int) *big.Int {
+	_z := *z
+	_z.fromMont()
+	return _z.toBigInt(res)
+}
+
+// ToBigIntRegular returns z as a big.Int in regular form
+//
+// Deprecated: use BigInt(*big.Int) instead
+func (z Element) ToBigIntRegular(res *big.Int) *big.Int {
+	z.fromMont()
+	return z.toBigInt(res)
+}
+
+// Bits provides access to z by returning its value as a little-endian [1]uint32 array.
+// Bits is intended to support implementation of missing low-level Element
+// functionality outside this package; it should be avoided otherwise.
+func (z *Element) Bits() [1]uint32 {
+	_z := *z
+	fromMont(&_z)
+	return _z
+}
+
+// Bytes returns the value of z as a big-endian byte array
+func (z *Element) Bytes() (res [Bytes]byte) {
+	BigEndian.PutElement(&res, *z)
+	return
+}
+
+// Marshal returns the value of z as a big-endian byte slice
+func (z *Element) Marshal() []byte {
+	b := z.Bytes()
+	return b[:]
+}
+
+// Unmarshal is an alias for SetBytes, it sets z to the value of e.
+func (z *Element) Unmarshal(e []byte) {
+	z.SetBytes(e)
+}
+
+// SetBytes interprets e as the bytes of a big-endian unsigned integer,
+// sets z to that value, and returns z.
+func (z *Element) SetBytes(e []byte) *Element {
+	if len(e) == Bytes {
+		// fast path
+		v, err := BigEndian.Element((*[Bytes]byte)(e))
+		if err == nil {
+			*z = v
+			return z
+		}
+	}
+
+	// slow path.
+	// get a big int from our pool
+	vv := pool.BigInt.Get()
+	vv.SetBytes(e)
+
+	// set big int
+	z.SetBigInt(vv)
+
+	// put temporary object back in pool
+	pool.BigInt.Put(vv)
+
+	return z
+}
+
+// SetBytesCanonical interprets e as the bytes of a big-endian 4-byte integer.
+// If e is not a 4-byte slice or encodes a value higher than q,
+// SetBytesCanonical returns an error.
+func (z *Element) SetBytesCanonical(e []byte) error {
+	if len(e) != Bytes {
+		return errors.New("invalid koalabear.Element encoding")
+	}
+	v, err := BigEndian.Element((*[Bytes]byte)(e))
+	if err != nil {
+		return err
+	}
+	*z = v
+	return nil
+}
+
+// SetBigInt sets z to v and returns z
+func (z *Element) SetBigInt(v *big.Int) *Element {
+	z.SetZero()
+
+	var zero big.Int
+
+	// fast path
+	c := v.Cmp(&_modulus)
+	if c == 0 {
+		// v == 0
+		return z
+	} else if c != 1 && v.Cmp(&zero) != -1 {
+		// 0 < v < q
+		return z.setBigInt(v)
+	}
+
+	// get temporary big int from the pool
+	vv := pool.BigInt.Get()
+
+	// copy input + modular reduction
+	vv.Mod(v, &_modulus)
+
+	// set big int byte value
+	z.setBigInt(vv)
+
+	// release object into pool
+	pool.BigInt.Put(vv)
+	return z
+}
+
+// setBigInt assumes 0 ⩽ v < q
+func (z *Element) setBigInt(v *big.Int) *Element {
+	vBits := v.Bits()
+	// we assume v < q, so even if big.Int words are on 64bits, we can safely cast them to 32bits
+	for i := 0; i < len(vBits); i++ {
+		z[i] = uint32(vBits[i])
+	}
+
+	return z.toMont()
+}
+
+// SetString creates a big.Int with number and calls SetBigInt on z
+//
+// The number prefix determines the actual base: A prefix of
+// ”0b” or ”0B” selects base 2, ”0”, ”0o” or ”0O” selects base 8,
+// and ”0x” or ”0X” selects base 16. Otherwise, the selected base is 10
+// and no prefix is accepted.
+//
+// For base 16, lower and upper case letters are considered the same:
+// The letters 'a' to 'f' and 'A' to 'F' represent digit values 10 to 15.
+//
+// An underscore character ”_” may appear between a base
+// prefix and an adjacent digit, and between successive digits; such
+// underscores do not change the value of the number.
+// Incorrect placement of underscores is reported as a panic if there
+// are no other errors.
+//
+// If the number is invalid this method leaves z unchanged and returns nil, error.
+func (z *Element) SetString(number string) (*Element, error) {
+	// get temporary big int from the pool
+	vv := pool.BigInt.Get()
+
+	if _, ok := vv.SetString(number, 0); !ok {
+		return nil, errors.New("Element.SetString failed -> can't parse number into a big.Int " + number)
+	}
+
+	z.SetBigInt(vv)
+
+	// release object into pool
+	pool.BigInt.Put(vv)
+
+	return z, nil
+}
+
+// MarshalJSON returns json encoding of z (z.Text(10))
+// If z == nil, returns null
+func (z *Element) MarshalJSON() ([]byte, error) {
+	if z == nil {
+		return []byte("null"), nil
+	}
+	const maxSafeBound = 15 // we encode it as number if it's small
+	s := z.Text(10)
+	if len(s) <= maxSafeBound {
+		return []byte(s), nil
+	}
+	var sbb strings.Builder
+	sbb.WriteByte('"')
+	sbb.WriteString(s)
+	sbb.WriteByte('"')
+	return []byte(sbb.String()), nil
+}
+
+// UnmarshalJSON accepts numbers and strings as input
+// See Element.SetString for valid prefixes (0x, 0b, ...)
+func (z *Element) UnmarshalJSON(data []byte) error {
+	s := string(data)
+	if len(s) > Bits*3 {
+		return errors.New("value too large (max = Element.Bits * 3)")
+	}
+
+	// we accept numbers and strings, remove leading and trailing quotes if any
+	if len(s) > 0 && s[0] == '"' {
+		s = s[1:]
+	}
+	if len(s) > 0 && s[len(s)-1] == '"' {
+		s = s[:len(s)-1]
+	}
+
+	// get temporary big int from the pool
+	vv := pool.BigInt.Get()
+
+	if _, ok := vv.SetString(s, 0); !ok {
+		return errors.New("can't parse into a big.Int: " + s)
+	}
+
+	z.SetBigInt(vv)
+
+	// release object into pool
+	pool.BigInt.Put(vv)
+	return nil
+}
+
+// A ByteOrder specifies how to convert byte slices into a Element
+type ByteOrder interface {
+	Element(*[Bytes]byte) (Element, error)
+	PutElement(*[Bytes]byte, Element)
+	String() string
+}
+
+// BigEndian is the big-endian implementation of ByteOrder and AppendByteOrder.
+var BigEndian bigEndian
+
+type bigEndian struct{}
+
+// Element interpret b is a big-endian 4-byte slice.
+// If b encodes a value higher than q, Element returns error.
+func (bigEndian) Element(b *[Bytes]byte) (Element, error) {
+	var z Element
+	z[0] = binary.BigEndian.Uint32((*b)[0:4])
+
+	if !z.smallerThanModulus() {
+		return Element{}, errors.New("invalid koalabear.Element encoding")
+	}
+
+	z.toMont()
+	return z, nil
+}
+
+func (bigEndian) PutElement(b *[Bytes]byte, e Element) {
+	e.fromMont()
+	binary.BigEndian.PutUint32((*b)[0:4], e[0])
+}
+
+func (bigEndian) String() string { return "BigEndian" }
+
+// LittleEndian is the little-endian implementation of ByteOrder and AppendByteOrder.
+var LittleEndian littleEndian
+
+type littleEndian struct{}
+
+func (littleEndian) Element(b *[Bytes]byte) (Element, error) {
+	var z Element
+	z[0] = binary.LittleEndian.Uint32((*b)[0:4])
+
+	if !z.smallerThanModulus() {
+		return Element{}, errors.New("invalid koalabear.Element encoding")
+	}
+
+	z.toMont()
+	return z, nil
+}
+
+func (littleEndian) PutElement(b *[Bytes]byte, e Element) {
+	e.fromMont()
+	binary.LittleEndian.PutUint32((*b)[0:4], e[0])
+}
+
+func (littleEndian) String() string { return "LittleEndian" }
+
+// Legendre returns the Legendre symbol of z (either +1, -1, or 0.)
+func (z *Element) Legendre() int {
+	var l Element
+	// z^((q-1)/2)
+	l.expByLegendreExp(*z)
+
+	if l.IsZero() {
+		return 0
+	}
+
+	// if l == 1
+	if l.IsOne() {
+		return 1
+	}
+	return -1
+}
+
+// Sqrt z = √x (mod q)
+// if the square root doesn't exist (x is not a square mod q)
+// Sqrt leaves z unchanged and returns nil
+func (z *Element) Sqrt(x *Element) *Element {
+	// q ≡ 1 (mod 4)
+	// see modSqrtTonelliShanks in math/big/int.go
+	// using https://www.maa.org/sites/default/files/pdf/upload_library/22/Polya/07468342.di020786.02p0470a.pdf
+
+	var y, b, t, w Element
+	// w = x^((s-1)/2))
+	w.expBySqrtExp(*x)
+
+	// y = x^((s+1)/2)) = w * x
+	y.Mul(x, &w)
+
+	// b = xˢ = w * w * x = y * x
+	b.Mul(&w, &y)
+
+	// g = nonResidue ^ s
+	var g = Element{
+		331895189,
+	}
+	r := uint64(24)
+
+	// compute legendre symbol
+	// t = x^((q-1)/2) = r-1 squaring of xˢ
+	t = b
+	for i := uint64(0); i < r-1; i++ {
+		t.Square(&t)
+	}
+	if t.IsZero() {
+		return z.SetZero()
+	}
+	if !t.IsOne() {
+		// t != 1, we don't have a square root
+		return nil
+	}
+	for {
+		var m uint64
+		t = b
+
+		// for t != 1
+		for !t.IsOne() {
+			t.Square(&t)
+			m++
+		}
+
+		if m == 0 {
+			return z.Set(&y)
+		}
+		// t = g^(2^(r-m-1)) (mod q)
+		ge := int(r - m - 1)
+		t = g
+		for ge > 0 {
+			t.Square(&t)
+			ge--
+		}
+
+		g.Square(&t)
+		y.Mul(&y, &t)
+		b.Mul(&b, &g)
+		r = m
+	}
+}
+
+// Inverse z = x⁻¹ (mod q)
+//
+// if x == 0, sets and returns z = x
+func (z *Element) Inverse(x *Element) *Element {
+	// Algorithm 16 in "Efficient Software-Implementation of Finite Fields with Applications to Cryptography"
+	const q uint32 = q0
+	if x.IsZero() {
+		z.SetZero()
+		return z
+	}
+
+	var r, s, u, v uint32
+	u = q
+	s = 402124772 // s = r²
+	r = 0
+	v = x[0]
+
+	var carry, borrow uint32
+
+	for (u != 1) && (v != 1) {
+		for v&1 == 0 {
+			v >>= 1
+			if s&1 == 0 {
+				s >>= 1
+			} else {
+				s, carry = bits.Add32(s, q, 0)
+				s >>= 1
+				if carry != 0 {
+					s |= (1 << 31)
+				}
+			}
+		}
+		for u&1 == 0 {
+			u >>= 1
+			if r&1 == 0 {
+				r >>= 1
+			} else {
+				r, carry = bits.Add32(r, q, 0)
+				r >>= 1
+				if carry != 0 {
+					r |= (1 << 31)
+				}
+			}
+		}
+		if v >= u {
+			v -= u
+			s, borrow = bits.Sub32(s, r, 0)
+			if borrow == 1 {
+				s += q
+			}
+		} else {
+			u -= v
+			r, borrow = bits.Sub32(r, s, 0)
+			if borrow == 1 {
+				r += q
+			}
+		}
+	}
+
+	if u == 1 {
+		z[0] = r
+	} else {
+		z[0] = s
+	}
+
+	return z
+}
diff --git a/field/koalabear/element_exp.go b/field/koalabear/element_exp.go
new file mode 100644
index 0000000000..ea8c27d6ca
--- /dev/null
+++ b/field/koalabear/element_exp.go
@@ -0,0 +1,122 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package koalabear
+
+// expBySqrtExp is equivalent to z.Exp(x, 3f)
+//
+// uses github.com/mmcloughlin/addchain v0.4.0 to generate a shorter addition chain
+func (z *Element) expBySqrtExp(x Element) *Element {
+	// addition chain:
+	//
+	//	_10     = 2*1
+	//	_11     = 1 + _10
+	//	_1100   = _11 << 2
+	//	_1111   = _11 + _1100
+	//	_111100 = _1111 << 2
+	//	return    _11 + _111100
+	//
+	// Operations: 5 squares 3 multiplies
+
+	// Allocate Temporaries.
+	var (
+		t0 = new(Element)
+	)
+
+	// var t0 Element
+	// Step 1: z = x^0x2
+	z.Square(&x)
+
+	// Step 2: z = x^0x3
+	z.Mul(&x, z)
+
+	// Step 4: t0 = x^0xc
+	t0.Square(z)
+	for s := 1; s < 2; s++ {
+		t0.Square(t0)
+	}
+
+	// Step 5: t0 = x^0xf
+	t0.Mul(z, t0)
+
+	// Step 7: t0 = x^0x3c
+	for s := 0; s < 2; s++ {
+		t0.Square(t0)
+	}
+
+	// Step 8: z = x^0x3f
+	z.Mul(z, t0)
+
+	return z
+}
+
+// expByLegendreExp is equivalent to z.Exp(x, 3f800000)
+//
+// uses github.com/mmcloughlin/addchain v0.4.0 to generate a shorter addition chain
+func (z *Element) expByLegendreExp(x Element) *Element {
+	// addition chain:
+	//
+	//	_10      = 2*1
+	//	_11      = 1 + _10
+	//	_110     = 2*_11
+	//	_111     = 1 + _110
+	//	_1110    = 2*_111
+	//	_1111    = 1 + _1110
+	//	_1111000 = _1111 << 3
+	//	_1111111 = _111 + _1111000
+	//	return     _1111111 << 23
+	//
+	// Operations: 29 squares 4 multiplies
+
+	// Allocate Temporaries.
+	var (
+		t0 = new(Element)
+	)
+
+	// var t0 Element
+	// Step 1: z = x^0x2
+	z.Square(&x)
+
+	// Step 2: z = x^0x3
+	z.Mul(&x, z)
+
+	// Step 3: z = x^0x6
+	z.Square(z)
+
+	// Step 4: z = x^0x7
+	z.Mul(&x, z)
+
+	// Step 5: t0 = x^0xe
+	t0.Square(z)
+
+	// Step 6: t0 = x^0xf
+	t0.Mul(&x, t0)
+
+	// Step 9: t0 = x^0x78
+	for s := 0; s < 3; s++ {
+		t0.Square(t0)
+	}
+
+	// Step 10: z = x^0x7f
+	z.Mul(z, t0)
+
+	// Step 33: z = x^0x3f800000
+	for s := 0; s < 23; s++ {
+		z.Square(z)
+	}
+
+	return z
+}
diff --git a/field/koalabear/element_purego.go b/field/koalabear/element_purego.go
new file mode 100644
index 0000000000..137f5eb77d
--- /dev/null
+++ b/field/koalabear/element_purego.go
@@ -0,0 +1,81 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package koalabear
+
+// MulBy3 x *= 3 (mod q)
+func MulBy3(x *Element) {
+	var y Element
+	y.SetUint64(3)
+	x.Mul(x, &y)
+}
+
+// MulBy5 x *= 5 (mod q)
+func MulBy5(x *Element) {
+	var y Element
+	y.SetUint64(5)
+	x.Mul(x, &y)
+}
+
+// MulBy13 x *= 13 (mod q)
+func MulBy13(x *Element) {
+	var y Element
+	y.SetUint64(13)
+	x.Mul(x, &y)
+}
+
+func fromMont(z *Element) {
+	_fromMontGeneric(z)
+}
+
+func reduce(z *Element) {
+	_reduceGeneric(z)
+}
+func montReduce(v uint64) uint32 {
+	m := uint32(v) * qInvNeg
+	t := uint32((v + uint64(m)*q) >> 32)
+	if t >= q {
+		t -= q
+	}
+	return t
+}
+
+// Mul z = x * y (mod q)
+//
+// x and y must be less than q
+func (z *Element) Mul(x, y *Element) *Element {
+	v := uint64(x[0]) * uint64(y[0])
+	z[0] = montReduce(v)
+	return z
+}
+
+// Square z = x * x (mod q)
+//
+// x must be less than q
+func (z *Element) Square(x *Element) *Element {
+	// see Mul for algorithm documentation
+	v := uint64(x[0]) * uint64(x[0])
+	z[0] = montReduce(v)
+	return z
+}
+
+// Butterfly sets
+//
+//	a = a + b (mod q)
+//	b = a - b (mod q)
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
diff --git a/field/koalabear/element_test.go b/field/koalabear/element_test.go
new file mode 100644
index 0000000000..ac6f3a8a70
--- /dev/null
+++ b/field/koalabear/element_test.go
@@ -0,0 +1,2230 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package koalabear
+
+import (
+	"crypto/rand"
+	"encoding/json"
+	"fmt"
+	"math/big"
+	"math/bits"
+
+	"testing"
+
+	"github.com/leanovate/gopter"
+	ggen "github.com/leanovate/gopter/gen"
+	"github.com/leanovate/gopter/prop"
+
+	"github.com/stretchr/testify/require"
+)
+
+// -------------------------------------------------------------------------------------------------
+// benchmarks
+// most benchmarks are rudimentary and should sample a large number of random inputs
+// or be run multiple times to ensure it didn't measure the fastest path of the function
+
+var benchResElement Element
+
+func BenchmarkElementSelect(b *testing.B) {
+	var x, y Element
+	x.SetRandom()
+	y.SetRandom()
+
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Select(i%3, &x, &y)
+	}
+}
+
+func BenchmarkElementSetRandom(b *testing.B) {
+	var x Element
+	x.SetRandom()
+
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		_, _ = x.SetRandom()
+	}
+}
+
+func BenchmarkElementSetBytes(b *testing.B) {
+	var x Element
+	x.SetRandom()
+	bb := x.Bytes()
+	b.ResetTimer()
+
+	for i := 0; i < b.N; i++ {
+		benchResElement.SetBytes(bb[:])
+	}
+
+}
+
+func BenchmarkElementMulByConstants(b *testing.B) {
+	b.Run("mulBy3", func(b *testing.B) {
+		benchResElement.SetRandom()
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			MulBy3(&benchResElement)
+		}
+	})
+	b.Run("mulBy5", func(b *testing.B) {
+		benchResElement.SetRandom()
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			MulBy5(&benchResElement)
+		}
+	})
+	b.Run("mulBy13", func(b *testing.B) {
+		benchResElement.SetRandom()
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			MulBy13(&benchResElement)
+		}
+	})
+}
+
+func BenchmarkElementInverse(b *testing.B) {
+	var x Element
+	x.SetRandom()
+	benchResElement.SetRandom()
+	b.ResetTimer()
+
+	for i := 0; i < b.N; i++ {
+		benchResElement.Inverse(&x)
+	}
+
+}
+
+func BenchmarkElementButterfly(b *testing.B) {
+	var x Element
+	x.SetRandom()
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		Butterfly(&x, &benchResElement)
+	}
+}
+
+func BenchmarkElementExp(b *testing.B) {
+	var x Element
+	x.SetRandom()
+	benchResElement.SetRandom()
+	b1, _ := rand.Int(rand.Reader, Modulus())
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Exp(x, b1)
+	}
+}
+
+func BenchmarkElementDouble(b *testing.B) {
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Double(&benchResElement)
+	}
+}
+
+func BenchmarkElementAdd(b *testing.B) {
+	var x Element
+	x.SetRandom()
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Add(&x, &benchResElement)
+	}
+}
+
+func BenchmarkElementSub(b *testing.B) {
+	var x Element
+	x.SetRandom()
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Sub(&x, &benchResElement)
+	}
+}
+
+func BenchmarkElementNeg(b *testing.B) {
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Neg(&benchResElement)
+	}
+}
+
+func BenchmarkElementDiv(b *testing.B) {
+	var x Element
+	x.SetRandom()
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Div(&x, &benchResElement)
+	}
+}
+
+func BenchmarkElementFromMont(b *testing.B) {
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.fromMont()
+	}
+}
+
+func BenchmarkElementSquare(b *testing.B) {
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Square(&benchResElement)
+	}
+}
+
+func BenchmarkElementSqrt(b *testing.B) {
+	var a Element
+	a.SetUint64(4)
+	a.Neg(&a)
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Sqrt(&a)
+	}
+}
+
+func BenchmarkElementMul(b *testing.B) {
+	x := Element{
+		402124772,
+	}
+	benchResElement.SetOne()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Mul(&benchResElement, &x)
+	}
+}
+
+func BenchmarkElementCmp(b *testing.B) {
+	x := Element{
+		402124772,
+	}
+	benchResElement = x
+	benchResElement[0] = 0
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Cmp(&x)
+	}
+}
+
+func TestElementCmp(t *testing.T) {
+	var x, y Element
+
+	if x.Cmp(&y) != 0 {
+		t.Fatal("x == y")
+	}
+
+	one := One()
+	y.Sub(&y, &one)
+
+	if x.Cmp(&y) != -1 {
+		t.Fatal("x < y")
+	}
+	if y.Cmp(&x) != 1 {
+		t.Fatal("x < y")
+	}
+
+	x = y
+	if x.Cmp(&y) != 0 {
+		t.Fatal("x == y")
+	}
+
+	x.Sub(&x, &one)
+	if x.Cmp(&y) != -1 {
+		t.Fatal("x < y")
+	}
+	if y.Cmp(&x) != 1 {
+		t.Fatal("x < y")
+	}
+}
+
+func TestElementNegZero(t *testing.T) {
+	var a, b Element
+	b.SetZero()
+	for a.IsZero() {
+		a.SetRandom()
+	}
+	a.Neg(&b)
+	if !a.IsZero() {
+		t.Fatal("neg(0) != 0")
+	}
+}
+
+// -------------------------------------------------------------------------------------------------
+// Gopter tests
+// most of them are generated with a template
+
+const (
+	nbFuzzShort = 200
+	nbFuzz      = 1000
+)
+
+// special values to be used in tests
+var staticTestValues []Element
+
+func init() {
+	staticTestValues = append(staticTestValues, Element{}) // zero
+	staticTestValues = append(staticTestValues, One())     // one
+	staticTestValues = append(staticTestValues, rSquare)   // r²
+	var e, one Element
+	one.SetOne()
+	e.Sub(&qElement, &one)
+	staticTestValues = append(staticTestValues, e) // q - 1
+	e.Double(&one)
+	staticTestValues = append(staticTestValues, e) // 2
+
+	{
+		a := qElement
+		a[0]--
+		staticTestValues = append(staticTestValues, a)
+	}
+	staticTestValues = append(staticTestValues, Element{0})
+	staticTestValues = append(staticTestValues, Element{1})
+	staticTestValues = append(staticTestValues, Element{2})
+
+	{
+		a := qElement
+		a[0]--
+		staticTestValues = append(staticTestValues, a)
+	}
+
+	{
+		a := qElement
+		a[0] = 0
+		staticTestValues = append(staticTestValues, a)
+	}
+
+}
+
+func TestElementReduce(t *testing.T) {
+	testValues := make([]Element, len(staticTestValues))
+	copy(testValues, staticTestValues)
+
+	for i := range testValues {
+		s := testValues[i]
+		expected := s
+		reduce(&s)
+		_reduceGeneric(&expected)
+		if !s.Equal(&expected) {
+			t.Fatal("reduce failed: asm and generic impl don't match")
+		}
+	}
+
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := genFull()
+
+	properties.Property("reduce should output a result smaller than modulus", prop.ForAll(
+		func(a Element) bool {
+			b := a
+			reduce(&a)
+			_reduceGeneric(&b)
+			return a.smallerThanModulus() && a.Equal(&b)
+		},
+		genA,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+
+}
+
+func TestElementEqual(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+	genB := gen()
+
+	properties.Property("x.Equal(&y) iff x == y; likely false for random pairs", prop.ForAll(
+		func(a testPairElement, b testPairElement) bool {
+			return a.element.Equal(&b.element) == (a.element == b.element)
+		},
+		genA,
+		genB,
+	))
+
+	properties.Property("x.Equal(&y) if x == y", prop.ForAll(
+		func(a testPairElement) bool {
+			b := a.element
+			return a.element.Equal(&b)
+		},
+		genA,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+}
+
+func TestElementBytes(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("SetBytes(Bytes()) should stay constant", prop.ForAll(
+		func(a testPairElement) bool {
+			var b Element
+			bytes := a.element.Bytes()
+			b.SetBytes(bytes[:])
+			return a.element.Equal(&b)
+		},
+		genA,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+}
+
+func TestElementInverseExp(t *testing.T) {
+	// inverse must be equal to exp^-2
+	exp := Modulus()
+	exp.Sub(exp, new(big.Int).SetUint64(2))
+
+	invMatchExp := func(a testPairElement) bool {
+		var b Element
+		b.Set(&a.element)
+		a.element.Inverse(&a.element)
+		b.Exp(b, exp)
+
+		return a.element.Equal(&b)
+	}
+
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+	properties := gopter.NewProperties(parameters)
+	genA := gen()
+	properties.Property("inv == exp^-2", prop.ForAll(invMatchExp, genA))
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+
+	parameters.MinSuccessfulTests = 1
+	properties = gopter.NewProperties(parameters)
+	properties.Property("inv(0) == 0", prop.ForAll(invMatchExp, ggen.OneConstOf(testPairElement{})))
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+
+}
+
+func mulByConstant(z *Element, c uint8) {
+	var y Element
+	y.SetUint64(uint64(c))
+	z.Mul(z, &y)
+}
+
+func TestElementMulByConstants(t *testing.T) {
+
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	implemented := []uint8{0, 1, 2, 3, 5, 13}
+	properties.Property("mulByConstant", prop.ForAll(
+		func(a testPairElement) bool {
+			for _, c := range implemented {
+				var constant Element
+				constant.SetUint64(uint64(c))
+
+				b := a.element
+				b.Mul(&b, &constant)
+
+				aa := a.element
+				mulByConstant(&aa, c)
+
+				if !aa.Equal(&b) {
+					return false
+				}
+			}
+
+			return true
+		},
+		genA,
+	))
+
+	properties.Property("MulBy3(x) == Mul(x, 3)", prop.ForAll(
+		func(a testPairElement) bool {
+			var constant Element
+			constant.SetUint64(3)
+
+			b := a.element
+			b.Mul(&b, &constant)
+
+			MulBy3(&a.element)
+
+			return a.element.Equal(&b)
+		},
+		genA,
+	))
+
+	properties.Property("MulBy5(x) == Mul(x, 5)", prop.ForAll(
+		func(a testPairElement) bool {
+			var constant Element
+			constant.SetUint64(5)
+
+			b := a.element
+			b.Mul(&b, &constant)
+
+			MulBy5(&a.element)
+
+			return a.element.Equal(&b)
+		},
+		genA,
+	))
+
+	properties.Property("MulBy13(x) == Mul(x, 13)", prop.ForAll(
+		func(a testPairElement) bool {
+			var constant Element
+			constant.SetUint64(13)
+
+			b := a.element
+			b.Mul(&b, &constant)
+
+			MulBy13(&a.element)
+
+			return a.element.Equal(&b)
+		},
+		genA,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+
+}
+
+func TestElementLegendre(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("legendre should output same result than big.Int.Jacobi", prop.ForAll(
+		func(a testPairElement) bool {
+			return a.element.Legendre() == big.Jacobi(&a.bigint, Modulus())
+		},
+		genA,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+
+}
+
+func TestElementBitLen(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("BitLen should output same result than big.Int.BitLen", prop.ForAll(
+		func(a testPairElement) bool {
+			return a.element.fromMont().BitLen() == a.bigint.BitLen()
+		},
+		genA,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+}
+
+func TestElementButterflies(t *testing.T) {
+
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("butterfly0 == a -b; a +b", prop.ForAll(
+		func(a, b testPairElement) bool {
+			a0, b0 := a.element, b.element
+
+			_butterflyGeneric(&a.element, &b.element)
+			Butterfly(&a0, &b0)
+
+			return a.element.Equal(&a0) && b.element.Equal(&b0)
+		},
+		genA,
+		genA,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+
+}
+
+func TestElementLexicographicallyLargest(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("element.Cmp should match LexicographicallyLargest output", prop.ForAll(
+		func(a testPairElement) bool {
+			var negA Element
+			negA.Neg(&a.element)
+
+			cmpResult := a.element.Cmp(&negA)
+			lResult := a.element.LexicographicallyLargest()
+
+			if lResult && cmpResult == 1 {
+				return true
+			}
+			if !lResult && cmpResult != 1 {
+				return true
+			}
+			return false
+		},
+		genA,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+
+}
+
+func TestElementAdd(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+	genB := gen()
+
+	properties.Property("Add: having the receiver as operand should output the same result", prop.ForAll(
+		func(a, b testPairElement) bool {
+			var c, d Element
+			d.Set(&a.element)
+
+			c.Add(&a.element, &b.element)
+			a.element.Add(&a.element, &b.element)
+			b.element.Add(&d, &b.element)
+
+			return a.element.Equal(&b.element) && a.element.Equal(&c) && b.element.Equal(&c)
+		},
+		genA,
+		genB,
+	))
+
+	properties.Property("Add: operation result must match big.Int result", prop.ForAll(
+		func(a, b testPairElement) bool {
+			{
+				var c Element
+
+				c.Add(&a.element, &b.element)
+
+				var d, e big.Int
+				d.Add(&a.bigint, &b.bigint).Mod(&d, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					return false
+				}
+			}
+
+			// fixed elements
+			// a is random
+			// r takes special values
+			testValues := make([]Element, len(staticTestValues))
+			copy(testValues, staticTestValues)
+
+			for i := range testValues {
+				r := testValues[i]
+				var d, e, rb big.Int
+				r.BigInt(&rb)
+
+				var c Element
+				c.Add(&a.element, &r)
+				d.Add(&a.bigint, &rb).Mod(&d, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					return false
+				}
+			}
+			return true
+		},
+		genA,
+		genB,
+	))
+
+	properties.Property("Add: operation result must be smaller than modulus", prop.ForAll(
+		func(a, b testPairElement) bool {
+			var c Element
+
+			c.Add(&a.element, &b.element)
+
+			return c.smallerThanModulus()
+		},
+		genA,
+		genB,
+	))
+
+	specialValueTest := func() {
+		// test special values against special values
+		testValues := make([]Element, len(staticTestValues))
+		copy(testValues, staticTestValues)
+
+		for i := range testValues {
+			a := testValues[i]
+			var aBig big.Int
+			a.BigInt(&aBig)
+			for j := range testValues {
+				b := testValues[j]
+				var bBig, d, e big.Int
+				b.BigInt(&bBig)
+
+				var c Element
+				c.Add(&a, &b)
+				d.Add(&aBig, &bBig).Mod(&d, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					t.Fatal("Add failed special test values")
+				}
+			}
+		}
+	}
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+	specialValueTest()
+
+}
+
+func TestElementSub(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+	genB := gen()
+
+	properties.Property("Sub: having the receiver as operand should output the same result", prop.ForAll(
+		func(a, b testPairElement) bool {
+			var c, d Element
+			d.Set(&a.element)
+
+			c.Sub(&a.element, &b.element)
+			a.element.Sub(&a.element, &b.element)
+			b.element.Sub(&d, &b.element)
+
+			return a.element.Equal(&b.element) && a.element.Equal(&c) && b.element.Equal(&c)
+		},
+		genA,
+		genB,
+	))
+
+	properties.Property("Sub: operation result must match big.Int result", prop.ForAll(
+		func(a, b testPairElement) bool {
+			{
+				var c Element
+
+				c.Sub(&a.element, &b.element)
+
+				var d, e big.Int
+				d.Sub(&a.bigint, &b.bigint).Mod(&d, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					return false
+				}
+			}
+
+			// fixed elements
+			// a is random
+			// r takes special values
+			testValues := make([]Element, len(staticTestValues))
+			copy(testValues, staticTestValues)
+
+			for i := range testValues {
+				r := testValues[i]
+				var d, e, rb big.Int
+				r.BigInt(&rb)
+
+				var c Element
+				c.Sub(&a.element, &r)
+				d.Sub(&a.bigint, &rb).Mod(&d, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					return false
+				}
+			}
+			return true
+		},
+		genA,
+		genB,
+	))
+
+	properties.Property("Sub: operation result must be smaller than modulus", prop.ForAll(
+		func(a, b testPairElement) bool {
+			var c Element
+
+			c.Sub(&a.element, &b.element)
+
+			return c.smallerThanModulus()
+		},
+		genA,
+		genB,
+	))
+
+	specialValueTest := func() {
+		// test special values against special values
+		testValues := make([]Element, len(staticTestValues))
+		copy(testValues, staticTestValues)
+
+		for i := range testValues {
+			a := testValues[i]
+			var aBig big.Int
+			a.BigInt(&aBig)
+			for j := range testValues {
+				b := testValues[j]
+				var bBig, d, e big.Int
+				b.BigInt(&bBig)
+
+				var c Element
+				c.Sub(&a, &b)
+				d.Sub(&aBig, &bBig).Mod(&d, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					t.Fatal("Sub failed special test values")
+				}
+			}
+		}
+	}
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+	specialValueTest()
+
+}
+
+func TestElementMul(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+	genB := gen()
+
+	properties.Property("Mul: having the receiver as operand should output the same result", prop.ForAll(
+		func(a, b testPairElement) bool {
+			var c, d Element
+			d.Set(&a.element)
+
+			c.Mul(&a.element, &b.element)
+			a.element.Mul(&a.element, &b.element)
+			b.element.Mul(&d, &b.element)
+
+			return a.element.Equal(&b.element) && a.element.Equal(&c) && b.element.Equal(&c)
+		},
+		genA,
+		genB,
+	))
+
+	properties.Property("Mul: operation result must match big.Int result", prop.ForAll(
+		func(a, b testPairElement) bool {
+			{
+				var c Element
+
+				c.Mul(&a.element, &b.element)
+
+				var d, e big.Int
+				d.Mul(&a.bigint, &b.bigint).Mod(&d, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					return false
+				}
+			}
+
+			// fixed elements
+			// a is random
+			// r takes special values
+			testValues := make([]Element, len(staticTestValues))
+			copy(testValues, staticTestValues)
+
+			for i := range testValues {
+				r := testValues[i]
+				var d, e, rb big.Int
+				r.BigInt(&rb)
+
+				var c Element
+				c.Mul(&a.element, &r)
+				d.Mul(&a.bigint, &rb).Mod(&d, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					return false
+				}
+			}
+			return true
+		},
+		genA,
+		genB,
+	))
+
+	properties.Property("Mul: operation result must be smaller than modulus", prop.ForAll(
+		func(a, b testPairElement) bool {
+			var c Element
+
+			c.Mul(&a.element, &b.element)
+
+			return c.smallerThanModulus()
+		},
+		genA,
+		genB,
+	))
+
+	specialValueTest := func() {
+		// test special values against special values
+		testValues := make([]Element, len(staticTestValues))
+		copy(testValues, staticTestValues)
+
+		for i := range testValues {
+			a := testValues[i]
+			var aBig big.Int
+			a.BigInt(&aBig)
+			for j := range testValues {
+				b := testValues[j]
+				var bBig, d, e big.Int
+				b.BigInt(&bBig)
+
+				var c Element
+				c.Mul(&a, &b)
+				d.Mul(&aBig, &bBig).Mod(&d, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					t.Fatal("Mul failed special test values")
+				}
+			}
+		}
+	}
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+	specialValueTest()
+
+}
+
+func TestElementDiv(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+	genB := gen()
+
+	properties.Property("Div: having the receiver as operand should output the same result", prop.ForAll(
+		func(a, b testPairElement) bool {
+			var c, d Element
+			d.Set(&a.element)
+
+			c.Div(&a.element, &b.element)
+			a.element.Div(&a.element, &b.element)
+			b.element.Div(&d, &b.element)
+
+			return a.element.Equal(&b.element) && a.element.Equal(&c) && b.element.Equal(&c)
+		},
+		genA,
+		genB,
+	))
+
+	properties.Property("Div: operation result must match big.Int result", prop.ForAll(
+		func(a, b testPairElement) bool {
+			{
+				var c Element
+
+				c.Div(&a.element, &b.element)
+
+				var d, e big.Int
+				d.ModInverse(&b.bigint, Modulus())
+				d.Mul(&d, &a.bigint).Mod(&d, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					return false
+				}
+			}
+
+			// fixed elements
+			// a is random
+			// r takes special values
+			testValues := make([]Element, len(staticTestValues))
+			copy(testValues, staticTestValues)
+
+			for i := range testValues {
+				r := testValues[i]
+				var d, e, rb big.Int
+				r.BigInt(&rb)
+
+				var c Element
+				c.Div(&a.element, &r)
+				d.ModInverse(&rb, Modulus())
+				d.Mul(&d, &a.bigint).Mod(&d, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					return false
+				}
+			}
+			return true
+		},
+		genA,
+		genB,
+	))
+
+	properties.Property("Div: operation result must be smaller than modulus", prop.ForAll(
+		func(a, b testPairElement) bool {
+			var c Element
+
+			c.Div(&a.element, &b.element)
+
+			return c.smallerThanModulus()
+		},
+		genA,
+		genB,
+	))
+
+	specialValueTest := func() {
+		// test special values against special values
+		testValues := make([]Element, len(staticTestValues))
+		copy(testValues, staticTestValues)
+
+		for i := range testValues {
+			a := testValues[i]
+			var aBig big.Int
+			a.BigInt(&aBig)
+			for j := range testValues {
+				b := testValues[j]
+				var bBig, d, e big.Int
+				b.BigInt(&bBig)
+
+				var c Element
+				c.Div(&a, &b)
+				d.ModInverse(&bBig, Modulus())
+				d.Mul(&d, &aBig).Mod(&d, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					t.Fatal("Div failed special test values")
+				}
+			}
+		}
+	}
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+	specialValueTest()
+
+}
+
+func TestElementExp(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+	genB := gen()
+
+	properties.Property("Exp: having the receiver as operand should output the same result", prop.ForAll(
+		func(a, b testPairElement) bool {
+			var c, d Element
+			d.Set(&a.element)
+
+			c.Exp(a.element, &b.bigint)
+			a.element.Exp(a.element, &b.bigint)
+			b.element.Exp(d, &b.bigint)
+
+			return a.element.Equal(&b.element) && a.element.Equal(&c) && b.element.Equal(&c)
+		},
+		genA,
+		genB,
+	))
+
+	properties.Property("Exp: operation result must match big.Int result", prop.ForAll(
+		func(a, b testPairElement) bool {
+			{
+				var c Element
+
+				c.Exp(a.element, &b.bigint)
+
+				var d, e big.Int
+				d.Exp(&a.bigint, &b.bigint, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					return false
+				}
+			}
+
+			// fixed elements
+			// a is random
+			// r takes special values
+			testValues := make([]Element, len(staticTestValues))
+			copy(testValues, staticTestValues)
+
+			for i := range testValues {
+				r := testValues[i]
+				var d, e, rb big.Int
+				r.BigInt(&rb)
+
+				var c Element
+				c.Exp(a.element, &rb)
+				d.Exp(&a.bigint, &rb, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					return false
+				}
+			}
+			return true
+		},
+		genA,
+		genB,
+	))
+
+	properties.Property("Exp: operation result must be smaller than modulus", prop.ForAll(
+		func(a, b testPairElement) bool {
+			var c Element
+
+			c.Exp(a.element, &b.bigint)
+
+			return c.smallerThanModulus()
+		},
+		genA,
+		genB,
+	))
+
+	specialValueTest := func() {
+		// test special values against special values
+		testValues := make([]Element, len(staticTestValues))
+		copy(testValues, staticTestValues)
+
+		for i := range testValues {
+			a := testValues[i]
+			var aBig big.Int
+			a.BigInt(&aBig)
+			for j := range testValues {
+				b := testValues[j]
+				var bBig, d, e big.Int
+				b.BigInt(&bBig)
+
+				var c Element
+				c.Exp(a, &bBig)
+				d.Exp(&aBig, &bBig, Modulus())
+
+				if c.BigInt(&e).Cmp(&d) != 0 {
+					t.Fatal("Exp failed special test values")
+				}
+			}
+		}
+	}
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+	specialValueTest()
+
+}
+
+func TestElementSquare(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("Square: having the receiver as operand should output the same result", prop.ForAll(
+		func(a testPairElement) bool {
+
+			var b Element
+
+			b.Square(&a.element)
+			a.element.Square(&a.element)
+			return a.element.Equal(&b)
+		},
+		genA,
+	))
+
+	properties.Property("Square: operation result must match big.Int result", prop.ForAll(
+		func(a testPairElement) bool {
+			var c Element
+			c.Square(&a.element)
+
+			var d, e big.Int
+			d.Mul(&a.bigint, &a.bigint).Mod(&d, Modulus())
+
+			return c.BigInt(&e).Cmp(&d) == 0
+		},
+		genA,
+	))
+
+	properties.Property("Square: operation result must be smaller than modulus", prop.ForAll(
+		func(a testPairElement) bool {
+			var c Element
+			c.Square(&a.element)
+			return c.smallerThanModulus()
+		},
+		genA,
+	))
+
+	specialValueTest := func() {
+		// test special values
+		testValues := make([]Element, len(staticTestValues))
+		copy(testValues, staticTestValues)
+
+		for i := range testValues {
+			a := testValues[i]
+			var aBig big.Int
+			a.BigInt(&aBig)
+			var c Element
+			c.Square(&a)
+
+			var d, e big.Int
+			d.Mul(&aBig, &aBig).Mod(&d, Modulus())
+
+			if c.BigInt(&e).Cmp(&d) != 0 {
+				t.Fatal("Square failed special test values")
+			}
+		}
+	}
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+	specialValueTest()
+
+}
+
+func TestElementInverse(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("Inverse: having the receiver as operand should output the same result", prop.ForAll(
+		func(a testPairElement) bool {
+
+			var b Element
+
+			b.Inverse(&a.element)
+			a.element.Inverse(&a.element)
+			return a.element.Equal(&b)
+		},
+		genA,
+	))
+
+	properties.Property("Inverse: operation result must match big.Int result", prop.ForAll(
+		func(a testPairElement) bool {
+			var c Element
+			c.Inverse(&a.element)
+
+			var d, e big.Int
+			d.ModInverse(&a.bigint, Modulus())
+
+			return c.BigInt(&e).Cmp(&d) == 0
+		},
+		genA,
+	))
+
+	properties.Property("Inverse: operation result must be smaller than modulus", prop.ForAll(
+		func(a testPairElement) bool {
+			var c Element
+			c.Inverse(&a.element)
+			return c.smallerThanModulus()
+		},
+		genA,
+	))
+
+	specialValueTest := func() {
+		// test special values
+		testValues := make([]Element, len(staticTestValues))
+		copy(testValues, staticTestValues)
+
+		for i := range testValues {
+			a := testValues[i]
+			var aBig big.Int
+			a.BigInt(&aBig)
+			var c Element
+			c.Inverse(&a)
+
+			var d, e big.Int
+			d.ModInverse(&aBig, Modulus())
+
+			if c.BigInt(&e).Cmp(&d) != 0 {
+				t.Fatal("Inverse failed special test values")
+			}
+		}
+	}
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+	specialValueTest()
+
+}
+
+func TestElementSqrt(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("Sqrt: having the receiver as operand should output the same result", prop.ForAll(
+		func(a testPairElement) bool {
+
+			b := a.element
+
+			b.Sqrt(&a.element)
+			a.element.Sqrt(&a.element)
+			return a.element.Equal(&b)
+		},
+		genA,
+	))
+
+	properties.Property("Sqrt: operation result must match big.Int result", prop.ForAll(
+		func(a testPairElement) bool {
+			var c Element
+			c.Sqrt(&a.element)
+
+			var d, e big.Int
+			d.ModSqrt(&a.bigint, Modulus())
+
+			return c.BigInt(&e).Cmp(&d) == 0
+		},
+		genA,
+	))
+
+	properties.Property("Sqrt: operation result must be smaller than modulus", prop.ForAll(
+		func(a testPairElement) bool {
+			var c Element
+			c.Sqrt(&a.element)
+			return c.smallerThanModulus()
+		},
+		genA,
+	))
+
+	specialValueTest := func() {
+		// test special values
+		testValues := make([]Element, len(staticTestValues))
+		copy(testValues, staticTestValues)
+
+		for i := range testValues {
+			a := testValues[i]
+			var aBig big.Int
+			a.BigInt(&aBig)
+			var c Element
+			c.Sqrt(&a)
+
+			var d, e big.Int
+			d.ModSqrt(&aBig, Modulus())
+
+			if c.BigInt(&e).Cmp(&d) != 0 {
+				t.Fatal("Sqrt failed special test values")
+			}
+		}
+	}
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+	specialValueTest()
+
+}
+
+func TestElementDouble(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("Double: having the receiver as operand should output the same result", prop.ForAll(
+		func(a testPairElement) bool {
+
+			var b Element
+
+			b.Double(&a.element)
+			a.element.Double(&a.element)
+			return a.element.Equal(&b)
+		},
+		genA,
+	))
+
+	properties.Property("Double: operation result must match big.Int result", prop.ForAll(
+		func(a testPairElement) bool {
+			var c Element
+			c.Double(&a.element)
+
+			var d, e big.Int
+			d.Lsh(&a.bigint, 1).Mod(&d, Modulus())
+
+			return c.BigInt(&e).Cmp(&d) == 0
+		},
+		genA,
+	))
+
+	properties.Property("Double: operation result must be smaller than modulus", prop.ForAll(
+		func(a testPairElement) bool {
+			var c Element
+			c.Double(&a.element)
+			return c.smallerThanModulus()
+		},
+		genA,
+	))
+
+	specialValueTest := func() {
+		// test special values
+		testValues := make([]Element, len(staticTestValues))
+		copy(testValues, staticTestValues)
+
+		for i := range testValues {
+			a := testValues[i]
+			var aBig big.Int
+			a.BigInt(&aBig)
+			var c Element
+			c.Double(&a)
+
+			var d, e big.Int
+			d.Lsh(&aBig, 1).Mod(&d, Modulus())
+
+			if c.BigInt(&e).Cmp(&d) != 0 {
+				t.Fatal("Double failed special test values")
+			}
+		}
+	}
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+	specialValueTest()
+
+}
+
+func TestElementNeg(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("Neg: having the receiver as operand should output the same result", prop.ForAll(
+		func(a testPairElement) bool {
+
+			var b Element
+
+			b.Neg(&a.element)
+			a.element.Neg(&a.element)
+			return a.element.Equal(&b)
+		},
+		genA,
+	))
+
+	properties.Property("Neg: operation result must match big.Int result", prop.ForAll(
+		func(a testPairElement) bool {
+			var c Element
+			c.Neg(&a.element)
+
+			var d, e big.Int
+			d.Neg(&a.bigint).Mod(&d, Modulus())
+
+			return c.BigInt(&e).Cmp(&d) == 0
+		},
+		genA,
+	))
+
+	properties.Property("Neg: operation result must be smaller than modulus", prop.ForAll(
+		func(a testPairElement) bool {
+			var c Element
+			c.Neg(&a.element)
+			return c.smallerThanModulus()
+		},
+		genA,
+	))
+
+	specialValueTest := func() {
+		// test special values
+		testValues := make([]Element, len(staticTestValues))
+		copy(testValues, staticTestValues)
+
+		for i := range testValues {
+			a := testValues[i]
+			var aBig big.Int
+			a.BigInt(&aBig)
+			var c Element
+			c.Neg(&a)
+
+			var d, e big.Int
+			d.Neg(&aBig).Mod(&d, Modulus())
+
+			if c.BigInt(&e).Cmp(&d) != 0 {
+				t.Fatal("Neg failed special test values")
+			}
+		}
+	}
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+	specialValueTest()
+
+}
+
+func TestElementFixedExp(t *testing.T) {
+
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	var (
+		_bLegendreExponentElement *big.Int
+		_bSqrtExponentElement     *big.Int
+	)
+
+	_bLegendreExponentElement, _ = new(big.Int).SetString("3f800000", 16)
+	const sqrtExponentElement = "3f"
+	_bSqrtExponentElement, _ = new(big.Int).SetString(sqrtExponentElement, 16)
+
+	genA := gen()
+
+	properties.Property(fmt.Sprintf("expBySqrtExp must match Exp(%s)", sqrtExponentElement), prop.ForAll(
+		func(a testPairElement) bool {
+			c := a.element
+			d := a.element
+			c.expBySqrtExp(c)
+			d.Exp(d, _bSqrtExponentElement)
+			return c.Equal(&d)
+		},
+		genA,
+	))
+
+	properties.Property("expByLegendreExp must match Exp(3f800000)", prop.ForAll(
+		func(a testPairElement) bool {
+			c := a.element
+			d := a.element
+			c.expByLegendreExp(c)
+			d.Exp(d, _bLegendreExponentElement)
+			return c.Equal(&d)
+		},
+		genA,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+}
+
+func TestElementHalve(t *testing.T) {
+
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+	var twoInv Element
+	twoInv.SetUint64(2)
+	twoInv.Inverse(&twoInv)
+
+	properties.Property("z.Halve must match z / 2", prop.ForAll(
+		func(a testPairElement) bool {
+			c := a.element
+			d := a.element
+			c.Halve()
+			d.Mul(&d, &twoInv)
+			return c.Equal(&d)
+		},
+		genA,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+}
+
+func combineSelectionArguments(c int64, z int8) int {
+	if z%3 == 0 {
+		return 0
+	}
+	return int(c)
+}
+
+func TestElementSelect(t *testing.T) {
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := genFull()
+	genB := genFull()
+	genC := ggen.Int64() //the condition
+	genZ := ggen.Int8()  //to make zeros artificially more likely
+
+	properties.Property("Select: must select correctly", prop.ForAll(
+		func(a, b Element, cond int64, z int8) bool {
+			condC := combineSelectionArguments(cond, z)
+
+			var c Element
+			c.Select(condC, &a, &b)
+
+			if condC == 0 {
+				return c.Equal(&a)
+			}
+			return c.Equal(&b)
+		},
+		genA,
+		genB,
+		genC,
+		genZ,
+	))
+
+	properties.Property("Select: having the receiver as operand should output the same result", prop.ForAll(
+		func(a, b Element, cond int64, z int8) bool {
+			condC := combineSelectionArguments(cond, z)
+
+			var c, d Element
+			d.Set(&a)
+			c.Select(condC, &a, &b)
+			a.Select(condC, &a, &b)
+			b.Select(condC, &d, &b)
+			return a.Equal(&b) && a.Equal(&c) && b.Equal(&c)
+		},
+		genA,
+		genB,
+		genC,
+		genZ,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+}
+
+func TestElementSetInt64(t *testing.T) {
+
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("z.SetInt64 must match z.SetString", prop.ForAll(
+		func(a testPairElement, v int64) bool {
+			c := a.element
+			d := a.element
+
+			c.SetInt64(v)
+			d.SetString(fmt.Sprintf("%v", v))
+
+			return c.Equal(&d)
+		},
+		genA, ggen.Int64(),
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+}
+
+func TestElementSetInterface(t *testing.T) {
+
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+	genInt := ggen.Int
+	genInt8 := ggen.Int8
+	genInt16 := ggen.Int16
+	genInt32 := ggen.Int32
+	genInt64 := ggen.Int64
+
+	genUint := ggen.UInt
+	genUint8 := ggen.UInt8
+	genUint16 := ggen.UInt16
+	genUint32 := ggen.UInt32
+	genUint64 := ggen.UInt64
+
+	properties.Property("z.SetInterface must match z.SetString with int8", prop.ForAll(
+		func(a testPairElement, v int8) bool {
+			c := a.element
+			d := a.element
+
+			c.SetInterface(v)
+			d.SetString(fmt.Sprintf("%v", v))
+
+			return c.Equal(&d)
+		},
+		genA, genInt8(),
+	))
+
+	properties.Property("z.SetInterface must match z.SetString with int16", prop.ForAll(
+		func(a testPairElement, v int16) bool {
+			c := a.element
+			d := a.element
+
+			c.SetInterface(v)
+			d.SetString(fmt.Sprintf("%v", v))
+
+			return c.Equal(&d)
+		},
+		genA, genInt16(),
+	))
+
+	properties.Property("z.SetInterface must match z.SetString with int32", prop.ForAll(
+		func(a testPairElement, v int32) bool {
+			c := a.element
+			d := a.element
+
+			c.SetInterface(v)
+			d.SetString(fmt.Sprintf("%v", v))
+
+			return c.Equal(&d)
+		},
+		genA, genInt32(),
+	))
+
+	properties.Property("z.SetInterface must match z.SetString with int64", prop.ForAll(
+		func(a testPairElement, v int64) bool {
+			c := a.element
+			d := a.element
+
+			c.SetInterface(v)
+			d.SetString(fmt.Sprintf("%v", v))
+
+			return c.Equal(&d)
+		},
+		genA, genInt64(),
+	))
+
+	properties.Property("z.SetInterface must match z.SetString with int", prop.ForAll(
+		func(a testPairElement, v int) bool {
+			c := a.element
+			d := a.element
+
+			c.SetInterface(v)
+			d.SetString(fmt.Sprintf("%v", v))
+
+			return c.Equal(&d)
+		},
+		genA, genInt(),
+	))
+
+	properties.Property("z.SetInterface must match z.SetString with uint8", prop.ForAll(
+		func(a testPairElement, v uint8) bool {
+			c := a.element
+			d := a.element
+
+			c.SetInterface(v)
+			d.SetString(fmt.Sprintf("%v", v))
+
+			return c.Equal(&d)
+		},
+		genA, genUint8(),
+	))
+
+	properties.Property("z.SetInterface must match z.SetString with uint16", prop.ForAll(
+		func(a testPairElement, v uint16) bool {
+			c := a.element
+			d := a.element
+
+			c.SetInterface(v)
+			d.SetString(fmt.Sprintf("%v", v))
+
+			return c.Equal(&d)
+		},
+		genA, genUint16(),
+	))
+
+	properties.Property("z.SetInterface must match z.SetString with uint32", prop.ForAll(
+		func(a testPairElement, v uint32) bool {
+			c := a.element
+			d := a.element
+
+			c.SetInterface(v)
+			d.SetString(fmt.Sprintf("%v", v))
+
+			return c.Equal(&d)
+		},
+		genA, genUint32(),
+	))
+
+	properties.Property("z.SetInterface must match z.SetString with uint64", prop.ForAll(
+		func(a testPairElement, v uint64) bool {
+			c := a.element
+			d := a.element
+
+			c.SetInterface(v)
+			d.SetString(fmt.Sprintf("%v", v))
+
+			return c.Equal(&d)
+		},
+		genA, genUint64(),
+	))
+
+	properties.Property("z.SetInterface must match z.SetString with uint", prop.ForAll(
+		func(a testPairElement, v uint) bool {
+			c := a.element
+			d := a.element
+
+			c.SetInterface(v)
+			d.SetString(fmt.Sprintf("%v", v))
+
+			return c.Equal(&d)
+		},
+		genA, genUint(),
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+
+	{
+		assert := require.New(t)
+		var e Element
+		r, err := e.SetInterface(nil)
+		assert.Nil(r)
+		assert.Error(err)
+
+		var ptE *Element
+		var ptB *big.Int
+
+		r, err = e.SetInterface(ptE)
+		assert.Nil(r)
+		assert.Error(err)
+		ptE = new(Element).SetOne()
+		r, err = e.SetInterface(ptE)
+		assert.NoError(err)
+		assert.True(r.IsOne())
+
+		r, err = e.SetInterface(ptB)
+		assert.Nil(r)
+		assert.Error(err)
+
+	}
+}
+
+func TestElementNegativeExp(t *testing.T) {
+	t.Parallel()
+
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("x⁻ᵏ == 1/xᵏ", prop.ForAll(
+		func(a, b testPairElement) bool {
+
+			var nb, d, e big.Int
+			nb.Neg(&b.bigint)
+
+			var c Element
+			c.Exp(a.element, &nb)
+
+			d.Exp(&a.bigint, &nb, Modulus())
+
+			return c.BigInt(&e).Cmp(&d) == 0
+		},
+		genA, genA,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+}
+
+func TestElementNewElement(t *testing.T) {
+	assert := require.New(t)
+
+	t.Parallel()
+
+	e := NewElement(1)
+	assert.True(e.IsOne())
+
+	e = NewElement(0)
+	assert.True(e.IsZero())
+}
+
+func TestElementBatchInvert(t *testing.T) {
+	assert := require.New(t)
+
+	t.Parallel()
+
+	// ensure batchInvert([x]) == invert(x)
+	for i := int64(-1); i <= 2; i++ {
+		var e, eInv Element
+		e.SetInt64(i)
+		eInv.Inverse(&e)
+
+		a := []Element{e}
+		aInv := BatchInvert(a)
+
+		assert.True(aInv[0].Equal(&eInv), "batchInvert != invert")
+
+	}
+
+	// test x * x⁻¹ == 1
+	tData := [][]int64{
+		{-1, 1, 2, 3},
+		{0, -1, 1, 2, 3, 0},
+		{0, -1, 1, 0, 2, 3, 0},
+		{-1, 1, 0, 2, 3},
+		{0, 0, 1},
+		{1, 0, 0},
+		{0, 0, 0},
+	}
+
+	for _, t := range tData {
+		a := make([]Element, len(t))
+		for i := 0; i < len(a); i++ {
+			a[i].SetInt64(t[i])
+		}
+
+		aInv := BatchInvert(a)
+
+		assert.True(len(aInv) == len(a))
+
+		for i := 0; i < len(a); i++ {
+			if a[i].IsZero() {
+				assert.True(aInv[i].IsZero(), "0⁻¹ != 0")
+			} else {
+				assert.True(a[i].Mul(&a[i], &aInv[i]).IsOne(), "x * x⁻¹ != 1")
+			}
+		}
+	}
+
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("batchInvert --> x * x⁻¹ == 1", prop.ForAll(
+		func(tp testPairElement, r uint8) bool {
+
+			a := make([]Element, r)
+			if r != 0 {
+				a[0] = tp.element
+
+			}
+			one := One()
+			for i := 1; i < len(a); i++ {
+				a[i].Add(&a[i-1], &one)
+			}
+
+			aInv := BatchInvert(a)
+
+			assert.True(len(aInv) == len(a))
+
+			for i := 0; i < len(a); i++ {
+				if a[i].IsZero() {
+					if !aInv[i].IsZero() {
+						return false
+					}
+				} else {
+					if !a[i].Mul(&a[i], &aInv[i]).IsOne() {
+						return false
+					}
+				}
+			}
+			return true
+		},
+		genA, ggen.UInt8(),
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+}
+
+func TestElementFromMont(t *testing.T) {
+
+	t.Parallel()
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = nbFuzzShort
+	} else {
+		parameters.MinSuccessfulTests = nbFuzz
+	}
+
+	properties := gopter.NewProperties(parameters)
+
+	genA := gen()
+
+	properties.Property("Assembly implementation must be consistent with generic one", prop.ForAll(
+		func(a testPairElement) bool {
+			c := a.element
+			d := a.element
+			c.fromMont()
+			_fromMontGeneric(&d)
+			return c.Equal(&d)
+		},
+		genA,
+	))
+
+	properties.Property("x.fromMont().toMont() == x", prop.ForAll(
+		func(a testPairElement) bool {
+			c := a.element
+			c.fromMont().toMont()
+			return c.Equal(&a.element)
+		},
+		genA,
+	))
+
+	properties.TestingRun(t, gopter.ConsoleReporter(false))
+}
+
+func TestElementJSON(t *testing.T) {
+	assert := require.New(t)
+
+	type S struct {
+		A Element
+		B [3]Element
+		C *Element
+		D *Element
+	}
+
+	// encode to JSON
+	var s S
+	s.A.SetString("-1")
+	s.B[2].SetUint64(42)
+	s.D = new(Element).SetUint64(8000)
+
+	encoded, err := json.Marshal(&s)
+	assert.NoError(err)
+	// we may need to adjust "42" and "8000" values for some moduli; see Text() method for more details.
+	formatValue := func(v int64) string {
+		var a big.Int
+		a.SetInt64(v)
+		a.Mod(&a, Modulus())
+		const maxUint16 = 65535
+		var aNeg big.Int
+		aNeg.Neg(&a).Mod(&aNeg, Modulus())
+		if aNeg.Uint64() != 0 && aNeg.Uint64() <= maxUint16 {
+			return "-" + aNeg.Text(10)
+		}
+		return a.Text(10)
+	}
+	expected := fmt.Sprintf("{\"A\":%s,\"B\":[0,0,%s],\"C\":null,\"D\":%s}", formatValue(-1), formatValue(42), formatValue(8000))
+	assert.Equal(expected, string(encoded))
+
+	// decode valid
+	var decoded S
+	err = json.Unmarshal([]byte(expected), &decoded)
+	assert.NoError(err)
+
+	assert.Equal(s, decoded, "element -> json -> element round trip failed")
+
+	// decode hex and string values
+	withHexValues := "{\"A\":\"-1\",\"B\":[0,\"0x00000\",\"0x2A\"],\"C\":null,\"D\":\"8000\"}"
+
+	var decodedS S
+	err = json.Unmarshal([]byte(withHexValues), &decodedS)
+	assert.NoError(err)
+
+	assert.Equal(s, decodedS, " json with strings  -> element  failed")
+
+}
+
+type testPairElement struct {
+	element Element
+	bigint  big.Int
+}
+
+func gen() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		var g testPairElement
+
+		g.element = Element{
+			uint32(genParams.NextUint64()),
+		}
+		if qElement[0] != ^uint32(0) {
+			g.element[0] %= (qElement[0] + 1)
+		}
+
+		for !g.element.smallerThanModulus() {
+			g.element = Element{
+				uint32(genParams.NextUint64()),
+			}
+			if qElement[0] != ^uint32(0) {
+				g.element[0] %= (qElement[0] + 1)
+			}
+		}
+
+		g.element.BigInt(&g.bigint)
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genRandomFq(genParams *gopter.GenParameters) Element {
+	var g Element
+
+	g = Element{
+		uint32(genParams.NextUint64()),
+	}
+
+	if qElement[0] != ^uint32(0) {
+		g[0] %= (qElement[0] + 1)
+	}
+
+	for !g.smallerThanModulus() {
+		g = Element{
+			uint32(genParams.NextUint64()),
+		}
+		if qElement[0] != ^uint32(0) {
+			g[0] %= (qElement[0] + 1)
+		}
+	}
+
+	return g
+}
+
+func genFull() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
+
+		var carry uint32
+		a[0], _ = bits.Add32(a[0], qElement[0], carry)
+
+		genResult := gopter.NewGenResult(a, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genElement() gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		a := genRandomFq(genParams)
+		genResult := gopter.NewGenResult(a, gopter.NoShrinker)
+		return genResult
+	}
+}
diff --git a/field/koalabear/vector.go b/field/koalabear/vector.go
new file mode 100644
index 0000000000..60fa5f6183
--- /dev/null
+++ b/field/koalabear/vector.go
@@ -0,0 +1,303 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package koalabear
+
+import (
+	"bytes"
+	"encoding/binary"
+	"fmt"
+	"io"
+	"runtime"
+	"strings"
+	"sync"
+	"sync/atomic"
+	"unsafe"
+)
+
+// Vector represents a slice of Element.
+//
+// It implements the following interfaces:
+//   - Stringer
+//   - io.WriterTo
+//   - io.ReaderFrom
+//   - encoding.BinaryMarshaler
+//   - encoding.BinaryUnmarshaler
+//   - sort.Interface
+type Vector []Element
+
+// MarshalBinary implements encoding.BinaryMarshaler
+func (vector *Vector) MarshalBinary() (data []byte, err error) {
+	var buf bytes.Buffer
+
+	if _, err = vector.WriteTo(&buf); err != nil {
+		return
+	}
+	return buf.Bytes(), nil
+}
+
+// UnmarshalBinary implements encoding.BinaryUnmarshaler
+func (vector *Vector) UnmarshalBinary(data []byte) error {
+	r := bytes.NewReader(data)
+	_, err := vector.ReadFrom(r)
+	return err
+}
+
+// WriteTo implements io.WriterTo and writes a vector of big endian encoded Element.
+// Length of the vector is encoded as a uint32 on the first 4 bytes.
+func (vector *Vector) WriteTo(w io.Writer) (int64, error) {
+	// encode slice length
+	if err := binary.Write(w, binary.BigEndian, uint32(len(*vector))); err != nil {
+		return 0, err
+	}
+
+	n := int64(4)
+
+	var buf [Bytes]byte
+	for i := 0; i < len(*vector); i++ {
+		BigEndian.PutElement(&buf, (*vector)[i])
+		m, err := w.Write(buf[:])
+		n += int64(m)
+		if err != nil {
+			return n, err
+		}
+	}
+	return n, nil
+}
+
+// AsyncReadFrom reads a vector of big endian encoded Element.
+// Length of the vector must be encoded as a uint32 on the first 4 bytes.
+// It consumes the needed bytes from the reader and returns the number of bytes read and an error if any.
+// It also returns a channel that will be closed when the validation is done.
+// The validation consist of checking that the elements are smaller than the modulus, and
+// converting them to montgomery form.
+func (vector *Vector) AsyncReadFrom(r io.Reader) (int64, error, chan error) {
+	chErr := make(chan error, 1)
+	var buf [Bytes]byte
+	if read, err := io.ReadFull(r, buf[:4]); err != nil {
+		close(chErr)
+		return int64(read), err, chErr
+	}
+	sliceLen := binary.BigEndian.Uint32(buf[:4])
+
+	n := int64(4)
+	(*vector) = make(Vector, sliceLen)
+	if sliceLen == 0 {
+		close(chErr)
+		return n, nil, chErr
+	}
+
+	bSlice := unsafe.Slice((*byte)(unsafe.Pointer(&(*vector)[0])), sliceLen*Bytes)
+	read, err := io.ReadFull(r, bSlice)
+	n += int64(read)
+	if err != nil {
+		close(chErr)
+		return n, err, chErr
+	}
+
+	go func() {
+		var cptErrors uint64
+		// process the elements in parallel
+		execute(int(sliceLen), func(start, end int) {
+
+			var z Element
+			for i := start; i < end; i++ {
+				// we have to set vector[i]
+				bstart := i * Bytes
+				bend := bstart + Bytes
+				b := bSlice[bstart:bend]
+				z[0] = binary.BigEndian.Uint32(b[0:4])
+
+				if !z.smallerThanModulus() {
+					atomic.AddUint64(&cptErrors, 1)
+					return
+				}
+				z.toMont()
+				(*vector)[i] = z
+			}
+		})
+
+		if cptErrors > 0 {
+			chErr <- fmt.Errorf("async read: %d elements failed validation", cptErrors)
+		}
+		close(chErr)
+	}()
+	return n, nil, chErr
+}
+
+// ReadFrom implements io.ReaderFrom and reads a vector of big endian encoded Element.
+// Length of the vector must be encoded as a uint32 on the first 4 bytes.
+func (vector *Vector) ReadFrom(r io.Reader) (int64, error) {
+
+	var buf [Bytes]byte
+	if read, err := io.ReadFull(r, buf[:4]); err != nil {
+		return int64(read), err
+	}
+	sliceLen := binary.BigEndian.Uint32(buf[:4])
+
+	n := int64(4)
+	(*vector) = make(Vector, sliceLen)
+
+	for i := 0; i < int(sliceLen); i++ {
+		read, err := io.ReadFull(r, buf[:])
+		n += int64(read)
+		if err != nil {
+			return n, err
+		}
+		(*vector)[i], err = BigEndian.Element(&buf)
+		if err != nil {
+			return n, err
+		}
+	}
+
+	return n, nil
+}
+
+// String implements fmt.Stringer interface
+func (vector Vector) String() string {
+	var sbb strings.Builder
+	sbb.WriteByte('[')
+	for i := 0; i < len(vector); i++ {
+		sbb.WriteString(vector[i].String())
+		if i != len(vector)-1 {
+			sbb.WriteByte(',')
+		}
+	}
+	sbb.WriteByte(']')
+	return sbb.String()
+}
+
+// Len is the number of elements in the collection.
+func (vector Vector) Len() int {
+	return len(vector)
+}
+
+// Less reports whether the element with
+// index i should sort before the element with index j.
+func (vector Vector) Less(i, j int) bool {
+	return vector[i].Cmp(&vector[j]) == -1
+}
+
+// Swap swaps the elements with indexes i and j.
+func (vector Vector) Swap(i, j int) {
+	vector[i], vector[j] = vector[j], vector[i]
+}
+
+func addVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Add: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Add(&a[i], &b[i])
+	}
+}
+
+func subVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Sub: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Sub(&a[i], &b[i])
+	}
+}
+
+func scalarMulVecGeneric(res, a Vector, b *Element) {
+	if len(a) != len(res) {
+		panic("vector.ScalarMul: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Mul(&a[i], b)
+	}
+}
+
+func sumVecGeneric(res *Element, a Vector) {
+	for i := 0; i < len(a); i++ {
+		res.Add(res, &a[i])
+	}
+}
+
+func innerProductVecGeneric(res *Element, a, b Vector) {
+	if len(a) != len(b) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	var tmp Element
+	for i := 0; i < len(a); i++ {
+		tmp.Mul(&a[i], &b[i])
+		res.Add(res, &tmp)
+	}
+}
+
+func mulVecGeneric(res, a, b Vector) {
+	if len(a) != len(b) || len(a) != len(res) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	for i := 0; i < len(a); i++ {
+		res[i].Mul(&a[i], &b[i])
+	}
+}
+
+// TODO @gbotrel make a public package out of that.
+// execute executes the work function in parallel.
+// this is copy paste from internal/parallel/parallel.go
+// as we don't want to generate code importing internal/
+func execute(nbIterations int, work func(int, int), maxCpus ...int) {
+
+	nbTasks := runtime.NumCPU()
+	if len(maxCpus) == 1 {
+		nbTasks = maxCpus[0]
+		if nbTasks < 1 {
+			nbTasks = 1
+		} else if nbTasks > 512 {
+			nbTasks = 512
+		}
+	}
+
+	if nbTasks == 1 {
+		// no go routines
+		work(0, nbIterations)
+		return
+	}
+
+	nbIterationsPerCpus := nbIterations / nbTasks
+
+	// more CPUs than tasks: a CPU will work on exactly one iteration
+	if nbIterationsPerCpus < 1 {
+		nbIterationsPerCpus = 1
+		nbTasks = nbIterations
+	}
+
+	var wg sync.WaitGroup
+
+	extraTasks := nbIterations - (nbTasks * nbIterationsPerCpus)
+	extraTasksOffset := 0
+
+	for i := 0; i < nbTasks; i++ {
+		wg.Add(1)
+		_start := i*nbIterationsPerCpus + extraTasksOffset
+		_end := _start + nbIterationsPerCpus
+		if extraTasks > 0 {
+			_end++
+			extraTasks--
+			extraTasksOffset++
+		}
+		go func() {
+			work(_start, _end)
+			wg.Done()
+		}()
+	}
+
+	wg.Wait()
+}
diff --git a/field/koalabear/vector_purego.go b/field/koalabear/vector_purego.go
new file mode 100644
index 0000000000..71dc2cc0c3
--- /dev/null
+++ b/field/koalabear/vector_purego.go
@@ -0,0 +1,54 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package koalabear
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	addVecGeneric(*vector, a, b)
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	subVecGeneric(*vector, a, b)
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	sumVecGeneric(&res, *vector)
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
diff --git a/field/koalabear/vector_test.go b/field/koalabear/vector_test.go
new file mode 100644
index 0000000000..b91728a8ac
--- /dev/null
+++ b/field/koalabear/vector_test.go
@@ -0,0 +1,365 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package koalabear
+
+import (
+	"bytes"
+	"fmt"
+	"github.com/stretchr/testify/require"
+	"os"
+	"reflect"
+	"sort"
+	"testing"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/prop"
+)
+
+func TestVectorSort(t *testing.T) {
+	assert := require.New(t)
+
+	v := make(Vector, 3)
+	v[0].SetUint64(2)
+	v[1].SetUint64(3)
+	v[2].SetUint64(1)
+
+	sort.Sort(v)
+
+	assert.Equal("[1,2,3]", v.String())
+}
+
+func TestVectorRoundTrip(t *testing.T) {
+	assert := require.New(t)
+
+	v1 := make(Vector, 3)
+	v1[0].SetUint64(2)
+	v1[1].SetUint64(3)
+	v1[2].SetUint64(1)
+
+	b, err := v1.MarshalBinary()
+	assert.NoError(err)
+
+	var v2, v3 Vector
+
+	err = v2.UnmarshalBinary(b)
+	assert.NoError(err)
+
+	err = v3.unmarshalBinaryAsync(b)
+	assert.NoError(err)
+
+	assert.True(reflect.DeepEqual(v1, v2))
+	assert.True(reflect.DeepEqual(v3, v2))
+}
+
+func TestVectorEmptyRoundTrip(t *testing.T) {
+	assert := require.New(t)
+
+	v1 := make(Vector, 0)
+
+	b, err := v1.MarshalBinary()
+	assert.NoError(err)
+
+	var v2, v3 Vector
+
+	err = v2.UnmarshalBinary(b)
+	assert.NoError(err)
+
+	err = v3.unmarshalBinaryAsync(b)
+	assert.NoError(err)
+
+	assert.True(reflect.DeepEqual(v1, v2))
+	assert.True(reflect.DeepEqual(v3, v2))
+}
+
+func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
+	r := bytes.NewReader(data)
+	_, err, chErr := vector.AsyncReadFrom(r)
+	if err != nil {
+		return err
+	}
+	return <-chErr
+}
+
+func TestVectorOps(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	if testing.Short() {
+		parameters.MinSuccessfulTests = 2
+	} else {
+		parameters.MinSuccessfulTests = 10
+	}
+	properties := gopter.NewProperties(parameters)
+
+	addVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Add(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Add(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	subVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		c.Sub(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Sub(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	scalarMulVector := func(a Vector, b Element) bool {
+		c := make(Vector, len(a))
+		c.ScalarMul(a, &b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b)
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sumVector := func(a Vector) bool {
+		var sum Element
+		computed := a.Sum()
+		for i := 0; i < len(a); i++ {
+			sum.Add(&sum, &a[i])
+		}
+
+		return sum.Equal(&computed)
+	}
+
+	innerProductVector := func(a, b Vector) bool {
+		computed := a.InnerProduct(b)
+		var innerProduct Element
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			innerProduct.Add(&innerProduct, &tmp)
+		}
+
+		return innerProduct.Equal(&computed)
+	}
+
+	mulVector := func(a, b Vector) bool {
+		c := make(Vector, len(a))
+		a[0].SetUint64(0x24)
+		b[0].SetUint64(0x42)
+		c.Mul(a, b)
+
+		for i := 0; i < len(a); i++ {
+			var tmp Element
+			tmp.Mul(&a[i], &b[i])
+			if !tmp.Equal(&c[i]) {
+				return false
+			}
+		}
+		return true
+	}
+
+	sizes := []int{1, 2, 3, 4, 8, 9, 15, 16, 509, 510, 511, 512, 513, 514}
+	type genPair struct {
+		g1, g2 gopter.Gen
+		label  string
+	}
+
+	for _, size := range sizes {
+		generators := []genPair{
+			{genZeroVector(size), genZeroVector(size), "zero vectors"},
+			{genMaxVector(size), genMaxVector(size), "max vectors"},
+			{genVector(size), genVector(size), "random vectors"},
+			{genVector(size), genZeroVector(size), "random and zero vectors"},
+		}
+		for _, gp := range generators {
+			properties.Property(fmt.Sprintf("vector addition %d - %s", size, gp.label), prop.ForAll(
+				addVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector subtraction %d - %s", size, gp.label), prop.ForAll(
+				subVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector scalar multiplication %d - %s", size, gp.label), prop.ForAll(
+				scalarMulVector,
+				gp.g1,
+				genElement(),
+			))
+
+			properties.Property(fmt.Sprintf("vector sum %d - %s", size, gp.label), prop.ForAll(
+				sumVector,
+				gp.g1,
+			))
+
+			properties.Property(fmt.Sprintf("vector inner product %d - %s", size, gp.label), prop.ForAll(
+				innerProductVector,
+				gp.g1,
+				gp.g2,
+			))
+
+			properties.Property(fmt.Sprintf("vector multiplication %d - %s", size, gp.label), prop.ForAll(
+				mulVector,
+				gp.g1,
+				gp.g2,
+			))
+		}
+	}
+
+	properties.TestingRun(t, gopter.NewFormatedReporter(false, 260, os.Stdout))
+}
+
+func BenchmarkVectorOps(b *testing.B) {
+	// note; to benchmark against "no asm" version, use the following
+	// build tag: -tags purego
+	const N = 1 << 24
+	a1 := make(Vector, N)
+	b1 := make(Vector, N)
+	c1 := make(Vector, N)
+	var mixer Element
+	mixer.SetRandom()
+	for i := 1; i < N; i++ {
+		a1[i-1].SetUint64(uint64(i)).
+			Mul(&a1[i-1], &mixer)
+		b1[i-1].SetUint64(^uint64(i)).
+			Mul(&b1[i-1], &mixer)
+	}
+
+	for n := 1 << 4; n <= N; n <<= 1 {
+		b.Run(fmt.Sprintf("add %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Add(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sub %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Sub(_a, _b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("scalarMul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.ScalarMul(_a, &mixer)
+			}
+		})
+
+		b.Run(fmt.Sprintf("sum %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.Sum()
+			}
+		})
+
+		b.Run(fmt.Sprintf("innerProduct %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = _a.InnerProduct(_b)
+			}
+		})
+
+		b.Run(fmt.Sprintf("mul %d", n), func(b *testing.B) {
+			_a := a1[:n]
+			_b := b1[:n]
+			_c := c1[:n]
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_c.Mul(_a, _b)
+			}
+		})
+	}
+}
+
+func genZeroVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genMaxVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+
+		qMinusOne := qElement
+		qMinusOne[0]--
+
+		for i := 0; i < size; i++ {
+			g[i] = qMinusOne
+		}
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}
+
+func genVector(size int) gopter.Gen {
+	return func(genParams *gopter.GenParameters) *gopter.GenResult {
+		g := make(Vector, size)
+		mixer := Element{
+			uint32(genParams.NextUint64()),
+		}
+		if qElement[0] != ^uint32(0) {
+			mixer[0] %= (qElement[0] + 1)
+		}
+
+		for !mixer.smallerThanModulus() {
+			mixer = Element{
+				uint32(genParams.NextUint64()),
+			}
+			if qElement[0] != ^uint32(0) {
+				mixer[0] %= (qElement[0] + 1)
+			}
+		}
+
+		for i := 1; i <= size; i++ {
+			g[i-1].SetUint64(uint64(i)).
+				Mul(&g[i-1], &mixer)
+		}
+
+		genResult := gopter.NewGenResult(g, gopter.NoShrinker)
+		return genResult
+	}
+}

From 19b6b55168c2ae7dfe57566ef9296afa3a1cf8e8 Mon Sep 17 00:00:00 2001
From: Gautam Botrel <gautam.botrel@gmail.com>
Date: Tue, 10 Dec 2024 13:13:55 -0600
Subject: [PATCH 092/114] docs: less verbose Apache 2 header, latest bavard
 (#570)

---
 ecc/bls12-377/ecdsa/doc.go                        | 13 +------------
 ecc/bls12-377/ecdsa/ecdsa.go                      | 13 +------------
 ecc/bls12-377/ecdsa/ecdsa_test.go                 | 13 +------------
 ecc/bls12-377/ecdsa/marshal.go                    | 13 +------------
 ecc/bls12-377/ecdsa/marshal_test.go               | 13 +------------
 ecc/bls12-377/fflonk/doc.go                       | 13 +------------
 ecc/bls12-377/fflonk/example_test.go              | 13 +------------
 ecc/bls12-377/fflonk/fflonk.go                    | 13 +------------
 ecc/bls12-377/fflonk/fflonk_test.go               | 13 +------------
 ecc/bls12-377/fflonk/marshal.go                   | 13 +------------
 ecc/bls12-377/fp/arith.go                         | 15 ++-------------
 ecc/bls12-377/fp/asm_adx.go                       | 15 ++-------------
 ecc/bls12-377/fp/asm_noadx.go                     | 15 ++-------------
 ecc/bls12-377/fp/doc.go                           | 15 ++-------------
 ecc/bls12-377/fp/element.go                       | 15 ++-------------
 ecc/bls12-377/fp/element_amd64.go                 | 15 ++-------------
 ecc/bls12-377/fp/element_amd64.s                  | 15 ++-------------
 ecc/bls12-377/fp/element_arm64.go                 | 15 ++-------------
 ecc/bls12-377/fp/element_arm64.s                  | 15 ++-------------
 ecc/bls12-377/fp/element_exp.go                   | 15 ++-------------
 ecc/bls12-377/fp/element_purego.go                | 15 ++-------------
 ecc/bls12-377/fp/element_test.go                  | 15 ++-------------
 ecc/bls12-377/fp/hash_to_field/doc.go             | 13 +------------
 ecc/bls12-377/fp/hash_to_field/hash_to_field.go   | 13 +------------
 .../fp/hash_to_field/hash_to_field_test.go        | 13 +------------
 ecc/bls12-377/fp/vector.go                        | 15 ++-------------
 ecc/bls12-377/fp/vector_purego.go                 | 15 ++-------------
 ecc/bls12-377/fp/vector_test.go                   | 15 ++-------------
 ecc/bls12-377/fr/arith.go                         | 15 ++-------------
 ecc/bls12-377/fr/asm_adx.go                       | 15 ++-------------
 ecc/bls12-377/fr/asm_avx.go                       | 15 ++-------------
 ecc/bls12-377/fr/asm_noadx.go                     | 15 ++-------------
 ecc/bls12-377/fr/asm_noavx.go                     | 15 ++-------------
 ecc/bls12-377/fr/doc.go                           | 15 ++-------------
 ecc/bls12-377/fr/element.go                       | 15 ++-------------
 ecc/bls12-377/fr/element_amd64.go                 | 15 ++-------------
 ecc/bls12-377/fr/element_amd64.s                  | 15 ++-------------
 ecc/bls12-377/fr/element_arm64.go                 | 15 ++-------------
 ecc/bls12-377/fr/element_arm64.s                  | 15 ++-------------
 ecc/bls12-377/fr/element_exp.go                   | 15 ++-------------
 ecc/bls12-377/fr/element_purego.go                | 15 ++-------------
 ecc/bls12-377/fr/element_test.go                  | 15 ++-------------
 ecc/bls12-377/fr/fft/bitreverse.go                | 13 +------------
 ecc/bls12-377/fr/fft/bitreverse_test.go           | 13 +------------
 ecc/bls12-377/fr/fft/doc.go                       | 13 +------------
 ecc/bls12-377/fr/fft/domain.go                    | 13 +------------
 ecc/bls12-377/fr/fft/domain_test.go               | 13 +------------
 ecc/bls12-377/fr/fft/fft.go                       | 13 +------------
 ecc/bls12-377/fr/fft/fft_test.go                  | 13 +------------
 ecc/bls12-377/fr/fft/options.go                   | 13 +------------
 ecc/bls12-377/fr/fri/doc.go                       | 13 +------------
 ecc/bls12-377/fr/fri/fri.go                       | 13 +------------
 ecc/bls12-377/fr/fri/fri_test.go                  | 13 +------------
 ecc/bls12-377/fr/generator.go                     | 13 +------------
 ecc/bls12-377/fr/gkr/gkr.go                       | 13 +------------
 ecc/bls12-377/fr/gkr/gkr_test.go                  | 13 +------------
 ecc/bls12-377/fr/hash_to_field/doc.go             | 13 +------------
 ecc/bls12-377/fr/hash_to_field/hash_to_field.go   | 13 +------------
 .../fr/hash_to_field/hash_to_field_test.go        | 13 +------------
 ecc/bls12-377/fr/iop/doc.go                       | 13 +------------
 ecc/bls12-377/fr/iop/expressions.go               | 13 +------------
 ecc/bls12-377/fr/iop/expressions_test.go          | 13 +------------
 ecc/bls12-377/fr/iop/polynomial.go                | 13 +------------
 ecc/bls12-377/fr/iop/polynomial_test.go           | 13 +------------
 ecc/bls12-377/fr/iop/quotient.go                  | 13 +------------
 ecc/bls12-377/fr/iop/quotient_test.go             | 13 +------------
 ecc/bls12-377/fr/iop/ratios.go                    | 13 +------------
 ecc/bls12-377/fr/iop/ratios_test.go               | 13 +------------
 ecc/bls12-377/fr/iop/utils.go                     | 13 +------------
 ecc/bls12-377/fr/mimc/doc.go                      | 13 +------------
 ecc/bls12-377/fr/mimc/mimc.go                     | 13 +------------
 ecc/bls12-377/fr/mimc/options.go                  | 13 +------------
 ecc/bls12-377/fr/pedersen/doc.go                  | 13 +------------
 ecc/bls12-377/fr/pedersen/example_test.go         | 13 +------------
 ecc/bls12-377/fr/pedersen/pedersen.go             | 13 +------------
 ecc/bls12-377/fr/pedersen/pedersen_test.go        | 13 +------------
 ecc/bls12-377/fr/permutation/doc.go               | 13 +------------
 ecc/bls12-377/fr/permutation/permutation.go       | 13 +------------
 ecc/bls12-377/fr/permutation/permutation_test.go  | 13 +------------
 ecc/bls12-377/fr/plookup/doc.go                   | 13 +------------
 ecc/bls12-377/fr/plookup/plookup_test.go          | 13 +------------
 ecc/bls12-377/fr/plookup/table.go                 | 13 +------------
 ecc/bls12-377/fr/plookup/vector.go                | 13 +------------
 ecc/bls12-377/fr/polynomial/doc.go                | 13 +------------
 ecc/bls12-377/fr/polynomial/multilin.go           | 13 +------------
 ecc/bls12-377/fr/polynomial/multilin_test.go      | 13 +------------
 ecc/bls12-377/fr/polynomial/polynomial.go         | 13 +------------
 ecc/bls12-377/fr/polynomial/polynomial_test.go    | 13 +------------
 ecc/bls12-377/fr/polynomial/pool.go               | 13 +------------
 ecc/bls12-377/fr/poseidon2/poseidon2.go           | 13 +------------
 ecc/bls12-377/fr/poseidon2/poseidon2_test.go      | 13 +------------
 ecc/bls12-377/fr/sis/sis_fft.go                   | 13 +------------
 ecc/bls12-377/fr/sumcheck/sumcheck.go             | 13 +------------
 ecc/bls12-377/fr/sumcheck/sumcheck_test.go        | 13 +------------
 .../fr/test_vector_utils/test_vector_utils.go     | 13 +------------
 ecc/bls12-377/fr/vector.go                        | 15 ++-------------
 ecc/bls12-377/fr/vector_amd64.go                  | 15 ++-------------
 ecc/bls12-377/fr/vector_purego.go                 | 15 ++-------------
 ecc/bls12-377/fr/vector_test.go                   | 15 ++-------------
 ecc/bls12-377/g1.go                               | 13 +------------
 ecc/bls12-377/g1_test.go                          | 13 +------------
 ecc/bls12-377/g2.go                               | 13 +------------
 ecc/bls12-377/g2_test.go                          | 13 +------------
 ecc/bls12-377/hash_to_g1.go                       | 13 +------------
 ecc/bls12-377/hash_to_g1_test.go                  | 13 +------------
 ecc/bls12-377/hash_to_g2.go                       | 13 +------------
 ecc/bls12-377/hash_to_g2_test.go                  | 13 +------------
 ecc/bls12-377/internal/fptower/asm.go             | 13 +------------
 ecc/bls12-377/internal/fptower/asm_noadx.go       | 13 +------------
 ecc/bls12-377/internal/fptower/e12.go             | 13 +------------
 ecc/bls12-377/internal/fptower/e12_test.go        | 13 +------------
 ecc/bls12-377/internal/fptower/e2.go              | 13 +------------
 ecc/bls12-377/internal/fptower/e2_amd64.go        | 13 +------------
 ecc/bls12-377/internal/fptower/e2_amd64.s         | 13 +------------
 ecc/bls12-377/internal/fptower/e2_fallback.go     | 13 +------------
 ecc/bls12-377/internal/fptower/e2_test.go         | 13 +------------
 ecc/bls12-377/internal/fptower/e6.go              | 13 +------------
 ecc/bls12-377/internal/fptower/e6_test.go         | 13 +------------
 ecc/bls12-377/kzg/doc.go                          | 13 +------------
 ecc/bls12-377/kzg/kzg.go                          | 13 +------------
 ecc/bls12-377/kzg/kzg_test.go                     | 13 +------------
 ecc/bls12-377/kzg/marshal.go                      | 13 +------------
 ecc/bls12-377/kzg/utils.go                        | 13 +------------
 ecc/bls12-377/marshal.go                          | 13 +------------
 ecc/bls12-377/marshal_test.go                     | 13 +------------
 ecc/bls12-377/multiexp.go                         | 13 +------------
 ecc/bls12-377/multiexp_affine.go                  | 13 +------------
 ecc/bls12-377/multiexp_jacobian.go                | 13 +------------
 ecc/bls12-377/multiexp_test.go                    | 13 +------------
 ecc/bls12-377/pairing_test.go                     | 13 +------------
 ecc/bls12-377/shplonk/doc.go                      | 13 +------------
 ecc/bls12-377/shplonk/example_test.go             | 13 +------------
 ecc/bls12-377/shplonk/marshal.go                  | 13 +------------
 ecc/bls12-377/shplonk/shplonk.go                  | 13 +------------
 ecc/bls12-377/shplonk/shplonk_test.go             | 13 +------------
 ecc/bls12-377/twistededwards/curve.go             | 13 +------------
 ecc/bls12-377/twistededwards/doc.go               | 13 +------------
 ecc/bls12-377/twistededwards/eddsa/doc.go         | 13 +------------
 ecc/bls12-377/twistededwards/eddsa/eddsa.go       | 13 +------------
 ecc/bls12-377/twistededwards/eddsa/eddsa_test.go  | 13 +------------
 ecc/bls12-377/twistededwards/eddsa/marshal.go     | 13 +------------
 ecc/bls12-377/twistededwards/point.go             | 13 +------------
 ecc/bls12-377/twistededwards/point_test.go        | 13 +------------
 ecc/bls12-381/bandersnatch/curve.go               | 13 +------------
 ecc/bls12-381/bandersnatch/doc.go                 | 13 +------------
 ecc/bls12-381/bandersnatch/eddsa/doc.go           | 13 +------------
 ecc/bls12-381/bandersnatch/eddsa/eddsa.go         | 13 +------------
 ecc/bls12-381/bandersnatch/eddsa/eddsa_test.go    | 13 +------------
 ecc/bls12-381/bandersnatch/eddsa/marshal.go       | 13 +------------
 ecc/bls12-381/bandersnatch/point.go               | 13 +------------
 ecc/bls12-381/bandersnatch/point_test.go          | 13 +------------
 ecc/bls12-381/ecdsa/doc.go                        | 13 +------------
 ecc/bls12-381/ecdsa/ecdsa.go                      | 13 +------------
 ecc/bls12-381/ecdsa/ecdsa_test.go                 | 13 +------------
 ecc/bls12-381/ecdsa/marshal.go                    | 13 +------------
 ecc/bls12-381/ecdsa/marshal_test.go               | 13 +------------
 ecc/bls12-381/fflonk/doc.go                       | 13 +------------
 ecc/bls12-381/fflonk/example_test.go              | 13 +------------
 ecc/bls12-381/fflonk/fflonk.go                    | 13 +------------
 ecc/bls12-381/fflonk/fflonk_test.go               | 13 +------------
 ecc/bls12-381/fflonk/marshal.go                   | 13 +------------
 ecc/bls12-381/fp/arith.go                         | 15 ++-------------
 ecc/bls12-381/fp/asm_adx.go                       | 15 ++-------------
 ecc/bls12-381/fp/asm_noadx.go                     | 15 ++-------------
 ecc/bls12-381/fp/doc.go                           | 15 ++-------------
 ecc/bls12-381/fp/element.go                       | 15 ++-------------
 ecc/bls12-381/fp/element_amd64.go                 | 15 ++-------------
 ecc/bls12-381/fp/element_amd64.s                  | 15 ++-------------
 ecc/bls12-381/fp/element_arm64.go                 | 15 ++-------------
 ecc/bls12-381/fp/element_arm64.s                  | 15 ++-------------
 ecc/bls12-381/fp/element_exp.go                   | 15 ++-------------
 ecc/bls12-381/fp/element_purego.go                | 15 ++-------------
 ecc/bls12-381/fp/element_test.go                  | 15 ++-------------
 ecc/bls12-381/fp/hash_to_field/doc.go             | 13 +------------
 ecc/bls12-381/fp/hash_to_field/hash_to_field.go   | 13 +------------
 .../fp/hash_to_field/hash_to_field_test.go        | 13 +------------
 ecc/bls12-381/fp/vector.go                        | 15 ++-------------
 ecc/bls12-381/fp/vector_purego.go                 | 15 ++-------------
 ecc/bls12-381/fp/vector_test.go                   | 15 ++-------------
 ecc/bls12-381/fr/arith.go                         | 15 ++-------------
 ecc/bls12-381/fr/asm_adx.go                       | 15 ++-------------
 ecc/bls12-381/fr/asm_avx.go                       | 15 ++-------------
 ecc/bls12-381/fr/asm_noadx.go                     | 15 ++-------------
 ecc/bls12-381/fr/asm_noavx.go                     | 15 ++-------------
 ecc/bls12-381/fr/doc.go                           | 15 ++-------------
 ecc/bls12-381/fr/element.go                       | 15 ++-------------
 ecc/bls12-381/fr/element_amd64.go                 | 15 ++-------------
 ecc/bls12-381/fr/element_amd64.s                  | 15 ++-------------
 ecc/bls12-381/fr/element_arm64.go                 | 15 ++-------------
 ecc/bls12-381/fr/element_arm64.s                  | 15 ++-------------
 ecc/bls12-381/fr/element_exp.go                   | 15 ++-------------
 ecc/bls12-381/fr/element_purego.go                | 15 ++-------------
 ecc/bls12-381/fr/element_test.go                  | 15 ++-------------
 ecc/bls12-381/fr/fft/bitreverse.go                | 13 +------------
 ecc/bls12-381/fr/fft/bitreverse_test.go           | 13 +------------
 ecc/bls12-381/fr/fft/doc.go                       | 13 +------------
 ecc/bls12-381/fr/fft/domain.go                    | 13 +------------
 ecc/bls12-381/fr/fft/domain_test.go               | 13 +------------
 ecc/bls12-381/fr/fft/fft.go                       | 13 +------------
 ecc/bls12-381/fr/fft/fft_test.go                  | 13 +------------
 ecc/bls12-381/fr/fft/options.go                   | 13 +------------
 ecc/bls12-381/fr/fri/doc.go                       | 13 +------------
 ecc/bls12-381/fr/fri/fri.go                       | 13 +------------
 ecc/bls12-381/fr/fri/fri_test.go                  | 13 +------------
 ecc/bls12-381/fr/generator.go                     | 13 +------------
 ecc/bls12-381/fr/gkr/gkr.go                       | 13 +------------
 ecc/bls12-381/fr/gkr/gkr_test.go                  | 13 +------------
 ecc/bls12-381/fr/hash_to_field/doc.go             | 13 +------------
 ecc/bls12-381/fr/hash_to_field/hash_to_field.go   | 13 +------------
 .../fr/hash_to_field/hash_to_field_test.go        | 13 +------------
 ecc/bls12-381/fr/iop/doc.go                       | 13 +------------
 ecc/bls12-381/fr/iop/expressions.go               | 13 +------------
 ecc/bls12-381/fr/iop/expressions_test.go          | 13 +------------
 ecc/bls12-381/fr/iop/polynomial.go                | 13 +------------
 ecc/bls12-381/fr/iop/polynomial_test.go           | 13 +------------
 ecc/bls12-381/fr/iop/quotient.go                  | 13 +------------
 ecc/bls12-381/fr/iop/quotient_test.go             | 13 +------------
 ecc/bls12-381/fr/iop/ratios.go                    | 13 +------------
 ecc/bls12-381/fr/iop/ratios_test.go               | 13 +------------
 ecc/bls12-381/fr/iop/utils.go                     | 13 +------------
 ecc/bls12-381/fr/mimc/doc.go                      | 13 +------------
 ecc/bls12-381/fr/mimc/mimc.go                     | 13 +------------
 ecc/bls12-381/fr/mimc/options.go                  | 13 +------------
 ecc/bls12-381/fr/pedersen/doc.go                  | 13 +------------
 ecc/bls12-381/fr/pedersen/example_test.go         | 13 +------------
 ecc/bls12-381/fr/pedersen/pedersen.go             | 13 +------------
 ecc/bls12-381/fr/pedersen/pedersen_test.go        | 13 +------------
 ecc/bls12-381/fr/permutation/doc.go               | 13 +------------
 ecc/bls12-381/fr/permutation/permutation.go       | 13 +------------
 ecc/bls12-381/fr/permutation/permutation_test.go  | 13 +------------
 ecc/bls12-381/fr/plookup/doc.go                   | 13 +------------
 ecc/bls12-381/fr/plookup/plookup_test.go          | 13 +------------
 ecc/bls12-381/fr/plookup/table.go                 | 13 +------------
 ecc/bls12-381/fr/plookup/vector.go                | 13 +------------
 ecc/bls12-381/fr/polynomial/doc.go                | 13 +------------
 ecc/bls12-381/fr/polynomial/multilin.go           | 13 +------------
 ecc/bls12-381/fr/polynomial/multilin_test.go      | 13 +------------
 ecc/bls12-381/fr/polynomial/polynomial.go         | 13 +------------
 ecc/bls12-381/fr/polynomial/polynomial_test.go    | 13 +------------
 ecc/bls12-381/fr/polynomial/pool.go               | 13 +------------
 ecc/bls12-381/fr/poseidon2/poseidon2.go           | 13 +------------
 ecc/bls12-381/fr/poseidon2/poseidon2_test.go      | 13 +------------
 ecc/bls12-381/fr/sumcheck/sumcheck.go             | 13 +------------
 ecc/bls12-381/fr/sumcheck/sumcheck_test.go        | 13 +------------
 .../fr/test_vector_utils/test_vector_utils.go     | 13 +------------
 ecc/bls12-381/fr/vector.go                        | 15 ++-------------
 ecc/bls12-381/fr/vector_amd64.go                  | 15 ++-------------
 ecc/bls12-381/fr/vector_purego.go                 | 15 ++-------------
 ecc/bls12-381/fr/vector_test.go                   | 15 ++-------------
 ecc/bls12-381/g1.go                               | 13 +------------
 ecc/bls12-381/g1_test.go                          | 13 +------------
 ecc/bls12-381/g2.go                               | 13 +------------
 ecc/bls12-381/g2_test.go                          | 13 +------------
 ecc/bls12-381/hash_to_g1.go                       | 13 +------------
 ecc/bls12-381/hash_to_g1_test.go                  | 13 +------------
 ecc/bls12-381/hash_to_g2.go                       | 13 +------------
 ecc/bls12-381/hash_to_g2_test.go                  | 13 +------------
 ecc/bls12-381/internal/fptower/asm.go             | 13 +------------
 ecc/bls12-381/internal/fptower/asm_noadx.go       | 13 +------------
 ecc/bls12-381/internal/fptower/e12.go             | 13 +------------
 ecc/bls12-381/internal/fptower/e12_test.go        | 13 +------------
 ecc/bls12-381/internal/fptower/e2.go              | 13 +------------
 ecc/bls12-381/internal/fptower/e2_amd64.go        | 13 +------------
 ecc/bls12-381/internal/fptower/e2_amd64.s         | 13 +------------
 ecc/bls12-381/internal/fptower/e2_fallback.go     | 13 +------------
 ecc/bls12-381/internal/fptower/e2_test.go         | 13 +------------
 ecc/bls12-381/internal/fptower/e6.go              | 13 +------------
 ecc/bls12-381/internal/fptower/e6_test.go         | 13 +------------
 ecc/bls12-381/kzg/doc.go                          | 13 +------------
 ecc/bls12-381/kzg/kzg.go                          | 13 +------------
 ecc/bls12-381/kzg/kzg_test.go                     | 13 +------------
 ecc/bls12-381/kzg/marshal.go                      | 13 +------------
 ecc/bls12-381/kzg/utils.go                        | 13 +------------
 ecc/bls12-381/marshal.go                          | 13 +------------
 ecc/bls12-381/marshal_test.go                     | 13 +------------
 ecc/bls12-381/multiexp.go                         | 13 +------------
 ecc/bls12-381/multiexp_affine.go                  | 13 +------------
 ecc/bls12-381/multiexp_jacobian.go                | 13 +------------
 ecc/bls12-381/multiexp_test.go                    | 13 +------------
 ecc/bls12-381/pairing_test.go                     | 13 +------------
 ecc/bls12-381/shplonk/doc.go                      | 13 +------------
 ecc/bls12-381/shplonk/example_test.go             | 13 +------------
 ecc/bls12-381/shplonk/marshal.go                  | 13 +------------
 ecc/bls12-381/shplonk/shplonk.go                  | 13 +------------
 ecc/bls12-381/shplonk/shplonk_test.go             | 13 +------------
 ecc/bls12-381/twistededwards/curve.go             | 13 +------------
 ecc/bls12-381/twistededwards/doc.go               | 13 +------------
 ecc/bls12-381/twistededwards/eddsa/doc.go         | 13 +------------
 ecc/bls12-381/twistededwards/eddsa/eddsa.go       | 13 +------------
 ecc/bls12-381/twistededwards/eddsa/eddsa_test.go  | 13 +------------
 ecc/bls12-381/twistededwards/eddsa/marshal.go     | 13 +------------
 ecc/bls12-381/twistededwards/point.go             | 13 +------------
 ecc/bls12-381/twistededwards/point_test.go        | 13 +------------
 ecc/bls24-315/ecdsa/doc.go                        | 13 +------------
 ecc/bls24-315/ecdsa/ecdsa.go                      | 13 +------------
 ecc/bls24-315/ecdsa/ecdsa_test.go                 | 13 +------------
 ecc/bls24-315/ecdsa/marshal.go                    | 13 +------------
 ecc/bls24-315/ecdsa/marshal_test.go               | 13 +------------
 ecc/bls24-315/fflonk/doc.go                       | 13 +------------
 ecc/bls24-315/fflonk/example_test.go              | 13 +------------
 ecc/bls24-315/fflonk/fflonk.go                    | 13 +------------
 ecc/bls24-315/fflonk/fflonk_test.go               | 13 +------------
 ecc/bls24-315/fflonk/marshal.go                   | 13 +------------
 ecc/bls24-315/fp/arith.go                         | 15 ++-------------
 ecc/bls24-315/fp/asm_adx.go                       | 15 ++-------------
 ecc/bls24-315/fp/asm_noadx.go                     | 15 ++-------------
 ecc/bls24-315/fp/doc.go                           | 15 ++-------------
 ecc/bls24-315/fp/element.go                       | 15 ++-------------
 ecc/bls24-315/fp/element_amd64.go                 | 15 ++-------------
 ecc/bls24-315/fp/element_amd64.s                  | 15 ++-------------
 ecc/bls24-315/fp/element_exp.go                   | 15 ++-------------
 ecc/bls24-315/fp/element_purego.go                | 15 ++-------------
 ecc/bls24-315/fp/element_test.go                  | 15 ++-------------
 ecc/bls24-315/fp/hash_to_field/doc.go             | 13 +------------
 ecc/bls24-315/fp/hash_to_field/hash_to_field.go   | 13 +------------
 .../fp/hash_to_field/hash_to_field_test.go        | 13 +------------
 ecc/bls24-315/fp/vector.go                        | 15 ++-------------
 ecc/bls24-315/fp/vector_purego.go                 | 15 ++-------------
 ecc/bls24-315/fp/vector_test.go                   | 15 ++-------------
 ecc/bls24-315/fr/arith.go                         | 15 ++-------------
 ecc/bls24-315/fr/asm_adx.go                       | 15 ++-------------
 ecc/bls24-315/fr/asm_avx.go                       | 15 ++-------------
 ecc/bls24-315/fr/asm_noadx.go                     | 15 ++-------------
 ecc/bls24-315/fr/asm_noavx.go                     | 15 ++-------------
 ecc/bls24-315/fr/doc.go                           | 15 ++-------------
 ecc/bls24-315/fr/element.go                       | 15 ++-------------
 ecc/bls24-315/fr/element_amd64.go                 | 15 ++-------------
 ecc/bls24-315/fr/element_amd64.s                  | 15 ++-------------
 ecc/bls24-315/fr/element_arm64.go                 | 15 ++-------------
 ecc/bls24-315/fr/element_arm64.s                  | 15 ++-------------
 ecc/bls24-315/fr/element_exp.go                   | 15 ++-------------
 ecc/bls24-315/fr/element_purego.go                | 15 ++-------------
 ecc/bls24-315/fr/element_test.go                  | 15 ++-------------
 ecc/bls24-315/fr/fft/bitreverse.go                | 13 +------------
 ecc/bls24-315/fr/fft/bitreverse_test.go           | 13 +------------
 ecc/bls24-315/fr/fft/doc.go                       | 13 +------------
 ecc/bls24-315/fr/fft/domain.go                    | 13 +------------
 ecc/bls24-315/fr/fft/domain_test.go               | 13 +------------
 ecc/bls24-315/fr/fft/fft.go                       | 13 +------------
 ecc/bls24-315/fr/fft/fft_test.go                  | 13 +------------
 ecc/bls24-315/fr/fft/options.go                   | 13 +------------
 ecc/bls24-315/fr/fri/doc.go                       | 13 +------------
 ecc/bls24-315/fr/fri/fri.go                       | 13 +------------
 ecc/bls24-315/fr/fri/fri_test.go                  | 13 +------------
 ecc/bls24-315/fr/generator.go                     | 13 +------------
 ecc/bls24-315/fr/gkr/gkr.go                       | 13 +------------
 ecc/bls24-315/fr/gkr/gkr_test.go                  | 13 +------------
 ecc/bls24-315/fr/hash_to_field/doc.go             | 13 +------------
 ecc/bls24-315/fr/hash_to_field/hash_to_field.go   | 13 +------------
 .../fr/hash_to_field/hash_to_field_test.go        | 13 +------------
 ecc/bls24-315/fr/iop/doc.go                       | 13 +------------
 ecc/bls24-315/fr/iop/expressions.go               | 13 +------------
 ecc/bls24-315/fr/iop/expressions_test.go          | 13 +------------
 ecc/bls24-315/fr/iop/polynomial.go                | 13 +------------
 ecc/bls24-315/fr/iop/polynomial_test.go           | 13 +------------
 ecc/bls24-315/fr/iop/quotient.go                  | 13 +------------
 ecc/bls24-315/fr/iop/quotient_test.go             | 13 +------------
 ecc/bls24-315/fr/iop/ratios.go                    | 13 +------------
 ecc/bls24-315/fr/iop/ratios_test.go               | 13 +------------
 ecc/bls24-315/fr/iop/utils.go                     | 13 +------------
 ecc/bls24-315/fr/mimc/doc.go                      | 13 +------------
 ecc/bls24-315/fr/mimc/mimc.go                     | 13 +------------
 ecc/bls24-315/fr/mimc/options.go                  | 13 +------------
 ecc/bls24-315/fr/pedersen/doc.go                  | 13 +------------
 ecc/bls24-315/fr/pedersen/example_test.go         | 13 +------------
 ecc/bls24-315/fr/pedersen/pedersen.go             | 13 +------------
 ecc/bls24-315/fr/pedersen/pedersen_test.go        | 13 +------------
 ecc/bls24-315/fr/permutation/doc.go               | 13 +------------
 ecc/bls24-315/fr/permutation/permutation.go       | 13 +------------
 ecc/bls24-315/fr/permutation/permutation_test.go  | 13 +------------
 ecc/bls24-315/fr/plookup/doc.go                   | 13 +------------
 ecc/bls24-315/fr/plookup/plookup_test.go          | 13 +------------
 ecc/bls24-315/fr/plookup/table.go                 | 13 +------------
 ecc/bls24-315/fr/plookup/vector.go                | 13 +------------
 ecc/bls24-315/fr/polynomial/doc.go                | 13 +------------
 ecc/bls24-315/fr/polynomial/multilin.go           | 13 +------------
 ecc/bls24-315/fr/polynomial/multilin_test.go      | 13 +------------
 ecc/bls24-315/fr/polynomial/polynomial.go         | 13 +------------
 ecc/bls24-315/fr/polynomial/polynomial_test.go    | 13 +------------
 ecc/bls24-315/fr/polynomial/pool.go               | 13 +------------
 ecc/bls24-315/fr/poseidon2/poseidon2.go           | 13 +------------
 ecc/bls24-315/fr/poseidon2/poseidon2_test.go      | 13 +------------
 ecc/bls24-315/fr/sumcheck/sumcheck.go             | 13 +------------
 ecc/bls24-315/fr/sumcheck/sumcheck_test.go        | 13 +------------
 .../fr/test_vector_utils/test_vector_utils.go     | 13 +------------
 ecc/bls24-315/fr/vector.go                        | 15 ++-------------
 ecc/bls24-315/fr/vector_amd64.go                  | 15 ++-------------
 ecc/bls24-315/fr/vector_purego.go                 | 15 ++-------------
 ecc/bls24-315/fr/vector_test.go                   | 15 ++-------------
 ecc/bls24-315/g1.go                               | 13 +------------
 ecc/bls24-315/g1_test.go                          | 13 +------------
 ecc/bls24-315/g2.go                               | 13 +------------
 ecc/bls24-315/g2_test.go                          | 13 +------------
 ecc/bls24-315/hash_to_g1.go                       | 13 +------------
 ecc/bls24-315/hash_to_g1_test.go                  | 13 +------------
 ecc/bls24-315/kzg/doc.go                          | 13 +------------
 ecc/bls24-315/kzg/kzg.go                          | 13 +------------
 ecc/bls24-315/kzg/kzg_test.go                     | 13 +------------
 ecc/bls24-315/kzg/marshal.go                      | 13 +------------
 ecc/bls24-315/kzg/utils.go                        | 13 +------------
 ecc/bls24-315/marshal.go                          | 13 +------------
 ecc/bls24-315/marshal_test.go                     | 13 +------------
 ecc/bls24-315/multiexp.go                         | 13 +------------
 ecc/bls24-315/multiexp_affine.go                  | 13 +------------
 ecc/bls24-315/multiexp_jacobian.go                | 13 +------------
 ecc/bls24-315/multiexp_test.go                    | 13 +------------
 ecc/bls24-315/pairing_test.go                     | 13 +------------
 ecc/bls24-315/shplonk/doc.go                      | 13 +------------
 ecc/bls24-315/shplonk/example_test.go             | 13 +------------
 ecc/bls24-315/shplonk/marshal.go                  | 13 +------------
 ecc/bls24-315/shplonk/shplonk.go                  | 13 +------------
 ecc/bls24-315/shplonk/shplonk_test.go             | 13 +------------
 ecc/bls24-315/twistededwards/curve.go             | 13 +------------
 ecc/bls24-315/twistededwards/doc.go               | 13 +------------
 ecc/bls24-315/twistededwards/eddsa/doc.go         | 13 +------------
 ecc/bls24-315/twistededwards/eddsa/eddsa.go       | 13 +------------
 ecc/bls24-315/twistededwards/eddsa/eddsa_test.go  | 13 +------------
 ecc/bls24-315/twistededwards/eddsa/marshal.go     | 13 +------------
 ecc/bls24-315/twistededwards/point.go             | 13 +------------
 ecc/bls24-315/twistededwards/point_test.go        | 13 +------------
 ecc/bls24-317/ecdsa/doc.go                        | 13 +------------
 ecc/bls24-317/ecdsa/ecdsa.go                      | 13 +------------
 ecc/bls24-317/ecdsa/ecdsa_test.go                 | 13 +------------
 ecc/bls24-317/ecdsa/marshal.go                    | 13 +------------
 ecc/bls24-317/ecdsa/marshal_test.go               | 13 +------------
 ecc/bls24-317/fflonk/doc.go                       | 13 +------------
 ecc/bls24-317/fflonk/example_test.go              | 13 +------------
 ecc/bls24-317/fflonk/fflonk.go                    | 13 +------------
 ecc/bls24-317/fflonk/fflonk_test.go               | 13 +------------
 ecc/bls24-317/fflonk/marshal.go                   | 13 +------------
 ecc/bls24-317/fp/arith.go                         | 15 ++-------------
 ecc/bls24-317/fp/asm_adx.go                       | 15 ++-------------
 ecc/bls24-317/fp/asm_noadx.go                     | 15 ++-------------
 ecc/bls24-317/fp/doc.go                           | 15 ++-------------
 ecc/bls24-317/fp/element.go                       | 15 ++-------------
 ecc/bls24-317/fp/element_amd64.go                 | 15 ++-------------
 ecc/bls24-317/fp/element_amd64.s                  | 15 ++-------------
 ecc/bls24-317/fp/element_exp.go                   | 15 ++-------------
 ecc/bls24-317/fp/element_purego.go                | 15 ++-------------
 ecc/bls24-317/fp/element_test.go                  | 15 ++-------------
 ecc/bls24-317/fp/hash_to_field/doc.go             | 13 +------------
 ecc/bls24-317/fp/hash_to_field/hash_to_field.go   | 13 +------------
 .../fp/hash_to_field/hash_to_field_test.go        | 13 +------------
 ecc/bls24-317/fp/vector.go                        | 15 ++-------------
 ecc/bls24-317/fp/vector_purego.go                 | 15 ++-------------
 ecc/bls24-317/fp/vector_test.go                   | 15 ++-------------
 ecc/bls24-317/fr/arith.go                         | 15 ++-------------
 ecc/bls24-317/fr/asm_adx.go                       | 15 ++-------------
 ecc/bls24-317/fr/asm_avx.go                       | 15 ++-------------
 ecc/bls24-317/fr/asm_noadx.go                     | 15 ++-------------
 ecc/bls24-317/fr/asm_noavx.go                     | 15 ++-------------
 ecc/bls24-317/fr/doc.go                           | 15 ++-------------
 ecc/bls24-317/fr/element.go                       | 15 ++-------------
 ecc/bls24-317/fr/element_amd64.go                 | 15 ++-------------
 ecc/bls24-317/fr/element_amd64.s                  | 15 ++-------------
 ecc/bls24-317/fr/element_arm64.go                 | 15 ++-------------
 ecc/bls24-317/fr/element_arm64.s                  | 15 ++-------------
 ecc/bls24-317/fr/element_exp.go                   | 15 ++-------------
 ecc/bls24-317/fr/element_purego.go                | 15 ++-------------
 ecc/bls24-317/fr/element_test.go                  | 15 ++-------------
 ecc/bls24-317/fr/fft/bitreverse.go                | 13 +------------
 ecc/bls24-317/fr/fft/bitreverse_test.go           | 13 +------------
 ecc/bls24-317/fr/fft/doc.go                       | 13 +------------
 ecc/bls24-317/fr/fft/domain.go                    | 13 +------------
 ecc/bls24-317/fr/fft/domain_test.go               | 13 +------------
 ecc/bls24-317/fr/fft/fft.go                       | 13 +------------
 ecc/bls24-317/fr/fft/fft_test.go                  | 13 +------------
 ecc/bls24-317/fr/fft/options.go                   | 13 +------------
 ecc/bls24-317/fr/fri/doc.go                       | 13 +------------
 ecc/bls24-317/fr/fri/fri.go                       | 13 +------------
 ecc/bls24-317/fr/fri/fri_test.go                  | 13 +------------
 ecc/bls24-317/fr/generator.go                     | 13 +------------
 ecc/bls24-317/fr/gkr/gkr.go                       | 13 +------------
 ecc/bls24-317/fr/gkr/gkr_test.go                  | 13 +------------
 ecc/bls24-317/fr/hash_to_field/doc.go             | 13 +------------
 ecc/bls24-317/fr/hash_to_field/hash_to_field.go   | 13 +------------
 .../fr/hash_to_field/hash_to_field_test.go        | 13 +------------
 ecc/bls24-317/fr/iop/doc.go                       | 13 +------------
 ecc/bls24-317/fr/iop/expressions.go               | 13 +------------
 ecc/bls24-317/fr/iop/expressions_test.go          | 13 +------------
 ecc/bls24-317/fr/iop/polynomial.go                | 13 +------------
 ecc/bls24-317/fr/iop/polynomial_test.go           | 13 +------------
 ecc/bls24-317/fr/iop/quotient.go                  | 13 +------------
 ecc/bls24-317/fr/iop/quotient_test.go             | 13 +------------
 ecc/bls24-317/fr/iop/ratios.go                    | 13 +------------
 ecc/bls24-317/fr/iop/ratios_test.go               | 13 +------------
 ecc/bls24-317/fr/iop/utils.go                     | 13 +------------
 ecc/bls24-317/fr/mimc/doc.go                      | 13 +------------
 ecc/bls24-317/fr/mimc/mimc.go                     | 13 +------------
 ecc/bls24-317/fr/mimc/options.go                  | 13 +------------
 ecc/bls24-317/fr/pedersen/doc.go                  | 13 +------------
 ecc/bls24-317/fr/pedersen/example_test.go         | 13 +------------
 ecc/bls24-317/fr/pedersen/pedersen.go             | 13 +------------
 ecc/bls24-317/fr/pedersen/pedersen_test.go        | 13 +------------
 ecc/bls24-317/fr/permutation/doc.go               | 13 +------------
 ecc/bls24-317/fr/permutation/permutation.go       | 13 +------------
 ecc/bls24-317/fr/permutation/permutation_test.go  | 13 +------------
 ecc/bls24-317/fr/plookup/doc.go                   | 13 +------------
 ecc/bls24-317/fr/plookup/plookup_test.go          | 13 +------------
 ecc/bls24-317/fr/plookup/table.go                 | 13 +------------
 ecc/bls24-317/fr/plookup/vector.go                | 13 +------------
 ecc/bls24-317/fr/polynomial/doc.go                | 13 +------------
 ecc/bls24-317/fr/polynomial/multilin.go           | 13 +------------
 ecc/bls24-317/fr/polynomial/multilin_test.go      | 13 +------------
 ecc/bls24-317/fr/polynomial/polynomial.go         | 13 +------------
 ecc/bls24-317/fr/polynomial/polynomial_test.go    | 13 +------------
 ecc/bls24-317/fr/polynomial/pool.go               | 13 +------------
 ecc/bls24-317/fr/poseidon2/poseidon2.go           | 13 +------------
 ecc/bls24-317/fr/poseidon2/poseidon2_test.go      | 13 +------------
 ecc/bls24-317/fr/sumcheck/sumcheck.go             | 13 +------------
 ecc/bls24-317/fr/sumcheck/sumcheck_test.go        | 13 +------------
 .../fr/test_vector_utils/test_vector_utils.go     | 13 +------------
 ecc/bls24-317/fr/vector.go                        | 15 ++-------------
 ecc/bls24-317/fr/vector_amd64.go                  | 15 ++-------------
 ecc/bls24-317/fr/vector_purego.go                 | 15 ++-------------
 ecc/bls24-317/fr/vector_test.go                   | 15 ++-------------
 ecc/bls24-317/g1.go                               | 13 +------------
 ecc/bls24-317/g1_test.go                          | 13 +------------
 ecc/bls24-317/g2.go                               | 13 +------------
 ecc/bls24-317/g2_test.go                          | 13 +------------
 ecc/bls24-317/hash_to_g1.go                       | 13 +------------
 ecc/bls24-317/hash_to_g1_test.go                  | 13 +------------
 ecc/bls24-317/kzg/doc.go                          | 13 +------------
 ecc/bls24-317/kzg/kzg.go                          | 13 +------------
 ecc/bls24-317/kzg/kzg_test.go                     | 13 +------------
 ecc/bls24-317/kzg/marshal.go                      | 13 +------------
 ecc/bls24-317/kzg/utils.go                        | 13 +------------
 ecc/bls24-317/marshal.go                          | 13 +------------
 ecc/bls24-317/marshal_test.go                     | 13 +------------
 ecc/bls24-317/multiexp.go                         | 13 +------------
 ecc/bls24-317/multiexp_affine.go                  | 13 +------------
 ecc/bls24-317/multiexp_jacobian.go                | 13 +------------
 ecc/bls24-317/multiexp_test.go                    | 13 +------------
 ecc/bls24-317/pairing_test.go                     | 13 +------------
 ecc/bls24-317/shplonk/doc.go                      | 13 +------------
 ecc/bls24-317/shplonk/example_test.go             | 13 +------------
 ecc/bls24-317/shplonk/marshal.go                  | 13 +------------
 ecc/bls24-317/shplonk/shplonk.go                  | 13 +------------
 ecc/bls24-317/shplonk/shplonk_test.go             | 13 +------------
 ecc/bls24-317/twistededwards/curve.go             | 13 +------------
 ecc/bls24-317/twistededwards/doc.go               | 13 +------------
 ecc/bls24-317/twistededwards/eddsa/doc.go         | 13 +------------
 ecc/bls24-317/twistededwards/eddsa/eddsa.go       | 13 +------------
 ecc/bls24-317/twistededwards/eddsa/eddsa_test.go  | 13 +------------
 ecc/bls24-317/twistededwards/eddsa/marshal.go     | 13 +------------
 ecc/bls24-317/twistededwards/point.go             | 13 +------------
 ecc/bls24-317/twistededwards/point_test.go        | 13 +------------
 ecc/bn254/ecdsa/doc.go                            | 13 +------------
 ecc/bn254/ecdsa/ecdsa.go                          | 13 +------------
 ecc/bn254/ecdsa/ecdsa_test.go                     | 13 +------------
 ecc/bn254/ecdsa/marshal.go                        | 13 +------------
 ecc/bn254/ecdsa/marshal_test.go                   | 13 +------------
 ecc/bn254/fflonk/doc.go                           | 13 +------------
 ecc/bn254/fflonk/example_test.go                  | 13 +------------
 ecc/bn254/fflonk/fflonk.go                        | 13 +------------
 ecc/bn254/fflonk/fflonk_test.go                   | 13 +------------
 ecc/bn254/fflonk/marshal.go                       | 13 +------------
 ecc/bn254/fp/arith.go                             | 15 ++-------------
 ecc/bn254/fp/asm_adx.go                           | 15 ++-------------
 ecc/bn254/fp/asm_avx.go                           | 15 ++-------------
 ecc/bn254/fp/asm_noadx.go                         | 15 ++-------------
 ecc/bn254/fp/asm_noavx.go                         | 15 ++-------------
 ecc/bn254/fp/doc.go                               | 15 ++-------------
 ecc/bn254/fp/element.go                           | 15 ++-------------
 ecc/bn254/fp/element_amd64.go                     | 15 ++-------------
 ecc/bn254/fp/element_amd64.s                      | 15 ++-------------
 ecc/bn254/fp/element_arm64.go                     | 15 ++-------------
 ecc/bn254/fp/element_arm64.s                      | 15 ++-------------
 ecc/bn254/fp/element_exp.go                       | 15 ++-------------
 ecc/bn254/fp/element_purego.go                    | 15 ++-------------
 ecc/bn254/fp/element_test.go                      | 15 ++-------------
 ecc/bn254/fp/hash_to_field/doc.go                 | 13 +------------
 ecc/bn254/fp/hash_to_field/hash_to_field.go       | 13 +------------
 ecc/bn254/fp/hash_to_field/hash_to_field_test.go  | 13 +------------
 ecc/bn254/fp/vector.go                            | 15 ++-------------
 ecc/bn254/fp/vector_amd64.go                      | 15 ++-------------
 ecc/bn254/fp/vector_purego.go                     | 15 ++-------------
 ecc/bn254/fp/vector_test.go                       | 15 ++-------------
 ecc/bn254/fr/arith.go                             | 15 ++-------------
 ecc/bn254/fr/asm_adx.go                           | 15 ++-------------
 ecc/bn254/fr/asm_avx.go                           | 15 ++-------------
 ecc/bn254/fr/asm_noadx.go                         | 15 ++-------------
 ecc/bn254/fr/asm_noavx.go                         | 15 ++-------------
 ecc/bn254/fr/doc.go                               | 15 ++-------------
 ecc/bn254/fr/element.go                           | 15 ++-------------
 ecc/bn254/fr/element_amd64.go                     | 15 ++-------------
 ecc/bn254/fr/element_amd64.s                      | 15 ++-------------
 ecc/bn254/fr/element_arm64.go                     | 15 ++-------------
 ecc/bn254/fr/element_arm64.s                      | 15 ++-------------
 ecc/bn254/fr/element_exp.go                       | 15 ++-------------
 ecc/bn254/fr/element_purego.go                    | 15 ++-------------
 ecc/bn254/fr/element_test.go                      | 15 ++-------------
 ecc/bn254/fr/fft/bitreverse.go                    | 13 +------------
 ecc/bn254/fr/fft/bitreverse_test.go               | 13 +------------
 ecc/bn254/fr/fft/doc.go                           | 13 +------------
 ecc/bn254/fr/fft/domain.go                        | 13 +------------
 ecc/bn254/fr/fft/domain_test.go                   | 13 +------------
 ecc/bn254/fr/fft/fft.go                           | 13 +------------
 ecc/bn254/fr/fft/fft_test.go                      | 13 +------------
 ecc/bn254/fr/fft/options.go                       | 13 +------------
 ecc/bn254/fr/fri/doc.go                           | 13 +------------
 ecc/bn254/fr/fri/fri.go                           | 13 +------------
 ecc/bn254/fr/fri/fri_test.go                      | 13 +------------
 ecc/bn254/fr/generator.go                         | 13 +------------
 ecc/bn254/fr/gkr/gkr.go                           | 13 +------------
 ecc/bn254/fr/gkr/gkr_test.go                      | 13 +------------
 ecc/bn254/fr/hash_to_field/doc.go                 | 13 +------------
 ecc/bn254/fr/hash_to_field/hash_to_field.go       | 13 +------------
 ecc/bn254/fr/hash_to_field/hash_to_field_test.go  | 13 +------------
 ecc/bn254/fr/iop/doc.go                           | 13 +------------
 ecc/bn254/fr/iop/expressions.go                   | 13 +------------
 ecc/bn254/fr/iop/expressions_test.go              | 13 +------------
 ecc/bn254/fr/iop/polynomial.go                    | 13 +------------
 ecc/bn254/fr/iop/polynomial_test.go               | 13 +------------
 ecc/bn254/fr/iop/quotient.go                      | 13 +------------
 ecc/bn254/fr/iop/quotient_test.go                 | 13 +------------
 ecc/bn254/fr/iop/ratios.go                        | 13 +------------
 ecc/bn254/fr/iop/ratios_test.go                   | 13 +------------
 ecc/bn254/fr/iop/utils.go                         | 13 +------------
 ecc/bn254/fr/mimc/doc.go                          | 13 +------------
 ecc/bn254/fr/mimc/mimc.go                         | 13 +------------
 ecc/bn254/fr/mimc/options.go                      | 13 +------------
 ecc/bn254/fr/pedersen/doc.go                      | 13 +------------
 ecc/bn254/fr/pedersen/example_test.go             | 13 +------------
 ecc/bn254/fr/pedersen/pedersen.go                 | 13 +------------
 ecc/bn254/fr/pedersen/pedersen_test.go            | 13 +------------
 ecc/bn254/fr/permutation/doc.go                   | 13 +------------
 ecc/bn254/fr/permutation/permutation.go           | 13 +------------
 ecc/bn254/fr/permutation/permutation_test.go      | 13 +------------
 ecc/bn254/fr/plookup/doc.go                       | 13 +------------
 ecc/bn254/fr/plookup/plookup_test.go              | 13 +------------
 ecc/bn254/fr/plookup/table.go                     | 13 +------------
 ecc/bn254/fr/plookup/vector.go                    | 13 +------------
 ecc/bn254/fr/polynomial/doc.go                    | 13 +------------
 ecc/bn254/fr/polynomial/multilin.go               | 13 +------------
 ecc/bn254/fr/polynomial/multilin_test.go          | 13 +------------
 ecc/bn254/fr/polynomial/polynomial.go             | 13 +------------
 ecc/bn254/fr/polynomial/polynomial_test.go        | 13 +------------
 ecc/bn254/fr/polynomial/pool.go                   | 13 +------------
 ecc/bn254/fr/poseidon2/poseidon2.go               | 13 +------------
 ecc/bn254/fr/poseidon2/poseidon2_test.go          | 13 +------------
 ecc/bn254/fr/sis/sis_fft.go                       | 13 +------------
 ecc/bn254/fr/sumcheck/sumcheck.go                 | 13 +------------
 ecc/bn254/fr/sumcheck/sumcheck_test.go            | 13 +------------
 .../fr/test_vector_utils/test_vector_utils.go     | 13 +------------
 ecc/bn254/fr/vector.go                            | 15 ++-------------
 ecc/bn254/fr/vector_amd64.go                      | 15 ++-------------
 ecc/bn254/fr/vector_purego.go                     | 15 ++-------------
 ecc/bn254/fr/vector_test.go                       | 15 ++-------------
 ecc/bn254/g1.go                                   | 13 +------------
 ecc/bn254/g1_test.go                              | 13 +------------
 ecc/bn254/g2.go                                   | 13 +------------
 ecc/bn254/g2_test.go                              | 13 +------------
 ecc/bn254/hash_to_g1.go                           | 13 +------------
 ecc/bn254/hash_to_g1_test.go                      | 13 +------------
 ecc/bn254/hash_to_g2.go                           | 13 +------------
 ecc/bn254/hash_to_g2_test.go                      | 13 +------------
 ecc/bn254/internal/fptower/asm.go                 | 13 +------------
 ecc/bn254/internal/fptower/asm_noadx.go           | 13 +------------
 ecc/bn254/internal/fptower/e12.go                 | 13 +------------
 ecc/bn254/internal/fptower/e12_test.go            | 13 +------------
 ecc/bn254/internal/fptower/e2.go                  | 13 +------------
 ecc/bn254/internal/fptower/e2_amd64.go            | 13 +------------
 ecc/bn254/internal/fptower/e2_amd64.s             | 13 +------------
 ecc/bn254/internal/fptower/e2_fallback.go         | 13 +------------
 ecc/bn254/internal/fptower/e2_test.go             | 13 +------------
 ecc/bn254/internal/fptower/e6.go                  | 13 +------------
 ecc/bn254/internal/fptower/e6_test.go             | 13 +------------
 ecc/bn254/kzg/doc.go                              | 13 +------------
 ecc/bn254/kzg/kzg.go                              | 13 +------------
 ecc/bn254/kzg/kzg_test.go                         | 13 +------------
 ecc/bn254/kzg/marshal.go                          | 13 +------------
 ecc/bn254/kzg/utils.go                            | 13 +------------
 ecc/bn254/marshal.go                              | 13 +------------
 ecc/bn254/marshal_test.go                         | 13 +------------
 ecc/bn254/multiexp.go                             | 13 +------------
 ecc/bn254/multiexp_affine.go                      | 13 +------------
 ecc/bn254/multiexp_jacobian.go                    | 13 +------------
 ecc/bn254/multiexp_test.go                        | 13 +------------
 ecc/bn254/pairing_test.go                         | 13 +------------
 ecc/bn254/shplonk/doc.go                          | 13 +------------
 ecc/bn254/shplonk/example_test.go                 | 13 +------------
 ecc/bn254/shplonk/marshal.go                      | 13 +------------
 ecc/bn254/shplonk/shplonk.go                      | 13 +------------
 ecc/bn254/shplonk/shplonk_test.go                 | 13 +------------
 ecc/bn254/twistededwards/curve.go                 | 13 +------------
 ecc/bn254/twistededwards/doc.go                   | 13 +------------
 ecc/bn254/twistededwards/eddsa/doc.go             | 13 +------------
 ecc/bn254/twistededwards/eddsa/eddsa.go           | 13 +------------
 ecc/bn254/twistededwards/eddsa/eddsa_test.go      | 13 +------------
 ecc/bn254/twistededwards/eddsa/marshal.go         | 13 +------------
 ecc/bn254/twistededwards/point.go                 | 13 +------------
 ecc/bn254/twistededwards/point_test.go            | 13 +------------
 ecc/bw6-633/ecdsa/doc.go                          | 13 +------------
 ecc/bw6-633/ecdsa/ecdsa.go                        | 13 +------------
 ecc/bw6-633/ecdsa/ecdsa_test.go                   | 13 +------------
 ecc/bw6-633/ecdsa/marshal.go                      | 13 +------------
 ecc/bw6-633/ecdsa/marshal_test.go                 | 13 +------------
 ecc/bw6-633/fflonk/doc.go                         | 13 +------------
 ecc/bw6-633/fflonk/example_test.go                | 13 +------------
 ecc/bw6-633/fflonk/fflonk.go                      | 13 +------------
 ecc/bw6-633/fflonk/fflonk_test.go                 | 13 +------------
 ecc/bw6-633/fflonk/marshal.go                     | 13 +------------
 ecc/bw6-633/fp/arith.go                           | 15 ++-------------
 ecc/bw6-633/fp/asm_adx.go                         | 15 ++-------------
 ecc/bw6-633/fp/asm_noadx.go                       | 15 ++-------------
 ecc/bw6-633/fp/doc.go                             | 15 ++-------------
 ecc/bw6-633/fp/element.go                         | 15 ++-------------
 ecc/bw6-633/fp/element_amd64.go                   | 15 ++-------------
 ecc/bw6-633/fp/element_amd64.s                    | 15 ++-------------
 ecc/bw6-633/fp/element_arm64.go                   | 15 ++-------------
 ecc/bw6-633/fp/element_arm64.s                    | 15 ++-------------
 ecc/bw6-633/fp/element_exp.go                     | 15 ++-------------
 ecc/bw6-633/fp/element_purego.go                  | 15 ++-------------
 ecc/bw6-633/fp/element_test.go                    | 15 ++-------------
 ecc/bw6-633/fp/hash_to_field/doc.go               | 13 +------------
 ecc/bw6-633/fp/hash_to_field/hash_to_field.go     | 13 +------------
 .../fp/hash_to_field/hash_to_field_test.go        | 13 +------------
 ecc/bw6-633/fp/vector.go                          | 15 ++-------------
 ecc/bw6-633/fp/vector_purego.go                   | 15 ++-------------
 ecc/bw6-633/fp/vector_test.go                     | 15 ++-------------
 ecc/bw6-633/fr/arith.go                           | 15 ++-------------
 ecc/bw6-633/fr/asm_adx.go                         | 15 ++-------------
 ecc/bw6-633/fr/asm_noadx.go                       | 15 ++-------------
 ecc/bw6-633/fr/doc.go                             | 15 ++-------------
 ecc/bw6-633/fr/element.go                         | 15 ++-------------
 ecc/bw6-633/fr/element_amd64.go                   | 15 ++-------------
 ecc/bw6-633/fr/element_amd64.s                    | 15 ++-------------
 ecc/bw6-633/fr/element_exp.go                     | 15 ++-------------
 ecc/bw6-633/fr/element_purego.go                  | 15 ++-------------
 ecc/bw6-633/fr/element_test.go                    | 15 ++-------------
 ecc/bw6-633/fr/fft/bitreverse.go                  | 13 +------------
 ecc/bw6-633/fr/fft/bitreverse_test.go             | 13 +------------
 ecc/bw6-633/fr/fft/doc.go                         | 13 +------------
 ecc/bw6-633/fr/fft/domain.go                      | 13 +------------
 ecc/bw6-633/fr/fft/domain_test.go                 | 13 +------------
 ecc/bw6-633/fr/fft/fft.go                         | 13 +------------
 ecc/bw6-633/fr/fft/fft_test.go                    | 13 +------------
 ecc/bw6-633/fr/fft/options.go                     | 13 +------------
 ecc/bw6-633/fr/fri/doc.go                         | 13 +------------
 ecc/bw6-633/fr/fri/fri.go                         | 13 +------------
 ecc/bw6-633/fr/fri/fri_test.go                    | 13 +------------
 ecc/bw6-633/fr/generator.go                       | 13 +------------
 ecc/bw6-633/fr/gkr/gkr.go                         | 13 +------------
 ecc/bw6-633/fr/gkr/gkr_test.go                    | 13 +------------
 ecc/bw6-633/fr/hash_to_field/doc.go               | 13 +------------
 ecc/bw6-633/fr/hash_to_field/hash_to_field.go     | 13 +------------
 .../fr/hash_to_field/hash_to_field_test.go        | 13 +------------
 ecc/bw6-633/fr/iop/doc.go                         | 13 +------------
 ecc/bw6-633/fr/iop/expressions.go                 | 13 +------------
 ecc/bw6-633/fr/iop/expressions_test.go            | 13 +------------
 ecc/bw6-633/fr/iop/polynomial.go                  | 13 +------------
 ecc/bw6-633/fr/iop/polynomial_test.go             | 13 +------------
 ecc/bw6-633/fr/iop/quotient.go                    | 13 +------------
 ecc/bw6-633/fr/iop/quotient_test.go               | 13 +------------
 ecc/bw6-633/fr/iop/ratios.go                      | 13 +------------
 ecc/bw6-633/fr/iop/ratios_test.go                 | 13 +------------
 ecc/bw6-633/fr/iop/utils.go                       | 13 +------------
 ecc/bw6-633/fr/mimc/doc.go                        | 13 +------------
 ecc/bw6-633/fr/mimc/mimc.go                       | 13 +------------
 ecc/bw6-633/fr/mimc/options.go                    | 13 +------------
 ecc/bw6-633/fr/pedersen/doc.go                    | 13 +------------
 ecc/bw6-633/fr/pedersen/example_test.go           | 13 +------------
 ecc/bw6-633/fr/pedersen/pedersen.go               | 13 +------------
 ecc/bw6-633/fr/pedersen/pedersen_test.go          | 13 +------------
 ecc/bw6-633/fr/permutation/doc.go                 | 13 +------------
 ecc/bw6-633/fr/permutation/permutation.go         | 13 +------------
 ecc/bw6-633/fr/permutation/permutation_test.go    | 13 +------------
 ecc/bw6-633/fr/plookup/doc.go                     | 13 +------------
 ecc/bw6-633/fr/plookup/plookup_test.go            | 13 +------------
 ecc/bw6-633/fr/plookup/table.go                   | 13 +------------
 ecc/bw6-633/fr/plookup/vector.go                  | 13 +------------
 ecc/bw6-633/fr/polynomial/doc.go                  | 13 +------------
 ecc/bw6-633/fr/polynomial/multilin.go             | 13 +------------
 ecc/bw6-633/fr/polynomial/multilin_test.go        | 13 +------------
 ecc/bw6-633/fr/polynomial/polynomial.go           | 13 +------------
 ecc/bw6-633/fr/polynomial/polynomial_test.go      | 13 +------------
 ecc/bw6-633/fr/polynomial/pool.go                 | 13 +------------
 ecc/bw6-633/fr/poseidon2/poseidon2.go             | 13 +------------
 ecc/bw6-633/fr/poseidon2/poseidon2_test.go        | 13 +------------
 ecc/bw6-633/fr/sumcheck/sumcheck.go               | 13 +------------
 ecc/bw6-633/fr/sumcheck/sumcheck_test.go          | 13 +------------
 .../fr/test_vector_utils/test_vector_utils.go     | 13 +------------
 ecc/bw6-633/fr/vector.go                          | 15 ++-------------
 ecc/bw6-633/fr/vector_purego.go                   | 15 ++-------------
 ecc/bw6-633/fr/vector_test.go                     | 15 ++-------------
 ecc/bw6-633/g1.go                                 | 13 +------------
 ecc/bw6-633/g1_test.go                            | 13 +------------
 ecc/bw6-633/g2.go                                 | 13 +------------
 ecc/bw6-633/g2_test.go                            | 13 +------------
 ecc/bw6-633/hash_to_g1.go                         | 13 +------------
 ecc/bw6-633/hash_to_g1_test.go                    | 13 +------------
 ecc/bw6-633/hash_to_g2.go                         | 13 +------------
 ecc/bw6-633/hash_to_g2_test.go                    | 13 +------------
 ecc/bw6-633/kzg/doc.go                            | 13 +------------
 ecc/bw6-633/kzg/kzg.go                            | 13 +------------
 ecc/bw6-633/kzg/kzg_test.go                       | 13 +------------
 ecc/bw6-633/kzg/marshal.go                        | 13 +------------
 ecc/bw6-633/kzg/utils.go                          | 13 +------------
 ecc/bw6-633/marshal.go                            | 13 +------------
 ecc/bw6-633/marshal_test.go                       | 13 +------------
 ecc/bw6-633/multiexp.go                           | 13 +------------
 ecc/bw6-633/multiexp_affine.go                    | 13 +------------
 ecc/bw6-633/multiexp_jacobian.go                  | 13 +------------
 ecc/bw6-633/multiexp_test.go                      | 13 +------------
 ecc/bw6-633/pairing_test.go                       | 13 +------------
 ecc/bw6-633/shplonk/doc.go                        | 13 +------------
 ecc/bw6-633/shplonk/example_test.go               | 13 +------------
 ecc/bw6-633/shplonk/marshal.go                    | 13 +------------
 ecc/bw6-633/shplonk/shplonk.go                    | 13 +------------
 ecc/bw6-633/shplonk/shplonk_test.go               | 13 +------------
 ecc/bw6-633/twistededwards/curve.go               | 13 +------------
 ecc/bw6-633/twistededwards/doc.go                 | 13 +------------
 ecc/bw6-633/twistededwards/eddsa/doc.go           | 13 +------------
 ecc/bw6-633/twistededwards/eddsa/eddsa.go         | 13 +------------
 ecc/bw6-633/twistededwards/eddsa/eddsa_test.go    | 13 +------------
 ecc/bw6-633/twistededwards/eddsa/marshal.go       | 13 +------------
 ecc/bw6-633/twistededwards/point.go               | 13 +------------
 ecc/bw6-633/twistededwards/point_test.go          | 13 +------------
 ecc/bw6-761/ecdsa/doc.go                          | 13 +------------
 ecc/bw6-761/ecdsa/ecdsa.go                        | 13 +------------
 ecc/bw6-761/ecdsa/ecdsa_test.go                   | 13 +------------
 ecc/bw6-761/ecdsa/marshal.go                      | 13 +------------
 ecc/bw6-761/ecdsa/marshal_test.go                 | 13 +------------
 ecc/bw6-761/fflonk/doc.go                         | 13 +------------
 ecc/bw6-761/fflonk/example_test.go                | 13 +------------
 ecc/bw6-761/fflonk/fflonk.go                      | 13 +------------
 ecc/bw6-761/fflonk/fflonk_test.go                 | 13 +------------
 ecc/bw6-761/fflonk/marshal.go                     | 13 +------------
 ecc/bw6-761/fp/arith.go                           | 15 ++-------------
 ecc/bw6-761/fp/asm_adx.go                         | 15 ++-------------
 ecc/bw6-761/fp/asm_noadx.go                       | 15 ++-------------
 ecc/bw6-761/fp/doc.go                             | 15 ++-------------
 ecc/bw6-761/fp/element.go                         | 15 ++-------------
 ecc/bw6-761/fp/element_amd64.go                   | 15 ++-------------
 ecc/bw6-761/fp/element_amd64.s                    | 15 ++-------------
 ecc/bw6-761/fp/element_arm64.go                   | 15 ++-------------
 ecc/bw6-761/fp/element_arm64.s                    | 15 ++-------------
 ecc/bw6-761/fp/element_exp.go                     | 15 ++-------------
 ecc/bw6-761/fp/element_purego.go                  | 15 ++-------------
 ecc/bw6-761/fp/element_test.go                    | 15 ++-------------
 ecc/bw6-761/fp/hash_to_field/doc.go               | 13 +------------
 ecc/bw6-761/fp/hash_to_field/hash_to_field.go     | 13 +------------
 .../fp/hash_to_field/hash_to_field_test.go        | 13 +------------
 ecc/bw6-761/fp/vector.go                          | 15 ++-------------
 ecc/bw6-761/fp/vector_purego.go                   | 15 ++-------------
 ecc/bw6-761/fp/vector_test.go                     | 15 ++-------------
 ecc/bw6-761/fr/arith.go                           | 15 ++-------------
 ecc/bw6-761/fr/asm_adx.go                         | 15 ++-------------
 ecc/bw6-761/fr/asm_noadx.go                       | 15 ++-------------
 ecc/bw6-761/fr/doc.go                             | 15 ++-------------
 ecc/bw6-761/fr/element.go                         | 15 ++-------------
 ecc/bw6-761/fr/element_amd64.go                   | 15 ++-------------
 ecc/bw6-761/fr/element_amd64.s                    | 15 ++-------------
 ecc/bw6-761/fr/element_arm64.go                   | 15 ++-------------
 ecc/bw6-761/fr/element_arm64.s                    | 15 ++-------------
 ecc/bw6-761/fr/element_exp.go                     | 15 ++-------------
 ecc/bw6-761/fr/element_purego.go                  | 15 ++-------------
 ecc/bw6-761/fr/element_test.go                    | 15 ++-------------
 ecc/bw6-761/fr/fft/bitreverse.go                  | 13 +------------
 ecc/bw6-761/fr/fft/bitreverse_test.go             | 13 +------------
 ecc/bw6-761/fr/fft/doc.go                         | 13 +------------
 ecc/bw6-761/fr/fft/domain.go                      | 13 +------------
 ecc/bw6-761/fr/fft/domain_test.go                 | 13 +------------
 ecc/bw6-761/fr/fft/fft.go                         | 13 +------------
 ecc/bw6-761/fr/fft/fft_test.go                    | 13 +------------
 ecc/bw6-761/fr/fft/options.go                     | 13 +------------
 ecc/bw6-761/fr/fri/doc.go                         | 13 +------------
 ecc/bw6-761/fr/fri/fri.go                         | 13 +------------
 ecc/bw6-761/fr/fri/fri_test.go                    | 13 +------------
 ecc/bw6-761/fr/generator.go                       | 13 +------------
 ecc/bw6-761/fr/gkr/gkr.go                         | 13 +------------
 ecc/bw6-761/fr/gkr/gkr_test.go                    | 13 +------------
 ecc/bw6-761/fr/hash_to_field/doc.go               | 13 +------------
 ecc/bw6-761/fr/hash_to_field/hash_to_field.go     | 13 +------------
 .../fr/hash_to_field/hash_to_field_test.go        | 13 +------------
 ecc/bw6-761/fr/iop/doc.go                         | 13 +------------
 ecc/bw6-761/fr/iop/expressions.go                 | 13 +------------
 ecc/bw6-761/fr/iop/expressions_test.go            | 13 +------------
 ecc/bw6-761/fr/iop/polynomial.go                  | 13 +------------
 ecc/bw6-761/fr/iop/polynomial_test.go             | 13 +------------
 ecc/bw6-761/fr/iop/quotient.go                    | 13 +------------
 ecc/bw6-761/fr/iop/quotient_test.go               | 13 +------------
 ecc/bw6-761/fr/iop/ratios.go                      | 13 +------------
 ecc/bw6-761/fr/iop/ratios_test.go                 | 13 +------------
 ecc/bw6-761/fr/iop/utils.go                       | 13 +------------
 ecc/bw6-761/fr/mimc/doc.go                        | 13 +------------
 ecc/bw6-761/fr/mimc/mimc.go                       | 13 +------------
 ecc/bw6-761/fr/mimc/options.go                    | 13 +------------
 ecc/bw6-761/fr/pedersen/doc.go                    | 13 +------------
 ecc/bw6-761/fr/pedersen/example_test.go           | 13 +------------
 ecc/bw6-761/fr/pedersen/pedersen.go               | 13 +------------
 ecc/bw6-761/fr/pedersen/pedersen_test.go          | 13 +------------
 ecc/bw6-761/fr/permutation/doc.go                 | 13 +------------
 ecc/bw6-761/fr/permutation/permutation.go         | 13 +------------
 ecc/bw6-761/fr/permutation/permutation_test.go    | 13 +------------
 ecc/bw6-761/fr/plookup/doc.go                     | 13 +------------
 ecc/bw6-761/fr/plookup/plookup_test.go            | 13 +------------
 ecc/bw6-761/fr/plookup/table.go                   | 13 +------------
 ecc/bw6-761/fr/plookup/vector.go                  | 13 +------------
 ecc/bw6-761/fr/polynomial/doc.go                  | 13 +------------
 ecc/bw6-761/fr/polynomial/multilin.go             | 13 +------------
 ecc/bw6-761/fr/polynomial/multilin_test.go        | 13 +------------
 ecc/bw6-761/fr/polynomial/polynomial.go           | 13 +------------
 ecc/bw6-761/fr/polynomial/polynomial_test.go      | 13 +------------
 ecc/bw6-761/fr/polynomial/pool.go                 | 13 +------------
 ecc/bw6-761/fr/poseidon2/poseidon2.go             | 13 +------------
 ecc/bw6-761/fr/poseidon2/poseidon2_test.go        | 13 +------------
 ecc/bw6-761/fr/sumcheck/sumcheck.go               | 13 +------------
 ecc/bw6-761/fr/sumcheck/sumcheck_test.go          | 13 +------------
 .../fr/test_vector_utils/test_vector_utils.go     | 13 +------------
 ecc/bw6-761/fr/vector.go                          | 15 ++-------------
 ecc/bw6-761/fr/vector_purego.go                   | 15 ++-------------
 ecc/bw6-761/fr/vector_test.go                     | 15 ++-------------
 ecc/bw6-761/g1.go                                 | 13 +------------
 ecc/bw6-761/g1_test.go                            | 13 +------------
 ecc/bw6-761/g2.go                                 | 13 +------------
 ecc/bw6-761/g2_test.go                            | 13 +------------
 ecc/bw6-761/hash_to_g1.go                         | 13 +------------
 ecc/bw6-761/hash_to_g1_test.go                    | 13 +------------
 ecc/bw6-761/hash_to_g2.go                         | 13 +------------
 ecc/bw6-761/hash_to_g2_test.go                    | 13 +------------
 ecc/bw6-761/kzg/doc.go                            | 13 +------------
 ecc/bw6-761/kzg/kzg.go                            | 13 +------------
 ecc/bw6-761/kzg/kzg_test.go                       | 13 +------------
 ecc/bw6-761/kzg/marshal.go                        | 13 +------------
 ecc/bw6-761/kzg/utils.go                          | 13 +------------
 ecc/bw6-761/marshal.go                            | 13 +------------
 ecc/bw6-761/marshal_test.go                       | 13 +------------
 ecc/bw6-761/multiexp.go                           | 13 +------------
 ecc/bw6-761/multiexp_affine.go                    | 13 +------------
 ecc/bw6-761/multiexp_jacobian.go                  | 13 +------------
 ecc/bw6-761/multiexp_test.go                      | 13 +------------
 ecc/bw6-761/pairing_test.go                       | 13 +------------
 ecc/bw6-761/shplonk/doc.go                        | 13 +------------
 ecc/bw6-761/shplonk/example_test.go               | 13 +------------
 ecc/bw6-761/shplonk/marshal.go                    | 13 +------------
 ecc/bw6-761/shplonk/shplonk.go                    | 13 +------------
 ecc/bw6-761/shplonk/shplonk_test.go               | 13 +------------
 ecc/bw6-761/twistededwards/curve.go               | 13 +------------
 ecc/bw6-761/twistededwards/doc.go                 | 13 +------------
 ecc/bw6-761/twistededwards/eddsa/doc.go           | 13 +------------
 ecc/bw6-761/twistededwards/eddsa/eddsa.go         | 13 +------------
 ecc/bw6-761/twistededwards/eddsa/eddsa_test.go    | 13 +------------
 ecc/bw6-761/twistededwards/eddsa/marshal.go       | 13 +------------
 ecc/bw6-761/twistededwards/point.go               | 13 +------------
 ecc/bw6-761/twistededwards/point_test.go          | 13 +------------
 ecc/secp256k1/ecdsa/doc.go                        | 13 +------------
 ecc/secp256k1/ecdsa/ecdsa.go                      | 13 +------------
 ecc/secp256k1/ecdsa/ecdsa_test.go                 | 13 +------------
 ecc/secp256k1/ecdsa/marshal.go                    | 13 +------------
 ecc/secp256k1/ecdsa/marshal_test.go               | 13 +------------
 ecc/secp256k1/fp/arith.go                         | 15 ++-------------
 ecc/secp256k1/fp/doc.go                           | 15 ++-------------
 ecc/secp256k1/fp/element.go                       | 15 ++-------------
 ecc/secp256k1/fp/element_exp.go                   | 15 ++-------------
 ecc/secp256k1/fp/element_purego.go                | 15 ++-------------
 ecc/secp256k1/fp/element_test.go                  | 15 ++-------------
 ecc/secp256k1/fp/vector.go                        | 15 ++-------------
 ecc/secp256k1/fp/vector_purego.go                 | 15 ++-------------
 ecc/secp256k1/fp/vector_test.go                   | 15 ++-------------
 ecc/secp256k1/fr/arith.go                         | 15 ++-------------
 ecc/secp256k1/fr/doc.go                           | 15 ++-------------
 ecc/secp256k1/fr/element.go                       | 15 ++-------------
 ecc/secp256k1/fr/element_exp.go                   | 15 ++-------------
 ecc/secp256k1/fr/element_purego.go                | 15 ++-------------
 ecc/secp256k1/fr/element_test.go                  | 15 ++-------------
 ecc/secp256k1/fr/vector.go                        | 15 ++-------------
 ecc/secp256k1/fr/vector_purego.go                 | 15 ++-------------
 ecc/secp256k1/fr/vector_test.go                   | 15 ++-------------
 ecc/secp256k1/g1.go                               | 13 +------------
 ecc/secp256k1/g1_test.go                          | 13 +------------
 ecc/secp256k1/hash_to_g1.go                       | 13 +------------
 ecc/secp256k1/hash_to_g1_test.go                  | 13 +------------
 ecc/secp256k1/multiexp.go                         | 13 +------------
 ecc/secp256k1/multiexp_affine.go                  | 13 +------------
 ecc/secp256k1/multiexp_jacobian.go                | 13 +------------
 ecc/secp256k1/multiexp_test.go                    | 13 +------------
 ecc/stark-curve/ecdsa/doc.go                      | 13 +------------
 ecc/stark-curve/ecdsa/ecdsa.go                    | 13 +------------
 ecc/stark-curve/ecdsa/ecdsa_test.go               | 13 +------------
 ecc/stark-curve/ecdsa/marshal.go                  | 13 +------------
 ecc/stark-curve/ecdsa/marshal_test.go             | 13 +------------
 ecc/stark-curve/fp/arith.go                       | 15 ++-------------
 ecc/stark-curve/fp/asm_adx.go                     | 15 ++-------------
 ecc/stark-curve/fp/asm_avx.go                     | 15 ++-------------
 ecc/stark-curve/fp/asm_noadx.go                   | 15 ++-------------
 ecc/stark-curve/fp/asm_noavx.go                   | 15 ++-------------
 ecc/stark-curve/fp/doc.go                         | 15 ++-------------
 ecc/stark-curve/fp/element.go                     | 15 ++-------------
 ecc/stark-curve/fp/element_amd64.go               | 15 ++-------------
 ecc/stark-curve/fp/element_amd64.s                | 15 ++-------------
 ecc/stark-curve/fp/element_arm64.go               | 15 ++-------------
 ecc/stark-curve/fp/element_arm64.s                | 15 ++-------------
 ecc/stark-curve/fp/element_exp.go                 | 15 ++-------------
 ecc/stark-curve/fp/element_purego.go              | 15 ++-------------
 ecc/stark-curve/fp/element_test.go                | 15 ++-------------
 ecc/stark-curve/fp/vector.go                      | 15 ++-------------
 ecc/stark-curve/fp/vector_amd64.go                | 15 ++-------------
 ecc/stark-curve/fp/vector_purego.go               | 15 ++-------------
 ecc/stark-curve/fp/vector_test.go                 | 15 ++-------------
 ecc/stark-curve/fr/arith.go                       | 15 ++-------------
 ecc/stark-curve/fr/asm_adx.go                     | 15 ++-------------
 ecc/stark-curve/fr/asm_avx.go                     | 15 ++-------------
 ecc/stark-curve/fr/asm_noadx.go                   | 15 ++-------------
 ecc/stark-curve/fr/asm_noavx.go                   | 15 ++-------------
 ecc/stark-curve/fr/doc.go                         | 15 ++-------------
 ecc/stark-curve/fr/element.go                     | 15 ++-------------
 ecc/stark-curve/fr/element_amd64.go               | 15 ++-------------
 ecc/stark-curve/fr/element_amd64.s                | 15 ++-------------
 ecc/stark-curve/fr/element_arm64.go               | 15 ++-------------
 ecc/stark-curve/fr/element_arm64.s                | 15 ++-------------
 ecc/stark-curve/fr/element_purego.go              | 15 ++-------------
 ecc/stark-curve/fr/element_test.go                | 15 ++-------------
 ecc/stark-curve/fr/vector.go                      | 15 ++-------------
 ecc/stark-curve/fr/vector_amd64.go                | 15 ++-------------
 ecc/stark-curve/fr/vector_purego.go               | 15 ++-------------
 ecc/stark-curve/fr/vector_test.go                 | 15 ++-------------
 field/babybear/doc.go                             | 15 ++-------------
 field/babybear/element.go                         | 15 ++-------------
 field/babybear/element_exp.go                     | 15 ++-------------
 field/babybear/element_purego.go                  | 15 ++-------------
 field/babybear/element_test.go                    | 15 ++-------------
 field/babybear/vector.go                          | 15 ++-------------
 field/babybear/vector_purego.go                   | 15 ++-------------
 field/babybear/vector_test.go                     | 15 ++-------------
 field/generator/generator.go                      |  2 +-
 field/goldilocks/arith.go                         | 15 ++-------------
 field/goldilocks/doc.go                           | 15 ++-------------
 field/goldilocks/element.go                       | 15 ++-------------
 field/goldilocks/element_exp.go                   | 15 ++-------------
 field/goldilocks/element_purego.go                | 15 ++-------------
 field/goldilocks/element_test.go                  | 15 ++-------------
 field/goldilocks/vector.go                        | 15 ++-------------
 field/goldilocks/vector_purego.go                 | 15 ++-------------
 field/goldilocks/vector_test.go                   | 15 ++-------------
 field/koalabear/doc.go                            | 15 ++-------------
 field/koalabear/element.go                        | 15 ++-------------
 field/koalabear/element_exp.go                    | 15 ++-------------
 field/koalabear/element_purego.go                 | 15 ++-------------
 field/koalabear/element_test.go                   | 15 ++-------------
 field/koalabear/vector.go                         | 15 ++-------------
 field/koalabear/vector_purego.go                  | 15 ++-------------
 field/koalabear/vector_test.go                    | 15 ++-------------
 go.mod                                            |  2 +-
 go.sum                                            |  4 ++--
 internal/generator/gkr/test_vectors/main.go       | 13 +------------
 .../test_vector_utils/small_rational/gkr/gkr.go   | 13 +------------
 .../small_rational/polynomial/doc.go              | 13 +------------
 .../small_rational/polynomial/multilin.go         | 13 +------------
 .../small_rational/polynomial/polynomial.go       | 13 +------------
 .../small_rational/polynomial/pool.go             | 13 +------------
 .../small_rational/sumcheck/sumcheck.go           | 13 +------------
 .../small_rational/sumcheck/sumcheck_test.go      | 13 +------------
 .../test_vector_utils/test_vector_utils.go        | 13 +------------
 1055 files changed, 1356 insertions(+), 12928 deletions(-)

diff --git a/ecc/bls12-377/ecdsa/doc.go b/ecc/bls12-377/ecdsa/doc.go
index 085a3829dd..793c3ccf61 100644
--- a/ecc/bls12-377/ecdsa/doc.go
+++ b/ecc/bls12-377/ecdsa/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/ecdsa/ecdsa.go b/ecc/bls12-377/ecdsa/ecdsa.go
index d0ca345014..67908ce003 100644
--- a/ecc/bls12-377/ecdsa/ecdsa.go
+++ b/ecc/bls12-377/ecdsa/ecdsa.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/ecdsa/ecdsa_test.go b/ecc/bls12-377/ecdsa/ecdsa_test.go
index e833733346..5385c3b02f 100644
--- a/ecc/bls12-377/ecdsa/ecdsa_test.go
+++ b/ecc/bls12-377/ecdsa/ecdsa_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/ecdsa/marshal.go b/ecc/bls12-377/ecdsa/marshal.go
index 81dfd806b4..845bb92cbe 100644
--- a/ecc/bls12-377/ecdsa/marshal.go
+++ b/ecc/bls12-377/ecdsa/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/ecdsa/marshal_test.go b/ecc/bls12-377/ecdsa/marshal_test.go
index 7ad094fb9a..42f7f7b08c 100644
--- a/ecc/bls12-377/ecdsa/marshal_test.go
+++ b/ecc/bls12-377/ecdsa/marshal_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fflonk/doc.go b/ecc/bls12-377/fflonk/doc.go
index 694eaa9734..b717383d87 100644
--- a/ecc/bls12-377/fflonk/doc.go
+++ b/ecc/bls12-377/fflonk/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fflonk/example_test.go b/ecc/bls12-377/fflonk/example_test.go
index 43bde4e804..8a0ffbe630 100644
--- a/ecc/bls12-377/fflonk/example_test.go
+++ b/ecc/bls12-377/fflonk/example_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fflonk/fflonk.go b/ecc/bls12-377/fflonk/fflonk.go
index 65c19b0516..68b147e5e0 100644
--- a/ecc/bls12-377/fflonk/fflonk.go
+++ b/ecc/bls12-377/fflonk/fflonk.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fflonk/fflonk_test.go b/ecc/bls12-377/fflonk/fflonk_test.go
index 55e2dcc78b..767046034e 100644
--- a/ecc/bls12-377/fflonk/fflonk_test.go
+++ b/ecc/bls12-377/fflonk/fflonk_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fflonk/marshal.go b/ecc/bls12-377/fflonk/marshal.go
index b5dd8da92e..06d50938ad 100644
--- a/ecc/bls12-377/fflonk/marshal.go
+++ b/ecc/bls12-377/fflonk/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fp/arith.go b/ecc/bls12-377/fp/arith.go
index 66fa667482..b202a1549a 100644
--- a/ecc/bls12-377/fp/arith.go
+++ b/ecc/bls12-377/fp/arith.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fp/asm_adx.go b/ecc/bls12-377/fp/asm_adx.go
index f8e29bd1a7..fe25e82db2 100644
--- a/ecc/bls12-377/fp/asm_adx.go
+++ b/ecc/bls12-377/fp/asm_adx.go
@@ -1,18 +1,7 @@
 //go:build !noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fp/asm_noadx.go b/ecc/bls12-377/fp/asm_noadx.go
index cb6cfa0f50..95085a8e6f 100644
--- a/ecc/bls12-377/fp/asm_noadx.go
+++ b/ecc/bls12-377/fp/asm_noadx.go
@@ -1,18 +1,7 @@
 //go:build noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fp/doc.go b/ecc/bls12-377/fp/doc.go
index c4d87f7b01..f06378d9e5 100644
--- a/ecc/bls12-377/fp/doc.go
+++ b/ecc/bls12-377/fp/doc.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fp/element.go b/ecc/bls12-377/fp/element.go
index 1c135e16f9..b96aa88e41 100644
--- a/ecc/bls12-377/fp/element.go
+++ b/ecc/bls12-377/fp/element.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fp/element_amd64.go b/ecc/bls12-377/fp/element_amd64.go
index 77a51ee25e..e72f552ad9 100644
--- a/ecc/bls12-377/fp/element_amd64.go
+++ b/ecc/bls12-377/fp/element_amd64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fp/element_amd64.s b/ecc/bls12-377/fp/element_amd64.s
index 872eddf5d6..b73d1a484e 100644
--- a/ecc/bls12-377/fp/element_amd64.s
+++ b/ecc/bls12-377/fp/element_amd64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fp/element_arm64.go b/ecc/bls12-377/fp/element_arm64.go
index 9793f7eb28..c8eed53698 100644
--- a/ecc/bls12-377/fp/element_arm64.go
+++ b/ecc/bls12-377/fp/element_arm64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fp/element_arm64.s b/ecc/bls12-377/fp/element_arm64.s
index 2a3f7d0b2c..58d21358b0 100644
--- a/ecc/bls12-377/fp/element_arm64.s
+++ b/ecc/bls12-377/fp/element_arm64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fp/element_exp.go b/ecc/bls12-377/fp/element_exp.go
index e3d936dfc1..3434e177e7 100644
--- a/ecc/bls12-377/fp/element_exp.go
+++ b/ecc/bls12-377/fp/element_exp.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fp/element_purego.go b/ecc/bls12-377/fp/element_purego.go
index 93afd90757..fe1b9f55e7 100644
--- a/ecc/bls12-377/fp/element_purego.go
+++ b/ecc/bls12-377/fp/element_purego.go
@@ -1,18 +1,7 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fp/element_test.go b/ecc/bls12-377/fp/element_test.go
index a060095a0a..997dbf4b30 100644
--- a/ecc/bls12-377/fp/element_test.go
+++ b/ecc/bls12-377/fp/element_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fp/hash_to_field/doc.go b/ecc/bls12-377/fp/hash_to_field/doc.go
index 9bb000c8cb..7e034fdde8 100644
--- a/ecc/bls12-377/fp/hash_to_field/doc.go
+++ b/ecc/bls12-377/fp/hash_to_field/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fp/hash_to_field/hash_to_field.go b/ecc/bls12-377/fp/hash_to_field/hash_to_field.go
index 97557a7d48..346b9f4acf 100644
--- a/ecc/bls12-377/fp/hash_to_field/hash_to_field.go
+++ b/ecc/bls12-377/fp/hash_to_field/hash_to_field.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fp/hash_to_field/hash_to_field_test.go b/ecc/bls12-377/fp/hash_to_field/hash_to_field_test.go
index 53f250d110..61b8d32b40 100644
--- a/ecc/bls12-377/fp/hash_to_field/hash_to_field_test.go
+++ b/ecc/bls12-377/fp/hash_to_field/hash_to_field_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fp/vector.go b/ecc/bls12-377/fp/vector.go
index 64228605a8..aba4a810c9 100644
--- a/ecc/bls12-377/fp/vector.go
+++ b/ecc/bls12-377/fp/vector.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fp/vector_purego.go b/ecc/bls12-377/fp/vector_purego.go
index 798b669887..347b0df594 100644
--- a/ecc/bls12-377/fp/vector_purego.go
+++ b/ecc/bls12-377/fp/vector_purego.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fp/vector_test.go b/ecc/bls12-377/fp/vector_test.go
index a8deef9451..9584d79b8b 100644
--- a/ecc/bls12-377/fp/vector_test.go
+++ b/ecc/bls12-377/fp/vector_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/arith.go b/ecc/bls12-377/fr/arith.go
index 83c9fd9ef9..9285041f4b 100644
--- a/ecc/bls12-377/fr/arith.go
+++ b/ecc/bls12-377/fr/arith.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/asm_adx.go b/ecc/bls12-377/fr/asm_adx.go
index 9273ea23ab..9e7da5e865 100644
--- a/ecc/bls12-377/fr/asm_adx.go
+++ b/ecc/bls12-377/fr/asm_adx.go
@@ -1,18 +1,7 @@
 //go:build !noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/asm_avx.go b/ecc/bls12-377/fr/asm_avx.go
index 1cc06c6e8d..d6d7d7f87a 100644
--- a/ecc/bls12-377/fr/asm_avx.go
+++ b/ecc/bls12-377/fr/asm_avx.go
@@ -1,18 +1,7 @@
 //go:build !noavx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/asm_noadx.go b/ecc/bls12-377/fr/asm_noadx.go
index b784a24247..3456158655 100644
--- a/ecc/bls12-377/fr/asm_noadx.go
+++ b/ecc/bls12-377/fr/asm_noadx.go
@@ -1,18 +1,7 @@
 //go:build noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/asm_noavx.go b/ecc/bls12-377/fr/asm_noavx.go
index 66bfc00772..4eb73e9a78 100644
--- a/ecc/bls12-377/fr/asm_noavx.go
+++ b/ecc/bls12-377/fr/asm_noavx.go
@@ -1,18 +1,7 @@
 //go:build noavx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/doc.go b/ecc/bls12-377/fr/doc.go
index 08f1a0ba2e..6e9b45bb4c 100644
--- a/ecc/bls12-377/fr/doc.go
+++ b/ecc/bls12-377/fr/doc.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/element.go b/ecc/bls12-377/fr/element.go
index 93c0d1cc7d..bbcea221bf 100644
--- a/ecc/bls12-377/fr/element.go
+++ b/ecc/bls12-377/fr/element.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/element_amd64.go b/ecc/bls12-377/fr/element_amd64.go
index 0ddb905f7b..ca49d12590 100644
--- a/ecc/bls12-377/fr/element_amd64.go
+++ b/ecc/bls12-377/fr/element_amd64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/element_amd64.s b/ecc/bls12-377/fr/element_amd64.s
index fb00194d7e..ed8a36e04d 100644
--- a/ecc/bls12-377/fr/element_amd64.s
+++ b/ecc/bls12-377/fr/element_amd64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/element_arm64.go b/ecc/bls12-377/fr/element_arm64.go
index fce7cbcd94..a080e8ecab 100644
--- a/ecc/bls12-377/fr/element_arm64.go
+++ b/ecc/bls12-377/fr/element_arm64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/element_arm64.s b/ecc/bls12-377/fr/element_arm64.s
index 5d328815aa..a7bd036553 100644
--- a/ecc/bls12-377/fr/element_arm64.s
+++ b/ecc/bls12-377/fr/element_arm64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/element_exp.go b/ecc/bls12-377/fr/element_exp.go
index 654ea55faa..687051a763 100644
--- a/ecc/bls12-377/fr/element_exp.go
+++ b/ecc/bls12-377/fr/element_exp.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/element_purego.go b/ecc/bls12-377/fr/element_purego.go
index 60de099977..6fd5816ab5 100644
--- a/ecc/bls12-377/fr/element_purego.go
+++ b/ecc/bls12-377/fr/element_purego.go
@@ -1,18 +1,7 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/element_test.go b/ecc/bls12-377/fr/element_test.go
index 27f878c17f..8a527c1ce6 100644
--- a/ecc/bls12-377/fr/element_test.go
+++ b/ecc/bls12-377/fr/element_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/fft/bitreverse.go b/ecc/bls12-377/fr/fft/bitreverse.go
index 104ea5c445..e6e22fad63 100644
--- a/ecc/bls12-377/fr/fft/bitreverse.go
+++ b/ecc/bls12-377/fr/fft/bitreverse.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/fft/bitreverse_test.go b/ecc/bls12-377/fr/fft/bitreverse_test.go
index 0687c079dd..5060ab3649 100644
--- a/ecc/bls12-377/fr/fft/bitreverse_test.go
+++ b/ecc/bls12-377/fr/fft/bitreverse_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/fft/doc.go b/ecc/bls12-377/fr/fft/doc.go
index b5dd44e642..1ef04db2df 100644
--- a/ecc/bls12-377/fr/fft/doc.go
+++ b/ecc/bls12-377/fr/fft/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/fft/domain.go b/ecc/bls12-377/fr/fft/domain.go
index 645b68f4e7..806cf75ce8 100644
--- a/ecc/bls12-377/fr/fft/domain.go
+++ b/ecc/bls12-377/fr/fft/domain.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/fft/domain_test.go b/ecc/bls12-377/fr/fft/domain_test.go
index 83186cb7c9..d95288076c 100644
--- a/ecc/bls12-377/fr/fft/domain_test.go
+++ b/ecc/bls12-377/fr/fft/domain_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/fft/fft.go b/ecc/bls12-377/fr/fft/fft.go
index 634dc309bc..f8b7fe9fcb 100644
--- a/ecc/bls12-377/fr/fft/fft.go
+++ b/ecc/bls12-377/fr/fft/fft.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/fft/fft_test.go b/ecc/bls12-377/fr/fft/fft_test.go
index 9a66ae36e3..36e38e1d90 100644
--- a/ecc/bls12-377/fr/fft/fft_test.go
+++ b/ecc/bls12-377/fr/fft/fft_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/fft/options.go b/ecc/bls12-377/fr/fft/options.go
index e86234633f..ee226588b0 100644
--- a/ecc/bls12-377/fr/fft/options.go
+++ b/ecc/bls12-377/fr/fft/options.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/fri/doc.go b/ecc/bls12-377/fr/fri/doc.go
index 3333ad41f5..428dabf625 100644
--- a/ecc/bls12-377/fr/fri/doc.go
+++ b/ecc/bls12-377/fr/fri/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/fri/fri.go b/ecc/bls12-377/fr/fri/fri.go
index 9a4a8bee11..4556e62599 100644
--- a/ecc/bls12-377/fr/fri/fri.go
+++ b/ecc/bls12-377/fr/fri/fri.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/fri/fri_test.go b/ecc/bls12-377/fr/fri/fri_test.go
index 0da4f02a7e..18cf3780af 100644
--- a/ecc/bls12-377/fr/fri/fri_test.go
+++ b/ecc/bls12-377/fr/fri/fri_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/generator.go b/ecc/bls12-377/fr/generator.go
index 138f039e84..cd232f68b5 100644
--- a/ecc/bls12-377/fr/generator.go
+++ b/ecc/bls12-377/fr/generator.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/gkr/gkr.go b/ecc/bls12-377/fr/gkr/gkr.go
index 5eb0e2c617..05d10acfe8 100644
--- a/ecc/bls12-377/fr/gkr/gkr.go
+++ b/ecc/bls12-377/fr/gkr/gkr.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/gkr/gkr_test.go b/ecc/bls12-377/fr/gkr/gkr_test.go
index d80d1e39f8..b3237624f7 100644
--- a/ecc/bls12-377/fr/gkr/gkr_test.go
+++ b/ecc/bls12-377/fr/gkr/gkr_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/hash_to_field/doc.go b/ecc/bls12-377/fr/hash_to_field/doc.go
index 18904fe7a6..c0e0e7cee4 100644
--- a/ecc/bls12-377/fr/hash_to_field/doc.go
+++ b/ecc/bls12-377/fr/hash_to_field/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/hash_to_field/hash_to_field.go b/ecc/bls12-377/fr/hash_to_field/hash_to_field.go
index d9511f8b9e..27723160a6 100644
--- a/ecc/bls12-377/fr/hash_to_field/hash_to_field.go
+++ b/ecc/bls12-377/fr/hash_to_field/hash_to_field.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/hash_to_field/hash_to_field_test.go b/ecc/bls12-377/fr/hash_to_field/hash_to_field_test.go
index 34d59c231e..16ec5e2e19 100644
--- a/ecc/bls12-377/fr/hash_to_field/hash_to_field_test.go
+++ b/ecc/bls12-377/fr/hash_to_field/hash_to_field_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/iop/doc.go b/ecc/bls12-377/fr/iop/doc.go
index 20f8b1a302..ee3facf1e1 100644
--- a/ecc/bls12-377/fr/iop/doc.go
+++ b/ecc/bls12-377/fr/iop/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/iop/expressions.go b/ecc/bls12-377/fr/iop/expressions.go
index 9b5ffa4de5..c5985c87e9 100644
--- a/ecc/bls12-377/fr/iop/expressions.go
+++ b/ecc/bls12-377/fr/iop/expressions.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/iop/expressions_test.go b/ecc/bls12-377/fr/iop/expressions_test.go
index 60a55ae4c5..5449f30af2 100644
--- a/ecc/bls12-377/fr/iop/expressions_test.go
+++ b/ecc/bls12-377/fr/iop/expressions_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/iop/polynomial.go b/ecc/bls12-377/fr/iop/polynomial.go
index 42bcf9f270..763ad3c070 100644
--- a/ecc/bls12-377/fr/iop/polynomial.go
+++ b/ecc/bls12-377/fr/iop/polynomial.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/iop/polynomial_test.go b/ecc/bls12-377/fr/iop/polynomial_test.go
index b84c4be894..9e9b8ab597 100644
--- a/ecc/bls12-377/fr/iop/polynomial_test.go
+++ b/ecc/bls12-377/fr/iop/polynomial_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/iop/quotient.go b/ecc/bls12-377/fr/iop/quotient.go
index bda2144dd4..dfdafb4a89 100644
--- a/ecc/bls12-377/fr/iop/quotient.go
+++ b/ecc/bls12-377/fr/iop/quotient.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/iop/quotient_test.go b/ecc/bls12-377/fr/iop/quotient_test.go
index 927de2c29e..9d6ae0cfa5 100644
--- a/ecc/bls12-377/fr/iop/quotient_test.go
+++ b/ecc/bls12-377/fr/iop/quotient_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/iop/ratios.go b/ecc/bls12-377/fr/iop/ratios.go
index 1a98136fa9..419cc7a713 100644
--- a/ecc/bls12-377/fr/iop/ratios.go
+++ b/ecc/bls12-377/fr/iop/ratios.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/iop/ratios_test.go b/ecc/bls12-377/fr/iop/ratios_test.go
index 21ae8391dd..a608cf6d1f 100644
--- a/ecc/bls12-377/fr/iop/ratios_test.go
+++ b/ecc/bls12-377/fr/iop/ratios_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/iop/utils.go b/ecc/bls12-377/fr/iop/utils.go
index 5ff7c582d7..beba12b442 100644
--- a/ecc/bls12-377/fr/iop/utils.go
+++ b/ecc/bls12-377/fr/iop/utils.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/mimc/doc.go b/ecc/bls12-377/fr/mimc/doc.go
index 78837e1c80..cc7b101eb4 100644
--- a/ecc/bls12-377/fr/mimc/doc.go
+++ b/ecc/bls12-377/fr/mimc/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/mimc/mimc.go b/ecc/bls12-377/fr/mimc/mimc.go
index ea08f11742..7532333dc1 100644
--- a/ecc/bls12-377/fr/mimc/mimc.go
+++ b/ecc/bls12-377/fr/mimc/mimc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/mimc/options.go b/ecc/bls12-377/fr/mimc/options.go
index be68e4b58f..3c5ad55522 100644
--- a/ecc/bls12-377/fr/mimc/options.go
+++ b/ecc/bls12-377/fr/mimc/options.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/pedersen/doc.go b/ecc/bls12-377/fr/pedersen/doc.go
index 944679f5c5..62a62f179f 100644
--- a/ecc/bls12-377/fr/pedersen/doc.go
+++ b/ecc/bls12-377/fr/pedersen/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/pedersen/example_test.go b/ecc/bls12-377/fr/pedersen/example_test.go
index 8943136ca4..98817493d0 100644
--- a/ecc/bls12-377/fr/pedersen/example_test.go
+++ b/ecc/bls12-377/fr/pedersen/example_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/pedersen/pedersen.go b/ecc/bls12-377/fr/pedersen/pedersen.go
index 1ff3fda8d9..53d0b6823c 100644
--- a/ecc/bls12-377/fr/pedersen/pedersen.go
+++ b/ecc/bls12-377/fr/pedersen/pedersen.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/pedersen/pedersen_test.go b/ecc/bls12-377/fr/pedersen/pedersen_test.go
index 80718aa750..be491105e5 100644
--- a/ecc/bls12-377/fr/pedersen/pedersen_test.go
+++ b/ecc/bls12-377/fr/pedersen/pedersen_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/permutation/doc.go b/ecc/bls12-377/fr/permutation/doc.go
index 7ef21ffb9e..5f346b5a53 100644
--- a/ecc/bls12-377/fr/permutation/doc.go
+++ b/ecc/bls12-377/fr/permutation/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/permutation/permutation.go b/ecc/bls12-377/fr/permutation/permutation.go
index e5c2770dfc..306dbea24c 100644
--- a/ecc/bls12-377/fr/permutation/permutation.go
+++ b/ecc/bls12-377/fr/permutation/permutation.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/permutation/permutation_test.go b/ecc/bls12-377/fr/permutation/permutation_test.go
index d5be9b34b0..68f44d6c1c 100644
--- a/ecc/bls12-377/fr/permutation/permutation_test.go
+++ b/ecc/bls12-377/fr/permutation/permutation_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/plookup/doc.go b/ecc/bls12-377/fr/plookup/doc.go
index b3af019687..d163104002 100644
--- a/ecc/bls12-377/fr/plookup/doc.go
+++ b/ecc/bls12-377/fr/plookup/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/plookup/plookup_test.go b/ecc/bls12-377/fr/plookup/plookup_test.go
index 869922b921..b24b51530c 100644
--- a/ecc/bls12-377/fr/plookup/plookup_test.go
+++ b/ecc/bls12-377/fr/plookup/plookup_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/plookup/table.go b/ecc/bls12-377/fr/plookup/table.go
index 4a299138a1..2dda6bab65 100644
--- a/ecc/bls12-377/fr/plookup/table.go
+++ b/ecc/bls12-377/fr/plookup/table.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/plookup/vector.go b/ecc/bls12-377/fr/plookup/vector.go
index 98583fded9..456c916a3a 100644
--- a/ecc/bls12-377/fr/plookup/vector.go
+++ b/ecc/bls12-377/fr/plookup/vector.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/polynomial/doc.go b/ecc/bls12-377/fr/polynomial/doc.go
index 747da41f2c..35b3f725c1 100644
--- a/ecc/bls12-377/fr/polynomial/doc.go
+++ b/ecc/bls12-377/fr/polynomial/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/polynomial/multilin.go b/ecc/bls12-377/fr/polynomial/multilin.go
index 99538e05aa..e0c5279482 100644
--- a/ecc/bls12-377/fr/polynomial/multilin.go
+++ b/ecc/bls12-377/fr/polynomial/multilin.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/polynomial/multilin_test.go b/ecc/bls12-377/fr/polynomial/multilin_test.go
index 97d95251cd..0ae8feef40 100644
--- a/ecc/bls12-377/fr/polynomial/multilin_test.go
+++ b/ecc/bls12-377/fr/polynomial/multilin_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/polynomial/polynomial.go b/ecc/bls12-377/fr/polynomial/polynomial.go
index cedccbabfc..07f87f7d48 100644
--- a/ecc/bls12-377/fr/polynomial/polynomial.go
+++ b/ecc/bls12-377/fr/polynomial/polynomial.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/polynomial/polynomial_test.go b/ecc/bls12-377/fr/polynomial/polynomial_test.go
index 7909a14b40..a746364b3e 100644
--- a/ecc/bls12-377/fr/polynomial/polynomial_test.go
+++ b/ecc/bls12-377/fr/polynomial/polynomial_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/polynomial/pool.go b/ecc/bls12-377/fr/polynomial/pool.go
index b083a3a8d7..d4c9eb4c21 100644
--- a/ecc/bls12-377/fr/polynomial/pool.go
+++ b/ecc/bls12-377/fr/polynomial/pool.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/poseidon2/poseidon2.go b/ecc/bls12-377/fr/poseidon2/poseidon2.go
index 89e51de1d1..5cf806a339 100644
--- a/ecc/bls12-377/fr/poseidon2/poseidon2.go
+++ b/ecc/bls12-377/fr/poseidon2/poseidon2.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/poseidon2/poseidon2_test.go b/ecc/bls12-377/fr/poseidon2/poseidon2_test.go
index 3c99a43c92..7b19890262 100644
--- a/ecc/bls12-377/fr/poseidon2/poseidon2_test.go
+++ b/ecc/bls12-377/fr/poseidon2/poseidon2_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/sis/sis_fft.go b/ecc/bls12-377/fr/sis/sis_fft.go
index 46e583004d..94523ff134 100644
--- a/ecc/bls12-377/fr/sis/sis_fft.go
+++ b/ecc/bls12-377/fr/sis/sis_fft.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/sumcheck/sumcheck.go b/ecc/bls12-377/fr/sumcheck/sumcheck.go
index cdea58ba86..e053218dd7 100644
--- a/ecc/bls12-377/fr/sumcheck/sumcheck.go
+++ b/ecc/bls12-377/fr/sumcheck/sumcheck.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/sumcheck/sumcheck_test.go b/ecc/bls12-377/fr/sumcheck/sumcheck_test.go
index c26db3571d..ca748084a0 100644
--- a/ecc/bls12-377/fr/sumcheck/sumcheck_test.go
+++ b/ecc/bls12-377/fr/sumcheck/sumcheck_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/test_vector_utils/test_vector_utils.go b/ecc/bls12-377/fr/test_vector_utils/test_vector_utils.go
index 2fb1325877..323f024f55 100644
--- a/ecc/bls12-377/fr/test_vector_utils/test_vector_utils.go
+++ b/ecc/bls12-377/fr/test_vector_utils/test_vector_utils.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/vector.go b/ecc/bls12-377/fr/vector.go
index 867cabbc3d..8b59bd36e9 100644
--- a/ecc/bls12-377/fr/vector.go
+++ b/ecc/bls12-377/fr/vector.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/vector_amd64.go b/ecc/bls12-377/fr/vector_amd64.go
index 0164ecb382..b27679827c 100644
--- a/ecc/bls12-377/fr/vector_amd64.go
+++ b/ecc/bls12-377/fr/vector_amd64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/vector_purego.go b/ecc/bls12-377/fr/vector_purego.go
index 84f86a40b1..5973d16ce2 100644
--- a/ecc/bls12-377/fr/vector_purego.go
+++ b/ecc/bls12-377/fr/vector_purego.go
@@ -1,18 +1,7 @@
 //go:build purego || !amd64
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/fr/vector_test.go b/ecc/bls12-377/fr/vector_test.go
index b6344c18b7..a094bc0ac6 100644
--- a/ecc/bls12-377/fr/vector_test.go
+++ b/ecc/bls12-377/fr/vector_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/g1.go b/ecc/bls12-377/g1.go
index 0cf4f746fd..28ebdceeaf 100644
--- a/ecc/bls12-377/g1.go
+++ b/ecc/bls12-377/g1.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/g1_test.go b/ecc/bls12-377/g1_test.go
index a110a1bf57..e0a147f1fc 100644
--- a/ecc/bls12-377/g1_test.go
+++ b/ecc/bls12-377/g1_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/g2.go b/ecc/bls12-377/g2.go
index 5cb8240d80..68345d1577 100644
--- a/ecc/bls12-377/g2.go
+++ b/ecc/bls12-377/g2.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/g2_test.go b/ecc/bls12-377/g2_test.go
index f18dcdf9d4..397fa2f8e3 100644
--- a/ecc/bls12-377/g2_test.go
+++ b/ecc/bls12-377/g2_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/hash_to_g1.go b/ecc/bls12-377/hash_to_g1.go
index 20306ba879..479a6bfe3e 100644
--- a/ecc/bls12-377/hash_to_g1.go
+++ b/ecc/bls12-377/hash_to_g1.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/hash_to_g1_test.go b/ecc/bls12-377/hash_to_g1_test.go
index 3b7eee61d9..763b1c16f9 100644
--- a/ecc/bls12-377/hash_to_g1_test.go
+++ b/ecc/bls12-377/hash_to_g1_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/hash_to_g2.go b/ecc/bls12-377/hash_to_g2.go
index 66aae9fcc7..d13eb598bf 100644
--- a/ecc/bls12-377/hash_to_g2.go
+++ b/ecc/bls12-377/hash_to_g2.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/hash_to_g2_test.go b/ecc/bls12-377/hash_to_g2_test.go
index d0e2fd6d2a..96d16f74f4 100644
--- a/ecc/bls12-377/hash_to_g2_test.go
+++ b/ecc/bls12-377/hash_to_g2_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/internal/fptower/asm.go b/ecc/bls12-377/internal/fptower/asm.go
index 03b1160807..f1ff282d0b 100644
--- a/ecc/bls12-377/internal/fptower/asm.go
+++ b/ecc/bls12-377/internal/fptower/asm.go
@@ -1,18 +1,7 @@
 //go:build !noadx
 
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/internal/fptower/asm_noadx.go b/ecc/bls12-377/internal/fptower/asm_noadx.go
index ea7782392c..3885d93d55 100644
--- a/ecc/bls12-377/internal/fptower/asm_noadx.go
+++ b/ecc/bls12-377/internal/fptower/asm_noadx.go
@@ -1,18 +1,7 @@
 //go:build noadx
 
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/internal/fptower/e12.go b/ecc/bls12-377/internal/fptower/e12.go
index ca7aef9edb..b60331ac61 100644
--- a/ecc/bls12-377/internal/fptower/e12.go
+++ b/ecc/bls12-377/internal/fptower/e12.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/internal/fptower/e12_test.go b/ecc/bls12-377/internal/fptower/e12_test.go
index ee84fb1c7d..38fa25d17c 100644
--- a/ecc/bls12-377/internal/fptower/e12_test.go
+++ b/ecc/bls12-377/internal/fptower/e12_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/internal/fptower/e2.go b/ecc/bls12-377/internal/fptower/e2.go
index c5f7aaaa26..1979b60dac 100644
--- a/ecc/bls12-377/internal/fptower/e2.go
+++ b/ecc/bls12-377/internal/fptower/e2.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/internal/fptower/e2_amd64.go b/ecc/bls12-377/internal/fptower/e2_amd64.go
index 7df0c375f5..0261c75f69 100644
--- a/ecc/bls12-377/internal/fptower/e2_amd64.go
+++ b/ecc/bls12-377/internal/fptower/e2_amd64.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/internal/fptower/e2_amd64.s b/ecc/bls12-377/internal/fptower/e2_amd64.s
index b52a56a856..78dbffd405 100644
--- a/ecc/bls12-377/internal/fptower/e2_amd64.s
+++ b/ecc/bls12-377/internal/fptower/e2_amd64.s
@@ -1,16 +1,5 @@
 // Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 #include "textflag.h"
 #include "funcdata.h"
diff --git a/ecc/bls12-377/internal/fptower/e2_fallback.go b/ecc/bls12-377/internal/fptower/e2_fallback.go
index 1b6011564f..eaea355699 100644
--- a/ecc/bls12-377/internal/fptower/e2_fallback.go
+++ b/ecc/bls12-377/internal/fptower/e2_fallback.go
@@ -1,18 +1,7 @@
 //go:build !amd64
 
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/internal/fptower/e2_test.go b/ecc/bls12-377/internal/fptower/e2_test.go
index 0546357255..bbca702a27 100644
--- a/ecc/bls12-377/internal/fptower/e2_test.go
+++ b/ecc/bls12-377/internal/fptower/e2_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/internal/fptower/e6.go b/ecc/bls12-377/internal/fptower/e6.go
index 1867470a88..5f2cca6625 100644
--- a/ecc/bls12-377/internal/fptower/e6.go
+++ b/ecc/bls12-377/internal/fptower/e6.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/internal/fptower/e6_test.go b/ecc/bls12-377/internal/fptower/e6_test.go
index b77369e34f..6a1fe41d95 100644
--- a/ecc/bls12-377/internal/fptower/e6_test.go
+++ b/ecc/bls12-377/internal/fptower/e6_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/kzg/doc.go b/ecc/bls12-377/kzg/doc.go
index d1045726f2..6c3454a2d9 100644
--- a/ecc/bls12-377/kzg/doc.go
+++ b/ecc/bls12-377/kzg/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/kzg/kzg.go b/ecc/bls12-377/kzg/kzg.go
index 592858d9e9..4229c90290 100644
--- a/ecc/bls12-377/kzg/kzg.go
+++ b/ecc/bls12-377/kzg/kzg.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/kzg/kzg_test.go b/ecc/bls12-377/kzg/kzg_test.go
index 8110a9be4a..1a2d93402b 100644
--- a/ecc/bls12-377/kzg/kzg_test.go
+++ b/ecc/bls12-377/kzg/kzg_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/kzg/marshal.go b/ecc/bls12-377/kzg/marshal.go
index 64e344ee4e..f4668cae7b 100644
--- a/ecc/bls12-377/kzg/marshal.go
+++ b/ecc/bls12-377/kzg/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/kzg/utils.go b/ecc/bls12-377/kzg/utils.go
index fa89fabde4..31bfffd589 100644
--- a/ecc/bls12-377/kzg/utils.go
+++ b/ecc/bls12-377/kzg/utils.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/marshal.go b/ecc/bls12-377/marshal.go
index 100fad0520..80aeb57ae1 100644
--- a/ecc/bls12-377/marshal.go
+++ b/ecc/bls12-377/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/marshal_test.go b/ecc/bls12-377/marshal_test.go
index 33aeb216ae..2d2561c07c 100644
--- a/ecc/bls12-377/marshal_test.go
+++ b/ecc/bls12-377/marshal_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/multiexp.go b/ecc/bls12-377/multiexp.go
index 6fb9180786..03b7899c09 100644
--- a/ecc/bls12-377/multiexp.go
+++ b/ecc/bls12-377/multiexp.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/multiexp_affine.go b/ecc/bls12-377/multiexp_affine.go
index fcb768be9f..bb1ff3e1d9 100644
--- a/ecc/bls12-377/multiexp_affine.go
+++ b/ecc/bls12-377/multiexp_affine.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/multiexp_jacobian.go b/ecc/bls12-377/multiexp_jacobian.go
index 1c20a8b05b..108879548c 100644
--- a/ecc/bls12-377/multiexp_jacobian.go
+++ b/ecc/bls12-377/multiexp_jacobian.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/multiexp_test.go b/ecc/bls12-377/multiexp_test.go
index 059cf586c3..85b8f6f4cc 100644
--- a/ecc/bls12-377/multiexp_test.go
+++ b/ecc/bls12-377/multiexp_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/pairing_test.go b/ecc/bls12-377/pairing_test.go
index ab01c347e2..0fcc40ac3d 100644
--- a/ecc/bls12-377/pairing_test.go
+++ b/ecc/bls12-377/pairing_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/shplonk/doc.go b/ecc/bls12-377/shplonk/doc.go
index e048f46009..17b34373c2 100644
--- a/ecc/bls12-377/shplonk/doc.go
+++ b/ecc/bls12-377/shplonk/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/shplonk/example_test.go b/ecc/bls12-377/shplonk/example_test.go
index 88c7e07c8d..6b48e973fd 100644
--- a/ecc/bls12-377/shplonk/example_test.go
+++ b/ecc/bls12-377/shplonk/example_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/shplonk/marshal.go b/ecc/bls12-377/shplonk/marshal.go
index c2b805a8b5..8a68a95010 100644
--- a/ecc/bls12-377/shplonk/marshal.go
+++ b/ecc/bls12-377/shplonk/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/shplonk/shplonk.go b/ecc/bls12-377/shplonk/shplonk.go
index 2124ccc6ac..8d8c2ef540 100644
--- a/ecc/bls12-377/shplonk/shplonk.go
+++ b/ecc/bls12-377/shplonk/shplonk.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/shplonk/shplonk_test.go b/ecc/bls12-377/shplonk/shplonk_test.go
index 9b321fa4ef..6edbb14ccd 100644
--- a/ecc/bls12-377/shplonk/shplonk_test.go
+++ b/ecc/bls12-377/shplonk/shplonk_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/twistededwards/curve.go b/ecc/bls12-377/twistededwards/curve.go
index dda19edc93..da66dbc9c3 100644
--- a/ecc/bls12-377/twistededwards/curve.go
+++ b/ecc/bls12-377/twistededwards/curve.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/twistededwards/doc.go b/ecc/bls12-377/twistededwards/doc.go
index d5f67e943b..4f80a5f527 100644
--- a/ecc/bls12-377/twistededwards/doc.go
+++ b/ecc/bls12-377/twistededwards/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/twistededwards/eddsa/doc.go b/ecc/bls12-377/twistededwards/eddsa/doc.go
index 9aa1570fe1..ed4b44dc87 100644
--- a/ecc/bls12-377/twistededwards/eddsa/doc.go
+++ b/ecc/bls12-377/twistededwards/eddsa/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/twistededwards/eddsa/eddsa.go b/ecc/bls12-377/twistededwards/eddsa/eddsa.go
index 0c33c4bafe..4003fda0b5 100644
--- a/ecc/bls12-377/twistededwards/eddsa/eddsa.go
+++ b/ecc/bls12-377/twistededwards/eddsa/eddsa.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/twistededwards/eddsa/eddsa_test.go b/ecc/bls12-377/twistededwards/eddsa/eddsa_test.go
index 807a290e02..54d82cb647 100644
--- a/ecc/bls12-377/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bls12-377/twistededwards/eddsa/eddsa_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/twistededwards/eddsa/marshal.go b/ecc/bls12-377/twistededwards/eddsa/marshal.go
index 38abf01ce7..c6c2295ae9 100644
--- a/ecc/bls12-377/twistededwards/eddsa/marshal.go
+++ b/ecc/bls12-377/twistededwards/eddsa/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/twistededwards/point.go b/ecc/bls12-377/twistededwards/point.go
index 4bd6487dfc..5a7b088e72 100644
--- a/ecc/bls12-377/twistededwards/point.go
+++ b/ecc/bls12-377/twistededwards/point.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-377/twistededwards/point_test.go b/ecc/bls12-377/twistededwards/point_test.go
index 451a00d172..6875b7aa9a 100644
--- a/ecc/bls12-377/twistededwards/point_test.go
+++ b/ecc/bls12-377/twistededwards/point_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/bandersnatch/curve.go b/ecc/bls12-381/bandersnatch/curve.go
index e146c9c334..ba94898222 100644
--- a/ecc/bls12-381/bandersnatch/curve.go
+++ b/ecc/bls12-381/bandersnatch/curve.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/bandersnatch/doc.go b/ecc/bls12-381/bandersnatch/doc.go
index 39d67510d5..66d3b68eaa 100644
--- a/ecc/bls12-381/bandersnatch/doc.go
+++ b/ecc/bls12-381/bandersnatch/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/bandersnatch/eddsa/doc.go b/ecc/bls12-381/bandersnatch/eddsa/doc.go
index acd950c598..2e2ee33568 100644
--- a/ecc/bls12-381/bandersnatch/eddsa/doc.go
+++ b/ecc/bls12-381/bandersnatch/eddsa/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/bandersnatch/eddsa/eddsa.go b/ecc/bls12-381/bandersnatch/eddsa/eddsa.go
index f68b7ce7de..3bab9a4046 100644
--- a/ecc/bls12-381/bandersnatch/eddsa/eddsa.go
+++ b/ecc/bls12-381/bandersnatch/eddsa/eddsa.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/bandersnatch/eddsa/eddsa_test.go b/ecc/bls12-381/bandersnatch/eddsa/eddsa_test.go
index 91cd6b5f59..972c06d0d0 100644
--- a/ecc/bls12-381/bandersnatch/eddsa/eddsa_test.go
+++ b/ecc/bls12-381/bandersnatch/eddsa/eddsa_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/bandersnatch/eddsa/marshal.go b/ecc/bls12-381/bandersnatch/eddsa/marshal.go
index eb55b12c55..2f4f26d4f3 100644
--- a/ecc/bls12-381/bandersnatch/eddsa/marshal.go
+++ b/ecc/bls12-381/bandersnatch/eddsa/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/bandersnatch/point.go b/ecc/bls12-381/bandersnatch/point.go
index ab8691abfc..5507adf2d7 100644
--- a/ecc/bls12-381/bandersnatch/point.go
+++ b/ecc/bls12-381/bandersnatch/point.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/bandersnatch/point_test.go b/ecc/bls12-381/bandersnatch/point_test.go
index 173f6da392..d67906e7ff 100644
--- a/ecc/bls12-381/bandersnatch/point_test.go
+++ b/ecc/bls12-381/bandersnatch/point_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/ecdsa/doc.go b/ecc/bls12-381/ecdsa/doc.go
index d8d1f366e4..b9a6baabd1 100644
--- a/ecc/bls12-381/ecdsa/doc.go
+++ b/ecc/bls12-381/ecdsa/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/ecdsa/ecdsa.go b/ecc/bls12-381/ecdsa/ecdsa.go
index 9944b89543..9c4745741f 100644
--- a/ecc/bls12-381/ecdsa/ecdsa.go
+++ b/ecc/bls12-381/ecdsa/ecdsa.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/ecdsa/ecdsa_test.go b/ecc/bls12-381/ecdsa/ecdsa_test.go
index dae3a56b1c..aa704d9e66 100644
--- a/ecc/bls12-381/ecdsa/ecdsa_test.go
+++ b/ecc/bls12-381/ecdsa/ecdsa_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/ecdsa/marshal.go b/ecc/bls12-381/ecdsa/marshal.go
index a580e4da98..09877ff47c 100644
--- a/ecc/bls12-381/ecdsa/marshal.go
+++ b/ecc/bls12-381/ecdsa/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/ecdsa/marshal_test.go b/ecc/bls12-381/ecdsa/marshal_test.go
index 1b61b07144..1b32bceb36 100644
--- a/ecc/bls12-381/ecdsa/marshal_test.go
+++ b/ecc/bls12-381/ecdsa/marshal_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fflonk/doc.go b/ecc/bls12-381/fflonk/doc.go
index 694eaa9734..b717383d87 100644
--- a/ecc/bls12-381/fflonk/doc.go
+++ b/ecc/bls12-381/fflonk/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fflonk/example_test.go b/ecc/bls12-381/fflonk/example_test.go
index 61bd6079f4..7a44bac8c6 100644
--- a/ecc/bls12-381/fflonk/example_test.go
+++ b/ecc/bls12-381/fflonk/example_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fflonk/fflonk.go b/ecc/bls12-381/fflonk/fflonk.go
index 293d58f181..fe4bb1710b 100644
--- a/ecc/bls12-381/fflonk/fflonk.go
+++ b/ecc/bls12-381/fflonk/fflonk.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fflonk/fflonk_test.go b/ecc/bls12-381/fflonk/fflonk_test.go
index ad8519fedc..a15e154d32 100644
--- a/ecc/bls12-381/fflonk/fflonk_test.go
+++ b/ecc/bls12-381/fflonk/fflonk_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fflonk/marshal.go b/ecc/bls12-381/fflonk/marshal.go
index cdf278f6f5..d1147eac9b 100644
--- a/ecc/bls12-381/fflonk/marshal.go
+++ b/ecc/bls12-381/fflonk/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fp/arith.go b/ecc/bls12-381/fp/arith.go
index 66fa667482..b202a1549a 100644
--- a/ecc/bls12-381/fp/arith.go
+++ b/ecc/bls12-381/fp/arith.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fp/asm_adx.go b/ecc/bls12-381/fp/asm_adx.go
index f8e29bd1a7..fe25e82db2 100644
--- a/ecc/bls12-381/fp/asm_adx.go
+++ b/ecc/bls12-381/fp/asm_adx.go
@@ -1,18 +1,7 @@
 //go:build !noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fp/asm_noadx.go b/ecc/bls12-381/fp/asm_noadx.go
index cb6cfa0f50..95085a8e6f 100644
--- a/ecc/bls12-381/fp/asm_noadx.go
+++ b/ecc/bls12-381/fp/asm_noadx.go
@@ -1,18 +1,7 @@
 //go:build noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fp/doc.go b/ecc/bls12-381/fp/doc.go
index bf5b82c113..d6b85f7ead 100644
--- a/ecc/bls12-381/fp/doc.go
+++ b/ecc/bls12-381/fp/doc.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fp/element.go b/ecc/bls12-381/fp/element.go
index d5c6cefb2a..2e4225b51b 100644
--- a/ecc/bls12-381/fp/element.go
+++ b/ecc/bls12-381/fp/element.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fp/element_amd64.go b/ecc/bls12-381/fp/element_amd64.go
index 77a51ee25e..e72f552ad9 100644
--- a/ecc/bls12-381/fp/element_amd64.go
+++ b/ecc/bls12-381/fp/element_amd64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fp/element_amd64.s b/ecc/bls12-381/fp/element_amd64.s
index 872eddf5d6..b73d1a484e 100644
--- a/ecc/bls12-381/fp/element_amd64.s
+++ b/ecc/bls12-381/fp/element_amd64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fp/element_arm64.go b/ecc/bls12-381/fp/element_arm64.go
index 044b606293..152c411bf3 100644
--- a/ecc/bls12-381/fp/element_arm64.go
+++ b/ecc/bls12-381/fp/element_arm64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fp/element_arm64.s b/ecc/bls12-381/fp/element_arm64.s
index 2a3f7d0b2c..58d21358b0 100644
--- a/ecc/bls12-381/fp/element_arm64.s
+++ b/ecc/bls12-381/fp/element_arm64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fp/element_exp.go b/ecc/bls12-381/fp/element_exp.go
index 4d7fafa0a1..1b611bf6d9 100644
--- a/ecc/bls12-381/fp/element_exp.go
+++ b/ecc/bls12-381/fp/element_exp.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fp/element_purego.go b/ecc/bls12-381/fp/element_purego.go
index ac96223a0a..40760eceec 100644
--- a/ecc/bls12-381/fp/element_purego.go
+++ b/ecc/bls12-381/fp/element_purego.go
@@ -1,18 +1,7 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fp/element_test.go b/ecc/bls12-381/fp/element_test.go
index af57409dab..35f8d69404 100644
--- a/ecc/bls12-381/fp/element_test.go
+++ b/ecc/bls12-381/fp/element_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fp/hash_to_field/doc.go b/ecc/bls12-381/fp/hash_to_field/doc.go
index 62985095c3..fff88b2c11 100644
--- a/ecc/bls12-381/fp/hash_to_field/doc.go
+++ b/ecc/bls12-381/fp/hash_to_field/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fp/hash_to_field/hash_to_field.go b/ecc/bls12-381/fp/hash_to_field/hash_to_field.go
index e93aad9b8a..3a895a5321 100644
--- a/ecc/bls12-381/fp/hash_to_field/hash_to_field.go
+++ b/ecc/bls12-381/fp/hash_to_field/hash_to_field.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fp/hash_to_field/hash_to_field_test.go b/ecc/bls12-381/fp/hash_to_field/hash_to_field_test.go
index 0caad4c595..5ae9b78072 100644
--- a/ecc/bls12-381/fp/hash_to_field/hash_to_field_test.go
+++ b/ecc/bls12-381/fp/hash_to_field/hash_to_field_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fp/vector.go b/ecc/bls12-381/fp/vector.go
index 64228605a8..aba4a810c9 100644
--- a/ecc/bls12-381/fp/vector.go
+++ b/ecc/bls12-381/fp/vector.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fp/vector_purego.go b/ecc/bls12-381/fp/vector_purego.go
index 798b669887..347b0df594 100644
--- a/ecc/bls12-381/fp/vector_purego.go
+++ b/ecc/bls12-381/fp/vector_purego.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fp/vector_test.go b/ecc/bls12-381/fp/vector_test.go
index a8deef9451..9584d79b8b 100644
--- a/ecc/bls12-381/fp/vector_test.go
+++ b/ecc/bls12-381/fp/vector_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/arith.go b/ecc/bls12-381/fr/arith.go
index 83c9fd9ef9..9285041f4b 100644
--- a/ecc/bls12-381/fr/arith.go
+++ b/ecc/bls12-381/fr/arith.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/asm_adx.go b/ecc/bls12-381/fr/asm_adx.go
index 9273ea23ab..9e7da5e865 100644
--- a/ecc/bls12-381/fr/asm_adx.go
+++ b/ecc/bls12-381/fr/asm_adx.go
@@ -1,18 +1,7 @@
 //go:build !noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/asm_avx.go b/ecc/bls12-381/fr/asm_avx.go
index 1cc06c6e8d..d6d7d7f87a 100644
--- a/ecc/bls12-381/fr/asm_avx.go
+++ b/ecc/bls12-381/fr/asm_avx.go
@@ -1,18 +1,7 @@
 //go:build !noavx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/asm_noadx.go b/ecc/bls12-381/fr/asm_noadx.go
index b784a24247..3456158655 100644
--- a/ecc/bls12-381/fr/asm_noadx.go
+++ b/ecc/bls12-381/fr/asm_noadx.go
@@ -1,18 +1,7 @@
 //go:build noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/asm_noavx.go b/ecc/bls12-381/fr/asm_noavx.go
index 66bfc00772..4eb73e9a78 100644
--- a/ecc/bls12-381/fr/asm_noavx.go
+++ b/ecc/bls12-381/fr/asm_noavx.go
@@ -1,18 +1,7 @@
 //go:build noavx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/doc.go b/ecc/bls12-381/fr/doc.go
index 71ea8a2dc9..6aa24dfcc3 100644
--- a/ecc/bls12-381/fr/doc.go
+++ b/ecc/bls12-381/fr/doc.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/element.go b/ecc/bls12-381/fr/element.go
index 5d218be808..62f75ce27b 100644
--- a/ecc/bls12-381/fr/element.go
+++ b/ecc/bls12-381/fr/element.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/element_amd64.go b/ecc/bls12-381/fr/element_amd64.go
index 0ddb905f7b..ca49d12590 100644
--- a/ecc/bls12-381/fr/element_amd64.go
+++ b/ecc/bls12-381/fr/element_amd64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/element_amd64.s b/ecc/bls12-381/fr/element_amd64.s
index fb00194d7e..ed8a36e04d 100644
--- a/ecc/bls12-381/fr/element_amd64.s
+++ b/ecc/bls12-381/fr/element_amd64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/element_arm64.go b/ecc/bls12-381/fr/element_arm64.go
index e82da3dad7..c87ab28031 100644
--- a/ecc/bls12-381/fr/element_arm64.go
+++ b/ecc/bls12-381/fr/element_arm64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/element_arm64.s b/ecc/bls12-381/fr/element_arm64.s
index 5d328815aa..a7bd036553 100644
--- a/ecc/bls12-381/fr/element_arm64.s
+++ b/ecc/bls12-381/fr/element_arm64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/element_exp.go b/ecc/bls12-381/fr/element_exp.go
index 48073af8e6..6abe0add74 100644
--- a/ecc/bls12-381/fr/element_exp.go
+++ b/ecc/bls12-381/fr/element_exp.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/element_purego.go b/ecc/bls12-381/fr/element_purego.go
index 193edfb5d2..57f00871c2 100644
--- a/ecc/bls12-381/fr/element_purego.go
+++ b/ecc/bls12-381/fr/element_purego.go
@@ -1,18 +1,7 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/element_test.go b/ecc/bls12-381/fr/element_test.go
index b9bc1e3979..049a31f4be 100644
--- a/ecc/bls12-381/fr/element_test.go
+++ b/ecc/bls12-381/fr/element_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/fft/bitreverse.go b/ecc/bls12-381/fr/fft/bitreverse.go
index 9721f5454d..d8482da16e 100644
--- a/ecc/bls12-381/fr/fft/bitreverse.go
+++ b/ecc/bls12-381/fr/fft/bitreverse.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/fft/bitreverse_test.go b/ecc/bls12-381/fr/fft/bitreverse_test.go
index 8bffd1270a..98ebd726bb 100644
--- a/ecc/bls12-381/fr/fft/bitreverse_test.go
+++ b/ecc/bls12-381/fr/fft/bitreverse_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/fft/doc.go b/ecc/bls12-381/fr/fft/doc.go
index b5dd44e642..1ef04db2df 100644
--- a/ecc/bls12-381/fr/fft/doc.go
+++ b/ecc/bls12-381/fr/fft/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/fft/domain.go b/ecc/bls12-381/fr/fft/domain.go
index 7913415e10..cadf32fcd1 100644
--- a/ecc/bls12-381/fr/fft/domain.go
+++ b/ecc/bls12-381/fr/fft/domain.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/fft/domain_test.go b/ecc/bls12-381/fr/fft/domain_test.go
index 83186cb7c9..d95288076c 100644
--- a/ecc/bls12-381/fr/fft/domain_test.go
+++ b/ecc/bls12-381/fr/fft/domain_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/fft/fft.go b/ecc/bls12-381/fr/fft/fft.go
index c6e1cf2622..85722b5eb1 100644
--- a/ecc/bls12-381/fr/fft/fft.go
+++ b/ecc/bls12-381/fr/fft/fft.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/fft/fft_test.go b/ecc/bls12-381/fr/fft/fft_test.go
index 9956baf638..774b42ab43 100644
--- a/ecc/bls12-381/fr/fft/fft_test.go
+++ b/ecc/bls12-381/fr/fft/fft_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/fft/options.go b/ecc/bls12-381/fr/fft/options.go
index 5ae24b7098..cdd4fa97ff 100644
--- a/ecc/bls12-381/fr/fft/options.go
+++ b/ecc/bls12-381/fr/fft/options.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/fri/doc.go b/ecc/bls12-381/fr/fri/doc.go
index 3333ad41f5..428dabf625 100644
--- a/ecc/bls12-381/fr/fri/doc.go
+++ b/ecc/bls12-381/fr/fri/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/fri/fri.go b/ecc/bls12-381/fr/fri/fri.go
index c206e7c5b4..1ac43ff169 100644
--- a/ecc/bls12-381/fr/fri/fri.go
+++ b/ecc/bls12-381/fr/fri/fri.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/fri/fri_test.go b/ecc/bls12-381/fr/fri/fri_test.go
index 049723ae5a..8cc11c42f4 100644
--- a/ecc/bls12-381/fr/fri/fri_test.go
+++ b/ecc/bls12-381/fr/fri/fri_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/generator.go b/ecc/bls12-381/fr/generator.go
index 15f2595e40..6d9ebe7a2f 100644
--- a/ecc/bls12-381/fr/generator.go
+++ b/ecc/bls12-381/fr/generator.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/gkr/gkr.go b/ecc/bls12-381/fr/gkr/gkr.go
index b4d322ad16..0d3dabbd1a 100644
--- a/ecc/bls12-381/fr/gkr/gkr.go
+++ b/ecc/bls12-381/fr/gkr/gkr.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/gkr/gkr_test.go b/ecc/bls12-381/fr/gkr/gkr_test.go
index 1c3ee3d233..a6c5e86119 100644
--- a/ecc/bls12-381/fr/gkr/gkr_test.go
+++ b/ecc/bls12-381/fr/gkr/gkr_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/hash_to_field/doc.go b/ecc/bls12-381/fr/hash_to_field/doc.go
index 1f8351d2a6..345c8b57df 100644
--- a/ecc/bls12-381/fr/hash_to_field/doc.go
+++ b/ecc/bls12-381/fr/hash_to_field/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/hash_to_field/hash_to_field.go b/ecc/bls12-381/fr/hash_to_field/hash_to_field.go
index 6febcadd1e..174e7f6303 100644
--- a/ecc/bls12-381/fr/hash_to_field/hash_to_field.go
+++ b/ecc/bls12-381/fr/hash_to_field/hash_to_field.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/hash_to_field/hash_to_field_test.go b/ecc/bls12-381/fr/hash_to_field/hash_to_field_test.go
index 3558a524f7..67fe5640d6 100644
--- a/ecc/bls12-381/fr/hash_to_field/hash_to_field_test.go
+++ b/ecc/bls12-381/fr/hash_to_field/hash_to_field_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/iop/doc.go b/ecc/bls12-381/fr/iop/doc.go
index 20f8b1a302..ee3facf1e1 100644
--- a/ecc/bls12-381/fr/iop/doc.go
+++ b/ecc/bls12-381/fr/iop/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/iop/expressions.go b/ecc/bls12-381/fr/iop/expressions.go
index 8435c07b1b..bd85279e75 100644
--- a/ecc/bls12-381/fr/iop/expressions.go
+++ b/ecc/bls12-381/fr/iop/expressions.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/iop/expressions_test.go b/ecc/bls12-381/fr/iop/expressions_test.go
index 78b89d4382..003c4ee78a 100644
--- a/ecc/bls12-381/fr/iop/expressions_test.go
+++ b/ecc/bls12-381/fr/iop/expressions_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/iop/polynomial.go b/ecc/bls12-381/fr/iop/polynomial.go
index a928787e41..8bb33d05c6 100644
--- a/ecc/bls12-381/fr/iop/polynomial.go
+++ b/ecc/bls12-381/fr/iop/polynomial.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/iop/polynomial_test.go b/ecc/bls12-381/fr/iop/polynomial_test.go
index 9d4455ead4..dcc85a2193 100644
--- a/ecc/bls12-381/fr/iop/polynomial_test.go
+++ b/ecc/bls12-381/fr/iop/polynomial_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/iop/quotient.go b/ecc/bls12-381/fr/iop/quotient.go
index 84cb272af6..9c2b4a3f6d 100644
--- a/ecc/bls12-381/fr/iop/quotient.go
+++ b/ecc/bls12-381/fr/iop/quotient.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/iop/quotient_test.go b/ecc/bls12-381/fr/iop/quotient_test.go
index 722d2397cc..0981a0a411 100644
--- a/ecc/bls12-381/fr/iop/quotient_test.go
+++ b/ecc/bls12-381/fr/iop/quotient_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/iop/ratios.go b/ecc/bls12-381/fr/iop/ratios.go
index 17cd7b98d2..39adead354 100644
--- a/ecc/bls12-381/fr/iop/ratios.go
+++ b/ecc/bls12-381/fr/iop/ratios.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/iop/ratios_test.go b/ecc/bls12-381/fr/iop/ratios_test.go
index 0c80a19580..7d0e8b0030 100644
--- a/ecc/bls12-381/fr/iop/ratios_test.go
+++ b/ecc/bls12-381/fr/iop/ratios_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/iop/utils.go b/ecc/bls12-381/fr/iop/utils.go
index 53de1e2bec..e65cafda8e 100644
--- a/ecc/bls12-381/fr/iop/utils.go
+++ b/ecc/bls12-381/fr/iop/utils.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/mimc/doc.go b/ecc/bls12-381/fr/mimc/doc.go
index 78837e1c80..cc7b101eb4 100644
--- a/ecc/bls12-381/fr/mimc/doc.go
+++ b/ecc/bls12-381/fr/mimc/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/mimc/mimc.go b/ecc/bls12-381/fr/mimc/mimc.go
index f492cadf96..8455789c59 100644
--- a/ecc/bls12-381/fr/mimc/mimc.go
+++ b/ecc/bls12-381/fr/mimc/mimc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/mimc/options.go b/ecc/bls12-381/fr/mimc/options.go
index 20d1dafba8..25f1e024b2 100644
--- a/ecc/bls12-381/fr/mimc/options.go
+++ b/ecc/bls12-381/fr/mimc/options.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/pedersen/doc.go b/ecc/bls12-381/fr/pedersen/doc.go
index 944679f5c5..62a62f179f 100644
--- a/ecc/bls12-381/fr/pedersen/doc.go
+++ b/ecc/bls12-381/fr/pedersen/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/pedersen/example_test.go b/ecc/bls12-381/fr/pedersen/example_test.go
index 5273b0b901..23a97be288 100644
--- a/ecc/bls12-381/fr/pedersen/example_test.go
+++ b/ecc/bls12-381/fr/pedersen/example_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/pedersen/pedersen.go b/ecc/bls12-381/fr/pedersen/pedersen.go
index 09830a7759..ffbd2bc283 100644
--- a/ecc/bls12-381/fr/pedersen/pedersen.go
+++ b/ecc/bls12-381/fr/pedersen/pedersen.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/pedersen/pedersen_test.go b/ecc/bls12-381/fr/pedersen/pedersen_test.go
index 833f0c66a1..6728acb8ab 100644
--- a/ecc/bls12-381/fr/pedersen/pedersen_test.go
+++ b/ecc/bls12-381/fr/pedersen/pedersen_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/permutation/doc.go b/ecc/bls12-381/fr/permutation/doc.go
index 7ef21ffb9e..5f346b5a53 100644
--- a/ecc/bls12-381/fr/permutation/doc.go
+++ b/ecc/bls12-381/fr/permutation/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/permutation/permutation.go b/ecc/bls12-381/fr/permutation/permutation.go
index 00c0cebfdb..0e8623fcb0 100644
--- a/ecc/bls12-381/fr/permutation/permutation.go
+++ b/ecc/bls12-381/fr/permutation/permutation.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/permutation/permutation_test.go b/ecc/bls12-381/fr/permutation/permutation_test.go
index 980db6fae0..b95c1e45c8 100644
--- a/ecc/bls12-381/fr/permutation/permutation_test.go
+++ b/ecc/bls12-381/fr/permutation/permutation_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/plookup/doc.go b/ecc/bls12-381/fr/plookup/doc.go
index b3af019687..d163104002 100644
--- a/ecc/bls12-381/fr/plookup/doc.go
+++ b/ecc/bls12-381/fr/plookup/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/plookup/plookup_test.go b/ecc/bls12-381/fr/plookup/plookup_test.go
index f92fecdf11..6155368448 100644
--- a/ecc/bls12-381/fr/plookup/plookup_test.go
+++ b/ecc/bls12-381/fr/plookup/plookup_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/plookup/table.go b/ecc/bls12-381/fr/plookup/table.go
index c191752dad..cb08029bb7 100644
--- a/ecc/bls12-381/fr/plookup/table.go
+++ b/ecc/bls12-381/fr/plookup/table.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/plookup/vector.go b/ecc/bls12-381/fr/plookup/vector.go
index 4ed22fb165..f5dfd96335 100644
--- a/ecc/bls12-381/fr/plookup/vector.go
+++ b/ecc/bls12-381/fr/plookup/vector.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/polynomial/doc.go b/ecc/bls12-381/fr/polynomial/doc.go
index 747da41f2c..35b3f725c1 100644
--- a/ecc/bls12-381/fr/polynomial/doc.go
+++ b/ecc/bls12-381/fr/polynomial/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/polynomial/multilin.go b/ecc/bls12-381/fr/polynomial/multilin.go
index 91d205e8e1..2210816ca7 100644
--- a/ecc/bls12-381/fr/polynomial/multilin.go
+++ b/ecc/bls12-381/fr/polynomial/multilin.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/polynomial/multilin_test.go b/ecc/bls12-381/fr/polynomial/multilin_test.go
index 70cf0daf63..cca2a08d24 100644
--- a/ecc/bls12-381/fr/polynomial/multilin_test.go
+++ b/ecc/bls12-381/fr/polynomial/multilin_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/polynomial/polynomial.go b/ecc/bls12-381/fr/polynomial/polynomial.go
index ca0956eb81..a5acca4a65 100644
--- a/ecc/bls12-381/fr/polynomial/polynomial.go
+++ b/ecc/bls12-381/fr/polynomial/polynomial.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/polynomial/polynomial_test.go b/ecc/bls12-381/fr/polynomial/polynomial_test.go
index bdd50748c5..12868919f9 100644
--- a/ecc/bls12-381/fr/polynomial/polynomial_test.go
+++ b/ecc/bls12-381/fr/polynomial/polynomial_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/polynomial/pool.go b/ecc/bls12-381/fr/polynomial/pool.go
index 016ca4265e..fd736e33b8 100644
--- a/ecc/bls12-381/fr/polynomial/pool.go
+++ b/ecc/bls12-381/fr/polynomial/pool.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/poseidon2/poseidon2.go b/ecc/bls12-381/fr/poseidon2/poseidon2.go
index a3bf1b14de..e33bff9bce 100644
--- a/ecc/bls12-381/fr/poseidon2/poseidon2.go
+++ b/ecc/bls12-381/fr/poseidon2/poseidon2.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/poseidon2/poseidon2_test.go b/ecc/bls12-381/fr/poseidon2/poseidon2_test.go
index c41de997cc..0345323466 100644
--- a/ecc/bls12-381/fr/poseidon2/poseidon2_test.go
+++ b/ecc/bls12-381/fr/poseidon2/poseidon2_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/sumcheck/sumcheck.go b/ecc/bls12-381/fr/sumcheck/sumcheck.go
index 7f7d605ef0..b15dfc199b 100644
--- a/ecc/bls12-381/fr/sumcheck/sumcheck.go
+++ b/ecc/bls12-381/fr/sumcheck/sumcheck.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/sumcheck/sumcheck_test.go b/ecc/bls12-381/fr/sumcheck/sumcheck_test.go
index 778b9ca8da..b0ef690a61 100644
--- a/ecc/bls12-381/fr/sumcheck/sumcheck_test.go
+++ b/ecc/bls12-381/fr/sumcheck/sumcheck_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/test_vector_utils/test_vector_utils.go b/ecc/bls12-381/fr/test_vector_utils/test_vector_utils.go
index 7360ff314f..95d4ab283e 100644
--- a/ecc/bls12-381/fr/test_vector_utils/test_vector_utils.go
+++ b/ecc/bls12-381/fr/test_vector_utils/test_vector_utils.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/vector.go b/ecc/bls12-381/fr/vector.go
index 867cabbc3d..8b59bd36e9 100644
--- a/ecc/bls12-381/fr/vector.go
+++ b/ecc/bls12-381/fr/vector.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/vector_amd64.go b/ecc/bls12-381/fr/vector_amd64.go
index 0164ecb382..b27679827c 100644
--- a/ecc/bls12-381/fr/vector_amd64.go
+++ b/ecc/bls12-381/fr/vector_amd64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/vector_purego.go b/ecc/bls12-381/fr/vector_purego.go
index 84f86a40b1..5973d16ce2 100644
--- a/ecc/bls12-381/fr/vector_purego.go
+++ b/ecc/bls12-381/fr/vector_purego.go
@@ -1,18 +1,7 @@
 //go:build purego || !amd64
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/fr/vector_test.go b/ecc/bls12-381/fr/vector_test.go
index b6344c18b7..a094bc0ac6 100644
--- a/ecc/bls12-381/fr/vector_test.go
+++ b/ecc/bls12-381/fr/vector_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/g1.go b/ecc/bls12-381/g1.go
index 9ecf220da7..1744ec2816 100644
--- a/ecc/bls12-381/g1.go
+++ b/ecc/bls12-381/g1.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/g1_test.go b/ecc/bls12-381/g1_test.go
index 507fa71160..20d77f4b2f 100644
--- a/ecc/bls12-381/g1_test.go
+++ b/ecc/bls12-381/g1_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/g2.go b/ecc/bls12-381/g2.go
index 51b03fc595..b725907acb 100644
--- a/ecc/bls12-381/g2.go
+++ b/ecc/bls12-381/g2.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/g2_test.go b/ecc/bls12-381/g2_test.go
index d15ac8715a..244c6ae3b8 100644
--- a/ecc/bls12-381/g2_test.go
+++ b/ecc/bls12-381/g2_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/hash_to_g1.go b/ecc/bls12-381/hash_to_g1.go
index 7152782835..1ba586b5fa 100644
--- a/ecc/bls12-381/hash_to_g1.go
+++ b/ecc/bls12-381/hash_to_g1.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/hash_to_g1_test.go b/ecc/bls12-381/hash_to_g1_test.go
index bb9dd54431..2bfa52ae4f 100644
--- a/ecc/bls12-381/hash_to_g1_test.go
+++ b/ecc/bls12-381/hash_to_g1_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/hash_to_g2.go b/ecc/bls12-381/hash_to_g2.go
index 4feafbfb14..43833ecda0 100644
--- a/ecc/bls12-381/hash_to_g2.go
+++ b/ecc/bls12-381/hash_to_g2.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/hash_to_g2_test.go b/ecc/bls12-381/hash_to_g2_test.go
index cb4fb085e9..142dd2695a 100644
--- a/ecc/bls12-381/hash_to_g2_test.go
+++ b/ecc/bls12-381/hash_to_g2_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/internal/fptower/asm.go b/ecc/bls12-381/internal/fptower/asm.go
index 03b1160807..f1ff282d0b 100644
--- a/ecc/bls12-381/internal/fptower/asm.go
+++ b/ecc/bls12-381/internal/fptower/asm.go
@@ -1,18 +1,7 @@
 //go:build !noadx
 
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/internal/fptower/asm_noadx.go b/ecc/bls12-381/internal/fptower/asm_noadx.go
index ea7782392c..3885d93d55 100644
--- a/ecc/bls12-381/internal/fptower/asm_noadx.go
+++ b/ecc/bls12-381/internal/fptower/asm_noadx.go
@@ -1,18 +1,7 @@
 //go:build noadx
 
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/internal/fptower/e12.go b/ecc/bls12-381/internal/fptower/e12.go
index 65945c3d9d..8664b8f175 100644
--- a/ecc/bls12-381/internal/fptower/e12.go
+++ b/ecc/bls12-381/internal/fptower/e12.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/internal/fptower/e12_test.go b/ecc/bls12-381/internal/fptower/e12_test.go
index 4552be864e..b7b1f6181a 100644
--- a/ecc/bls12-381/internal/fptower/e12_test.go
+++ b/ecc/bls12-381/internal/fptower/e12_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/internal/fptower/e2.go b/ecc/bls12-381/internal/fptower/e2.go
index 75fd711c78..64c535073b 100644
--- a/ecc/bls12-381/internal/fptower/e2.go
+++ b/ecc/bls12-381/internal/fptower/e2.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/internal/fptower/e2_amd64.go b/ecc/bls12-381/internal/fptower/e2_amd64.go
index 469d319277..872fb85e56 100644
--- a/ecc/bls12-381/internal/fptower/e2_amd64.go
+++ b/ecc/bls12-381/internal/fptower/e2_amd64.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/internal/fptower/e2_amd64.s b/ecc/bls12-381/internal/fptower/e2_amd64.s
index e90e3ed545..6163a305b6 100644
--- a/ecc/bls12-381/internal/fptower/e2_amd64.s
+++ b/ecc/bls12-381/internal/fptower/e2_amd64.s
@@ -1,16 +1,5 @@
 // Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 #include "textflag.h"
 #include "funcdata.h"
diff --git a/ecc/bls12-381/internal/fptower/e2_fallback.go b/ecc/bls12-381/internal/fptower/e2_fallback.go
index 1b6011564f..eaea355699 100644
--- a/ecc/bls12-381/internal/fptower/e2_fallback.go
+++ b/ecc/bls12-381/internal/fptower/e2_fallback.go
@@ -1,18 +1,7 @@
 //go:build !amd64
 
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/internal/fptower/e2_test.go b/ecc/bls12-381/internal/fptower/e2_test.go
index 6938e67b09..e5e2a26bc7 100644
--- a/ecc/bls12-381/internal/fptower/e2_test.go
+++ b/ecc/bls12-381/internal/fptower/e2_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/internal/fptower/e6.go b/ecc/bls12-381/internal/fptower/e6.go
index 1867470a88..5f2cca6625 100644
--- a/ecc/bls12-381/internal/fptower/e6.go
+++ b/ecc/bls12-381/internal/fptower/e6.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/internal/fptower/e6_test.go b/ecc/bls12-381/internal/fptower/e6_test.go
index fda2f22838..c6e33e9766 100644
--- a/ecc/bls12-381/internal/fptower/e6_test.go
+++ b/ecc/bls12-381/internal/fptower/e6_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/kzg/doc.go b/ecc/bls12-381/kzg/doc.go
index d1045726f2..6c3454a2d9 100644
--- a/ecc/bls12-381/kzg/doc.go
+++ b/ecc/bls12-381/kzg/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/kzg/kzg.go b/ecc/bls12-381/kzg/kzg.go
index 9813880c0a..f043d0eb34 100644
--- a/ecc/bls12-381/kzg/kzg.go
+++ b/ecc/bls12-381/kzg/kzg.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/kzg/kzg_test.go b/ecc/bls12-381/kzg/kzg_test.go
index cfc72f3878..2734f35a5e 100644
--- a/ecc/bls12-381/kzg/kzg_test.go
+++ b/ecc/bls12-381/kzg/kzg_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/kzg/marshal.go b/ecc/bls12-381/kzg/marshal.go
index bbfe032976..0682d13a32 100644
--- a/ecc/bls12-381/kzg/marshal.go
+++ b/ecc/bls12-381/kzg/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/kzg/utils.go b/ecc/bls12-381/kzg/utils.go
index 857889d8a6..a803f99624 100644
--- a/ecc/bls12-381/kzg/utils.go
+++ b/ecc/bls12-381/kzg/utils.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/marshal.go b/ecc/bls12-381/marshal.go
index 50ce63d9b6..4b23d88aba 100644
--- a/ecc/bls12-381/marshal.go
+++ b/ecc/bls12-381/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/marshal_test.go b/ecc/bls12-381/marshal_test.go
index 2d232f19bf..f8f8ffc6c7 100644
--- a/ecc/bls12-381/marshal_test.go
+++ b/ecc/bls12-381/marshal_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/multiexp.go b/ecc/bls12-381/multiexp.go
index bfea254036..967701d077 100644
--- a/ecc/bls12-381/multiexp.go
+++ b/ecc/bls12-381/multiexp.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/multiexp_affine.go b/ecc/bls12-381/multiexp_affine.go
index 9988b02544..db91c99abe 100644
--- a/ecc/bls12-381/multiexp_affine.go
+++ b/ecc/bls12-381/multiexp_affine.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/multiexp_jacobian.go b/ecc/bls12-381/multiexp_jacobian.go
index da3445bd69..4dab02eb7d 100644
--- a/ecc/bls12-381/multiexp_jacobian.go
+++ b/ecc/bls12-381/multiexp_jacobian.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/multiexp_test.go b/ecc/bls12-381/multiexp_test.go
index 60ced46ca3..fdda872161 100644
--- a/ecc/bls12-381/multiexp_test.go
+++ b/ecc/bls12-381/multiexp_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/pairing_test.go b/ecc/bls12-381/pairing_test.go
index 48a8ade0a6..8ee0d8c553 100644
--- a/ecc/bls12-381/pairing_test.go
+++ b/ecc/bls12-381/pairing_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/shplonk/doc.go b/ecc/bls12-381/shplonk/doc.go
index e048f46009..17b34373c2 100644
--- a/ecc/bls12-381/shplonk/doc.go
+++ b/ecc/bls12-381/shplonk/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/shplonk/example_test.go b/ecc/bls12-381/shplonk/example_test.go
index f575f56875..2025360358 100644
--- a/ecc/bls12-381/shplonk/example_test.go
+++ b/ecc/bls12-381/shplonk/example_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/shplonk/marshal.go b/ecc/bls12-381/shplonk/marshal.go
index e013c2d3ef..ce2d5ffe26 100644
--- a/ecc/bls12-381/shplonk/marshal.go
+++ b/ecc/bls12-381/shplonk/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/shplonk/shplonk.go b/ecc/bls12-381/shplonk/shplonk.go
index 9c7a0de36d..b3d9ec3240 100644
--- a/ecc/bls12-381/shplonk/shplonk.go
+++ b/ecc/bls12-381/shplonk/shplonk.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/shplonk/shplonk_test.go b/ecc/bls12-381/shplonk/shplonk_test.go
index e2295bbe36..682a21ff9d 100644
--- a/ecc/bls12-381/shplonk/shplonk_test.go
+++ b/ecc/bls12-381/shplonk/shplonk_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/twistededwards/curve.go b/ecc/bls12-381/twistededwards/curve.go
index 7de87ac42f..9239aabf63 100644
--- a/ecc/bls12-381/twistededwards/curve.go
+++ b/ecc/bls12-381/twistededwards/curve.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/twistededwards/doc.go b/ecc/bls12-381/twistededwards/doc.go
index 4ec54375c8..a284750f5b 100644
--- a/ecc/bls12-381/twistededwards/doc.go
+++ b/ecc/bls12-381/twistededwards/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/twistededwards/eddsa/doc.go b/ecc/bls12-381/twistededwards/eddsa/doc.go
index acd950c598..2e2ee33568 100644
--- a/ecc/bls12-381/twistededwards/eddsa/doc.go
+++ b/ecc/bls12-381/twistededwards/eddsa/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/twistededwards/eddsa/eddsa.go b/ecc/bls12-381/twistededwards/eddsa/eddsa.go
index f68b7ce7de..3bab9a4046 100644
--- a/ecc/bls12-381/twistededwards/eddsa/eddsa.go
+++ b/ecc/bls12-381/twistededwards/eddsa/eddsa.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/twistededwards/eddsa/eddsa_test.go b/ecc/bls12-381/twistededwards/eddsa/eddsa_test.go
index 91cd6b5f59..972c06d0d0 100644
--- a/ecc/bls12-381/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bls12-381/twistededwards/eddsa/eddsa_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/twistededwards/eddsa/marshal.go b/ecc/bls12-381/twistededwards/eddsa/marshal.go
index eb55b12c55..2f4f26d4f3 100644
--- a/ecc/bls12-381/twistededwards/eddsa/marshal.go
+++ b/ecc/bls12-381/twistededwards/eddsa/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/twistededwards/point.go b/ecc/bls12-381/twistededwards/point.go
index 32fa82e5d3..651f32b9ff 100644
--- a/ecc/bls12-381/twistededwards/point.go
+++ b/ecc/bls12-381/twistededwards/point.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls12-381/twistededwards/point_test.go b/ecc/bls12-381/twistededwards/point_test.go
index 699a1fe518..af063f4a85 100644
--- a/ecc/bls12-381/twistededwards/point_test.go
+++ b/ecc/bls12-381/twistededwards/point_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/ecdsa/doc.go b/ecc/bls24-315/ecdsa/doc.go
index 52ee2d2203..3ac19094ff 100644
--- a/ecc/bls24-315/ecdsa/doc.go
+++ b/ecc/bls24-315/ecdsa/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/ecdsa/ecdsa.go b/ecc/bls24-315/ecdsa/ecdsa.go
index 747f3fca42..51719a4d32 100644
--- a/ecc/bls24-315/ecdsa/ecdsa.go
+++ b/ecc/bls24-315/ecdsa/ecdsa.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/ecdsa/ecdsa_test.go b/ecc/bls24-315/ecdsa/ecdsa_test.go
index 361a4b624c..0854c572b6 100644
--- a/ecc/bls24-315/ecdsa/ecdsa_test.go
+++ b/ecc/bls24-315/ecdsa/ecdsa_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/ecdsa/marshal.go b/ecc/bls24-315/ecdsa/marshal.go
index bafa85b968..be6bca16e2 100644
--- a/ecc/bls24-315/ecdsa/marshal.go
+++ b/ecc/bls24-315/ecdsa/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/ecdsa/marshal_test.go b/ecc/bls24-315/ecdsa/marshal_test.go
index fb5f453b4c..1195565dc0 100644
--- a/ecc/bls24-315/ecdsa/marshal_test.go
+++ b/ecc/bls24-315/ecdsa/marshal_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fflonk/doc.go b/ecc/bls24-315/fflonk/doc.go
index 694eaa9734..b717383d87 100644
--- a/ecc/bls24-315/fflonk/doc.go
+++ b/ecc/bls24-315/fflonk/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fflonk/example_test.go b/ecc/bls24-315/fflonk/example_test.go
index ffc84295c6..bd2882d654 100644
--- a/ecc/bls24-315/fflonk/example_test.go
+++ b/ecc/bls24-315/fflonk/example_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fflonk/fflonk.go b/ecc/bls24-315/fflonk/fflonk.go
index d33a0cac62..65001bf7ac 100644
--- a/ecc/bls24-315/fflonk/fflonk.go
+++ b/ecc/bls24-315/fflonk/fflonk.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fflonk/fflonk_test.go b/ecc/bls24-315/fflonk/fflonk_test.go
index aed1030914..6c8d9cc9b9 100644
--- a/ecc/bls24-315/fflonk/fflonk_test.go
+++ b/ecc/bls24-315/fflonk/fflonk_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fflonk/marshal.go b/ecc/bls24-315/fflonk/marshal.go
index f706558a7b..7024c2ead4 100644
--- a/ecc/bls24-315/fflonk/marshal.go
+++ b/ecc/bls24-315/fflonk/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fp/arith.go b/ecc/bls24-315/fp/arith.go
index 66fa667482..b202a1549a 100644
--- a/ecc/bls24-315/fp/arith.go
+++ b/ecc/bls24-315/fp/arith.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fp/asm_adx.go b/ecc/bls24-315/fp/asm_adx.go
index f8e29bd1a7..fe25e82db2 100644
--- a/ecc/bls24-315/fp/asm_adx.go
+++ b/ecc/bls24-315/fp/asm_adx.go
@@ -1,18 +1,7 @@
 //go:build !noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fp/asm_noadx.go b/ecc/bls24-315/fp/asm_noadx.go
index cb6cfa0f50..95085a8e6f 100644
--- a/ecc/bls24-315/fp/asm_noadx.go
+++ b/ecc/bls24-315/fp/asm_noadx.go
@@ -1,18 +1,7 @@
 //go:build noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fp/doc.go b/ecc/bls24-315/fp/doc.go
index 10acfff5d5..e9ea7b8d1b 100644
--- a/ecc/bls24-315/fp/doc.go
+++ b/ecc/bls24-315/fp/doc.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fp/element.go b/ecc/bls24-315/fp/element.go
index 361e0482c6..d6c40f6ebf 100644
--- a/ecc/bls24-315/fp/element.go
+++ b/ecc/bls24-315/fp/element.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fp/element_amd64.go b/ecc/bls24-315/fp/element_amd64.go
index 77a51ee25e..e72f552ad9 100644
--- a/ecc/bls24-315/fp/element_amd64.go
+++ b/ecc/bls24-315/fp/element_amd64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fp/element_amd64.s b/ecc/bls24-315/fp/element_amd64.s
index 00858d648e..599977a11a 100644
--- a/ecc/bls24-315/fp/element_amd64.s
+++ b/ecc/bls24-315/fp/element_amd64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fp/element_exp.go b/ecc/bls24-315/fp/element_exp.go
index 884d51fc76..b374460884 100644
--- a/ecc/bls24-315/fp/element_exp.go
+++ b/ecc/bls24-315/fp/element_exp.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fp/element_purego.go b/ecc/bls24-315/fp/element_purego.go
index f5c6690f7e..abd4a49579 100644
--- a/ecc/bls24-315/fp/element_purego.go
+++ b/ecc/bls24-315/fp/element_purego.go
@@ -1,18 +1,7 @@
 //go:build purego || !amd64
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fp/element_test.go b/ecc/bls24-315/fp/element_test.go
index d4656a26d3..7e0e258fcc 100644
--- a/ecc/bls24-315/fp/element_test.go
+++ b/ecc/bls24-315/fp/element_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fp/hash_to_field/doc.go b/ecc/bls24-315/fp/hash_to_field/doc.go
index ed0207f2e3..c5a207e06d 100644
--- a/ecc/bls24-315/fp/hash_to_field/doc.go
+++ b/ecc/bls24-315/fp/hash_to_field/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fp/hash_to_field/hash_to_field.go b/ecc/bls24-315/fp/hash_to_field/hash_to_field.go
index 85f1df7442..e18be48acf 100644
--- a/ecc/bls24-315/fp/hash_to_field/hash_to_field.go
+++ b/ecc/bls24-315/fp/hash_to_field/hash_to_field.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fp/hash_to_field/hash_to_field_test.go b/ecc/bls24-315/fp/hash_to_field/hash_to_field_test.go
index 09e50dd6c0..01296b0350 100644
--- a/ecc/bls24-315/fp/hash_to_field/hash_to_field_test.go
+++ b/ecc/bls24-315/fp/hash_to_field/hash_to_field_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fp/vector.go b/ecc/bls24-315/fp/vector.go
index 5d7cd31fe6..6f62d12f76 100644
--- a/ecc/bls24-315/fp/vector.go
+++ b/ecc/bls24-315/fp/vector.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fp/vector_purego.go b/ecc/bls24-315/fp/vector_purego.go
index 798b669887..347b0df594 100644
--- a/ecc/bls24-315/fp/vector_purego.go
+++ b/ecc/bls24-315/fp/vector_purego.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fp/vector_test.go b/ecc/bls24-315/fp/vector_test.go
index c60ee08440..0300a21e40 100644
--- a/ecc/bls24-315/fp/vector_test.go
+++ b/ecc/bls24-315/fp/vector_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/arith.go b/ecc/bls24-315/fr/arith.go
index 83c9fd9ef9..9285041f4b 100644
--- a/ecc/bls24-315/fr/arith.go
+++ b/ecc/bls24-315/fr/arith.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/asm_adx.go b/ecc/bls24-315/fr/asm_adx.go
index 9273ea23ab..9e7da5e865 100644
--- a/ecc/bls24-315/fr/asm_adx.go
+++ b/ecc/bls24-315/fr/asm_adx.go
@@ -1,18 +1,7 @@
 //go:build !noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/asm_avx.go b/ecc/bls24-315/fr/asm_avx.go
index 1cc06c6e8d..d6d7d7f87a 100644
--- a/ecc/bls24-315/fr/asm_avx.go
+++ b/ecc/bls24-315/fr/asm_avx.go
@@ -1,18 +1,7 @@
 //go:build !noavx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/asm_noadx.go b/ecc/bls24-315/fr/asm_noadx.go
index b784a24247..3456158655 100644
--- a/ecc/bls24-315/fr/asm_noadx.go
+++ b/ecc/bls24-315/fr/asm_noadx.go
@@ -1,18 +1,7 @@
 //go:build noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/asm_noavx.go b/ecc/bls24-315/fr/asm_noavx.go
index 66bfc00772..4eb73e9a78 100644
--- a/ecc/bls24-315/fr/asm_noavx.go
+++ b/ecc/bls24-315/fr/asm_noavx.go
@@ -1,18 +1,7 @@
 //go:build noavx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/doc.go b/ecc/bls24-315/fr/doc.go
index 087f41798a..ba6f150f02 100644
--- a/ecc/bls24-315/fr/doc.go
+++ b/ecc/bls24-315/fr/doc.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/element.go b/ecc/bls24-315/fr/element.go
index 2fe6f12cdc..a7b73b96b2 100644
--- a/ecc/bls24-315/fr/element.go
+++ b/ecc/bls24-315/fr/element.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/element_amd64.go b/ecc/bls24-315/fr/element_amd64.go
index 0ddb905f7b..ca49d12590 100644
--- a/ecc/bls24-315/fr/element_amd64.go
+++ b/ecc/bls24-315/fr/element_amd64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/element_amd64.s b/ecc/bls24-315/fr/element_amd64.s
index fb00194d7e..ed8a36e04d 100644
--- a/ecc/bls24-315/fr/element_amd64.s
+++ b/ecc/bls24-315/fr/element_amd64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/element_arm64.go b/ecc/bls24-315/fr/element_arm64.go
index cdf726a8eb..22360d5f6e 100644
--- a/ecc/bls24-315/fr/element_arm64.go
+++ b/ecc/bls24-315/fr/element_arm64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/element_arm64.s b/ecc/bls24-315/fr/element_arm64.s
index 5d328815aa..a7bd036553 100644
--- a/ecc/bls24-315/fr/element_arm64.s
+++ b/ecc/bls24-315/fr/element_arm64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/element_exp.go b/ecc/bls24-315/fr/element_exp.go
index 4be61fa12d..a3ace60bd8 100644
--- a/ecc/bls24-315/fr/element_exp.go
+++ b/ecc/bls24-315/fr/element_exp.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/element_purego.go b/ecc/bls24-315/fr/element_purego.go
index a93f64f06e..7aa329a8be 100644
--- a/ecc/bls24-315/fr/element_purego.go
+++ b/ecc/bls24-315/fr/element_purego.go
@@ -1,18 +1,7 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/element_test.go b/ecc/bls24-315/fr/element_test.go
index 7933f3aa3c..b0b1e10600 100644
--- a/ecc/bls24-315/fr/element_test.go
+++ b/ecc/bls24-315/fr/element_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/fft/bitreverse.go b/ecc/bls24-315/fr/fft/bitreverse.go
index 5d208c5040..2fad50e345 100644
--- a/ecc/bls24-315/fr/fft/bitreverse.go
+++ b/ecc/bls24-315/fr/fft/bitreverse.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/fft/bitreverse_test.go b/ecc/bls24-315/fr/fft/bitreverse_test.go
index c19ccc7fa6..a9482b11a8 100644
--- a/ecc/bls24-315/fr/fft/bitreverse_test.go
+++ b/ecc/bls24-315/fr/fft/bitreverse_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/fft/doc.go b/ecc/bls24-315/fr/fft/doc.go
index b5dd44e642..1ef04db2df 100644
--- a/ecc/bls24-315/fr/fft/doc.go
+++ b/ecc/bls24-315/fr/fft/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/fft/domain.go b/ecc/bls24-315/fr/fft/domain.go
index 1226a1b856..7c8c82f1f3 100644
--- a/ecc/bls24-315/fr/fft/domain.go
+++ b/ecc/bls24-315/fr/fft/domain.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/fft/domain_test.go b/ecc/bls24-315/fr/fft/domain_test.go
index 83186cb7c9..d95288076c 100644
--- a/ecc/bls24-315/fr/fft/domain_test.go
+++ b/ecc/bls24-315/fr/fft/domain_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/fft/fft.go b/ecc/bls24-315/fr/fft/fft.go
index e17e666e79..cd6c810b01 100644
--- a/ecc/bls24-315/fr/fft/fft.go
+++ b/ecc/bls24-315/fr/fft/fft.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/fft/fft_test.go b/ecc/bls24-315/fr/fft/fft_test.go
index 73538234da..ae82a57626 100644
--- a/ecc/bls24-315/fr/fft/fft_test.go
+++ b/ecc/bls24-315/fr/fft/fft_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/fft/options.go b/ecc/bls24-315/fr/fft/options.go
index cdb7f7f79f..1ec17e0cf9 100644
--- a/ecc/bls24-315/fr/fft/options.go
+++ b/ecc/bls24-315/fr/fft/options.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/fri/doc.go b/ecc/bls24-315/fr/fri/doc.go
index 3333ad41f5..428dabf625 100644
--- a/ecc/bls24-315/fr/fri/doc.go
+++ b/ecc/bls24-315/fr/fri/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/fri/fri.go b/ecc/bls24-315/fr/fri/fri.go
index 10156d62fd..faacb699c7 100644
--- a/ecc/bls24-315/fr/fri/fri.go
+++ b/ecc/bls24-315/fr/fri/fri.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/fri/fri_test.go b/ecc/bls24-315/fr/fri/fri_test.go
index 5b316bf7ef..614ffa853f 100644
--- a/ecc/bls24-315/fr/fri/fri_test.go
+++ b/ecc/bls24-315/fr/fri/fri_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/generator.go b/ecc/bls24-315/fr/generator.go
index 616e9eaad0..7a1886db28 100644
--- a/ecc/bls24-315/fr/generator.go
+++ b/ecc/bls24-315/fr/generator.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/gkr/gkr.go b/ecc/bls24-315/fr/gkr/gkr.go
index 49d6a05543..3d53bb6e2a 100644
--- a/ecc/bls24-315/fr/gkr/gkr.go
+++ b/ecc/bls24-315/fr/gkr/gkr.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/gkr/gkr_test.go b/ecc/bls24-315/fr/gkr/gkr_test.go
index fd14819be1..747739befd 100644
--- a/ecc/bls24-315/fr/gkr/gkr_test.go
+++ b/ecc/bls24-315/fr/gkr/gkr_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/hash_to_field/doc.go b/ecc/bls24-315/fr/hash_to_field/doc.go
index 6423272af2..d21cb934e8 100644
--- a/ecc/bls24-315/fr/hash_to_field/doc.go
+++ b/ecc/bls24-315/fr/hash_to_field/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/hash_to_field/hash_to_field.go b/ecc/bls24-315/fr/hash_to_field/hash_to_field.go
index 60883ba310..4b76f2e5d0 100644
--- a/ecc/bls24-315/fr/hash_to_field/hash_to_field.go
+++ b/ecc/bls24-315/fr/hash_to_field/hash_to_field.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/hash_to_field/hash_to_field_test.go b/ecc/bls24-315/fr/hash_to_field/hash_to_field_test.go
index 4df406f344..6b66ee6993 100644
--- a/ecc/bls24-315/fr/hash_to_field/hash_to_field_test.go
+++ b/ecc/bls24-315/fr/hash_to_field/hash_to_field_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/iop/doc.go b/ecc/bls24-315/fr/iop/doc.go
index 20f8b1a302..ee3facf1e1 100644
--- a/ecc/bls24-315/fr/iop/doc.go
+++ b/ecc/bls24-315/fr/iop/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/iop/expressions.go b/ecc/bls24-315/fr/iop/expressions.go
index fcc8de6cc7..37acd066e9 100644
--- a/ecc/bls24-315/fr/iop/expressions.go
+++ b/ecc/bls24-315/fr/iop/expressions.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/iop/expressions_test.go b/ecc/bls24-315/fr/iop/expressions_test.go
index bc7bb921db..df720a4072 100644
--- a/ecc/bls24-315/fr/iop/expressions_test.go
+++ b/ecc/bls24-315/fr/iop/expressions_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/iop/polynomial.go b/ecc/bls24-315/fr/iop/polynomial.go
index 3b1deecdf4..b8727248a2 100644
--- a/ecc/bls24-315/fr/iop/polynomial.go
+++ b/ecc/bls24-315/fr/iop/polynomial.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/iop/polynomial_test.go b/ecc/bls24-315/fr/iop/polynomial_test.go
index ca52163f3e..71b63b1058 100644
--- a/ecc/bls24-315/fr/iop/polynomial_test.go
+++ b/ecc/bls24-315/fr/iop/polynomial_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/iop/quotient.go b/ecc/bls24-315/fr/iop/quotient.go
index b86dd34872..36fffc9edb 100644
--- a/ecc/bls24-315/fr/iop/quotient.go
+++ b/ecc/bls24-315/fr/iop/quotient.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/iop/quotient_test.go b/ecc/bls24-315/fr/iop/quotient_test.go
index d1a89dcb97..ad7b8b2590 100644
--- a/ecc/bls24-315/fr/iop/quotient_test.go
+++ b/ecc/bls24-315/fr/iop/quotient_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/iop/ratios.go b/ecc/bls24-315/fr/iop/ratios.go
index 1d8832c347..c814d85f94 100644
--- a/ecc/bls24-315/fr/iop/ratios.go
+++ b/ecc/bls24-315/fr/iop/ratios.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/iop/ratios_test.go b/ecc/bls24-315/fr/iop/ratios_test.go
index affc88f479..3480ce3d70 100644
--- a/ecc/bls24-315/fr/iop/ratios_test.go
+++ b/ecc/bls24-315/fr/iop/ratios_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/iop/utils.go b/ecc/bls24-315/fr/iop/utils.go
index cc44e91d0d..cf4e53c00c 100644
--- a/ecc/bls24-315/fr/iop/utils.go
+++ b/ecc/bls24-315/fr/iop/utils.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/mimc/doc.go b/ecc/bls24-315/fr/mimc/doc.go
index 78837e1c80..cc7b101eb4 100644
--- a/ecc/bls24-315/fr/mimc/doc.go
+++ b/ecc/bls24-315/fr/mimc/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/mimc/mimc.go b/ecc/bls24-315/fr/mimc/mimc.go
index 289944edc4..0415a19f30 100644
--- a/ecc/bls24-315/fr/mimc/mimc.go
+++ b/ecc/bls24-315/fr/mimc/mimc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/mimc/options.go b/ecc/bls24-315/fr/mimc/options.go
index e25f3cce22..17e9bdb16f 100644
--- a/ecc/bls24-315/fr/mimc/options.go
+++ b/ecc/bls24-315/fr/mimc/options.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/pedersen/doc.go b/ecc/bls24-315/fr/pedersen/doc.go
index 944679f5c5..62a62f179f 100644
--- a/ecc/bls24-315/fr/pedersen/doc.go
+++ b/ecc/bls24-315/fr/pedersen/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/pedersen/example_test.go b/ecc/bls24-315/fr/pedersen/example_test.go
index dc63ecad7c..4d93e82b01 100644
--- a/ecc/bls24-315/fr/pedersen/example_test.go
+++ b/ecc/bls24-315/fr/pedersen/example_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/pedersen/pedersen.go b/ecc/bls24-315/fr/pedersen/pedersen.go
index 8bc6fef455..2fa8fd038b 100644
--- a/ecc/bls24-315/fr/pedersen/pedersen.go
+++ b/ecc/bls24-315/fr/pedersen/pedersen.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/pedersen/pedersen_test.go b/ecc/bls24-315/fr/pedersen/pedersen_test.go
index 5c162db58d..f44841537a 100644
--- a/ecc/bls24-315/fr/pedersen/pedersen_test.go
+++ b/ecc/bls24-315/fr/pedersen/pedersen_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/permutation/doc.go b/ecc/bls24-315/fr/permutation/doc.go
index 7ef21ffb9e..5f346b5a53 100644
--- a/ecc/bls24-315/fr/permutation/doc.go
+++ b/ecc/bls24-315/fr/permutation/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/permutation/permutation.go b/ecc/bls24-315/fr/permutation/permutation.go
index 6a87a7c921..dfe5b2d736 100644
--- a/ecc/bls24-315/fr/permutation/permutation.go
+++ b/ecc/bls24-315/fr/permutation/permutation.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/permutation/permutation_test.go b/ecc/bls24-315/fr/permutation/permutation_test.go
index dac1e7a784..b68ea7357b 100644
--- a/ecc/bls24-315/fr/permutation/permutation_test.go
+++ b/ecc/bls24-315/fr/permutation/permutation_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/plookup/doc.go b/ecc/bls24-315/fr/plookup/doc.go
index b3af019687..d163104002 100644
--- a/ecc/bls24-315/fr/plookup/doc.go
+++ b/ecc/bls24-315/fr/plookup/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/plookup/plookup_test.go b/ecc/bls24-315/fr/plookup/plookup_test.go
index 19f988efbb..d96da661d7 100644
--- a/ecc/bls24-315/fr/plookup/plookup_test.go
+++ b/ecc/bls24-315/fr/plookup/plookup_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/plookup/table.go b/ecc/bls24-315/fr/plookup/table.go
index b710796f24..da09ef6bc9 100644
--- a/ecc/bls24-315/fr/plookup/table.go
+++ b/ecc/bls24-315/fr/plookup/table.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/plookup/vector.go b/ecc/bls24-315/fr/plookup/vector.go
index 6fefe36acc..a63bc9d504 100644
--- a/ecc/bls24-315/fr/plookup/vector.go
+++ b/ecc/bls24-315/fr/plookup/vector.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/polynomial/doc.go b/ecc/bls24-315/fr/polynomial/doc.go
index 747da41f2c..35b3f725c1 100644
--- a/ecc/bls24-315/fr/polynomial/doc.go
+++ b/ecc/bls24-315/fr/polynomial/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/polynomial/multilin.go b/ecc/bls24-315/fr/polynomial/multilin.go
index 8cc02bb754..04849a2c45 100644
--- a/ecc/bls24-315/fr/polynomial/multilin.go
+++ b/ecc/bls24-315/fr/polynomial/multilin.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/polynomial/multilin_test.go b/ecc/bls24-315/fr/polynomial/multilin_test.go
index 1965344660..5540f39a06 100644
--- a/ecc/bls24-315/fr/polynomial/multilin_test.go
+++ b/ecc/bls24-315/fr/polynomial/multilin_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/polynomial/polynomial.go b/ecc/bls24-315/fr/polynomial/polynomial.go
index 81064b814b..38bd18f60a 100644
--- a/ecc/bls24-315/fr/polynomial/polynomial.go
+++ b/ecc/bls24-315/fr/polynomial/polynomial.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/polynomial/polynomial_test.go b/ecc/bls24-315/fr/polynomial/polynomial_test.go
index 37143c9361..08cd6b789d 100644
--- a/ecc/bls24-315/fr/polynomial/polynomial_test.go
+++ b/ecc/bls24-315/fr/polynomial/polynomial_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/polynomial/pool.go b/ecc/bls24-315/fr/polynomial/pool.go
index 381a611877..49895f16cc 100644
--- a/ecc/bls24-315/fr/polynomial/pool.go
+++ b/ecc/bls24-315/fr/polynomial/pool.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/poseidon2/poseidon2.go b/ecc/bls24-315/fr/poseidon2/poseidon2.go
index 6f0f4fdb32..41e79d3f58 100644
--- a/ecc/bls24-315/fr/poseidon2/poseidon2.go
+++ b/ecc/bls24-315/fr/poseidon2/poseidon2.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/poseidon2/poseidon2_test.go b/ecc/bls24-315/fr/poseidon2/poseidon2_test.go
index eaade1b7f8..16b9f702f1 100644
--- a/ecc/bls24-315/fr/poseidon2/poseidon2_test.go
+++ b/ecc/bls24-315/fr/poseidon2/poseidon2_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/sumcheck/sumcheck.go b/ecc/bls24-315/fr/sumcheck/sumcheck.go
index 3c74123475..d99787acfa 100644
--- a/ecc/bls24-315/fr/sumcheck/sumcheck.go
+++ b/ecc/bls24-315/fr/sumcheck/sumcheck.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/sumcheck/sumcheck_test.go b/ecc/bls24-315/fr/sumcheck/sumcheck_test.go
index f6fda91678..edf64e3f75 100644
--- a/ecc/bls24-315/fr/sumcheck/sumcheck_test.go
+++ b/ecc/bls24-315/fr/sumcheck/sumcheck_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/test_vector_utils/test_vector_utils.go b/ecc/bls24-315/fr/test_vector_utils/test_vector_utils.go
index b59a699a5d..5c581de8d8 100644
--- a/ecc/bls24-315/fr/test_vector_utils/test_vector_utils.go
+++ b/ecc/bls24-315/fr/test_vector_utils/test_vector_utils.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/vector.go b/ecc/bls24-315/fr/vector.go
index 867cabbc3d..8b59bd36e9 100644
--- a/ecc/bls24-315/fr/vector.go
+++ b/ecc/bls24-315/fr/vector.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/vector_amd64.go b/ecc/bls24-315/fr/vector_amd64.go
index 0164ecb382..b27679827c 100644
--- a/ecc/bls24-315/fr/vector_amd64.go
+++ b/ecc/bls24-315/fr/vector_amd64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/vector_purego.go b/ecc/bls24-315/fr/vector_purego.go
index 84f86a40b1..5973d16ce2 100644
--- a/ecc/bls24-315/fr/vector_purego.go
+++ b/ecc/bls24-315/fr/vector_purego.go
@@ -1,18 +1,7 @@
 //go:build purego || !amd64
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/fr/vector_test.go b/ecc/bls24-315/fr/vector_test.go
index b6344c18b7..a094bc0ac6 100644
--- a/ecc/bls24-315/fr/vector_test.go
+++ b/ecc/bls24-315/fr/vector_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/g1.go b/ecc/bls24-315/g1.go
index ab872e9986..e34e6fac32 100644
--- a/ecc/bls24-315/g1.go
+++ b/ecc/bls24-315/g1.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/g1_test.go b/ecc/bls24-315/g1_test.go
index 8f99519348..20e6008e02 100644
--- a/ecc/bls24-315/g1_test.go
+++ b/ecc/bls24-315/g1_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/g2.go b/ecc/bls24-315/g2.go
index ad3b75b7c0..a99cda6d0a 100644
--- a/ecc/bls24-315/g2.go
+++ b/ecc/bls24-315/g2.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/g2_test.go b/ecc/bls24-315/g2_test.go
index a42966a99c..ba45cd7ba3 100644
--- a/ecc/bls24-315/g2_test.go
+++ b/ecc/bls24-315/g2_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/hash_to_g1.go b/ecc/bls24-315/hash_to_g1.go
index 396678cc57..2c334c3642 100644
--- a/ecc/bls24-315/hash_to_g1.go
+++ b/ecc/bls24-315/hash_to_g1.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/hash_to_g1_test.go b/ecc/bls24-315/hash_to_g1_test.go
index f7349347ab..0e41f4fd53 100644
--- a/ecc/bls24-315/hash_to_g1_test.go
+++ b/ecc/bls24-315/hash_to_g1_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/kzg/doc.go b/ecc/bls24-315/kzg/doc.go
index d1045726f2..6c3454a2d9 100644
--- a/ecc/bls24-315/kzg/doc.go
+++ b/ecc/bls24-315/kzg/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/kzg/kzg.go b/ecc/bls24-315/kzg/kzg.go
index 0cd7cfbbf9..41bb1e9b09 100644
--- a/ecc/bls24-315/kzg/kzg.go
+++ b/ecc/bls24-315/kzg/kzg.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/kzg/kzg_test.go b/ecc/bls24-315/kzg/kzg_test.go
index 805b6aaed5..b27de2332f 100644
--- a/ecc/bls24-315/kzg/kzg_test.go
+++ b/ecc/bls24-315/kzg/kzg_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/kzg/marshal.go b/ecc/bls24-315/kzg/marshal.go
index 2d5c4ead9f..5335f2b360 100644
--- a/ecc/bls24-315/kzg/marshal.go
+++ b/ecc/bls24-315/kzg/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/kzg/utils.go b/ecc/bls24-315/kzg/utils.go
index 80fa5b89e7..f77285fe91 100644
--- a/ecc/bls24-315/kzg/utils.go
+++ b/ecc/bls24-315/kzg/utils.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/marshal.go b/ecc/bls24-315/marshal.go
index 71e4d00afe..584c86f086 100644
--- a/ecc/bls24-315/marshal.go
+++ b/ecc/bls24-315/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/marshal_test.go b/ecc/bls24-315/marshal_test.go
index 54047721c0..670322eccb 100644
--- a/ecc/bls24-315/marshal_test.go
+++ b/ecc/bls24-315/marshal_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/multiexp.go b/ecc/bls24-315/multiexp.go
index ab15b8af0b..efd1ab0756 100644
--- a/ecc/bls24-315/multiexp.go
+++ b/ecc/bls24-315/multiexp.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/multiexp_affine.go b/ecc/bls24-315/multiexp_affine.go
index c020191bdd..7fe32aed72 100644
--- a/ecc/bls24-315/multiexp_affine.go
+++ b/ecc/bls24-315/multiexp_affine.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/multiexp_jacobian.go b/ecc/bls24-315/multiexp_jacobian.go
index 8ffc4d04ae..dc866aa15a 100644
--- a/ecc/bls24-315/multiexp_jacobian.go
+++ b/ecc/bls24-315/multiexp_jacobian.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/multiexp_test.go b/ecc/bls24-315/multiexp_test.go
index 2c46aa2286..beaca7c932 100644
--- a/ecc/bls24-315/multiexp_test.go
+++ b/ecc/bls24-315/multiexp_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/pairing_test.go b/ecc/bls24-315/pairing_test.go
index 5ba06138ce..c168e97a88 100644
--- a/ecc/bls24-315/pairing_test.go
+++ b/ecc/bls24-315/pairing_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/shplonk/doc.go b/ecc/bls24-315/shplonk/doc.go
index e048f46009..17b34373c2 100644
--- a/ecc/bls24-315/shplonk/doc.go
+++ b/ecc/bls24-315/shplonk/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/shplonk/example_test.go b/ecc/bls24-315/shplonk/example_test.go
index 2185a37ccb..dd775e5d45 100644
--- a/ecc/bls24-315/shplonk/example_test.go
+++ b/ecc/bls24-315/shplonk/example_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/shplonk/marshal.go b/ecc/bls24-315/shplonk/marshal.go
index a936f40bbe..10f7584165 100644
--- a/ecc/bls24-315/shplonk/marshal.go
+++ b/ecc/bls24-315/shplonk/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/shplonk/shplonk.go b/ecc/bls24-315/shplonk/shplonk.go
index f583310e1a..618607300c 100644
--- a/ecc/bls24-315/shplonk/shplonk.go
+++ b/ecc/bls24-315/shplonk/shplonk.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/shplonk/shplonk_test.go b/ecc/bls24-315/shplonk/shplonk_test.go
index 4f7f41f122..fbabc5c99d 100644
--- a/ecc/bls24-315/shplonk/shplonk_test.go
+++ b/ecc/bls24-315/shplonk/shplonk_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/twistededwards/curve.go b/ecc/bls24-315/twistededwards/curve.go
index 4dd14ca173..9864bfc984 100644
--- a/ecc/bls24-315/twistededwards/curve.go
+++ b/ecc/bls24-315/twistededwards/curve.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/twistededwards/doc.go b/ecc/bls24-315/twistededwards/doc.go
index 21a3ed50bf..20a3090d78 100644
--- a/ecc/bls24-315/twistededwards/doc.go
+++ b/ecc/bls24-315/twistededwards/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/twistededwards/eddsa/doc.go b/ecc/bls24-315/twistededwards/eddsa/doc.go
index f749787180..dff0c7391d 100644
--- a/ecc/bls24-315/twistededwards/eddsa/doc.go
+++ b/ecc/bls24-315/twistededwards/eddsa/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/twistededwards/eddsa/eddsa.go b/ecc/bls24-315/twistededwards/eddsa/eddsa.go
index 5f831c2fc2..57f2f3f03e 100644
--- a/ecc/bls24-315/twistededwards/eddsa/eddsa.go
+++ b/ecc/bls24-315/twistededwards/eddsa/eddsa.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/twistededwards/eddsa/eddsa_test.go b/ecc/bls24-315/twistededwards/eddsa/eddsa_test.go
index aacce3f454..5785b16f2c 100644
--- a/ecc/bls24-315/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bls24-315/twistededwards/eddsa/eddsa_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/twistededwards/eddsa/marshal.go b/ecc/bls24-315/twistededwards/eddsa/marshal.go
index add6fb14ef..2d7499ceda 100644
--- a/ecc/bls24-315/twistededwards/eddsa/marshal.go
+++ b/ecc/bls24-315/twistededwards/eddsa/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/twistededwards/point.go b/ecc/bls24-315/twistededwards/point.go
index 32868a7466..bfb715d07a 100644
--- a/ecc/bls24-315/twistededwards/point.go
+++ b/ecc/bls24-315/twistededwards/point.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-315/twistededwards/point_test.go b/ecc/bls24-315/twistededwards/point_test.go
index 9d57e542b1..4daedb3d69 100644
--- a/ecc/bls24-315/twistededwards/point_test.go
+++ b/ecc/bls24-315/twistededwards/point_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/ecdsa/doc.go b/ecc/bls24-317/ecdsa/doc.go
index 71b1377488..1196c03f82 100644
--- a/ecc/bls24-317/ecdsa/doc.go
+++ b/ecc/bls24-317/ecdsa/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/ecdsa/ecdsa.go b/ecc/bls24-317/ecdsa/ecdsa.go
index 4fb8355e85..c3ce5b6722 100644
--- a/ecc/bls24-317/ecdsa/ecdsa.go
+++ b/ecc/bls24-317/ecdsa/ecdsa.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/ecdsa/ecdsa_test.go b/ecc/bls24-317/ecdsa/ecdsa_test.go
index c510b7ae6a..eb1176310e 100644
--- a/ecc/bls24-317/ecdsa/ecdsa_test.go
+++ b/ecc/bls24-317/ecdsa/ecdsa_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/ecdsa/marshal.go b/ecc/bls24-317/ecdsa/marshal.go
index 0db443032a..3c32bc454c 100644
--- a/ecc/bls24-317/ecdsa/marshal.go
+++ b/ecc/bls24-317/ecdsa/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/ecdsa/marshal_test.go b/ecc/bls24-317/ecdsa/marshal_test.go
index 88e52beb1c..9d24be8307 100644
--- a/ecc/bls24-317/ecdsa/marshal_test.go
+++ b/ecc/bls24-317/ecdsa/marshal_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fflonk/doc.go b/ecc/bls24-317/fflonk/doc.go
index 694eaa9734..b717383d87 100644
--- a/ecc/bls24-317/fflonk/doc.go
+++ b/ecc/bls24-317/fflonk/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fflonk/example_test.go b/ecc/bls24-317/fflonk/example_test.go
index 3d58b2b5aa..bb9e6be7ea 100644
--- a/ecc/bls24-317/fflonk/example_test.go
+++ b/ecc/bls24-317/fflonk/example_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fflonk/fflonk.go b/ecc/bls24-317/fflonk/fflonk.go
index 79bca3973b..b191c6a7ca 100644
--- a/ecc/bls24-317/fflonk/fflonk.go
+++ b/ecc/bls24-317/fflonk/fflonk.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fflonk/fflonk_test.go b/ecc/bls24-317/fflonk/fflonk_test.go
index f6d8213874..aa0b10fb55 100644
--- a/ecc/bls24-317/fflonk/fflonk_test.go
+++ b/ecc/bls24-317/fflonk/fflonk_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fflonk/marshal.go b/ecc/bls24-317/fflonk/marshal.go
index 1129b6a503..35f8f022dc 100644
--- a/ecc/bls24-317/fflonk/marshal.go
+++ b/ecc/bls24-317/fflonk/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fp/arith.go b/ecc/bls24-317/fp/arith.go
index 66fa667482..b202a1549a 100644
--- a/ecc/bls24-317/fp/arith.go
+++ b/ecc/bls24-317/fp/arith.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fp/asm_adx.go b/ecc/bls24-317/fp/asm_adx.go
index f8e29bd1a7..fe25e82db2 100644
--- a/ecc/bls24-317/fp/asm_adx.go
+++ b/ecc/bls24-317/fp/asm_adx.go
@@ -1,18 +1,7 @@
 //go:build !noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fp/asm_noadx.go b/ecc/bls24-317/fp/asm_noadx.go
index cb6cfa0f50..95085a8e6f 100644
--- a/ecc/bls24-317/fp/asm_noadx.go
+++ b/ecc/bls24-317/fp/asm_noadx.go
@@ -1,18 +1,7 @@
 //go:build noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fp/doc.go b/ecc/bls24-317/fp/doc.go
index 59f6de3421..81296d0270 100644
--- a/ecc/bls24-317/fp/doc.go
+++ b/ecc/bls24-317/fp/doc.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fp/element.go b/ecc/bls24-317/fp/element.go
index 80bab83a71..2277f984e9 100644
--- a/ecc/bls24-317/fp/element.go
+++ b/ecc/bls24-317/fp/element.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fp/element_amd64.go b/ecc/bls24-317/fp/element_amd64.go
index 77a51ee25e..e72f552ad9 100644
--- a/ecc/bls24-317/fp/element_amd64.go
+++ b/ecc/bls24-317/fp/element_amd64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fp/element_amd64.s b/ecc/bls24-317/fp/element_amd64.s
index 00858d648e..599977a11a 100644
--- a/ecc/bls24-317/fp/element_amd64.s
+++ b/ecc/bls24-317/fp/element_amd64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fp/element_exp.go b/ecc/bls24-317/fp/element_exp.go
index 00960590de..508e6afb9e 100644
--- a/ecc/bls24-317/fp/element_exp.go
+++ b/ecc/bls24-317/fp/element_exp.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fp/element_purego.go b/ecc/bls24-317/fp/element_purego.go
index 0f21692f40..11740a36cd 100644
--- a/ecc/bls24-317/fp/element_purego.go
+++ b/ecc/bls24-317/fp/element_purego.go
@@ -1,18 +1,7 @@
 //go:build purego || !amd64
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fp/element_test.go b/ecc/bls24-317/fp/element_test.go
index 7d179efec4..f347cf5e8e 100644
--- a/ecc/bls24-317/fp/element_test.go
+++ b/ecc/bls24-317/fp/element_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fp/hash_to_field/doc.go b/ecc/bls24-317/fp/hash_to_field/doc.go
index 68ee4656ce..8e8b8feea0 100644
--- a/ecc/bls24-317/fp/hash_to_field/doc.go
+++ b/ecc/bls24-317/fp/hash_to_field/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fp/hash_to_field/hash_to_field.go b/ecc/bls24-317/fp/hash_to_field/hash_to_field.go
index 32d5d8de98..6c9726b2eb 100644
--- a/ecc/bls24-317/fp/hash_to_field/hash_to_field.go
+++ b/ecc/bls24-317/fp/hash_to_field/hash_to_field.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fp/hash_to_field/hash_to_field_test.go b/ecc/bls24-317/fp/hash_to_field/hash_to_field_test.go
index 45873b268e..928a3475fe 100644
--- a/ecc/bls24-317/fp/hash_to_field/hash_to_field_test.go
+++ b/ecc/bls24-317/fp/hash_to_field/hash_to_field_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fp/vector.go b/ecc/bls24-317/fp/vector.go
index 5d7cd31fe6..6f62d12f76 100644
--- a/ecc/bls24-317/fp/vector.go
+++ b/ecc/bls24-317/fp/vector.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fp/vector_purego.go b/ecc/bls24-317/fp/vector_purego.go
index 798b669887..347b0df594 100644
--- a/ecc/bls24-317/fp/vector_purego.go
+++ b/ecc/bls24-317/fp/vector_purego.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fp/vector_test.go b/ecc/bls24-317/fp/vector_test.go
index c60ee08440..0300a21e40 100644
--- a/ecc/bls24-317/fp/vector_test.go
+++ b/ecc/bls24-317/fp/vector_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/arith.go b/ecc/bls24-317/fr/arith.go
index 83c9fd9ef9..9285041f4b 100644
--- a/ecc/bls24-317/fr/arith.go
+++ b/ecc/bls24-317/fr/arith.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/asm_adx.go b/ecc/bls24-317/fr/asm_adx.go
index 9273ea23ab..9e7da5e865 100644
--- a/ecc/bls24-317/fr/asm_adx.go
+++ b/ecc/bls24-317/fr/asm_adx.go
@@ -1,18 +1,7 @@
 //go:build !noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/asm_avx.go b/ecc/bls24-317/fr/asm_avx.go
index 1cc06c6e8d..d6d7d7f87a 100644
--- a/ecc/bls24-317/fr/asm_avx.go
+++ b/ecc/bls24-317/fr/asm_avx.go
@@ -1,18 +1,7 @@
 //go:build !noavx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/asm_noadx.go b/ecc/bls24-317/fr/asm_noadx.go
index b784a24247..3456158655 100644
--- a/ecc/bls24-317/fr/asm_noadx.go
+++ b/ecc/bls24-317/fr/asm_noadx.go
@@ -1,18 +1,7 @@
 //go:build noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/asm_noavx.go b/ecc/bls24-317/fr/asm_noavx.go
index 66bfc00772..4eb73e9a78 100644
--- a/ecc/bls24-317/fr/asm_noavx.go
+++ b/ecc/bls24-317/fr/asm_noavx.go
@@ -1,18 +1,7 @@
 //go:build noavx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/doc.go b/ecc/bls24-317/fr/doc.go
index 860ebf253a..587707f13a 100644
--- a/ecc/bls24-317/fr/doc.go
+++ b/ecc/bls24-317/fr/doc.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/element.go b/ecc/bls24-317/fr/element.go
index df5f9dc4cf..2567fe7d46 100644
--- a/ecc/bls24-317/fr/element.go
+++ b/ecc/bls24-317/fr/element.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/element_amd64.go b/ecc/bls24-317/fr/element_amd64.go
index 0ddb905f7b..ca49d12590 100644
--- a/ecc/bls24-317/fr/element_amd64.go
+++ b/ecc/bls24-317/fr/element_amd64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/element_amd64.s b/ecc/bls24-317/fr/element_amd64.s
index fb00194d7e..ed8a36e04d 100644
--- a/ecc/bls24-317/fr/element_amd64.s
+++ b/ecc/bls24-317/fr/element_amd64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/element_arm64.go b/ecc/bls24-317/fr/element_arm64.go
index 7a483d1551..f50af4849b 100644
--- a/ecc/bls24-317/fr/element_arm64.go
+++ b/ecc/bls24-317/fr/element_arm64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/element_arm64.s b/ecc/bls24-317/fr/element_arm64.s
index 5d328815aa..a7bd036553 100644
--- a/ecc/bls24-317/fr/element_arm64.s
+++ b/ecc/bls24-317/fr/element_arm64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/element_exp.go b/ecc/bls24-317/fr/element_exp.go
index e43618fab3..dcf74b036c 100644
--- a/ecc/bls24-317/fr/element_exp.go
+++ b/ecc/bls24-317/fr/element_exp.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/element_purego.go b/ecc/bls24-317/fr/element_purego.go
index c9b8bd4616..50df3223b4 100644
--- a/ecc/bls24-317/fr/element_purego.go
+++ b/ecc/bls24-317/fr/element_purego.go
@@ -1,18 +1,7 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/element_test.go b/ecc/bls24-317/fr/element_test.go
index b5db750d64..42f075f40b 100644
--- a/ecc/bls24-317/fr/element_test.go
+++ b/ecc/bls24-317/fr/element_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/fft/bitreverse.go b/ecc/bls24-317/fr/fft/bitreverse.go
index 85a392372d..329e4c7a43 100644
--- a/ecc/bls24-317/fr/fft/bitreverse.go
+++ b/ecc/bls24-317/fr/fft/bitreverse.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/fft/bitreverse_test.go b/ecc/bls24-317/fr/fft/bitreverse_test.go
index d5352c4c04..8028806cd7 100644
--- a/ecc/bls24-317/fr/fft/bitreverse_test.go
+++ b/ecc/bls24-317/fr/fft/bitreverse_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/fft/doc.go b/ecc/bls24-317/fr/fft/doc.go
index b5dd44e642..1ef04db2df 100644
--- a/ecc/bls24-317/fr/fft/doc.go
+++ b/ecc/bls24-317/fr/fft/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/fft/domain.go b/ecc/bls24-317/fr/fft/domain.go
index e60bb48d9d..c2d12cb3b7 100644
--- a/ecc/bls24-317/fr/fft/domain.go
+++ b/ecc/bls24-317/fr/fft/domain.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/fft/domain_test.go b/ecc/bls24-317/fr/fft/domain_test.go
index 83186cb7c9..d95288076c 100644
--- a/ecc/bls24-317/fr/fft/domain_test.go
+++ b/ecc/bls24-317/fr/fft/domain_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/fft/fft.go b/ecc/bls24-317/fr/fft/fft.go
index 22c476632c..5f1249f0bc 100644
--- a/ecc/bls24-317/fr/fft/fft.go
+++ b/ecc/bls24-317/fr/fft/fft.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/fft/fft_test.go b/ecc/bls24-317/fr/fft/fft_test.go
index 92311e2f60..ce75bd3cb1 100644
--- a/ecc/bls24-317/fr/fft/fft_test.go
+++ b/ecc/bls24-317/fr/fft/fft_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/fft/options.go b/ecc/bls24-317/fr/fft/options.go
index 0bb0391256..0771a67910 100644
--- a/ecc/bls24-317/fr/fft/options.go
+++ b/ecc/bls24-317/fr/fft/options.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/fri/doc.go b/ecc/bls24-317/fr/fri/doc.go
index 3333ad41f5..428dabf625 100644
--- a/ecc/bls24-317/fr/fri/doc.go
+++ b/ecc/bls24-317/fr/fri/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/fri/fri.go b/ecc/bls24-317/fr/fri/fri.go
index cbac4e3783..0abf70e8a2 100644
--- a/ecc/bls24-317/fr/fri/fri.go
+++ b/ecc/bls24-317/fr/fri/fri.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/fri/fri_test.go b/ecc/bls24-317/fr/fri/fri_test.go
index fa6b568979..a05f7ca68b 100644
--- a/ecc/bls24-317/fr/fri/fri_test.go
+++ b/ecc/bls24-317/fr/fri/fri_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/generator.go b/ecc/bls24-317/fr/generator.go
index b2acc7ab14..db8e5d4024 100644
--- a/ecc/bls24-317/fr/generator.go
+++ b/ecc/bls24-317/fr/generator.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/gkr/gkr.go b/ecc/bls24-317/fr/gkr/gkr.go
index fde5babfd4..057b9f946e 100644
--- a/ecc/bls24-317/fr/gkr/gkr.go
+++ b/ecc/bls24-317/fr/gkr/gkr.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/gkr/gkr_test.go b/ecc/bls24-317/fr/gkr/gkr_test.go
index 2d6134f87f..bd28b5d2a1 100644
--- a/ecc/bls24-317/fr/gkr/gkr_test.go
+++ b/ecc/bls24-317/fr/gkr/gkr_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/hash_to_field/doc.go b/ecc/bls24-317/fr/hash_to_field/doc.go
index b1c77a2e4e..97326bc039 100644
--- a/ecc/bls24-317/fr/hash_to_field/doc.go
+++ b/ecc/bls24-317/fr/hash_to_field/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/hash_to_field/hash_to_field.go b/ecc/bls24-317/fr/hash_to_field/hash_to_field.go
index fa1f7700e2..2c51e5fd51 100644
--- a/ecc/bls24-317/fr/hash_to_field/hash_to_field.go
+++ b/ecc/bls24-317/fr/hash_to_field/hash_to_field.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/hash_to_field/hash_to_field_test.go b/ecc/bls24-317/fr/hash_to_field/hash_to_field_test.go
index 5445fcef98..bca80332aa 100644
--- a/ecc/bls24-317/fr/hash_to_field/hash_to_field_test.go
+++ b/ecc/bls24-317/fr/hash_to_field/hash_to_field_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/iop/doc.go b/ecc/bls24-317/fr/iop/doc.go
index 20f8b1a302..ee3facf1e1 100644
--- a/ecc/bls24-317/fr/iop/doc.go
+++ b/ecc/bls24-317/fr/iop/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/iop/expressions.go b/ecc/bls24-317/fr/iop/expressions.go
index 7c0304026e..904c5cad0d 100644
--- a/ecc/bls24-317/fr/iop/expressions.go
+++ b/ecc/bls24-317/fr/iop/expressions.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/iop/expressions_test.go b/ecc/bls24-317/fr/iop/expressions_test.go
index a7f58a8a33..aba2e4e755 100644
--- a/ecc/bls24-317/fr/iop/expressions_test.go
+++ b/ecc/bls24-317/fr/iop/expressions_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/iop/polynomial.go b/ecc/bls24-317/fr/iop/polynomial.go
index 6b4988d988..1869ba8fce 100644
--- a/ecc/bls24-317/fr/iop/polynomial.go
+++ b/ecc/bls24-317/fr/iop/polynomial.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/iop/polynomial_test.go b/ecc/bls24-317/fr/iop/polynomial_test.go
index 9e3524f070..2d14b63fff 100644
--- a/ecc/bls24-317/fr/iop/polynomial_test.go
+++ b/ecc/bls24-317/fr/iop/polynomial_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/iop/quotient.go b/ecc/bls24-317/fr/iop/quotient.go
index 0ad638ccc9..63d501b366 100644
--- a/ecc/bls24-317/fr/iop/quotient.go
+++ b/ecc/bls24-317/fr/iop/quotient.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/iop/quotient_test.go b/ecc/bls24-317/fr/iop/quotient_test.go
index e9b2ef53e0..e66e506ccb 100644
--- a/ecc/bls24-317/fr/iop/quotient_test.go
+++ b/ecc/bls24-317/fr/iop/quotient_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/iop/ratios.go b/ecc/bls24-317/fr/iop/ratios.go
index e71f9547bb..777c70384a 100644
--- a/ecc/bls24-317/fr/iop/ratios.go
+++ b/ecc/bls24-317/fr/iop/ratios.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/iop/ratios_test.go b/ecc/bls24-317/fr/iop/ratios_test.go
index bb70bc686e..5e17c09cc5 100644
--- a/ecc/bls24-317/fr/iop/ratios_test.go
+++ b/ecc/bls24-317/fr/iop/ratios_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/iop/utils.go b/ecc/bls24-317/fr/iop/utils.go
index edbffb4658..b6a8b103e7 100644
--- a/ecc/bls24-317/fr/iop/utils.go
+++ b/ecc/bls24-317/fr/iop/utils.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/mimc/doc.go b/ecc/bls24-317/fr/mimc/doc.go
index 78837e1c80..cc7b101eb4 100644
--- a/ecc/bls24-317/fr/mimc/doc.go
+++ b/ecc/bls24-317/fr/mimc/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/mimc/mimc.go b/ecc/bls24-317/fr/mimc/mimc.go
index b9024e7e5b..9a47f6f527 100644
--- a/ecc/bls24-317/fr/mimc/mimc.go
+++ b/ecc/bls24-317/fr/mimc/mimc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/mimc/options.go b/ecc/bls24-317/fr/mimc/options.go
index 2ef5de3f57..fc10eb61e6 100644
--- a/ecc/bls24-317/fr/mimc/options.go
+++ b/ecc/bls24-317/fr/mimc/options.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/pedersen/doc.go b/ecc/bls24-317/fr/pedersen/doc.go
index 944679f5c5..62a62f179f 100644
--- a/ecc/bls24-317/fr/pedersen/doc.go
+++ b/ecc/bls24-317/fr/pedersen/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/pedersen/example_test.go b/ecc/bls24-317/fr/pedersen/example_test.go
index 6362474b11..d52b40c47f 100644
--- a/ecc/bls24-317/fr/pedersen/example_test.go
+++ b/ecc/bls24-317/fr/pedersen/example_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/pedersen/pedersen.go b/ecc/bls24-317/fr/pedersen/pedersen.go
index 9fca8b9fce..1e5e96e6f4 100644
--- a/ecc/bls24-317/fr/pedersen/pedersen.go
+++ b/ecc/bls24-317/fr/pedersen/pedersen.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/pedersen/pedersen_test.go b/ecc/bls24-317/fr/pedersen/pedersen_test.go
index b732b3e025..5a703fc260 100644
--- a/ecc/bls24-317/fr/pedersen/pedersen_test.go
+++ b/ecc/bls24-317/fr/pedersen/pedersen_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/permutation/doc.go b/ecc/bls24-317/fr/permutation/doc.go
index 7ef21ffb9e..5f346b5a53 100644
--- a/ecc/bls24-317/fr/permutation/doc.go
+++ b/ecc/bls24-317/fr/permutation/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/permutation/permutation.go b/ecc/bls24-317/fr/permutation/permutation.go
index ef7b7d2e35..fb8eea5312 100644
--- a/ecc/bls24-317/fr/permutation/permutation.go
+++ b/ecc/bls24-317/fr/permutation/permutation.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/permutation/permutation_test.go b/ecc/bls24-317/fr/permutation/permutation_test.go
index e67a7795e4..46faf9d2d3 100644
--- a/ecc/bls24-317/fr/permutation/permutation_test.go
+++ b/ecc/bls24-317/fr/permutation/permutation_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/plookup/doc.go b/ecc/bls24-317/fr/plookup/doc.go
index b3af019687..d163104002 100644
--- a/ecc/bls24-317/fr/plookup/doc.go
+++ b/ecc/bls24-317/fr/plookup/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/plookup/plookup_test.go b/ecc/bls24-317/fr/plookup/plookup_test.go
index ac4384f301..1c6637987d 100644
--- a/ecc/bls24-317/fr/plookup/plookup_test.go
+++ b/ecc/bls24-317/fr/plookup/plookup_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/plookup/table.go b/ecc/bls24-317/fr/plookup/table.go
index 5c1607cdb1..2a0ffcd26f 100644
--- a/ecc/bls24-317/fr/plookup/table.go
+++ b/ecc/bls24-317/fr/plookup/table.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/plookup/vector.go b/ecc/bls24-317/fr/plookup/vector.go
index 05f9167883..8bcb7fb4bd 100644
--- a/ecc/bls24-317/fr/plookup/vector.go
+++ b/ecc/bls24-317/fr/plookup/vector.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/polynomial/doc.go b/ecc/bls24-317/fr/polynomial/doc.go
index 747da41f2c..35b3f725c1 100644
--- a/ecc/bls24-317/fr/polynomial/doc.go
+++ b/ecc/bls24-317/fr/polynomial/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/polynomial/multilin.go b/ecc/bls24-317/fr/polynomial/multilin.go
index 1b06f84612..09f8babe95 100644
--- a/ecc/bls24-317/fr/polynomial/multilin.go
+++ b/ecc/bls24-317/fr/polynomial/multilin.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/polynomial/multilin_test.go b/ecc/bls24-317/fr/polynomial/multilin_test.go
index 0faff7a22e..6f04c4efc3 100644
--- a/ecc/bls24-317/fr/polynomial/multilin_test.go
+++ b/ecc/bls24-317/fr/polynomial/multilin_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/polynomial/polynomial.go b/ecc/bls24-317/fr/polynomial/polynomial.go
index e2e6192391..d86ec7b036 100644
--- a/ecc/bls24-317/fr/polynomial/polynomial.go
+++ b/ecc/bls24-317/fr/polynomial/polynomial.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/polynomial/polynomial_test.go b/ecc/bls24-317/fr/polynomial/polynomial_test.go
index 89d8599ce0..46f3058bbd 100644
--- a/ecc/bls24-317/fr/polynomial/polynomial_test.go
+++ b/ecc/bls24-317/fr/polynomial/polynomial_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/polynomial/pool.go b/ecc/bls24-317/fr/polynomial/pool.go
index 4839cf863c..978088df4c 100644
--- a/ecc/bls24-317/fr/polynomial/pool.go
+++ b/ecc/bls24-317/fr/polynomial/pool.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/poseidon2/poseidon2.go b/ecc/bls24-317/fr/poseidon2/poseidon2.go
index 5a9a72a721..26c7bc1b7d 100644
--- a/ecc/bls24-317/fr/poseidon2/poseidon2.go
+++ b/ecc/bls24-317/fr/poseidon2/poseidon2.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/poseidon2/poseidon2_test.go b/ecc/bls24-317/fr/poseidon2/poseidon2_test.go
index f41efef59a..c89bc2caa6 100644
--- a/ecc/bls24-317/fr/poseidon2/poseidon2_test.go
+++ b/ecc/bls24-317/fr/poseidon2/poseidon2_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/sumcheck/sumcheck.go b/ecc/bls24-317/fr/sumcheck/sumcheck.go
index 81ff2e5f2e..1c5c06b356 100644
--- a/ecc/bls24-317/fr/sumcheck/sumcheck.go
+++ b/ecc/bls24-317/fr/sumcheck/sumcheck.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/sumcheck/sumcheck_test.go b/ecc/bls24-317/fr/sumcheck/sumcheck_test.go
index 3ff045288f..678e9c0d2e 100644
--- a/ecc/bls24-317/fr/sumcheck/sumcheck_test.go
+++ b/ecc/bls24-317/fr/sumcheck/sumcheck_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/test_vector_utils/test_vector_utils.go b/ecc/bls24-317/fr/test_vector_utils/test_vector_utils.go
index 091236b767..60bdbbd25a 100644
--- a/ecc/bls24-317/fr/test_vector_utils/test_vector_utils.go
+++ b/ecc/bls24-317/fr/test_vector_utils/test_vector_utils.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/vector.go b/ecc/bls24-317/fr/vector.go
index 867cabbc3d..8b59bd36e9 100644
--- a/ecc/bls24-317/fr/vector.go
+++ b/ecc/bls24-317/fr/vector.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/vector_amd64.go b/ecc/bls24-317/fr/vector_amd64.go
index 0164ecb382..b27679827c 100644
--- a/ecc/bls24-317/fr/vector_amd64.go
+++ b/ecc/bls24-317/fr/vector_amd64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/vector_purego.go b/ecc/bls24-317/fr/vector_purego.go
index 84f86a40b1..5973d16ce2 100644
--- a/ecc/bls24-317/fr/vector_purego.go
+++ b/ecc/bls24-317/fr/vector_purego.go
@@ -1,18 +1,7 @@
 //go:build purego || !amd64
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/fr/vector_test.go b/ecc/bls24-317/fr/vector_test.go
index b6344c18b7..a094bc0ac6 100644
--- a/ecc/bls24-317/fr/vector_test.go
+++ b/ecc/bls24-317/fr/vector_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/g1.go b/ecc/bls24-317/g1.go
index b0a28327b9..1c9b24d0f8 100644
--- a/ecc/bls24-317/g1.go
+++ b/ecc/bls24-317/g1.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/g1_test.go b/ecc/bls24-317/g1_test.go
index c64e8ccef4..068f77f102 100644
--- a/ecc/bls24-317/g1_test.go
+++ b/ecc/bls24-317/g1_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/g2.go b/ecc/bls24-317/g2.go
index 2def434850..c1f602e3b1 100644
--- a/ecc/bls24-317/g2.go
+++ b/ecc/bls24-317/g2.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/g2_test.go b/ecc/bls24-317/g2_test.go
index cd8a859095..8406f2dd34 100644
--- a/ecc/bls24-317/g2_test.go
+++ b/ecc/bls24-317/g2_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/hash_to_g1.go b/ecc/bls24-317/hash_to_g1.go
index c2aa1c0da5..01bac28c85 100644
--- a/ecc/bls24-317/hash_to_g1.go
+++ b/ecc/bls24-317/hash_to_g1.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/hash_to_g1_test.go b/ecc/bls24-317/hash_to_g1_test.go
index 85749898c4..7dce6376dd 100644
--- a/ecc/bls24-317/hash_to_g1_test.go
+++ b/ecc/bls24-317/hash_to_g1_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/kzg/doc.go b/ecc/bls24-317/kzg/doc.go
index d1045726f2..6c3454a2d9 100644
--- a/ecc/bls24-317/kzg/doc.go
+++ b/ecc/bls24-317/kzg/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/kzg/kzg.go b/ecc/bls24-317/kzg/kzg.go
index fc4d67762e..c5760f968e 100644
--- a/ecc/bls24-317/kzg/kzg.go
+++ b/ecc/bls24-317/kzg/kzg.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/kzg/kzg_test.go b/ecc/bls24-317/kzg/kzg_test.go
index ebf4a58f11..4dff6ced17 100644
--- a/ecc/bls24-317/kzg/kzg_test.go
+++ b/ecc/bls24-317/kzg/kzg_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/kzg/marshal.go b/ecc/bls24-317/kzg/marshal.go
index 3bab6e0062..1bba0bd644 100644
--- a/ecc/bls24-317/kzg/marshal.go
+++ b/ecc/bls24-317/kzg/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/kzg/utils.go b/ecc/bls24-317/kzg/utils.go
index 036a080825..8eaba1c186 100644
--- a/ecc/bls24-317/kzg/utils.go
+++ b/ecc/bls24-317/kzg/utils.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/marshal.go b/ecc/bls24-317/marshal.go
index 3698554e2f..7066467c0f 100644
--- a/ecc/bls24-317/marshal.go
+++ b/ecc/bls24-317/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/marshal_test.go b/ecc/bls24-317/marshal_test.go
index fc8673e207..e19a3e92db 100644
--- a/ecc/bls24-317/marshal_test.go
+++ b/ecc/bls24-317/marshal_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/multiexp.go b/ecc/bls24-317/multiexp.go
index a9be7e1680..84b445dd83 100644
--- a/ecc/bls24-317/multiexp.go
+++ b/ecc/bls24-317/multiexp.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/multiexp_affine.go b/ecc/bls24-317/multiexp_affine.go
index b05471f593..1083d5835d 100644
--- a/ecc/bls24-317/multiexp_affine.go
+++ b/ecc/bls24-317/multiexp_affine.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/multiexp_jacobian.go b/ecc/bls24-317/multiexp_jacobian.go
index 04a8103691..afd3216e92 100644
--- a/ecc/bls24-317/multiexp_jacobian.go
+++ b/ecc/bls24-317/multiexp_jacobian.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/multiexp_test.go b/ecc/bls24-317/multiexp_test.go
index 75a6f165db..81a5085300 100644
--- a/ecc/bls24-317/multiexp_test.go
+++ b/ecc/bls24-317/multiexp_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/pairing_test.go b/ecc/bls24-317/pairing_test.go
index 1c995257dc..e76da2defe 100644
--- a/ecc/bls24-317/pairing_test.go
+++ b/ecc/bls24-317/pairing_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/shplonk/doc.go b/ecc/bls24-317/shplonk/doc.go
index e048f46009..17b34373c2 100644
--- a/ecc/bls24-317/shplonk/doc.go
+++ b/ecc/bls24-317/shplonk/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/shplonk/example_test.go b/ecc/bls24-317/shplonk/example_test.go
index 237b13ef60..cc7fb5d0fd 100644
--- a/ecc/bls24-317/shplonk/example_test.go
+++ b/ecc/bls24-317/shplonk/example_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/shplonk/marshal.go b/ecc/bls24-317/shplonk/marshal.go
index f3f4520ac2..89f133be45 100644
--- a/ecc/bls24-317/shplonk/marshal.go
+++ b/ecc/bls24-317/shplonk/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/shplonk/shplonk.go b/ecc/bls24-317/shplonk/shplonk.go
index 9e3642463b..242cb99922 100644
--- a/ecc/bls24-317/shplonk/shplonk.go
+++ b/ecc/bls24-317/shplonk/shplonk.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/shplonk/shplonk_test.go b/ecc/bls24-317/shplonk/shplonk_test.go
index 33d055815e..0e49a01865 100644
--- a/ecc/bls24-317/shplonk/shplonk_test.go
+++ b/ecc/bls24-317/shplonk/shplonk_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/twistededwards/curve.go b/ecc/bls24-317/twistededwards/curve.go
index 5c122cb3cc..7840ef8d97 100644
--- a/ecc/bls24-317/twistededwards/curve.go
+++ b/ecc/bls24-317/twistededwards/curve.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/twistededwards/doc.go b/ecc/bls24-317/twistededwards/doc.go
index 15c802b595..0a77cade57 100644
--- a/ecc/bls24-317/twistededwards/doc.go
+++ b/ecc/bls24-317/twistededwards/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/twistededwards/eddsa/doc.go b/ecc/bls24-317/twistededwards/eddsa/doc.go
index 10253fce8c..adc990eae4 100644
--- a/ecc/bls24-317/twistededwards/eddsa/doc.go
+++ b/ecc/bls24-317/twistededwards/eddsa/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/twistededwards/eddsa/eddsa.go b/ecc/bls24-317/twistededwards/eddsa/eddsa.go
index 7f12426e27..0019620804 100644
--- a/ecc/bls24-317/twistededwards/eddsa/eddsa.go
+++ b/ecc/bls24-317/twistededwards/eddsa/eddsa.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/twistededwards/eddsa/eddsa_test.go b/ecc/bls24-317/twistededwards/eddsa/eddsa_test.go
index 4bf88b2da7..04d36aeb12 100644
--- a/ecc/bls24-317/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bls24-317/twistededwards/eddsa/eddsa_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/twistededwards/eddsa/marshal.go b/ecc/bls24-317/twistededwards/eddsa/marshal.go
index cfd74f51cf..3dcd026688 100644
--- a/ecc/bls24-317/twistededwards/eddsa/marshal.go
+++ b/ecc/bls24-317/twistededwards/eddsa/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/twistededwards/point.go b/ecc/bls24-317/twistededwards/point.go
index 3bbcd3dc99..cb16ff3442 100644
--- a/ecc/bls24-317/twistededwards/point.go
+++ b/ecc/bls24-317/twistededwards/point.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bls24-317/twistededwards/point_test.go b/ecc/bls24-317/twistededwards/point_test.go
index 985bf83301..0ad9b0b084 100644
--- a/ecc/bls24-317/twistededwards/point_test.go
+++ b/ecc/bls24-317/twistededwards/point_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/ecdsa/doc.go b/ecc/bn254/ecdsa/doc.go
index ca7ca8f8a2..5820113b67 100644
--- a/ecc/bn254/ecdsa/doc.go
+++ b/ecc/bn254/ecdsa/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/ecdsa/ecdsa.go b/ecc/bn254/ecdsa/ecdsa.go
index 414a7e9402..5d9d9a8b2a 100644
--- a/ecc/bn254/ecdsa/ecdsa.go
+++ b/ecc/bn254/ecdsa/ecdsa.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/ecdsa/ecdsa_test.go b/ecc/bn254/ecdsa/ecdsa_test.go
index 7f8a1347c0..9c6b4d4993 100644
--- a/ecc/bn254/ecdsa/ecdsa_test.go
+++ b/ecc/bn254/ecdsa/ecdsa_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/ecdsa/marshal.go b/ecc/bn254/ecdsa/marshal.go
index eb618f2d63..57554a0b0b 100644
--- a/ecc/bn254/ecdsa/marshal.go
+++ b/ecc/bn254/ecdsa/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/ecdsa/marshal_test.go b/ecc/bn254/ecdsa/marshal_test.go
index 629107488c..3cf033cab5 100644
--- a/ecc/bn254/ecdsa/marshal_test.go
+++ b/ecc/bn254/ecdsa/marshal_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fflonk/doc.go b/ecc/bn254/fflonk/doc.go
index 694eaa9734..b717383d87 100644
--- a/ecc/bn254/fflonk/doc.go
+++ b/ecc/bn254/fflonk/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fflonk/example_test.go b/ecc/bn254/fflonk/example_test.go
index a3c26b50b2..9614b401a3 100644
--- a/ecc/bn254/fflonk/example_test.go
+++ b/ecc/bn254/fflonk/example_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fflonk/fflonk.go b/ecc/bn254/fflonk/fflonk.go
index dc7b99e70b..fdd29ccf70 100644
--- a/ecc/bn254/fflonk/fflonk.go
+++ b/ecc/bn254/fflonk/fflonk.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fflonk/fflonk_test.go b/ecc/bn254/fflonk/fflonk_test.go
index 7f9441f4fb..a75b371d42 100644
--- a/ecc/bn254/fflonk/fflonk_test.go
+++ b/ecc/bn254/fflonk/fflonk_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fflonk/marshal.go b/ecc/bn254/fflonk/marshal.go
index ff35b08e26..8d08502778 100644
--- a/ecc/bn254/fflonk/marshal.go
+++ b/ecc/bn254/fflonk/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fp/arith.go b/ecc/bn254/fp/arith.go
index 66fa667482..b202a1549a 100644
--- a/ecc/bn254/fp/arith.go
+++ b/ecc/bn254/fp/arith.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fp/asm_adx.go b/ecc/bn254/fp/asm_adx.go
index f8e29bd1a7..fe25e82db2 100644
--- a/ecc/bn254/fp/asm_adx.go
+++ b/ecc/bn254/fp/asm_adx.go
@@ -1,18 +1,7 @@
 //go:build !noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fp/asm_avx.go b/ecc/bn254/fp/asm_avx.go
index 52fc07a325..fdb65bb8f2 100644
--- a/ecc/bn254/fp/asm_avx.go
+++ b/ecc/bn254/fp/asm_avx.go
@@ -1,18 +1,7 @@
 //go:build !noavx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fp/asm_noadx.go b/ecc/bn254/fp/asm_noadx.go
index cb6cfa0f50..95085a8e6f 100644
--- a/ecc/bn254/fp/asm_noadx.go
+++ b/ecc/bn254/fp/asm_noadx.go
@@ -1,18 +1,7 @@
 //go:build noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fp/asm_noavx.go b/ecc/bn254/fp/asm_noavx.go
index 12261b1f03..c5fec182cd 100644
--- a/ecc/bn254/fp/asm_noavx.go
+++ b/ecc/bn254/fp/asm_noavx.go
@@ -1,18 +1,7 @@
 //go:build noavx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fp/doc.go b/ecc/bn254/fp/doc.go
index ac24d2e0de..4319c7913d 100644
--- a/ecc/bn254/fp/doc.go
+++ b/ecc/bn254/fp/doc.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fp/element.go b/ecc/bn254/fp/element.go
index 395030094f..313a1e3869 100644
--- a/ecc/bn254/fp/element.go
+++ b/ecc/bn254/fp/element.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fp/element_amd64.go b/ecc/bn254/fp/element_amd64.go
index 77a51ee25e..e72f552ad9 100644
--- a/ecc/bn254/fp/element_amd64.go
+++ b/ecc/bn254/fp/element_amd64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fp/element_amd64.s b/ecc/bn254/fp/element_amd64.s
index fb00194d7e..ed8a36e04d 100644
--- a/ecc/bn254/fp/element_amd64.s
+++ b/ecc/bn254/fp/element_amd64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fp/element_arm64.go b/ecc/bn254/fp/element_arm64.go
index dfb583df86..3eb868d38b 100644
--- a/ecc/bn254/fp/element_arm64.go
+++ b/ecc/bn254/fp/element_arm64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fp/element_arm64.s b/ecc/bn254/fp/element_arm64.s
index 5d328815aa..a7bd036553 100644
--- a/ecc/bn254/fp/element_arm64.s
+++ b/ecc/bn254/fp/element_arm64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fp/element_exp.go b/ecc/bn254/fp/element_exp.go
index 315a40b9fb..662e780e58 100644
--- a/ecc/bn254/fp/element_exp.go
+++ b/ecc/bn254/fp/element_exp.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fp/element_purego.go b/ecc/bn254/fp/element_purego.go
index ded61b6088..008cec50b2 100644
--- a/ecc/bn254/fp/element_purego.go
+++ b/ecc/bn254/fp/element_purego.go
@@ -1,18 +1,7 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fp/element_test.go b/ecc/bn254/fp/element_test.go
index 22d11d4acc..b49a4d6ffe 100644
--- a/ecc/bn254/fp/element_test.go
+++ b/ecc/bn254/fp/element_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fp/hash_to_field/doc.go b/ecc/bn254/fp/hash_to_field/doc.go
index 3f658d71d8..bc05bf9bcd 100644
--- a/ecc/bn254/fp/hash_to_field/doc.go
+++ b/ecc/bn254/fp/hash_to_field/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fp/hash_to_field/hash_to_field.go b/ecc/bn254/fp/hash_to_field/hash_to_field.go
index 582315f2d5..f229f83b36 100644
--- a/ecc/bn254/fp/hash_to_field/hash_to_field.go
+++ b/ecc/bn254/fp/hash_to_field/hash_to_field.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fp/hash_to_field/hash_to_field_test.go b/ecc/bn254/fp/hash_to_field/hash_to_field_test.go
index c22acb3d10..605f379235 100644
--- a/ecc/bn254/fp/hash_to_field/hash_to_field_test.go
+++ b/ecc/bn254/fp/hash_to_field/hash_to_field_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fp/vector.go b/ecc/bn254/fp/vector.go
index c97b4283ce..ec52314aa7 100644
--- a/ecc/bn254/fp/vector.go
+++ b/ecc/bn254/fp/vector.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fp/vector_amd64.go b/ecc/bn254/fp/vector_amd64.go
index 75719deedb..39666a2df7 100644
--- a/ecc/bn254/fp/vector_amd64.go
+++ b/ecc/bn254/fp/vector_amd64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fp/vector_purego.go b/ecc/bn254/fp/vector_purego.go
index fc0f66e2a3..16afa898d4 100644
--- a/ecc/bn254/fp/vector_purego.go
+++ b/ecc/bn254/fp/vector_purego.go
@@ -1,18 +1,7 @@
 //go:build purego || !amd64
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fp/vector_test.go b/ecc/bn254/fp/vector_test.go
index 12f17e21fb..06fe1084a8 100644
--- a/ecc/bn254/fp/vector_test.go
+++ b/ecc/bn254/fp/vector_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/arith.go b/ecc/bn254/fr/arith.go
index 83c9fd9ef9..9285041f4b 100644
--- a/ecc/bn254/fr/arith.go
+++ b/ecc/bn254/fr/arith.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/asm_adx.go b/ecc/bn254/fr/asm_adx.go
index 9273ea23ab..9e7da5e865 100644
--- a/ecc/bn254/fr/asm_adx.go
+++ b/ecc/bn254/fr/asm_adx.go
@@ -1,18 +1,7 @@
 //go:build !noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/asm_avx.go b/ecc/bn254/fr/asm_avx.go
index 1cc06c6e8d..d6d7d7f87a 100644
--- a/ecc/bn254/fr/asm_avx.go
+++ b/ecc/bn254/fr/asm_avx.go
@@ -1,18 +1,7 @@
 //go:build !noavx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/asm_noadx.go b/ecc/bn254/fr/asm_noadx.go
index b784a24247..3456158655 100644
--- a/ecc/bn254/fr/asm_noadx.go
+++ b/ecc/bn254/fr/asm_noadx.go
@@ -1,18 +1,7 @@
 //go:build noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/asm_noavx.go b/ecc/bn254/fr/asm_noavx.go
index 66bfc00772..4eb73e9a78 100644
--- a/ecc/bn254/fr/asm_noavx.go
+++ b/ecc/bn254/fr/asm_noavx.go
@@ -1,18 +1,7 @@
 //go:build noavx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/doc.go b/ecc/bn254/fr/doc.go
index 35388f880f..759f5d2511 100644
--- a/ecc/bn254/fr/doc.go
+++ b/ecc/bn254/fr/doc.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/element.go b/ecc/bn254/fr/element.go
index f8b6c10840..589c9f99bb 100644
--- a/ecc/bn254/fr/element.go
+++ b/ecc/bn254/fr/element.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/element_amd64.go b/ecc/bn254/fr/element_amd64.go
index 0ddb905f7b..ca49d12590 100644
--- a/ecc/bn254/fr/element_amd64.go
+++ b/ecc/bn254/fr/element_amd64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/element_amd64.s b/ecc/bn254/fr/element_amd64.s
index fb00194d7e..ed8a36e04d 100644
--- a/ecc/bn254/fr/element_amd64.s
+++ b/ecc/bn254/fr/element_amd64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/element_arm64.go b/ecc/bn254/fr/element_arm64.go
index 8b28f5123b..7189fe30d5 100644
--- a/ecc/bn254/fr/element_arm64.go
+++ b/ecc/bn254/fr/element_arm64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/element_arm64.s b/ecc/bn254/fr/element_arm64.s
index 5d328815aa..a7bd036553 100644
--- a/ecc/bn254/fr/element_arm64.s
+++ b/ecc/bn254/fr/element_arm64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/element_exp.go b/ecc/bn254/fr/element_exp.go
index e8c4da7928..d22db08600 100644
--- a/ecc/bn254/fr/element_exp.go
+++ b/ecc/bn254/fr/element_exp.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/element_purego.go b/ecc/bn254/fr/element_purego.go
index 034ee75ffe..647d39dd42 100644
--- a/ecc/bn254/fr/element_purego.go
+++ b/ecc/bn254/fr/element_purego.go
@@ -1,18 +1,7 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/element_test.go b/ecc/bn254/fr/element_test.go
index 5bac70c4b4..15785410c4 100644
--- a/ecc/bn254/fr/element_test.go
+++ b/ecc/bn254/fr/element_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/fft/bitreverse.go b/ecc/bn254/fr/fft/bitreverse.go
index a4fc200e14..b575154fa4 100644
--- a/ecc/bn254/fr/fft/bitreverse.go
+++ b/ecc/bn254/fr/fft/bitreverse.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/fft/bitreverse_test.go b/ecc/bn254/fr/fft/bitreverse_test.go
index 8bdf34182e..1c23996f51 100644
--- a/ecc/bn254/fr/fft/bitreverse_test.go
+++ b/ecc/bn254/fr/fft/bitreverse_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/fft/doc.go b/ecc/bn254/fr/fft/doc.go
index b5dd44e642..1ef04db2df 100644
--- a/ecc/bn254/fr/fft/doc.go
+++ b/ecc/bn254/fr/fft/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/fft/domain.go b/ecc/bn254/fr/fft/domain.go
index f80b4e95f8..48a84a9e1c 100644
--- a/ecc/bn254/fr/fft/domain.go
+++ b/ecc/bn254/fr/fft/domain.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/fft/domain_test.go b/ecc/bn254/fr/fft/domain_test.go
index 83186cb7c9..d95288076c 100644
--- a/ecc/bn254/fr/fft/domain_test.go
+++ b/ecc/bn254/fr/fft/domain_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/fft/fft.go b/ecc/bn254/fr/fft/fft.go
index 9dd6694767..6281c866aa 100644
--- a/ecc/bn254/fr/fft/fft.go
+++ b/ecc/bn254/fr/fft/fft.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/fft/fft_test.go b/ecc/bn254/fr/fft/fft_test.go
index e1aabf841f..9cfaf96110 100644
--- a/ecc/bn254/fr/fft/fft_test.go
+++ b/ecc/bn254/fr/fft/fft_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/fft/options.go b/ecc/bn254/fr/fft/options.go
index d2b44ec8b3..904036e7cc 100644
--- a/ecc/bn254/fr/fft/options.go
+++ b/ecc/bn254/fr/fft/options.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/fri/doc.go b/ecc/bn254/fr/fri/doc.go
index 3333ad41f5..428dabf625 100644
--- a/ecc/bn254/fr/fri/doc.go
+++ b/ecc/bn254/fr/fri/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/fri/fri.go b/ecc/bn254/fr/fri/fri.go
index 0bec8575de..a76e40d4a3 100644
--- a/ecc/bn254/fr/fri/fri.go
+++ b/ecc/bn254/fr/fri/fri.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/fri/fri_test.go b/ecc/bn254/fr/fri/fri_test.go
index 9639f147b1..d4629fd050 100644
--- a/ecc/bn254/fr/fri/fri_test.go
+++ b/ecc/bn254/fr/fri/fri_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/generator.go b/ecc/bn254/fr/generator.go
index fa7b82df0b..5a6a0e9571 100644
--- a/ecc/bn254/fr/generator.go
+++ b/ecc/bn254/fr/generator.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/gkr/gkr.go b/ecc/bn254/fr/gkr/gkr.go
index 94a2735b91..6b6e6c05a9 100644
--- a/ecc/bn254/fr/gkr/gkr.go
+++ b/ecc/bn254/fr/gkr/gkr.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/gkr/gkr_test.go b/ecc/bn254/fr/gkr/gkr_test.go
index 422ddb9979..b60faf98a1 100644
--- a/ecc/bn254/fr/gkr/gkr_test.go
+++ b/ecc/bn254/fr/gkr/gkr_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/hash_to_field/doc.go b/ecc/bn254/fr/hash_to_field/doc.go
index 34ead0afd8..6986d9ba80 100644
--- a/ecc/bn254/fr/hash_to_field/doc.go
+++ b/ecc/bn254/fr/hash_to_field/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/hash_to_field/hash_to_field.go b/ecc/bn254/fr/hash_to_field/hash_to_field.go
index 191f03c771..6ead221a31 100644
--- a/ecc/bn254/fr/hash_to_field/hash_to_field.go
+++ b/ecc/bn254/fr/hash_to_field/hash_to_field.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/hash_to_field/hash_to_field_test.go b/ecc/bn254/fr/hash_to_field/hash_to_field_test.go
index 690eca914d..895dc83d94 100644
--- a/ecc/bn254/fr/hash_to_field/hash_to_field_test.go
+++ b/ecc/bn254/fr/hash_to_field/hash_to_field_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/iop/doc.go b/ecc/bn254/fr/iop/doc.go
index 20f8b1a302..ee3facf1e1 100644
--- a/ecc/bn254/fr/iop/doc.go
+++ b/ecc/bn254/fr/iop/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/iop/expressions.go b/ecc/bn254/fr/iop/expressions.go
index b19fc77851..3361af0357 100644
--- a/ecc/bn254/fr/iop/expressions.go
+++ b/ecc/bn254/fr/iop/expressions.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/iop/expressions_test.go b/ecc/bn254/fr/iop/expressions_test.go
index b5530173d3..4bb0851f0b 100644
--- a/ecc/bn254/fr/iop/expressions_test.go
+++ b/ecc/bn254/fr/iop/expressions_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/iop/polynomial.go b/ecc/bn254/fr/iop/polynomial.go
index d8a1b7b0ec..fa5310479b 100644
--- a/ecc/bn254/fr/iop/polynomial.go
+++ b/ecc/bn254/fr/iop/polynomial.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/iop/polynomial_test.go b/ecc/bn254/fr/iop/polynomial_test.go
index 1d0588deaf..b1077bedab 100644
--- a/ecc/bn254/fr/iop/polynomial_test.go
+++ b/ecc/bn254/fr/iop/polynomial_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/iop/quotient.go b/ecc/bn254/fr/iop/quotient.go
index 59142c5792..085f771af9 100644
--- a/ecc/bn254/fr/iop/quotient.go
+++ b/ecc/bn254/fr/iop/quotient.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/iop/quotient_test.go b/ecc/bn254/fr/iop/quotient_test.go
index 7359fdf0b2..603a619d0e 100644
--- a/ecc/bn254/fr/iop/quotient_test.go
+++ b/ecc/bn254/fr/iop/quotient_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/iop/ratios.go b/ecc/bn254/fr/iop/ratios.go
index 7d9000ccd9..def50bc64a 100644
--- a/ecc/bn254/fr/iop/ratios.go
+++ b/ecc/bn254/fr/iop/ratios.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/iop/ratios_test.go b/ecc/bn254/fr/iop/ratios_test.go
index 588eb4335a..a9a8a47a82 100644
--- a/ecc/bn254/fr/iop/ratios_test.go
+++ b/ecc/bn254/fr/iop/ratios_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/iop/utils.go b/ecc/bn254/fr/iop/utils.go
index d8eb7fea4d..44d187446b 100644
--- a/ecc/bn254/fr/iop/utils.go
+++ b/ecc/bn254/fr/iop/utils.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/mimc/doc.go b/ecc/bn254/fr/mimc/doc.go
index 78837e1c80..cc7b101eb4 100644
--- a/ecc/bn254/fr/mimc/doc.go
+++ b/ecc/bn254/fr/mimc/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/mimc/mimc.go b/ecc/bn254/fr/mimc/mimc.go
index c0158fc3a8..9a7619bb89 100644
--- a/ecc/bn254/fr/mimc/mimc.go
+++ b/ecc/bn254/fr/mimc/mimc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/mimc/options.go b/ecc/bn254/fr/mimc/options.go
index ae82317a1a..a53abb2def 100644
--- a/ecc/bn254/fr/mimc/options.go
+++ b/ecc/bn254/fr/mimc/options.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/pedersen/doc.go b/ecc/bn254/fr/pedersen/doc.go
index 944679f5c5..62a62f179f 100644
--- a/ecc/bn254/fr/pedersen/doc.go
+++ b/ecc/bn254/fr/pedersen/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/pedersen/example_test.go b/ecc/bn254/fr/pedersen/example_test.go
index 101688b70f..6b46f1aafa 100644
--- a/ecc/bn254/fr/pedersen/example_test.go
+++ b/ecc/bn254/fr/pedersen/example_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/pedersen/pedersen.go b/ecc/bn254/fr/pedersen/pedersen.go
index 1d0969fadf..ebbd9914ad 100644
--- a/ecc/bn254/fr/pedersen/pedersen.go
+++ b/ecc/bn254/fr/pedersen/pedersen.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/pedersen/pedersen_test.go b/ecc/bn254/fr/pedersen/pedersen_test.go
index 1dc736cddd..b2f095f6e8 100644
--- a/ecc/bn254/fr/pedersen/pedersen_test.go
+++ b/ecc/bn254/fr/pedersen/pedersen_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/permutation/doc.go b/ecc/bn254/fr/permutation/doc.go
index 7ef21ffb9e..5f346b5a53 100644
--- a/ecc/bn254/fr/permutation/doc.go
+++ b/ecc/bn254/fr/permutation/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/permutation/permutation.go b/ecc/bn254/fr/permutation/permutation.go
index 83abd07c26..42ced0634c 100644
--- a/ecc/bn254/fr/permutation/permutation.go
+++ b/ecc/bn254/fr/permutation/permutation.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/permutation/permutation_test.go b/ecc/bn254/fr/permutation/permutation_test.go
index 70296970cf..5745d7e922 100644
--- a/ecc/bn254/fr/permutation/permutation_test.go
+++ b/ecc/bn254/fr/permutation/permutation_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/plookup/doc.go b/ecc/bn254/fr/plookup/doc.go
index b3af019687..d163104002 100644
--- a/ecc/bn254/fr/plookup/doc.go
+++ b/ecc/bn254/fr/plookup/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/plookup/plookup_test.go b/ecc/bn254/fr/plookup/plookup_test.go
index 14dbeff39a..8af42ee374 100644
--- a/ecc/bn254/fr/plookup/plookup_test.go
+++ b/ecc/bn254/fr/plookup/plookup_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/plookup/table.go b/ecc/bn254/fr/plookup/table.go
index fe37c0d1bf..7cc0ecaf80 100644
--- a/ecc/bn254/fr/plookup/table.go
+++ b/ecc/bn254/fr/plookup/table.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/plookup/vector.go b/ecc/bn254/fr/plookup/vector.go
index f6adf0bde4..cd9b2509ac 100644
--- a/ecc/bn254/fr/plookup/vector.go
+++ b/ecc/bn254/fr/plookup/vector.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/polynomial/doc.go b/ecc/bn254/fr/polynomial/doc.go
index 747da41f2c..35b3f725c1 100644
--- a/ecc/bn254/fr/polynomial/doc.go
+++ b/ecc/bn254/fr/polynomial/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/polynomial/multilin.go b/ecc/bn254/fr/polynomial/multilin.go
index a78479b4d7..0c10a86ee1 100644
--- a/ecc/bn254/fr/polynomial/multilin.go
+++ b/ecc/bn254/fr/polynomial/multilin.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/polynomial/multilin_test.go b/ecc/bn254/fr/polynomial/multilin_test.go
index 271d282415..1a32cc334a 100644
--- a/ecc/bn254/fr/polynomial/multilin_test.go
+++ b/ecc/bn254/fr/polynomial/multilin_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/polynomial/polynomial.go b/ecc/bn254/fr/polynomial/polynomial.go
index 0da76e377e..fe096e5556 100644
--- a/ecc/bn254/fr/polynomial/polynomial.go
+++ b/ecc/bn254/fr/polynomial/polynomial.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/polynomial/polynomial_test.go b/ecc/bn254/fr/polynomial/polynomial_test.go
index 778c88a239..cd1c9219ee 100644
--- a/ecc/bn254/fr/polynomial/polynomial_test.go
+++ b/ecc/bn254/fr/polynomial/polynomial_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/polynomial/pool.go b/ecc/bn254/fr/polynomial/pool.go
index 763c71e1c5..59b2e1868b 100644
--- a/ecc/bn254/fr/polynomial/pool.go
+++ b/ecc/bn254/fr/polynomial/pool.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/poseidon2/poseidon2.go b/ecc/bn254/fr/poseidon2/poseidon2.go
index dd3302de4c..c9b3e2d023 100644
--- a/ecc/bn254/fr/poseidon2/poseidon2.go
+++ b/ecc/bn254/fr/poseidon2/poseidon2.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/poseidon2/poseidon2_test.go b/ecc/bn254/fr/poseidon2/poseidon2_test.go
index 91fa4cd47c..ec371ab244 100644
--- a/ecc/bn254/fr/poseidon2/poseidon2_test.go
+++ b/ecc/bn254/fr/poseidon2/poseidon2_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/sis/sis_fft.go b/ecc/bn254/fr/sis/sis_fft.go
index 99eb21888a..25ff7f8235 100644
--- a/ecc/bn254/fr/sis/sis_fft.go
+++ b/ecc/bn254/fr/sis/sis_fft.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/sumcheck/sumcheck.go b/ecc/bn254/fr/sumcheck/sumcheck.go
index 473066bb52..fea037b974 100644
--- a/ecc/bn254/fr/sumcheck/sumcheck.go
+++ b/ecc/bn254/fr/sumcheck/sumcheck.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/sumcheck/sumcheck_test.go b/ecc/bn254/fr/sumcheck/sumcheck_test.go
index a4b11424c8..8330f3e7c6 100644
--- a/ecc/bn254/fr/sumcheck/sumcheck_test.go
+++ b/ecc/bn254/fr/sumcheck/sumcheck_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/test_vector_utils/test_vector_utils.go b/ecc/bn254/fr/test_vector_utils/test_vector_utils.go
index aedbd8fb61..09087f9b03 100644
--- a/ecc/bn254/fr/test_vector_utils/test_vector_utils.go
+++ b/ecc/bn254/fr/test_vector_utils/test_vector_utils.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/vector.go b/ecc/bn254/fr/vector.go
index 867cabbc3d..8b59bd36e9 100644
--- a/ecc/bn254/fr/vector.go
+++ b/ecc/bn254/fr/vector.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/vector_amd64.go b/ecc/bn254/fr/vector_amd64.go
index 0164ecb382..b27679827c 100644
--- a/ecc/bn254/fr/vector_amd64.go
+++ b/ecc/bn254/fr/vector_amd64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/vector_purego.go b/ecc/bn254/fr/vector_purego.go
index 84f86a40b1..5973d16ce2 100644
--- a/ecc/bn254/fr/vector_purego.go
+++ b/ecc/bn254/fr/vector_purego.go
@@ -1,18 +1,7 @@
 //go:build purego || !amd64
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/fr/vector_test.go b/ecc/bn254/fr/vector_test.go
index b6344c18b7..a094bc0ac6 100644
--- a/ecc/bn254/fr/vector_test.go
+++ b/ecc/bn254/fr/vector_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/g1.go b/ecc/bn254/g1.go
index e2c4a1d96d..afddf318c2 100644
--- a/ecc/bn254/g1.go
+++ b/ecc/bn254/g1.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/g1_test.go b/ecc/bn254/g1_test.go
index a358dbcc86..970369c503 100644
--- a/ecc/bn254/g1_test.go
+++ b/ecc/bn254/g1_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/g2.go b/ecc/bn254/g2.go
index 83c00364d5..36b3168d1c 100644
--- a/ecc/bn254/g2.go
+++ b/ecc/bn254/g2.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/g2_test.go b/ecc/bn254/g2_test.go
index a9a153a7c3..5367b79b02 100644
--- a/ecc/bn254/g2_test.go
+++ b/ecc/bn254/g2_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/hash_to_g1.go b/ecc/bn254/hash_to_g1.go
index 6be3be8e10..a1791f6e5a 100644
--- a/ecc/bn254/hash_to_g1.go
+++ b/ecc/bn254/hash_to_g1.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/hash_to_g1_test.go b/ecc/bn254/hash_to_g1_test.go
index 9278aa85a0..3bb56740eb 100644
--- a/ecc/bn254/hash_to_g1_test.go
+++ b/ecc/bn254/hash_to_g1_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/hash_to_g2.go b/ecc/bn254/hash_to_g2.go
index fa81853d03..ae3dbfd41d 100644
--- a/ecc/bn254/hash_to_g2.go
+++ b/ecc/bn254/hash_to_g2.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/hash_to_g2_test.go b/ecc/bn254/hash_to_g2_test.go
index 1800838a7f..47700eb9e8 100644
--- a/ecc/bn254/hash_to_g2_test.go
+++ b/ecc/bn254/hash_to_g2_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/internal/fptower/asm.go b/ecc/bn254/internal/fptower/asm.go
index 03b1160807..f1ff282d0b 100644
--- a/ecc/bn254/internal/fptower/asm.go
+++ b/ecc/bn254/internal/fptower/asm.go
@@ -1,18 +1,7 @@
 //go:build !noadx
 
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/internal/fptower/asm_noadx.go b/ecc/bn254/internal/fptower/asm_noadx.go
index ea7782392c..3885d93d55 100644
--- a/ecc/bn254/internal/fptower/asm_noadx.go
+++ b/ecc/bn254/internal/fptower/asm_noadx.go
@@ -1,18 +1,7 @@
 //go:build noadx
 
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/internal/fptower/e12.go b/ecc/bn254/internal/fptower/e12.go
index d2d7893104..319c2c3462 100644
--- a/ecc/bn254/internal/fptower/e12.go
+++ b/ecc/bn254/internal/fptower/e12.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/internal/fptower/e12_test.go b/ecc/bn254/internal/fptower/e12_test.go
index 54ab6e185d..b61d36078a 100644
--- a/ecc/bn254/internal/fptower/e12_test.go
+++ b/ecc/bn254/internal/fptower/e12_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/internal/fptower/e2.go b/ecc/bn254/internal/fptower/e2.go
index d227087563..eacac97603 100644
--- a/ecc/bn254/internal/fptower/e2.go
+++ b/ecc/bn254/internal/fptower/e2.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/internal/fptower/e2_amd64.go b/ecc/bn254/internal/fptower/e2_amd64.go
index b6db5715a3..4049fd2bed 100644
--- a/ecc/bn254/internal/fptower/e2_amd64.go
+++ b/ecc/bn254/internal/fptower/e2_amd64.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/internal/fptower/e2_amd64.s b/ecc/bn254/internal/fptower/e2_amd64.s
index 172cd67e82..ce5a3624bc 100644
--- a/ecc/bn254/internal/fptower/e2_amd64.s
+++ b/ecc/bn254/internal/fptower/e2_amd64.s
@@ -1,16 +1,5 @@
 // Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 #include "textflag.h"
 #include "funcdata.h"
diff --git a/ecc/bn254/internal/fptower/e2_fallback.go b/ecc/bn254/internal/fptower/e2_fallback.go
index 1b6011564f..eaea355699 100644
--- a/ecc/bn254/internal/fptower/e2_fallback.go
+++ b/ecc/bn254/internal/fptower/e2_fallback.go
@@ -1,18 +1,7 @@
 //go:build !amd64
 
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/internal/fptower/e2_test.go b/ecc/bn254/internal/fptower/e2_test.go
index 09e0ede173..808b48e27a 100644
--- a/ecc/bn254/internal/fptower/e2_test.go
+++ b/ecc/bn254/internal/fptower/e2_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/internal/fptower/e6.go b/ecc/bn254/internal/fptower/e6.go
index 1867470a88..5f2cca6625 100644
--- a/ecc/bn254/internal/fptower/e6.go
+++ b/ecc/bn254/internal/fptower/e6.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/internal/fptower/e6_test.go b/ecc/bn254/internal/fptower/e6_test.go
index b374b9b1f1..a82cc881aa 100644
--- a/ecc/bn254/internal/fptower/e6_test.go
+++ b/ecc/bn254/internal/fptower/e6_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/kzg/doc.go b/ecc/bn254/kzg/doc.go
index d1045726f2..6c3454a2d9 100644
--- a/ecc/bn254/kzg/doc.go
+++ b/ecc/bn254/kzg/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/kzg/kzg.go b/ecc/bn254/kzg/kzg.go
index 2689f970dc..157accfa99 100644
--- a/ecc/bn254/kzg/kzg.go
+++ b/ecc/bn254/kzg/kzg.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/kzg/kzg_test.go b/ecc/bn254/kzg/kzg_test.go
index b9cd530535..ad94918d7e 100644
--- a/ecc/bn254/kzg/kzg_test.go
+++ b/ecc/bn254/kzg/kzg_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/kzg/marshal.go b/ecc/bn254/kzg/marshal.go
index b633b9bcbd..1953bd8cb9 100644
--- a/ecc/bn254/kzg/marshal.go
+++ b/ecc/bn254/kzg/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/kzg/utils.go b/ecc/bn254/kzg/utils.go
index 796a0362fc..d14204dbd3 100644
--- a/ecc/bn254/kzg/utils.go
+++ b/ecc/bn254/kzg/utils.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/marshal.go b/ecc/bn254/marshal.go
index 7fb2512948..95afd6bac0 100644
--- a/ecc/bn254/marshal.go
+++ b/ecc/bn254/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/marshal_test.go b/ecc/bn254/marshal_test.go
index 0477bf036f..b2ed1ba2c7 100644
--- a/ecc/bn254/marshal_test.go
+++ b/ecc/bn254/marshal_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/multiexp.go b/ecc/bn254/multiexp.go
index 3190e1fd88..46f12095e7 100644
--- a/ecc/bn254/multiexp.go
+++ b/ecc/bn254/multiexp.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/multiexp_affine.go b/ecc/bn254/multiexp_affine.go
index f3a929a635..b3cc2d47a2 100644
--- a/ecc/bn254/multiexp_affine.go
+++ b/ecc/bn254/multiexp_affine.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/multiexp_jacobian.go b/ecc/bn254/multiexp_jacobian.go
index 199b781ca3..f1557637fe 100644
--- a/ecc/bn254/multiexp_jacobian.go
+++ b/ecc/bn254/multiexp_jacobian.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/multiexp_test.go b/ecc/bn254/multiexp_test.go
index 4c8303ad61..bbdc88d5ac 100644
--- a/ecc/bn254/multiexp_test.go
+++ b/ecc/bn254/multiexp_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/pairing_test.go b/ecc/bn254/pairing_test.go
index e8107a44b2..dd7fbfd2fa 100644
--- a/ecc/bn254/pairing_test.go
+++ b/ecc/bn254/pairing_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/shplonk/doc.go b/ecc/bn254/shplonk/doc.go
index e048f46009..17b34373c2 100644
--- a/ecc/bn254/shplonk/doc.go
+++ b/ecc/bn254/shplonk/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/shplonk/example_test.go b/ecc/bn254/shplonk/example_test.go
index e839ce1e16..4d0ce3c2d3 100644
--- a/ecc/bn254/shplonk/example_test.go
+++ b/ecc/bn254/shplonk/example_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/shplonk/marshal.go b/ecc/bn254/shplonk/marshal.go
index 5da8c732a5..df73ab2bea 100644
--- a/ecc/bn254/shplonk/marshal.go
+++ b/ecc/bn254/shplonk/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
index 1c6e6ad849..8335b78aa8 100644
--- a/ecc/bn254/shplonk/shplonk.go
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/shplonk/shplonk_test.go b/ecc/bn254/shplonk/shplonk_test.go
index d0558c4725..7955cd7bfc 100644
--- a/ecc/bn254/shplonk/shplonk_test.go
+++ b/ecc/bn254/shplonk/shplonk_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/twistededwards/curve.go b/ecc/bn254/twistededwards/curve.go
index beeddab765..aaf24dd341 100644
--- a/ecc/bn254/twistededwards/curve.go
+++ b/ecc/bn254/twistededwards/curve.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/twistededwards/doc.go b/ecc/bn254/twistededwards/doc.go
index 970cc24092..02a4aaf565 100644
--- a/ecc/bn254/twistededwards/doc.go
+++ b/ecc/bn254/twistededwards/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/twistededwards/eddsa/doc.go b/ecc/bn254/twistededwards/eddsa/doc.go
index ee1c7ba2a3..1e50b3f6a9 100644
--- a/ecc/bn254/twistededwards/eddsa/doc.go
+++ b/ecc/bn254/twistededwards/eddsa/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/twistededwards/eddsa/eddsa.go b/ecc/bn254/twistededwards/eddsa/eddsa.go
index 91b520e2ed..0fae94c13e 100644
--- a/ecc/bn254/twistededwards/eddsa/eddsa.go
+++ b/ecc/bn254/twistededwards/eddsa/eddsa.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/twistededwards/eddsa/eddsa_test.go b/ecc/bn254/twistededwards/eddsa/eddsa_test.go
index 973bd0e45c..0df6b846dc 100644
--- a/ecc/bn254/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bn254/twistededwards/eddsa/eddsa_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/twistededwards/eddsa/marshal.go b/ecc/bn254/twistededwards/eddsa/marshal.go
index dad7b3e930..997d632b52 100644
--- a/ecc/bn254/twistededwards/eddsa/marshal.go
+++ b/ecc/bn254/twistededwards/eddsa/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/twistededwards/point.go b/ecc/bn254/twistededwards/point.go
index 67e1ca47f5..981ce89b7b 100644
--- a/ecc/bn254/twistededwards/point.go
+++ b/ecc/bn254/twistededwards/point.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bn254/twistededwards/point_test.go b/ecc/bn254/twistededwards/point_test.go
index 5a0f200934..80c0b1299d 100644
--- a/ecc/bn254/twistededwards/point_test.go
+++ b/ecc/bn254/twistededwards/point_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/ecdsa/doc.go b/ecc/bw6-633/ecdsa/doc.go
index 156e20b9fd..59f91a57cd 100644
--- a/ecc/bw6-633/ecdsa/doc.go
+++ b/ecc/bw6-633/ecdsa/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/ecdsa/ecdsa.go b/ecc/bw6-633/ecdsa/ecdsa.go
index 649a8efe0e..0f2f7593bb 100644
--- a/ecc/bw6-633/ecdsa/ecdsa.go
+++ b/ecc/bw6-633/ecdsa/ecdsa.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/ecdsa/ecdsa_test.go b/ecc/bw6-633/ecdsa/ecdsa_test.go
index a99f1abdd3..002945c411 100644
--- a/ecc/bw6-633/ecdsa/ecdsa_test.go
+++ b/ecc/bw6-633/ecdsa/ecdsa_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/ecdsa/marshal.go b/ecc/bw6-633/ecdsa/marshal.go
index 3feaabddf1..8d78088705 100644
--- a/ecc/bw6-633/ecdsa/marshal.go
+++ b/ecc/bw6-633/ecdsa/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/ecdsa/marshal_test.go b/ecc/bw6-633/ecdsa/marshal_test.go
index 181d406379..87f4dbed9d 100644
--- a/ecc/bw6-633/ecdsa/marshal_test.go
+++ b/ecc/bw6-633/ecdsa/marshal_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fflonk/doc.go b/ecc/bw6-633/fflonk/doc.go
index 694eaa9734..b717383d87 100644
--- a/ecc/bw6-633/fflonk/doc.go
+++ b/ecc/bw6-633/fflonk/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fflonk/example_test.go b/ecc/bw6-633/fflonk/example_test.go
index c02b2b8ae8..7e1b0173af 100644
--- a/ecc/bw6-633/fflonk/example_test.go
+++ b/ecc/bw6-633/fflonk/example_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fflonk/fflonk.go b/ecc/bw6-633/fflonk/fflonk.go
index a66233e78d..c22d719fe7 100644
--- a/ecc/bw6-633/fflonk/fflonk.go
+++ b/ecc/bw6-633/fflonk/fflonk.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fflonk/fflonk_test.go b/ecc/bw6-633/fflonk/fflonk_test.go
index ae1755145c..d74bb16130 100644
--- a/ecc/bw6-633/fflonk/fflonk_test.go
+++ b/ecc/bw6-633/fflonk/fflonk_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fflonk/marshal.go b/ecc/bw6-633/fflonk/marshal.go
index a8b354e6c4..d30b5d7ac2 100644
--- a/ecc/bw6-633/fflonk/marshal.go
+++ b/ecc/bw6-633/fflonk/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fp/arith.go b/ecc/bw6-633/fp/arith.go
index 66fa667482..b202a1549a 100644
--- a/ecc/bw6-633/fp/arith.go
+++ b/ecc/bw6-633/fp/arith.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fp/asm_adx.go b/ecc/bw6-633/fp/asm_adx.go
index f8e29bd1a7..fe25e82db2 100644
--- a/ecc/bw6-633/fp/asm_adx.go
+++ b/ecc/bw6-633/fp/asm_adx.go
@@ -1,18 +1,7 @@
 //go:build !noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fp/asm_noadx.go b/ecc/bw6-633/fp/asm_noadx.go
index cb6cfa0f50..95085a8e6f 100644
--- a/ecc/bw6-633/fp/asm_noadx.go
+++ b/ecc/bw6-633/fp/asm_noadx.go
@@ -1,18 +1,7 @@
 //go:build noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fp/doc.go b/ecc/bw6-633/fp/doc.go
index ac522839db..f4bd26cf51 100644
--- a/ecc/bw6-633/fp/doc.go
+++ b/ecc/bw6-633/fp/doc.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fp/element.go b/ecc/bw6-633/fp/element.go
index 6f2565eaf7..021561c553 100644
--- a/ecc/bw6-633/fp/element.go
+++ b/ecc/bw6-633/fp/element.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fp/element_amd64.go b/ecc/bw6-633/fp/element_amd64.go
index 77a51ee25e..e72f552ad9 100644
--- a/ecc/bw6-633/fp/element_amd64.go
+++ b/ecc/bw6-633/fp/element_amd64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fp/element_amd64.s b/ecc/bw6-633/fp/element_amd64.s
index 4820949b69..0db47520d3 100644
--- a/ecc/bw6-633/fp/element_amd64.s
+++ b/ecc/bw6-633/fp/element_amd64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fp/element_arm64.go b/ecc/bw6-633/fp/element_arm64.go
index aeabec816c..febbad8296 100644
--- a/ecc/bw6-633/fp/element_arm64.go
+++ b/ecc/bw6-633/fp/element_arm64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fp/element_arm64.s b/ecc/bw6-633/fp/element_arm64.s
index 19ca3bc382..537ac0b636 100644
--- a/ecc/bw6-633/fp/element_arm64.s
+++ b/ecc/bw6-633/fp/element_arm64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fp/element_exp.go b/ecc/bw6-633/fp/element_exp.go
index b6f1086d9d..846338367d 100644
--- a/ecc/bw6-633/fp/element_exp.go
+++ b/ecc/bw6-633/fp/element_exp.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fp/element_purego.go b/ecc/bw6-633/fp/element_purego.go
index 637ecd9d67..cabb8ff2b3 100644
--- a/ecc/bw6-633/fp/element_purego.go
+++ b/ecc/bw6-633/fp/element_purego.go
@@ -1,18 +1,7 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fp/element_test.go b/ecc/bw6-633/fp/element_test.go
index 2aaadfa902..33266dd93e 100644
--- a/ecc/bw6-633/fp/element_test.go
+++ b/ecc/bw6-633/fp/element_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fp/hash_to_field/doc.go b/ecc/bw6-633/fp/hash_to_field/doc.go
index 91716313b8..4dee7c4096 100644
--- a/ecc/bw6-633/fp/hash_to_field/doc.go
+++ b/ecc/bw6-633/fp/hash_to_field/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fp/hash_to_field/hash_to_field.go b/ecc/bw6-633/fp/hash_to_field/hash_to_field.go
index c04f3fdbae..853d1a5aac 100644
--- a/ecc/bw6-633/fp/hash_to_field/hash_to_field.go
+++ b/ecc/bw6-633/fp/hash_to_field/hash_to_field.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fp/hash_to_field/hash_to_field_test.go b/ecc/bw6-633/fp/hash_to_field/hash_to_field_test.go
index f7e4e191d4..8fc6ccdbe7 100644
--- a/ecc/bw6-633/fp/hash_to_field/hash_to_field_test.go
+++ b/ecc/bw6-633/fp/hash_to_field/hash_to_field_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fp/vector.go b/ecc/bw6-633/fp/vector.go
index 9f86d6d8e7..05a1b66f95 100644
--- a/ecc/bw6-633/fp/vector.go
+++ b/ecc/bw6-633/fp/vector.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fp/vector_purego.go b/ecc/bw6-633/fp/vector_purego.go
index 798b669887..347b0df594 100644
--- a/ecc/bw6-633/fp/vector_purego.go
+++ b/ecc/bw6-633/fp/vector_purego.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fp/vector_test.go b/ecc/bw6-633/fp/vector_test.go
index 94d6557e20..ac54705fea 100644
--- a/ecc/bw6-633/fp/vector_test.go
+++ b/ecc/bw6-633/fp/vector_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/arith.go b/ecc/bw6-633/fr/arith.go
index 83c9fd9ef9..9285041f4b 100644
--- a/ecc/bw6-633/fr/arith.go
+++ b/ecc/bw6-633/fr/arith.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/asm_adx.go b/ecc/bw6-633/fr/asm_adx.go
index 9273ea23ab..9e7da5e865 100644
--- a/ecc/bw6-633/fr/asm_adx.go
+++ b/ecc/bw6-633/fr/asm_adx.go
@@ -1,18 +1,7 @@
 //go:build !noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/asm_noadx.go b/ecc/bw6-633/fr/asm_noadx.go
index b784a24247..3456158655 100644
--- a/ecc/bw6-633/fr/asm_noadx.go
+++ b/ecc/bw6-633/fr/asm_noadx.go
@@ -1,18 +1,7 @@
 //go:build noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/doc.go b/ecc/bw6-633/fr/doc.go
index cbb3894044..a2b7cfd871 100644
--- a/ecc/bw6-633/fr/doc.go
+++ b/ecc/bw6-633/fr/doc.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/element.go b/ecc/bw6-633/fr/element.go
index b9cff65b7a..d9671b7d08 100644
--- a/ecc/bw6-633/fr/element.go
+++ b/ecc/bw6-633/fr/element.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/element_amd64.go b/ecc/bw6-633/fr/element_amd64.go
index 0ddb905f7b..ca49d12590 100644
--- a/ecc/bw6-633/fr/element_amd64.go
+++ b/ecc/bw6-633/fr/element_amd64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/element_amd64.s b/ecc/bw6-633/fr/element_amd64.s
index 00858d648e..599977a11a 100644
--- a/ecc/bw6-633/fr/element_amd64.s
+++ b/ecc/bw6-633/fr/element_amd64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/element_exp.go b/ecc/bw6-633/fr/element_exp.go
index ffd72839e6..11528df7d0 100644
--- a/ecc/bw6-633/fr/element_exp.go
+++ b/ecc/bw6-633/fr/element_exp.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/element_purego.go b/ecc/bw6-633/fr/element_purego.go
index 93ea6339b3..7d2053163c 100644
--- a/ecc/bw6-633/fr/element_purego.go
+++ b/ecc/bw6-633/fr/element_purego.go
@@ -1,18 +1,7 @@
 //go:build purego || !amd64
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/element_test.go b/ecc/bw6-633/fr/element_test.go
index b7acc3840a..aec1350323 100644
--- a/ecc/bw6-633/fr/element_test.go
+++ b/ecc/bw6-633/fr/element_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/fft/bitreverse.go b/ecc/bw6-633/fr/fft/bitreverse.go
index 4618d97f88..b495f43b30 100644
--- a/ecc/bw6-633/fr/fft/bitreverse.go
+++ b/ecc/bw6-633/fr/fft/bitreverse.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/fft/bitreverse_test.go b/ecc/bw6-633/fr/fft/bitreverse_test.go
index 12755a6893..c14e2905c3 100644
--- a/ecc/bw6-633/fr/fft/bitreverse_test.go
+++ b/ecc/bw6-633/fr/fft/bitreverse_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/fft/doc.go b/ecc/bw6-633/fr/fft/doc.go
index b5dd44e642..1ef04db2df 100644
--- a/ecc/bw6-633/fr/fft/doc.go
+++ b/ecc/bw6-633/fr/fft/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/fft/domain.go b/ecc/bw6-633/fr/fft/domain.go
index 3174495684..e8c95c7bb8 100644
--- a/ecc/bw6-633/fr/fft/domain.go
+++ b/ecc/bw6-633/fr/fft/domain.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/fft/domain_test.go b/ecc/bw6-633/fr/fft/domain_test.go
index 83186cb7c9..d95288076c 100644
--- a/ecc/bw6-633/fr/fft/domain_test.go
+++ b/ecc/bw6-633/fr/fft/domain_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/fft/fft.go b/ecc/bw6-633/fr/fft/fft.go
index 205f21f3fd..c4f306cbc1 100644
--- a/ecc/bw6-633/fr/fft/fft.go
+++ b/ecc/bw6-633/fr/fft/fft.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/fft/fft_test.go b/ecc/bw6-633/fr/fft/fft_test.go
index 84b71d3d16..6ff132f4db 100644
--- a/ecc/bw6-633/fr/fft/fft_test.go
+++ b/ecc/bw6-633/fr/fft/fft_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/fft/options.go b/ecc/bw6-633/fr/fft/options.go
index c77a1c7725..b7abd2878c 100644
--- a/ecc/bw6-633/fr/fft/options.go
+++ b/ecc/bw6-633/fr/fft/options.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/fri/doc.go b/ecc/bw6-633/fr/fri/doc.go
index 3333ad41f5..428dabf625 100644
--- a/ecc/bw6-633/fr/fri/doc.go
+++ b/ecc/bw6-633/fr/fri/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/fri/fri.go b/ecc/bw6-633/fr/fri/fri.go
index b90dbc75f7..c720a643fa 100644
--- a/ecc/bw6-633/fr/fri/fri.go
+++ b/ecc/bw6-633/fr/fri/fri.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/fri/fri_test.go b/ecc/bw6-633/fr/fri/fri_test.go
index 7fcf8dd707..299f1b7187 100644
--- a/ecc/bw6-633/fr/fri/fri_test.go
+++ b/ecc/bw6-633/fr/fri/fri_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/generator.go b/ecc/bw6-633/fr/generator.go
index 808b18106c..d18f530e8e 100644
--- a/ecc/bw6-633/fr/generator.go
+++ b/ecc/bw6-633/fr/generator.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/gkr/gkr.go b/ecc/bw6-633/fr/gkr/gkr.go
index 8997297237..5f251d6742 100644
--- a/ecc/bw6-633/fr/gkr/gkr.go
+++ b/ecc/bw6-633/fr/gkr/gkr.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/gkr/gkr_test.go b/ecc/bw6-633/fr/gkr/gkr_test.go
index 7b2abc9dc2..0c7fbc9cb6 100644
--- a/ecc/bw6-633/fr/gkr/gkr_test.go
+++ b/ecc/bw6-633/fr/gkr/gkr_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/hash_to_field/doc.go b/ecc/bw6-633/fr/hash_to_field/doc.go
index 15a7663914..298175d9f9 100644
--- a/ecc/bw6-633/fr/hash_to_field/doc.go
+++ b/ecc/bw6-633/fr/hash_to_field/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/hash_to_field/hash_to_field.go b/ecc/bw6-633/fr/hash_to_field/hash_to_field.go
index fcc3357c3a..e504f76259 100644
--- a/ecc/bw6-633/fr/hash_to_field/hash_to_field.go
+++ b/ecc/bw6-633/fr/hash_to_field/hash_to_field.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/hash_to_field/hash_to_field_test.go b/ecc/bw6-633/fr/hash_to_field/hash_to_field_test.go
index a7c8a03072..e5e9595d90 100644
--- a/ecc/bw6-633/fr/hash_to_field/hash_to_field_test.go
+++ b/ecc/bw6-633/fr/hash_to_field/hash_to_field_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/iop/doc.go b/ecc/bw6-633/fr/iop/doc.go
index 20f8b1a302..ee3facf1e1 100644
--- a/ecc/bw6-633/fr/iop/doc.go
+++ b/ecc/bw6-633/fr/iop/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/iop/expressions.go b/ecc/bw6-633/fr/iop/expressions.go
index 558bab7c73..7d239194ca 100644
--- a/ecc/bw6-633/fr/iop/expressions.go
+++ b/ecc/bw6-633/fr/iop/expressions.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/iop/expressions_test.go b/ecc/bw6-633/fr/iop/expressions_test.go
index c1b449e390..ec0e96da8c 100644
--- a/ecc/bw6-633/fr/iop/expressions_test.go
+++ b/ecc/bw6-633/fr/iop/expressions_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/iop/polynomial.go b/ecc/bw6-633/fr/iop/polynomial.go
index 8be0f8ece3..c496dcf9a5 100644
--- a/ecc/bw6-633/fr/iop/polynomial.go
+++ b/ecc/bw6-633/fr/iop/polynomial.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/iop/polynomial_test.go b/ecc/bw6-633/fr/iop/polynomial_test.go
index 72d8dade56..08e97903aa 100644
--- a/ecc/bw6-633/fr/iop/polynomial_test.go
+++ b/ecc/bw6-633/fr/iop/polynomial_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/iop/quotient.go b/ecc/bw6-633/fr/iop/quotient.go
index 41a8ba0118..8e4239ebdb 100644
--- a/ecc/bw6-633/fr/iop/quotient.go
+++ b/ecc/bw6-633/fr/iop/quotient.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/iop/quotient_test.go b/ecc/bw6-633/fr/iop/quotient_test.go
index 52a5716d1e..da0f0bfc41 100644
--- a/ecc/bw6-633/fr/iop/quotient_test.go
+++ b/ecc/bw6-633/fr/iop/quotient_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/iop/ratios.go b/ecc/bw6-633/fr/iop/ratios.go
index 17913fd970..876c380c94 100644
--- a/ecc/bw6-633/fr/iop/ratios.go
+++ b/ecc/bw6-633/fr/iop/ratios.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/iop/ratios_test.go b/ecc/bw6-633/fr/iop/ratios_test.go
index 6c9ed5862d..03c076bb75 100644
--- a/ecc/bw6-633/fr/iop/ratios_test.go
+++ b/ecc/bw6-633/fr/iop/ratios_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/iop/utils.go b/ecc/bw6-633/fr/iop/utils.go
index faf1c2137d..5a4fb37c09 100644
--- a/ecc/bw6-633/fr/iop/utils.go
+++ b/ecc/bw6-633/fr/iop/utils.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/mimc/doc.go b/ecc/bw6-633/fr/mimc/doc.go
index 78837e1c80..cc7b101eb4 100644
--- a/ecc/bw6-633/fr/mimc/doc.go
+++ b/ecc/bw6-633/fr/mimc/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/mimc/mimc.go b/ecc/bw6-633/fr/mimc/mimc.go
index bbf620172b..cfa98c7a5c 100644
--- a/ecc/bw6-633/fr/mimc/mimc.go
+++ b/ecc/bw6-633/fr/mimc/mimc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/mimc/options.go b/ecc/bw6-633/fr/mimc/options.go
index 420ddbd064..6afaa999d2 100644
--- a/ecc/bw6-633/fr/mimc/options.go
+++ b/ecc/bw6-633/fr/mimc/options.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/pedersen/doc.go b/ecc/bw6-633/fr/pedersen/doc.go
index 944679f5c5..62a62f179f 100644
--- a/ecc/bw6-633/fr/pedersen/doc.go
+++ b/ecc/bw6-633/fr/pedersen/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/pedersen/example_test.go b/ecc/bw6-633/fr/pedersen/example_test.go
index 7a51260c4c..5e32ec591f 100644
--- a/ecc/bw6-633/fr/pedersen/example_test.go
+++ b/ecc/bw6-633/fr/pedersen/example_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/pedersen/pedersen.go b/ecc/bw6-633/fr/pedersen/pedersen.go
index be584fdcd3..acca5002c6 100644
--- a/ecc/bw6-633/fr/pedersen/pedersen.go
+++ b/ecc/bw6-633/fr/pedersen/pedersen.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/pedersen/pedersen_test.go b/ecc/bw6-633/fr/pedersen/pedersen_test.go
index 24e4e60948..1de99bdbdb 100644
--- a/ecc/bw6-633/fr/pedersen/pedersen_test.go
+++ b/ecc/bw6-633/fr/pedersen/pedersen_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/permutation/doc.go b/ecc/bw6-633/fr/permutation/doc.go
index 7ef21ffb9e..5f346b5a53 100644
--- a/ecc/bw6-633/fr/permutation/doc.go
+++ b/ecc/bw6-633/fr/permutation/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/permutation/permutation.go b/ecc/bw6-633/fr/permutation/permutation.go
index 7ec0969dd4..828b04c983 100644
--- a/ecc/bw6-633/fr/permutation/permutation.go
+++ b/ecc/bw6-633/fr/permutation/permutation.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/permutation/permutation_test.go b/ecc/bw6-633/fr/permutation/permutation_test.go
index 91bfccb378..da06886a14 100644
--- a/ecc/bw6-633/fr/permutation/permutation_test.go
+++ b/ecc/bw6-633/fr/permutation/permutation_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/plookup/doc.go b/ecc/bw6-633/fr/plookup/doc.go
index b3af019687..d163104002 100644
--- a/ecc/bw6-633/fr/plookup/doc.go
+++ b/ecc/bw6-633/fr/plookup/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/plookup/plookup_test.go b/ecc/bw6-633/fr/plookup/plookup_test.go
index d69c94f264..2d654beeaf 100644
--- a/ecc/bw6-633/fr/plookup/plookup_test.go
+++ b/ecc/bw6-633/fr/plookup/plookup_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/plookup/table.go b/ecc/bw6-633/fr/plookup/table.go
index eb80ef8c6d..9863ccd2f4 100644
--- a/ecc/bw6-633/fr/plookup/table.go
+++ b/ecc/bw6-633/fr/plookup/table.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/plookup/vector.go b/ecc/bw6-633/fr/plookup/vector.go
index a50eb00011..25acc02ecb 100644
--- a/ecc/bw6-633/fr/plookup/vector.go
+++ b/ecc/bw6-633/fr/plookup/vector.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/polynomial/doc.go b/ecc/bw6-633/fr/polynomial/doc.go
index 747da41f2c..35b3f725c1 100644
--- a/ecc/bw6-633/fr/polynomial/doc.go
+++ b/ecc/bw6-633/fr/polynomial/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/polynomial/multilin.go b/ecc/bw6-633/fr/polynomial/multilin.go
index 743331f10b..1b98d88c83 100644
--- a/ecc/bw6-633/fr/polynomial/multilin.go
+++ b/ecc/bw6-633/fr/polynomial/multilin.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/polynomial/multilin_test.go b/ecc/bw6-633/fr/polynomial/multilin_test.go
index b141532ff0..f1b0c1f746 100644
--- a/ecc/bw6-633/fr/polynomial/multilin_test.go
+++ b/ecc/bw6-633/fr/polynomial/multilin_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/polynomial/polynomial.go b/ecc/bw6-633/fr/polynomial/polynomial.go
index 1edc739be8..1265961519 100644
--- a/ecc/bw6-633/fr/polynomial/polynomial.go
+++ b/ecc/bw6-633/fr/polynomial/polynomial.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/polynomial/polynomial_test.go b/ecc/bw6-633/fr/polynomial/polynomial_test.go
index dd0e94f429..75e6b9c7a0 100644
--- a/ecc/bw6-633/fr/polynomial/polynomial_test.go
+++ b/ecc/bw6-633/fr/polynomial/polynomial_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/polynomial/pool.go b/ecc/bw6-633/fr/polynomial/pool.go
index bfec9a2066..d58cb5d680 100644
--- a/ecc/bw6-633/fr/polynomial/pool.go
+++ b/ecc/bw6-633/fr/polynomial/pool.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/poseidon2/poseidon2.go b/ecc/bw6-633/fr/poseidon2/poseidon2.go
index 4415e87ed5..d9583a8eb0 100644
--- a/ecc/bw6-633/fr/poseidon2/poseidon2.go
+++ b/ecc/bw6-633/fr/poseidon2/poseidon2.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/poseidon2/poseidon2_test.go b/ecc/bw6-633/fr/poseidon2/poseidon2_test.go
index 4bf1e0f1bf..e601f0f082 100644
--- a/ecc/bw6-633/fr/poseidon2/poseidon2_test.go
+++ b/ecc/bw6-633/fr/poseidon2/poseidon2_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/sumcheck/sumcheck.go b/ecc/bw6-633/fr/sumcheck/sumcheck.go
index db7abdaccb..192f993ce0 100644
--- a/ecc/bw6-633/fr/sumcheck/sumcheck.go
+++ b/ecc/bw6-633/fr/sumcheck/sumcheck.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/sumcheck/sumcheck_test.go b/ecc/bw6-633/fr/sumcheck/sumcheck_test.go
index 5086d2d354..4a7a939a41 100644
--- a/ecc/bw6-633/fr/sumcheck/sumcheck_test.go
+++ b/ecc/bw6-633/fr/sumcheck/sumcheck_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/test_vector_utils/test_vector_utils.go b/ecc/bw6-633/fr/test_vector_utils/test_vector_utils.go
index 44825e980d..48c3f18b7a 100644
--- a/ecc/bw6-633/fr/test_vector_utils/test_vector_utils.go
+++ b/ecc/bw6-633/fr/test_vector_utils/test_vector_utils.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/vector.go b/ecc/bw6-633/fr/vector.go
index 146828f9f7..6f87987b48 100644
--- a/ecc/bw6-633/fr/vector.go
+++ b/ecc/bw6-633/fr/vector.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/vector_purego.go b/ecc/bw6-633/fr/vector_purego.go
index 04662dde33..3c81210b58 100644
--- a/ecc/bw6-633/fr/vector_purego.go
+++ b/ecc/bw6-633/fr/vector_purego.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/fr/vector_test.go b/ecc/bw6-633/fr/vector_test.go
index 8245cc9287..b7fd253809 100644
--- a/ecc/bw6-633/fr/vector_test.go
+++ b/ecc/bw6-633/fr/vector_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/g1.go b/ecc/bw6-633/g1.go
index a40bcfc6f8..875a4c48cc 100644
--- a/ecc/bw6-633/g1.go
+++ b/ecc/bw6-633/g1.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/g1_test.go b/ecc/bw6-633/g1_test.go
index 52e7955454..69fc2bbf4f 100644
--- a/ecc/bw6-633/g1_test.go
+++ b/ecc/bw6-633/g1_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/g2.go b/ecc/bw6-633/g2.go
index 7e55beadf2..63912e698f 100644
--- a/ecc/bw6-633/g2.go
+++ b/ecc/bw6-633/g2.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/g2_test.go b/ecc/bw6-633/g2_test.go
index 5ecdebd9d8..d69c0235d5 100644
--- a/ecc/bw6-633/g2_test.go
+++ b/ecc/bw6-633/g2_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/hash_to_g1.go b/ecc/bw6-633/hash_to_g1.go
index ede1bd9da6..caba82f431 100644
--- a/ecc/bw6-633/hash_to_g1.go
+++ b/ecc/bw6-633/hash_to_g1.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/hash_to_g1_test.go b/ecc/bw6-633/hash_to_g1_test.go
index 72bb795e71..15201b3bc7 100644
--- a/ecc/bw6-633/hash_to_g1_test.go
+++ b/ecc/bw6-633/hash_to_g1_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/hash_to_g2.go b/ecc/bw6-633/hash_to_g2.go
index a6244504cf..b5b0fd99de 100644
--- a/ecc/bw6-633/hash_to_g2.go
+++ b/ecc/bw6-633/hash_to_g2.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/hash_to_g2_test.go b/ecc/bw6-633/hash_to_g2_test.go
index 85db98ee0c..020784d358 100644
--- a/ecc/bw6-633/hash_to_g2_test.go
+++ b/ecc/bw6-633/hash_to_g2_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/kzg/doc.go b/ecc/bw6-633/kzg/doc.go
index d1045726f2..6c3454a2d9 100644
--- a/ecc/bw6-633/kzg/doc.go
+++ b/ecc/bw6-633/kzg/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/kzg/kzg.go b/ecc/bw6-633/kzg/kzg.go
index 041f45b3d1..b9fae65ab1 100644
--- a/ecc/bw6-633/kzg/kzg.go
+++ b/ecc/bw6-633/kzg/kzg.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/kzg/kzg_test.go b/ecc/bw6-633/kzg/kzg_test.go
index 62fad1e7ac..ac64838478 100644
--- a/ecc/bw6-633/kzg/kzg_test.go
+++ b/ecc/bw6-633/kzg/kzg_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/kzg/marshal.go b/ecc/bw6-633/kzg/marshal.go
index 8cbce1f179..f120926571 100644
--- a/ecc/bw6-633/kzg/marshal.go
+++ b/ecc/bw6-633/kzg/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/kzg/utils.go b/ecc/bw6-633/kzg/utils.go
index dec3dba874..00006d1c20 100644
--- a/ecc/bw6-633/kzg/utils.go
+++ b/ecc/bw6-633/kzg/utils.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/marshal.go b/ecc/bw6-633/marshal.go
index 499b1ad26c..b10cc1b70a 100644
--- a/ecc/bw6-633/marshal.go
+++ b/ecc/bw6-633/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/marshal_test.go b/ecc/bw6-633/marshal_test.go
index 942a44f7fc..d68198dc29 100644
--- a/ecc/bw6-633/marshal_test.go
+++ b/ecc/bw6-633/marshal_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/multiexp.go b/ecc/bw6-633/multiexp.go
index 0d5b6fba94..37f75c2729 100644
--- a/ecc/bw6-633/multiexp.go
+++ b/ecc/bw6-633/multiexp.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/multiexp_affine.go b/ecc/bw6-633/multiexp_affine.go
index 73e875fa8b..67c19aa4a2 100644
--- a/ecc/bw6-633/multiexp_affine.go
+++ b/ecc/bw6-633/multiexp_affine.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/multiexp_jacobian.go b/ecc/bw6-633/multiexp_jacobian.go
index fce9735a1c..ee53a3a060 100644
--- a/ecc/bw6-633/multiexp_jacobian.go
+++ b/ecc/bw6-633/multiexp_jacobian.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/multiexp_test.go b/ecc/bw6-633/multiexp_test.go
index 2de5f7b732..0513c193c6 100644
--- a/ecc/bw6-633/multiexp_test.go
+++ b/ecc/bw6-633/multiexp_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/pairing_test.go b/ecc/bw6-633/pairing_test.go
index 70300a8272..606068693e 100644
--- a/ecc/bw6-633/pairing_test.go
+++ b/ecc/bw6-633/pairing_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/shplonk/doc.go b/ecc/bw6-633/shplonk/doc.go
index e048f46009..17b34373c2 100644
--- a/ecc/bw6-633/shplonk/doc.go
+++ b/ecc/bw6-633/shplonk/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/shplonk/example_test.go b/ecc/bw6-633/shplonk/example_test.go
index d13fd51dfe..fd6e34394e 100644
--- a/ecc/bw6-633/shplonk/example_test.go
+++ b/ecc/bw6-633/shplonk/example_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/shplonk/marshal.go b/ecc/bw6-633/shplonk/marshal.go
index 80661c53db..ab4d61b642 100644
--- a/ecc/bw6-633/shplonk/marshal.go
+++ b/ecc/bw6-633/shplonk/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/shplonk/shplonk.go b/ecc/bw6-633/shplonk/shplonk.go
index 56375f157f..925074f864 100644
--- a/ecc/bw6-633/shplonk/shplonk.go
+++ b/ecc/bw6-633/shplonk/shplonk.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/shplonk/shplonk_test.go b/ecc/bw6-633/shplonk/shplonk_test.go
index 2cc4d27f57..aefbb8a6a3 100644
--- a/ecc/bw6-633/shplonk/shplonk_test.go
+++ b/ecc/bw6-633/shplonk/shplonk_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/twistededwards/curve.go b/ecc/bw6-633/twistededwards/curve.go
index ec256ef527..671cbc95ac 100644
--- a/ecc/bw6-633/twistededwards/curve.go
+++ b/ecc/bw6-633/twistededwards/curve.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/twistededwards/doc.go b/ecc/bw6-633/twistededwards/doc.go
index 9137c46a8c..cdf5b586ff 100644
--- a/ecc/bw6-633/twistededwards/doc.go
+++ b/ecc/bw6-633/twistededwards/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/twistededwards/eddsa/doc.go b/ecc/bw6-633/twistededwards/eddsa/doc.go
index 37913c3587..501d823f75 100644
--- a/ecc/bw6-633/twistededwards/eddsa/doc.go
+++ b/ecc/bw6-633/twistededwards/eddsa/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/twistededwards/eddsa/eddsa.go b/ecc/bw6-633/twistededwards/eddsa/eddsa.go
index 20099f8378..47ba6425b7 100644
--- a/ecc/bw6-633/twistededwards/eddsa/eddsa.go
+++ b/ecc/bw6-633/twistededwards/eddsa/eddsa.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/twistededwards/eddsa/eddsa_test.go b/ecc/bw6-633/twistededwards/eddsa/eddsa_test.go
index aecc6ba1b0..de9fea0a8e 100644
--- a/ecc/bw6-633/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bw6-633/twistededwards/eddsa/eddsa_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/twistededwards/eddsa/marshal.go b/ecc/bw6-633/twistededwards/eddsa/marshal.go
index 2c2583f285..8c8dab8a85 100644
--- a/ecc/bw6-633/twistededwards/eddsa/marshal.go
+++ b/ecc/bw6-633/twistededwards/eddsa/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/twistededwards/point.go b/ecc/bw6-633/twistededwards/point.go
index e47b6f14bd..0016475b23 100644
--- a/ecc/bw6-633/twistededwards/point.go
+++ b/ecc/bw6-633/twistededwards/point.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-633/twistededwards/point_test.go b/ecc/bw6-633/twistededwards/point_test.go
index a898db8ada..fb8ec7efa8 100644
--- a/ecc/bw6-633/twistededwards/point_test.go
+++ b/ecc/bw6-633/twistededwards/point_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/ecdsa/doc.go b/ecc/bw6-761/ecdsa/doc.go
index 855e796eb2..84fc6c059a 100644
--- a/ecc/bw6-761/ecdsa/doc.go
+++ b/ecc/bw6-761/ecdsa/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/ecdsa/ecdsa.go b/ecc/bw6-761/ecdsa/ecdsa.go
index 0c77b0b0b8..ea3338651c 100644
--- a/ecc/bw6-761/ecdsa/ecdsa.go
+++ b/ecc/bw6-761/ecdsa/ecdsa.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/ecdsa/ecdsa_test.go b/ecc/bw6-761/ecdsa/ecdsa_test.go
index da97ae9a2b..4c7dc6f362 100644
--- a/ecc/bw6-761/ecdsa/ecdsa_test.go
+++ b/ecc/bw6-761/ecdsa/ecdsa_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/ecdsa/marshal.go b/ecc/bw6-761/ecdsa/marshal.go
index 3e3261c94c..e3d2d6dd35 100644
--- a/ecc/bw6-761/ecdsa/marshal.go
+++ b/ecc/bw6-761/ecdsa/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/ecdsa/marshal_test.go b/ecc/bw6-761/ecdsa/marshal_test.go
index c627ffa3e4..e189bb247f 100644
--- a/ecc/bw6-761/ecdsa/marshal_test.go
+++ b/ecc/bw6-761/ecdsa/marshal_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fflonk/doc.go b/ecc/bw6-761/fflonk/doc.go
index 694eaa9734..b717383d87 100644
--- a/ecc/bw6-761/fflonk/doc.go
+++ b/ecc/bw6-761/fflonk/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fflonk/example_test.go b/ecc/bw6-761/fflonk/example_test.go
index ea35977108..5576eeca34 100644
--- a/ecc/bw6-761/fflonk/example_test.go
+++ b/ecc/bw6-761/fflonk/example_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fflonk/fflonk.go b/ecc/bw6-761/fflonk/fflonk.go
index 3a18d58b65..e592fe11a4 100644
--- a/ecc/bw6-761/fflonk/fflonk.go
+++ b/ecc/bw6-761/fflonk/fflonk.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fflonk/fflonk_test.go b/ecc/bw6-761/fflonk/fflonk_test.go
index 0802648d0e..f81e8fa0c9 100644
--- a/ecc/bw6-761/fflonk/fflonk_test.go
+++ b/ecc/bw6-761/fflonk/fflonk_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fflonk/marshal.go b/ecc/bw6-761/fflonk/marshal.go
index 243d3035f1..945cbeb7d5 100644
--- a/ecc/bw6-761/fflonk/marshal.go
+++ b/ecc/bw6-761/fflonk/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fp/arith.go b/ecc/bw6-761/fp/arith.go
index 66fa667482..b202a1549a 100644
--- a/ecc/bw6-761/fp/arith.go
+++ b/ecc/bw6-761/fp/arith.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fp/asm_adx.go b/ecc/bw6-761/fp/asm_adx.go
index f8e29bd1a7..fe25e82db2 100644
--- a/ecc/bw6-761/fp/asm_adx.go
+++ b/ecc/bw6-761/fp/asm_adx.go
@@ -1,18 +1,7 @@
 //go:build !noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fp/asm_noadx.go b/ecc/bw6-761/fp/asm_noadx.go
index cb6cfa0f50..95085a8e6f 100644
--- a/ecc/bw6-761/fp/asm_noadx.go
+++ b/ecc/bw6-761/fp/asm_noadx.go
@@ -1,18 +1,7 @@
 //go:build noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fp/doc.go b/ecc/bw6-761/fp/doc.go
index 1e84636b7c..79fbd8d702 100644
--- a/ecc/bw6-761/fp/doc.go
+++ b/ecc/bw6-761/fp/doc.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fp/element.go b/ecc/bw6-761/fp/element.go
index a266ee9014..3dbb53b4b7 100644
--- a/ecc/bw6-761/fp/element.go
+++ b/ecc/bw6-761/fp/element.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fp/element_amd64.go b/ecc/bw6-761/fp/element_amd64.go
index 77a51ee25e..e72f552ad9 100644
--- a/ecc/bw6-761/fp/element_amd64.go
+++ b/ecc/bw6-761/fp/element_amd64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fp/element_amd64.s b/ecc/bw6-761/fp/element_amd64.s
index 8bee44a5e7..b44c78d9ed 100644
--- a/ecc/bw6-761/fp/element_amd64.s
+++ b/ecc/bw6-761/fp/element_amd64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fp/element_arm64.go b/ecc/bw6-761/fp/element_arm64.go
index df5acdc99a..cf4f884270 100644
--- a/ecc/bw6-761/fp/element_arm64.go
+++ b/ecc/bw6-761/fp/element_arm64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fp/element_arm64.s b/ecc/bw6-761/fp/element_arm64.s
index 9ed6049e69..051a143619 100644
--- a/ecc/bw6-761/fp/element_arm64.s
+++ b/ecc/bw6-761/fp/element_arm64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fp/element_exp.go b/ecc/bw6-761/fp/element_exp.go
index ab7fc6d848..87e0135c53 100644
--- a/ecc/bw6-761/fp/element_exp.go
+++ b/ecc/bw6-761/fp/element_exp.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fp/element_purego.go b/ecc/bw6-761/fp/element_purego.go
index 4338d90c2b..0b478029e3 100644
--- a/ecc/bw6-761/fp/element_purego.go
+++ b/ecc/bw6-761/fp/element_purego.go
@@ -1,18 +1,7 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fp/element_test.go b/ecc/bw6-761/fp/element_test.go
index 5df3d0de53..d57c1a4137 100644
--- a/ecc/bw6-761/fp/element_test.go
+++ b/ecc/bw6-761/fp/element_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fp/hash_to_field/doc.go b/ecc/bw6-761/fp/hash_to_field/doc.go
index fbd3b76a9a..2248500dd4 100644
--- a/ecc/bw6-761/fp/hash_to_field/doc.go
+++ b/ecc/bw6-761/fp/hash_to_field/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fp/hash_to_field/hash_to_field.go b/ecc/bw6-761/fp/hash_to_field/hash_to_field.go
index dd12c1e9d0..4c3d232a30 100644
--- a/ecc/bw6-761/fp/hash_to_field/hash_to_field.go
+++ b/ecc/bw6-761/fp/hash_to_field/hash_to_field.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fp/hash_to_field/hash_to_field_test.go b/ecc/bw6-761/fp/hash_to_field/hash_to_field_test.go
index edd7e59e3a..9c54650caf 100644
--- a/ecc/bw6-761/fp/hash_to_field/hash_to_field_test.go
+++ b/ecc/bw6-761/fp/hash_to_field/hash_to_field_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fp/vector.go b/ecc/bw6-761/fp/vector.go
index 66d5027f64..18fd592d85 100644
--- a/ecc/bw6-761/fp/vector.go
+++ b/ecc/bw6-761/fp/vector.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fp/vector_purego.go b/ecc/bw6-761/fp/vector_purego.go
index 798b669887..347b0df594 100644
--- a/ecc/bw6-761/fp/vector_purego.go
+++ b/ecc/bw6-761/fp/vector_purego.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fp/vector_test.go b/ecc/bw6-761/fp/vector_test.go
index 9f59efdd32..65e92b3d04 100644
--- a/ecc/bw6-761/fp/vector_test.go
+++ b/ecc/bw6-761/fp/vector_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/arith.go b/ecc/bw6-761/fr/arith.go
index 83c9fd9ef9..9285041f4b 100644
--- a/ecc/bw6-761/fr/arith.go
+++ b/ecc/bw6-761/fr/arith.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/asm_adx.go b/ecc/bw6-761/fr/asm_adx.go
index 9273ea23ab..9e7da5e865 100644
--- a/ecc/bw6-761/fr/asm_adx.go
+++ b/ecc/bw6-761/fr/asm_adx.go
@@ -1,18 +1,7 @@
 //go:build !noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/asm_noadx.go b/ecc/bw6-761/fr/asm_noadx.go
index b784a24247..3456158655 100644
--- a/ecc/bw6-761/fr/asm_noadx.go
+++ b/ecc/bw6-761/fr/asm_noadx.go
@@ -1,18 +1,7 @@
 //go:build noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/doc.go b/ecc/bw6-761/fr/doc.go
index e3d46536b6..6904be877b 100644
--- a/ecc/bw6-761/fr/doc.go
+++ b/ecc/bw6-761/fr/doc.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/element.go b/ecc/bw6-761/fr/element.go
index dad9bbec1c..ebd218e002 100644
--- a/ecc/bw6-761/fr/element.go
+++ b/ecc/bw6-761/fr/element.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/element_amd64.go b/ecc/bw6-761/fr/element_amd64.go
index 0ddb905f7b..ca49d12590 100644
--- a/ecc/bw6-761/fr/element_amd64.go
+++ b/ecc/bw6-761/fr/element_amd64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/element_amd64.s b/ecc/bw6-761/fr/element_amd64.s
index 872eddf5d6..b73d1a484e 100644
--- a/ecc/bw6-761/fr/element_amd64.s
+++ b/ecc/bw6-761/fr/element_amd64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/element_arm64.go b/ecc/bw6-761/fr/element_arm64.go
index 7b389c515b..e1d3e0bead 100644
--- a/ecc/bw6-761/fr/element_arm64.go
+++ b/ecc/bw6-761/fr/element_arm64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/element_arm64.s b/ecc/bw6-761/fr/element_arm64.s
index 2a3f7d0b2c..58d21358b0 100644
--- a/ecc/bw6-761/fr/element_arm64.s
+++ b/ecc/bw6-761/fr/element_arm64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/element_exp.go b/ecc/bw6-761/fr/element_exp.go
index 5c764aa836..c9df4d675c 100644
--- a/ecc/bw6-761/fr/element_exp.go
+++ b/ecc/bw6-761/fr/element_exp.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/element_purego.go b/ecc/bw6-761/fr/element_purego.go
index 5d56b28300..15fab63d4c 100644
--- a/ecc/bw6-761/fr/element_purego.go
+++ b/ecc/bw6-761/fr/element_purego.go
@@ -1,18 +1,7 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/element_test.go b/ecc/bw6-761/fr/element_test.go
index bcc35c4841..8974a228ac 100644
--- a/ecc/bw6-761/fr/element_test.go
+++ b/ecc/bw6-761/fr/element_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/fft/bitreverse.go b/ecc/bw6-761/fr/fft/bitreverse.go
index a632937985..ec82646978 100644
--- a/ecc/bw6-761/fr/fft/bitreverse.go
+++ b/ecc/bw6-761/fr/fft/bitreverse.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/fft/bitreverse_test.go b/ecc/bw6-761/fr/fft/bitreverse_test.go
index ec150c8b93..d32144152c 100644
--- a/ecc/bw6-761/fr/fft/bitreverse_test.go
+++ b/ecc/bw6-761/fr/fft/bitreverse_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/fft/doc.go b/ecc/bw6-761/fr/fft/doc.go
index b5dd44e642..1ef04db2df 100644
--- a/ecc/bw6-761/fr/fft/doc.go
+++ b/ecc/bw6-761/fr/fft/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/fft/domain.go b/ecc/bw6-761/fr/fft/domain.go
index ba2932fb9f..e8d349dee2 100644
--- a/ecc/bw6-761/fr/fft/domain.go
+++ b/ecc/bw6-761/fr/fft/domain.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/fft/domain_test.go b/ecc/bw6-761/fr/fft/domain_test.go
index 83186cb7c9..d95288076c 100644
--- a/ecc/bw6-761/fr/fft/domain_test.go
+++ b/ecc/bw6-761/fr/fft/domain_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/fft/fft.go b/ecc/bw6-761/fr/fft/fft.go
index d91e975d10..a7d6a44736 100644
--- a/ecc/bw6-761/fr/fft/fft.go
+++ b/ecc/bw6-761/fr/fft/fft.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/fft/fft_test.go b/ecc/bw6-761/fr/fft/fft_test.go
index 5e2b0ea0ac..4ba89f360b 100644
--- a/ecc/bw6-761/fr/fft/fft_test.go
+++ b/ecc/bw6-761/fr/fft/fft_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/fft/options.go b/ecc/bw6-761/fr/fft/options.go
index b3372f244e..ec6214e752 100644
--- a/ecc/bw6-761/fr/fft/options.go
+++ b/ecc/bw6-761/fr/fft/options.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/fri/doc.go b/ecc/bw6-761/fr/fri/doc.go
index 3333ad41f5..428dabf625 100644
--- a/ecc/bw6-761/fr/fri/doc.go
+++ b/ecc/bw6-761/fr/fri/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/fri/fri.go b/ecc/bw6-761/fr/fri/fri.go
index 0ebeec0958..d04ac242c9 100644
--- a/ecc/bw6-761/fr/fri/fri.go
+++ b/ecc/bw6-761/fr/fri/fri.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/fri/fri_test.go b/ecc/bw6-761/fr/fri/fri_test.go
index 14f5798e2f..2eb5fb3c29 100644
--- a/ecc/bw6-761/fr/fri/fri_test.go
+++ b/ecc/bw6-761/fr/fri/fri_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/generator.go b/ecc/bw6-761/fr/generator.go
index edf50be31e..6399ad9926 100644
--- a/ecc/bw6-761/fr/generator.go
+++ b/ecc/bw6-761/fr/generator.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/gkr/gkr.go b/ecc/bw6-761/fr/gkr/gkr.go
index fda1028698..bd46e4abe1 100644
--- a/ecc/bw6-761/fr/gkr/gkr.go
+++ b/ecc/bw6-761/fr/gkr/gkr.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/gkr/gkr_test.go b/ecc/bw6-761/fr/gkr/gkr_test.go
index 976fb661d7..d3d18dfcba 100644
--- a/ecc/bw6-761/fr/gkr/gkr_test.go
+++ b/ecc/bw6-761/fr/gkr/gkr_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/hash_to_field/doc.go b/ecc/bw6-761/fr/hash_to_field/doc.go
index 8bb5b62b98..d03ec39735 100644
--- a/ecc/bw6-761/fr/hash_to_field/doc.go
+++ b/ecc/bw6-761/fr/hash_to_field/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/hash_to_field/hash_to_field.go b/ecc/bw6-761/fr/hash_to_field/hash_to_field.go
index 01650f8bbf..0eda792a28 100644
--- a/ecc/bw6-761/fr/hash_to_field/hash_to_field.go
+++ b/ecc/bw6-761/fr/hash_to_field/hash_to_field.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/hash_to_field/hash_to_field_test.go b/ecc/bw6-761/fr/hash_to_field/hash_to_field_test.go
index 05dedfa272..731929288b 100644
--- a/ecc/bw6-761/fr/hash_to_field/hash_to_field_test.go
+++ b/ecc/bw6-761/fr/hash_to_field/hash_to_field_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/iop/doc.go b/ecc/bw6-761/fr/iop/doc.go
index 20f8b1a302..ee3facf1e1 100644
--- a/ecc/bw6-761/fr/iop/doc.go
+++ b/ecc/bw6-761/fr/iop/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/iop/expressions.go b/ecc/bw6-761/fr/iop/expressions.go
index 5bb5c2670e..72fbfd169f 100644
--- a/ecc/bw6-761/fr/iop/expressions.go
+++ b/ecc/bw6-761/fr/iop/expressions.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/iop/expressions_test.go b/ecc/bw6-761/fr/iop/expressions_test.go
index f1823dfb23..51e837ead1 100644
--- a/ecc/bw6-761/fr/iop/expressions_test.go
+++ b/ecc/bw6-761/fr/iop/expressions_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/iop/polynomial.go b/ecc/bw6-761/fr/iop/polynomial.go
index 6626eb5d3f..0b72fe3c16 100644
--- a/ecc/bw6-761/fr/iop/polynomial.go
+++ b/ecc/bw6-761/fr/iop/polynomial.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/iop/polynomial_test.go b/ecc/bw6-761/fr/iop/polynomial_test.go
index 15f3040fee..5b6e5d5fd3 100644
--- a/ecc/bw6-761/fr/iop/polynomial_test.go
+++ b/ecc/bw6-761/fr/iop/polynomial_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/iop/quotient.go b/ecc/bw6-761/fr/iop/quotient.go
index 1267bc4b60..1f90c46385 100644
--- a/ecc/bw6-761/fr/iop/quotient.go
+++ b/ecc/bw6-761/fr/iop/quotient.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/iop/quotient_test.go b/ecc/bw6-761/fr/iop/quotient_test.go
index 6d99f59f50..e16d6dbf17 100644
--- a/ecc/bw6-761/fr/iop/quotient_test.go
+++ b/ecc/bw6-761/fr/iop/quotient_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/iop/ratios.go b/ecc/bw6-761/fr/iop/ratios.go
index 035d558b99..4e38401ac0 100644
--- a/ecc/bw6-761/fr/iop/ratios.go
+++ b/ecc/bw6-761/fr/iop/ratios.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/iop/ratios_test.go b/ecc/bw6-761/fr/iop/ratios_test.go
index b42149d4f3..78bf6823e1 100644
--- a/ecc/bw6-761/fr/iop/ratios_test.go
+++ b/ecc/bw6-761/fr/iop/ratios_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/iop/utils.go b/ecc/bw6-761/fr/iop/utils.go
index f5330ba035..e061ac5f0f 100644
--- a/ecc/bw6-761/fr/iop/utils.go
+++ b/ecc/bw6-761/fr/iop/utils.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/mimc/doc.go b/ecc/bw6-761/fr/mimc/doc.go
index 78837e1c80..cc7b101eb4 100644
--- a/ecc/bw6-761/fr/mimc/doc.go
+++ b/ecc/bw6-761/fr/mimc/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/mimc/mimc.go b/ecc/bw6-761/fr/mimc/mimc.go
index b53d52abfb..16c96957fd 100644
--- a/ecc/bw6-761/fr/mimc/mimc.go
+++ b/ecc/bw6-761/fr/mimc/mimc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/mimc/options.go b/ecc/bw6-761/fr/mimc/options.go
index 996bb8862e..347e79e576 100644
--- a/ecc/bw6-761/fr/mimc/options.go
+++ b/ecc/bw6-761/fr/mimc/options.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/pedersen/doc.go b/ecc/bw6-761/fr/pedersen/doc.go
index 944679f5c5..62a62f179f 100644
--- a/ecc/bw6-761/fr/pedersen/doc.go
+++ b/ecc/bw6-761/fr/pedersen/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/pedersen/example_test.go b/ecc/bw6-761/fr/pedersen/example_test.go
index 48c7ba70b6..39ebdddb9f 100644
--- a/ecc/bw6-761/fr/pedersen/example_test.go
+++ b/ecc/bw6-761/fr/pedersen/example_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/pedersen/pedersen.go b/ecc/bw6-761/fr/pedersen/pedersen.go
index 8b761fe4ac..cef2884f62 100644
--- a/ecc/bw6-761/fr/pedersen/pedersen.go
+++ b/ecc/bw6-761/fr/pedersen/pedersen.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/pedersen/pedersen_test.go b/ecc/bw6-761/fr/pedersen/pedersen_test.go
index d8ba4a1f16..e36f0c4acc 100644
--- a/ecc/bw6-761/fr/pedersen/pedersen_test.go
+++ b/ecc/bw6-761/fr/pedersen/pedersen_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/permutation/doc.go b/ecc/bw6-761/fr/permutation/doc.go
index 7ef21ffb9e..5f346b5a53 100644
--- a/ecc/bw6-761/fr/permutation/doc.go
+++ b/ecc/bw6-761/fr/permutation/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/permutation/permutation.go b/ecc/bw6-761/fr/permutation/permutation.go
index d06ec57e01..4846ce844d 100644
--- a/ecc/bw6-761/fr/permutation/permutation.go
+++ b/ecc/bw6-761/fr/permutation/permutation.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/permutation/permutation_test.go b/ecc/bw6-761/fr/permutation/permutation_test.go
index 23f7f73642..8dac14d91d 100644
--- a/ecc/bw6-761/fr/permutation/permutation_test.go
+++ b/ecc/bw6-761/fr/permutation/permutation_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/plookup/doc.go b/ecc/bw6-761/fr/plookup/doc.go
index b3af019687..d163104002 100644
--- a/ecc/bw6-761/fr/plookup/doc.go
+++ b/ecc/bw6-761/fr/plookup/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/plookup/plookup_test.go b/ecc/bw6-761/fr/plookup/plookup_test.go
index c4b6d7c88f..72da216a03 100644
--- a/ecc/bw6-761/fr/plookup/plookup_test.go
+++ b/ecc/bw6-761/fr/plookup/plookup_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/plookup/table.go b/ecc/bw6-761/fr/plookup/table.go
index cd90fb6eea..ed0fd8ba76 100644
--- a/ecc/bw6-761/fr/plookup/table.go
+++ b/ecc/bw6-761/fr/plookup/table.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/plookup/vector.go b/ecc/bw6-761/fr/plookup/vector.go
index 508ceb539e..e136a5f3f8 100644
--- a/ecc/bw6-761/fr/plookup/vector.go
+++ b/ecc/bw6-761/fr/plookup/vector.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/polynomial/doc.go b/ecc/bw6-761/fr/polynomial/doc.go
index 747da41f2c..35b3f725c1 100644
--- a/ecc/bw6-761/fr/polynomial/doc.go
+++ b/ecc/bw6-761/fr/polynomial/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/polynomial/multilin.go b/ecc/bw6-761/fr/polynomial/multilin.go
index 916c96660b..85015f1a34 100644
--- a/ecc/bw6-761/fr/polynomial/multilin.go
+++ b/ecc/bw6-761/fr/polynomial/multilin.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/polynomial/multilin_test.go b/ecc/bw6-761/fr/polynomial/multilin_test.go
index 4c574976b6..37d9d1d079 100644
--- a/ecc/bw6-761/fr/polynomial/multilin_test.go
+++ b/ecc/bw6-761/fr/polynomial/multilin_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/polynomial/polynomial.go b/ecc/bw6-761/fr/polynomial/polynomial.go
index c0ec2235b9..9e17273b00 100644
--- a/ecc/bw6-761/fr/polynomial/polynomial.go
+++ b/ecc/bw6-761/fr/polynomial/polynomial.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/polynomial/polynomial_test.go b/ecc/bw6-761/fr/polynomial/polynomial_test.go
index 487bfe6309..c51c6e41a4 100644
--- a/ecc/bw6-761/fr/polynomial/polynomial_test.go
+++ b/ecc/bw6-761/fr/polynomial/polynomial_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/polynomial/pool.go b/ecc/bw6-761/fr/polynomial/pool.go
index ef5c934683..41c1fa6041 100644
--- a/ecc/bw6-761/fr/polynomial/pool.go
+++ b/ecc/bw6-761/fr/polynomial/pool.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/poseidon2/poseidon2.go b/ecc/bw6-761/fr/poseidon2/poseidon2.go
index 80283bcf46..ff49613b1a 100644
--- a/ecc/bw6-761/fr/poseidon2/poseidon2.go
+++ b/ecc/bw6-761/fr/poseidon2/poseidon2.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/poseidon2/poseidon2_test.go b/ecc/bw6-761/fr/poseidon2/poseidon2_test.go
index acb3ea1cef..11f1d7ed64 100644
--- a/ecc/bw6-761/fr/poseidon2/poseidon2_test.go
+++ b/ecc/bw6-761/fr/poseidon2/poseidon2_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/sumcheck/sumcheck.go b/ecc/bw6-761/fr/sumcheck/sumcheck.go
index 6a8554c202..64f3115343 100644
--- a/ecc/bw6-761/fr/sumcheck/sumcheck.go
+++ b/ecc/bw6-761/fr/sumcheck/sumcheck.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/sumcheck/sumcheck_test.go b/ecc/bw6-761/fr/sumcheck/sumcheck_test.go
index f7502c70aa..eee8ae452c 100644
--- a/ecc/bw6-761/fr/sumcheck/sumcheck_test.go
+++ b/ecc/bw6-761/fr/sumcheck/sumcheck_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/test_vector_utils/test_vector_utils.go b/ecc/bw6-761/fr/test_vector_utils/test_vector_utils.go
index 0394936dac..2005b5e824 100644
--- a/ecc/bw6-761/fr/test_vector_utils/test_vector_utils.go
+++ b/ecc/bw6-761/fr/test_vector_utils/test_vector_utils.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/vector.go b/ecc/bw6-761/fr/vector.go
index 47b20efbed..5f5187cc51 100644
--- a/ecc/bw6-761/fr/vector.go
+++ b/ecc/bw6-761/fr/vector.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/vector_purego.go b/ecc/bw6-761/fr/vector_purego.go
index 04662dde33..3c81210b58 100644
--- a/ecc/bw6-761/fr/vector_purego.go
+++ b/ecc/bw6-761/fr/vector_purego.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/fr/vector_test.go b/ecc/bw6-761/fr/vector_test.go
index ad574704b1..a5369902cd 100644
--- a/ecc/bw6-761/fr/vector_test.go
+++ b/ecc/bw6-761/fr/vector_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/g1.go b/ecc/bw6-761/g1.go
index 2f4196f73c..8a4da31f52 100644
--- a/ecc/bw6-761/g1.go
+++ b/ecc/bw6-761/g1.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/g1_test.go b/ecc/bw6-761/g1_test.go
index e6f79f4dde..bd42889c0f 100644
--- a/ecc/bw6-761/g1_test.go
+++ b/ecc/bw6-761/g1_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/g2.go b/ecc/bw6-761/g2.go
index 72ed4b08bd..1edf22552c 100644
--- a/ecc/bw6-761/g2.go
+++ b/ecc/bw6-761/g2.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/g2_test.go b/ecc/bw6-761/g2_test.go
index 1de4bd3956..f3aec712c1 100644
--- a/ecc/bw6-761/g2_test.go
+++ b/ecc/bw6-761/g2_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/hash_to_g1.go b/ecc/bw6-761/hash_to_g1.go
index 19d7008a5a..54115d76f8 100644
--- a/ecc/bw6-761/hash_to_g1.go
+++ b/ecc/bw6-761/hash_to_g1.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/hash_to_g1_test.go b/ecc/bw6-761/hash_to_g1_test.go
index 3e111436d6..59464b31d5 100644
--- a/ecc/bw6-761/hash_to_g1_test.go
+++ b/ecc/bw6-761/hash_to_g1_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/hash_to_g2.go b/ecc/bw6-761/hash_to_g2.go
index 04deda08fb..21acc97de8 100644
--- a/ecc/bw6-761/hash_to_g2.go
+++ b/ecc/bw6-761/hash_to_g2.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/hash_to_g2_test.go b/ecc/bw6-761/hash_to_g2_test.go
index 14d7bb5af8..e891f374ae 100644
--- a/ecc/bw6-761/hash_to_g2_test.go
+++ b/ecc/bw6-761/hash_to_g2_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/kzg/doc.go b/ecc/bw6-761/kzg/doc.go
index d1045726f2..6c3454a2d9 100644
--- a/ecc/bw6-761/kzg/doc.go
+++ b/ecc/bw6-761/kzg/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/kzg/kzg.go b/ecc/bw6-761/kzg/kzg.go
index 1ee2f5009b..5c61a6b1b7 100644
--- a/ecc/bw6-761/kzg/kzg.go
+++ b/ecc/bw6-761/kzg/kzg.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/kzg/kzg_test.go b/ecc/bw6-761/kzg/kzg_test.go
index fdec0e1885..1fca86f6e6 100644
--- a/ecc/bw6-761/kzg/kzg_test.go
+++ b/ecc/bw6-761/kzg/kzg_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/kzg/marshal.go b/ecc/bw6-761/kzg/marshal.go
index ca9e1452bb..86a5b42ae2 100644
--- a/ecc/bw6-761/kzg/marshal.go
+++ b/ecc/bw6-761/kzg/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/kzg/utils.go b/ecc/bw6-761/kzg/utils.go
index c973971859..2e12e76bd0 100644
--- a/ecc/bw6-761/kzg/utils.go
+++ b/ecc/bw6-761/kzg/utils.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/marshal.go b/ecc/bw6-761/marshal.go
index 7af9978a10..5c57294e3b 100644
--- a/ecc/bw6-761/marshal.go
+++ b/ecc/bw6-761/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/marshal_test.go b/ecc/bw6-761/marshal_test.go
index d4df8e88b9..db3f7ad4e1 100644
--- a/ecc/bw6-761/marshal_test.go
+++ b/ecc/bw6-761/marshal_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/multiexp.go b/ecc/bw6-761/multiexp.go
index 0a1164e7f6..1e87efcd61 100644
--- a/ecc/bw6-761/multiexp.go
+++ b/ecc/bw6-761/multiexp.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/multiexp_affine.go b/ecc/bw6-761/multiexp_affine.go
index f8427f4ba0..4a33d4fb0d 100644
--- a/ecc/bw6-761/multiexp_affine.go
+++ b/ecc/bw6-761/multiexp_affine.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/multiexp_jacobian.go b/ecc/bw6-761/multiexp_jacobian.go
index cb022606f9..abe9c17245 100644
--- a/ecc/bw6-761/multiexp_jacobian.go
+++ b/ecc/bw6-761/multiexp_jacobian.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/multiexp_test.go b/ecc/bw6-761/multiexp_test.go
index f4da37fc2e..f212cd5a01 100644
--- a/ecc/bw6-761/multiexp_test.go
+++ b/ecc/bw6-761/multiexp_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/pairing_test.go b/ecc/bw6-761/pairing_test.go
index 7d8e85771e..c2946357d8 100644
--- a/ecc/bw6-761/pairing_test.go
+++ b/ecc/bw6-761/pairing_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/shplonk/doc.go b/ecc/bw6-761/shplonk/doc.go
index e048f46009..17b34373c2 100644
--- a/ecc/bw6-761/shplonk/doc.go
+++ b/ecc/bw6-761/shplonk/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/shplonk/example_test.go b/ecc/bw6-761/shplonk/example_test.go
index 6beff08c10..1206bccc1e 100644
--- a/ecc/bw6-761/shplonk/example_test.go
+++ b/ecc/bw6-761/shplonk/example_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/shplonk/marshal.go b/ecc/bw6-761/shplonk/marshal.go
index 6e03808eeb..be1e4acde3 100644
--- a/ecc/bw6-761/shplonk/marshal.go
+++ b/ecc/bw6-761/shplonk/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/shplonk/shplonk.go b/ecc/bw6-761/shplonk/shplonk.go
index aec562df5c..19eb2433e5 100644
--- a/ecc/bw6-761/shplonk/shplonk.go
+++ b/ecc/bw6-761/shplonk/shplonk.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/shplonk/shplonk_test.go b/ecc/bw6-761/shplonk/shplonk_test.go
index bcdbccea65..ebc7a57517 100644
--- a/ecc/bw6-761/shplonk/shplonk_test.go
+++ b/ecc/bw6-761/shplonk/shplonk_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/twistededwards/curve.go b/ecc/bw6-761/twistededwards/curve.go
index 3050d84b8f..bf0345c523 100644
--- a/ecc/bw6-761/twistededwards/curve.go
+++ b/ecc/bw6-761/twistededwards/curve.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/twistededwards/doc.go b/ecc/bw6-761/twistededwards/doc.go
index bcfe56cd49..3172ca7194 100644
--- a/ecc/bw6-761/twistededwards/doc.go
+++ b/ecc/bw6-761/twistededwards/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/twistededwards/eddsa/doc.go b/ecc/bw6-761/twistededwards/eddsa/doc.go
index 20bd6b502f..0aaf99ef4c 100644
--- a/ecc/bw6-761/twistededwards/eddsa/doc.go
+++ b/ecc/bw6-761/twistededwards/eddsa/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/twistededwards/eddsa/eddsa.go b/ecc/bw6-761/twistededwards/eddsa/eddsa.go
index 0211368c99..1d464b279a 100644
--- a/ecc/bw6-761/twistededwards/eddsa/eddsa.go
+++ b/ecc/bw6-761/twistededwards/eddsa/eddsa.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/twistededwards/eddsa/eddsa_test.go b/ecc/bw6-761/twistededwards/eddsa/eddsa_test.go
index ede04f01c8..d85f4c6c51 100644
--- a/ecc/bw6-761/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bw6-761/twistededwards/eddsa/eddsa_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/twistededwards/eddsa/marshal.go b/ecc/bw6-761/twistededwards/eddsa/marshal.go
index 1a9254a978..9532895007 100644
--- a/ecc/bw6-761/twistededwards/eddsa/marshal.go
+++ b/ecc/bw6-761/twistededwards/eddsa/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/twistededwards/point.go b/ecc/bw6-761/twistededwards/point.go
index b4a566b192..95af453d49 100644
--- a/ecc/bw6-761/twistededwards/point.go
+++ b/ecc/bw6-761/twistededwards/point.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/bw6-761/twistededwards/point_test.go b/ecc/bw6-761/twistededwards/point_test.go
index 650c166e0d..b1e526022f 100644
--- a/ecc/bw6-761/twistededwards/point_test.go
+++ b/ecc/bw6-761/twistededwards/point_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/ecdsa/doc.go b/ecc/secp256k1/ecdsa/doc.go
index cca66227a6..a0ad0656cc 100644
--- a/ecc/secp256k1/ecdsa/doc.go
+++ b/ecc/secp256k1/ecdsa/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/ecdsa/ecdsa.go b/ecc/secp256k1/ecdsa/ecdsa.go
index 689bc5003e..dfba9976c2 100644
--- a/ecc/secp256k1/ecdsa/ecdsa.go
+++ b/ecc/secp256k1/ecdsa/ecdsa.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/ecdsa/ecdsa_test.go b/ecc/secp256k1/ecdsa/ecdsa_test.go
index d924b1d2ab..c3550765bd 100644
--- a/ecc/secp256k1/ecdsa/ecdsa_test.go
+++ b/ecc/secp256k1/ecdsa/ecdsa_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/ecdsa/marshal.go b/ecc/secp256k1/ecdsa/marshal.go
index bc2be013c1..7c297b6529 100644
--- a/ecc/secp256k1/ecdsa/marshal.go
+++ b/ecc/secp256k1/ecdsa/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/ecdsa/marshal_test.go b/ecc/secp256k1/ecdsa/marshal_test.go
index a880e63010..434a18c025 100644
--- a/ecc/secp256k1/ecdsa/marshal_test.go
+++ b/ecc/secp256k1/ecdsa/marshal_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/fp/arith.go b/ecc/secp256k1/fp/arith.go
index 66fa667482..b202a1549a 100644
--- a/ecc/secp256k1/fp/arith.go
+++ b/ecc/secp256k1/fp/arith.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/fp/doc.go b/ecc/secp256k1/fp/doc.go
index 6e11299df2..d5b439ad72 100644
--- a/ecc/secp256k1/fp/doc.go
+++ b/ecc/secp256k1/fp/doc.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/fp/element.go b/ecc/secp256k1/fp/element.go
index cb1b02995e..c98ef9e599 100644
--- a/ecc/secp256k1/fp/element.go
+++ b/ecc/secp256k1/fp/element.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/fp/element_exp.go b/ecc/secp256k1/fp/element_exp.go
index 7b2f8cb832..827dafc296 100644
--- a/ecc/secp256k1/fp/element_exp.go
+++ b/ecc/secp256k1/fp/element_exp.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/fp/element_purego.go b/ecc/secp256k1/fp/element_purego.go
index 3be147f51a..fc9fec8677 100644
--- a/ecc/secp256k1/fp/element_purego.go
+++ b/ecc/secp256k1/fp/element_purego.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/fp/element_test.go b/ecc/secp256k1/fp/element_test.go
index cbe2b50a0c..a29f105ef8 100644
--- a/ecc/secp256k1/fp/element_test.go
+++ b/ecc/secp256k1/fp/element_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/fp/vector.go b/ecc/secp256k1/fp/vector.go
index c97b4283ce..ec52314aa7 100644
--- a/ecc/secp256k1/fp/vector.go
+++ b/ecc/secp256k1/fp/vector.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/fp/vector_purego.go b/ecc/secp256k1/fp/vector_purego.go
index 798b669887..347b0df594 100644
--- a/ecc/secp256k1/fp/vector_purego.go
+++ b/ecc/secp256k1/fp/vector_purego.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/fp/vector_test.go b/ecc/secp256k1/fp/vector_test.go
index 12f17e21fb..06fe1084a8 100644
--- a/ecc/secp256k1/fp/vector_test.go
+++ b/ecc/secp256k1/fp/vector_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/fr/arith.go b/ecc/secp256k1/fr/arith.go
index 83c9fd9ef9..9285041f4b 100644
--- a/ecc/secp256k1/fr/arith.go
+++ b/ecc/secp256k1/fr/arith.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/fr/doc.go b/ecc/secp256k1/fr/doc.go
index 3c90f775e3..f440ce29b1 100644
--- a/ecc/secp256k1/fr/doc.go
+++ b/ecc/secp256k1/fr/doc.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/fr/element.go b/ecc/secp256k1/fr/element.go
index d0684c6cc1..8d0a11fd43 100644
--- a/ecc/secp256k1/fr/element.go
+++ b/ecc/secp256k1/fr/element.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/fr/element_exp.go b/ecc/secp256k1/fr/element_exp.go
index a93ff54597..f65be913cc 100644
--- a/ecc/secp256k1/fr/element_exp.go
+++ b/ecc/secp256k1/fr/element_exp.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/fr/element_purego.go b/ecc/secp256k1/fr/element_purego.go
index 80b3116256..1e6c57d0f8 100644
--- a/ecc/secp256k1/fr/element_purego.go
+++ b/ecc/secp256k1/fr/element_purego.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/fr/element_test.go b/ecc/secp256k1/fr/element_test.go
index 2ab020991b..663205a9a8 100644
--- a/ecc/secp256k1/fr/element_test.go
+++ b/ecc/secp256k1/fr/element_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/fr/vector.go b/ecc/secp256k1/fr/vector.go
index 867cabbc3d..8b59bd36e9 100644
--- a/ecc/secp256k1/fr/vector.go
+++ b/ecc/secp256k1/fr/vector.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/fr/vector_purego.go b/ecc/secp256k1/fr/vector_purego.go
index 04662dde33..3c81210b58 100644
--- a/ecc/secp256k1/fr/vector_purego.go
+++ b/ecc/secp256k1/fr/vector_purego.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/fr/vector_test.go b/ecc/secp256k1/fr/vector_test.go
index b6344c18b7..a094bc0ac6 100644
--- a/ecc/secp256k1/fr/vector_test.go
+++ b/ecc/secp256k1/fr/vector_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/g1.go b/ecc/secp256k1/g1.go
index c5714c3324..123a7f69ea 100644
--- a/ecc/secp256k1/g1.go
+++ b/ecc/secp256k1/g1.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/g1_test.go b/ecc/secp256k1/g1_test.go
index 2acef064ae..b57acc5635 100644
--- a/ecc/secp256k1/g1_test.go
+++ b/ecc/secp256k1/g1_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/hash_to_g1.go b/ecc/secp256k1/hash_to_g1.go
index 41bec83c06..35a42ee2ff 100644
--- a/ecc/secp256k1/hash_to_g1.go
+++ b/ecc/secp256k1/hash_to_g1.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/hash_to_g1_test.go b/ecc/secp256k1/hash_to_g1_test.go
index 8dcbc249d4..37579c66fd 100644
--- a/ecc/secp256k1/hash_to_g1_test.go
+++ b/ecc/secp256k1/hash_to_g1_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/multiexp.go b/ecc/secp256k1/multiexp.go
index 44958e7a76..2ad970a1ed 100644
--- a/ecc/secp256k1/multiexp.go
+++ b/ecc/secp256k1/multiexp.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/multiexp_affine.go b/ecc/secp256k1/multiexp_affine.go
index 64bdcf759a..c0e5d12e18 100644
--- a/ecc/secp256k1/multiexp_affine.go
+++ b/ecc/secp256k1/multiexp_affine.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/multiexp_jacobian.go b/ecc/secp256k1/multiexp_jacobian.go
index 69b25b089f..541fa208cd 100644
--- a/ecc/secp256k1/multiexp_jacobian.go
+++ b/ecc/secp256k1/multiexp_jacobian.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/secp256k1/multiexp_test.go b/ecc/secp256k1/multiexp_test.go
index 3f2c2c7908..f30b924dd2 100644
--- a/ecc/secp256k1/multiexp_test.go
+++ b/ecc/secp256k1/multiexp_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/ecdsa/doc.go b/ecc/stark-curve/ecdsa/doc.go
index 9adee15667..599535ea05 100644
--- a/ecc/stark-curve/ecdsa/doc.go
+++ b/ecc/stark-curve/ecdsa/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/ecdsa/ecdsa.go b/ecc/stark-curve/ecdsa/ecdsa.go
index de997d8aef..e43c51879a 100644
--- a/ecc/stark-curve/ecdsa/ecdsa.go
+++ b/ecc/stark-curve/ecdsa/ecdsa.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/ecdsa/ecdsa_test.go b/ecc/stark-curve/ecdsa/ecdsa_test.go
index c9c3a7fed3..30324ed6c3 100644
--- a/ecc/stark-curve/ecdsa/ecdsa_test.go
+++ b/ecc/stark-curve/ecdsa/ecdsa_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/ecdsa/marshal.go b/ecc/stark-curve/ecdsa/marshal.go
index 8860f427e0..a838742bfa 100644
--- a/ecc/stark-curve/ecdsa/marshal.go
+++ b/ecc/stark-curve/ecdsa/marshal.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/ecdsa/marshal_test.go b/ecc/stark-curve/ecdsa/marshal_test.go
index f20fb8167e..21a4d96b10 100644
--- a/ecc/stark-curve/ecdsa/marshal_test.go
+++ b/ecc/stark-curve/ecdsa/marshal_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fp/arith.go b/ecc/stark-curve/fp/arith.go
index 66fa667482..b202a1549a 100644
--- a/ecc/stark-curve/fp/arith.go
+++ b/ecc/stark-curve/fp/arith.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fp/asm_adx.go b/ecc/stark-curve/fp/asm_adx.go
index f8e29bd1a7..fe25e82db2 100644
--- a/ecc/stark-curve/fp/asm_adx.go
+++ b/ecc/stark-curve/fp/asm_adx.go
@@ -1,18 +1,7 @@
 //go:build !noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fp/asm_avx.go b/ecc/stark-curve/fp/asm_avx.go
index 52fc07a325..fdb65bb8f2 100644
--- a/ecc/stark-curve/fp/asm_avx.go
+++ b/ecc/stark-curve/fp/asm_avx.go
@@ -1,18 +1,7 @@
 //go:build !noavx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fp/asm_noadx.go b/ecc/stark-curve/fp/asm_noadx.go
index cb6cfa0f50..95085a8e6f 100644
--- a/ecc/stark-curve/fp/asm_noadx.go
+++ b/ecc/stark-curve/fp/asm_noadx.go
@@ -1,18 +1,7 @@
 //go:build noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fp/asm_noavx.go b/ecc/stark-curve/fp/asm_noavx.go
index 12261b1f03..c5fec182cd 100644
--- a/ecc/stark-curve/fp/asm_noavx.go
+++ b/ecc/stark-curve/fp/asm_noavx.go
@@ -1,18 +1,7 @@
 //go:build noavx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fp/doc.go b/ecc/stark-curve/fp/doc.go
index a3dbdcf89b..4f31576c24 100644
--- a/ecc/stark-curve/fp/doc.go
+++ b/ecc/stark-curve/fp/doc.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fp/element.go b/ecc/stark-curve/fp/element.go
index 4b14ff1149..2c6fe84459 100644
--- a/ecc/stark-curve/fp/element.go
+++ b/ecc/stark-curve/fp/element.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fp/element_amd64.go b/ecc/stark-curve/fp/element_amd64.go
index 77a51ee25e..e72f552ad9 100644
--- a/ecc/stark-curve/fp/element_amd64.go
+++ b/ecc/stark-curve/fp/element_amd64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fp/element_amd64.s b/ecc/stark-curve/fp/element_amd64.s
index fb00194d7e..ed8a36e04d 100644
--- a/ecc/stark-curve/fp/element_amd64.s
+++ b/ecc/stark-curve/fp/element_amd64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fp/element_arm64.go b/ecc/stark-curve/fp/element_arm64.go
index 776a544644..eeeb12930d 100644
--- a/ecc/stark-curve/fp/element_arm64.go
+++ b/ecc/stark-curve/fp/element_arm64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fp/element_arm64.s b/ecc/stark-curve/fp/element_arm64.s
index 5d328815aa..a7bd036553 100644
--- a/ecc/stark-curve/fp/element_arm64.s
+++ b/ecc/stark-curve/fp/element_arm64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fp/element_exp.go b/ecc/stark-curve/fp/element_exp.go
index 92f615bb25..e2fddd105a 100644
--- a/ecc/stark-curve/fp/element_exp.go
+++ b/ecc/stark-curve/fp/element_exp.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fp/element_purego.go b/ecc/stark-curve/fp/element_purego.go
index 5308610f0b..5062b3185a 100644
--- a/ecc/stark-curve/fp/element_purego.go
+++ b/ecc/stark-curve/fp/element_purego.go
@@ -1,18 +1,7 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fp/element_test.go b/ecc/stark-curve/fp/element_test.go
index c33f3f21b6..eab8b6eca3 100644
--- a/ecc/stark-curve/fp/element_test.go
+++ b/ecc/stark-curve/fp/element_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fp/vector.go b/ecc/stark-curve/fp/vector.go
index c97b4283ce..ec52314aa7 100644
--- a/ecc/stark-curve/fp/vector.go
+++ b/ecc/stark-curve/fp/vector.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fp/vector_amd64.go b/ecc/stark-curve/fp/vector_amd64.go
index 75719deedb..39666a2df7 100644
--- a/ecc/stark-curve/fp/vector_amd64.go
+++ b/ecc/stark-curve/fp/vector_amd64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fp/vector_purego.go b/ecc/stark-curve/fp/vector_purego.go
index fc0f66e2a3..16afa898d4 100644
--- a/ecc/stark-curve/fp/vector_purego.go
+++ b/ecc/stark-curve/fp/vector_purego.go
@@ -1,18 +1,7 @@
 //go:build purego || !amd64
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fp/vector_test.go b/ecc/stark-curve/fp/vector_test.go
index 12f17e21fb..06fe1084a8 100644
--- a/ecc/stark-curve/fp/vector_test.go
+++ b/ecc/stark-curve/fp/vector_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fr/arith.go b/ecc/stark-curve/fr/arith.go
index 83c9fd9ef9..9285041f4b 100644
--- a/ecc/stark-curve/fr/arith.go
+++ b/ecc/stark-curve/fr/arith.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fr/asm_adx.go b/ecc/stark-curve/fr/asm_adx.go
index 9273ea23ab..9e7da5e865 100644
--- a/ecc/stark-curve/fr/asm_adx.go
+++ b/ecc/stark-curve/fr/asm_adx.go
@@ -1,18 +1,7 @@
 //go:build !noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fr/asm_avx.go b/ecc/stark-curve/fr/asm_avx.go
index 1cc06c6e8d..d6d7d7f87a 100644
--- a/ecc/stark-curve/fr/asm_avx.go
+++ b/ecc/stark-curve/fr/asm_avx.go
@@ -1,18 +1,7 @@
 //go:build !noavx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fr/asm_noadx.go b/ecc/stark-curve/fr/asm_noadx.go
index b784a24247..3456158655 100644
--- a/ecc/stark-curve/fr/asm_noadx.go
+++ b/ecc/stark-curve/fr/asm_noadx.go
@@ -1,18 +1,7 @@
 //go:build noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fr/asm_noavx.go b/ecc/stark-curve/fr/asm_noavx.go
index 66bfc00772..4eb73e9a78 100644
--- a/ecc/stark-curve/fr/asm_noavx.go
+++ b/ecc/stark-curve/fr/asm_noavx.go
@@ -1,18 +1,7 @@
 //go:build noavx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fr/doc.go b/ecc/stark-curve/fr/doc.go
index 268ea7e2ad..7b99c5c2cc 100644
--- a/ecc/stark-curve/fr/doc.go
+++ b/ecc/stark-curve/fr/doc.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fr/element.go b/ecc/stark-curve/fr/element.go
index 2acb6e46b7..68352c754d 100644
--- a/ecc/stark-curve/fr/element.go
+++ b/ecc/stark-curve/fr/element.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fr/element_amd64.go b/ecc/stark-curve/fr/element_amd64.go
index 0ddb905f7b..ca49d12590 100644
--- a/ecc/stark-curve/fr/element_amd64.go
+++ b/ecc/stark-curve/fr/element_amd64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fr/element_amd64.s b/ecc/stark-curve/fr/element_amd64.s
index fb00194d7e..ed8a36e04d 100644
--- a/ecc/stark-curve/fr/element_amd64.s
+++ b/ecc/stark-curve/fr/element_amd64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fr/element_arm64.go b/ecc/stark-curve/fr/element_arm64.go
index 69e7dd8b03..13632a244b 100644
--- a/ecc/stark-curve/fr/element_arm64.go
+++ b/ecc/stark-curve/fr/element_arm64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fr/element_arm64.s b/ecc/stark-curve/fr/element_arm64.s
index 5d328815aa..a7bd036553 100644
--- a/ecc/stark-curve/fr/element_arm64.s
+++ b/ecc/stark-curve/fr/element_arm64.s
@@ -1,18 +1,7 @@
 //go:build  !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fr/element_purego.go b/ecc/stark-curve/fr/element_purego.go
index ae05fe839b..85a7015090 100644
--- a/ecc/stark-curve/fr/element_purego.go
+++ b/ecc/stark-curve/fr/element_purego.go
@@ -1,18 +1,7 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fr/element_test.go b/ecc/stark-curve/fr/element_test.go
index fb10e5a55a..78aa20965c 100644
--- a/ecc/stark-curve/fr/element_test.go
+++ b/ecc/stark-curve/fr/element_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fr/vector.go b/ecc/stark-curve/fr/vector.go
index 867cabbc3d..8b59bd36e9 100644
--- a/ecc/stark-curve/fr/vector.go
+++ b/ecc/stark-curve/fr/vector.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fr/vector_amd64.go b/ecc/stark-curve/fr/vector_amd64.go
index 0164ecb382..b27679827c 100644
--- a/ecc/stark-curve/fr/vector_amd64.go
+++ b/ecc/stark-curve/fr/vector_amd64.go
@@ -1,18 +1,7 @@
 //go:build !purego
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fr/vector_purego.go b/ecc/stark-curve/fr/vector_purego.go
index 84f86a40b1..5973d16ce2 100644
--- a/ecc/stark-curve/fr/vector_purego.go
+++ b/ecc/stark-curve/fr/vector_purego.go
@@ -1,18 +1,7 @@
 //go:build purego || !amd64
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/ecc/stark-curve/fr/vector_test.go b/ecc/stark-curve/fr/vector_test.go
index b6344c18b7..a094bc0ac6 100644
--- a/ecc/stark-curve/fr/vector_test.go
+++ b/ecc/stark-curve/fr/vector_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/babybear/doc.go b/field/babybear/doc.go
index 65011bef3f..76ec16e7d3 100644
--- a/field/babybear/doc.go
+++ b/field/babybear/doc.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/babybear/element.go b/field/babybear/element.go
index a9f524fa84..fe21d3d87a 100644
--- a/field/babybear/element.go
+++ b/field/babybear/element.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/babybear/element_exp.go b/field/babybear/element_exp.go
index 44675979e6..470040b7dd 100644
--- a/field/babybear/element_exp.go
+++ b/field/babybear/element_exp.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/babybear/element_purego.go b/field/babybear/element_purego.go
index e618e83fd8..f30766fdfe 100644
--- a/field/babybear/element_purego.go
+++ b/field/babybear/element_purego.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/babybear/element_test.go b/field/babybear/element_test.go
index 161c977b72..ed2fe025d3 100644
--- a/field/babybear/element_test.go
+++ b/field/babybear/element_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/babybear/vector.go b/field/babybear/vector.go
index 19a57ac10d..b9a91e68bc 100644
--- a/field/babybear/vector.go
+++ b/field/babybear/vector.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/babybear/vector_purego.go b/field/babybear/vector_purego.go
index 8843280543..296122be81 100644
--- a/field/babybear/vector_purego.go
+++ b/field/babybear/vector_purego.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/babybear/vector_test.go b/field/babybear/vector_test.go
index 5d35c3e7bb..d7660863db 100644
--- a/field/babybear/vector_test.go
+++ b/field/babybear/vector_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/generator/generator.go b/field/generator/generator.go
index 7547db305a..388eb0cd49 100644
--- a/field/generator/generator.go
+++ b/field/generator/generator.go
@@ -69,7 +69,7 @@ func GenerateFF(F *config.FieldConfig, outputDir, asmDirBuildPath, asmDirInclude
 		}
 		return func() error {
 			bavardOpts := []func(*bavard.Bavard) error{
-				bavard.Apache2("ConsenSys Software Inc.", 2020),
+				bavard.Apache2("Consensys Software Inc.", 2020),
 				bavard.GeneratedBy("consensys/gnark-crypto"),
 				bavard.Funcs(funcs),
 			}
diff --git a/field/goldilocks/arith.go b/field/goldilocks/arith.go
index 99941ffdf9..95d2a32596 100644
--- a/field/goldilocks/arith.go
+++ b/field/goldilocks/arith.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/goldilocks/doc.go b/field/goldilocks/doc.go
index 076637815c..209714e87e 100644
--- a/field/goldilocks/doc.go
+++ b/field/goldilocks/doc.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/goldilocks/element.go b/field/goldilocks/element.go
index 207ee7fbb5..b707bcd996 100644
--- a/field/goldilocks/element.go
+++ b/field/goldilocks/element.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/goldilocks/element_exp.go b/field/goldilocks/element_exp.go
index 46d391d031..2de013154a 100644
--- a/field/goldilocks/element_exp.go
+++ b/field/goldilocks/element_exp.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/goldilocks/element_purego.go b/field/goldilocks/element_purego.go
index 2dfbd7dbd3..aa6c1053f2 100644
--- a/field/goldilocks/element_purego.go
+++ b/field/goldilocks/element_purego.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/goldilocks/element_test.go b/field/goldilocks/element_test.go
index 52fa5e2691..e4c179aed6 100644
--- a/field/goldilocks/element_test.go
+++ b/field/goldilocks/element_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/goldilocks/vector.go b/field/goldilocks/vector.go
index 47b0664aa3..55f9cb5266 100644
--- a/field/goldilocks/vector.go
+++ b/field/goldilocks/vector.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/goldilocks/vector_purego.go b/field/goldilocks/vector_purego.go
index 857d3e9f4c..c964b4150e 100644
--- a/field/goldilocks/vector_purego.go
+++ b/field/goldilocks/vector_purego.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/goldilocks/vector_test.go b/field/goldilocks/vector_test.go
index 8d45c0f5dc..cecc96eb3a 100644
--- a/field/goldilocks/vector_test.go
+++ b/field/goldilocks/vector_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/koalabear/doc.go b/field/koalabear/doc.go
index 6c49ce3be1..8b6839411f 100644
--- a/field/koalabear/doc.go
+++ b/field/koalabear/doc.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/koalabear/element.go b/field/koalabear/element.go
index 280a57d50f..0549df00c4 100644
--- a/field/koalabear/element.go
+++ b/field/koalabear/element.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/koalabear/element_exp.go b/field/koalabear/element_exp.go
index ea8c27d6ca..ebf5ea1c26 100644
--- a/field/koalabear/element_exp.go
+++ b/field/koalabear/element_exp.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/koalabear/element_purego.go b/field/koalabear/element_purego.go
index 137f5eb77d..02f9da17d9 100644
--- a/field/koalabear/element_purego.go
+++ b/field/koalabear/element_purego.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/koalabear/element_test.go b/field/koalabear/element_test.go
index ac6f3a8a70..d8670b0888 100644
--- a/field/koalabear/element_test.go
+++ b/field/koalabear/element_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/koalabear/vector.go b/field/koalabear/vector.go
index 60fa5f6183..0490927d51 100644
--- a/field/koalabear/vector.go
+++ b/field/koalabear/vector.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/koalabear/vector_purego.go b/field/koalabear/vector_purego.go
index 71dc2cc0c3..6e9b038922 100644
--- a/field/koalabear/vector_purego.go
+++ b/field/koalabear/vector_purego.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/koalabear/vector_test.go b/field/koalabear/vector_test.go
index b91728a8ac..8f3c20664b 100644
--- a/field/koalabear/vector_test.go
+++ b/field/koalabear/vector_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/go.mod b/go.mod
index c4dbc8bc84..ae2d6988c6 100644
--- a/go.mod
+++ b/go.mod
@@ -4,7 +4,7 @@ go 1.22
 
 require (
 	github.com/bits-and-blooms/bitset v1.14.2
-	github.com/consensys/bavard v0.1.23-0.20241022191302-a6fdcdb6e8f3
+	github.com/consensys/bavard v0.1.23
 	github.com/leanovate/gopter v0.2.11
 	github.com/mmcloughlin/addchain v0.4.0
 	github.com/spf13/cobra v1.8.1
diff --git a/go.sum b/go.sum
index 54ef0689c1..9e1af01c23 100644
--- a/go.sum
+++ b/go.sum
@@ -55,8 +55,8 @@ github.com/client9/misspell v0.3.4/go.mod h1:qj6jICC3Q7zFZvVWo7KLAzC3yx5G7kyvSDk
 github.com/cncf/udpa/go v0.0.0-20191209042840-269d4d468f6f/go.mod h1:M8M6+tZqaGXZJjfX53e64911xZQV5JYwmTeXPW+k8Sc=
 github.com/cncf/udpa/go v0.0.0-20200629203442-efcf912fb354/go.mod h1:WmhPx2Nbnhtbo57+VJT5O0JRkEi1Wbu0z5j0R8u5Hbk=
 github.com/cncf/udpa/go v0.0.0-20201120205902-5459f2c99403/go.mod h1:WmhPx2Nbnhtbo57+VJT5O0JRkEi1Wbu0z5j0R8u5Hbk=
-github.com/consensys/bavard v0.1.23-0.20241022191302-a6fdcdb6e8f3 h1:8gPxbjhwhxXTakOXII32eLlAFLlYImoENa3uQ6iP+go=
-github.com/consensys/bavard v0.1.23-0.20241022191302-a6fdcdb6e8f3/go.mod h1:k/zVjHHC4B+PQy1Pg7fgvG3ALicQw540Crag8qx+dZs=
+github.com/consensys/bavard v0.1.23 h1:EUMTIayTeUqb7tPy7n0IMrBM/GeEHGBSEkR8G5JE0po=
+github.com/consensys/bavard v0.1.23/go.mod h1:k/zVjHHC4B+PQy1Pg7fgvG3ALicQw540Crag8qx+dZs=
 github.com/coreos/go-semver v0.3.0/go.mod h1:nnelYz7RCh+5ahJtPPxZlU+153eP4D4r3EedlOD2RNk=
 github.com/coreos/go-systemd/v22 v22.3.2/go.mod h1:Y58oyj3AT4RCenI/lSvhwexgC+NSVTIJ3seZv2GcEnc=
 github.com/cpuguy83/go-md2man/v2 v2.0.0/go.mod h1:maD7wRr/U5Z6m/iR4s+kqSMx2CaBsrgA7czyZG/E6dU=
diff --git a/internal/generator/gkr/test_vectors/main.go b/internal/generator/gkr/test_vectors/main.go
index c1b01aa825..f4e6429e82 100644
--- a/internal/generator/gkr/test_vectors/main.go
+++ b/internal/generator/gkr/test_vectors/main.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/internal/generator/test_vector_utils/small_rational/gkr/gkr.go b/internal/generator/test_vector_utils/small_rational/gkr/gkr.go
index d0dae64a6f..a5bcb55b94 100644
--- a/internal/generator/test_vector_utils/small_rational/gkr/gkr.go
+++ b/internal/generator/test_vector_utils/small_rational/gkr/gkr.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/internal/generator/test_vector_utils/small_rational/polynomial/doc.go b/internal/generator/test_vector_utils/small_rational/polynomial/doc.go
index 747da41f2c..35b3f725c1 100644
--- a/internal/generator/test_vector_utils/small_rational/polynomial/doc.go
+++ b/internal/generator/test_vector_utils/small_rational/polynomial/doc.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/internal/generator/test_vector_utils/small_rational/polynomial/multilin.go b/internal/generator/test_vector_utils/small_rational/polynomial/multilin.go
index 5f4217ad2f..20915de419 100644
--- a/internal/generator/test_vector_utils/small_rational/polynomial/multilin.go
+++ b/internal/generator/test_vector_utils/small_rational/polynomial/multilin.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/internal/generator/test_vector_utils/small_rational/polynomial/polynomial.go b/internal/generator/test_vector_utils/small_rational/polynomial/polynomial.go
index 610e1c9c6e..2c76a20288 100644
--- a/internal/generator/test_vector_utils/small_rational/polynomial/polynomial.go
+++ b/internal/generator/test_vector_utils/small_rational/polynomial/polynomial.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/internal/generator/test_vector_utils/small_rational/polynomial/pool.go b/internal/generator/test_vector_utils/small_rational/polynomial/pool.go
index 15d4f871d6..e9fc5204a2 100644
--- a/internal/generator/test_vector_utils/small_rational/polynomial/pool.go
+++ b/internal/generator/test_vector_utils/small_rational/polynomial/pool.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck.go b/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck.go
index cb86eb419e..61ed654aec 100644
--- a/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck.go
+++ b/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck_test.go b/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck_test.go
index 0c816fe436..012aae6598 100644
--- a/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck_test.go
+++ b/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck_test.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/internal/generator/test_vector_utils/small_rational/test_vector_utils/test_vector_utils.go b/internal/generator/test_vector_utils/small_rational/test_vector_utils/test_vector_utils.go
index ca8307853b..0432ac7bfc 100644
--- a/internal/generator/test_vector_utils/small_rational/test_vector_utils/test_vector_utils.go
+++ b/internal/generator/test_vector_utils/small_rational/test_vector_utils/test_vector_utils.go
@@ -1,16 +1,5 @@
 // Copyright 2020 Consensys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 

From 47c09c6fe3738a0eace946060ec927cab4788697 Mon Sep 17 00:00:00 2001
From: Gautam Botrel <gautam.botrel@gmail.com>
Date: Tue, 10 Dec 2024 13:40:33 -0600
Subject: [PATCH 093/114] docs: fix non generated headers (#571)

---
 .chglog/config.yml                            |   2 +-
 CHANGELOG.md                                  | 678 +++++++++---------
 CITATION.bib                                  |   2 +-
 README.md                                     |  46 +-
 ecc/bls12-377/ecdsa/doc.go                    |   2 +-
 ecc/bls12-377/ecdsa/ecdsa.go                  |   2 +-
 ecc/bls12-377/ecdsa/ecdsa_test.go             |   2 +-
 ecc/bls12-377/ecdsa/marshal.go                |   2 +-
 ecc/bls12-377/ecdsa/marshal_test.go           |   2 +-
 ecc/bls12-377/fflonk/doc.go                   |   2 +-
 ecc/bls12-377/fflonk/example_test.go          |   2 +-
 ecc/bls12-377/fflonk/fflonk.go                |   2 +-
 ecc/bls12-377/fflonk/fflonk_test.go           |   2 +-
 ecc/bls12-377/fflonk/marshal.go               |   2 +-
 ecc/bls12-377/fp/arith.go                     |   2 +-
 ecc/bls12-377/fp/asm_adx.go                   |   2 +-
 ecc/bls12-377/fp/asm_noadx.go                 |   2 +-
 ecc/bls12-377/fp/doc.go                       |   2 +-
 ecc/bls12-377/fp/element.go                   |   2 +-
 ecc/bls12-377/fp/element_amd64.go             |   2 +-
 ecc/bls12-377/fp/element_amd64.s              |   4 +-
 ecc/bls12-377/fp/element_arm64.go             |   2 +-
 ecc/bls12-377/fp/element_arm64.s              |   2 +-
 ecc/bls12-377/fp/element_exp.go               |   2 +-
 ecc/bls12-377/fp/element_purego.go            |   2 +-
 ecc/bls12-377/fp/element_test.go              |   2 +-
 ecc/bls12-377/fp/element_utils.go             |  15 +-
 ecc/bls12-377/fp/hash_to_field/doc.go         |   2 +-
 .../fp/hash_to_field/hash_to_field.go         |   2 +-
 .../fp/hash_to_field/hash_to_field_test.go    |   2 +-
 ecc/bls12-377/fp/vector.go                    |   2 +-
 ecc/bls12-377/fp/vector_purego.go             |   2 +-
 ecc/bls12-377/fp/vector_test.go               |   2 +-
 ecc/bls12-377/fr/arith.go                     |   2 +-
 ecc/bls12-377/fr/asm_adx.go                   |   2 +-
 ecc/bls12-377/fr/asm_avx.go                   |   2 +-
 ecc/bls12-377/fr/asm_noadx.go                 |   2 +-
 ecc/bls12-377/fr/asm_noavx.go                 |   2 +-
 ecc/bls12-377/fr/doc.go                       |   2 +-
 ecc/bls12-377/fr/element.go                   |   2 +-
 ecc/bls12-377/fr/element_amd64.go             |   2 +-
 ecc/bls12-377/fr/element_amd64.s              |   4 +-
 ecc/bls12-377/fr/element_arm64.go             |   2 +-
 ecc/bls12-377/fr/element_arm64.s              |   2 +-
 ecc/bls12-377/fr/element_exp.go               |   2 +-
 ecc/bls12-377/fr/element_purego.go            |   2 +-
 ecc/bls12-377/fr/element_test.go              |   2 +-
 ecc/bls12-377/fr/fft/bitreverse.go            |   2 +-
 ecc/bls12-377/fr/fft/bitreverse_test.go       |   2 +-
 ecc/bls12-377/fr/fft/doc.go                   |   2 +-
 ecc/bls12-377/fr/fft/domain.go                |   2 +-
 ecc/bls12-377/fr/fft/domain_test.go           |   2 +-
 ecc/bls12-377/fr/fft/fft.go                   |   2 +-
 ecc/bls12-377/fr/fft/fft_test.go              |   2 +-
 ecc/bls12-377/fr/fft/options.go               |   2 +-
 ecc/bls12-377/fr/fri/doc.go                   |   2 +-
 ecc/bls12-377/fr/fri/fri.go                   |   2 +-
 ecc/bls12-377/fr/fri/fri_test.go              |   2 +-
 ecc/bls12-377/fr/generator.go                 |   2 +-
 ecc/bls12-377/fr/gkr/gkr.go                   |   2 +-
 ecc/bls12-377/fr/gkr/gkr_test.go              |   4 +-
 ecc/bls12-377/fr/hash_to_field/doc.go         |   2 +-
 .../fr/hash_to_field/hash_to_field.go         |   2 +-
 .../fr/hash_to_field/hash_to_field_test.go    |   2 +-
 ecc/bls12-377/fr/iop/doc.go                   |   2 +-
 ecc/bls12-377/fr/iop/expressions.go           |   2 +-
 ecc/bls12-377/fr/iop/expressions_test.go      |   2 +-
 ecc/bls12-377/fr/iop/polynomial.go            |   2 +-
 ecc/bls12-377/fr/iop/polynomial_test.go       |   2 +-
 ecc/bls12-377/fr/iop/quotient.go              |   2 +-
 ecc/bls12-377/fr/iop/quotient_test.go         |   2 +-
 ecc/bls12-377/fr/iop/ratios.go                |   2 +-
 ecc/bls12-377/fr/iop/ratios_test.go           |   2 +-
 ecc/bls12-377/fr/iop/utils.go                 |   2 +-
 ecc/bls12-377/fr/mimc/doc.go                  |   2 +-
 ecc/bls12-377/fr/mimc/mimc.go                 |   2 +-
 ecc/bls12-377/fr/mimc/options.go              |   2 +-
 ecc/bls12-377/fr/pedersen/doc.go              |   2 +-
 ecc/bls12-377/fr/pedersen/example_test.go     |   2 +-
 ecc/bls12-377/fr/pedersen/pedersen.go         |   8 +-
 ecc/bls12-377/fr/pedersen/pedersen_test.go    |   2 +-
 ecc/bls12-377/fr/permutation/doc.go           |   2 +-
 ecc/bls12-377/fr/permutation/permutation.go   |   2 +-
 .../fr/permutation/permutation_test.go        |   2 +-
 ecc/bls12-377/fr/plookup/doc.go               |   2 +-
 ecc/bls12-377/fr/plookup/plookup_test.go      |   2 +-
 ecc/bls12-377/fr/plookup/table.go             |   2 +-
 ecc/bls12-377/fr/plookup/vector.go            |   2 +-
 ecc/bls12-377/fr/polynomial/doc.go            |   2 +-
 ecc/bls12-377/fr/polynomial/multilin.go       |   2 +-
 ecc/bls12-377/fr/polynomial/multilin_test.go  |   2 +-
 ecc/bls12-377/fr/polynomial/polynomial.go     |   2 +-
 .../fr/polynomial/polynomial_test.go          |   2 +-
 ecc/bls12-377/fr/polynomial/pool.go           |   2 +-
 ecc/bls12-377/fr/poseidon2/poseidon2.go       |   2 +-
 ecc/bls12-377/fr/poseidon2/poseidon2_test.go  |   2 +-
 ecc/bls12-377/fr/sis/sis.go                   |  15 +-
 ecc/bls12-377/fr/sis/sis_fft.go               |   2 +-
 ecc/bls12-377/fr/sis/sis_test.go              |  15 +-
 ecc/bls12-377/fr/sumcheck/sumcheck.go         |   2 +-
 ecc/bls12-377/fr/sumcheck/sumcheck_test.go    |   2 +-
 .../fr/test_vector_utils/test_vector_utils.go |   2 +-
 ecc/bls12-377/fr/vector.go                    |   2 +-
 ecc/bls12-377/fr/vector_amd64.go              |   2 +-
 ecc/bls12-377/fr/vector_purego.go             |   2 +-
 ecc/bls12-377/fr/vector_test.go               |   2 +-
 ecc/bls12-377/g1.go                           |   2 +-
 ecc/bls12-377/g1_test.go                      |   2 +-
 ecc/bls12-377/g2.go                           |   2 +-
 ecc/bls12-377/g2_test.go                      |   2 +-
 ecc/bls12-377/hash_to_g1.go                   |   2 +-
 ecc/bls12-377/hash_to_g1_test.go              |   2 +-
 ecc/bls12-377/hash_to_g2.go                   |   2 +-
 ecc/bls12-377/hash_to_g2_test.go              |   2 +-
 ecc/bls12-377/internal/fptower/asm.go         |   2 +-
 ecc/bls12-377/internal/fptower/asm_noadx.go   |   2 +-
 ecc/bls12-377/internal/fptower/e12.go         |   2 +-
 ecc/bls12-377/internal/fptower/e12_test.go    |   2 +-
 ecc/bls12-377/internal/fptower/e2.go          |   2 +-
 ecc/bls12-377/internal/fptower/e2_amd64.go    |   2 +-
 ecc/bls12-377/internal/fptower/e2_amd64.s     |   2 +-
 ecc/bls12-377/internal/fptower/e2_bls377.go   |  15 +-
 ecc/bls12-377/internal/fptower/e2_fallback.go |   2 +-
 ecc/bls12-377/internal/fptower/e2_test.go     |   2 +-
 ecc/bls12-377/internal/fptower/e6.go          |   2 +-
 ecc/bls12-377/internal/fptower/e6_test.go     |   2 +-
 ecc/bls12-377/internal/fptower/frobenius.go   |  15 +-
 ecc/bls12-377/internal/fptower/parameters.go  |  15 +-
 ecc/bls12-377/kzg/doc.go                      |   2 +-
 ecc/bls12-377/kzg/kzg.go                      |   2 +-
 ecc/bls12-377/kzg/kzg_test.go                 |   2 +-
 ecc/bls12-377/kzg/marshal.go                  |   2 +-
 ecc/bls12-377/kzg/utils.go                    |   2 +-
 ecc/bls12-377/marshal.go                      |   2 +-
 ecc/bls12-377/marshal_test.go                 |   2 +-
 ecc/bls12-377/multiexp.go                     |   2 +-
 ecc/bls12-377/multiexp_affine.go              |   6 +-
 ecc/bls12-377/multiexp_jacobian.go            |   2 +-
 ecc/bls12-377/multiexp_test.go                |   2 +-
 ecc/bls12-377/pairing.go                      |  15 +-
 ecc/bls12-377/pairing_test.go                 |   2 +-
 ecc/bls12-377/shplonk/doc.go                  |   2 +-
 ecc/bls12-377/shplonk/example_test.go         |   2 +-
 ecc/bls12-377/shplonk/marshal.go              |   2 +-
 ecc/bls12-377/shplonk/shplonk.go              |   2 +-
 ecc/bls12-377/shplonk/shplonk_test.go         |   2 +-
 ecc/bls12-377/twistededwards/curve.go         |   2 +-
 ecc/bls12-377/twistededwards/doc.go           |   2 +-
 ecc/bls12-377/twistededwards/eddsa/doc.go     |   2 +-
 ecc/bls12-377/twistededwards/eddsa/eddsa.go   |   2 +-
 .../twistededwards/eddsa/eddsa_test.go        |   2 +-
 ecc/bls12-377/twistededwards/eddsa/marshal.go |   2 +-
 ecc/bls12-377/twistededwards/point.go         |   2 +-
 ecc/bls12-377/twistededwards/point_test.go    |   2 +-
 ecc/bls12-381/bandersnatch/curve.go           |   2 +-
 ecc/bls12-381/bandersnatch/doc.go             |   2 +-
 ecc/bls12-381/bandersnatch/eddsa/doc.go       |   2 +-
 ecc/bls12-381/bandersnatch/eddsa/eddsa.go     |   2 +-
 .../bandersnatch/eddsa/eddsa_test.go          |   2 +-
 ecc/bls12-381/bandersnatch/eddsa/marshal.go   |   2 +-
 ecc/bls12-381/bandersnatch/point.go           |   2 +-
 ecc/bls12-381/bandersnatch/point_test.go      |   2 +-
 ecc/bls12-381/ecdsa/doc.go                    |   2 +-
 ecc/bls12-381/ecdsa/ecdsa.go                  |   2 +-
 ecc/bls12-381/ecdsa/ecdsa_test.go             |   2 +-
 ecc/bls12-381/ecdsa/marshal.go                |   2 +-
 ecc/bls12-381/ecdsa/marshal_test.go           |   2 +-
 ecc/bls12-381/fflonk/doc.go                   |   2 +-
 ecc/bls12-381/fflonk/example_test.go          |   2 +-
 ecc/bls12-381/fflonk/fflonk.go                |   2 +-
 ecc/bls12-381/fflonk/fflonk_test.go           |   2 +-
 ecc/bls12-381/fflonk/marshal.go               |   2 +-
 ecc/bls12-381/fp/arith.go                     |   2 +-
 ecc/bls12-381/fp/asm_adx.go                   |   2 +-
 ecc/bls12-381/fp/asm_noadx.go                 |   2 +-
 ecc/bls12-381/fp/doc.go                       |   2 +-
 ecc/bls12-381/fp/element.go                   |   2 +-
 ecc/bls12-381/fp/element_amd64.go             |   2 +-
 ecc/bls12-381/fp/element_amd64.s              |   4 +-
 ecc/bls12-381/fp/element_arm64.go             |   2 +-
 ecc/bls12-381/fp/element_arm64.s              |   2 +-
 ecc/bls12-381/fp/element_exp.go               |   2 +-
 ecc/bls12-381/fp/element_purego.go            |   2 +-
 ecc/bls12-381/fp/element_test.go              |   2 +-
 ecc/bls12-381/fp/hash_to_field/doc.go         |   2 +-
 .../fp/hash_to_field/hash_to_field.go         |   2 +-
 .../fp/hash_to_field/hash_to_field_test.go    |   2 +-
 ecc/bls12-381/fp/vector.go                    |   2 +-
 ecc/bls12-381/fp/vector_purego.go             |   2 +-
 ecc/bls12-381/fp/vector_test.go               |   2 +-
 ecc/bls12-381/fr/arith.go                     |   2 +-
 ecc/bls12-381/fr/asm_adx.go                   |   2 +-
 ecc/bls12-381/fr/asm_avx.go                   |   2 +-
 ecc/bls12-381/fr/asm_noadx.go                 |   2 +-
 ecc/bls12-381/fr/asm_noavx.go                 |   2 +-
 ecc/bls12-381/fr/doc.go                       |   2 +-
 ecc/bls12-381/fr/element.go                   |   2 +-
 ecc/bls12-381/fr/element_amd64.go             |   2 +-
 ecc/bls12-381/fr/element_amd64.s              |   4 +-
 ecc/bls12-381/fr/element_arm64.go             |   2 +-
 ecc/bls12-381/fr/element_arm64.s              |   2 +-
 ecc/bls12-381/fr/element_exp.go               |   2 +-
 ecc/bls12-381/fr/element_purego.go            |   2 +-
 ecc/bls12-381/fr/element_test.go              |   2 +-
 ecc/bls12-381/fr/fft/bitreverse.go            |   2 +-
 ecc/bls12-381/fr/fft/bitreverse_test.go       |   2 +-
 ecc/bls12-381/fr/fft/doc.go                   |   2 +-
 ecc/bls12-381/fr/fft/domain.go                |   2 +-
 ecc/bls12-381/fr/fft/domain_test.go           |   2 +-
 ecc/bls12-381/fr/fft/fft.go                   |   2 +-
 ecc/bls12-381/fr/fft/fft_test.go              |   2 +-
 ecc/bls12-381/fr/fft/options.go               |   2 +-
 ecc/bls12-381/fr/fri/doc.go                   |   2 +-
 ecc/bls12-381/fr/fri/fri.go                   |   2 +-
 ecc/bls12-381/fr/fri/fri_test.go              |   2 +-
 ecc/bls12-381/fr/generator.go                 |   2 +-
 ecc/bls12-381/fr/gkr/gkr.go                   |   2 +-
 ecc/bls12-381/fr/gkr/gkr_test.go              |   4 +-
 ecc/bls12-381/fr/hash_to_field/doc.go         |   2 +-
 .../fr/hash_to_field/hash_to_field.go         |   2 +-
 .../fr/hash_to_field/hash_to_field_test.go    |   2 +-
 ecc/bls12-381/fr/iop/doc.go                   |   2 +-
 ecc/bls12-381/fr/iop/expressions.go           |   2 +-
 ecc/bls12-381/fr/iop/expressions_test.go      |   2 +-
 ecc/bls12-381/fr/iop/polynomial.go            |   2 +-
 ecc/bls12-381/fr/iop/polynomial_test.go       |   2 +-
 ecc/bls12-381/fr/iop/quotient.go              |   2 +-
 ecc/bls12-381/fr/iop/quotient_test.go         |   2 +-
 ecc/bls12-381/fr/iop/ratios.go                |   2 +-
 ecc/bls12-381/fr/iop/ratios_test.go           |   2 +-
 ecc/bls12-381/fr/iop/utils.go                 |   2 +-
 ecc/bls12-381/fr/mimc/doc.go                  |   2 +-
 ecc/bls12-381/fr/mimc/mimc.go                 |   2 +-
 ecc/bls12-381/fr/mimc/options.go              |   2 +-
 ecc/bls12-381/fr/pedersen/doc.go              |   2 +-
 ecc/bls12-381/fr/pedersen/example_test.go     |   2 +-
 ecc/bls12-381/fr/pedersen/pedersen.go         |   8 +-
 ecc/bls12-381/fr/pedersen/pedersen_test.go    |   2 +-
 ecc/bls12-381/fr/permutation/doc.go           |   2 +-
 ecc/bls12-381/fr/permutation/permutation.go   |   2 +-
 .../fr/permutation/permutation_test.go        |   2 +-
 ecc/bls12-381/fr/plookup/doc.go               |   2 +-
 ecc/bls12-381/fr/plookup/plookup_test.go      |   2 +-
 ecc/bls12-381/fr/plookup/table.go             |   2 +-
 ecc/bls12-381/fr/plookup/vector.go            |   2 +-
 ecc/bls12-381/fr/polynomial/doc.go            |   2 +-
 ecc/bls12-381/fr/polynomial/multilin.go       |   2 +-
 ecc/bls12-381/fr/polynomial/multilin_test.go  |   2 +-
 ecc/bls12-381/fr/polynomial/polynomial.go     |   2 +-
 .../fr/polynomial/polynomial_test.go          |   2 +-
 ecc/bls12-381/fr/polynomial/pool.go           |   2 +-
 ecc/bls12-381/fr/poseidon2/poseidon2.go       |   2 +-
 ecc/bls12-381/fr/poseidon2/poseidon2_test.go  |   2 +-
 ecc/bls12-381/fr/sumcheck/sumcheck.go         |   2 +-
 ecc/bls12-381/fr/sumcheck/sumcheck_test.go    |   2 +-
 .../fr/test_vector_utils/test_vector_utils.go |   2 +-
 ecc/bls12-381/fr/vector.go                    |   2 +-
 ecc/bls12-381/fr/vector_amd64.go              |   2 +-
 ecc/bls12-381/fr/vector_purego.go             |   2 +-
 ecc/bls12-381/fr/vector_test.go               |   2 +-
 ecc/bls12-381/g1.go                           |   2 +-
 ecc/bls12-381/g1_test.go                      |   2 +-
 ecc/bls12-381/g2.go                           |   2 +-
 ecc/bls12-381/g2_test.go                      |   2 +-
 ecc/bls12-381/hash_to_g1.go                   |   2 +-
 ecc/bls12-381/hash_to_g1_test.go              |   2 +-
 ecc/bls12-381/hash_to_g2.go                   |   2 +-
 ecc/bls12-381/hash_to_g2_test.go              |   2 +-
 ecc/bls12-381/internal/fptower/asm.go         |   2 +-
 ecc/bls12-381/internal/fptower/asm_noadx.go   |   2 +-
 ecc/bls12-381/internal/fptower/e12.go         |   2 +-
 ecc/bls12-381/internal/fptower/e12_test.go    |   2 +-
 ecc/bls12-381/internal/fptower/e2.go          |   2 +-
 ecc/bls12-381/internal/fptower/e2_amd64.go    |   2 +-
 ecc/bls12-381/internal/fptower/e2_amd64.s     |   2 +-
 ecc/bls12-381/internal/fptower/e2_bls381.go   |  15 +-
 .../internal/fptower/e2_bls381_fallback.go    |  15 +-
 ecc/bls12-381/internal/fptower/e2_fallback.go |   2 +-
 ecc/bls12-381/internal/fptower/e2_test.go     |   2 +-
 ecc/bls12-381/internal/fptower/e6.go          |   2 +-
 ecc/bls12-381/internal/fptower/e6_test.go     |   2 +-
 ecc/bls12-381/internal/fptower/frobenius.go   |  15 +-
 ecc/bls12-381/internal/fptower/parameters.go  |  15 +-
 ecc/bls12-381/kzg/doc.go                      |   2 +-
 ecc/bls12-381/kzg/kzg.go                      |   2 +-
 ecc/bls12-381/kzg/kzg_test.go                 |   2 +-
 ecc/bls12-381/kzg/marshal.go                  |   2 +-
 ecc/bls12-381/kzg/utils.go                    |   2 +-
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 ecc/bw6-761/fr/plookup/doc.go                 |   2 +-
 ecc/bw6-761/fr/plookup/plookup_test.go        |   2 +-
 ecc/bw6-761/fr/plookup/table.go               |   2 +-
 ecc/bw6-761/fr/plookup/vector.go              |   2 +-
 ecc/bw6-761/fr/polynomial/doc.go              |   2 +-
 ecc/bw6-761/fr/polynomial/multilin.go         |   2 +-
 ecc/bw6-761/fr/polynomial/multilin_test.go    |   2 +-
 ecc/bw6-761/fr/polynomial/polynomial.go       |   2 +-
 ecc/bw6-761/fr/polynomial/polynomial_test.go  |   2 +-
 ecc/bw6-761/fr/polynomial/pool.go             |   2 +-
 ecc/bw6-761/fr/poseidon2/poseidon2.go         |   2 +-
 ecc/bw6-761/fr/poseidon2/poseidon2_test.go    |   2 +-
 ecc/bw6-761/fr/sumcheck/sumcheck.go           |   2 +-
 ecc/bw6-761/fr/sumcheck/sumcheck_test.go      |   2 +-
 .../fr/test_vector_utils/test_vector_utils.go |   2 +-
 ecc/bw6-761/fr/vector.go                      |   2 +-
 ecc/bw6-761/fr/vector_purego.go               |   2 +-
 ecc/bw6-761/fr/vector_test.go                 |   2 +-
 ecc/bw6-761/g1.go                             |   2 +-
 ecc/bw6-761/g1_test.go                        |   2 +-
 ecc/bw6-761/g2.go                             |   2 +-
 ecc/bw6-761/g2_test.go                        |   2 +-
 ecc/bw6-761/hash_to_g1.go                     |   2 +-
 ecc/bw6-761/hash_to_g1_test.go                |   2 +-
 ecc/bw6-761/hash_to_g2.go                     |   2 +-
 ecc/bw6-761/hash_to_g2_test.go                |   2 +-
 ecc/bw6-761/internal/fptower/e3.go            |  13 +-
 ecc/bw6-761/internal/fptower/e6.go            |  15 +-
 ecc/bw6-761/internal/fptower/e6_test.go       |  15 +-
 ecc/bw6-761/internal/fptower/frobenius.go     |  15 +-
 ecc/bw6-761/internal/fptower/parameters.go    |  15 +-
 ecc/bw6-761/kzg/doc.go                        |   2 +-
 ecc/bw6-761/kzg/kzg.go                        |   2 +-
 ecc/bw6-761/kzg/kzg_test.go                   |   2 +-
 ecc/bw6-761/kzg/marshal.go                    |   2 +-
 ecc/bw6-761/kzg/utils.go                      |   2 +-
 ecc/bw6-761/marshal.go                        |   2 +-
 ecc/bw6-761/marshal_test.go                   |   2 +-
 ecc/bw6-761/multiexp.go                       |   2 +-
 ecc/bw6-761/multiexp_affine.go                |   6 +-
 ecc/bw6-761/multiexp_jacobian.go              |   2 +-
 ecc/bw6-761/multiexp_test.go                  |   2 +-
 ecc/bw6-761/pairing_test.go                   |   2 +-
 ecc/bw6-761/shplonk/doc.go                    |   2 +-
 ecc/bw6-761/shplonk/example_test.go           |   2 +-
 ecc/bw6-761/shplonk/marshal.go                |   2 +-
 ecc/bw6-761/shplonk/shplonk.go                |   2 +-
 ecc/bw6-761/shplonk/shplonk_test.go           |   2 +-
 ecc/bw6-761/twistededwards/curve.go           |   2 +-
 ecc/bw6-761/twistededwards/doc.go             |   2 +-
 ecc/bw6-761/twistededwards/eddsa/doc.go       |   2 +-
 ecc/bw6-761/twistededwards/eddsa/eddsa.go     |   2 +-
 .../twistededwards/eddsa/eddsa_test.go        |   2 +-
 ecc/bw6-761/twistededwards/eddsa/marshal.go   |   2 +-
 ecc/bw6-761/twistededwards/point.go           |   2 +-
 ecc/bw6-761/twistededwards/point_test.go      |   2 +-
 ecc/ecc.go                                    |  17 +-
 ecc/secp256k1/ecdsa/doc.go                    |   2 +-
 ecc/secp256k1/ecdsa/ecdsa.go                  |   2 +-
 ecc/secp256k1/ecdsa/ecdsa_test.go             |   2 +-
 ecc/secp256k1/ecdsa/marshal.go                |   2 +-
 ecc/secp256k1/ecdsa/marshal_test.go           |   2 +-
 ecc/secp256k1/fp/arith.go                     |   2 +-
 ecc/secp256k1/fp/doc.go                       |   2 +-
 ecc/secp256k1/fp/element.go                   |   2 +-
 ecc/secp256k1/fp/element_exp.go               |   2 +-
 ecc/secp256k1/fp/element_purego.go            |   2 +-
 ecc/secp256k1/fp/element_test.go              |   2 +-
 ecc/secp256k1/fp/vector.go                    |   2 +-
 ecc/secp256k1/fp/vector_purego.go             |   2 +-
 ecc/secp256k1/fp/vector_test.go               |   2 +-
 ecc/secp256k1/fr/arith.go                     |   2 +-
 ecc/secp256k1/fr/doc.go                       |   2 +-
 ecc/secp256k1/fr/element.go                   |   2 +-
 ecc/secp256k1/fr/element_exp.go               |   2 +-
 ecc/secp256k1/fr/element_purego.go            |   2 +-
 ecc/secp256k1/fr/element_test.go              |   2 +-
 ecc/secp256k1/fr/vector.go                    |   2 +-
 ecc/secp256k1/fr/vector_purego.go             |   2 +-
 ecc/secp256k1/fr/vector_test.go               |   2 +-
 ecc/secp256k1/g1.go                           |   2 +-
 ecc/secp256k1/g1_test.go                      |   2 +-
 ecc/secp256k1/hash_to_g1.go                   |   2 +-
 ecc/secp256k1/hash_to_g1_test.go              |   2 +-
 ecc/secp256k1/marshal.go                      |  15 +-
 ecc/secp256k1/marshal_test.go                 |  15 +-
 ecc/secp256k1/multiexp.go                     |   2 +-
 ecc/secp256k1/multiexp_affine.go              |   4 +-
 ecc/secp256k1/multiexp_jacobian.go            |   2 +-
 ecc/secp256k1/multiexp_test.go                |   2 +-
 ecc/secp256k1/secp256k1.go                    |  15 +-
 ecc/stark-curve/ecdsa/doc.go                  |   2 +-
 ecc/stark-curve/ecdsa/ecdsa.go                |   2 +-
 ecc/stark-curve/ecdsa/ecdsa_test.go           |   2 +-
 ecc/stark-curve/ecdsa/marshal.go              |   2 +-
 ecc/stark-curve/ecdsa/marshal_test.go         |   2 +-
 ecc/stark-curve/fp/arith.go                   |   2 +-
 ecc/stark-curve/fp/asm_adx.go                 |   2 +-
 ecc/stark-curve/fp/asm_avx.go                 |   2 +-
 ecc/stark-curve/fp/asm_noadx.go               |   2 +-
 ecc/stark-curve/fp/asm_noavx.go               |   2 +-
 ecc/stark-curve/fp/doc.go                     |   2 +-
 ecc/stark-curve/fp/element.go                 |   2 +-
 ecc/stark-curve/fp/element_amd64.go           |   2 +-
 ecc/stark-curve/fp/element_amd64.s            |   4 +-
 ecc/stark-curve/fp/element_arm64.go           |   2 +-
 ecc/stark-curve/fp/element_arm64.s            |   2 +-
 ecc/stark-curve/fp/element_exp.go             |   2 +-
 ecc/stark-curve/fp/element_purego.go          |   2 +-
 ecc/stark-curve/fp/element_test.go            |   2 +-
 ecc/stark-curve/fp/vector.go                  |   2 +-
 ecc/stark-curve/fp/vector_amd64.go            |   2 +-
 ecc/stark-curve/fp/vector_purego.go           |   2 +-
 ecc/stark-curve/fp/vector_test.go             |   2 +-
 ecc/stark-curve/fr/arith.go                   |   2 +-
 ecc/stark-curve/fr/asm_adx.go                 |   2 +-
 ecc/stark-curve/fr/asm_avx.go                 |   2 +-
 ecc/stark-curve/fr/asm_noadx.go               |   2 +-
 ecc/stark-curve/fr/asm_noavx.go               |   2 +-
 ecc/stark-curve/fr/doc.go                     |   2 +-
 ecc/stark-curve/fr/element.go                 |   2 +-
 ecc/stark-curve/fr/element_amd64.go           |   2 +-
 ecc/stark-curve/fr/element_amd64.s            |   4 +-
 ecc/stark-curve/fr/element_arm64.go           |   2 +-
 ecc/stark-curve/fr/element_arm64.s            |   2 +-
 ecc/stark-curve/fr/element_purego.go          |   2 +-
 ecc/stark-curve/fr/element_test.go            |   2 +-
 ecc/stark-curve/fr/vector.go                  |   2 +-
 ecc/stark-curve/fr/vector_amd64.go            |   2 +-
 ecc/stark-curve/fr/vector_purego.go           |   2 +-
 ecc/stark-curve/fr/vector_test.go             |   2 +-
 ecc/stark-curve/g1.go                         |  15 +-
 ecc/stark-curve/g1_test.go                    |  15 +-
 ecc/stark-curve/hash_to_g1.go                 |  15 +-
 ecc/stark-curve/hash_to_g1_test.go            |  20 +-
 ecc/stark-curve/marshal.go                    |  15 +-
 ecc/stark-curve/marshal_test.go               |  15 +-
 ecc/stark-curve/stark_curve.go                |  15 +-
 fiat-shamir/transcript.go                     |  15 +-
 fiat-shamir/transcript_test.go                |  15 +-
 field/asm/element_10w_amd64.s                 |   2 +-
 field/asm/element_12w_amd64.s                 |   2 +-
 field/asm/element_4w_amd64.s                  |   2 +-
 field/asm/element_5w_amd64.s                  |   2 +-
 field/asm/element_6w_amd64.s                  |   2 +-
 field/babybear/arith.go                       |  15 +-
 field/babybear/doc.go                         |   2 +-
 field/babybear/element.go                     |   2 +-
 field/babybear/element_exp.go                 |   2 +-
 field/babybear/element_purego.go              |   2 +-
 field/babybear/element_test.go                |   2 +-
 field/babybear/vector.go                      |   2 +-
 field/babybear/vector_purego.go               |   2 +-
 field/babybear/vector_test.go                 |   2 +-
 field/generator/asm/amd64/asm_macros.go       |  15 +-
 field/generator/asm/amd64/build.go            |  15 +-
 .../generator/asm/amd64/element_butterfly.go  |  15 +-
 field/generator/asm/amd64/element_frommont.go |  17 +-
 field/generator/asm/amd64/element_mul.go      |  19 +-
 .../asm/amd64/element_mul_constants.go        |  15 +-
 field/generator/asm/amd64/element_reduce.go   |  15 +-
 field/generator/asm/amd64/element_vec.go      |  15 +-
 field/generator/asm/arm64/element_mul.go      |  15 +-
 field/generator/config/field_config.go        |  15 +-
 field/generator/generator_test.go             |  15 +-
 field/goff/cmd/errors.go                      |  15 +-
 field/goff/cmd/root.go                        |  15 +-
 field/goff/cmd/version.go                     |  15 +-
 field/goff/main.go                            |  15 +-
 field/goldilocks/arith.go                     |   2 +-
 field/goldilocks/doc.go                       |   2 +-
 field/goldilocks/element.go                   |   2 +-
 field/goldilocks/element_exp.go               |   2 +-
 field/goldilocks/element_purego.go            |   2 +-
 field/goldilocks/element_test.go              |   2 +-
 field/goldilocks/vector.go                    |   2 +-
 field/goldilocks/vector_purego.go             |   2 +-
 field/goldilocks/vector_test.go               |   2 +-
 field/koalabear/arith.go                      |  15 +-
 field/koalabear/doc.go                        |   2 +-
 field/koalabear/element.go                    |   2 +-
 field/koalabear/element_exp.go                |   2 +-
 field/koalabear/element_purego.go             |   2 +-
 field/koalabear/element_test.go               |   2 +-
 field/koalabear/vector.go                     |   2 +-
 field/koalabear/vector_purego.go              |   2 +-
 field/koalabear/vector_test.go                |   2 +-
 field/pool/pool.go                            |   2 +-
 go.mod                                        |   2 +-
 go.sum                                        |   4 +-
 hash/hashes.go                                |  15 +-
 .../ecc/template/multiexp_affine.go.tmpl      |   2 +-
 .../generator/gkr/template/gkr.test.go.tmpl   |   2 +-
 internal/generator/gkr/test_vectors/main.go   |   2 +-
 .../pedersen/template/pedersen.go.tmpl        |  10 +-
 .../small_rational/gkr/gkr.go                 |   2 +-
 .../small_rational/polynomial/doc.go          |   2 +-
 .../small_rational/polynomial/multilin.go     |   2 +-
 .../small_rational/polynomial/polynomial.go   |   2 +-
 .../small_rational/polynomial/pool.go         |   2 +-
 .../small_rational/sumcheck/sumcheck.go       |   2 +-
 .../small_rational/sumcheck/sumcheck_test.go  |   2 +-
 .../test_vector_utils/test_vector_utils.go    |   2 +-
 internal/generator/tower/asm/amd64/e2.go      |  17 +-
 .../generator/tower/asm/amd64/e2_bls381.go    |  15 +-
 .../generator/tower/asm/amd64/e2_bn254.go     |  15 +-
 signature/ecdsa/ecdsa.go                      |  17 +-
 signature/eddsa/eddsa.go                      |  17 +-
 signature/signature.go                        |  17 +-
 1178 files changed, 1720 insertions(+), 2944 deletions(-)

diff --git a/.chglog/config.yml b/.chglog/config.yml
index 2df0aa33e7..bce9ec4957 100755
--- a/.chglog/config.yml
+++ b/.chglog/config.yml
@@ -2,7 +2,7 @@ style: github
 template: CHANGELOG.tpl.md
 info:
   title: CHANGELOG
-  repository_url: https://github.com/ConsenSys/gnark-crypto
+  repository_url: https://github.com/Consensys/gnark-crypto
 options:
   commits:
     # filters:
diff --git a/CHANGELOG.md b/CHANGELOG.md
index 50700990dc..9cfa5d42ad 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,13 +1,13 @@
 <a name="v0.14.0"></a>
 ## [v0.14.0] - 2024-09-03
 ### Build
-- update runner and go version ([#531](https://github.com/ConsenSys/gnark-crypto/issues/531))
+- update runner and go version ([#531](https://github.com/Consensys/gnark-crypto/issues/531))
 - generify g2.go changes
 - generify pedersen_test.go changes
 - generify pedersen.go changes
 
 ### Chore
-- fix some function names ([#526](https://github.com/ConsenSys/gnark-crypto/issues/526))
+- fix some function names ([#526](https://github.com/Consensys/gnark-crypto/issues/526))
 - go generate
 - go generate
 - go generate
@@ -32,11 +32,11 @@
 - pedersen batch verify bn254
 
 ### Fix
-- fixes [#522](https://github.com/ConsenSys/gnark-crypto/issues/522) with bound check before computing twiddles when domain has no precompute set ([#523](https://github.com/ConsenSys/gnark-crypto/issues/523))
+- fixes [#522](https://github.com/Consensys/gnark-crypto/issues/522) with bound check before computing twiddles when domain has no precompute set ([#523](https://github.com/Consensys/gnark-crypto/issues/523))
 - resolve conflict around kzg
 
 ### Perf
-- remove uneeded bucket init in affine coordinates fixes [#529](https://github.com/ConsenSys/gnark-crypto/issues/529) ([#530](https://github.com/ConsenSys/gnark-crypto/issues/530))
+- remove uneeded bucket init in affine coordinates fixes [#529](https://github.com/Consensys/gnark-crypto/issues/529) ([#530](https://github.com/Consensys/gnark-crypto/issues/530))
 
 ### Refactor
 - variable name
@@ -49,10 +49,10 @@
 - fix example test
 
 ### Pull Requests
-- Merge pull request [#524](https://github.com/ConsenSys/gnark-crypto/issues/524) from Consensys/refactor/bls12-MillerLoopFixed
-- Merge pull request [#527](https://github.com/ConsenSys/gnark-crypto/issues/527) from Consensys/feat/pedersen-batchmultivk
-- Merge pull request [#517](https://github.com/ConsenSys/gnark-crypto/issues/517) from Consensys/feat/pedersen-batch-verify
-- Merge pull request [#511](https://github.com/ConsenSys/gnark-crypto/issues/511) from Consensys/docs/up-comments
+- Merge pull request [#524](https://github.com/Consensys/gnark-crypto/issues/524) from Consensys/refactor/bls12-MillerLoopFixed
+- Merge pull request [#527](https://github.com/Consensys/gnark-crypto/issues/527) from Consensys/feat/pedersen-batchmultivk
+- Merge pull request [#517](https://github.com/Consensys/gnark-crypto/issues/517) from Consensys/feat/pedersen-batch-verify
+- Merge pull request [#511](https://github.com/Consensys/gnark-crypto/issues/511) from Consensys/docs/up-comments
 
 
 <a name="v0.13.0"></a>
@@ -62,20 +62,20 @@
 - go generate
 - make recoverP internal
 - go generate
-- **deps:** bump golang.org/x/crypto from 0.10.0 to 0.17.0 ([#473](https://github.com/ConsenSys/gnark-crypto/issues/473))
+- **deps:** bump golang.org/x/crypto from 0.10.0 to 0.17.0 ([#473](https://github.com/Consensys/gnark-crypto/issues/473))
 
 ### Ci
 - new attempt to fix push to master workflow
 - grmpppf
 - add missing message field
 - use runner.os
-- update ci workflows ([#460](https://github.com/ConsenSys/gnark-crypto/issues/460))
+- update ci workflows ([#460](https://github.com/Consensys/gnark-crypto/issues/460))
 
 ### Doc
-- update hash to curve rfc ref and impl comment ([#478](https://github.com/ConsenSys/gnark-crypto/issues/478))
+- update hash to curve rfc ref and impl comment ([#478](https://github.com/Consensys/gnark-crypto/issues/478))
 
 ### Docs
-- describe length extension attack for MiMC hash function. ([#520](https://github.com/ConsenSys/gnark-crypto/issues/520))
+- describe length extension attack for MiMC hash function. ([#520](https://github.com/Consensys/gnark-crypto/issues/520))
 - fix misspelled comment
 - skipping inf points in PairFixedQ is implicit
 - **ecc:** add comment in IsOnCurve()
@@ -85,12 +85,12 @@
 - mathfmt doc
 - added some docs
 - fixed comment, GenFrStar -> GeneratorFullMultiplicativeGroup
-- adds byteorder option in mimc `New`  ([#480](https://github.com/ConsenSys/gnark-crypto/issues/480))
-- allow hashing Fiat-Shamir transcript challenge without hashing to field first ([#474](https://github.com/ConsenSys/gnark-crypto/issues/474))
+- adds byteorder option in mimc `New`  ([#480](https://github.com/Consensys/gnark-crypto/issues/480))
+- allow hashing Fiat-Shamir transcript challenge without hashing to field first ([#474](https://github.com/Consensys/gnark-crypto/issues/474))
 - kzg.SRS implements UnsafeReadFrom
 - added missing WriteRawTo method for kzg.SRS
 - added ecc.IDFromString() method
-- wrap existing hash-to-field for implementing hash.Hash interface ([#464](https://github.com/ConsenSys/gnark-crypto/issues/464))
+- wrap existing hash-to-field for implementing hash.Hash interface ([#464](https://github.com/Consensys/gnark-crypto/issues/464))
 - quick SRS is now balanced
 - code gen for quick srs
 - avoid batch scalar mul when alpha=1 bn254
@@ -100,18 +100,18 @@
 - sis limb-decomposition works with log-two_bound > 8
 - fixed typo
 - template fix
-- fixes [#491](https://github.com/ConsenSys/gnark-crypto/issues/491)
-- gkr add gate evaluate ([#490](https://github.com/ConsenSys/gnark-crypto/issues/490))
-- handle edge case where provided domain cardinality is 1 ([#454](https://github.com/ConsenSys/gnark-crypto/issues/454))
+- fixes [#491](https://github.com/Consensys/gnark-crypto/issues/491)
+- gkr add gate evaluate ([#490](https://github.com/Consensys/gnark-crypto/issues/490))
+- handle edge case where provided domain cardinality is 1 ([#454](https://github.com/Consensys/gnark-crypto/issues/454))
 - kzg template for bn254
 - remove duplicate gkr template generation
-- **bandersnatch:** GLV bounds + test ([#516](https://github.com/ConsenSys/gnark-crypto/issues/516))
+- **bandersnatch:** GLV bounds + test ([#516](https://github.com/Consensys/gnark-crypto/issues/516))
 - **kzg:** bw6-633 vk marshal
 
 ### Perf
 - batchInvert 1/P.Y in fixed-arg pairing
-- unsafe.WriteSlice ([#501](https://github.com/ConsenSys/gnark-crypto/issues/501)) ([#503](https://github.com/ConsenSys/gnark-crypto/issues/503))
-- add kzg.UnsafeToBytes and kzg.UnsafeFromBytes methods ([#499](https://github.com/ConsenSys/gnark-crypto/issues/499))
+- unsafe.WriteSlice ([#501](https://github.com/Consensys/gnark-crypto/issues/501)) ([#503](https://github.com/Consensys/gnark-crypto/issues/503))
+- add kzg.UnsafeToBytes and kzg.UnsafeFromBytes methods ([#499](https://github.com/Consensys/gnark-crypto/issues/499))
 - specialize mul by affine lines
 - **bls12-377:** precomuting lines in pairing in affine
 - **bls12-377:** use precomputed affine lines in kzg
@@ -147,10 +147,10 @@
 
 ### Refactor
 - remove G1 from KZG verifiying key
-- move test util package into isolated one ([#500](https://github.com/ConsenSys/gnark-crypto/issues/500))
+- move test util package into isolated one ([#500](https://github.com/Consensys/gnark-crypto/issues/500))
 - remove dead ScalarMultiplicationAffine
-- make pedersen vk fields public ([#488](https://github.com/ConsenSys/gnark-crypto/issues/488))
-- kzg srs template ([#475](https://github.com/ConsenSys/gnark-crypto/issues/475))
+- make pedersen vk fields public ([#488](https://github.com/Consensys/gnark-crypto/issues/488))
+- kzg srs template ([#475](https://github.com/Consensys/gnark-crypto/issues/475))
 - re-introduce points in KZG verification key
 - apply code review suggestions
 - consolidate fixed-argument pairing across curves
@@ -169,29 +169,29 @@
 - **ecc:** benchmark affine ops
 
 ### Pull Requests
-- Merge pull request [#518](https://github.com/ConsenSys/gnark-crypto/issues/518) from Consensys/fix/flaky-fri-test
-- Merge pull request [#506](https://github.com/ConsenSys/gnark-crypto/issues/506) from Consensys/perf/affine-pairing
-- Merge pull request [#514](https://github.com/ConsenSys/gnark-crypto/issues/514) from Consensys/refactor/bw6-conj
-- Merge pull request [#512](https://github.com/ConsenSys/gnark-crypto/issues/512) from Consensys/fix/sis-issue-when-logTwoBound-larger-than-8
-- Merge pull request [#493](https://github.com/ConsenSys/gnark-crypto/issues/493) from Consensys/perf/kzg-verify
-- Merge pull request [#510](https://github.com/ConsenSys/gnark-crypto/issues/510) from Consensys/perf/faster-affine-arithmetic
-- Merge pull request [#509](https://github.com/ConsenSys/gnark-crypto/issues/509) from Consensys/perf/affine-arithmetic
-- Merge pull request [#497](https://github.com/ConsenSys/gnark-crypto/issues/497) from Consensys/feat/ecdsa-errors
-- Merge pull request [#496](https://github.com/ConsenSys/gnark-crypto/issues/496) from Consensys/sis/export-fft64
-- Merge pull request [#492](https://github.com/ConsenSys/gnark-crypto/issues/492) from Consensys/feat/gen_fr_star
-- Merge pull request [#487](https://github.com/ConsenSys/gnark-crypto/issues/487) from Consensys/perf/IsOnCurve
-- Merge pull request [#469](https://github.com/ConsenSys/gnark-crypto/issues/469) from Consensys/kzg/srs-vk
-- Merge pull request [#466](https://github.com/ConsenSys/gnark-crypto/issues/466) from Consensys/kzg/srs
-- Merge pull request [#439](https://github.com/ConsenSys/gnark-crypto/issues/439) from Consensys/fix/duplicate-gkr-gen
-- Merge pull request [#465](https://github.com/ConsenSys/gnark-crypto/issues/465) from Consensys/refactor/bw6761-pairing
-- Merge pull request [#459](https://github.com/ConsenSys/gnark-crypto/issues/459) from Consensys/perf/bw6-finalExp
-- Merge pull request [#458](https://github.com/ConsenSys/gnark-crypto/issues/458) from Consensys/feat/kzg_dummy_srs
+- Merge pull request [#518](https://github.com/Consensys/gnark-crypto/issues/518) from Consensys/fix/flaky-fri-test
+- Merge pull request [#506](https://github.com/Consensys/gnark-crypto/issues/506) from Consensys/perf/affine-pairing
+- Merge pull request [#514](https://github.com/Consensys/gnark-crypto/issues/514) from Consensys/refactor/bw6-conj
+- Merge pull request [#512](https://github.com/Consensys/gnark-crypto/issues/512) from Consensys/fix/sis-issue-when-logTwoBound-larger-than-8
+- Merge pull request [#493](https://github.com/Consensys/gnark-crypto/issues/493) from Consensys/perf/kzg-verify
+- Merge pull request [#510](https://github.com/Consensys/gnark-crypto/issues/510) from Consensys/perf/faster-affine-arithmetic
+- Merge pull request [#509](https://github.com/Consensys/gnark-crypto/issues/509) from Consensys/perf/affine-arithmetic
+- Merge pull request [#497](https://github.com/Consensys/gnark-crypto/issues/497) from Consensys/feat/ecdsa-errors
+- Merge pull request [#496](https://github.com/Consensys/gnark-crypto/issues/496) from Consensys/sis/export-fft64
+- Merge pull request [#492](https://github.com/Consensys/gnark-crypto/issues/492) from Consensys/feat/gen_fr_star
+- Merge pull request [#487](https://github.com/Consensys/gnark-crypto/issues/487) from Consensys/perf/IsOnCurve
+- Merge pull request [#469](https://github.com/Consensys/gnark-crypto/issues/469) from Consensys/kzg/srs-vk
+- Merge pull request [#466](https://github.com/Consensys/gnark-crypto/issues/466) from Consensys/kzg/srs
+- Merge pull request [#439](https://github.com/Consensys/gnark-crypto/issues/439) from Consensys/fix/duplicate-gkr-gen
+- Merge pull request [#465](https://github.com/Consensys/gnark-crypto/issues/465) from Consensys/refactor/bw6761-pairing
+- Merge pull request [#459](https://github.com/Consensys/gnark-crypto/issues/459) from Consensys/perf/bw6-finalExp
+- Merge pull request [#458](https://github.com/Consensys/gnark-crypto/issues/458) from Consensys/feat/kzg_dummy_srs
 
 
 <a name="v0.12.1"></a>
 ## [v0.12.1] - 2023-10-05
 ### Clean
-- remove useless snippet in mulWindowed ([#453](https://github.com/ConsenSys/gnark-crypto/issues/453))
+- remove useless snippet in mulWindowed ([#453](https://github.com/Consensys/gnark-crypto/issues/453))
 
 ### Ecc
 - fix neutral elements cases
@@ -214,11 +214,11 @@
 - fixed ExpGLV in GT
 
 ### Perf
-- **fft:** introduce cache efficient bit reverse shuffling ([#446](https://github.com/ConsenSys/gnark-crypto/issues/446))
+- **fft:** introduce cache efficient bit reverse shuffling ([#446](https://github.com/Consensys/gnark-crypto/issues/446))
 
 ### Pull Requests
-- Merge pull request [#451](https://github.com/ConsenSys/gnark-crypto/issues/451) from Consensys/fix/glv
-- Merge pull request [#450](https://github.com/ConsenSys/gnark-crypto/issues/450) from jsign/jsign-eq-improv
+- Merge pull request [#451](https://github.com/Consensys/gnark-crypto/issues/451) from Consensys/fix/glv
+- Merge pull request [#450](https://github.com/Consensys/gnark-crypto/issues/450) from jsign/jsign-eq-improv
 
 
 <a name="v0.12.0"></a>
@@ -235,10 +235,10 @@
 - remove extra file
 
 ### Ci
-- update ci workflows ([#447](https://github.com/ConsenSys/gnark-crypto/issues/447))
+- update ci workflows ([#447](https://github.com/Consensys/gnark-crypto/issues/447))
 
 ### Edwards
-- improve the performance of Add, MixedAdd and IsOnCurve ([#441](https://github.com/ConsenSys/gnark-crypto/issues/441))
+- improve the performance of Add, MixedAdd and IsOnCurve ([#441](https://github.com/Consensys/gnark-crypto/issues/441))
 
 ### Feat
 - delete playground
@@ -256,7 +256,7 @@
 - fixed ambiguous unmarshalling eddsa
 
 ### Multiexp
-- avoid direct coordinate access to check for zero points ([#414](https://github.com/ConsenSys/gnark-crypto/issues/414))
+- avoid direct coordinate access to check for zero points ([#414](https://github.com/Consensys/gnark-crypto/issues/414))
 
 ### Refactor
 - make marshal errors private
@@ -267,8 +267,8 @@
 - implement malleability tests as subtests
 
 ### Pull Requests
-- Merge pull request [#449](https://github.com/ConsenSys/gnark-crypto/issues/449) from Consensys/fix/malleability_sig
-- Merge pull request [#442](https://github.com/ConsenSys/gnark-crypto/issues/442) from jsign/jsign-edwards-extended
+- Merge pull request [#449](https://github.com/Consensys/gnark-crypto/issues/449) from Consensys/fix/malleability_sig
+- Merge pull request [#442](https://github.com/Consensys/gnark-crypto/issues/442) from jsign/jsign-edwards-extended
 
 
 <a name="v0.11.2"></a>
@@ -295,7 +295,7 @@
 - PR feedback
 
 ### Docs
-- ConsenSys -> Consensys ([#406](https://github.com/ConsenSys/gnark-crypto/issues/406))
+- ConsenSys -> Consensys ([#406](https://github.com/Consensys/gnark-crypto/issues/406))
 - explain FoldCommitments
 - make comments more godoc friendly
 - remove comment
@@ -305,13 +305,13 @@
 - **pairing:** add comments
 
 ### Edwards
-- optimize point negation ([#413](https://github.com/ConsenSys/gnark-crypto/issues/413))
+- optimize point negation ([#413](https://github.com/Consensys/gnark-crypto/issues/413))
 
 ### Feat
 - add Double in affine coordinates
 - experiment parallel sis
-- add AsyncReadFrom to fr.Vector and fft.Domain ([#424](https://github.com/ConsenSys/gnark-crypto/issues/424))
-- added WriteRawTo to kzg.ProvingKey ([#422](https://github.com/ConsenSys/gnark-crypto/issues/422))
+- add AsyncReadFrom to fr.Vector and fft.Domain ([#424](https://github.com/Consensys/gnark-crypto/issues/424))
+- added WriteRawTo to kzg.ProvingKey ([#422](https://github.com/Consensys/gnark-crypto/issues/422))
 - more gkr gates
 - Gates var for bn254
 - added size accessor on poly
@@ -321,14 +321,14 @@
 - pedersen(bn254).WriteRawTo
 - fold 0 proofs edge case
 - pedersen folding proofs
-- Marshal [][]fr.Element ([#400](https://github.com/ConsenSys/gnark-crypto/issues/400))
+- Marshal [][]fr.Element ([#400](https://github.com/Consensys/gnark-crypto/issues/400))
 - restored fp, fr, etc
 - added polynomial.SetSize
-- added element.Unmarshal closes [#348](https://github.com/ConsenSys/gnark-crypto/issues/348)
+- added element.Unmarshal closes [#348](https://github.com/Consensys/gnark-crypto/issues/348)
 - kzg.Vk.WriteRawTo
 - bn254 encoder to support uint64 slices
-- fix v computation in ECDSA signature ([#385](https://github.com/ConsenSys/gnark-crypto/issues/385))
-- add ECDSA public key recover from message, signature and recovery info ([#347](https://github.com/ConsenSys/gnark-crypto/issues/347))
+- fix v computation in ECDSA signature ([#385](https://github.com/Consensys/gnark-crypto/issues/385))
+- add ECDSA public key recover from message, signature and recovery info ([#347](https://github.com/Consensys/gnark-crypto/issues/347))
 - added comment for bitAt function
 - added sis.py
 - add reference test
@@ -337,7 +337,7 @@
 - added fft.WithNbTasks
 - FFT signature now takes an option variadic
 - expose NaiveMulMod for gnark
-- make `mapToCurve` public to allow for custom cofactor clearing ([#372](https://github.com/ConsenSys/gnark-crypto/issues/372))
+- make `mapToCurve` public to allow for custom cofactor clearing ([#372](https://github.com/Consensys/gnark-crypto/issues/372))
 - restored latest fft
 - **pairing:** return 1 after easy part if result is 1
 
@@ -348,14 +348,14 @@
 - dont use internal package in vector.go
 - import utils
 - remove redundant mulGate
-- incorrect semaphore initialization ([#411](https://github.com/ConsenSys/gnark-crypto/issues/411))
+- incorrect semaphore initialization ([#411](https://github.com/Consensys/gnark-crypto/issues/411))
 - don't ignore multiexp error
 - pedersen folding bug
 - more innef assign
 - innef assignment in test
 - handle all bitmask in point deserialization
-- ECDSA HashToInt bytes-bits mismatch ([#428](https://github.com/ConsenSys/gnark-crypto/issues/428))
-- ECDSA HashToInt bytes-bits mismatch ([#428](https://github.com/ConsenSys/gnark-crypto/issues/428))
+- ECDSA HashToInt bytes-bits mismatch ([#428](https://github.com/Consensys/gnark-crypto/issues/428))
+- ECDSA HashToInt bytes-bits mismatch ([#428](https://github.com/Consensys/gnark-crypto/issues/428))
 - do not read empty slices as nil
 - minor errors
 - generation mistake
@@ -369,7 +369,7 @@
 - **linter:** ineffassign in Fpk marshal
 
 ### Msm
-- semaphore to limit CPUs + better split strategy (up to 25% perf boost on 96cores) ([#403](https://github.com/ConsenSys/gnark-crypto/issues/403))
+- semaphore to limit CPUs + better split strategy (up to 25% perf boost on 96cores) ([#403](https://github.com/Consensys/gnark-crypto/issues/403))
 
 ### Perf
 - experiment without memcopy not great
@@ -378,11 +378,11 @@
 - kept the fastest method for sis
 - minor optim in iop package
 - 3 muls instead of 4 sis
-- small memory alloc optimization ([#435](https://github.com/ConsenSys/gnark-crypto/issues/435))
-- dont waste too much memory in fft domain ([#437](https://github.com/ConsenSys/gnark-crypto/issues/437))
+- small memory alloc optimization ([#435](https://github.com/Consensys/gnark-crypto/issues/435))
+- dont waste too much memory in fft domain ([#437](https://github.com/Consensys/gnark-crypto/issues/437))
 - fix todo with small domain path
 - use bitset in batch invert
-- fast path for SIS with logTwoBound: 8, logTwoDegree: 6 ([#416](https://github.com/ConsenSys/gnark-crypto/issues/416))
+- fast path for SIS with logTwoBound: 8, logTwoDegree: 6 ([#416](https://github.com/Consensys/gnark-crypto/issues/416))
 - optimized sis
 - less memallocs, check for zeroes
 - faster init + simplify bit processing loop
@@ -439,40 +439,40 @@
 - still good
 
 ### Pull Requests
-- Merge pull request [#438](https://github.com/ConsenSys/gnark-crypto/issues/438) from Consensys/develop
-- Merge pull request [#429](https://github.com/ConsenSys/gnark-crypto/issues/429) from Consensys/release/v0.11.1
-- Merge pull request [#419](https://github.com/ConsenSys/gnark-crypto/issues/419) from Consensys/feat/gkr-custom-gates
-- Merge pull request [#410](https://github.com/ConsenSys/gnark-crypto/issues/410) from ConsenSys/fix/decode-empty-slice
-- Merge pull request [#407](https://github.com/ConsenSys/gnark-crypto/issues/407) from ConsenSys/feat/fold-pedersen
-- Merge pull request [#391](https://github.com/ConsenSys/gnark-crypto/issues/391) from ConsenSys/develop
-- Merge pull request [#386](https://github.com/ConsenSys/gnark-crypto/issues/386) from ConsenSys/perf/kzg-verify
-- Merge pull request [#384](https://github.com/ConsenSys/gnark-crypto/issues/384) from ConsenSys/refactor/break-pedersen-notowermod
-- Merge pull request [#379](https://github.com/ConsenSys/gnark-crypto/issues/379) from ConsenSys/feat/encode-uint64-slices
-- Merge pull request [#378](https://github.com/ConsenSys/gnark-crypto/issues/378) from ConsenSys/refactor/break-kzg-srs
-- Merge pull request [#382](https://github.com/ConsenSys/gnark-crypto/issues/382) from ConsenSys/refactor/not-export-endo
-- Merge pull request [#380](https://github.com/ConsenSys/gnark-crypto/issues/380) from omerfirmak/elim-pedersen-alloc
-- Merge pull request [#374](https://github.com/ConsenSys/gnark-crypto/issues/374) from ConsenSys/fix/BatchVerifyMultiPoints-0
-- Merge pull request [#376](https://github.com/ConsenSys/gnark-crypto/issues/376) from ConsenSys/refactor/export-endo
-- Merge pull request [#375](https://github.com/ConsenSys/gnark-crypto/issues/375) from ConsenSys/refactor/FinalExp
-- Merge pull request [#377](https://github.com/ConsenSys/gnark-crypto/issues/377) from ConsenSys/fix/fold-kzg-fs
-- Merge pull request [#371](https://github.com/ConsenSys/gnark-crypto/issues/371) from omerfirmak/elim-pedersen-alloc
-- Merge pull request [#369](https://github.com/ConsenSys/gnark-crypto/issues/369) from ConsenSys/build/updateci
-- Merge pull request [#368](https://github.com/ConsenSys/gnark-crypto/issues/368) from ConsenSys/develop
-- Merge pull request [#366](https://github.com/ConsenSys/gnark-crypto/issues/366) from ConsenSys/refactor/pairings
-- Merge pull request [#365](https://github.com/ConsenSys/gnark-crypto/issues/365) from ConsenSys/fix/gentime-field-bugs
-- Merge pull request [#364](https://github.com/ConsenSys/gnark-crypto/issues/364) from jtraglia/update-tested-go-versions
-- Merge pull request [#363](https://github.com/ConsenSys/gnark-crypto/issues/363) from ConsenSys/fix/infencoding
-- Merge pull request [#361](https://github.com/ConsenSys/gnark-crypto/issues/361) from ConsenSys/perf/plonk
-- Merge pull request [#360](https://github.com/ConsenSys/gnark-crypto/issues/360) from ConsenSys/bls12381-tower-gnark
-- Merge pull request [#359](https://github.com/ConsenSys/gnark-crypto/issues/359) from SherLzp/develop
-- Merge pull request [#356](https://github.com/ConsenSys/gnark-crypto/issues/356) from ConsenSys/perf/bn24317-FinalExp
-- Merge pull request [#354](https://github.com/ConsenSys/gnark-crypto/issues/354) from ConsenSys/bn254-tower-gnark
-- Merge pull request [#351](https://github.com/ConsenSys/gnark-crypto/issues/351) from ConsenSys/perf/bw6-756/GT-subgroup-check
-- Merge pull request [#349](https://github.com/ConsenSys/gnark-crypto/issues/349) from ConsenSys/perf/subgroup-check-stark
-- Merge pull request [#344](https://github.com/ConsenSys/gnark-crypto/issues/344) from ConsenSys/perf/tensor-commitment
-- Merge pull request [#345](https://github.com/ConsenSys/gnark-crypto/issues/345) from ConsenSys/feat/fftopt
-- Merge pull request [#263](https://github.com/ConsenSys/gnark-crypto/issues/263) from AlexandreBelling/perf/tensor-commitment
-- Merge pull request [#260](https://github.com/ConsenSys/gnark-crypto/issues/260) from AlexandreBelling/experimental/tensor-commitment
+- Merge pull request [#438](https://github.com/Consensys/gnark-crypto/issues/438) from Consensys/develop
+- Merge pull request [#429](https://github.com/Consensys/gnark-crypto/issues/429) from Consensys/release/v0.11.1
+- Merge pull request [#419](https://github.com/Consensys/gnark-crypto/issues/419) from Consensys/feat/gkr-custom-gates
+- Merge pull request [#410](https://github.com/Consensys/gnark-crypto/issues/410) from ConsenSys/fix/decode-empty-slice
+- Merge pull request [#407](https://github.com/Consensys/gnark-crypto/issues/407) from ConsenSys/feat/fold-pedersen
+- Merge pull request [#391](https://github.com/Consensys/gnark-crypto/issues/391) from ConsenSys/develop
+- Merge pull request [#386](https://github.com/Consensys/gnark-crypto/issues/386) from ConsenSys/perf/kzg-verify
+- Merge pull request [#384](https://github.com/Consensys/gnark-crypto/issues/384) from ConsenSys/refactor/break-pedersen-notowermod
+- Merge pull request [#379](https://github.com/Consensys/gnark-crypto/issues/379) from ConsenSys/feat/encode-uint64-slices
+- Merge pull request [#378](https://github.com/Consensys/gnark-crypto/issues/378) from ConsenSys/refactor/break-kzg-srs
+- Merge pull request [#382](https://github.com/Consensys/gnark-crypto/issues/382) from ConsenSys/refactor/not-export-endo
+- Merge pull request [#380](https://github.com/Consensys/gnark-crypto/issues/380) from omerfirmak/elim-pedersen-alloc
+- Merge pull request [#374](https://github.com/Consensys/gnark-crypto/issues/374) from ConsenSys/fix/BatchVerifyMultiPoints-0
+- Merge pull request [#376](https://github.com/Consensys/gnark-crypto/issues/376) from ConsenSys/refactor/export-endo
+- Merge pull request [#375](https://github.com/Consensys/gnark-crypto/issues/375) from ConsenSys/refactor/FinalExp
+- Merge pull request [#377](https://github.com/Consensys/gnark-crypto/issues/377) from ConsenSys/fix/fold-kzg-fs
+- Merge pull request [#371](https://github.com/Consensys/gnark-crypto/issues/371) from omerfirmak/elim-pedersen-alloc
+- Merge pull request [#369](https://github.com/Consensys/gnark-crypto/issues/369) from ConsenSys/build/updateci
+- Merge pull request [#368](https://github.com/Consensys/gnark-crypto/issues/368) from ConsenSys/develop
+- Merge pull request [#366](https://github.com/Consensys/gnark-crypto/issues/366) from ConsenSys/refactor/pairings
+- Merge pull request [#365](https://github.com/Consensys/gnark-crypto/issues/365) from ConsenSys/fix/gentime-field-bugs
+- Merge pull request [#364](https://github.com/Consensys/gnark-crypto/issues/364) from jtraglia/update-tested-go-versions
+- Merge pull request [#363](https://github.com/Consensys/gnark-crypto/issues/363) from ConsenSys/fix/infencoding
+- Merge pull request [#361](https://github.com/Consensys/gnark-crypto/issues/361) from ConsenSys/perf/plonk
+- Merge pull request [#360](https://github.com/Consensys/gnark-crypto/issues/360) from ConsenSys/bls12381-tower-gnark
+- Merge pull request [#359](https://github.com/Consensys/gnark-crypto/issues/359) from SherLzp/develop
+- Merge pull request [#356](https://github.com/Consensys/gnark-crypto/issues/356) from ConsenSys/perf/bn24317-FinalExp
+- Merge pull request [#354](https://github.com/Consensys/gnark-crypto/issues/354) from ConsenSys/bn254-tower-gnark
+- Merge pull request [#351](https://github.com/Consensys/gnark-crypto/issues/351) from ConsenSys/perf/bw6-756/GT-subgroup-check
+- Merge pull request [#349](https://github.com/Consensys/gnark-crypto/issues/349) from ConsenSys/perf/subgroup-check-stark
+- Merge pull request [#344](https://github.com/Consensys/gnark-crypto/issues/344) from ConsenSys/perf/tensor-commitment
+- Merge pull request [#345](https://github.com/Consensys/gnark-crypto/issues/345) from ConsenSys/feat/fftopt
+- Merge pull request [#263](https://github.com/Consensys/gnark-crypto/issues/263) from AlexandreBelling/perf/tensor-commitment
+- Merge pull request [#260](https://github.com/Consensys/gnark-crypto/issues/260) from AlexandreBelling/experimental/tensor-commitment
 
 
 <a name="v0.9.2"></a>
@@ -481,7 +481,7 @@
 - update CHANGELOG
 
 ### Fix
-- ECDSA HashToInt bytes-bits mismatch ([#428](https://github.com/ConsenSys/gnark-crypto/issues/428))
+- ECDSA HashToInt bytes-bits mismatch ([#428](https://github.com/Consensys/gnark-crypto/issues/428))
 
 
 <a name="v0.11.1"></a>
@@ -505,15 +505,15 @@
 - remove DO NOT EDIT from non-autogenerated files
 
 ### Feat
-- fix v computation in ECDSA signature ([#385](https://github.com/ConsenSys/gnark-crypto/issues/385))
-- make `mapToCurve` public to allow for custom cofactor clearing ([#372](https://github.com/ConsenSys/gnark-crypto/issues/372))
+- fix v computation in ECDSA signature ([#385](https://github.com/Consensys/gnark-crypto/issues/385))
+- make `mapToCurve` public to allow for custom cofactor clearing ([#372](https://github.com/Consensys/gnark-crypto/issues/372))
 - add Double in affine coordinates
 - kzg.Vk.WriteRawTo
 - bn254 encoder to support uint64 slices
 - **pairing:** return 1 after easy part if result is 1
 
 ### Fix
-- ECDSA HashToInt bytes-bits mismatch ([#428](https://github.com/ConsenSys/gnark-crypto/issues/428))
+- ECDSA HashToInt bytes-bits mismatch ([#428](https://github.com/Consensys/gnark-crypto/issues/428))
 - handle all bitmask in point deserialization
 - littleEndian -> bigEndian
 - import utils
@@ -551,20 +551,20 @@
 - no loop when serializing one object only
 
 ### Pull Requests
-- Merge pull request [#429](https://github.com/ConsenSys/gnark-crypto/issues/429) from Consensys/release/v0.11.1
-- Merge pull request [#391](https://github.com/ConsenSys/gnark-crypto/issues/391) from ConsenSys/develop
-- Merge pull request [#386](https://github.com/ConsenSys/gnark-crypto/issues/386) from ConsenSys/perf/kzg-verify
-- Merge pull request [#384](https://github.com/ConsenSys/gnark-crypto/issues/384) from ConsenSys/refactor/break-pedersen-notowermod
-- Merge pull request [#379](https://github.com/ConsenSys/gnark-crypto/issues/379) from ConsenSys/feat/encode-uint64-slices
-- Merge pull request [#378](https://github.com/ConsenSys/gnark-crypto/issues/378) from ConsenSys/refactor/break-kzg-srs
-- Merge pull request [#382](https://github.com/ConsenSys/gnark-crypto/issues/382) from ConsenSys/refactor/not-export-endo
-- Merge pull request [#380](https://github.com/ConsenSys/gnark-crypto/issues/380) from omerfirmak/elim-pedersen-alloc
-- Merge pull request [#374](https://github.com/ConsenSys/gnark-crypto/issues/374) from ConsenSys/fix/BatchVerifyMultiPoints-0
-- Merge pull request [#376](https://github.com/ConsenSys/gnark-crypto/issues/376) from ConsenSys/refactor/export-endo
-- Merge pull request [#375](https://github.com/ConsenSys/gnark-crypto/issues/375) from ConsenSys/refactor/FinalExp
-- Merge pull request [#377](https://github.com/ConsenSys/gnark-crypto/issues/377) from ConsenSys/fix/fold-kzg-fs
-- Merge pull request [#371](https://github.com/ConsenSys/gnark-crypto/issues/371) from omerfirmak/elim-pedersen-alloc
-- Merge pull request [#369](https://github.com/ConsenSys/gnark-crypto/issues/369) from ConsenSys/build/updateci
+- Merge pull request [#429](https://github.com/Consensys/gnark-crypto/issues/429) from Consensys/release/v0.11.1
+- Merge pull request [#391](https://github.com/Consensys/gnark-crypto/issues/391) from ConsenSys/develop
+- Merge pull request [#386](https://github.com/Consensys/gnark-crypto/issues/386) from ConsenSys/perf/kzg-verify
+- Merge pull request [#384](https://github.com/Consensys/gnark-crypto/issues/384) from ConsenSys/refactor/break-pedersen-notowermod
+- Merge pull request [#379](https://github.com/Consensys/gnark-crypto/issues/379) from ConsenSys/feat/encode-uint64-slices
+- Merge pull request [#378](https://github.com/Consensys/gnark-crypto/issues/378) from ConsenSys/refactor/break-kzg-srs
+- Merge pull request [#382](https://github.com/Consensys/gnark-crypto/issues/382) from ConsenSys/refactor/not-export-endo
+- Merge pull request [#380](https://github.com/Consensys/gnark-crypto/issues/380) from omerfirmak/elim-pedersen-alloc
+- Merge pull request [#374](https://github.com/Consensys/gnark-crypto/issues/374) from ConsenSys/fix/BatchVerifyMultiPoints-0
+- Merge pull request [#376](https://github.com/Consensys/gnark-crypto/issues/376) from ConsenSys/refactor/export-endo
+- Merge pull request [#375](https://github.com/Consensys/gnark-crypto/issues/375) from ConsenSys/refactor/FinalExp
+- Merge pull request [#377](https://github.com/Consensys/gnark-crypto/issues/377) from ConsenSys/fix/fold-kzg-fs
+- Merge pull request [#371](https://github.com/Consensys/gnark-crypto/issues/371) from omerfirmak/elim-pedersen-alloc
+- Merge pull request [#369](https://github.com/Consensys/gnark-crypto/issues/369) from ConsenSys/build/updateci
 
 
 <a name="v0.10.1"></a>
@@ -573,7 +573,7 @@
 - update CHANGELOG
 
 ### Fix
-- ECDSA HashToInt bytes-bits mismatch ([#428](https://github.com/ConsenSys/gnark-crypto/issues/428))
+- ECDSA HashToInt bytes-bits mismatch ([#428](https://github.com/Consensys/gnark-crypto/issues/428))
 
 
 <a name="v0.11.0"></a>
@@ -596,8 +596,8 @@
 - remove DO NOT EDIT from non-autogenerated files
 
 ### Feat
-- fix v computation in ECDSA signature ([#385](https://github.com/ConsenSys/gnark-crypto/issues/385))
-- make `mapToCurve` public to allow for custom cofactor clearing ([#372](https://github.com/ConsenSys/gnark-crypto/issues/372))
+- fix v computation in ECDSA signature ([#385](https://github.com/Consensys/gnark-crypto/issues/385))
+- make `mapToCurve` public to allow for custom cofactor clearing ([#372](https://github.com/Consensys/gnark-crypto/issues/372))
 - add Double in affine coordinates
 - kzg.Vk.WriteRawTo
 - bn254 encoder to support uint64 slices
@@ -641,19 +641,19 @@
 - no loop when serializing one object only
 
 ### Pull Requests
-- Merge pull request [#391](https://github.com/ConsenSys/gnark-crypto/issues/391) from ConsenSys/develop
-- Merge pull request [#386](https://github.com/ConsenSys/gnark-crypto/issues/386) from ConsenSys/perf/kzg-verify
-- Merge pull request [#384](https://github.com/ConsenSys/gnark-crypto/issues/384) from ConsenSys/refactor/break-pedersen-notowermod
-- Merge pull request [#379](https://github.com/ConsenSys/gnark-crypto/issues/379) from ConsenSys/feat/encode-uint64-slices
-- Merge pull request [#378](https://github.com/ConsenSys/gnark-crypto/issues/378) from ConsenSys/refactor/break-kzg-srs
-- Merge pull request [#382](https://github.com/ConsenSys/gnark-crypto/issues/382) from ConsenSys/refactor/not-export-endo
-- Merge pull request [#380](https://github.com/ConsenSys/gnark-crypto/issues/380) from omerfirmak/elim-pedersen-alloc
-- Merge pull request [#374](https://github.com/ConsenSys/gnark-crypto/issues/374) from ConsenSys/fix/BatchVerifyMultiPoints-0
-- Merge pull request [#376](https://github.com/ConsenSys/gnark-crypto/issues/376) from ConsenSys/refactor/export-endo
-- Merge pull request [#375](https://github.com/ConsenSys/gnark-crypto/issues/375) from ConsenSys/refactor/FinalExp
-- Merge pull request [#377](https://github.com/ConsenSys/gnark-crypto/issues/377) from ConsenSys/fix/fold-kzg-fs
-- Merge pull request [#371](https://github.com/ConsenSys/gnark-crypto/issues/371) from omerfirmak/elim-pedersen-alloc
-- Merge pull request [#369](https://github.com/ConsenSys/gnark-crypto/issues/369) from ConsenSys/build/updateci
+- Merge pull request [#391](https://github.com/Consensys/gnark-crypto/issues/391) from ConsenSys/develop
+- Merge pull request [#386](https://github.com/Consensys/gnark-crypto/issues/386) from ConsenSys/perf/kzg-verify
+- Merge pull request [#384](https://github.com/Consensys/gnark-crypto/issues/384) from ConsenSys/refactor/break-pedersen-notowermod
+- Merge pull request [#379](https://github.com/Consensys/gnark-crypto/issues/379) from ConsenSys/feat/encode-uint64-slices
+- Merge pull request [#378](https://github.com/Consensys/gnark-crypto/issues/378) from ConsenSys/refactor/break-kzg-srs
+- Merge pull request [#382](https://github.com/Consensys/gnark-crypto/issues/382) from ConsenSys/refactor/not-export-endo
+- Merge pull request [#380](https://github.com/Consensys/gnark-crypto/issues/380) from omerfirmak/elim-pedersen-alloc
+- Merge pull request [#374](https://github.com/Consensys/gnark-crypto/issues/374) from ConsenSys/fix/BatchVerifyMultiPoints-0
+- Merge pull request [#376](https://github.com/Consensys/gnark-crypto/issues/376) from ConsenSys/refactor/export-endo
+- Merge pull request [#375](https://github.com/Consensys/gnark-crypto/issues/375) from ConsenSys/refactor/FinalExp
+- Merge pull request [#377](https://github.com/Consensys/gnark-crypto/issues/377) from ConsenSys/fix/fold-kzg-fs
+- Merge pull request [#371](https://github.com/Consensys/gnark-crypto/issues/371) from omerfirmak/elim-pedersen-alloc
+- Merge pull request [#369](https://github.com/Consensys/gnark-crypto/issues/369) from ConsenSys/build/updateci
 
 
 <a name="v0.10.0"></a>
@@ -667,7 +667,7 @@
 - **pairing:** add comments
 
 ### Feat
-- add ECDSA public key recover from message, signature and recovery info ([#347](https://github.com/ConsenSys/gnark-crypto/issues/347))
+- add ECDSA public key recover from message, signature and recovery info ([#347](https://github.com/Consensys/gnark-crypto/issues/347))
 - added comment for bitAt function
 - added sis.py
 - add reference test
@@ -730,22 +730,22 @@
 - still good
 
 ### Pull Requests
-- Merge pull request [#368](https://github.com/ConsenSys/gnark-crypto/issues/368) from ConsenSys/develop
-- Merge pull request [#366](https://github.com/ConsenSys/gnark-crypto/issues/366) from ConsenSys/refactor/pairings
-- Merge pull request [#365](https://github.com/ConsenSys/gnark-crypto/issues/365) from ConsenSys/fix/gentime-field-bugs
-- Merge pull request [#364](https://github.com/ConsenSys/gnark-crypto/issues/364) from jtraglia/update-tested-go-versions
-- Merge pull request [#363](https://github.com/ConsenSys/gnark-crypto/issues/363) from ConsenSys/fix/infencoding
-- Merge pull request [#361](https://github.com/ConsenSys/gnark-crypto/issues/361) from ConsenSys/perf/plonk
-- Merge pull request [#360](https://github.com/ConsenSys/gnark-crypto/issues/360) from ConsenSys/bls12381-tower-gnark
-- Merge pull request [#359](https://github.com/ConsenSys/gnark-crypto/issues/359) from SherLzp/develop
-- Merge pull request [#356](https://github.com/ConsenSys/gnark-crypto/issues/356) from ConsenSys/perf/bn24317-FinalExp
-- Merge pull request [#354](https://github.com/ConsenSys/gnark-crypto/issues/354) from ConsenSys/bn254-tower-gnark
-- Merge pull request [#351](https://github.com/ConsenSys/gnark-crypto/issues/351) from ConsenSys/perf/bw6-756/GT-subgroup-check
-- Merge pull request [#349](https://github.com/ConsenSys/gnark-crypto/issues/349) from ConsenSys/perf/subgroup-check-stark
-- Merge pull request [#344](https://github.com/ConsenSys/gnark-crypto/issues/344) from ConsenSys/perf/tensor-commitment
-- Merge pull request [#345](https://github.com/ConsenSys/gnark-crypto/issues/345) from ConsenSys/feat/fftopt
-- Merge pull request [#263](https://github.com/ConsenSys/gnark-crypto/issues/263) from AlexandreBelling/perf/tensor-commitment
-- Merge pull request [#260](https://github.com/ConsenSys/gnark-crypto/issues/260) from AlexandreBelling/experimental/tensor-commitment
+- Merge pull request [#368](https://github.com/Consensys/gnark-crypto/issues/368) from ConsenSys/develop
+- Merge pull request [#366](https://github.com/Consensys/gnark-crypto/issues/366) from ConsenSys/refactor/pairings
+- Merge pull request [#365](https://github.com/Consensys/gnark-crypto/issues/365) from ConsenSys/fix/gentime-field-bugs
+- Merge pull request [#364](https://github.com/Consensys/gnark-crypto/issues/364) from jtraglia/update-tested-go-versions
+- Merge pull request [#363](https://github.com/Consensys/gnark-crypto/issues/363) from ConsenSys/fix/infencoding
+- Merge pull request [#361](https://github.com/Consensys/gnark-crypto/issues/361) from ConsenSys/perf/plonk
+- Merge pull request [#360](https://github.com/Consensys/gnark-crypto/issues/360) from ConsenSys/bls12381-tower-gnark
+- Merge pull request [#359](https://github.com/Consensys/gnark-crypto/issues/359) from SherLzp/develop
+- Merge pull request [#356](https://github.com/Consensys/gnark-crypto/issues/356) from ConsenSys/perf/bn24317-FinalExp
+- Merge pull request [#354](https://github.com/Consensys/gnark-crypto/issues/354) from ConsenSys/bn254-tower-gnark
+- Merge pull request [#351](https://github.com/Consensys/gnark-crypto/issues/351) from ConsenSys/perf/bw6-756/GT-subgroup-check
+- Merge pull request [#349](https://github.com/Consensys/gnark-crypto/issues/349) from ConsenSys/perf/subgroup-check-stark
+- Merge pull request [#344](https://github.com/Consensys/gnark-crypto/issues/344) from ConsenSys/perf/tensor-commitment
+- Merge pull request [#345](https://github.com/Consensys/gnark-crypto/issues/345) from ConsenSys/feat/fftopt
+- Merge pull request [#263](https://github.com/Consensys/gnark-crypto/issues/263) from AlexandreBelling/perf/tensor-commitment
+- Merge pull request [#260](https://github.com/Consensys/gnark-crypto/issues/260) from AlexandreBelling/experimental/tensor-commitment
 
 
 <a name="v0.9.1"></a>
@@ -783,7 +783,7 @@
 - Merkle tree to panic upon hash write error
 - pedersen_hash added to stark curve
 - signing interface changes and bn254 impl
-- add Vector support to ecc marshal encoder ([#336](https://github.com/ConsenSys/gnark-crypto/issues/336))
+- add Vector support to ecc marshal encoder ([#336](https://github.com/Consensys/gnark-crypto/issues/336))
 - gkr.Circuit.MemoryRequirements
 - can pass workers pool in
 - parallel versions of computing gate inputs
@@ -815,7 +815,7 @@
 - some test generification
 - generify gkr.tmpl
 - edDsa SignFr and VerifyFr
-- nuke element.Bit() closes [#306](https://github.com/ConsenSys/gnark-crypto/issues/306) ([#331](https://github.com/ConsenSys/gnark-crypto/issues/331))
+- nuke element.Bit() closes [#306](https://github.com/Consensys/gnark-crypto/issues/306) ([#331](https://github.com/Consensys/gnark-crypto/issues/331))
 - generic pool
 - generify multi-fan-out input bugfix
 - generified benchmark, parallelism and top sort
@@ -903,7 +903,7 @@
 - bn254 sumcheck tests pass
 - fiatshamir to write bindings one by one
 - single input two identity gates test fixed, but fails
-- closes [#316](https://github.com/ConsenSys/gnark-crypto/issues/316) big int pool doesn't allow nil values
+- closes [#316](https://github.com/Consensys/gnark-crypto/issues/316) big int pool doesn't allow nil values
 - no expectation of ins/outs lumped together in tests
 - topological sort no longer group inputs and outputs
 - reintroduce some deleted autogens
@@ -958,7 +958,7 @@
 - parallel Fold
 - step 2 Combine
 - step 1, use the new pool for computeGJ and next
-- minor adjustements to iop package ([#334](https://github.com/ConsenSys/gnark-crypto/issues/334))
+- minor adjustements to iop package ([#334](https://github.com/Consensys/gnark-crypto/issues/334))
 - mimc on bls12-377/fr uses x^17 as a permutation
 - multilin.Fold without writing top part in memory
 - parallel WireAssignment.Complete for bn254
@@ -990,7 +990,7 @@
 - include secp256k1 in code generation
 - move all fake hashes to test_vector_utils
 - cleaner sumcheck test-vec generation
-- clean iop APIs + add Marshal methods ([#337](https://github.com/ConsenSys/gnark-crypto/issues/337))
+- clean iop APIs + add Marshal methods ([#337](https://github.com/Consensys/gnark-crypto/issues/337))
 - gkr tests to work with fiatshamir.transcript
 - remove unused file
 - fixing gkr tests
@@ -1044,22 +1044,22 @@
 - simplest possible test, two instances of an identity gate
 
 ### Pull Requests
-- Merge pull request [#342](https://github.com/ConsenSys/gnark-crypto/issues/342) from ConsenSys/develop
-- Merge pull request [#308](https://github.com/ConsenSys/gnark-crypto/issues/308) from ConsenSys/304-field-agnostic-fiat-shamir-challenge-names
-- Merge pull request [#319](https://github.com/ConsenSys/gnark-crypto/issues/319) from ConsenSys/perf/gkr
-- Merge pull request [#328](https://github.com/ConsenSys/gnark-crypto/issues/328) from ConsenSys/perf/gkrpool
-- Merge pull request [#333](https://github.com/ConsenSys/gnark-crypto/issues/333) from ConsenSys/fix/mimc-pow7
-- Merge pull request [#327](https://github.com/ConsenSys/gnark-crypto/issues/327) from ConsenSys/pedersen-hash
-- Merge pull request [#320](https://github.com/ConsenSys/gnark-crypto/issues/320) from ConsenSys/fix/mimc-rounds
-- Merge pull request [#312](https://github.com/ConsenSys/gnark-crypto/issues/312) from ConsenSys/signature/pre-hashed
-- Merge pull request [#311](https://github.com/ConsenSys/gnark-crypto/issues/311) from ConsenSys/feat/element/vector
-- Merge pull request [#310](https://github.com/ConsenSys/gnark-crypto/issues/310) from ConsenSys/feat/ecdsa
-- Merge pull request [#298](https://github.com/ConsenSys/gnark-crypto/issues/298) from ConsenSys/secp256k1/MSM
-- Merge pull request [#309](https://github.com/ConsenSys/gnark-crypto/issues/309) from ConsenSys/chore/tobigintregular-deprecated
-- Merge pull request [#305](https://github.com/ConsenSys/gnark-crypto/issues/305) from ConsenSys/test/fiatshamir-mimc
-- Merge pull request [#299](https://github.com/ConsenSys/gnark-crypto/issues/299) from ConsenSys/feat/stark-curve
-- Merge pull request [#285](https://github.com/ConsenSys/gnark-crypto/issues/285) from ConsenSys/refac/gkr-fiatshamir
-- Merge pull request [#259](https://github.com/ConsenSys/gnark-crypto/issues/259) from ConsenSys/bench/gkr
+- Merge pull request [#342](https://github.com/Consensys/gnark-crypto/issues/342) from ConsenSys/develop
+- Merge pull request [#308](https://github.com/Consensys/gnark-crypto/issues/308) from ConsenSys/304-field-agnostic-fiat-shamir-challenge-names
+- Merge pull request [#319](https://github.com/Consensys/gnark-crypto/issues/319) from ConsenSys/perf/gkr
+- Merge pull request [#328](https://github.com/Consensys/gnark-crypto/issues/328) from ConsenSys/perf/gkrpool
+- Merge pull request [#333](https://github.com/Consensys/gnark-crypto/issues/333) from ConsenSys/fix/mimc-pow7
+- Merge pull request [#327](https://github.com/Consensys/gnark-crypto/issues/327) from ConsenSys/pedersen-hash
+- Merge pull request [#320](https://github.com/Consensys/gnark-crypto/issues/320) from ConsenSys/fix/mimc-rounds
+- Merge pull request [#312](https://github.com/Consensys/gnark-crypto/issues/312) from ConsenSys/signature/pre-hashed
+- Merge pull request [#311](https://github.com/Consensys/gnark-crypto/issues/311) from ConsenSys/feat/element/vector
+- Merge pull request [#310](https://github.com/Consensys/gnark-crypto/issues/310) from ConsenSys/feat/ecdsa
+- Merge pull request [#298](https://github.com/Consensys/gnark-crypto/issues/298) from ConsenSys/secp256k1/MSM
+- Merge pull request [#309](https://github.com/Consensys/gnark-crypto/issues/309) from ConsenSys/chore/tobigintregular-deprecated
+- Merge pull request [#305](https://github.com/Consensys/gnark-crypto/issues/305) from ConsenSys/test/fiatshamir-mimc
+- Merge pull request [#299](https://github.com/Consensys/gnark-crypto/issues/299) from ConsenSys/feat/stark-curve
+- Merge pull request [#285](https://github.com/Consensys/gnark-crypto/issues/285) from ConsenSys/refac/gkr-fiatshamir
+- Merge pull request [#259](https://github.com/Consensys/gnark-crypto/issues/259) from ConsenSys/bench/gkr
 
 
 <a name="v0.9.0"></a>
@@ -1071,7 +1071,7 @@
 - added audit.pdf and updated link in README
 
 ### Feat
-- field.Hash ([#271](https://github.com/ConsenSys/gnark-crypto/issues/271))
+- field.Hash ([#271](https://github.com/Consensys/gnark-crypto/issues/271))
 - add secp256k1 curve
 
 ### Fix
@@ -1082,7 +1082,7 @@
 - **secp256k1:** no partitionScalars because there is no spare bit
 
 ### Fix
-- typos ([#262](https://github.com/ConsenSys/gnark-crypto/issues/262))
+- typos ([#262](https://github.com/Consensys/gnark-crypto/issues/262))
 
 ### Perf
 - **MSM:** save 4 mul in ext-Jac add
@@ -1090,20 +1090,20 @@
 
 ### Refactor
 - rebase on develop (field api)
-- mark ToBigIntRegular as deprecated, introduce BigInt method ([#290](https://github.com/ConsenSys/gnark-crypto/issues/290))
-- clean code generation for endo-based computations ([#281](https://github.com/ConsenSys/gnark-crypto/issues/281))
+- mark ToBigIntRegular as deprecated, introduce BigInt method ([#290](https://github.com/Consensys/gnark-crypto/issues/290))
+- clean code generation for endo-based computations ([#281](https://github.com/Consensys/gnark-crypto/issues/281))
 - **bn254:** remove unused variable (fixedCoeff)
 
 ### Style
 - typo
 
 ### Pull Requests
-- Merge pull request [#297](https://github.com/ConsenSys/gnark-crypto/issues/297) from ConsenSys/develop
-- Merge pull request [#277](https://github.com/ConsenSys/gnark-crypto/issues/277) from ConsenSys/feat/secp256k1
-- Merge pull request [#251](https://github.com/ConsenSys/gnark-crypto/issues/251) from ConsenSys/perf/IsInSubGroup-BN
-- Merge pull request [#250](https://github.com/ConsenSys/gnark-crypto/issues/250) from ConsenSys/docs/audit
-- Merge pull request [#245](https://github.com/ConsenSys/gnark-crypto/issues/245) from ConsenSys/perf/extJac-add
-- Merge pull request [#240](https://github.com/ConsenSys/gnark-crypto/issues/240) from ConsenSys/go1.19
+- Merge pull request [#297](https://github.com/Consensys/gnark-crypto/issues/297) from ConsenSys/develop
+- Merge pull request [#277](https://github.com/Consensys/gnark-crypto/issues/277) from ConsenSys/feat/secp256k1
+- Merge pull request [#251](https://github.com/Consensys/gnark-crypto/issues/251) from ConsenSys/perf/IsInSubGroup-BN
+- Merge pull request [#250](https://github.com/Consensys/gnark-crypto/issues/250) from ConsenSys/docs/audit
+- Merge pull request [#245](https://github.com/Consensys/gnark-crypto/issues/245) from ConsenSys/perf/extJac-add
+- Merge pull request [#240](https://github.com/Consensys/gnark-crypto/issues/240) from ConsenSys/go1.19
 
 
 <a name="v0.8.0"></a>
@@ -1113,7 +1113,7 @@
 - go mod tidy
 - update bavard dep
 - ran go generate after dev merge
-- faster ci path ([#185](https://github.com/ConsenSys/gnark-crypto/issues/185))
+- faster ci path ([#185](https://github.com/Consensys/gnark-crypto/issues/185))
 - increase CI timeout
 - fix BatchInvert renaming in SSWU templates
 
@@ -1124,20 +1124,20 @@
 - resolve conflicts with non-mont-params
 
 ### Ci
-- fix slack integration + adds golanglint-ci ([#184](https://github.com/ConsenSys/gnark-crypto/issues/184))
+- fix slack integration + adds golanglint-ci ([#184](https://github.com/Consensys/gnark-crypto/issues/184))
 - revert most of last commit
 - use self hosted runners
 
 ### Clean
-- replace modulus generated by constants, add zero-alloc SetRandom ([#194](https://github.com/ConsenSys/gnark-crypto/issues/194))
-- remove uneeded x86 asm and files ([#192](https://github.com/ConsenSys/gnark-crypto/issues/192))
+- replace modulus generated by constants, add zero-alloc SetRandom ([#194](https://github.com/Consensys/gnark-crypto/issues/194))
+- remove uneeded x86 asm and files ([#192](https://github.com/Consensys/gnark-crypto/issues/192))
 
 ### Docs
 - updated changelog for v0.8.0
-- polish readme.md with updated godoc subpackage links ([#235](https://github.com/ConsenSys/gnark-crypto/issues/235))
-- acknowledge that inv(0)==0 in comments as a convention ([#233](https://github.com/ConsenSys/gnark-crypto/issues/233))
+- polish readme.md with updated godoc subpackage links ([#235](https://github.com/Consensys/gnark-crypto/issues/235))
+- acknowledge that inv(0)==0 in comments as a convention ([#233](https://github.com/Consensys/gnark-crypto/issues/233))
 - correct some comments
-- added note in pairing godoc - doesn't check inputs are in correct subgroup ([#231](https://github.com/ConsenSys/gnark-crypto/issues/231))
+- added note in pairing godoc - doesn't check inputs are in correct subgroup ([#231](https://github.com/Consensys/gnark-crypto/issues/231))
 - add security estimates of implemented curves in comments
 - prepare v0.8.0 release notes
 - added twitter handle and security policy links
@@ -1150,14 +1150,14 @@
 - addition of multiple rounds in fri
 - some folding in bn254
 - supsub
-- closes [#137](https://github.com/ConsenSys/gnark-crypto/issues/137) moves consensys/goff into field/goff ([#204](https://github.com/ConsenSys/gnark-crypto/issues/204))
+- closes [#137](https://github.com/Consensys/gnark-crypto/issues/137) moves consensys/goff into field/goff ([#204](https://github.com/Consensys/gnark-crypto/issues/204))
 - tests used gopter for polynomials (bls377, no code gen yet)
 - multilin for all fields
-- field/goldilocks (more efficient 1-limb modulus arith) ([#177](https://github.com/ConsenSys/gnark-crypto/issues/177))
+- field/goldilocks (more efficient 1-limb modulus arith) ([#177](https://github.com/Consensys/gnark-crypto/issues/177))
 - fields in fri proofs are exported
 - code gen for previous commit
 - code gen for previous refactor
-- field/generator suppors 1-limb modulus ([#175](https://github.com/ConsenSys/gnark-crypto/issues/175))
+- field/generator suppors 1-limb modulus ([#175](https://github.com/Consensys/gnark-crypto/issues/175))
 - simplification of the final evaluation check
 - simplify deriveQueriesPositions
 - removed polynomial package bls24315
@@ -1189,10 +1189,10 @@
 - **fri:** removed unsused variable
 
 ### Fix
-- Handle edge case in Karabina decompression ([#219](https://github.com/ConsenSys/gnark-crypto/issues/219))
+- Handle edge case in Karabina decompression ([#219](https://github.com/Consensys/gnark-crypto/issues/219))
 
 ### Fix
-- check nbTasks config when running msm, test all possible c-bit windows in when testing.Short not set) ([#226](https://github.com/ConsenSys/gnark-crypto/issues/226))
+- check nbTasks config when running msm, test all possible c-bit windows in when testing.Short not set) ([#226](https://github.com/Consensys/gnark-crypto/issues/226))
 - race condition with supportAdx relique in internal/fptower
 - element.SetString(_) returns error if invalid input instead of panic
 - bavard dependency
@@ -1200,13 +1200,13 @@
 - ToMont takes non-reference
 - q in tests requires isogeny
 - svdw parameters: z=1 not i
-- expand_msg_xmd copy bug, a few tests ([#201](https://github.com/ConsenSys/gnark-crypto/issues/201))
+- expand_msg_xmd copy bug, a few tests ([#201](https://github.com/Consensys/gnark-crypto/issues/201))
 - "e3" bug and change sign0 to the recent std specification
-- closes [#199](https://github.com/ConsenSys/gnark-crypto/issues/199). Correct bound in eddsa key gen template
+- closes [#199](https://github.com/Consensys/gnark-crypto/issues/199). Correct bound in eddsa key gen template
 - expand_msg_xmd copy bug, a few tests
 - 8*Limbs could be too many bytes
 - right length argument for ExpandMsgXmd
-- remove supportAdx redundant test ([#186](https://github.com/ConsenSys/gnark-crypto/issues/186))
+- remove supportAdx redundant test ([#186](https://github.com/Consensys/gnark-crypto/issues/186))
 - evaluation is an array instead of a slice
 - twoInv defined in init, removed dead code, unexport nbRounds
 - fixed unhandled errors
@@ -1246,14 +1246,14 @@
 - NewPolynomial -> New
 - removed test DivPolyByXminusA from kzg, DivPolyBy -> DivBy
 - sswuMap -> mapToCurve
-- clean comments in curves ([#193](https://github.com/ConsenSys/gnark-crypto/issues/193))
+- clean comments in curves ([#193](https://github.com/Consensys/gnark-crypto/issues/193))
 - DivideByXMinusA returns a pointer
 - **polynomial:** Copy() --> GetCopy()
 
 ### Style
-- remove dead code ([#230](https://github.com/ConsenSys/gnark-crypto/issues/230))
+- remove dead code ([#230](https://github.com/Consensys/gnark-crypto/issues/230))
 - inneficient -> inefficient
-- cosmetic changes ([#197](https://github.com/ConsenSys/gnark-crypto/issues/197))
+- cosmetic changes ([#197](https://github.com/Consensys/gnark-crypto/issues/197))
 - use bytes package
 - removed dead code
 - fixed comment
@@ -1261,7 +1261,7 @@
 
 ### Test
 - cleanup
-- fix [#205](https://github.com/ConsenSys/gnark-crypto/issues/205) - msm bench with different bases ([#206](https://github.com/ConsenSys/gnark-crypto/issues/206))
+- fix [#205](https://github.com/Consensys/gnark-crypto/issues/205) - msm bench with different bases ([#206](https://github.com/Consensys/gnark-crypto/issues/206))
 - bn254 hash to g2
 - vectors generated using https://github.com/armfazh/h2c-go-ref
 - complete tests for bn254g1, not cross verified
@@ -1271,26 +1271,26 @@
 - **all curves:** compress/decompress pairing result
 
 ### Pull Requests
-- Merge pull request [#237](https://github.com/ConsenSys/gnark-crypto/issues/237) from ConsenSys/develop
-- Merge pull request [#232](https://github.com/ConsenSys/gnark-crypto/issues/232) from ConsenSys/docs/comments
-- Merge pull request [#229](https://github.com/ConsenSys/gnark-crypto/issues/229) from ConsenSys/update_deps
-- Merge pull request [#227](https://github.com/ConsenSys/gnark-crypto/issues/227) from ConsenSys/fix/element_setstring
-- Merge pull request [#228](https://github.com/ConsenSys/gnark-crypto/issues/228) from ConsenSys/fix/race/test
-- Merge pull request [#224](https://github.com/ConsenSys/gnark-crypto/issues/224) from ConsenSys/refactor/scalarmul
-- Merge pull request [#220](https://github.com/ConsenSys/gnark-crypto/issues/220) from ConsenSys/perf/kzg-verify
-- Merge pull request [#223](https://github.com/ConsenSys/gnark-crypto/issues/223) from ConsenSys/doc/security-estimates-curves
-- Merge pull request [#216](https://github.com/ConsenSys/gnark-crypto/issues/216) from ConsenSys/feat/poly
-- Merge pull request [#217](https://github.com/ConsenSys/gnark-crypto/issues/217) from ConsenSys/string-utils
-- Merge pull request [#215](https://github.com/ConsenSys/gnark-crypto/issues/215) from ConsenSys/develop
-- Merge pull request [#213](https://github.com/ConsenSys/gnark-crypto/issues/213) from ConsenSys/perf/glv
-- Merge pull request [#211](https://github.com/ConsenSys/gnark-crypto/issues/211) from ConsenSys/develop
-- Merge pull request [#129](https://github.com/ConsenSys/gnark-crypto/issues/129) from ConsenSys/feat/GT-compression
-- Merge pull request [#209](https://github.com/ConsenSys/gnark-crypto/issues/209) from ConsenSys/codegen/svdw-not-e4
-- Merge pull request [#203](https://github.com/ConsenSys/gnark-crypto/issues/203) from ConsenSys/tests/bn254-vectors
-- Merge pull request [#196](https://github.com/ConsenSys/gnark-crypto/issues/196) from ConsenSys/patch/hashToFpGeneric
-- Merge pull request [#202](https://github.com/ConsenSys/gnark-crypto/issues/202) from ConsenSys/gbotrel/issue199
-- Merge pull request [#200](https://github.com/ConsenSys/gnark-crypto/issues/200) from tyGavinZJU/develop
-- Merge pull request [#85](https://github.com/ConsenSys/gnark-crypto/issues/85) from ConsenSys/feat/fri
+- Merge pull request [#237](https://github.com/Consensys/gnark-crypto/issues/237) from ConsenSys/develop
+- Merge pull request [#232](https://github.com/Consensys/gnark-crypto/issues/232) from ConsenSys/docs/comments
+- Merge pull request [#229](https://github.com/Consensys/gnark-crypto/issues/229) from ConsenSys/update_deps
+- Merge pull request [#227](https://github.com/Consensys/gnark-crypto/issues/227) from ConsenSys/fix/element_setstring
+- Merge pull request [#228](https://github.com/Consensys/gnark-crypto/issues/228) from ConsenSys/fix/race/test
+- Merge pull request [#224](https://github.com/Consensys/gnark-crypto/issues/224) from ConsenSys/refactor/scalarmul
+- Merge pull request [#220](https://github.com/Consensys/gnark-crypto/issues/220) from ConsenSys/perf/kzg-verify
+- Merge pull request [#223](https://github.com/Consensys/gnark-crypto/issues/223) from ConsenSys/doc/security-estimates-curves
+- Merge pull request [#216](https://github.com/Consensys/gnark-crypto/issues/216) from ConsenSys/feat/poly
+- Merge pull request [#217](https://github.com/Consensys/gnark-crypto/issues/217) from ConsenSys/string-utils
+- Merge pull request [#215](https://github.com/Consensys/gnark-crypto/issues/215) from ConsenSys/develop
+- Merge pull request [#213](https://github.com/Consensys/gnark-crypto/issues/213) from ConsenSys/perf/glv
+- Merge pull request [#211](https://github.com/Consensys/gnark-crypto/issues/211) from ConsenSys/develop
+- Merge pull request [#129](https://github.com/Consensys/gnark-crypto/issues/129) from ConsenSys/feat/GT-compression
+- Merge pull request [#209](https://github.com/Consensys/gnark-crypto/issues/209) from ConsenSys/codegen/svdw-not-e4
+- Merge pull request [#203](https://github.com/Consensys/gnark-crypto/issues/203) from ConsenSys/tests/bn254-vectors
+- Merge pull request [#196](https://github.com/Consensys/gnark-crypto/issues/196) from ConsenSys/patch/hashToFpGeneric
+- Merge pull request [#202](https://github.com/Consensys/gnark-crypto/issues/202) from ConsenSys/gbotrel/issue199
+- Merge pull request [#200](https://github.com/Consensys/gnark-crypto/issues/200) from tyGavinZJU/develop
+- Merge pull request [#85](https://github.com/Consensys/gnark-crypto/issues/85) from ConsenSys/feat/fri
 
 
 <a name="v0.7.0"></a>
@@ -1347,8 +1347,8 @@
 ### Fix
 - IsUint64 coherence with other methods, convert from montgomery beforehands
 - twisted curve formulae for GT-strong embedded curve (a != -1)
-- templating twistededwards for BW6-756 after PR[#160](https://github.com/ConsenSys/gnark-crypto/issues/160)
-- templating twistededwards for BLS12-378 after PR[#160](https://github.com/ConsenSys/gnark-crypto/issues/160)
+- templating twistededwards for BW6-756 after PR[#160](https://github.com/Consensys/gnark-crypto/issues/160)
+- templating twistededwards for BLS12-378 after PR[#160](https://github.com/Consensys/gnark-crypto/issues/160)
 - run go generate on new curves
 - add bls12-378 to signature package after change
 - sswu gopter generators repeatable rng
@@ -1383,17 +1383,17 @@
 - mark test as Parallel. Check testing.Short() in most tests
 
 ### Pull Requests
-- Merge pull request [#171](https://github.com/ConsenSys/gnark-crypto/issues/171) from ConsenSys/test/twistedEdwards
-- Merge pull request [#170](https://github.com/ConsenSys/gnark-crypto/issues/170) from ConsenSys/fix/generators_sswu
-- Merge pull request [#167](https://github.com/ConsenSys/gnark-crypto/issues/167) from ConsenSys/ci/shorter-tests
-- Merge pull request [#166](https://github.com/ConsenSys/gnark-crypto/issues/166) from ConsenSys/ci_new
-- Merge pull request [#164](https://github.com/ConsenSys/gnark-crypto/issues/164) from ConsenSys/ci/go1.18
-- Merge pull request [#128](https://github.com/ConsenSys/gnark-crypto/issues/128) from ConsenSys/feat/GT-strong-BLS12-BW6
-- Merge pull request [#127](https://github.com/ConsenSys/gnark-crypto/issues/127) from ConsenSys/feat/GT-strong-BLS12
-- Merge pull request [#160](https://github.com/ConsenSys/gnark-crypto/issues/160) from ConsenSys/refactor-eddsa
-- Merge pull request [#156](https://github.com/ConsenSys/gnark-crypto/issues/156) from ConsenSys/sswu-all
-- Merge pull request [#154](https://github.com/ConsenSys/gnark-crypto/issues/154) from ConsenSys/fix/fft-mulGen
-- Merge pull request [#153](https://github.com/ConsenSys/gnark-crypto/issues/153) from zhiqiangxu/opt_NewDomain
+- Merge pull request [#171](https://github.com/Consensys/gnark-crypto/issues/171) from ConsenSys/test/twistedEdwards
+- Merge pull request [#170](https://github.com/Consensys/gnark-crypto/issues/170) from ConsenSys/fix/generators_sswu
+- Merge pull request [#167](https://github.com/Consensys/gnark-crypto/issues/167) from ConsenSys/ci/shorter-tests
+- Merge pull request [#166](https://github.com/Consensys/gnark-crypto/issues/166) from ConsenSys/ci_new
+- Merge pull request [#164](https://github.com/Consensys/gnark-crypto/issues/164) from ConsenSys/ci/go1.18
+- Merge pull request [#128](https://github.com/Consensys/gnark-crypto/issues/128) from ConsenSys/feat/GT-strong-BLS12-BW6
+- Merge pull request [#127](https://github.com/Consensys/gnark-crypto/issues/127) from ConsenSys/feat/GT-strong-BLS12
+- Merge pull request [#160](https://github.com/Consensys/gnark-crypto/issues/160) from ConsenSys/refactor-eddsa
+- Merge pull request [#156](https://github.com/Consensys/gnark-crypto/issues/156) from ConsenSys/sswu-all
+- Merge pull request [#154](https://github.com/Consensys/gnark-crypto/issues/154) from ConsenSys/fix/fft-mulGen
+- Merge pull request [#153](https://github.com/Consensys/gnark-crypto/issues/153) from zhiqiangxu/opt_NewDomain
 
 
 <a name="v0.6.1"></a>
@@ -1467,14 +1467,14 @@
 - fixed permutation proofs
 - fixed fuzzer
 - removed seed from Sum
-- removed seed from mimc (fixes [#194](https://github.com/ConsenSys/gnark-crypto/issues/194))
+- removed seed from mimc (fixes [#194](https://github.com/Consensys/gnark-crypto/issues/194))
 - clean, remove experimental second version of select
 - delete autogen assembly
 - delete unused assembly
 - errors in reversion
 - generate
 - fixed review: m is modified locally and returned
-- fixes [#126](https://github.com/ConsenSys/gnark-crypto/issues/126) the domain was not created correctly
+- fixes [#126](https://github.com/Consensys/gnark-crypto/issues/126) the domain was not created correctly
 - SetInterface returns error if input is nil
 - fixed gosec
 - mimc is compliant with ethereum
@@ -1518,16 +1518,16 @@
 - match against generic implementation
 
 ### Pull Requests
-- Merge pull request [#152](https://github.com/ConsenSys/gnark-crypto/issues/152) from ConsenSys/feat/clean_kzg
-- Merge pull request [#145](https://github.com/ConsenSys/gnark-crypto/issues/145) from ConsenSys/fix/fft_cosets
-- Merge pull request [#147](https://github.com/ConsenSys/gnark-crypto/issues/147) from ConsenSys/sswu-fp-generic-rebased
-- Merge pull request [#146](https://github.com/ConsenSys/gnark-crypto/issues/146) from ConsenSys/perf-mimc-constants
-- Merge pull request [#144](https://github.com/ConsenSys/gnark-crypto/issues/144) from ConsenSys/constant-time-equals
-- Merge pull request [#125](https://github.com/ConsenSys/gnark-crypto/issues/125) from ConsenSys/fix/mimc_miyaguchipreneel
-- Merge pull request [#143](https://github.com/ConsenSys/gnark-crypto/issues/143) from ConsenSys/feat/cmov
-- Merge pull request [#140](https://github.com/ConsenSys/gnark-crypto/issues/140) from ConsenSys/inv(0)=0
-- Merge pull request [#110](https://github.com/ConsenSys/gnark-crypto/issues/110) from ConsenSys/feat/tEd-extended
-- Merge pull request [#123](https://github.com/ConsenSys/gnark-crypto/issues/123) from ConsenSys/perf/BLS24-G2-IsInSubGroup
+- Merge pull request [#152](https://github.com/Consensys/gnark-crypto/issues/152) from ConsenSys/feat/clean_kzg
+- Merge pull request [#145](https://github.com/Consensys/gnark-crypto/issues/145) from ConsenSys/fix/fft_cosets
+- Merge pull request [#147](https://github.com/Consensys/gnark-crypto/issues/147) from ConsenSys/sswu-fp-generic-rebased
+- Merge pull request [#146](https://github.com/Consensys/gnark-crypto/issues/146) from ConsenSys/perf-mimc-constants
+- Merge pull request [#144](https://github.com/Consensys/gnark-crypto/issues/144) from ConsenSys/constant-time-equals
+- Merge pull request [#125](https://github.com/Consensys/gnark-crypto/issues/125) from ConsenSys/fix/mimc_miyaguchipreneel
+- Merge pull request [#143](https://github.com/Consensys/gnark-crypto/issues/143) from ConsenSys/feat/cmov
+- Merge pull request [#140](https://github.com/Consensys/gnark-crypto/issues/140) from ConsenSys/inv(0)=0
+- Merge pull request [#110](https://github.com/Consensys/gnark-crypto/issues/110) from ConsenSys/feat/tEd-extended
+- Merge pull request [#123](https://github.com/Consensys/gnark-crypto/issues/123) from ConsenSys/perf/BLS24-G2-IsInSubGroup
 
 
 <a name="v0.6.0"></a>
@@ -1574,7 +1574,7 @@
 - addition of benchmark
 - added field.SetInt64
 - added quick and dirty benchmarking script
-- added support for intX and uintX fixes [#109](https://github.com/ConsenSys/gnark-crypto/issues/109)
+- added support for intX and uintX fixes [#109](https://github.com/Consensys/gnark-crypto/issues/109)
 - pre-compute addition chains for Sqrt and Legendre exp functions
 - added addchain for all sqrt
 - Naive GCD improved
@@ -1604,13 +1604,13 @@
 - fix neg template to actually use borrow value
 - All bn254 tests pass but TestMonReduceNegFixed
 - ecc.Info() returns lightweight field info, without calling the whole field generation including addchain generations
-- fixes [#104](https://github.com/ConsenSys/gnark-crypto/issues/104) code generation for saturated modulus like secp256k1 incorrect. added secp256k1 test
+- fixes [#104](https://github.com/Consensys/gnark-crypto/issues/104) code generation for saturated modulus like secp256k1 incorrect. added secp256k1 test
 - fixed quotient computation
 - fixed test generation
 - fixed file generation
 - removed error for invalid domain size in kzg
 - Neg passes, lingering issues with test randomizer
-- remove use of R15 for small moduli mul [#113](https://github.com/ConsenSys/gnark-crypto/issues/113)
+- remove use of R15 for small moduli mul [#113](https://github.com/Consensys/gnark-crypto/issues/113)
 - fixed doc generation
 - template used file path for doc instead of file name
 - fixed exp takes a value, not a pointer. also random field generation test don't generate addchains
@@ -1691,16 +1691,16 @@
 - Consistency check on top
 
 ### Pull Requests
-- Merge pull request [#121](https://github.com/ConsenSys/gnark-crypto/issues/121) from ConsenSys/perf/ML-doubling
-- Merge pull request [#111](https://github.com/ConsenSys/gnark-crypto/issues/111) from ConsenSys/field-intX-support
-- Merge pull request [#114](https://github.com/ConsenSys/gnark-crypto/issues/114) from ConsenSys/fix-dynamic-link
-- Merge pull request [#108](https://github.com/ConsenSys/gnark-crypto/issues/108) from ConsenSys/perf/bls12381-pairing
-- Merge pull request [#106](https://github.com/ConsenSys/gnark-crypto/issues/106) from ConsenSys/improvement/field-inv-pornin20
-- Merge pull request [#105](https://github.com/ConsenSys/gnark-crypto/issues/105) from ConsenSys/field-from-json
-- Merge pull request [#83](https://github.com/ConsenSys/gnark-crypto/issues/83) from ConsenSys/experiment/BLS24
-- Merge pull request [#102](https://github.com/ConsenSys/gnark-crypto/issues/102) from ConsenSys/feat/plookup
-- Merge pull request [#97](https://github.com/ConsenSys/gnark-crypto/issues/97) from ConsenSys/feat-addchain
-- Merge pull request [#99](https://github.com/ConsenSys/gnark-crypto/issues/99) from ConsenSys/feat-addchain-expt
+- Merge pull request [#121](https://github.com/Consensys/gnark-crypto/issues/121) from ConsenSys/perf/ML-doubling
+- Merge pull request [#111](https://github.com/Consensys/gnark-crypto/issues/111) from ConsenSys/field-intX-support
+- Merge pull request [#114](https://github.com/Consensys/gnark-crypto/issues/114) from ConsenSys/fix-dynamic-link
+- Merge pull request [#108](https://github.com/Consensys/gnark-crypto/issues/108) from ConsenSys/perf/bls12381-pairing
+- Merge pull request [#106](https://github.com/Consensys/gnark-crypto/issues/106) from ConsenSys/improvement/field-inv-pornin20
+- Merge pull request [#105](https://github.com/Consensys/gnark-crypto/issues/105) from ConsenSys/field-from-json
+- Merge pull request [#83](https://github.com/Consensys/gnark-crypto/issues/83) from ConsenSys/experiment/BLS24
+- Merge pull request [#102](https://github.com/Consensys/gnark-crypto/issues/102) from ConsenSys/feat/plookup
+- Merge pull request [#97](https://github.com/Consensys/gnark-crypto/issues/97) from ConsenSys/feat-addchain
+- Merge pull request [#99](https://github.com/Consensys/gnark-crypto/issues/99) from ConsenSys/feat-addchain-expt
 
 
 <a name="v0.5.3"></a>
@@ -1722,8 +1722,8 @@
 - cmp(zero) == -1 -> sign() == -1
 
 ### Pull Requests
-- Merge pull request [#96](https://github.com/ConsenSys/gnark-crypto/issues/96) from ConsenSys/perf-decode-raw-points
-- Merge pull request [#95](https://github.com/ConsenSys/gnark-crypto/issues/95) from ConsenSys/perf/bn-g2-membership
+- Merge pull request [#96](https://github.com/Consensys/gnark-crypto/issues/96) from ConsenSys/perf-decode-raw-points
+- Merge pull request [#95](https://github.com/Consensys/gnark-crypto/issues/95) from ConsenSys/perf/bn-g2-membership
 
 
 <a name="v0.5.2"></a>
@@ -1766,12 +1766,12 @@
 - **tEdwards:** mulByA inside the package
 
 ### Pull Requests
-- Merge pull request [#93](https://github.com/ConsenSys/gnark-crypto/issues/93) from ConsenSys/bandersnatch
-- Merge pull request [#90](https://github.com/ConsenSys/gnark-crypto/issues/90) from ConsenSys/fix/tEdwards-addProj-issue89
-- Merge pull request [#82](https://github.com/ConsenSys/gnark-crypto/issues/82) from ConsenSys/perf/bn254-ML
-- Merge pull request [#88](https://github.com/ConsenSys/gnark-crypto/issues/88) from ConsenSys/issue-87/twistedEdwards
-- Merge pull request [#81](https://github.com/ConsenSys/gnark-crypto/issues/81) from ConsenSys/ML/DoubleStep-Halve
-- Merge pull request [#77](https://github.com/ConsenSys/gnark-crypto/issues/77) from ConsenSys/BW6
+- Merge pull request [#93](https://github.com/Consensys/gnark-crypto/issues/93) from ConsenSys/bandersnatch
+- Merge pull request [#90](https://github.com/Consensys/gnark-crypto/issues/90) from ConsenSys/fix/tEdwards-addProj-issue89
+- Merge pull request [#82](https://github.com/Consensys/gnark-crypto/issues/82) from ConsenSys/perf/bn254-ML
+- Merge pull request [#88](https://github.com/Consensys/gnark-crypto/issues/88) from ConsenSys/issue-87/twistedEdwards
+- Merge pull request [#81](https://github.com/Consensys/gnark-crypto/issues/81) from ConsenSys/ML/DoubleStep-Halve
+- Merge pull request [#77](https://github.com/Consensys/gnark-crypto/issues/77) from ConsenSys/BW6
 
 
 <a name="v0.5.1"></a>
@@ -1809,8 +1809,8 @@
 - **bw6-633:** fast GT-subgroup check
 
 ### Pull Requests
-- Merge pull request [#76](https://github.com/ConsenSys/gnark-crypto/issues/76) from ConsenSys/msm-ones
-- Merge pull request [#75](https://github.com/ConsenSys/gnark-crypto/issues/75) from ConsenSys/feat/karabina
+- Merge pull request [#76](https://github.com/Consensys/gnark-crypto/issues/76) from ConsenSys/msm-ones
+- Merge pull request [#75](https://github.com/Consensys/gnark-crypto/issues/75) from ConsenSys/feat/karabina
 
 
 <a name="v0.5.0"></a>
@@ -1860,7 +1860,7 @@
 - formated and expanded package godoc for field elements
 
 ### Feat
-- added Reference benchamrk for continuous benchmarking. fixes [#54](https://github.com/ConsenSys/gnark-crypto/issues/54)
+- added Reference benchamrk for continuous benchmarking. fixes [#54](https://github.com/Consensys/gnark-crypto/issues/54)
 - added curve level go-fuzz fuzz function
 - added ecc.utils.NextPowerOfTwo used in fft and kzg
 - kzg Commit takes an optional CPUSemaphore
@@ -1902,7 +1902,7 @@
 - tests for mock commitment (if claimed values are correct, etc)
 - addition of test for claimed values (polynomial commitments)
 - added subgroup check for proof and digests in kzg
-- fixes [#38](https://github.com/ConsenSys/gnark-crypto/issues/38)
+- fixes [#38](https://github.com/Consensys/gnark-crypto/issues/38)
 - **all curves:** faster GT memebership
 - **bw6:** GT membership
 - **bw6-633:** add bw6-633 to hash and fiat-shamir
@@ -1920,7 +1920,7 @@
 ### Fix
 - CommitmentScheme interface matches kzg and mockCommitment
 - fixed staticchek
-- fixes [#37](https://github.com/ConsenSys/gnark-crypto/issues/37)
+- fixes [#37](https://github.com/Consensys/gnark-crypto/issues/37)
 - fixed some errors handling in transcript.go
 - fixed unhandled errors (G104)
 - fixed conflicts
@@ -1936,10 +1936,10 @@
 - mock Digest ScalarMul didn't modify the caller
 - fft with coset is now thread safe. style adjustements in code
 - e2 x86 asm incorrect offset when x is 0
-- fixes [#49](https://github.com/ConsenSys/gnark-crypto/issues/49)
+- fixes [#49](https://github.com/Consensys/gnark-crypto/issues/49)
 - proper error handling for polynomial commitments + code gen
 - remove Code generated comments in bls24/internal which is not generated
-- fixes [#51](https://github.com/ConsenSys/gnark-crypto/issues/51)
+- fixes [#51](https://github.com/Consensys/gnark-crypto/issues/51)
 - use crypto/rand instead of math/rand in ecc/../utils.go
 - kzg serilization test comparing address instead of value
 - **all curves:** IsInSubGroup shouldn't test E12 elements but GT
@@ -1963,7 +1963,7 @@
 - **template:** cyclotomic suqare test
 - **template:** Expt test to include negative seed
 - **templates:** no psi for bw6 endomorphism test
-- **twisted Edwards:** fixed Neg(), and fixes [#57](https://github.com/ConsenSys/gnark-crypto/issues/57)
+- **twisted Edwards:** fixed Neg(), and fixes [#57](https://github.com/Consensys/gnark-crypto/issues/57)
 
 ### Perf
 - minor perf improvments in bw6 tower
@@ -2035,22 +2035,22 @@
 - added e2.Neg test in code generation
 
 ### Pull Requests
-- Merge pull request [#70](https://github.com/ConsenSys/gnark-crypto/issues/70) from ConsenSys/develop
-- Merge pull request [#68](https://github.com/ConsenSys/gnark-crypto/issues/68) from ConsenSys/fft-cleanup
-- Merge pull request [#64](https://github.com/ConsenSys/gnark-crypto/issues/64) from ConsenSys/feat/bw6-633
-- Merge pull request [#65](https://github.com/ConsenSys/gnark-crypto/issues/65) from ConsenSys/feat/kzgserialization
-- Merge pull request [#63](https://github.com/ConsenSys/gnark-crypto/issues/63) from ConsenSys/feat/kzg_update
-- Merge pull request [#61](https://github.com/ConsenSys/gnark-crypto/issues/61) from ConsenSys/feat/bls24-315
-- Merge pull request [#59](https://github.com/ConsenSys/gnark-crypto/issues/59) from ConsenSys/ci/fuzzandbench
-- Merge pull request [#58](https://github.com/ConsenSys/gnark-crypto/issues/58) from ConsenSys/refactor/bw6-761-pairing
-- Merge pull request [#55](https://github.com/ConsenSys/gnark-crypto/issues/55) from ConsenSys/feat/GT-membership
-- Merge pull request [#48](https://github.com/ConsenSys/gnark-crypto/issues/48) from ConsenSys/feat/kzg
-- Merge pull request [#50](https://github.com/ConsenSys/gnark-crypto/issues/50) from ConsenSys/fix/fft
-- Merge pull request [#46](https://github.com/ConsenSys/gnark-crypto/issues/46) from ConsenSys/fix/domain_precompute
-- Merge pull request [#45](https://github.com/ConsenSys/gnark-crypto/issues/45) from ConsenSys/hotfix/issue_36
-- Merge pull request [#44](https://github.com/ConsenSys/gnark-crypto/issues/44) from ConsenSys/feat/mul_by_13
-- Merge pull request [#42](https://github.com/ConsenSys/gnark-crypto/issues/42) from ConsenSys/feat/fiat_shamir
-- Merge pull request [#41](https://github.com/ConsenSys/gnark-crypto/issues/41) from ConsenSys/docs/godoc
+- Merge pull request [#70](https://github.com/Consensys/gnark-crypto/issues/70) from ConsenSys/develop
+- Merge pull request [#68](https://github.com/Consensys/gnark-crypto/issues/68) from ConsenSys/fft-cleanup
+- Merge pull request [#64](https://github.com/Consensys/gnark-crypto/issues/64) from ConsenSys/feat/bw6-633
+- Merge pull request [#65](https://github.com/Consensys/gnark-crypto/issues/65) from ConsenSys/feat/kzgserialization
+- Merge pull request [#63](https://github.com/Consensys/gnark-crypto/issues/63) from ConsenSys/feat/kzg_update
+- Merge pull request [#61](https://github.com/Consensys/gnark-crypto/issues/61) from ConsenSys/feat/bls24-315
+- Merge pull request [#59](https://github.com/Consensys/gnark-crypto/issues/59) from ConsenSys/ci/fuzzandbench
+- Merge pull request [#58](https://github.com/Consensys/gnark-crypto/issues/58) from ConsenSys/refactor/bw6-761-pairing
+- Merge pull request [#55](https://github.com/Consensys/gnark-crypto/issues/55) from ConsenSys/feat/GT-membership
+- Merge pull request [#48](https://github.com/Consensys/gnark-crypto/issues/48) from ConsenSys/feat/kzg
+- Merge pull request [#50](https://github.com/Consensys/gnark-crypto/issues/50) from ConsenSys/fix/fft
+- Merge pull request [#46](https://github.com/Consensys/gnark-crypto/issues/46) from ConsenSys/fix/domain_precompute
+- Merge pull request [#45](https://github.com/Consensys/gnark-crypto/issues/45) from ConsenSys/hotfix/issue_36
+- Merge pull request [#44](https://github.com/Consensys/gnark-crypto/issues/44) from ConsenSys/feat/mul_by_13
+- Merge pull request [#42](https://github.com/Consensys/gnark-crypto/issues/42) from ConsenSys/feat/fiat_shamir
+- Merge pull request [#41](https://github.com/Consensys/gnark-crypto/issues/41) from ConsenSys/docs/godoc
 
 
 <a name="v0.4.0"></a>
@@ -2091,7 +2091,7 @@
 
 ### Fix
 - handle case where numCPU < 4 in precomputeExpTable
-- incorrect comment and size returned in twistededwards SetBytes fixes [#34](https://github.com/ConsenSys/gnark-crypto/issues/34)
+- incorrect comment and size returned in twistededwards SetBytes fixes [#34](https://github.com/Consensys/gnark-crypto/issues/34)
 - add/dbl exJac
 - add/dbl exJac
 - point.SetBytes can now be called concurently with same byte slice input
@@ -2128,9 +2128,9 @@
 - rename point bench functions
 
 ### Pull Requests
-- Merge pull request [#35](https://github.com/ConsenSys/gnark-crypto/issues/35) from ConsenSys/refactor/monorepo
-- Merge pull request [#33](https://github.com/ConsenSys/gnark-crypto/issues/33) from ConsenSys/msm/full-extJac
-- Merge pull request [#32](https://github.com/ConsenSys/gnark-crypto/issues/32) from ConsenSys/fix/clobbered_bp
+- Merge pull request [#35](https://github.com/Consensys/gnark-crypto/issues/35) from ConsenSys/refactor/monorepo
+- Merge pull request [#33](https://github.com/Consensys/gnark-crypto/issues/33) from ConsenSys/msm/full-extJac
+- Merge pull request [#32](https://github.com/Consensys/gnark-crypto/issues/32) from ConsenSys/fix/clobbered_bp
 
 
 <a name="v0.3.8"></a>
@@ -2182,11 +2182,11 @@
 - addition of Marshal/Unmarshal+tests, addition of templates, modified GetEdwardsCurve to not expose order (in big.Int)
 
 ### Pull Requests
-- Merge pull request [#29](https://github.com/ConsenSys/gnark-crypto/issues/29) from ConsenSys/youssef/bls12-finalExp
-- Merge pull request [#27](https://github.com/ConsenSys/gnark-crypto/issues/27) from ConsenSys/experimental/pairing
-- Merge pull request [#26](https://github.com/ConsenSys/gnark-crypto/issues/26) from ConsenSys/youssef/ML-ABLR
-- Merge pull request [#25](https://github.com/ConsenSys/gnark-crypto/issues/25) from ConsenSys/csquare
-- Merge pull request [#23](https://github.com/ConsenSys/gnark-crypto/issues/23) from ConsenSys/youssef/bw6-API-pairing
+- Merge pull request [#29](https://github.com/Consensys/gnark-crypto/issues/29) from ConsenSys/youssef/bls12-finalExp
+- Merge pull request [#27](https://github.com/Consensys/gnark-crypto/issues/27) from ConsenSys/experimental/pairing
+- Merge pull request [#26](https://github.com/Consensys/gnark-crypto/issues/26) from ConsenSys/youssef/ML-ABLR
+- Merge pull request [#25](https://github.com/Consensys/gnark-crypto/issues/25) from ConsenSys/csquare
+- Merge pull request [#23](https://github.com/Consensys/gnark-crypto/issues/23) from ConsenSys/youssef/bw6-API-pairing
 
 
 <a name="v0.3.7"></a>
@@ -2259,8 +2259,8 @@
 - added Bytes() and SetBytes() method on point with binary encoding and optional point compression
 
 ### Pull Requests
-- Merge pull request [#21](https://github.com/ConsenSys/gnark-crypto/issues/21) from ConsenSys/youssef/MillerLoops
-- Merge pull request [#19](https://github.com/ConsenSys/gnark-crypto/issues/19) from ConsenSys/cleanup
+- Merge pull request [#21](https://github.com/Consensys/gnark-crypto/issues/21) from ConsenSys/youssef/MillerLoops
+- Merge pull request [#19](https://github.com/Consensys/gnark-crypto/issues/19) from ConsenSys/cleanup
 
 
 <a name="v0.3.5"></a>
@@ -2360,10 +2360,10 @@
 - optimized Miller loop
 
 ### Pull Requests
-- Merge pull request [#11](https://github.com/ConsenSys/gnark-crypto/issues/11) from ConsenSys/refactor-cyclotomicsquare
-- Merge pull request [#10](https://github.com/ConsenSys/gnark-crypto/issues/10) from ConsenSys/refactor-constants
-- Merge pull request [#5](https://github.com/ConsenSys/gnark-crypto/issues/5) from ConsenSys/experimental-pairing-gen
-- Merge pull request [#4](https://github.com/ConsenSys/gnark-crypto/issues/4) from ConsenSys/endomul-remove
+- Merge pull request [#11](https://github.com/Consensys/gnark-crypto/issues/11) from ConsenSys/refactor-cyclotomicsquare
+- Merge pull request [#10](https://github.com/Consensys/gnark-crypto/issues/10) from ConsenSys/refactor-constants
+- Merge pull request [#5](https://github.com/Consensys/gnark-crypto/issues/5) from ConsenSys/experimental-pairing-gen
+- Merge pull request [#4](https://github.com/Consensys/gnark-crypto/issues/4) from ConsenSys/endomul-remove
 
 
 <a name="v0.1.1"></a>
@@ -2372,41 +2372,41 @@
 <a name="v0.1.0"></a>
 ## [v0.1.0] - 2020-04-07
 ### Pull Requests
-- Merge pull request [#2](https://github.com/ConsenSys/gnark-crypto/issues/2) from ConsenSys/develop
+- Merge pull request [#2](https://github.com/Consensys/gnark-crypto/issues/2) from ConsenSys/develop
 
 
 <a name="v0.0.1"></a>
 ## v0.0.1 - 2020-03-23
 
-[v0.14.0]: https://github.com/ConsenSys/gnark-crypto/compare/v0.13.0...v0.14.0
-[v0.13.0]: https://github.com/ConsenSys/gnark-crypto/compare/v0.12.1...v0.13.0
-[v0.12.1]: https://github.com/ConsenSys/gnark-crypto/compare/v0.12.0...v0.12.1
-[v0.12.0]: https://github.com/ConsenSys/gnark-crypto/compare/v0.11.2...v0.12.0
-[v0.11.2]: https://github.com/ConsenSys/gnark-crypto/compare/v0.9.2...v0.11.2
-[v0.9.2]: https://github.com/ConsenSys/gnark-crypto/compare/v0.11.1...v0.9.2
-[v0.11.1]: https://github.com/ConsenSys/gnark-crypto/compare/v0.10.1...v0.11.1
-[v0.10.1]: https://github.com/ConsenSys/gnark-crypto/compare/v0.11.0...v0.10.1
-[v0.11.0]: https://github.com/ConsenSys/gnark-crypto/compare/v0.10.0...v0.11.0
-[v0.10.0]: https://github.com/ConsenSys/gnark-crypto/compare/v0.9.1...v0.10.0
-[v0.9.1]: https://github.com/ConsenSys/gnark-crypto/compare/v0.9.0...v0.9.1
-[v0.9.0]: https://github.com/ConsenSys/gnark-crypto/compare/v0.8.0...v0.9.0
-[v0.8.0]: https://github.com/ConsenSys/gnark-crypto/compare/v0.7.0...v0.8.0
-[v0.7.0]: https://github.com/ConsenSys/gnark-crypto/compare/v0.6.1...v0.7.0
-[v0.6.1]: https://github.com/ConsenSys/gnark-crypto/compare/v0.6.0...v0.6.1
-[v0.6.0]: https://github.com/ConsenSys/gnark-crypto/compare/v0.5.3...v0.6.0
-[v0.5.3]: https://github.com/ConsenSys/gnark-crypto/compare/v0.5.2...v0.5.3
-[v0.5.2]: https://github.com/ConsenSys/gnark-crypto/compare/v0.5.1...v0.5.2
-[v0.5.1]: https://github.com/ConsenSys/gnark-crypto/compare/v0.5.0...v0.5.1
-[v0.5.0]: https://github.com/ConsenSys/gnark-crypto/compare/v0.4.0...v0.5.0
-[v0.4.0]: https://github.com/ConsenSys/gnark-crypto/compare/v0.3.8...v0.4.0
-[v0.3.8]: https://github.com/ConsenSys/gnark-crypto/compare/v0.3.7...v0.3.8
-[v0.3.7]: https://github.com/ConsenSys/gnark-crypto/compare/v0.3.6...v0.3.7
-[v0.3.6]: https://github.com/ConsenSys/gnark-crypto/compare/v0.3.5...v0.3.6
-[v0.3.5]: https://github.com/ConsenSys/gnark-crypto/compare/v0.3.4...v0.3.5
-[v0.3.4]: https://github.com/ConsenSys/gnark-crypto/compare/v0.3.3...v0.3.4
-[v0.3.3]: https://github.com/ConsenSys/gnark-crypto/compare/v0.3.0...v0.3.3
-[v0.3.0]: https://github.com/ConsenSys/gnark-crypto/compare/v0.3.0-alpha...v0.3.0
-[v0.3.0-alpha]: https://github.com/ConsenSys/gnark-crypto/compare/v0.2.0...v0.3.0-alpha
-[v0.2.0]: https://github.com/ConsenSys/gnark-crypto/compare/v0.1.1...v0.2.0
-[v0.1.1]: https://github.com/ConsenSys/gnark-crypto/compare/v0.1.0...v0.1.1
-[v0.1.0]: https://github.com/ConsenSys/gnark-crypto/compare/v0.0.1...v0.1.0
+[v0.14.0]: https://github.com/Consensys/gnark-crypto/compare/v0.13.0...v0.14.0
+[v0.13.0]: https://github.com/Consensys/gnark-crypto/compare/v0.12.1...v0.13.0
+[v0.12.1]: https://github.com/Consensys/gnark-crypto/compare/v0.12.0...v0.12.1
+[v0.12.0]: https://github.com/Consensys/gnark-crypto/compare/v0.11.2...v0.12.0
+[v0.11.2]: https://github.com/Consensys/gnark-crypto/compare/v0.9.2...v0.11.2
+[v0.9.2]: https://github.com/Consensys/gnark-crypto/compare/v0.11.1...v0.9.2
+[v0.11.1]: https://github.com/Consensys/gnark-crypto/compare/v0.10.1...v0.11.1
+[v0.10.1]: https://github.com/Consensys/gnark-crypto/compare/v0.11.0...v0.10.1
+[v0.11.0]: https://github.com/Consensys/gnark-crypto/compare/v0.10.0...v0.11.0
+[v0.10.0]: https://github.com/Consensys/gnark-crypto/compare/v0.9.1...v0.10.0
+[v0.9.1]: https://github.com/Consensys/gnark-crypto/compare/v0.9.0...v0.9.1
+[v0.9.0]: https://github.com/Consensys/gnark-crypto/compare/v0.8.0...v0.9.0
+[v0.8.0]: https://github.com/Consensys/gnark-crypto/compare/v0.7.0...v0.8.0
+[v0.7.0]: https://github.com/Consensys/gnark-crypto/compare/v0.6.1...v0.7.0
+[v0.6.1]: https://github.com/Consensys/gnark-crypto/compare/v0.6.0...v0.6.1
+[v0.6.0]: https://github.com/Consensys/gnark-crypto/compare/v0.5.3...v0.6.0
+[v0.5.3]: https://github.com/Consensys/gnark-crypto/compare/v0.5.2...v0.5.3
+[v0.5.2]: https://github.com/Consensys/gnark-crypto/compare/v0.5.1...v0.5.2
+[v0.5.1]: https://github.com/Consensys/gnark-crypto/compare/v0.5.0...v0.5.1
+[v0.5.0]: https://github.com/Consensys/gnark-crypto/compare/v0.4.0...v0.5.0
+[v0.4.0]: https://github.com/Consensys/gnark-crypto/compare/v0.3.8...v0.4.0
+[v0.3.8]: https://github.com/Consensys/gnark-crypto/compare/v0.3.7...v0.3.8
+[v0.3.7]: https://github.com/Consensys/gnark-crypto/compare/v0.3.6...v0.3.7
+[v0.3.6]: https://github.com/Consensys/gnark-crypto/compare/v0.3.5...v0.3.6
+[v0.3.5]: https://github.com/Consensys/gnark-crypto/compare/v0.3.4...v0.3.5
+[v0.3.4]: https://github.com/Consensys/gnark-crypto/compare/v0.3.3...v0.3.4
+[v0.3.3]: https://github.com/Consensys/gnark-crypto/compare/v0.3.0...v0.3.3
+[v0.3.0]: https://github.com/Consensys/gnark-crypto/compare/v0.3.0-alpha...v0.3.0
+[v0.3.0-alpha]: https://github.com/Consensys/gnark-crypto/compare/v0.2.0...v0.3.0-alpha
+[v0.2.0]: https://github.com/Consensys/gnark-crypto/compare/v0.1.1...v0.2.0
+[v0.1.1]: https://github.com/Consensys/gnark-crypto/compare/v0.1.0...v0.1.1
+[v0.1.0]: https://github.com/Consensys/gnark-crypto/compare/v0.0.1...v0.1.0
diff --git a/CITATION.bib b/CITATION.bib
index 9a1675abbe..b14f26ca0e 100644
--- a/CITATION.bib
+++ b/CITATION.bib
@@ -4,7 +4,7 @@ @software{gnark-crypto-v0.7
                   Youssef El Housni and
                   Arya Tabaie and
                   Ivo Kubjas},
-  title        = {ConsenSys/gnark-crypto: v0.7.0},
+  title        = {Consensys/gnark-crypto: v0.7.0},
   month        = jan,
   year         = 2022,
   publisher    = {Zenodo},
diff --git a/README.md b/README.md
index 2cebaacbe0..c92ba7855c 100644
--- a/README.md
+++ b/README.md
@@ -1,6 +1,6 @@
 # gnark-crypto
 
-[![Twitter URL](https://img.shields.io/twitter/url/https/twitter.com/gnark_team.svg?style=social&label=Follow%20%40gnark_team)](https://twitter.com/gnark_team) [![License](https://img.shields.io/badge/license-Apache%202-blue)](LICENSE)  [![Go Report Card](https://goreportcard.com/badge/github.com/ConsenSys/gnark-crypto)](https://goreportcard.com/badge/github.com/ConsenSys/gnark-crypto) [![PkgGoDev](https://pkg.go.dev/badge/mod/github.com/consensys/gnark-crypto)](https://pkg.go.dev/mod/github.com/consensys/gnark-crypto) [![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.5815453.svg)](https://doi.org/10.5281/zenodo.5815453)
+[![Twitter URL](https://img.shields.io/twitter/url/https/twitter.com/gnark_team.svg?style=social&label=Follow%20%40gnark_team)](https://twitter.com/gnark_team) [![License](https://img.shields.io/badge/license-Apache%202-blue)](LICENSE)  [![Go Report Card](https://goreportcard.com/badge/github.com/Consensys/gnark-crypto)](https://goreportcard.com/badge/github.com/Consensys/gnark-crypto) [![PkgGoDev](https://pkg.go.dev/badge/mod/github.com/Consensys/gnark-crypto)](https://pkg.go.dev/mod/github.com/Consensys/gnark-crypto) [![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.5815453.svg)](https://doi.org/10.5281/zenodo.5815453)
 
 `gnark-crypto` provides efficient cryptographic primitives, in Go:
 
@@ -23,19 +23,19 @@
 
 `gnark-crypto` is actively developed and maintained by the team (gnark@consensys.net | [HackMD](https://hackmd.io/@gnark)) behind:
 
-* [`gnark`: a framework to execute (and verify) algorithms in zero-knowledge](https://github.com/consensys/gnark)
+* [`gnark`: a framework to execute (and verify) algorithms in zero-knowledge](https://github.com/Consensys/gnark)
 
 ## Warning
 
 **`gnark-crypto` is not fully audited and is provided as-is, use at your own risk. In particular, `gnark-crypto` makes no security guarantees such as constant time implementation or side-channel attack resistance.**
 
-**To report a security bug, please refer to [`gnark` Security Policy](https://github.com/ConsenSys/gnark/blob/master/SECURITY.md).**
+**To report a security bug, please refer to [`gnark` Security Policy](https://github.com/Consensys/gnark/blob/master/SECURITY.md).**
 
 `gnark-crypto` packages are optimized for 64bits architectures (x86 `amd64`) and tested on Unix (Linux / macOS).
 
 ## Audits
 
-See [list of audits for `gnark` and `gnark-crypto`](https://github.com/consensys/gnark?tab=readme-ov-file#audits)
+See [list of audits for `gnark` and `gnark-crypto`](https://github.com/Consensys/gnark?tab=readme-ov-file#audits)
 
 ## Getting started
 
@@ -46,7 +46,7 @@ See [list of audits for `gnark` and `gnark-crypto`](https://github.com/consensys
 ### Install `gnark-crypto`
 
 ```bash
-go get github.com/consensys/gnark-crypto
+go get github.com/Consensys/gnark-crypto
 ```
 
 Note that if you use go modules, in `go.mod` the module path is case sensitive (use `consensys` and not `ConsenSys`).
@@ -97,26 +97,26 @@ Please use the following BibTeX to cite the most recent release.
 
 ## Versioning
 
-We use [SemVer](http://semver.org/) for versioning. For the versions available, see the [tags on this repository](https://github.com/consensys/gnark-crypto/tags).
+We use [SemVer](http://semver.org/) for versioning. For the versions available, see the [tags on this repository](https://github.com/Consensys/gnark-crypto/tags).
 
 ## License
 
 This project is licensed under the Apache 2 License - see the [LICENSE](LICENSE) file for details.
 
-[`field/goff`]: https://pkg.go.dev/github.com/consensys/gnark-crypto/field/goff
-[`bn254`]: https://pkg.go.dev/github.com/consensys/gnark-crypto/ecc/bn254
-[`bls12-381`]: https://pkg.go.dev/github.com/consensys/gnark-crypto/ecc/bls12-381
-[`bls24-317`]: https://pkg.go.dev/github.com/consensys/gnark-crypto/ecc/bls24-317
-[`bls12-377`]: https://pkg.go.dev/github.com/consensys/gnark-crypto/ecc/bls12-377
-[`bls24-315`]: https://pkg.go.dev/github.com/consensys/gnark-crypto/ecc/bls24-315
-[`bw6-761`]: https://pkg.go.dev/github.com/consensys/gnark-crypto/ecc/bw6-761
-[`bw6-633`]: https://pkg.go.dev/github.com/consensys/gnark-crypto/ecc/bw6-633
-[`twistededwards`]: https://pkg.go.dev/github.com/consensys/gnark-crypto/ecc/bn254/twistededwards
-[`eddsa`]: https://pkg.go.dev/github.com/consensys/gnark-crypto/ecc/bn254/twistededwards/eddsa
-[`fft`]: https://pkg.go.dev/github.com/consensys/gnark-crypto/ecc/bn254/fr/fft
-[`fri`]: https://pkg.go.dev/github.com/consensys/gnark-crypto/ecc/bn254/fr/fri
-[`mimc`]: https://pkg.go.dev/github.com/consensys/gnark-crypto/ecc/bn254/fr/mimc
-[`kzg`]: https://pkg.go.dev/github.com/consensys/gnark-crypto/ecc/bn254/fr/kzg
-[`plookup`]: https://pkg.go.dev/github.com/consensys/gnark-crypto/ecc/bn254/fr/plookup
-[`permutation`]: https://pkg.go.dev/github.com/consensys/gnark-crypto/ecc/bn254/fr/permutation
-[`fiatshamir`]: https://pkg.go.dev/github.com/consensys/gnark-crypto/fiat-shamir
+[`field/goff`]: https://pkg.go.dev/github.com/Consensys/gnark-crypto/field/goff
+[`bn254`]: https://pkg.go.dev/github.com/Consensys/gnark-crypto/ecc/bn254
+[`bls12-381`]: https://pkg.go.dev/github.com/Consensys/gnark-crypto/ecc/bls12-381
+[`bls24-317`]: https://pkg.go.dev/github.com/Consensys/gnark-crypto/ecc/bls24-317
+[`bls12-377`]: https://pkg.go.dev/github.com/Consensys/gnark-crypto/ecc/bls12-377
+[`bls24-315`]: https://pkg.go.dev/github.com/Consensys/gnark-crypto/ecc/bls24-315
+[`bw6-761`]: https://pkg.go.dev/github.com/Consensys/gnark-crypto/ecc/bw6-761
+[`bw6-633`]: https://pkg.go.dev/github.com/Consensys/gnark-crypto/ecc/bw6-633
+[`twistededwards`]: https://pkg.go.dev/github.com/Consensys/gnark-crypto/ecc/bn254/twistededwards
+[`eddsa`]: https://pkg.go.dev/github.com/Consensys/gnark-crypto/ecc/bn254/twistededwards/eddsa
+[`fft`]: https://pkg.go.dev/github.com/Consensys/gnark-crypto/ecc/bn254/fr/fft
+[`fri`]: https://pkg.go.dev/github.com/Consensys/gnark-crypto/ecc/bn254/fr/fri
+[`mimc`]: https://pkg.go.dev/github.com/Consensys/gnark-crypto/ecc/bn254/fr/mimc
+[`kzg`]: https://pkg.go.dev/github.com/Consensys/gnark-crypto/ecc/bn254/fr/kzg
+[`plookup`]: https://pkg.go.dev/github.com/Consensys/gnark-crypto/ecc/bn254/fr/plookup
+[`permutation`]: https://pkg.go.dev/github.com/Consensys/gnark-crypto/ecc/bn254/fr/permutation
+[`fiatshamir`]: https://pkg.go.dev/github.com/Consensys/gnark-crypto/fiat-shamir
diff --git a/ecc/bls12-377/ecdsa/doc.go b/ecc/bls12-377/ecdsa/doc.go
index 793c3ccf61..90a024703d 100644
--- a/ecc/bls12-377/ecdsa/doc.go
+++ b/ecc/bls12-377/ecdsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/ecdsa/ecdsa.go b/ecc/bls12-377/ecdsa/ecdsa.go
index 67908ce003..f14ab0d480 100644
--- a/ecc/bls12-377/ecdsa/ecdsa.go
+++ b/ecc/bls12-377/ecdsa/ecdsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/ecdsa/ecdsa_test.go b/ecc/bls12-377/ecdsa/ecdsa_test.go
index 5385c3b02f..ccc12b07df 100644
--- a/ecc/bls12-377/ecdsa/ecdsa_test.go
+++ b/ecc/bls12-377/ecdsa/ecdsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/ecdsa/marshal.go b/ecc/bls12-377/ecdsa/marshal.go
index 845bb92cbe..8f1caa7d3b 100644
--- a/ecc/bls12-377/ecdsa/marshal.go
+++ b/ecc/bls12-377/ecdsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/ecdsa/marshal_test.go b/ecc/bls12-377/ecdsa/marshal_test.go
index 42f7f7b08c..68096e88c3 100644
--- a/ecc/bls12-377/ecdsa/marshal_test.go
+++ b/ecc/bls12-377/ecdsa/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fflonk/doc.go b/ecc/bls12-377/fflonk/doc.go
index b717383d87..67a8094e35 100644
--- a/ecc/bls12-377/fflonk/doc.go
+++ b/ecc/bls12-377/fflonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fflonk/example_test.go b/ecc/bls12-377/fflonk/example_test.go
index 8a0ffbe630..18961c170f 100644
--- a/ecc/bls12-377/fflonk/example_test.go
+++ b/ecc/bls12-377/fflonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fflonk/fflonk.go b/ecc/bls12-377/fflonk/fflonk.go
index 68b147e5e0..03f84b69bf 100644
--- a/ecc/bls12-377/fflonk/fflonk.go
+++ b/ecc/bls12-377/fflonk/fflonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fflonk/fflonk_test.go b/ecc/bls12-377/fflonk/fflonk_test.go
index 767046034e..3585194eca 100644
--- a/ecc/bls12-377/fflonk/fflonk_test.go
+++ b/ecc/bls12-377/fflonk/fflonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fflonk/marshal.go b/ecc/bls12-377/fflonk/marshal.go
index 06d50938ad..0a379f4681 100644
--- a/ecc/bls12-377/fflonk/marshal.go
+++ b/ecc/bls12-377/fflonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/arith.go b/ecc/bls12-377/fp/arith.go
index b202a1549a..bb63552f5a 100644
--- a/ecc/bls12-377/fp/arith.go
+++ b/ecc/bls12-377/fp/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/asm_adx.go b/ecc/bls12-377/fp/asm_adx.go
index fe25e82db2..75e92992fe 100644
--- a/ecc/bls12-377/fp/asm_adx.go
+++ b/ecc/bls12-377/fp/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/asm_noadx.go b/ecc/bls12-377/fp/asm_noadx.go
index 95085a8e6f..304dfb7209 100644
--- a/ecc/bls12-377/fp/asm_noadx.go
+++ b/ecc/bls12-377/fp/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/doc.go b/ecc/bls12-377/fp/doc.go
index f06378d9e5..feeae6fb8f 100644
--- a/ecc/bls12-377/fp/doc.go
+++ b/ecc/bls12-377/fp/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/element.go b/ecc/bls12-377/fp/element.go
index b96aa88e41..9358a37a88 100644
--- a/ecc/bls12-377/fp/element.go
+++ b/ecc/bls12-377/fp/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/element_amd64.go b/ecc/bls12-377/fp/element_amd64.go
index e72f552ad9..9cee062e5b 100644
--- a/ecc/bls12-377/fp/element_amd64.go
+++ b/ecc/bls12-377/fp/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/element_amd64.s b/ecc/bls12-377/fp/element_amd64.s
index b73d1a484e..719aecfbe9 100644
--- a/ecc/bls12-377/fp/element_amd64.s
+++ b/ecc/bls12-377/fp/element_amd64.s
@@ -1,10 +1,10 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
-// We include the hash to force the Go compiler to recompile: 11124594824487954849
+// We include the hash to force the Go compiler to recompile: 18408829383245254329
 #include "../../../field/asm/element_6w_amd64.s"
 
diff --git a/ecc/bls12-377/fp/element_arm64.go b/ecc/bls12-377/fp/element_arm64.go
index c8eed53698..4f2adff0c6 100644
--- a/ecc/bls12-377/fp/element_arm64.go
+++ b/ecc/bls12-377/fp/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/element_arm64.s b/ecc/bls12-377/fp/element_arm64.s
index 58d21358b0..b4dfd1612c 100644
--- a/ecc/bls12-377/fp/element_arm64.s
+++ b/ecc/bls12-377/fp/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/element_exp.go b/ecc/bls12-377/fp/element_exp.go
index 3434e177e7..004fc14c8e 100644
--- a/ecc/bls12-377/fp/element_exp.go
+++ b/ecc/bls12-377/fp/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/element_purego.go b/ecc/bls12-377/fp/element_purego.go
index fe1b9f55e7..5d4a91ae59 100644
--- a/ecc/bls12-377/fp/element_purego.go
+++ b/ecc/bls12-377/fp/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/element_test.go b/ecc/bls12-377/fp/element_test.go
index 997dbf4b30..0538bba1d7 100644
--- a/ecc/bls12-377/fp/element_test.go
+++ b/ecc/bls12-377/fp/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/element_utils.go b/ecc/bls12-377/fp/element_utils.go
index 6da4e95fd7..1e48d7386c 100644
--- a/ecc/bls12-377/fp/element_utils.go
+++ b/ecc/bls12-377/fp/element_utils.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fp
 
diff --git a/ecc/bls12-377/fp/hash_to_field/doc.go b/ecc/bls12-377/fp/hash_to_field/doc.go
index 7e034fdde8..08de8cbe24 100644
--- a/ecc/bls12-377/fp/hash_to_field/doc.go
+++ b/ecc/bls12-377/fp/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/hash_to_field/hash_to_field.go b/ecc/bls12-377/fp/hash_to_field/hash_to_field.go
index 346b9f4acf..2ac45dc6ea 100644
--- a/ecc/bls12-377/fp/hash_to_field/hash_to_field.go
+++ b/ecc/bls12-377/fp/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/hash_to_field/hash_to_field_test.go b/ecc/bls12-377/fp/hash_to_field/hash_to_field_test.go
index 61b8d32b40..320d2b607b 100644
--- a/ecc/bls12-377/fp/hash_to_field/hash_to_field_test.go
+++ b/ecc/bls12-377/fp/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/vector.go b/ecc/bls12-377/fp/vector.go
index aba4a810c9..93189079db 100644
--- a/ecc/bls12-377/fp/vector.go
+++ b/ecc/bls12-377/fp/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/vector_purego.go b/ecc/bls12-377/fp/vector_purego.go
index 347b0df594..0cda361871 100644
--- a/ecc/bls12-377/fp/vector_purego.go
+++ b/ecc/bls12-377/fp/vector_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/vector_test.go b/ecc/bls12-377/fp/vector_test.go
index 9584d79b8b..7075283b49 100644
--- a/ecc/bls12-377/fp/vector_test.go
+++ b/ecc/bls12-377/fp/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/arith.go b/ecc/bls12-377/fr/arith.go
index 9285041f4b..dbba8a9ae4 100644
--- a/ecc/bls12-377/fr/arith.go
+++ b/ecc/bls12-377/fr/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/asm_adx.go b/ecc/bls12-377/fr/asm_adx.go
index 9e7da5e865..9b970335f1 100644
--- a/ecc/bls12-377/fr/asm_adx.go
+++ b/ecc/bls12-377/fr/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/asm_avx.go b/ecc/bls12-377/fr/asm_avx.go
index d6d7d7f87a..2a0a166ed4 100644
--- a/ecc/bls12-377/fr/asm_avx.go
+++ b/ecc/bls12-377/fr/asm_avx.go
@@ -1,6 +1,6 @@
 //go:build !noavx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/asm_noadx.go b/ecc/bls12-377/fr/asm_noadx.go
index 3456158655..96741014f2 100644
--- a/ecc/bls12-377/fr/asm_noadx.go
+++ b/ecc/bls12-377/fr/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/asm_noavx.go b/ecc/bls12-377/fr/asm_noavx.go
index 4eb73e9a78..3cb6968fb8 100644
--- a/ecc/bls12-377/fr/asm_noavx.go
+++ b/ecc/bls12-377/fr/asm_noavx.go
@@ -1,6 +1,6 @@
 //go:build noavx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/doc.go b/ecc/bls12-377/fr/doc.go
index 6e9b45bb4c..0264190110 100644
--- a/ecc/bls12-377/fr/doc.go
+++ b/ecc/bls12-377/fr/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/element.go b/ecc/bls12-377/fr/element.go
index bbcea221bf..108ec017e7 100644
--- a/ecc/bls12-377/fr/element.go
+++ b/ecc/bls12-377/fr/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/element_amd64.go b/ecc/bls12-377/fr/element_amd64.go
index ca49d12590..4c3f2a8567 100644
--- a/ecc/bls12-377/fr/element_amd64.go
+++ b/ecc/bls12-377/fr/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/element_amd64.s b/ecc/bls12-377/fr/element_amd64.s
index ed8a36e04d..a7c6ffae66 100644
--- a/ecc/bls12-377/fr/element_amd64.s
+++ b/ecc/bls12-377/fr/element_amd64.s
@@ -1,10 +1,10 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
-// We include the hash to force the Go compiler to recompile: 9425145785761608449
+// We include the hash to force the Go compiler to recompile: 14652627197992229521
 #include "../../../field/asm/element_4w_amd64.s"
 
diff --git a/ecc/bls12-377/fr/element_arm64.go b/ecc/bls12-377/fr/element_arm64.go
index a080e8ecab..932dc0a9ec 100644
--- a/ecc/bls12-377/fr/element_arm64.go
+++ b/ecc/bls12-377/fr/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/element_arm64.s b/ecc/bls12-377/fr/element_arm64.s
index a7bd036553..ef16eaba35 100644
--- a/ecc/bls12-377/fr/element_arm64.s
+++ b/ecc/bls12-377/fr/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/element_exp.go b/ecc/bls12-377/fr/element_exp.go
index 687051a763..b007249841 100644
--- a/ecc/bls12-377/fr/element_exp.go
+++ b/ecc/bls12-377/fr/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/element_purego.go b/ecc/bls12-377/fr/element_purego.go
index 6fd5816ab5..de0345c006 100644
--- a/ecc/bls12-377/fr/element_purego.go
+++ b/ecc/bls12-377/fr/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/element_test.go b/ecc/bls12-377/fr/element_test.go
index 8a527c1ce6..9321545c8f 100644
--- a/ecc/bls12-377/fr/element_test.go
+++ b/ecc/bls12-377/fr/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/fft/bitreverse.go b/ecc/bls12-377/fr/fft/bitreverse.go
index e6e22fad63..c7c5bf6c29 100644
--- a/ecc/bls12-377/fr/fft/bitreverse.go
+++ b/ecc/bls12-377/fr/fft/bitreverse.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/fft/bitreverse_test.go b/ecc/bls12-377/fr/fft/bitreverse_test.go
index 5060ab3649..26ed691e24 100644
--- a/ecc/bls12-377/fr/fft/bitreverse_test.go
+++ b/ecc/bls12-377/fr/fft/bitreverse_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/fft/doc.go b/ecc/bls12-377/fr/fft/doc.go
index 1ef04db2df..4cce0f9779 100644
--- a/ecc/bls12-377/fr/fft/doc.go
+++ b/ecc/bls12-377/fr/fft/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/fft/domain.go b/ecc/bls12-377/fr/fft/domain.go
index 806cf75ce8..2ed09b4050 100644
--- a/ecc/bls12-377/fr/fft/domain.go
+++ b/ecc/bls12-377/fr/fft/domain.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/fft/domain_test.go b/ecc/bls12-377/fr/fft/domain_test.go
index d95288076c..e445d3cc12 100644
--- a/ecc/bls12-377/fr/fft/domain_test.go
+++ b/ecc/bls12-377/fr/fft/domain_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/fft/fft.go b/ecc/bls12-377/fr/fft/fft.go
index f8b7fe9fcb..1877098040 100644
--- a/ecc/bls12-377/fr/fft/fft.go
+++ b/ecc/bls12-377/fr/fft/fft.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/fft/fft_test.go b/ecc/bls12-377/fr/fft/fft_test.go
index 36e38e1d90..d20a8306b4 100644
--- a/ecc/bls12-377/fr/fft/fft_test.go
+++ b/ecc/bls12-377/fr/fft/fft_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/fft/options.go b/ecc/bls12-377/fr/fft/options.go
index ee226588b0..853704d864 100644
--- a/ecc/bls12-377/fr/fft/options.go
+++ b/ecc/bls12-377/fr/fft/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/fri/doc.go b/ecc/bls12-377/fr/fri/doc.go
index 428dabf625..cea69fc79a 100644
--- a/ecc/bls12-377/fr/fri/doc.go
+++ b/ecc/bls12-377/fr/fri/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/fri/fri.go b/ecc/bls12-377/fr/fri/fri.go
index 4556e62599..118feef439 100644
--- a/ecc/bls12-377/fr/fri/fri.go
+++ b/ecc/bls12-377/fr/fri/fri.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/fri/fri_test.go b/ecc/bls12-377/fr/fri/fri_test.go
index 18cf3780af..6d8b082ace 100644
--- a/ecc/bls12-377/fr/fri/fri_test.go
+++ b/ecc/bls12-377/fr/fri/fri_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/generator.go b/ecc/bls12-377/fr/generator.go
index cd232f68b5..56a2ff142f 100644
--- a/ecc/bls12-377/fr/generator.go
+++ b/ecc/bls12-377/fr/generator.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/gkr/gkr.go b/ecc/bls12-377/fr/gkr/gkr.go
index 05d10acfe8..fb3629fc0a 100644
--- a/ecc/bls12-377/fr/gkr/gkr.go
+++ b/ecc/bls12-377/fr/gkr/gkr.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/gkr/gkr_test.go b/ecc/bls12-377/fr/gkr/gkr_test.go
index b3237624f7..b85efd5dab 100644
--- a/ecc/bls12-377/fr/gkr/gkr_test.go
+++ b/ecc/bls12-377/fr/gkr/gkr_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
@@ -325,7 +325,7 @@ func mimcCircuit(numRounds int) Circuit {
 
 func testMimc(t *testing.T, numRounds int, inputAssignments ...[]fr.Element) {
 	//TODO: Implement mimc correctly. Currently, the computation is mimc(a,b) = cipher( cipher( ... cipher(a, b), b) ..., b)
-	// @AlexandreBelling: Please explain the extra layers in https://github.com/ConsenSys/gkr-mimc/blob/81eada039ab4ed403b7726b535adb63026e8011f/examples/mimc.go#L10
+	// @AlexandreBelling: Please explain the extra layers in https://github.com/Consensys/gkr-mimc/blob/81eada039ab4ed403b7726b535adb63026e8011f/examples/mimc.go#L10
 
 	c := mimcCircuit(numRounds)
 
diff --git a/ecc/bls12-377/fr/hash_to_field/doc.go b/ecc/bls12-377/fr/hash_to_field/doc.go
index c0e0e7cee4..589b45369b 100644
--- a/ecc/bls12-377/fr/hash_to_field/doc.go
+++ b/ecc/bls12-377/fr/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/hash_to_field/hash_to_field.go b/ecc/bls12-377/fr/hash_to_field/hash_to_field.go
index 27723160a6..19832eace7 100644
--- a/ecc/bls12-377/fr/hash_to_field/hash_to_field.go
+++ b/ecc/bls12-377/fr/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/hash_to_field/hash_to_field_test.go b/ecc/bls12-377/fr/hash_to_field/hash_to_field_test.go
index 16ec5e2e19..2db6460369 100644
--- a/ecc/bls12-377/fr/hash_to_field/hash_to_field_test.go
+++ b/ecc/bls12-377/fr/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/iop/doc.go b/ecc/bls12-377/fr/iop/doc.go
index ee3facf1e1..2ef06dfe1a 100644
--- a/ecc/bls12-377/fr/iop/doc.go
+++ b/ecc/bls12-377/fr/iop/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/iop/expressions.go b/ecc/bls12-377/fr/iop/expressions.go
index c5985c87e9..db75f5d8fc 100644
--- a/ecc/bls12-377/fr/iop/expressions.go
+++ b/ecc/bls12-377/fr/iop/expressions.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/iop/expressions_test.go b/ecc/bls12-377/fr/iop/expressions_test.go
index 5449f30af2..a116047266 100644
--- a/ecc/bls12-377/fr/iop/expressions_test.go
+++ b/ecc/bls12-377/fr/iop/expressions_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/iop/polynomial.go b/ecc/bls12-377/fr/iop/polynomial.go
index 763ad3c070..83ba068533 100644
--- a/ecc/bls12-377/fr/iop/polynomial.go
+++ b/ecc/bls12-377/fr/iop/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/iop/polynomial_test.go b/ecc/bls12-377/fr/iop/polynomial_test.go
index 9e9b8ab597..b0decababf 100644
--- a/ecc/bls12-377/fr/iop/polynomial_test.go
+++ b/ecc/bls12-377/fr/iop/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/iop/quotient.go b/ecc/bls12-377/fr/iop/quotient.go
index dfdafb4a89..698ff0bb37 100644
--- a/ecc/bls12-377/fr/iop/quotient.go
+++ b/ecc/bls12-377/fr/iop/quotient.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/iop/quotient_test.go b/ecc/bls12-377/fr/iop/quotient_test.go
index 9d6ae0cfa5..2050b7086f 100644
--- a/ecc/bls12-377/fr/iop/quotient_test.go
+++ b/ecc/bls12-377/fr/iop/quotient_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/iop/ratios.go b/ecc/bls12-377/fr/iop/ratios.go
index 419cc7a713..511a9a8b92 100644
--- a/ecc/bls12-377/fr/iop/ratios.go
+++ b/ecc/bls12-377/fr/iop/ratios.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/iop/ratios_test.go b/ecc/bls12-377/fr/iop/ratios_test.go
index a608cf6d1f..02c4080532 100644
--- a/ecc/bls12-377/fr/iop/ratios_test.go
+++ b/ecc/bls12-377/fr/iop/ratios_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/iop/utils.go b/ecc/bls12-377/fr/iop/utils.go
index beba12b442..e98ccac1be 100644
--- a/ecc/bls12-377/fr/iop/utils.go
+++ b/ecc/bls12-377/fr/iop/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/mimc/doc.go b/ecc/bls12-377/fr/mimc/doc.go
index cc7b101eb4..98aa3f8d81 100644
--- a/ecc/bls12-377/fr/mimc/doc.go
+++ b/ecc/bls12-377/fr/mimc/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/mimc/mimc.go b/ecc/bls12-377/fr/mimc/mimc.go
index 7532333dc1..2855e3ab8e 100644
--- a/ecc/bls12-377/fr/mimc/mimc.go
+++ b/ecc/bls12-377/fr/mimc/mimc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/mimc/options.go b/ecc/bls12-377/fr/mimc/options.go
index 3c5ad55522..a83f77c05d 100644
--- a/ecc/bls12-377/fr/mimc/options.go
+++ b/ecc/bls12-377/fr/mimc/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/pedersen/doc.go b/ecc/bls12-377/fr/pedersen/doc.go
index 62a62f179f..2e24034936 100644
--- a/ecc/bls12-377/fr/pedersen/doc.go
+++ b/ecc/bls12-377/fr/pedersen/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/pedersen/example_test.go b/ecc/bls12-377/fr/pedersen/example_test.go
index 98817493d0..cd7f417b6c 100644
--- a/ecc/bls12-377/fr/pedersen/example_test.go
+++ b/ecc/bls12-377/fr/pedersen/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/pedersen/pedersen.go b/ecc/bls12-377/fr/pedersen/pedersen.go
index 53d0b6823c..59a189ad4e 100644
--- a/ecc/bls12-377/fr/pedersen/pedersen.go
+++ b/ecc/bls12-377/fr/pedersen/pedersen.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
@@ -105,7 +105,7 @@ func (pk *ProvingKey) ProveKnowledge(values []fr.Element) (pok curve.G1Affine, e
 	}
 
 	// TODO @gbotrel this will spawn more than one task, see
-	// https://github.com/ConsenSys/gnark-crypto/issues/269
+	// https://github.com/Consensys/gnark-crypto/issues/269
 	config := ecc.MultiExpConfig{
 		NbTasks: 1, // TODO Experiment
 	}
@@ -123,7 +123,7 @@ func (pk *ProvingKey) Commit(values []fr.Element) (commitment curve.G1Affine, er
 	}
 
 	// TODO @gbotrel this will spawn more than one task, see
-	// https://github.com/ConsenSys/gnark-crypto/issues/269
+	// https://github.com/Consensys/gnark-crypto/issues/269
 	config := ecc.MultiExpConfig{
 		NbTasks: 1,
 	}
@@ -184,7 +184,7 @@ func BatchProve(pk []ProvingKey, values [][]fr.Element, combinationCoeff fr.Elem
 	}
 
 	// TODO @gbotrel this will spawn more than one task, see
-	// https://github.com/ConsenSys/gnark-crypto/issues/269
+	// https://github.com/Consensys/gnark-crypto/issues/269
 	config := ecc.MultiExpConfig{
 		NbTasks: 1,
 	}
diff --git a/ecc/bls12-377/fr/pedersen/pedersen_test.go b/ecc/bls12-377/fr/pedersen/pedersen_test.go
index be491105e5..6178150443 100644
--- a/ecc/bls12-377/fr/pedersen/pedersen_test.go
+++ b/ecc/bls12-377/fr/pedersen/pedersen_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/permutation/doc.go b/ecc/bls12-377/fr/permutation/doc.go
index 5f346b5a53..e24cd82923 100644
--- a/ecc/bls12-377/fr/permutation/doc.go
+++ b/ecc/bls12-377/fr/permutation/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/permutation/permutation.go b/ecc/bls12-377/fr/permutation/permutation.go
index 306dbea24c..81e3841775 100644
--- a/ecc/bls12-377/fr/permutation/permutation.go
+++ b/ecc/bls12-377/fr/permutation/permutation.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/permutation/permutation_test.go b/ecc/bls12-377/fr/permutation/permutation_test.go
index 68f44d6c1c..3f781c324a 100644
--- a/ecc/bls12-377/fr/permutation/permutation_test.go
+++ b/ecc/bls12-377/fr/permutation/permutation_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/plookup/doc.go b/ecc/bls12-377/fr/plookup/doc.go
index d163104002..7a02c59719 100644
--- a/ecc/bls12-377/fr/plookup/doc.go
+++ b/ecc/bls12-377/fr/plookup/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/plookup/plookup_test.go b/ecc/bls12-377/fr/plookup/plookup_test.go
index b24b51530c..317b54d27f 100644
--- a/ecc/bls12-377/fr/plookup/plookup_test.go
+++ b/ecc/bls12-377/fr/plookup/plookup_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/plookup/table.go b/ecc/bls12-377/fr/plookup/table.go
index 2dda6bab65..e23e0c54ff 100644
--- a/ecc/bls12-377/fr/plookup/table.go
+++ b/ecc/bls12-377/fr/plookup/table.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/plookup/vector.go b/ecc/bls12-377/fr/plookup/vector.go
index 456c916a3a..3b074b2bed 100644
--- a/ecc/bls12-377/fr/plookup/vector.go
+++ b/ecc/bls12-377/fr/plookup/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/polynomial/doc.go b/ecc/bls12-377/fr/polynomial/doc.go
index 35b3f725c1..fd96328e8f 100644
--- a/ecc/bls12-377/fr/polynomial/doc.go
+++ b/ecc/bls12-377/fr/polynomial/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/polynomial/multilin.go b/ecc/bls12-377/fr/polynomial/multilin.go
index e0c5279482..d7050da2a0 100644
--- a/ecc/bls12-377/fr/polynomial/multilin.go
+++ b/ecc/bls12-377/fr/polynomial/multilin.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/polynomial/multilin_test.go b/ecc/bls12-377/fr/polynomial/multilin_test.go
index 0ae8feef40..ec48360ad2 100644
--- a/ecc/bls12-377/fr/polynomial/multilin_test.go
+++ b/ecc/bls12-377/fr/polynomial/multilin_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/polynomial/polynomial.go b/ecc/bls12-377/fr/polynomial/polynomial.go
index 07f87f7d48..c108cbf852 100644
--- a/ecc/bls12-377/fr/polynomial/polynomial.go
+++ b/ecc/bls12-377/fr/polynomial/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/polynomial/polynomial_test.go b/ecc/bls12-377/fr/polynomial/polynomial_test.go
index a746364b3e..9d79bac673 100644
--- a/ecc/bls12-377/fr/polynomial/polynomial_test.go
+++ b/ecc/bls12-377/fr/polynomial/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/polynomial/pool.go b/ecc/bls12-377/fr/polynomial/pool.go
index d4c9eb4c21..939ed4d05e 100644
--- a/ecc/bls12-377/fr/polynomial/pool.go
+++ b/ecc/bls12-377/fr/polynomial/pool.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/poseidon2/poseidon2.go b/ecc/bls12-377/fr/poseidon2/poseidon2.go
index 5cf806a339..25b0cca670 100644
--- a/ecc/bls12-377/fr/poseidon2/poseidon2.go
+++ b/ecc/bls12-377/fr/poseidon2/poseidon2.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/poseidon2/poseidon2_test.go b/ecc/bls12-377/fr/poseidon2/poseidon2_test.go
index 7b19890262..220cc78db1 100644
--- a/ecc/bls12-377/fr/poseidon2/poseidon2_test.go
+++ b/ecc/bls12-377/fr/poseidon2/poseidon2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/sis/sis.go b/ecc/bls12-377/fr/sis/sis.go
index 954867a93f..d07717f8d3 100644
--- a/ecc/bls12-377/fr/sis/sis.go
+++ b/ecc/bls12-377/fr/sis/sis.go
@@ -1,16 +1,5 @@
-// Copyright 2023 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package sis
 
diff --git a/ecc/bls12-377/fr/sis/sis_fft.go b/ecc/bls12-377/fr/sis/sis_fft.go
index 94523ff134..79a4686489 100644
--- a/ecc/bls12-377/fr/sis/sis_fft.go
+++ b/ecc/bls12-377/fr/sis/sis_fft.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/sis/sis_test.go b/ecc/bls12-377/fr/sis/sis_test.go
index 9243aede27..73e26a32a2 100644
--- a/ecc/bls12-377/fr/sis/sis_test.go
+++ b/ecc/bls12-377/fr/sis/sis_test.go
@@ -1,16 +1,5 @@
-// Copyright 2023 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package sis
 
diff --git a/ecc/bls12-377/fr/sumcheck/sumcheck.go b/ecc/bls12-377/fr/sumcheck/sumcheck.go
index e053218dd7..71033d0dfe 100644
--- a/ecc/bls12-377/fr/sumcheck/sumcheck.go
+++ b/ecc/bls12-377/fr/sumcheck/sumcheck.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/sumcheck/sumcheck_test.go b/ecc/bls12-377/fr/sumcheck/sumcheck_test.go
index ca748084a0..bccfcf0c85 100644
--- a/ecc/bls12-377/fr/sumcheck/sumcheck_test.go
+++ b/ecc/bls12-377/fr/sumcheck/sumcheck_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/test_vector_utils/test_vector_utils.go b/ecc/bls12-377/fr/test_vector_utils/test_vector_utils.go
index 323f024f55..b5a617a620 100644
--- a/ecc/bls12-377/fr/test_vector_utils/test_vector_utils.go
+++ b/ecc/bls12-377/fr/test_vector_utils/test_vector_utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/vector.go b/ecc/bls12-377/fr/vector.go
index 8b59bd36e9..4654b1b2d3 100644
--- a/ecc/bls12-377/fr/vector.go
+++ b/ecc/bls12-377/fr/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/vector_amd64.go b/ecc/bls12-377/fr/vector_amd64.go
index b27679827c..a7dcec3b25 100644
--- a/ecc/bls12-377/fr/vector_amd64.go
+++ b/ecc/bls12-377/fr/vector_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/vector_purego.go b/ecc/bls12-377/fr/vector_purego.go
index 5973d16ce2..db43e73504 100644
--- a/ecc/bls12-377/fr/vector_purego.go
+++ b/ecc/bls12-377/fr/vector_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || !amd64
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/vector_test.go b/ecc/bls12-377/fr/vector_test.go
index a094bc0ac6..f6179e7824 100644
--- a/ecc/bls12-377/fr/vector_test.go
+++ b/ecc/bls12-377/fr/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/g1.go b/ecc/bls12-377/g1.go
index 28ebdceeaf..ade683e458 100644
--- a/ecc/bls12-377/g1.go
+++ b/ecc/bls12-377/g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/g1_test.go b/ecc/bls12-377/g1_test.go
index e0a147f1fc..97108da122 100644
--- a/ecc/bls12-377/g1_test.go
+++ b/ecc/bls12-377/g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/g2.go b/ecc/bls12-377/g2.go
index 68345d1577..8c4a0b487d 100644
--- a/ecc/bls12-377/g2.go
+++ b/ecc/bls12-377/g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/g2_test.go b/ecc/bls12-377/g2_test.go
index 397fa2f8e3..748685af26 100644
--- a/ecc/bls12-377/g2_test.go
+++ b/ecc/bls12-377/g2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/hash_to_g1.go b/ecc/bls12-377/hash_to_g1.go
index 479a6bfe3e..5359d355a8 100644
--- a/ecc/bls12-377/hash_to_g1.go
+++ b/ecc/bls12-377/hash_to_g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/hash_to_g1_test.go b/ecc/bls12-377/hash_to_g1_test.go
index 763b1c16f9..75f2c223cf 100644
--- a/ecc/bls12-377/hash_to_g1_test.go
+++ b/ecc/bls12-377/hash_to_g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/hash_to_g2.go b/ecc/bls12-377/hash_to_g2.go
index d13eb598bf..9a8780de73 100644
--- a/ecc/bls12-377/hash_to_g2.go
+++ b/ecc/bls12-377/hash_to_g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/hash_to_g2_test.go b/ecc/bls12-377/hash_to_g2_test.go
index 96d16f74f4..d1a47194a0 100644
--- a/ecc/bls12-377/hash_to_g2_test.go
+++ b/ecc/bls12-377/hash_to_g2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/internal/fptower/asm.go b/ecc/bls12-377/internal/fptower/asm.go
index f1ff282d0b..7d64458b6c 100644
--- a/ecc/bls12-377/internal/fptower/asm.go
+++ b/ecc/bls12-377/internal/fptower/asm.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/internal/fptower/asm_noadx.go b/ecc/bls12-377/internal/fptower/asm_noadx.go
index 3885d93d55..28588f65a0 100644
--- a/ecc/bls12-377/internal/fptower/asm_noadx.go
+++ b/ecc/bls12-377/internal/fptower/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/internal/fptower/e12.go b/ecc/bls12-377/internal/fptower/e12.go
index b60331ac61..1422adecd1 100644
--- a/ecc/bls12-377/internal/fptower/e12.go
+++ b/ecc/bls12-377/internal/fptower/e12.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/internal/fptower/e12_test.go b/ecc/bls12-377/internal/fptower/e12_test.go
index 38fa25d17c..6cca730b47 100644
--- a/ecc/bls12-377/internal/fptower/e12_test.go
+++ b/ecc/bls12-377/internal/fptower/e12_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/internal/fptower/e2.go b/ecc/bls12-377/internal/fptower/e2.go
index 1979b60dac..9fbdbd3d7c 100644
--- a/ecc/bls12-377/internal/fptower/e2.go
+++ b/ecc/bls12-377/internal/fptower/e2.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/internal/fptower/e2_amd64.go b/ecc/bls12-377/internal/fptower/e2_amd64.go
index 0261c75f69..6074023131 100644
--- a/ecc/bls12-377/internal/fptower/e2_amd64.go
+++ b/ecc/bls12-377/internal/fptower/e2_amd64.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/internal/fptower/e2_amd64.s b/ecc/bls12-377/internal/fptower/e2_amd64.s
index 78dbffd405..32e77dd787 100644
--- a/ecc/bls12-377/internal/fptower/e2_amd64.s
+++ b/ecc/bls12-377/internal/fptower/e2_amd64.s
@@ -1,4 +1,4 @@
-// Copyright 2020 ConsenSys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 #include "textflag.h"
diff --git a/ecc/bls12-377/internal/fptower/e2_bls377.go b/ecc/bls12-377/internal/fptower/e2_bls377.go
index 9505d53153..dcd9ad959e 100644
--- a/ecc/bls12-377/internal/fptower/e2_bls377.go
+++ b/ecc/bls12-377/internal/fptower/e2_bls377.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls12-377/internal/fptower/e2_fallback.go b/ecc/bls12-377/internal/fptower/e2_fallback.go
index eaea355699..3dff96dcea 100644
--- a/ecc/bls12-377/internal/fptower/e2_fallback.go
+++ b/ecc/bls12-377/internal/fptower/e2_fallback.go
@@ -1,6 +1,6 @@
 //go:build !amd64
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/internal/fptower/e2_test.go b/ecc/bls12-377/internal/fptower/e2_test.go
index bbca702a27..d9653036c5 100644
--- a/ecc/bls12-377/internal/fptower/e2_test.go
+++ b/ecc/bls12-377/internal/fptower/e2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/internal/fptower/e6.go b/ecc/bls12-377/internal/fptower/e6.go
index 5f2cca6625..a3bd71a6cc 100644
--- a/ecc/bls12-377/internal/fptower/e6.go
+++ b/ecc/bls12-377/internal/fptower/e6.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/internal/fptower/e6_test.go b/ecc/bls12-377/internal/fptower/e6_test.go
index 6a1fe41d95..d53b72ec93 100644
--- a/ecc/bls12-377/internal/fptower/e6_test.go
+++ b/ecc/bls12-377/internal/fptower/e6_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/internal/fptower/frobenius.go b/ecc/bls12-377/internal/fptower/frobenius.go
index a7e1b2a812..2c1cd967e5 100644
--- a/ecc/bls12-377/internal/fptower/frobenius.go
+++ b/ecc/bls12-377/internal/fptower/frobenius.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls12-377/internal/fptower/parameters.go b/ecc/bls12-377/internal/fptower/parameters.go
index 6f2b1d6c7e..89db97098c 100644
--- a/ecc/bls12-377/internal/fptower/parameters.go
+++ b/ecc/bls12-377/internal/fptower/parameters.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls12-377/kzg/doc.go b/ecc/bls12-377/kzg/doc.go
index 6c3454a2d9..226614bbdf 100644
--- a/ecc/bls12-377/kzg/doc.go
+++ b/ecc/bls12-377/kzg/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/kzg/kzg.go b/ecc/bls12-377/kzg/kzg.go
index 4229c90290..a9a5d0fd98 100644
--- a/ecc/bls12-377/kzg/kzg.go
+++ b/ecc/bls12-377/kzg/kzg.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/kzg/kzg_test.go b/ecc/bls12-377/kzg/kzg_test.go
index 1a2d93402b..a357b996d0 100644
--- a/ecc/bls12-377/kzg/kzg_test.go
+++ b/ecc/bls12-377/kzg/kzg_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/kzg/marshal.go b/ecc/bls12-377/kzg/marshal.go
index f4668cae7b..5561cb3786 100644
--- a/ecc/bls12-377/kzg/marshal.go
+++ b/ecc/bls12-377/kzg/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/kzg/utils.go b/ecc/bls12-377/kzg/utils.go
index 31bfffd589..10248b3ae3 100644
--- a/ecc/bls12-377/kzg/utils.go
+++ b/ecc/bls12-377/kzg/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/marshal.go b/ecc/bls12-377/marshal.go
index 80aeb57ae1..560b22a37e 100644
--- a/ecc/bls12-377/marshal.go
+++ b/ecc/bls12-377/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/marshal_test.go b/ecc/bls12-377/marshal_test.go
index 2d2561c07c..705a756a02 100644
--- a/ecc/bls12-377/marshal_test.go
+++ b/ecc/bls12-377/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/multiexp.go b/ecc/bls12-377/multiexp.go
index 03b7899c09..5aa960be69 100644
--- a/ecc/bls12-377/multiexp.go
+++ b/ecc/bls12-377/multiexp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/multiexp_affine.go b/ecc/bls12-377/multiexp_affine.go
index bb1ff3e1d9..ff392b910d 100644
--- a/ecc/bls12-377/multiexp_affine.go
+++ b/ecc/bls12-377/multiexp_affine.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
@@ -19,7 +19,7 @@ type batchOpG1Affine struct {
 // using affine coordinates for the buckets. To amortize the cost of the inverse in the affine addition
 // we use a batch affine addition.
 //
-// this is derived from a PR by 0x0ece : https://github.com/ConsenSys/gnark-crypto/pull/249
+// this is derived from a PR by 0x0ece : https://github.com/Consensys/gnark-crypto/pull/249
 // See Section 5.3: ia.cr/2022/1396
 func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP pG1Affine, TPP ppG1Affine, TQ qOpsG1Affine, TC cG1Affine](
 	chunk uint64,
@@ -346,7 +346,7 @@ type batchOpG2Affine struct {
 // using affine coordinates for the buckets. To amortize the cost of the inverse in the affine addition
 // we use a batch affine addition.
 //
-// this is derived from a PR by 0x0ece : https://github.com/ConsenSys/gnark-crypto/pull/249
+// this is derived from a PR by 0x0ece : https://github.com/Consensys/gnark-crypto/pull/249
 // See Section 5.3: ia.cr/2022/1396
 func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP pG2Affine, TPP ppG2Affine, TQ qOpsG2Affine, TC cG2Affine](
 	chunk uint64,
diff --git a/ecc/bls12-377/multiexp_jacobian.go b/ecc/bls12-377/multiexp_jacobian.go
index 108879548c..9e4f26ab79 100644
--- a/ecc/bls12-377/multiexp_jacobian.go
+++ b/ecc/bls12-377/multiexp_jacobian.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/multiexp_test.go b/ecc/bls12-377/multiexp_test.go
index 85b8f6f4cc..2dc1ccd9a4 100644
--- a/ecc/bls12-377/multiexp_test.go
+++ b/ecc/bls12-377/multiexp_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/pairing.go b/ecc/bls12-377/pairing.go
index 1b95a173f2..590e3867bb 100644
--- a/ecc/bls12-377/pairing.go
+++ b/ecc/bls12-377/pairing.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package bls12377
 
diff --git a/ecc/bls12-377/pairing_test.go b/ecc/bls12-377/pairing_test.go
index 0fcc40ac3d..d5a277eabf 100644
--- a/ecc/bls12-377/pairing_test.go
+++ b/ecc/bls12-377/pairing_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/shplonk/doc.go b/ecc/bls12-377/shplonk/doc.go
index 17b34373c2..0367893999 100644
--- a/ecc/bls12-377/shplonk/doc.go
+++ b/ecc/bls12-377/shplonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/shplonk/example_test.go b/ecc/bls12-377/shplonk/example_test.go
index 6b48e973fd..e08750a9e7 100644
--- a/ecc/bls12-377/shplonk/example_test.go
+++ b/ecc/bls12-377/shplonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/shplonk/marshal.go b/ecc/bls12-377/shplonk/marshal.go
index 8a68a95010..a2cb0ae8ba 100644
--- a/ecc/bls12-377/shplonk/marshal.go
+++ b/ecc/bls12-377/shplonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/shplonk/shplonk.go b/ecc/bls12-377/shplonk/shplonk.go
index 8d8c2ef540..b9d66a4cc4 100644
--- a/ecc/bls12-377/shplonk/shplonk.go
+++ b/ecc/bls12-377/shplonk/shplonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/shplonk/shplonk_test.go b/ecc/bls12-377/shplonk/shplonk_test.go
index 6edbb14ccd..a43a0677d2 100644
--- a/ecc/bls12-377/shplonk/shplonk_test.go
+++ b/ecc/bls12-377/shplonk/shplonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/twistededwards/curve.go b/ecc/bls12-377/twistededwards/curve.go
index da66dbc9c3..5db85c848a 100644
--- a/ecc/bls12-377/twistededwards/curve.go
+++ b/ecc/bls12-377/twistededwards/curve.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/twistededwards/doc.go b/ecc/bls12-377/twistededwards/doc.go
index 4f80a5f527..919017a004 100644
--- a/ecc/bls12-377/twistededwards/doc.go
+++ b/ecc/bls12-377/twistededwards/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/twistededwards/eddsa/doc.go b/ecc/bls12-377/twistededwards/eddsa/doc.go
index ed4b44dc87..c6e33c0bd7 100644
--- a/ecc/bls12-377/twistededwards/eddsa/doc.go
+++ b/ecc/bls12-377/twistededwards/eddsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/twistededwards/eddsa/eddsa.go b/ecc/bls12-377/twistededwards/eddsa/eddsa.go
index 4003fda0b5..ba9553e54c 100644
--- a/ecc/bls12-377/twistededwards/eddsa/eddsa.go
+++ b/ecc/bls12-377/twistededwards/eddsa/eddsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/twistededwards/eddsa/eddsa_test.go b/ecc/bls12-377/twistededwards/eddsa/eddsa_test.go
index 54d82cb647..09413696d2 100644
--- a/ecc/bls12-377/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bls12-377/twistededwards/eddsa/eddsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/twistededwards/eddsa/marshal.go b/ecc/bls12-377/twistededwards/eddsa/marshal.go
index c6c2295ae9..d50f80abdc 100644
--- a/ecc/bls12-377/twistededwards/eddsa/marshal.go
+++ b/ecc/bls12-377/twistededwards/eddsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/twistededwards/point.go b/ecc/bls12-377/twistededwards/point.go
index 5a7b088e72..aa9333823f 100644
--- a/ecc/bls12-377/twistededwards/point.go
+++ b/ecc/bls12-377/twistededwards/point.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/twistededwards/point_test.go b/ecc/bls12-377/twistededwards/point_test.go
index 6875b7aa9a..0b293e1870 100644
--- a/ecc/bls12-377/twistededwards/point_test.go
+++ b/ecc/bls12-377/twistededwards/point_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/bandersnatch/curve.go b/ecc/bls12-381/bandersnatch/curve.go
index ba94898222..a0223d5646 100644
--- a/ecc/bls12-381/bandersnatch/curve.go
+++ b/ecc/bls12-381/bandersnatch/curve.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/bandersnatch/doc.go b/ecc/bls12-381/bandersnatch/doc.go
index 66d3b68eaa..04d84007a8 100644
--- a/ecc/bls12-381/bandersnatch/doc.go
+++ b/ecc/bls12-381/bandersnatch/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/bandersnatch/eddsa/doc.go b/ecc/bls12-381/bandersnatch/eddsa/doc.go
index 2e2ee33568..5581f06406 100644
--- a/ecc/bls12-381/bandersnatch/eddsa/doc.go
+++ b/ecc/bls12-381/bandersnatch/eddsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/bandersnatch/eddsa/eddsa.go b/ecc/bls12-381/bandersnatch/eddsa/eddsa.go
index 3bab9a4046..c10e701839 100644
--- a/ecc/bls12-381/bandersnatch/eddsa/eddsa.go
+++ b/ecc/bls12-381/bandersnatch/eddsa/eddsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/bandersnatch/eddsa/eddsa_test.go b/ecc/bls12-381/bandersnatch/eddsa/eddsa_test.go
index 972c06d0d0..cccc545ff7 100644
--- a/ecc/bls12-381/bandersnatch/eddsa/eddsa_test.go
+++ b/ecc/bls12-381/bandersnatch/eddsa/eddsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/bandersnatch/eddsa/marshal.go b/ecc/bls12-381/bandersnatch/eddsa/marshal.go
index 2f4f26d4f3..39dabf92f7 100644
--- a/ecc/bls12-381/bandersnatch/eddsa/marshal.go
+++ b/ecc/bls12-381/bandersnatch/eddsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/bandersnatch/point.go b/ecc/bls12-381/bandersnatch/point.go
index 5507adf2d7..abe0bc2a92 100644
--- a/ecc/bls12-381/bandersnatch/point.go
+++ b/ecc/bls12-381/bandersnatch/point.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/bandersnatch/point_test.go b/ecc/bls12-381/bandersnatch/point_test.go
index d67906e7ff..09b26f5e34 100644
--- a/ecc/bls12-381/bandersnatch/point_test.go
+++ b/ecc/bls12-381/bandersnatch/point_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/ecdsa/doc.go b/ecc/bls12-381/ecdsa/doc.go
index b9a6baabd1..3f362de501 100644
--- a/ecc/bls12-381/ecdsa/doc.go
+++ b/ecc/bls12-381/ecdsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/ecdsa/ecdsa.go b/ecc/bls12-381/ecdsa/ecdsa.go
index 9c4745741f..514c3c8cfc 100644
--- a/ecc/bls12-381/ecdsa/ecdsa.go
+++ b/ecc/bls12-381/ecdsa/ecdsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/ecdsa/ecdsa_test.go b/ecc/bls12-381/ecdsa/ecdsa_test.go
index aa704d9e66..06e237766f 100644
--- a/ecc/bls12-381/ecdsa/ecdsa_test.go
+++ b/ecc/bls12-381/ecdsa/ecdsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/ecdsa/marshal.go b/ecc/bls12-381/ecdsa/marshal.go
index 09877ff47c..943016297d 100644
--- a/ecc/bls12-381/ecdsa/marshal.go
+++ b/ecc/bls12-381/ecdsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/ecdsa/marshal_test.go b/ecc/bls12-381/ecdsa/marshal_test.go
index 1b32bceb36..7fe8623740 100644
--- a/ecc/bls12-381/ecdsa/marshal_test.go
+++ b/ecc/bls12-381/ecdsa/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fflonk/doc.go b/ecc/bls12-381/fflonk/doc.go
index b717383d87..67a8094e35 100644
--- a/ecc/bls12-381/fflonk/doc.go
+++ b/ecc/bls12-381/fflonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fflonk/example_test.go b/ecc/bls12-381/fflonk/example_test.go
index 7a44bac8c6..ef4af9cc37 100644
--- a/ecc/bls12-381/fflonk/example_test.go
+++ b/ecc/bls12-381/fflonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fflonk/fflonk.go b/ecc/bls12-381/fflonk/fflonk.go
index fe4bb1710b..ef9af5489b 100644
--- a/ecc/bls12-381/fflonk/fflonk.go
+++ b/ecc/bls12-381/fflonk/fflonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fflonk/fflonk_test.go b/ecc/bls12-381/fflonk/fflonk_test.go
index a15e154d32..38be0889d1 100644
--- a/ecc/bls12-381/fflonk/fflonk_test.go
+++ b/ecc/bls12-381/fflonk/fflonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fflonk/marshal.go b/ecc/bls12-381/fflonk/marshal.go
index d1147eac9b..f8a6ff57fb 100644
--- a/ecc/bls12-381/fflonk/marshal.go
+++ b/ecc/bls12-381/fflonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/arith.go b/ecc/bls12-381/fp/arith.go
index b202a1549a..bb63552f5a 100644
--- a/ecc/bls12-381/fp/arith.go
+++ b/ecc/bls12-381/fp/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/asm_adx.go b/ecc/bls12-381/fp/asm_adx.go
index fe25e82db2..75e92992fe 100644
--- a/ecc/bls12-381/fp/asm_adx.go
+++ b/ecc/bls12-381/fp/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/asm_noadx.go b/ecc/bls12-381/fp/asm_noadx.go
index 95085a8e6f..304dfb7209 100644
--- a/ecc/bls12-381/fp/asm_noadx.go
+++ b/ecc/bls12-381/fp/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/doc.go b/ecc/bls12-381/fp/doc.go
index d6b85f7ead..752d084ce1 100644
--- a/ecc/bls12-381/fp/doc.go
+++ b/ecc/bls12-381/fp/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/element.go b/ecc/bls12-381/fp/element.go
index 2e4225b51b..0daf55c732 100644
--- a/ecc/bls12-381/fp/element.go
+++ b/ecc/bls12-381/fp/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/element_amd64.go b/ecc/bls12-381/fp/element_amd64.go
index e72f552ad9..9cee062e5b 100644
--- a/ecc/bls12-381/fp/element_amd64.go
+++ b/ecc/bls12-381/fp/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/element_amd64.s b/ecc/bls12-381/fp/element_amd64.s
index b73d1a484e..719aecfbe9 100644
--- a/ecc/bls12-381/fp/element_amd64.s
+++ b/ecc/bls12-381/fp/element_amd64.s
@@ -1,10 +1,10 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
-// We include the hash to force the Go compiler to recompile: 11124594824487954849
+// We include the hash to force the Go compiler to recompile: 18408829383245254329
 #include "../../../field/asm/element_6w_amd64.s"
 
diff --git a/ecc/bls12-381/fp/element_arm64.go b/ecc/bls12-381/fp/element_arm64.go
index 152c411bf3..59f2277cd2 100644
--- a/ecc/bls12-381/fp/element_arm64.go
+++ b/ecc/bls12-381/fp/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/element_arm64.s b/ecc/bls12-381/fp/element_arm64.s
index 58d21358b0..b4dfd1612c 100644
--- a/ecc/bls12-381/fp/element_arm64.s
+++ b/ecc/bls12-381/fp/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/element_exp.go b/ecc/bls12-381/fp/element_exp.go
index 1b611bf6d9..4c05637d56 100644
--- a/ecc/bls12-381/fp/element_exp.go
+++ b/ecc/bls12-381/fp/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/element_purego.go b/ecc/bls12-381/fp/element_purego.go
index 40760eceec..911496ec20 100644
--- a/ecc/bls12-381/fp/element_purego.go
+++ b/ecc/bls12-381/fp/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/element_test.go b/ecc/bls12-381/fp/element_test.go
index 35f8d69404..5a172e4fa7 100644
--- a/ecc/bls12-381/fp/element_test.go
+++ b/ecc/bls12-381/fp/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/hash_to_field/doc.go b/ecc/bls12-381/fp/hash_to_field/doc.go
index fff88b2c11..317d96a2fa 100644
--- a/ecc/bls12-381/fp/hash_to_field/doc.go
+++ b/ecc/bls12-381/fp/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/hash_to_field/hash_to_field.go b/ecc/bls12-381/fp/hash_to_field/hash_to_field.go
index 3a895a5321..d54a80c18b 100644
--- a/ecc/bls12-381/fp/hash_to_field/hash_to_field.go
+++ b/ecc/bls12-381/fp/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/hash_to_field/hash_to_field_test.go b/ecc/bls12-381/fp/hash_to_field/hash_to_field_test.go
index 5ae9b78072..2fa293df7c 100644
--- a/ecc/bls12-381/fp/hash_to_field/hash_to_field_test.go
+++ b/ecc/bls12-381/fp/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/vector.go b/ecc/bls12-381/fp/vector.go
index aba4a810c9..93189079db 100644
--- a/ecc/bls12-381/fp/vector.go
+++ b/ecc/bls12-381/fp/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/vector_purego.go b/ecc/bls12-381/fp/vector_purego.go
index 347b0df594..0cda361871 100644
--- a/ecc/bls12-381/fp/vector_purego.go
+++ b/ecc/bls12-381/fp/vector_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/vector_test.go b/ecc/bls12-381/fp/vector_test.go
index 9584d79b8b..7075283b49 100644
--- a/ecc/bls12-381/fp/vector_test.go
+++ b/ecc/bls12-381/fp/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/arith.go b/ecc/bls12-381/fr/arith.go
index 9285041f4b..dbba8a9ae4 100644
--- a/ecc/bls12-381/fr/arith.go
+++ b/ecc/bls12-381/fr/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/asm_adx.go b/ecc/bls12-381/fr/asm_adx.go
index 9e7da5e865..9b970335f1 100644
--- a/ecc/bls12-381/fr/asm_adx.go
+++ b/ecc/bls12-381/fr/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/asm_avx.go b/ecc/bls12-381/fr/asm_avx.go
index d6d7d7f87a..2a0a166ed4 100644
--- a/ecc/bls12-381/fr/asm_avx.go
+++ b/ecc/bls12-381/fr/asm_avx.go
@@ -1,6 +1,6 @@
 //go:build !noavx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/asm_noadx.go b/ecc/bls12-381/fr/asm_noadx.go
index 3456158655..96741014f2 100644
--- a/ecc/bls12-381/fr/asm_noadx.go
+++ b/ecc/bls12-381/fr/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/asm_noavx.go b/ecc/bls12-381/fr/asm_noavx.go
index 4eb73e9a78..3cb6968fb8 100644
--- a/ecc/bls12-381/fr/asm_noavx.go
+++ b/ecc/bls12-381/fr/asm_noavx.go
@@ -1,6 +1,6 @@
 //go:build noavx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/doc.go b/ecc/bls12-381/fr/doc.go
index 6aa24dfcc3..09174a90f5 100644
--- a/ecc/bls12-381/fr/doc.go
+++ b/ecc/bls12-381/fr/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/element.go b/ecc/bls12-381/fr/element.go
index 62f75ce27b..da8a896aa8 100644
--- a/ecc/bls12-381/fr/element.go
+++ b/ecc/bls12-381/fr/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/element_amd64.go b/ecc/bls12-381/fr/element_amd64.go
index ca49d12590..4c3f2a8567 100644
--- a/ecc/bls12-381/fr/element_amd64.go
+++ b/ecc/bls12-381/fr/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/element_amd64.s b/ecc/bls12-381/fr/element_amd64.s
index ed8a36e04d..a7c6ffae66 100644
--- a/ecc/bls12-381/fr/element_amd64.s
+++ b/ecc/bls12-381/fr/element_amd64.s
@@ -1,10 +1,10 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
-// We include the hash to force the Go compiler to recompile: 9425145785761608449
+// We include the hash to force the Go compiler to recompile: 14652627197992229521
 #include "../../../field/asm/element_4w_amd64.s"
 
diff --git a/ecc/bls12-381/fr/element_arm64.go b/ecc/bls12-381/fr/element_arm64.go
index c87ab28031..6f8a9cb915 100644
--- a/ecc/bls12-381/fr/element_arm64.go
+++ b/ecc/bls12-381/fr/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/element_arm64.s b/ecc/bls12-381/fr/element_arm64.s
index a7bd036553..ef16eaba35 100644
--- a/ecc/bls12-381/fr/element_arm64.s
+++ b/ecc/bls12-381/fr/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/element_exp.go b/ecc/bls12-381/fr/element_exp.go
index 6abe0add74..b57921366d 100644
--- a/ecc/bls12-381/fr/element_exp.go
+++ b/ecc/bls12-381/fr/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/element_purego.go b/ecc/bls12-381/fr/element_purego.go
index 57f00871c2..68bd074b07 100644
--- a/ecc/bls12-381/fr/element_purego.go
+++ b/ecc/bls12-381/fr/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/element_test.go b/ecc/bls12-381/fr/element_test.go
index 049a31f4be..b86236997c 100644
--- a/ecc/bls12-381/fr/element_test.go
+++ b/ecc/bls12-381/fr/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/fft/bitreverse.go b/ecc/bls12-381/fr/fft/bitreverse.go
index d8482da16e..4fb86452ec 100644
--- a/ecc/bls12-381/fr/fft/bitreverse.go
+++ b/ecc/bls12-381/fr/fft/bitreverse.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/fft/bitreverse_test.go b/ecc/bls12-381/fr/fft/bitreverse_test.go
index 98ebd726bb..849a16bb26 100644
--- a/ecc/bls12-381/fr/fft/bitreverse_test.go
+++ b/ecc/bls12-381/fr/fft/bitreverse_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/fft/doc.go b/ecc/bls12-381/fr/fft/doc.go
index 1ef04db2df..4cce0f9779 100644
--- a/ecc/bls12-381/fr/fft/doc.go
+++ b/ecc/bls12-381/fr/fft/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/fft/domain.go b/ecc/bls12-381/fr/fft/domain.go
index cadf32fcd1..db35cea919 100644
--- a/ecc/bls12-381/fr/fft/domain.go
+++ b/ecc/bls12-381/fr/fft/domain.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/fft/domain_test.go b/ecc/bls12-381/fr/fft/domain_test.go
index d95288076c..e445d3cc12 100644
--- a/ecc/bls12-381/fr/fft/domain_test.go
+++ b/ecc/bls12-381/fr/fft/domain_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/fft/fft.go b/ecc/bls12-381/fr/fft/fft.go
index 85722b5eb1..4279e93d18 100644
--- a/ecc/bls12-381/fr/fft/fft.go
+++ b/ecc/bls12-381/fr/fft/fft.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/fft/fft_test.go b/ecc/bls12-381/fr/fft/fft_test.go
index 774b42ab43..9858710ec2 100644
--- a/ecc/bls12-381/fr/fft/fft_test.go
+++ b/ecc/bls12-381/fr/fft/fft_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/fft/options.go b/ecc/bls12-381/fr/fft/options.go
index cdd4fa97ff..c1afb7b406 100644
--- a/ecc/bls12-381/fr/fft/options.go
+++ b/ecc/bls12-381/fr/fft/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/fri/doc.go b/ecc/bls12-381/fr/fri/doc.go
index 428dabf625..cea69fc79a 100644
--- a/ecc/bls12-381/fr/fri/doc.go
+++ b/ecc/bls12-381/fr/fri/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/fri/fri.go b/ecc/bls12-381/fr/fri/fri.go
index 1ac43ff169..c09db4bd72 100644
--- a/ecc/bls12-381/fr/fri/fri.go
+++ b/ecc/bls12-381/fr/fri/fri.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/fri/fri_test.go b/ecc/bls12-381/fr/fri/fri_test.go
index 8cc11c42f4..6f479e148e 100644
--- a/ecc/bls12-381/fr/fri/fri_test.go
+++ b/ecc/bls12-381/fr/fri/fri_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/generator.go b/ecc/bls12-381/fr/generator.go
index 6d9ebe7a2f..fc5403501e 100644
--- a/ecc/bls12-381/fr/generator.go
+++ b/ecc/bls12-381/fr/generator.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/gkr/gkr.go b/ecc/bls12-381/fr/gkr/gkr.go
index 0d3dabbd1a..64398b3e2a 100644
--- a/ecc/bls12-381/fr/gkr/gkr.go
+++ b/ecc/bls12-381/fr/gkr/gkr.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/gkr/gkr_test.go b/ecc/bls12-381/fr/gkr/gkr_test.go
index a6c5e86119..b3e91cab0f 100644
--- a/ecc/bls12-381/fr/gkr/gkr_test.go
+++ b/ecc/bls12-381/fr/gkr/gkr_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
@@ -325,7 +325,7 @@ func mimcCircuit(numRounds int) Circuit {
 
 func testMimc(t *testing.T, numRounds int, inputAssignments ...[]fr.Element) {
 	//TODO: Implement mimc correctly. Currently, the computation is mimc(a,b) = cipher( cipher( ... cipher(a, b), b) ..., b)
-	// @AlexandreBelling: Please explain the extra layers in https://github.com/ConsenSys/gkr-mimc/blob/81eada039ab4ed403b7726b535adb63026e8011f/examples/mimc.go#L10
+	// @AlexandreBelling: Please explain the extra layers in https://github.com/Consensys/gkr-mimc/blob/81eada039ab4ed403b7726b535adb63026e8011f/examples/mimc.go#L10
 
 	c := mimcCircuit(numRounds)
 
diff --git a/ecc/bls12-381/fr/hash_to_field/doc.go b/ecc/bls12-381/fr/hash_to_field/doc.go
index 345c8b57df..e50410d80a 100644
--- a/ecc/bls12-381/fr/hash_to_field/doc.go
+++ b/ecc/bls12-381/fr/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/hash_to_field/hash_to_field.go b/ecc/bls12-381/fr/hash_to_field/hash_to_field.go
index 174e7f6303..ef5ac1e400 100644
--- a/ecc/bls12-381/fr/hash_to_field/hash_to_field.go
+++ b/ecc/bls12-381/fr/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/hash_to_field/hash_to_field_test.go b/ecc/bls12-381/fr/hash_to_field/hash_to_field_test.go
index 67fe5640d6..6965382276 100644
--- a/ecc/bls12-381/fr/hash_to_field/hash_to_field_test.go
+++ b/ecc/bls12-381/fr/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/iop/doc.go b/ecc/bls12-381/fr/iop/doc.go
index ee3facf1e1..2ef06dfe1a 100644
--- a/ecc/bls12-381/fr/iop/doc.go
+++ b/ecc/bls12-381/fr/iop/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/iop/expressions.go b/ecc/bls12-381/fr/iop/expressions.go
index bd85279e75..2926911d05 100644
--- a/ecc/bls12-381/fr/iop/expressions.go
+++ b/ecc/bls12-381/fr/iop/expressions.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/iop/expressions_test.go b/ecc/bls12-381/fr/iop/expressions_test.go
index 003c4ee78a..c4d4e16273 100644
--- a/ecc/bls12-381/fr/iop/expressions_test.go
+++ b/ecc/bls12-381/fr/iop/expressions_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/iop/polynomial.go b/ecc/bls12-381/fr/iop/polynomial.go
index 8bb33d05c6..ed805584c0 100644
--- a/ecc/bls12-381/fr/iop/polynomial.go
+++ b/ecc/bls12-381/fr/iop/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/iop/polynomial_test.go b/ecc/bls12-381/fr/iop/polynomial_test.go
index dcc85a2193..cba62562d3 100644
--- a/ecc/bls12-381/fr/iop/polynomial_test.go
+++ b/ecc/bls12-381/fr/iop/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/iop/quotient.go b/ecc/bls12-381/fr/iop/quotient.go
index 9c2b4a3f6d..5c4b2a9eb8 100644
--- a/ecc/bls12-381/fr/iop/quotient.go
+++ b/ecc/bls12-381/fr/iop/quotient.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/iop/quotient_test.go b/ecc/bls12-381/fr/iop/quotient_test.go
index 0981a0a411..78035417c0 100644
--- a/ecc/bls12-381/fr/iop/quotient_test.go
+++ b/ecc/bls12-381/fr/iop/quotient_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/iop/ratios.go b/ecc/bls12-381/fr/iop/ratios.go
index 39adead354..91946e3bbd 100644
--- a/ecc/bls12-381/fr/iop/ratios.go
+++ b/ecc/bls12-381/fr/iop/ratios.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/iop/ratios_test.go b/ecc/bls12-381/fr/iop/ratios_test.go
index 7d0e8b0030..0bb1c9b036 100644
--- a/ecc/bls12-381/fr/iop/ratios_test.go
+++ b/ecc/bls12-381/fr/iop/ratios_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/iop/utils.go b/ecc/bls12-381/fr/iop/utils.go
index e65cafda8e..7f91ba67ee 100644
--- a/ecc/bls12-381/fr/iop/utils.go
+++ b/ecc/bls12-381/fr/iop/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/mimc/doc.go b/ecc/bls12-381/fr/mimc/doc.go
index cc7b101eb4..98aa3f8d81 100644
--- a/ecc/bls12-381/fr/mimc/doc.go
+++ b/ecc/bls12-381/fr/mimc/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/mimc/mimc.go b/ecc/bls12-381/fr/mimc/mimc.go
index 8455789c59..59899b3e92 100644
--- a/ecc/bls12-381/fr/mimc/mimc.go
+++ b/ecc/bls12-381/fr/mimc/mimc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/mimc/options.go b/ecc/bls12-381/fr/mimc/options.go
index 25f1e024b2..a9d4a57beb 100644
--- a/ecc/bls12-381/fr/mimc/options.go
+++ b/ecc/bls12-381/fr/mimc/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/pedersen/doc.go b/ecc/bls12-381/fr/pedersen/doc.go
index 62a62f179f..2e24034936 100644
--- a/ecc/bls12-381/fr/pedersen/doc.go
+++ b/ecc/bls12-381/fr/pedersen/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/pedersen/example_test.go b/ecc/bls12-381/fr/pedersen/example_test.go
index 23a97be288..2e61788603 100644
--- a/ecc/bls12-381/fr/pedersen/example_test.go
+++ b/ecc/bls12-381/fr/pedersen/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/pedersen/pedersen.go b/ecc/bls12-381/fr/pedersen/pedersen.go
index ffbd2bc283..1f9e904bff 100644
--- a/ecc/bls12-381/fr/pedersen/pedersen.go
+++ b/ecc/bls12-381/fr/pedersen/pedersen.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
@@ -105,7 +105,7 @@ func (pk *ProvingKey) ProveKnowledge(values []fr.Element) (pok curve.G1Affine, e
 	}
 
 	// TODO @gbotrel this will spawn more than one task, see
-	// https://github.com/ConsenSys/gnark-crypto/issues/269
+	// https://github.com/Consensys/gnark-crypto/issues/269
 	config := ecc.MultiExpConfig{
 		NbTasks: 1, // TODO Experiment
 	}
@@ -123,7 +123,7 @@ func (pk *ProvingKey) Commit(values []fr.Element) (commitment curve.G1Affine, er
 	}
 
 	// TODO @gbotrel this will spawn more than one task, see
-	// https://github.com/ConsenSys/gnark-crypto/issues/269
+	// https://github.com/Consensys/gnark-crypto/issues/269
 	config := ecc.MultiExpConfig{
 		NbTasks: 1,
 	}
@@ -184,7 +184,7 @@ func BatchProve(pk []ProvingKey, values [][]fr.Element, combinationCoeff fr.Elem
 	}
 
 	// TODO @gbotrel this will spawn more than one task, see
-	// https://github.com/ConsenSys/gnark-crypto/issues/269
+	// https://github.com/Consensys/gnark-crypto/issues/269
 	config := ecc.MultiExpConfig{
 		NbTasks: 1,
 	}
diff --git a/ecc/bls12-381/fr/pedersen/pedersen_test.go b/ecc/bls12-381/fr/pedersen/pedersen_test.go
index 6728acb8ab..db38149ebd 100644
--- a/ecc/bls12-381/fr/pedersen/pedersen_test.go
+++ b/ecc/bls12-381/fr/pedersen/pedersen_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/permutation/doc.go b/ecc/bls12-381/fr/permutation/doc.go
index 5f346b5a53..e24cd82923 100644
--- a/ecc/bls12-381/fr/permutation/doc.go
+++ b/ecc/bls12-381/fr/permutation/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/permutation/permutation.go b/ecc/bls12-381/fr/permutation/permutation.go
index 0e8623fcb0..598db32e18 100644
--- a/ecc/bls12-381/fr/permutation/permutation.go
+++ b/ecc/bls12-381/fr/permutation/permutation.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/permutation/permutation_test.go b/ecc/bls12-381/fr/permutation/permutation_test.go
index b95c1e45c8..4777690a36 100644
--- a/ecc/bls12-381/fr/permutation/permutation_test.go
+++ b/ecc/bls12-381/fr/permutation/permutation_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/plookup/doc.go b/ecc/bls12-381/fr/plookup/doc.go
index d163104002..7a02c59719 100644
--- a/ecc/bls12-381/fr/plookup/doc.go
+++ b/ecc/bls12-381/fr/plookup/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/plookup/plookup_test.go b/ecc/bls12-381/fr/plookup/plookup_test.go
index 6155368448..adaa0f4e0b 100644
--- a/ecc/bls12-381/fr/plookup/plookup_test.go
+++ b/ecc/bls12-381/fr/plookup/plookup_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/plookup/table.go b/ecc/bls12-381/fr/plookup/table.go
index cb08029bb7..2a87f1016c 100644
--- a/ecc/bls12-381/fr/plookup/table.go
+++ b/ecc/bls12-381/fr/plookup/table.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/plookup/vector.go b/ecc/bls12-381/fr/plookup/vector.go
index f5dfd96335..81099f9253 100644
--- a/ecc/bls12-381/fr/plookup/vector.go
+++ b/ecc/bls12-381/fr/plookup/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/polynomial/doc.go b/ecc/bls12-381/fr/polynomial/doc.go
index 35b3f725c1..fd96328e8f 100644
--- a/ecc/bls12-381/fr/polynomial/doc.go
+++ b/ecc/bls12-381/fr/polynomial/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/polynomial/multilin.go b/ecc/bls12-381/fr/polynomial/multilin.go
index 2210816ca7..6880aa976c 100644
--- a/ecc/bls12-381/fr/polynomial/multilin.go
+++ b/ecc/bls12-381/fr/polynomial/multilin.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/polynomial/multilin_test.go b/ecc/bls12-381/fr/polynomial/multilin_test.go
index cca2a08d24..a10ce6fada 100644
--- a/ecc/bls12-381/fr/polynomial/multilin_test.go
+++ b/ecc/bls12-381/fr/polynomial/multilin_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/polynomial/polynomial.go b/ecc/bls12-381/fr/polynomial/polynomial.go
index a5acca4a65..97821d7281 100644
--- a/ecc/bls12-381/fr/polynomial/polynomial.go
+++ b/ecc/bls12-381/fr/polynomial/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/polynomial/polynomial_test.go b/ecc/bls12-381/fr/polynomial/polynomial_test.go
index 12868919f9..33b8bc86e8 100644
--- a/ecc/bls12-381/fr/polynomial/polynomial_test.go
+++ b/ecc/bls12-381/fr/polynomial/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/polynomial/pool.go b/ecc/bls12-381/fr/polynomial/pool.go
index fd736e33b8..d8703606f0 100644
--- a/ecc/bls12-381/fr/polynomial/pool.go
+++ b/ecc/bls12-381/fr/polynomial/pool.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/poseidon2/poseidon2.go b/ecc/bls12-381/fr/poseidon2/poseidon2.go
index e33bff9bce..2933570497 100644
--- a/ecc/bls12-381/fr/poseidon2/poseidon2.go
+++ b/ecc/bls12-381/fr/poseidon2/poseidon2.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/poseidon2/poseidon2_test.go b/ecc/bls12-381/fr/poseidon2/poseidon2_test.go
index 0345323466..21ad142725 100644
--- a/ecc/bls12-381/fr/poseidon2/poseidon2_test.go
+++ b/ecc/bls12-381/fr/poseidon2/poseidon2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/sumcheck/sumcheck.go b/ecc/bls12-381/fr/sumcheck/sumcheck.go
index b15dfc199b..ee6e6d80d8 100644
--- a/ecc/bls12-381/fr/sumcheck/sumcheck.go
+++ b/ecc/bls12-381/fr/sumcheck/sumcheck.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/sumcheck/sumcheck_test.go b/ecc/bls12-381/fr/sumcheck/sumcheck_test.go
index b0ef690a61..e8c3134886 100644
--- a/ecc/bls12-381/fr/sumcheck/sumcheck_test.go
+++ b/ecc/bls12-381/fr/sumcheck/sumcheck_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/test_vector_utils/test_vector_utils.go b/ecc/bls12-381/fr/test_vector_utils/test_vector_utils.go
index 95d4ab283e..802a39e536 100644
--- a/ecc/bls12-381/fr/test_vector_utils/test_vector_utils.go
+++ b/ecc/bls12-381/fr/test_vector_utils/test_vector_utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/vector.go b/ecc/bls12-381/fr/vector.go
index 8b59bd36e9..4654b1b2d3 100644
--- a/ecc/bls12-381/fr/vector.go
+++ b/ecc/bls12-381/fr/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/vector_amd64.go b/ecc/bls12-381/fr/vector_amd64.go
index b27679827c..a7dcec3b25 100644
--- a/ecc/bls12-381/fr/vector_amd64.go
+++ b/ecc/bls12-381/fr/vector_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/vector_purego.go b/ecc/bls12-381/fr/vector_purego.go
index 5973d16ce2..db43e73504 100644
--- a/ecc/bls12-381/fr/vector_purego.go
+++ b/ecc/bls12-381/fr/vector_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || !amd64
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/vector_test.go b/ecc/bls12-381/fr/vector_test.go
index a094bc0ac6..f6179e7824 100644
--- a/ecc/bls12-381/fr/vector_test.go
+++ b/ecc/bls12-381/fr/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/g1.go b/ecc/bls12-381/g1.go
index 1744ec2816..6ab856ca90 100644
--- a/ecc/bls12-381/g1.go
+++ b/ecc/bls12-381/g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/g1_test.go b/ecc/bls12-381/g1_test.go
index 20d77f4b2f..db2782524e 100644
--- a/ecc/bls12-381/g1_test.go
+++ b/ecc/bls12-381/g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/g2.go b/ecc/bls12-381/g2.go
index b725907acb..a631408695 100644
--- a/ecc/bls12-381/g2.go
+++ b/ecc/bls12-381/g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/g2_test.go b/ecc/bls12-381/g2_test.go
index 244c6ae3b8..f2ff12473e 100644
--- a/ecc/bls12-381/g2_test.go
+++ b/ecc/bls12-381/g2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/hash_to_g1.go b/ecc/bls12-381/hash_to_g1.go
index 1ba586b5fa..a4b9f3d4c5 100644
--- a/ecc/bls12-381/hash_to_g1.go
+++ b/ecc/bls12-381/hash_to_g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/hash_to_g1_test.go b/ecc/bls12-381/hash_to_g1_test.go
index 2bfa52ae4f..47e20b0549 100644
--- a/ecc/bls12-381/hash_to_g1_test.go
+++ b/ecc/bls12-381/hash_to_g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/hash_to_g2.go b/ecc/bls12-381/hash_to_g2.go
index 43833ecda0..27e970b6db 100644
--- a/ecc/bls12-381/hash_to_g2.go
+++ b/ecc/bls12-381/hash_to_g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/hash_to_g2_test.go b/ecc/bls12-381/hash_to_g2_test.go
index 142dd2695a..b714de662c 100644
--- a/ecc/bls12-381/hash_to_g2_test.go
+++ b/ecc/bls12-381/hash_to_g2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/internal/fptower/asm.go b/ecc/bls12-381/internal/fptower/asm.go
index f1ff282d0b..7d64458b6c 100644
--- a/ecc/bls12-381/internal/fptower/asm.go
+++ b/ecc/bls12-381/internal/fptower/asm.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/internal/fptower/asm_noadx.go b/ecc/bls12-381/internal/fptower/asm_noadx.go
index 3885d93d55..28588f65a0 100644
--- a/ecc/bls12-381/internal/fptower/asm_noadx.go
+++ b/ecc/bls12-381/internal/fptower/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/internal/fptower/e12.go b/ecc/bls12-381/internal/fptower/e12.go
index 8664b8f175..03f0568455 100644
--- a/ecc/bls12-381/internal/fptower/e12.go
+++ b/ecc/bls12-381/internal/fptower/e12.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/internal/fptower/e12_test.go b/ecc/bls12-381/internal/fptower/e12_test.go
index b7b1f6181a..aac39f80f1 100644
--- a/ecc/bls12-381/internal/fptower/e12_test.go
+++ b/ecc/bls12-381/internal/fptower/e12_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/internal/fptower/e2.go b/ecc/bls12-381/internal/fptower/e2.go
index 64c535073b..11f9d4c3c0 100644
--- a/ecc/bls12-381/internal/fptower/e2.go
+++ b/ecc/bls12-381/internal/fptower/e2.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/internal/fptower/e2_amd64.go b/ecc/bls12-381/internal/fptower/e2_amd64.go
index 872fb85e56..a73ff678a9 100644
--- a/ecc/bls12-381/internal/fptower/e2_amd64.go
+++ b/ecc/bls12-381/internal/fptower/e2_amd64.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/internal/fptower/e2_amd64.s b/ecc/bls12-381/internal/fptower/e2_amd64.s
index 6163a305b6..8448eef7ca 100644
--- a/ecc/bls12-381/internal/fptower/e2_amd64.s
+++ b/ecc/bls12-381/internal/fptower/e2_amd64.s
@@ -1,4 +1,4 @@
-// Copyright 2020 ConsenSys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 #include "textflag.h"
diff --git a/ecc/bls12-381/internal/fptower/e2_bls381.go b/ecc/bls12-381/internal/fptower/e2_bls381.go
index 32fb644b69..9a498801b1 100644
--- a/ecc/bls12-381/internal/fptower/e2_bls381.go
+++ b/ecc/bls12-381/internal/fptower/e2_bls381.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls12-381/internal/fptower/e2_bls381_fallback.go b/ecc/bls12-381/internal/fptower/e2_bls381_fallback.go
index 0ae39042dc..34f5eccebb 100644
--- a/ecc/bls12-381/internal/fptower/e2_bls381_fallback.go
+++ b/ecc/bls12-381/internal/fptower/e2_bls381_fallback.go
@@ -1,19 +1,8 @@
 //go:build !amd64
 // +build !amd64
 
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls12-381/internal/fptower/e2_fallback.go b/ecc/bls12-381/internal/fptower/e2_fallback.go
index eaea355699..3dff96dcea 100644
--- a/ecc/bls12-381/internal/fptower/e2_fallback.go
+++ b/ecc/bls12-381/internal/fptower/e2_fallback.go
@@ -1,6 +1,6 @@
 //go:build !amd64
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/internal/fptower/e2_test.go b/ecc/bls12-381/internal/fptower/e2_test.go
index e5e2a26bc7..0f8a8ed5bc 100644
--- a/ecc/bls12-381/internal/fptower/e2_test.go
+++ b/ecc/bls12-381/internal/fptower/e2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/internal/fptower/e6.go b/ecc/bls12-381/internal/fptower/e6.go
index 5f2cca6625..a3bd71a6cc 100644
--- a/ecc/bls12-381/internal/fptower/e6.go
+++ b/ecc/bls12-381/internal/fptower/e6.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/internal/fptower/e6_test.go b/ecc/bls12-381/internal/fptower/e6_test.go
index c6e33e9766..776ace70ae 100644
--- a/ecc/bls12-381/internal/fptower/e6_test.go
+++ b/ecc/bls12-381/internal/fptower/e6_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/internal/fptower/frobenius.go b/ecc/bls12-381/internal/fptower/frobenius.go
index 94b38f4282..a127cd3c8e 100644
--- a/ecc/bls12-381/internal/fptower/frobenius.go
+++ b/ecc/bls12-381/internal/fptower/frobenius.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls12-381/internal/fptower/parameters.go b/ecc/bls12-381/internal/fptower/parameters.go
index 9f97e11751..2b225b06fd 100644
--- a/ecc/bls12-381/internal/fptower/parameters.go
+++ b/ecc/bls12-381/internal/fptower/parameters.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls12-381/kzg/doc.go b/ecc/bls12-381/kzg/doc.go
index 6c3454a2d9..226614bbdf 100644
--- a/ecc/bls12-381/kzg/doc.go
+++ b/ecc/bls12-381/kzg/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/kzg/kzg.go b/ecc/bls12-381/kzg/kzg.go
index f043d0eb34..14dfcef106 100644
--- a/ecc/bls12-381/kzg/kzg.go
+++ b/ecc/bls12-381/kzg/kzg.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/kzg/kzg_test.go b/ecc/bls12-381/kzg/kzg_test.go
index 2734f35a5e..0883287cf7 100644
--- a/ecc/bls12-381/kzg/kzg_test.go
+++ b/ecc/bls12-381/kzg/kzg_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/kzg/marshal.go b/ecc/bls12-381/kzg/marshal.go
index 0682d13a32..11b9d5e09b 100644
--- a/ecc/bls12-381/kzg/marshal.go
+++ b/ecc/bls12-381/kzg/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/kzg/utils.go b/ecc/bls12-381/kzg/utils.go
index a803f99624..f796b1171b 100644
--- a/ecc/bls12-381/kzg/utils.go
+++ b/ecc/bls12-381/kzg/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/marshal.go b/ecc/bls12-381/marshal.go
index 4b23d88aba..f647957143 100644
--- a/ecc/bls12-381/marshal.go
+++ b/ecc/bls12-381/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/marshal_test.go b/ecc/bls12-381/marshal_test.go
index f8f8ffc6c7..b7d0f1916b 100644
--- a/ecc/bls12-381/marshal_test.go
+++ b/ecc/bls12-381/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/multiexp.go b/ecc/bls12-381/multiexp.go
index 967701d077..319440b5d4 100644
--- a/ecc/bls12-381/multiexp.go
+++ b/ecc/bls12-381/multiexp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/multiexp_affine.go b/ecc/bls12-381/multiexp_affine.go
index db91c99abe..1df94806f3 100644
--- a/ecc/bls12-381/multiexp_affine.go
+++ b/ecc/bls12-381/multiexp_affine.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
@@ -19,7 +19,7 @@ type batchOpG1Affine struct {
 // using affine coordinates for the buckets. To amortize the cost of the inverse in the affine addition
 // we use a batch affine addition.
 //
-// this is derived from a PR by 0x0ece : https://github.com/ConsenSys/gnark-crypto/pull/249
+// this is derived from a PR by 0x0ece : https://github.com/Consensys/gnark-crypto/pull/249
 // See Section 5.3: ia.cr/2022/1396
 func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP pG1Affine, TPP ppG1Affine, TQ qOpsG1Affine, TC cG1Affine](
 	chunk uint64,
@@ -346,7 +346,7 @@ type batchOpG2Affine struct {
 // using affine coordinates for the buckets. To amortize the cost of the inverse in the affine addition
 // we use a batch affine addition.
 //
-// this is derived from a PR by 0x0ece : https://github.com/ConsenSys/gnark-crypto/pull/249
+// this is derived from a PR by 0x0ece : https://github.com/Consensys/gnark-crypto/pull/249
 // See Section 5.3: ia.cr/2022/1396
 func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP pG2Affine, TPP ppG2Affine, TQ qOpsG2Affine, TC cG2Affine](
 	chunk uint64,
diff --git a/ecc/bls12-381/multiexp_jacobian.go b/ecc/bls12-381/multiexp_jacobian.go
index 4dab02eb7d..3d8a187f4f 100644
--- a/ecc/bls12-381/multiexp_jacobian.go
+++ b/ecc/bls12-381/multiexp_jacobian.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/multiexp_test.go b/ecc/bls12-381/multiexp_test.go
index fdda872161..9336fb1058 100644
--- a/ecc/bls12-381/multiexp_test.go
+++ b/ecc/bls12-381/multiexp_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/pairing.go b/ecc/bls12-381/pairing.go
index be2e8bc74e..72266a8f39 100644
--- a/ecc/bls12-381/pairing.go
+++ b/ecc/bls12-381/pairing.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package bls12381
 
diff --git a/ecc/bls12-381/pairing_test.go b/ecc/bls12-381/pairing_test.go
index 8ee0d8c553..813c8c530d 100644
--- a/ecc/bls12-381/pairing_test.go
+++ b/ecc/bls12-381/pairing_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/shplonk/doc.go b/ecc/bls12-381/shplonk/doc.go
index 17b34373c2..0367893999 100644
--- a/ecc/bls12-381/shplonk/doc.go
+++ b/ecc/bls12-381/shplonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/shplonk/example_test.go b/ecc/bls12-381/shplonk/example_test.go
index 2025360358..a350302627 100644
--- a/ecc/bls12-381/shplonk/example_test.go
+++ b/ecc/bls12-381/shplonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/shplonk/marshal.go b/ecc/bls12-381/shplonk/marshal.go
index ce2d5ffe26..f477d4e248 100644
--- a/ecc/bls12-381/shplonk/marshal.go
+++ b/ecc/bls12-381/shplonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/shplonk/shplonk.go b/ecc/bls12-381/shplonk/shplonk.go
index b3d9ec3240..44a6ad5f23 100644
--- a/ecc/bls12-381/shplonk/shplonk.go
+++ b/ecc/bls12-381/shplonk/shplonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/shplonk/shplonk_test.go b/ecc/bls12-381/shplonk/shplonk_test.go
index 682a21ff9d..240092d53a 100644
--- a/ecc/bls12-381/shplonk/shplonk_test.go
+++ b/ecc/bls12-381/shplonk/shplonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/twistededwards/curve.go b/ecc/bls12-381/twistededwards/curve.go
index 9239aabf63..43b1da7ef3 100644
--- a/ecc/bls12-381/twistededwards/curve.go
+++ b/ecc/bls12-381/twistededwards/curve.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/twistededwards/doc.go b/ecc/bls12-381/twistededwards/doc.go
index a284750f5b..53880a954b 100644
--- a/ecc/bls12-381/twistededwards/doc.go
+++ b/ecc/bls12-381/twistededwards/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/twistededwards/eddsa/doc.go b/ecc/bls12-381/twistededwards/eddsa/doc.go
index 2e2ee33568..5581f06406 100644
--- a/ecc/bls12-381/twistededwards/eddsa/doc.go
+++ b/ecc/bls12-381/twistededwards/eddsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/twistededwards/eddsa/eddsa.go b/ecc/bls12-381/twistededwards/eddsa/eddsa.go
index 3bab9a4046..c10e701839 100644
--- a/ecc/bls12-381/twistededwards/eddsa/eddsa.go
+++ b/ecc/bls12-381/twistededwards/eddsa/eddsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/twistededwards/eddsa/eddsa_test.go b/ecc/bls12-381/twistededwards/eddsa/eddsa_test.go
index 972c06d0d0..cccc545ff7 100644
--- a/ecc/bls12-381/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bls12-381/twistededwards/eddsa/eddsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/twistededwards/eddsa/marshal.go b/ecc/bls12-381/twistededwards/eddsa/marshal.go
index 2f4f26d4f3..39dabf92f7 100644
--- a/ecc/bls12-381/twistededwards/eddsa/marshal.go
+++ b/ecc/bls12-381/twistededwards/eddsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/twistededwards/point.go b/ecc/bls12-381/twistededwards/point.go
index 651f32b9ff..7f759b673f 100644
--- a/ecc/bls12-381/twistededwards/point.go
+++ b/ecc/bls12-381/twistededwards/point.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/twistededwards/point_test.go b/ecc/bls12-381/twistededwards/point_test.go
index af063f4a85..e6918921a1 100644
--- a/ecc/bls12-381/twistededwards/point_test.go
+++ b/ecc/bls12-381/twistededwards/point_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/ecdsa/doc.go b/ecc/bls24-315/ecdsa/doc.go
index 3ac19094ff..f7d5d79b76 100644
--- a/ecc/bls24-315/ecdsa/doc.go
+++ b/ecc/bls24-315/ecdsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/ecdsa/ecdsa.go b/ecc/bls24-315/ecdsa/ecdsa.go
index 51719a4d32..386e61e249 100644
--- a/ecc/bls24-315/ecdsa/ecdsa.go
+++ b/ecc/bls24-315/ecdsa/ecdsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/ecdsa/ecdsa_test.go b/ecc/bls24-315/ecdsa/ecdsa_test.go
index 0854c572b6..a264c28340 100644
--- a/ecc/bls24-315/ecdsa/ecdsa_test.go
+++ b/ecc/bls24-315/ecdsa/ecdsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/ecdsa/marshal.go b/ecc/bls24-315/ecdsa/marshal.go
index be6bca16e2..754a709fa5 100644
--- a/ecc/bls24-315/ecdsa/marshal.go
+++ b/ecc/bls24-315/ecdsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/ecdsa/marshal_test.go b/ecc/bls24-315/ecdsa/marshal_test.go
index 1195565dc0..f82b378d8b 100644
--- a/ecc/bls24-315/ecdsa/marshal_test.go
+++ b/ecc/bls24-315/ecdsa/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fflonk/doc.go b/ecc/bls24-315/fflonk/doc.go
index b717383d87..67a8094e35 100644
--- a/ecc/bls24-315/fflonk/doc.go
+++ b/ecc/bls24-315/fflonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fflonk/example_test.go b/ecc/bls24-315/fflonk/example_test.go
index bd2882d654..64a58839b7 100644
--- a/ecc/bls24-315/fflonk/example_test.go
+++ b/ecc/bls24-315/fflonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fflonk/fflonk.go b/ecc/bls24-315/fflonk/fflonk.go
index 65001bf7ac..460b5e4ffc 100644
--- a/ecc/bls24-315/fflonk/fflonk.go
+++ b/ecc/bls24-315/fflonk/fflonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fflonk/fflonk_test.go b/ecc/bls24-315/fflonk/fflonk_test.go
index 6c8d9cc9b9..11d09c1e20 100644
--- a/ecc/bls24-315/fflonk/fflonk_test.go
+++ b/ecc/bls24-315/fflonk/fflonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fflonk/marshal.go b/ecc/bls24-315/fflonk/marshal.go
index 7024c2ead4..e73cc1c98f 100644
--- a/ecc/bls24-315/fflonk/marshal.go
+++ b/ecc/bls24-315/fflonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/arith.go b/ecc/bls24-315/fp/arith.go
index b202a1549a..bb63552f5a 100644
--- a/ecc/bls24-315/fp/arith.go
+++ b/ecc/bls24-315/fp/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/asm_adx.go b/ecc/bls24-315/fp/asm_adx.go
index fe25e82db2..75e92992fe 100644
--- a/ecc/bls24-315/fp/asm_adx.go
+++ b/ecc/bls24-315/fp/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/asm_noadx.go b/ecc/bls24-315/fp/asm_noadx.go
index 95085a8e6f..304dfb7209 100644
--- a/ecc/bls24-315/fp/asm_noadx.go
+++ b/ecc/bls24-315/fp/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/doc.go b/ecc/bls24-315/fp/doc.go
index e9ea7b8d1b..3d963966ed 100644
--- a/ecc/bls24-315/fp/doc.go
+++ b/ecc/bls24-315/fp/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/element.go b/ecc/bls24-315/fp/element.go
index d6c40f6ebf..6e044eb0a9 100644
--- a/ecc/bls24-315/fp/element.go
+++ b/ecc/bls24-315/fp/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/element_amd64.go b/ecc/bls24-315/fp/element_amd64.go
index e72f552ad9..9cee062e5b 100644
--- a/ecc/bls24-315/fp/element_amd64.go
+++ b/ecc/bls24-315/fp/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/element_amd64.s b/ecc/bls24-315/fp/element_amd64.s
index 599977a11a..0f7e0b89ff 100644
--- a/ecc/bls24-315/fp/element_amd64.s
+++ b/ecc/bls24-315/fp/element_amd64.s
@@ -1,10 +1,10 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
-// We include the hash to force the Go compiler to recompile: 18184981773209750009
+// We include the hash to force the Go compiler to recompile: 4600622797032586825
 #include "../../../field/asm/element_5w_amd64.s"
 
diff --git a/ecc/bls24-315/fp/element_exp.go b/ecc/bls24-315/fp/element_exp.go
index b374460884..f85a7b3c70 100644
--- a/ecc/bls24-315/fp/element_exp.go
+++ b/ecc/bls24-315/fp/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/element_purego.go b/ecc/bls24-315/fp/element_purego.go
index abd4a49579..a954563d21 100644
--- a/ecc/bls24-315/fp/element_purego.go
+++ b/ecc/bls24-315/fp/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || !amd64
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/element_test.go b/ecc/bls24-315/fp/element_test.go
index 7e0e258fcc..ada5a127d6 100644
--- a/ecc/bls24-315/fp/element_test.go
+++ b/ecc/bls24-315/fp/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/hash_to_field/doc.go b/ecc/bls24-315/fp/hash_to_field/doc.go
index c5a207e06d..8ca5ee83c1 100644
--- a/ecc/bls24-315/fp/hash_to_field/doc.go
+++ b/ecc/bls24-315/fp/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/hash_to_field/hash_to_field.go b/ecc/bls24-315/fp/hash_to_field/hash_to_field.go
index e18be48acf..5a5764ed80 100644
--- a/ecc/bls24-315/fp/hash_to_field/hash_to_field.go
+++ b/ecc/bls24-315/fp/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/hash_to_field/hash_to_field_test.go b/ecc/bls24-315/fp/hash_to_field/hash_to_field_test.go
index 01296b0350..114009b320 100644
--- a/ecc/bls24-315/fp/hash_to_field/hash_to_field_test.go
+++ b/ecc/bls24-315/fp/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/vector.go b/ecc/bls24-315/fp/vector.go
index 6f62d12f76..6734ac80a3 100644
--- a/ecc/bls24-315/fp/vector.go
+++ b/ecc/bls24-315/fp/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/vector_purego.go b/ecc/bls24-315/fp/vector_purego.go
index 347b0df594..0cda361871 100644
--- a/ecc/bls24-315/fp/vector_purego.go
+++ b/ecc/bls24-315/fp/vector_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/vector_test.go b/ecc/bls24-315/fp/vector_test.go
index 0300a21e40..46cad267bc 100644
--- a/ecc/bls24-315/fp/vector_test.go
+++ b/ecc/bls24-315/fp/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/arith.go b/ecc/bls24-315/fr/arith.go
index 9285041f4b..dbba8a9ae4 100644
--- a/ecc/bls24-315/fr/arith.go
+++ b/ecc/bls24-315/fr/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/asm_adx.go b/ecc/bls24-315/fr/asm_adx.go
index 9e7da5e865..9b970335f1 100644
--- a/ecc/bls24-315/fr/asm_adx.go
+++ b/ecc/bls24-315/fr/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/asm_avx.go b/ecc/bls24-315/fr/asm_avx.go
index d6d7d7f87a..2a0a166ed4 100644
--- a/ecc/bls24-315/fr/asm_avx.go
+++ b/ecc/bls24-315/fr/asm_avx.go
@@ -1,6 +1,6 @@
 //go:build !noavx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/asm_noadx.go b/ecc/bls24-315/fr/asm_noadx.go
index 3456158655..96741014f2 100644
--- a/ecc/bls24-315/fr/asm_noadx.go
+++ b/ecc/bls24-315/fr/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/asm_noavx.go b/ecc/bls24-315/fr/asm_noavx.go
index 4eb73e9a78..3cb6968fb8 100644
--- a/ecc/bls24-315/fr/asm_noavx.go
+++ b/ecc/bls24-315/fr/asm_noavx.go
@@ -1,6 +1,6 @@
 //go:build noavx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/doc.go b/ecc/bls24-315/fr/doc.go
index ba6f150f02..cc2554feb3 100644
--- a/ecc/bls24-315/fr/doc.go
+++ b/ecc/bls24-315/fr/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/element.go b/ecc/bls24-315/fr/element.go
index a7b73b96b2..26f9cdafd1 100644
--- a/ecc/bls24-315/fr/element.go
+++ b/ecc/bls24-315/fr/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/element_amd64.go b/ecc/bls24-315/fr/element_amd64.go
index ca49d12590..4c3f2a8567 100644
--- a/ecc/bls24-315/fr/element_amd64.go
+++ b/ecc/bls24-315/fr/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/element_amd64.s b/ecc/bls24-315/fr/element_amd64.s
index ed8a36e04d..a7c6ffae66 100644
--- a/ecc/bls24-315/fr/element_amd64.s
+++ b/ecc/bls24-315/fr/element_amd64.s
@@ -1,10 +1,10 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
-// We include the hash to force the Go compiler to recompile: 9425145785761608449
+// We include the hash to force the Go compiler to recompile: 14652627197992229521
 #include "../../../field/asm/element_4w_amd64.s"
 
diff --git a/ecc/bls24-315/fr/element_arm64.go b/ecc/bls24-315/fr/element_arm64.go
index 22360d5f6e..824692948c 100644
--- a/ecc/bls24-315/fr/element_arm64.go
+++ b/ecc/bls24-315/fr/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/element_arm64.s b/ecc/bls24-315/fr/element_arm64.s
index a7bd036553..ef16eaba35 100644
--- a/ecc/bls24-315/fr/element_arm64.s
+++ b/ecc/bls24-315/fr/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/element_exp.go b/ecc/bls24-315/fr/element_exp.go
index a3ace60bd8..34f838ed2c 100644
--- a/ecc/bls24-315/fr/element_exp.go
+++ b/ecc/bls24-315/fr/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/element_purego.go b/ecc/bls24-315/fr/element_purego.go
index 7aa329a8be..e490d3d702 100644
--- a/ecc/bls24-315/fr/element_purego.go
+++ b/ecc/bls24-315/fr/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/element_test.go b/ecc/bls24-315/fr/element_test.go
index b0b1e10600..4f9bba391c 100644
--- a/ecc/bls24-315/fr/element_test.go
+++ b/ecc/bls24-315/fr/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/fft/bitreverse.go b/ecc/bls24-315/fr/fft/bitreverse.go
index 2fad50e345..f8d74370ac 100644
--- a/ecc/bls24-315/fr/fft/bitreverse.go
+++ b/ecc/bls24-315/fr/fft/bitreverse.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/fft/bitreverse_test.go b/ecc/bls24-315/fr/fft/bitreverse_test.go
index a9482b11a8..b3bf26d767 100644
--- a/ecc/bls24-315/fr/fft/bitreverse_test.go
+++ b/ecc/bls24-315/fr/fft/bitreverse_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/fft/doc.go b/ecc/bls24-315/fr/fft/doc.go
index 1ef04db2df..4cce0f9779 100644
--- a/ecc/bls24-315/fr/fft/doc.go
+++ b/ecc/bls24-315/fr/fft/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/fft/domain.go b/ecc/bls24-315/fr/fft/domain.go
index 7c8c82f1f3..e624004bb8 100644
--- a/ecc/bls24-315/fr/fft/domain.go
+++ b/ecc/bls24-315/fr/fft/domain.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/fft/domain_test.go b/ecc/bls24-315/fr/fft/domain_test.go
index d95288076c..e445d3cc12 100644
--- a/ecc/bls24-315/fr/fft/domain_test.go
+++ b/ecc/bls24-315/fr/fft/domain_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/fft/fft.go b/ecc/bls24-315/fr/fft/fft.go
index cd6c810b01..aa3a9107b7 100644
--- a/ecc/bls24-315/fr/fft/fft.go
+++ b/ecc/bls24-315/fr/fft/fft.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/fft/fft_test.go b/ecc/bls24-315/fr/fft/fft_test.go
index ae82a57626..39fab1295d 100644
--- a/ecc/bls24-315/fr/fft/fft_test.go
+++ b/ecc/bls24-315/fr/fft/fft_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/fft/options.go b/ecc/bls24-315/fr/fft/options.go
index 1ec17e0cf9..83d439844a 100644
--- a/ecc/bls24-315/fr/fft/options.go
+++ b/ecc/bls24-315/fr/fft/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/fri/doc.go b/ecc/bls24-315/fr/fri/doc.go
index 428dabf625..cea69fc79a 100644
--- a/ecc/bls24-315/fr/fri/doc.go
+++ b/ecc/bls24-315/fr/fri/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/fri/fri.go b/ecc/bls24-315/fr/fri/fri.go
index faacb699c7..de0669a0f2 100644
--- a/ecc/bls24-315/fr/fri/fri.go
+++ b/ecc/bls24-315/fr/fri/fri.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/fri/fri_test.go b/ecc/bls24-315/fr/fri/fri_test.go
index 614ffa853f..d6731670d6 100644
--- a/ecc/bls24-315/fr/fri/fri_test.go
+++ b/ecc/bls24-315/fr/fri/fri_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/generator.go b/ecc/bls24-315/fr/generator.go
index 7a1886db28..8e93206d41 100644
--- a/ecc/bls24-315/fr/generator.go
+++ b/ecc/bls24-315/fr/generator.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/gkr/gkr.go b/ecc/bls24-315/fr/gkr/gkr.go
index 3d53bb6e2a..abeeb3c24a 100644
--- a/ecc/bls24-315/fr/gkr/gkr.go
+++ b/ecc/bls24-315/fr/gkr/gkr.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/gkr/gkr_test.go b/ecc/bls24-315/fr/gkr/gkr_test.go
index 747739befd..e4aecce756 100644
--- a/ecc/bls24-315/fr/gkr/gkr_test.go
+++ b/ecc/bls24-315/fr/gkr/gkr_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
@@ -325,7 +325,7 @@ func mimcCircuit(numRounds int) Circuit {
 
 func testMimc(t *testing.T, numRounds int, inputAssignments ...[]fr.Element) {
 	//TODO: Implement mimc correctly. Currently, the computation is mimc(a,b) = cipher( cipher( ... cipher(a, b), b) ..., b)
-	// @AlexandreBelling: Please explain the extra layers in https://github.com/ConsenSys/gkr-mimc/blob/81eada039ab4ed403b7726b535adb63026e8011f/examples/mimc.go#L10
+	// @AlexandreBelling: Please explain the extra layers in https://github.com/Consensys/gkr-mimc/blob/81eada039ab4ed403b7726b535adb63026e8011f/examples/mimc.go#L10
 
 	c := mimcCircuit(numRounds)
 
diff --git a/ecc/bls24-315/fr/hash_to_field/doc.go b/ecc/bls24-315/fr/hash_to_field/doc.go
index d21cb934e8..c912145689 100644
--- a/ecc/bls24-315/fr/hash_to_field/doc.go
+++ b/ecc/bls24-315/fr/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/hash_to_field/hash_to_field.go b/ecc/bls24-315/fr/hash_to_field/hash_to_field.go
index 4b76f2e5d0..077fd835f5 100644
--- a/ecc/bls24-315/fr/hash_to_field/hash_to_field.go
+++ b/ecc/bls24-315/fr/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/hash_to_field/hash_to_field_test.go b/ecc/bls24-315/fr/hash_to_field/hash_to_field_test.go
index 6b66ee6993..2d144d57f6 100644
--- a/ecc/bls24-315/fr/hash_to_field/hash_to_field_test.go
+++ b/ecc/bls24-315/fr/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/iop/doc.go b/ecc/bls24-315/fr/iop/doc.go
index ee3facf1e1..2ef06dfe1a 100644
--- a/ecc/bls24-315/fr/iop/doc.go
+++ b/ecc/bls24-315/fr/iop/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/iop/expressions.go b/ecc/bls24-315/fr/iop/expressions.go
index 37acd066e9..b4706d77d6 100644
--- a/ecc/bls24-315/fr/iop/expressions.go
+++ b/ecc/bls24-315/fr/iop/expressions.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/iop/expressions_test.go b/ecc/bls24-315/fr/iop/expressions_test.go
index df720a4072..9f151110f1 100644
--- a/ecc/bls24-315/fr/iop/expressions_test.go
+++ b/ecc/bls24-315/fr/iop/expressions_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/iop/polynomial.go b/ecc/bls24-315/fr/iop/polynomial.go
index b8727248a2..33a5265ee4 100644
--- a/ecc/bls24-315/fr/iop/polynomial.go
+++ b/ecc/bls24-315/fr/iop/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/iop/polynomial_test.go b/ecc/bls24-315/fr/iop/polynomial_test.go
index 71b63b1058..89d65b2fd6 100644
--- a/ecc/bls24-315/fr/iop/polynomial_test.go
+++ b/ecc/bls24-315/fr/iop/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/iop/quotient.go b/ecc/bls24-315/fr/iop/quotient.go
index 36fffc9edb..b023028856 100644
--- a/ecc/bls24-315/fr/iop/quotient.go
+++ b/ecc/bls24-315/fr/iop/quotient.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/iop/quotient_test.go b/ecc/bls24-315/fr/iop/quotient_test.go
index ad7b8b2590..acba6e7537 100644
--- a/ecc/bls24-315/fr/iop/quotient_test.go
+++ b/ecc/bls24-315/fr/iop/quotient_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/iop/ratios.go b/ecc/bls24-315/fr/iop/ratios.go
index c814d85f94..c770531d85 100644
--- a/ecc/bls24-315/fr/iop/ratios.go
+++ b/ecc/bls24-315/fr/iop/ratios.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/iop/ratios_test.go b/ecc/bls24-315/fr/iop/ratios_test.go
index 3480ce3d70..1a951f2769 100644
--- a/ecc/bls24-315/fr/iop/ratios_test.go
+++ b/ecc/bls24-315/fr/iop/ratios_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/iop/utils.go b/ecc/bls24-315/fr/iop/utils.go
index cf4e53c00c..7b70f0ad9c 100644
--- a/ecc/bls24-315/fr/iop/utils.go
+++ b/ecc/bls24-315/fr/iop/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/mimc/doc.go b/ecc/bls24-315/fr/mimc/doc.go
index cc7b101eb4..98aa3f8d81 100644
--- a/ecc/bls24-315/fr/mimc/doc.go
+++ b/ecc/bls24-315/fr/mimc/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/mimc/mimc.go b/ecc/bls24-315/fr/mimc/mimc.go
index 0415a19f30..c91ead0218 100644
--- a/ecc/bls24-315/fr/mimc/mimc.go
+++ b/ecc/bls24-315/fr/mimc/mimc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/mimc/options.go b/ecc/bls24-315/fr/mimc/options.go
index 17e9bdb16f..b850cc2ce3 100644
--- a/ecc/bls24-315/fr/mimc/options.go
+++ b/ecc/bls24-315/fr/mimc/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/pedersen/doc.go b/ecc/bls24-315/fr/pedersen/doc.go
index 62a62f179f..2e24034936 100644
--- a/ecc/bls24-315/fr/pedersen/doc.go
+++ b/ecc/bls24-315/fr/pedersen/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/pedersen/example_test.go b/ecc/bls24-315/fr/pedersen/example_test.go
index 4d93e82b01..dd071f1143 100644
--- a/ecc/bls24-315/fr/pedersen/example_test.go
+++ b/ecc/bls24-315/fr/pedersen/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/pedersen/pedersen.go b/ecc/bls24-315/fr/pedersen/pedersen.go
index 2fa8fd038b..fec061e224 100644
--- a/ecc/bls24-315/fr/pedersen/pedersen.go
+++ b/ecc/bls24-315/fr/pedersen/pedersen.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
@@ -105,7 +105,7 @@ func (pk *ProvingKey) ProveKnowledge(values []fr.Element) (pok curve.G1Affine, e
 	}
 
 	// TODO @gbotrel this will spawn more than one task, see
-	// https://github.com/ConsenSys/gnark-crypto/issues/269
+	// https://github.com/Consensys/gnark-crypto/issues/269
 	config := ecc.MultiExpConfig{
 		NbTasks: 1, // TODO Experiment
 	}
@@ -123,7 +123,7 @@ func (pk *ProvingKey) Commit(values []fr.Element) (commitment curve.G1Affine, er
 	}
 
 	// TODO @gbotrel this will spawn more than one task, see
-	// https://github.com/ConsenSys/gnark-crypto/issues/269
+	// https://github.com/Consensys/gnark-crypto/issues/269
 	config := ecc.MultiExpConfig{
 		NbTasks: 1,
 	}
@@ -184,7 +184,7 @@ func BatchProve(pk []ProvingKey, values [][]fr.Element, combinationCoeff fr.Elem
 	}
 
 	// TODO @gbotrel this will spawn more than one task, see
-	// https://github.com/ConsenSys/gnark-crypto/issues/269
+	// https://github.com/Consensys/gnark-crypto/issues/269
 	config := ecc.MultiExpConfig{
 		NbTasks: 1,
 	}
diff --git a/ecc/bls24-315/fr/pedersen/pedersen_test.go b/ecc/bls24-315/fr/pedersen/pedersen_test.go
index f44841537a..3fdc0ea160 100644
--- a/ecc/bls24-315/fr/pedersen/pedersen_test.go
+++ b/ecc/bls24-315/fr/pedersen/pedersen_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/permutation/doc.go b/ecc/bls24-315/fr/permutation/doc.go
index 5f346b5a53..e24cd82923 100644
--- a/ecc/bls24-315/fr/permutation/doc.go
+++ b/ecc/bls24-315/fr/permutation/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/permutation/permutation.go b/ecc/bls24-315/fr/permutation/permutation.go
index dfe5b2d736..fb99644a3a 100644
--- a/ecc/bls24-315/fr/permutation/permutation.go
+++ b/ecc/bls24-315/fr/permutation/permutation.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/permutation/permutation_test.go b/ecc/bls24-315/fr/permutation/permutation_test.go
index b68ea7357b..10e81920eb 100644
--- a/ecc/bls24-315/fr/permutation/permutation_test.go
+++ b/ecc/bls24-315/fr/permutation/permutation_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/plookup/doc.go b/ecc/bls24-315/fr/plookup/doc.go
index d163104002..7a02c59719 100644
--- a/ecc/bls24-315/fr/plookup/doc.go
+++ b/ecc/bls24-315/fr/plookup/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/plookup/plookup_test.go b/ecc/bls24-315/fr/plookup/plookup_test.go
index d96da661d7..2ea5988772 100644
--- a/ecc/bls24-315/fr/plookup/plookup_test.go
+++ b/ecc/bls24-315/fr/plookup/plookup_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/plookup/table.go b/ecc/bls24-315/fr/plookup/table.go
index da09ef6bc9..bf25270da3 100644
--- a/ecc/bls24-315/fr/plookup/table.go
+++ b/ecc/bls24-315/fr/plookup/table.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/plookup/vector.go b/ecc/bls24-315/fr/plookup/vector.go
index a63bc9d504..c271a720c7 100644
--- a/ecc/bls24-315/fr/plookup/vector.go
+++ b/ecc/bls24-315/fr/plookup/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/polynomial/doc.go b/ecc/bls24-315/fr/polynomial/doc.go
index 35b3f725c1..fd96328e8f 100644
--- a/ecc/bls24-315/fr/polynomial/doc.go
+++ b/ecc/bls24-315/fr/polynomial/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/polynomial/multilin.go b/ecc/bls24-315/fr/polynomial/multilin.go
index 04849a2c45..3e338d8bf3 100644
--- a/ecc/bls24-315/fr/polynomial/multilin.go
+++ b/ecc/bls24-315/fr/polynomial/multilin.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/polynomial/multilin_test.go b/ecc/bls24-315/fr/polynomial/multilin_test.go
index 5540f39a06..2d71dd8e7e 100644
--- a/ecc/bls24-315/fr/polynomial/multilin_test.go
+++ b/ecc/bls24-315/fr/polynomial/multilin_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/polynomial/polynomial.go b/ecc/bls24-315/fr/polynomial/polynomial.go
index 38bd18f60a..98aad0c7ff 100644
--- a/ecc/bls24-315/fr/polynomial/polynomial.go
+++ b/ecc/bls24-315/fr/polynomial/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/polynomial/polynomial_test.go b/ecc/bls24-315/fr/polynomial/polynomial_test.go
index 08cd6b789d..1ff8b39cf4 100644
--- a/ecc/bls24-315/fr/polynomial/polynomial_test.go
+++ b/ecc/bls24-315/fr/polynomial/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/polynomial/pool.go b/ecc/bls24-315/fr/polynomial/pool.go
index 49895f16cc..0e2fda71d6 100644
--- a/ecc/bls24-315/fr/polynomial/pool.go
+++ b/ecc/bls24-315/fr/polynomial/pool.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/poseidon2/poseidon2.go b/ecc/bls24-315/fr/poseidon2/poseidon2.go
index 41e79d3f58..c32028d7b0 100644
--- a/ecc/bls24-315/fr/poseidon2/poseidon2.go
+++ b/ecc/bls24-315/fr/poseidon2/poseidon2.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/poseidon2/poseidon2_test.go b/ecc/bls24-315/fr/poseidon2/poseidon2_test.go
index 16b9f702f1..3fb0bc5d6e 100644
--- a/ecc/bls24-315/fr/poseidon2/poseidon2_test.go
+++ b/ecc/bls24-315/fr/poseidon2/poseidon2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/sumcheck/sumcheck.go b/ecc/bls24-315/fr/sumcheck/sumcheck.go
index d99787acfa..6cf52ba6cb 100644
--- a/ecc/bls24-315/fr/sumcheck/sumcheck.go
+++ b/ecc/bls24-315/fr/sumcheck/sumcheck.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/sumcheck/sumcheck_test.go b/ecc/bls24-315/fr/sumcheck/sumcheck_test.go
index edf64e3f75..55e0ad74a5 100644
--- a/ecc/bls24-315/fr/sumcheck/sumcheck_test.go
+++ b/ecc/bls24-315/fr/sumcheck/sumcheck_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/test_vector_utils/test_vector_utils.go b/ecc/bls24-315/fr/test_vector_utils/test_vector_utils.go
index 5c581de8d8..57942f2951 100644
--- a/ecc/bls24-315/fr/test_vector_utils/test_vector_utils.go
+++ b/ecc/bls24-315/fr/test_vector_utils/test_vector_utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/vector.go b/ecc/bls24-315/fr/vector.go
index 8b59bd36e9..4654b1b2d3 100644
--- a/ecc/bls24-315/fr/vector.go
+++ b/ecc/bls24-315/fr/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/vector_amd64.go b/ecc/bls24-315/fr/vector_amd64.go
index b27679827c..a7dcec3b25 100644
--- a/ecc/bls24-315/fr/vector_amd64.go
+++ b/ecc/bls24-315/fr/vector_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/vector_purego.go b/ecc/bls24-315/fr/vector_purego.go
index 5973d16ce2..db43e73504 100644
--- a/ecc/bls24-315/fr/vector_purego.go
+++ b/ecc/bls24-315/fr/vector_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || !amd64
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/vector_test.go b/ecc/bls24-315/fr/vector_test.go
index a094bc0ac6..f6179e7824 100644
--- a/ecc/bls24-315/fr/vector_test.go
+++ b/ecc/bls24-315/fr/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/g1.go b/ecc/bls24-315/g1.go
index e34e6fac32..78d959ae2a 100644
--- a/ecc/bls24-315/g1.go
+++ b/ecc/bls24-315/g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/g1_test.go b/ecc/bls24-315/g1_test.go
index 20e6008e02..22597de99a 100644
--- a/ecc/bls24-315/g1_test.go
+++ b/ecc/bls24-315/g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/g2.go b/ecc/bls24-315/g2.go
index a99cda6d0a..5b96e16e1a 100644
--- a/ecc/bls24-315/g2.go
+++ b/ecc/bls24-315/g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/g2_test.go b/ecc/bls24-315/g2_test.go
index ba45cd7ba3..8d630fabed 100644
--- a/ecc/bls24-315/g2_test.go
+++ b/ecc/bls24-315/g2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/hash_to_g1.go b/ecc/bls24-315/hash_to_g1.go
index 2c334c3642..45e5381028 100644
--- a/ecc/bls24-315/hash_to_g1.go
+++ b/ecc/bls24-315/hash_to_g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/hash_to_g1_test.go b/ecc/bls24-315/hash_to_g1_test.go
index 0e41f4fd53..25f4f9aca4 100644
--- a/ecc/bls24-315/hash_to_g1_test.go
+++ b/ecc/bls24-315/hash_to_g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/hash_to_g2.go b/ecc/bls24-315/hash_to_g2.go
index df1af0d751..5d5c167292 100644
--- a/ecc/bls24-315/hash_to_g2.go
+++ b/ecc/bls24-315/hash_to_g2.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package bls24315
 
diff --git a/ecc/bls24-315/internal/fptower/asm.go b/ecc/bls24-315/internal/fptower/asm.go
index ba19dae3e6..5857e743a3 100644
--- a/ecc/bls24-315/internal/fptower/asm.go
+++ b/ecc/bls24-315/internal/fptower/asm.go
@@ -1,19 +1,8 @@
 //go:build !noadx
 // +build !noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-315/internal/fptower/asm_noadx.go b/ecc/bls24-315/internal/fptower/asm_noadx.go
index 5cfde1587f..2bd913581d 100644
--- a/ecc/bls24-315/internal/fptower/asm_noadx.go
+++ b/ecc/bls24-315/internal/fptower/asm_noadx.go
@@ -1,19 +1,8 @@
 //go:build noadx
 // +build noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-315/internal/fptower/e12.go b/ecc/bls24-315/internal/fptower/e12.go
index ca0f092167..f962123817 100644
--- a/ecc/bls24-315/internal/fptower/e12.go
+++ b/ecc/bls24-315/internal/fptower/e12.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-315/internal/fptower/e12_test.go b/ecc/bls24-315/internal/fptower/e12_test.go
index c4cec4957f..d78aa07bb8 100644
--- a/ecc/bls24-315/internal/fptower/e12_test.go
+++ b/ecc/bls24-315/internal/fptower/e12_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-315/internal/fptower/e2.go b/ecc/bls24-315/internal/fptower/e2.go
index 2c1d53fbbb..c6f688d6cb 100644
--- a/ecc/bls24-315/internal/fptower/e2.go
+++ b/ecc/bls24-315/internal/fptower/e2.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-315/internal/fptower/e24.go b/ecc/bls24-315/internal/fptower/e24.go
index 22b7183b15..c5752cc7d6 100644
--- a/ecc/bls24-315/internal/fptower/e24.go
+++ b/ecc/bls24-315/internal/fptower/e24.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-315/internal/fptower/e24_test.go b/ecc/bls24-315/internal/fptower/e24_test.go
index d57ee28066..38f7a8e4d9 100644
--- a/ecc/bls24-315/internal/fptower/e24_test.go
+++ b/ecc/bls24-315/internal/fptower/e24_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-315/internal/fptower/e2_amd64.go b/ecc/bls24-315/internal/fptower/e2_amd64.go
index 87581cec64..33d5ad58da 100644
--- a/ecc/bls24-315/internal/fptower/e2_amd64.go
+++ b/ecc/bls24-315/internal/fptower/e2_amd64.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-315/internal/fptower/e2_amd64.s b/ecc/bls24-315/internal/fptower/e2_amd64.s
index 6f9615547a..ec3c5dc2f0 100644
--- a/ecc/bls24-315/internal/fptower/e2_amd64.s
+++ b/ecc/bls24-315/internal/fptower/e2_amd64.s
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 #include "textflag.h"
 #include "funcdata.h"
diff --git a/ecc/bls24-315/internal/fptower/e2_bls315.go b/ecc/bls24-315/internal/fptower/e2_bls315.go
index d1f46e4e01..b3d94df547 100644
--- a/ecc/bls24-315/internal/fptower/e2_bls315.go
+++ b/ecc/bls24-315/internal/fptower/e2_bls315.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-315/internal/fptower/e2_bls315_fallback.go b/ecc/bls24-315/internal/fptower/e2_bls315_fallback.go
index 2faf656e97..850899eb4b 100644
--- a/ecc/bls24-315/internal/fptower/e2_bls315_fallback.go
+++ b/ecc/bls24-315/internal/fptower/e2_bls315_fallback.go
@@ -1,19 +1,8 @@
 //go:build !amd64
 // +build !amd64
 
-// Copyright 2021 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-315/internal/fptower/e2_fallback.go b/ecc/bls24-315/internal/fptower/e2_fallback.go
index 3e9886c87d..0a0166a0a2 100644
--- a/ecc/bls24-315/internal/fptower/e2_fallback.go
+++ b/ecc/bls24-315/internal/fptower/e2_fallback.go
@@ -1,19 +1,8 @@
 //go:build !amd64
 // +build !amd64
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-315/internal/fptower/e2_test.go b/ecc/bls24-315/internal/fptower/e2_test.go
index 8743507943..c6ac7b02fa 100644
--- a/ecc/bls24-315/internal/fptower/e2_test.go
+++ b/ecc/bls24-315/internal/fptower/e2_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-315/internal/fptower/e4.go b/ecc/bls24-315/internal/fptower/e4.go
index 3eb683b782..20c34ce359 100644
--- a/ecc/bls24-315/internal/fptower/e4.go
+++ b/ecc/bls24-315/internal/fptower/e4.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-315/internal/fptower/e4_bls315.go b/ecc/bls24-315/internal/fptower/e4_bls315.go
index 30982c6dc6..3114895f2b 100644
--- a/ecc/bls24-315/internal/fptower/e4_bls315.go
+++ b/ecc/bls24-315/internal/fptower/e4_bls315.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-315/internal/fptower/e4_test.go b/ecc/bls24-315/internal/fptower/e4_test.go
index a3a52e8f34..05dcbfbcf2 100644
--- a/ecc/bls24-315/internal/fptower/e4_test.go
+++ b/ecc/bls24-315/internal/fptower/e4_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-315/internal/fptower/frobenius.go b/ecc/bls24-315/internal/fptower/frobenius.go
index ca2c72636f..623069108c 100644
--- a/ecc/bls24-315/internal/fptower/frobenius.go
+++ b/ecc/bls24-315/internal/fptower/frobenius.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://wwwApache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-315/internal/fptower/parameters.go b/ecc/bls24-315/internal/fptower/parameters.go
index 71ac9072cd..dda047b542 100644
--- a/ecc/bls24-315/internal/fptower/parameters.go
+++ b/ecc/bls24-315/internal/fptower/parameters.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-315/kzg/doc.go b/ecc/bls24-315/kzg/doc.go
index 6c3454a2d9..226614bbdf 100644
--- a/ecc/bls24-315/kzg/doc.go
+++ b/ecc/bls24-315/kzg/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/kzg/kzg.go b/ecc/bls24-315/kzg/kzg.go
index 41bb1e9b09..1bad3cc88b 100644
--- a/ecc/bls24-315/kzg/kzg.go
+++ b/ecc/bls24-315/kzg/kzg.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/kzg/kzg_test.go b/ecc/bls24-315/kzg/kzg_test.go
index b27de2332f..5c8a7fd91c 100644
--- a/ecc/bls24-315/kzg/kzg_test.go
+++ b/ecc/bls24-315/kzg/kzg_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/kzg/marshal.go b/ecc/bls24-315/kzg/marshal.go
index 5335f2b360..a98fe4c32b 100644
--- a/ecc/bls24-315/kzg/marshal.go
+++ b/ecc/bls24-315/kzg/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/kzg/utils.go b/ecc/bls24-315/kzg/utils.go
index f77285fe91..d6a22906f3 100644
--- a/ecc/bls24-315/kzg/utils.go
+++ b/ecc/bls24-315/kzg/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/marshal.go b/ecc/bls24-315/marshal.go
index 584c86f086..3b6c69362f 100644
--- a/ecc/bls24-315/marshal.go
+++ b/ecc/bls24-315/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/marshal_test.go b/ecc/bls24-315/marshal_test.go
index 670322eccb..71be7ba234 100644
--- a/ecc/bls24-315/marshal_test.go
+++ b/ecc/bls24-315/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/multiexp.go b/ecc/bls24-315/multiexp.go
index efd1ab0756..e704b09943 100644
--- a/ecc/bls24-315/multiexp.go
+++ b/ecc/bls24-315/multiexp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/multiexp_affine.go b/ecc/bls24-315/multiexp_affine.go
index 7fe32aed72..154405428b 100644
--- a/ecc/bls24-315/multiexp_affine.go
+++ b/ecc/bls24-315/multiexp_affine.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
@@ -19,7 +19,7 @@ type batchOpG1Affine struct {
 // using affine coordinates for the buckets. To amortize the cost of the inverse in the affine addition
 // we use a batch affine addition.
 //
-// this is derived from a PR by 0x0ece : https://github.com/ConsenSys/gnark-crypto/pull/249
+// this is derived from a PR by 0x0ece : https://github.com/Consensys/gnark-crypto/pull/249
 // See Section 5.3: ia.cr/2022/1396
 func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP pG1Affine, TPP ppG1Affine, TQ qOpsG1Affine, TC cG1Affine](
 	chunk uint64,
@@ -346,7 +346,7 @@ type batchOpG2Affine struct {
 // using affine coordinates for the buckets. To amortize the cost of the inverse in the affine addition
 // we use a batch affine addition.
 //
-// this is derived from a PR by 0x0ece : https://github.com/ConsenSys/gnark-crypto/pull/249
+// this is derived from a PR by 0x0ece : https://github.com/Consensys/gnark-crypto/pull/249
 // See Section 5.3: ia.cr/2022/1396
 func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP pG2Affine, TPP ppG2Affine, TQ qOpsG2Affine, TC cG2Affine](
 	chunk uint64,
diff --git a/ecc/bls24-315/multiexp_jacobian.go b/ecc/bls24-315/multiexp_jacobian.go
index dc866aa15a..1c72b1e0e6 100644
--- a/ecc/bls24-315/multiexp_jacobian.go
+++ b/ecc/bls24-315/multiexp_jacobian.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/multiexp_test.go b/ecc/bls24-315/multiexp_test.go
index beaca7c932..25eeb0e8e1 100644
--- a/ecc/bls24-315/multiexp_test.go
+++ b/ecc/bls24-315/multiexp_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/pairing.go b/ecc/bls24-315/pairing.go
index 31ab7c6eb9..22c06b72b0 100644
--- a/ecc/bls24-315/pairing.go
+++ b/ecc/bls24-315/pairing.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package bls24315
 
diff --git a/ecc/bls24-315/pairing_test.go b/ecc/bls24-315/pairing_test.go
index c168e97a88..ed2f9bc485 100644
--- a/ecc/bls24-315/pairing_test.go
+++ b/ecc/bls24-315/pairing_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/shplonk/doc.go b/ecc/bls24-315/shplonk/doc.go
index 17b34373c2..0367893999 100644
--- a/ecc/bls24-315/shplonk/doc.go
+++ b/ecc/bls24-315/shplonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/shplonk/example_test.go b/ecc/bls24-315/shplonk/example_test.go
index dd775e5d45..317f412b39 100644
--- a/ecc/bls24-315/shplonk/example_test.go
+++ b/ecc/bls24-315/shplonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/shplonk/marshal.go b/ecc/bls24-315/shplonk/marshal.go
index 10f7584165..52940254e6 100644
--- a/ecc/bls24-315/shplonk/marshal.go
+++ b/ecc/bls24-315/shplonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/shplonk/shplonk.go b/ecc/bls24-315/shplonk/shplonk.go
index 618607300c..19b6b53340 100644
--- a/ecc/bls24-315/shplonk/shplonk.go
+++ b/ecc/bls24-315/shplonk/shplonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/shplonk/shplonk_test.go b/ecc/bls24-315/shplonk/shplonk_test.go
index fbabc5c99d..8ed6d65c5f 100644
--- a/ecc/bls24-315/shplonk/shplonk_test.go
+++ b/ecc/bls24-315/shplonk/shplonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/twistededwards/curve.go b/ecc/bls24-315/twistededwards/curve.go
index 9864bfc984..0a84cf5207 100644
--- a/ecc/bls24-315/twistededwards/curve.go
+++ b/ecc/bls24-315/twistededwards/curve.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/twistededwards/doc.go b/ecc/bls24-315/twistededwards/doc.go
index 20a3090d78..c513532070 100644
--- a/ecc/bls24-315/twistededwards/doc.go
+++ b/ecc/bls24-315/twistededwards/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/twistededwards/eddsa/doc.go b/ecc/bls24-315/twistededwards/eddsa/doc.go
index dff0c7391d..827da24f9f 100644
--- a/ecc/bls24-315/twistededwards/eddsa/doc.go
+++ b/ecc/bls24-315/twistededwards/eddsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/twistededwards/eddsa/eddsa.go b/ecc/bls24-315/twistededwards/eddsa/eddsa.go
index 57f2f3f03e..1b65d64116 100644
--- a/ecc/bls24-315/twistededwards/eddsa/eddsa.go
+++ b/ecc/bls24-315/twistededwards/eddsa/eddsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/twistededwards/eddsa/eddsa_test.go b/ecc/bls24-315/twistededwards/eddsa/eddsa_test.go
index 5785b16f2c..a08863e866 100644
--- a/ecc/bls24-315/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bls24-315/twistededwards/eddsa/eddsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/twistededwards/eddsa/marshal.go b/ecc/bls24-315/twistededwards/eddsa/marshal.go
index 2d7499ceda..0972cd871a 100644
--- a/ecc/bls24-315/twistededwards/eddsa/marshal.go
+++ b/ecc/bls24-315/twistededwards/eddsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/twistededwards/point.go b/ecc/bls24-315/twistededwards/point.go
index bfb715d07a..eaa9e57382 100644
--- a/ecc/bls24-315/twistededwards/point.go
+++ b/ecc/bls24-315/twistededwards/point.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/twistededwards/point_test.go b/ecc/bls24-315/twistededwards/point_test.go
index 4daedb3d69..e9ee8dafe8 100644
--- a/ecc/bls24-315/twistededwards/point_test.go
+++ b/ecc/bls24-315/twistededwards/point_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/ecdsa/doc.go b/ecc/bls24-317/ecdsa/doc.go
index 1196c03f82..0ca93ecba4 100644
--- a/ecc/bls24-317/ecdsa/doc.go
+++ b/ecc/bls24-317/ecdsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/ecdsa/ecdsa.go b/ecc/bls24-317/ecdsa/ecdsa.go
index c3ce5b6722..62f23ce1d6 100644
--- a/ecc/bls24-317/ecdsa/ecdsa.go
+++ b/ecc/bls24-317/ecdsa/ecdsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/ecdsa/ecdsa_test.go b/ecc/bls24-317/ecdsa/ecdsa_test.go
index eb1176310e..0fe31803be 100644
--- a/ecc/bls24-317/ecdsa/ecdsa_test.go
+++ b/ecc/bls24-317/ecdsa/ecdsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/ecdsa/marshal.go b/ecc/bls24-317/ecdsa/marshal.go
index 3c32bc454c..cab0aa0486 100644
--- a/ecc/bls24-317/ecdsa/marshal.go
+++ b/ecc/bls24-317/ecdsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/ecdsa/marshal_test.go b/ecc/bls24-317/ecdsa/marshal_test.go
index 9d24be8307..955f27d3ff 100644
--- a/ecc/bls24-317/ecdsa/marshal_test.go
+++ b/ecc/bls24-317/ecdsa/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fflonk/doc.go b/ecc/bls24-317/fflonk/doc.go
index b717383d87..67a8094e35 100644
--- a/ecc/bls24-317/fflonk/doc.go
+++ b/ecc/bls24-317/fflonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fflonk/example_test.go b/ecc/bls24-317/fflonk/example_test.go
index bb9e6be7ea..5515d272db 100644
--- a/ecc/bls24-317/fflonk/example_test.go
+++ b/ecc/bls24-317/fflonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fflonk/fflonk.go b/ecc/bls24-317/fflonk/fflonk.go
index b191c6a7ca..461c379e11 100644
--- a/ecc/bls24-317/fflonk/fflonk.go
+++ b/ecc/bls24-317/fflonk/fflonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fflonk/fflonk_test.go b/ecc/bls24-317/fflonk/fflonk_test.go
index aa0b10fb55..feeb7d0f94 100644
--- a/ecc/bls24-317/fflonk/fflonk_test.go
+++ b/ecc/bls24-317/fflonk/fflonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fflonk/marshal.go b/ecc/bls24-317/fflonk/marshal.go
index 35f8f022dc..ecc8c9c308 100644
--- a/ecc/bls24-317/fflonk/marshal.go
+++ b/ecc/bls24-317/fflonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/arith.go b/ecc/bls24-317/fp/arith.go
index b202a1549a..bb63552f5a 100644
--- a/ecc/bls24-317/fp/arith.go
+++ b/ecc/bls24-317/fp/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/asm_adx.go b/ecc/bls24-317/fp/asm_adx.go
index fe25e82db2..75e92992fe 100644
--- a/ecc/bls24-317/fp/asm_adx.go
+++ b/ecc/bls24-317/fp/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/asm_noadx.go b/ecc/bls24-317/fp/asm_noadx.go
index 95085a8e6f..304dfb7209 100644
--- a/ecc/bls24-317/fp/asm_noadx.go
+++ b/ecc/bls24-317/fp/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/doc.go b/ecc/bls24-317/fp/doc.go
index 81296d0270..1e89d00a80 100644
--- a/ecc/bls24-317/fp/doc.go
+++ b/ecc/bls24-317/fp/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/element.go b/ecc/bls24-317/fp/element.go
index 2277f984e9..45b1fdb2a6 100644
--- a/ecc/bls24-317/fp/element.go
+++ b/ecc/bls24-317/fp/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/element_amd64.go b/ecc/bls24-317/fp/element_amd64.go
index e72f552ad9..9cee062e5b 100644
--- a/ecc/bls24-317/fp/element_amd64.go
+++ b/ecc/bls24-317/fp/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/element_amd64.s b/ecc/bls24-317/fp/element_amd64.s
index 599977a11a..0f7e0b89ff 100644
--- a/ecc/bls24-317/fp/element_amd64.s
+++ b/ecc/bls24-317/fp/element_amd64.s
@@ -1,10 +1,10 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
-// We include the hash to force the Go compiler to recompile: 18184981773209750009
+// We include the hash to force the Go compiler to recompile: 4600622797032586825
 #include "../../../field/asm/element_5w_amd64.s"
 
diff --git a/ecc/bls24-317/fp/element_exp.go b/ecc/bls24-317/fp/element_exp.go
index 508e6afb9e..894c2b2c86 100644
--- a/ecc/bls24-317/fp/element_exp.go
+++ b/ecc/bls24-317/fp/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/element_purego.go b/ecc/bls24-317/fp/element_purego.go
index 11740a36cd..4dfa399e1d 100644
--- a/ecc/bls24-317/fp/element_purego.go
+++ b/ecc/bls24-317/fp/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || !amd64
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/element_test.go b/ecc/bls24-317/fp/element_test.go
index f347cf5e8e..2c6ee96935 100644
--- a/ecc/bls24-317/fp/element_test.go
+++ b/ecc/bls24-317/fp/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/hash_to_field/doc.go b/ecc/bls24-317/fp/hash_to_field/doc.go
index 8e8b8feea0..d867383832 100644
--- a/ecc/bls24-317/fp/hash_to_field/doc.go
+++ b/ecc/bls24-317/fp/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/hash_to_field/hash_to_field.go b/ecc/bls24-317/fp/hash_to_field/hash_to_field.go
index 6c9726b2eb..2790fa6e29 100644
--- a/ecc/bls24-317/fp/hash_to_field/hash_to_field.go
+++ b/ecc/bls24-317/fp/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/hash_to_field/hash_to_field_test.go b/ecc/bls24-317/fp/hash_to_field/hash_to_field_test.go
index 928a3475fe..388120a90b 100644
--- a/ecc/bls24-317/fp/hash_to_field/hash_to_field_test.go
+++ b/ecc/bls24-317/fp/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/vector.go b/ecc/bls24-317/fp/vector.go
index 6f62d12f76..6734ac80a3 100644
--- a/ecc/bls24-317/fp/vector.go
+++ b/ecc/bls24-317/fp/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/vector_purego.go b/ecc/bls24-317/fp/vector_purego.go
index 347b0df594..0cda361871 100644
--- a/ecc/bls24-317/fp/vector_purego.go
+++ b/ecc/bls24-317/fp/vector_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/vector_test.go b/ecc/bls24-317/fp/vector_test.go
index 0300a21e40..46cad267bc 100644
--- a/ecc/bls24-317/fp/vector_test.go
+++ b/ecc/bls24-317/fp/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/arith.go b/ecc/bls24-317/fr/arith.go
index 9285041f4b..dbba8a9ae4 100644
--- a/ecc/bls24-317/fr/arith.go
+++ b/ecc/bls24-317/fr/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/asm_adx.go b/ecc/bls24-317/fr/asm_adx.go
index 9e7da5e865..9b970335f1 100644
--- a/ecc/bls24-317/fr/asm_adx.go
+++ b/ecc/bls24-317/fr/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/asm_avx.go b/ecc/bls24-317/fr/asm_avx.go
index d6d7d7f87a..2a0a166ed4 100644
--- a/ecc/bls24-317/fr/asm_avx.go
+++ b/ecc/bls24-317/fr/asm_avx.go
@@ -1,6 +1,6 @@
 //go:build !noavx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/asm_noadx.go b/ecc/bls24-317/fr/asm_noadx.go
index 3456158655..96741014f2 100644
--- a/ecc/bls24-317/fr/asm_noadx.go
+++ b/ecc/bls24-317/fr/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/asm_noavx.go b/ecc/bls24-317/fr/asm_noavx.go
index 4eb73e9a78..3cb6968fb8 100644
--- a/ecc/bls24-317/fr/asm_noavx.go
+++ b/ecc/bls24-317/fr/asm_noavx.go
@@ -1,6 +1,6 @@
 //go:build noavx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/doc.go b/ecc/bls24-317/fr/doc.go
index 587707f13a..414b4e4577 100644
--- a/ecc/bls24-317/fr/doc.go
+++ b/ecc/bls24-317/fr/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/element.go b/ecc/bls24-317/fr/element.go
index 2567fe7d46..129e9307ac 100644
--- a/ecc/bls24-317/fr/element.go
+++ b/ecc/bls24-317/fr/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/element_amd64.go b/ecc/bls24-317/fr/element_amd64.go
index ca49d12590..4c3f2a8567 100644
--- a/ecc/bls24-317/fr/element_amd64.go
+++ b/ecc/bls24-317/fr/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/element_amd64.s b/ecc/bls24-317/fr/element_amd64.s
index ed8a36e04d..a7c6ffae66 100644
--- a/ecc/bls24-317/fr/element_amd64.s
+++ b/ecc/bls24-317/fr/element_amd64.s
@@ -1,10 +1,10 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
-// We include the hash to force the Go compiler to recompile: 9425145785761608449
+// We include the hash to force the Go compiler to recompile: 14652627197992229521
 #include "../../../field/asm/element_4w_amd64.s"
 
diff --git a/ecc/bls24-317/fr/element_arm64.go b/ecc/bls24-317/fr/element_arm64.go
index f50af4849b..0811487b48 100644
--- a/ecc/bls24-317/fr/element_arm64.go
+++ b/ecc/bls24-317/fr/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/element_arm64.s b/ecc/bls24-317/fr/element_arm64.s
index a7bd036553..ef16eaba35 100644
--- a/ecc/bls24-317/fr/element_arm64.s
+++ b/ecc/bls24-317/fr/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/element_exp.go b/ecc/bls24-317/fr/element_exp.go
index dcf74b036c..283689c158 100644
--- a/ecc/bls24-317/fr/element_exp.go
+++ b/ecc/bls24-317/fr/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/element_purego.go b/ecc/bls24-317/fr/element_purego.go
index 50df3223b4..41350c288f 100644
--- a/ecc/bls24-317/fr/element_purego.go
+++ b/ecc/bls24-317/fr/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/element_test.go b/ecc/bls24-317/fr/element_test.go
index 42f075f40b..01e1bd2b41 100644
--- a/ecc/bls24-317/fr/element_test.go
+++ b/ecc/bls24-317/fr/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/fft/bitreverse.go b/ecc/bls24-317/fr/fft/bitreverse.go
index 329e4c7a43..7f98fed65b 100644
--- a/ecc/bls24-317/fr/fft/bitreverse.go
+++ b/ecc/bls24-317/fr/fft/bitreverse.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/fft/bitreverse_test.go b/ecc/bls24-317/fr/fft/bitreverse_test.go
index 8028806cd7..1660d1a6a8 100644
--- a/ecc/bls24-317/fr/fft/bitreverse_test.go
+++ b/ecc/bls24-317/fr/fft/bitreverse_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/fft/doc.go b/ecc/bls24-317/fr/fft/doc.go
index 1ef04db2df..4cce0f9779 100644
--- a/ecc/bls24-317/fr/fft/doc.go
+++ b/ecc/bls24-317/fr/fft/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/fft/domain.go b/ecc/bls24-317/fr/fft/domain.go
index c2d12cb3b7..3ad6285647 100644
--- a/ecc/bls24-317/fr/fft/domain.go
+++ b/ecc/bls24-317/fr/fft/domain.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/fft/domain_test.go b/ecc/bls24-317/fr/fft/domain_test.go
index d95288076c..e445d3cc12 100644
--- a/ecc/bls24-317/fr/fft/domain_test.go
+++ b/ecc/bls24-317/fr/fft/domain_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/fft/fft.go b/ecc/bls24-317/fr/fft/fft.go
index 5f1249f0bc..2938090085 100644
--- a/ecc/bls24-317/fr/fft/fft.go
+++ b/ecc/bls24-317/fr/fft/fft.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/fft/fft_test.go b/ecc/bls24-317/fr/fft/fft_test.go
index ce75bd3cb1..f09a213089 100644
--- a/ecc/bls24-317/fr/fft/fft_test.go
+++ b/ecc/bls24-317/fr/fft/fft_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/fft/options.go b/ecc/bls24-317/fr/fft/options.go
index 0771a67910..b0c2cf89dc 100644
--- a/ecc/bls24-317/fr/fft/options.go
+++ b/ecc/bls24-317/fr/fft/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/fri/doc.go b/ecc/bls24-317/fr/fri/doc.go
index 428dabf625..cea69fc79a 100644
--- a/ecc/bls24-317/fr/fri/doc.go
+++ b/ecc/bls24-317/fr/fri/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/fri/fri.go b/ecc/bls24-317/fr/fri/fri.go
index 0abf70e8a2..5edecb72d7 100644
--- a/ecc/bls24-317/fr/fri/fri.go
+++ b/ecc/bls24-317/fr/fri/fri.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/fri/fri_test.go b/ecc/bls24-317/fr/fri/fri_test.go
index a05f7ca68b..90fda8fc02 100644
--- a/ecc/bls24-317/fr/fri/fri_test.go
+++ b/ecc/bls24-317/fr/fri/fri_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/generator.go b/ecc/bls24-317/fr/generator.go
index db8e5d4024..4c3e708ba0 100644
--- a/ecc/bls24-317/fr/generator.go
+++ b/ecc/bls24-317/fr/generator.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/gkr/gkr.go b/ecc/bls24-317/fr/gkr/gkr.go
index 057b9f946e..f0e865f872 100644
--- a/ecc/bls24-317/fr/gkr/gkr.go
+++ b/ecc/bls24-317/fr/gkr/gkr.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/gkr/gkr_test.go b/ecc/bls24-317/fr/gkr/gkr_test.go
index bd28b5d2a1..fd90fec0cd 100644
--- a/ecc/bls24-317/fr/gkr/gkr_test.go
+++ b/ecc/bls24-317/fr/gkr/gkr_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
@@ -325,7 +325,7 @@ func mimcCircuit(numRounds int) Circuit {
 
 func testMimc(t *testing.T, numRounds int, inputAssignments ...[]fr.Element) {
 	//TODO: Implement mimc correctly. Currently, the computation is mimc(a,b) = cipher( cipher( ... cipher(a, b), b) ..., b)
-	// @AlexandreBelling: Please explain the extra layers in https://github.com/ConsenSys/gkr-mimc/blob/81eada039ab4ed403b7726b535adb63026e8011f/examples/mimc.go#L10
+	// @AlexandreBelling: Please explain the extra layers in https://github.com/Consensys/gkr-mimc/blob/81eada039ab4ed403b7726b535adb63026e8011f/examples/mimc.go#L10
 
 	c := mimcCircuit(numRounds)
 
diff --git a/ecc/bls24-317/fr/hash_to_field/doc.go b/ecc/bls24-317/fr/hash_to_field/doc.go
index 97326bc039..e9ae11fec2 100644
--- a/ecc/bls24-317/fr/hash_to_field/doc.go
+++ b/ecc/bls24-317/fr/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/hash_to_field/hash_to_field.go b/ecc/bls24-317/fr/hash_to_field/hash_to_field.go
index 2c51e5fd51..c48bb88330 100644
--- a/ecc/bls24-317/fr/hash_to_field/hash_to_field.go
+++ b/ecc/bls24-317/fr/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/hash_to_field/hash_to_field_test.go b/ecc/bls24-317/fr/hash_to_field/hash_to_field_test.go
index bca80332aa..567bd8d19a 100644
--- a/ecc/bls24-317/fr/hash_to_field/hash_to_field_test.go
+++ b/ecc/bls24-317/fr/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/iop/doc.go b/ecc/bls24-317/fr/iop/doc.go
index ee3facf1e1..2ef06dfe1a 100644
--- a/ecc/bls24-317/fr/iop/doc.go
+++ b/ecc/bls24-317/fr/iop/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/iop/expressions.go b/ecc/bls24-317/fr/iop/expressions.go
index 904c5cad0d..5c4d901223 100644
--- a/ecc/bls24-317/fr/iop/expressions.go
+++ b/ecc/bls24-317/fr/iop/expressions.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/iop/expressions_test.go b/ecc/bls24-317/fr/iop/expressions_test.go
index aba2e4e755..d662b45c6e 100644
--- a/ecc/bls24-317/fr/iop/expressions_test.go
+++ b/ecc/bls24-317/fr/iop/expressions_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/iop/polynomial.go b/ecc/bls24-317/fr/iop/polynomial.go
index 1869ba8fce..701a833862 100644
--- a/ecc/bls24-317/fr/iop/polynomial.go
+++ b/ecc/bls24-317/fr/iop/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/iop/polynomial_test.go b/ecc/bls24-317/fr/iop/polynomial_test.go
index 2d14b63fff..3066d383ca 100644
--- a/ecc/bls24-317/fr/iop/polynomial_test.go
+++ b/ecc/bls24-317/fr/iop/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/iop/quotient.go b/ecc/bls24-317/fr/iop/quotient.go
index 63d501b366..22561fbdc1 100644
--- a/ecc/bls24-317/fr/iop/quotient.go
+++ b/ecc/bls24-317/fr/iop/quotient.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/iop/quotient_test.go b/ecc/bls24-317/fr/iop/quotient_test.go
index e66e506ccb..b932d330b2 100644
--- a/ecc/bls24-317/fr/iop/quotient_test.go
+++ b/ecc/bls24-317/fr/iop/quotient_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/iop/ratios.go b/ecc/bls24-317/fr/iop/ratios.go
index 777c70384a..ce121e0dfe 100644
--- a/ecc/bls24-317/fr/iop/ratios.go
+++ b/ecc/bls24-317/fr/iop/ratios.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/iop/ratios_test.go b/ecc/bls24-317/fr/iop/ratios_test.go
index 5e17c09cc5..6cea40ffd2 100644
--- a/ecc/bls24-317/fr/iop/ratios_test.go
+++ b/ecc/bls24-317/fr/iop/ratios_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/iop/utils.go b/ecc/bls24-317/fr/iop/utils.go
index b6a8b103e7..f0bf5c89b5 100644
--- a/ecc/bls24-317/fr/iop/utils.go
+++ b/ecc/bls24-317/fr/iop/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/mimc/doc.go b/ecc/bls24-317/fr/mimc/doc.go
index cc7b101eb4..98aa3f8d81 100644
--- a/ecc/bls24-317/fr/mimc/doc.go
+++ b/ecc/bls24-317/fr/mimc/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/mimc/mimc.go b/ecc/bls24-317/fr/mimc/mimc.go
index 9a47f6f527..4e5a82ccf7 100644
--- a/ecc/bls24-317/fr/mimc/mimc.go
+++ b/ecc/bls24-317/fr/mimc/mimc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/mimc/options.go b/ecc/bls24-317/fr/mimc/options.go
index fc10eb61e6..a212de8177 100644
--- a/ecc/bls24-317/fr/mimc/options.go
+++ b/ecc/bls24-317/fr/mimc/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/pedersen/doc.go b/ecc/bls24-317/fr/pedersen/doc.go
index 62a62f179f..2e24034936 100644
--- a/ecc/bls24-317/fr/pedersen/doc.go
+++ b/ecc/bls24-317/fr/pedersen/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/pedersen/example_test.go b/ecc/bls24-317/fr/pedersen/example_test.go
index d52b40c47f..55c9ce1004 100644
--- a/ecc/bls24-317/fr/pedersen/example_test.go
+++ b/ecc/bls24-317/fr/pedersen/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/pedersen/pedersen.go b/ecc/bls24-317/fr/pedersen/pedersen.go
index 1e5e96e6f4..17df43c6de 100644
--- a/ecc/bls24-317/fr/pedersen/pedersen.go
+++ b/ecc/bls24-317/fr/pedersen/pedersen.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
@@ -105,7 +105,7 @@ func (pk *ProvingKey) ProveKnowledge(values []fr.Element) (pok curve.G1Affine, e
 	}
 
 	// TODO @gbotrel this will spawn more than one task, see
-	// https://github.com/ConsenSys/gnark-crypto/issues/269
+	// https://github.com/Consensys/gnark-crypto/issues/269
 	config := ecc.MultiExpConfig{
 		NbTasks: 1, // TODO Experiment
 	}
@@ -123,7 +123,7 @@ func (pk *ProvingKey) Commit(values []fr.Element) (commitment curve.G1Affine, er
 	}
 
 	// TODO @gbotrel this will spawn more than one task, see
-	// https://github.com/ConsenSys/gnark-crypto/issues/269
+	// https://github.com/Consensys/gnark-crypto/issues/269
 	config := ecc.MultiExpConfig{
 		NbTasks: 1,
 	}
@@ -184,7 +184,7 @@ func BatchProve(pk []ProvingKey, values [][]fr.Element, combinationCoeff fr.Elem
 	}
 
 	// TODO @gbotrel this will spawn more than one task, see
-	// https://github.com/ConsenSys/gnark-crypto/issues/269
+	// https://github.com/Consensys/gnark-crypto/issues/269
 	config := ecc.MultiExpConfig{
 		NbTasks: 1,
 	}
diff --git a/ecc/bls24-317/fr/pedersen/pedersen_test.go b/ecc/bls24-317/fr/pedersen/pedersen_test.go
index 5a703fc260..98c3c808d2 100644
--- a/ecc/bls24-317/fr/pedersen/pedersen_test.go
+++ b/ecc/bls24-317/fr/pedersen/pedersen_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/permutation/doc.go b/ecc/bls24-317/fr/permutation/doc.go
index 5f346b5a53..e24cd82923 100644
--- a/ecc/bls24-317/fr/permutation/doc.go
+++ b/ecc/bls24-317/fr/permutation/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/permutation/permutation.go b/ecc/bls24-317/fr/permutation/permutation.go
index fb8eea5312..98e2033333 100644
--- a/ecc/bls24-317/fr/permutation/permutation.go
+++ b/ecc/bls24-317/fr/permutation/permutation.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/permutation/permutation_test.go b/ecc/bls24-317/fr/permutation/permutation_test.go
index 46faf9d2d3..88ab4f62fb 100644
--- a/ecc/bls24-317/fr/permutation/permutation_test.go
+++ b/ecc/bls24-317/fr/permutation/permutation_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/plookup/doc.go b/ecc/bls24-317/fr/plookup/doc.go
index d163104002..7a02c59719 100644
--- a/ecc/bls24-317/fr/plookup/doc.go
+++ b/ecc/bls24-317/fr/plookup/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/plookup/plookup_test.go b/ecc/bls24-317/fr/plookup/plookup_test.go
index 1c6637987d..27b71155d3 100644
--- a/ecc/bls24-317/fr/plookup/plookup_test.go
+++ b/ecc/bls24-317/fr/plookup/plookup_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/plookup/table.go b/ecc/bls24-317/fr/plookup/table.go
index 2a0ffcd26f..3b11b74f7e 100644
--- a/ecc/bls24-317/fr/plookup/table.go
+++ b/ecc/bls24-317/fr/plookup/table.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/plookup/vector.go b/ecc/bls24-317/fr/plookup/vector.go
index 8bcb7fb4bd..7b1abb02a2 100644
--- a/ecc/bls24-317/fr/plookup/vector.go
+++ b/ecc/bls24-317/fr/plookup/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/polynomial/doc.go b/ecc/bls24-317/fr/polynomial/doc.go
index 35b3f725c1..fd96328e8f 100644
--- a/ecc/bls24-317/fr/polynomial/doc.go
+++ b/ecc/bls24-317/fr/polynomial/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/polynomial/multilin.go b/ecc/bls24-317/fr/polynomial/multilin.go
index 09f8babe95..dd87335979 100644
--- a/ecc/bls24-317/fr/polynomial/multilin.go
+++ b/ecc/bls24-317/fr/polynomial/multilin.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/polynomial/multilin_test.go b/ecc/bls24-317/fr/polynomial/multilin_test.go
index 6f04c4efc3..cd7a79aef4 100644
--- a/ecc/bls24-317/fr/polynomial/multilin_test.go
+++ b/ecc/bls24-317/fr/polynomial/multilin_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/polynomial/polynomial.go b/ecc/bls24-317/fr/polynomial/polynomial.go
index d86ec7b036..9a5e88d50a 100644
--- a/ecc/bls24-317/fr/polynomial/polynomial.go
+++ b/ecc/bls24-317/fr/polynomial/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/polynomial/polynomial_test.go b/ecc/bls24-317/fr/polynomial/polynomial_test.go
index 46f3058bbd..405cee1554 100644
--- a/ecc/bls24-317/fr/polynomial/polynomial_test.go
+++ b/ecc/bls24-317/fr/polynomial/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/polynomial/pool.go b/ecc/bls24-317/fr/polynomial/pool.go
index 978088df4c..1d22d71c4a 100644
--- a/ecc/bls24-317/fr/polynomial/pool.go
+++ b/ecc/bls24-317/fr/polynomial/pool.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/poseidon2/poseidon2.go b/ecc/bls24-317/fr/poseidon2/poseidon2.go
index 26c7bc1b7d..d117b4cf24 100644
--- a/ecc/bls24-317/fr/poseidon2/poseidon2.go
+++ b/ecc/bls24-317/fr/poseidon2/poseidon2.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/poseidon2/poseidon2_test.go b/ecc/bls24-317/fr/poseidon2/poseidon2_test.go
index c89bc2caa6..3819256f1d 100644
--- a/ecc/bls24-317/fr/poseidon2/poseidon2_test.go
+++ b/ecc/bls24-317/fr/poseidon2/poseidon2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/sumcheck/sumcheck.go b/ecc/bls24-317/fr/sumcheck/sumcheck.go
index 1c5c06b356..0ba7de052b 100644
--- a/ecc/bls24-317/fr/sumcheck/sumcheck.go
+++ b/ecc/bls24-317/fr/sumcheck/sumcheck.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/sumcheck/sumcheck_test.go b/ecc/bls24-317/fr/sumcheck/sumcheck_test.go
index 678e9c0d2e..23e578f997 100644
--- a/ecc/bls24-317/fr/sumcheck/sumcheck_test.go
+++ b/ecc/bls24-317/fr/sumcheck/sumcheck_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/test_vector_utils/test_vector_utils.go b/ecc/bls24-317/fr/test_vector_utils/test_vector_utils.go
index 60bdbbd25a..457cd4f90a 100644
--- a/ecc/bls24-317/fr/test_vector_utils/test_vector_utils.go
+++ b/ecc/bls24-317/fr/test_vector_utils/test_vector_utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/vector.go b/ecc/bls24-317/fr/vector.go
index 8b59bd36e9..4654b1b2d3 100644
--- a/ecc/bls24-317/fr/vector.go
+++ b/ecc/bls24-317/fr/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/vector_amd64.go b/ecc/bls24-317/fr/vector_amd64.go
index b27679827c..a7dcec3b25 100644
--- a/ecc/bls24-317/fr/vector_amd64.go
+++ b/ecc/bls24-317/fr/vector_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/vector_purego.go b/ecc/bls24-317/fr/vector_purego.go
index 5973d16ce2..db43e73504 100644
--- a/ecc/bls24-317/fr/vector_purego.go
+++ b/ecc/bls24-317/fr/vector_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || !amd64
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/vector_test.go b/ecc/bls24-317/fr/vector_test.go
index a094bc0ac6..f6179e7824 100644
--- a/ecc/bls24-317/fr/vector_test.go
+++ b/ecc/bls24-317/fr/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/g1.go b/ecc/bls24-317/g1.go
index 1c9b24d0f8..5ef6d07fd5 100644
--- a/ecc/bls24-317/g1.go
+++ b/ecc/bls24-317/g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/g1_test.go b/ecc/bls24-317/g1_test.go
index 068f77f102..d1bd90ba35 100644
--- a/ecc/bls24-317/g1_test.go
+++ b/ecc/bls24-317/g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/g2.go b/ecc/bls24-317/g2.go
index c1f602e3b1..a5bfac4672 100644
--- a/ecc/bls24-317/g2.go
+++ b/ecc/bls24-317/g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/g2_test.go b/ecc/bls24-317/g2_test.go
index 8406f2dd34..df7af3eec8 100644
--- a/ecc/bls24-317/g2_test.go
+++ b/ecc/bls24-317/g2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/hash_to_g1.go b/ecc/bls24-317/hash_to_g1.go
index 01bac28c85..38211f5c36 100644
--- a/ecc/bls24-317/hash_to_g1.go
+++ b/ecc/bls24-317/hash_to_g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/hash_to_g1_test.go b/ecc/bls24-317/hash_to_g1_test.go
index 7dce6376dd..5c72f5ad0d 100644
--- a/ecc/bls24-317/hash_to_g1_test.go
+++ b/ecc/bls24-317/hash_to_g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/hash_to_g2.go b/ecc/bls24-317/hash_to_g2.go
index 597de9ed6c..4b8561997f 100644
--- a/ecc/bls24-317/hash_to_g2.go
+++ b/ecc/bls24-317/hash_to_g2.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package bls24317
 
diff --git a/ecc/bls24-317/internal/fptower/asm.go b/ecc/bls24-317/internal/fptower/asm.go
index ba19dae3e6..5857e743a3 100644
--- a/ecc/bls24-317/internal/fptower/asm.go
+++ b/ecc/bls24-317/internal/fptower/asm.go
@@ -1,19 +1,8 @@
 //go:build !noadx
 // +build !noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-317/internal/fptower/asm_noadx.go b/ecc/bls24-317/internal/fptower/asm_noadx.go
index 5cfde1587f..2bd913581d 100644
--- a/ecc/bls24-317/internal/fptower/asm_noadx.go
+++ b/ecc/bls24-317/internal/fptower/asm_noadx.go
@@ -1,19 +1,8 @@
 //go:build noadx
 // +build noadx
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-317/internal/fptower/e12.go b/ecc/bls24-317/internal/fptower/e12.go
index 9d48e0d727..2f0f222428 100644
--- a/ecc/bls24-317/internal/fptower/e12.go
+++ b/ecc/bls24-317/internal/fptower/e12.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-317/internal/fptower/e12_test.go b/ecc/bls24-317/internal/fptower/e12_test.go
index 76d4a6c9e0..22904788c5 100644
--- a/ecc/bls24-317/internal/fptower/e12_test.go
+++ b/ecc/bls24-317/internal/fptower/e12_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-317/internal/fptower/e2.go b/ecc/bls24-317/internal/fptower/e2.go
index b2195608f9..6fa66f5906 100644
--- a/ecc/bls24-317/internal/fptower/e2.go
+++ b/ecc/bls24-317/internal/fptower/e2.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-317/internal/fptower/e24.go b/ecc/bls24-317/internal/fptower/e24.go
index b0a4e99b90..44873ed128 100644
--- a/ecc/bls24-317/internal/fptower/e24.go
+++ b/ecc/bls24-317/internal/fptower/e24.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-317/internal/fptower/e24_test.go b/ecc/bls24-317/internal/fptower/e24_test.go
index 3d36a2142a..93058a9b56 100644
--- a/ecc/bls24-317/internal/fptower/e24_test.go
+++ b/ecc/bls24-317/internal/fptower/e24_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-317/internal/fptower/e2_amd64.go b/ecc/bls24-317/internal/fptower/e2_amd64.go
index 15488b613b..2dd35a29a5 100644
--- a/ecc/bls24-317/internal/fptower/e2_amd64.go
+++ b/ecc/bls24-317/internal/fptower/e2_amd64.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-317/internal/fptower/e2_amd64.s b/ecc/bls24-317/internal/fptower/e2_amd64.s
index b707a9a08e..1da5dfafd4 100644
--- a/ecc/bls24-317/internal/fptower/e2_amd64.s
+++ b/ecc/bls24-317/internal/fptower/e2_amd64.s
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 #include "textflag.h"
 #include "funcdata.h"
diff --git a/ecc/bls24-317/internal/fptower/e2_bls317.go b/ecc/bls24-317/internal/fptower/e2_bls317.go
index 96829d0618..cd1e34f840 100644
--- a/ecc/bls24-317/internal/fptower/e2_bls317.go
+++ b/ecc/bls24-317/internal/fptower/e2_bls317.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-317/internal/fptower/e2_fallback.go b/ecc/bls24-317/internal/fptower/e2_fallback.go
index 3e9886c87d..0a0166a0a2 100644
--- a/ecc/bls24-317/internal/fptower/e2_fallback.go
+++ b/ecc/bls24-317/internal/fptower/e2_fallback.go
@@ -1,19 +1,8 @@
 //go:build !amd64
 // +build !amd64
 
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-317/internal/fptower/e2_test.go b/ecc/bls24-317/internal/fptower/e2_test.go
index c68d3f1840..8238d4735a 100644
--- a/ecc/bls24-317/internal/fptower/e2_test.go
+++ b/ecc/bls24-317/internal/fptower/e2_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-317/internal/fptower/e4.go b/ecc/bls24-317/internal/fptower/e4.go
index 3641625120..147994de80 100644
--- a/ecc/bls24-317/internal/fptower/e4.go
+++ b/ecc/bls24-317/internal/fptower/e4.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-317/internal/fptower/e4_bls315.go b/ecc/bls24-317/internal/fptower/e4_bls315.go
index f94878489e..1afe60a032 100644
--- a/ecc/bls24-317/internal/fptower/e4_bls315.go
+++ b/ecc/bls24-317/internal/fptower/e4_bls315.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-317/internal/fptower/e4_test.go b/ecc/bls24-317/internal/fptower/e4_test.go
index f0f9932b52..a2a8c27962 100644
--- a/ecc/bls24-317/internal/fptower/e4_test.go
+++ b/ecc/bls24-317/internal/fptower/e4_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-317/internal/fptower/frobenius.go b/ecc/bls24-317/internal/fptower/frobenius.go
index beb0e1b448..53c8cb6071 100644
--- a/ecc/bls24-317/internal/fptower/frobenius.go
+++ b/ecc/bls24-317/internal/fptower/frobenius.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://wwwApache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-317/internal/fptower/parameters.go b/ecc/bls24-317/internal/fptower/parameters.go
index 6d637e8624..23033e8393 100644
--- a/ecc/bls24-317/internal/fptower/parameters.go
+++ b/ecc/bls24-317/internal/fptower/parameters.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bls24-317/kzg/doc.go b/ecc/bls24-317/kzg/doc.go
index 6c3454a2d9..226614bbdf 100644
--- a/ecc/bls24-317/kzg/doc.go
+++ b/ecc/bls24-317/kzg/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/kzg/kzg.go b/ecc/bls24-317/kzg/kzg.go
index c5760f968e..16008e9885 100644
--- a/ecc/bls24-317/kzg/kzg.go
+++ b/ecc/bls24-317/kzg/kzg.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/kzg/kzg_test.go b/ecc/bls24-317/kzg/kzg_test.go
index 4dff6ced17..10c75771a4 100644
--- a/ecc/bls24-317/kzg/kzg_test.go
+++ b/ecc/bls24-317/kzg/kzg_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/kzg/marshal.go b/ecc/bls24-317/kzg/marshal.go
index 1bba0bd644..6816b2f119 100644
--- a/ecc/bls24-317/kzg/marshal.go
+++ b/ecc/bls24-317/kzg/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/kzg/utils.go b/ecc/bls24-317/kzg/utils.go
index 8eaba1c186..898c7b3463 100644
--- a/ecc/bls24-317/kzg/utils.go
+++ b/ecc/bls24-317/kzg/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/marshal.go b/ecc/bls24-317/marshal.go
index 7066467c0f..cc267843bc 100644
--- a/ecc/bls24-317/marshal.go
+++ b/ecc/bls24-317/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/marshal_test.go b/ecc/bls24-317/marshal_test.go
index e19a3e92db..0322fefb3b 100644
--- a/ecc/bls24-317/marshal_test.go
+++ b/ecc/bls24-317/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/multiexp.go b/ecc/bls24-317/multiexp.go
index 84b445dd83..bf2504ddb5 100644
--- a/ecc/bls24-317/multiexp.go
+++ b/ecc/bls24-317/multiexp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/multiexp_affine.go b/ecc/bls24-317/multiexp_affine.go
index 1083d5835d..976580c294 100644
--- a/ecc/bls24-317/multiexp_affine.go
+++ b/ecc/bls24-317/multiexp_affine.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
@@ -19,7 +19,7 @@ type batchOpG1Affine struct {
 // using affine coordinates for the buckets. To amortize the cost of the inverse in the affine addition
 // we use a batch affine addition.
 //
-// this is derived from a PR by 0x0ece : https://github.com/ConsenSys/gnark-crypto/pull/249
+// this is derived from a PR by 0x0ece : https://github.com/Consensys/gnark-crypto/pull/249
 // See Section 5.3: ia.cr/2022/1396
 func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP pG1Affine, TPP ppG1Affine, TQ qOpsG1Affine, TC cG1Affine](
 	chunk uint64,
@@ -346,7 +346,7 @@ type batchOpG2Affine struct {
 // using affine coordinates for the buckets. To amortize the cost of the inverse in the affine addition
 // we use a batch affine addition.
 //
-// this is derived from a PR by 0x0ece : https://github.com/ConsenSys/gnark-crypto/pull/249
+// this is derived from a PR by 0x0ece : https://github.com/Consensys/gnark-crypto/pull/249
 // See Section 5.3: ia.cr/2022/1396
 func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP pG2Affine, TPP ppG2Affine, TQ qOpsG2Affine, TC cG2Affine](
 	chunk uint64,
diff --git a/ecc/bls24-317/multiexp_jacobian.go b/ecc/bls24-317/multiexp_jacobian.go
index afd3216e92..c0a5fbc7d4 100644
--- a/ecc/bls24-317/multiexp_jacobian.go
+++ b/ecc/bls24-317/multiexp_jacobian.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/multiexp_test.go b/ecc/bls24-317/multiexp_test.go
index 81a5085300..767ab56c23 100644
--- a/ecc/bls24-317/multiexp_test.go
+++ b/ecc/bls24-317/multiexp_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/pairing.go b/ecc/bls24-317/pairing.go
index c293458bda..0aa7f19d4e 100644
--- a/ecc/bls24-317/pairing.go
+++ b/ecc/bls24-317/pairing.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package bls24317
 
diff --git a/ecc/bls24-317/pairing_test.go b/ecc/bls24-317/pairing_test.go
index e76da2defe..0d7fa6d740 100644
--- a/ecc/bls24-317/pairing_test.go
+++ b/ecc/bls24-317/pairing_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/shplonk/doc.go b/ecc/bls24-317/shplonk/doc.go
index 17b34373c2..0367893999 100644
--- a/ecc/bls24-317/shplonk/doc.go
+++ b/ecc/bls24-317/shplonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/shplonk/example_test.go b/ecc/bls24-317/shplonk/example_test.go
index cc7fb5d0fd..3ecd80e281 100644
--- a/ecc/bls24-317/shplonk/example_test.go
+++ b/ecc/bls24-317/shplonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/shplonk/marshal.go b/ecc/bls24-317/shplonk/marshal.go
index 89f133be45..2345e8da9d 100644
--- a/ecc/bls24-317/shplonk/marshal.go
+++ b/ecc/bls24-317/shplonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/shplonk/shplonk.go b/ecc/bls24-317/shplonk/shplonk.go
index 242cb99922..f63bcc9dca 100644
--- a/ecc/bls24-317/shplonk/shplonk.go
+++ b/ecc/bls24-317/shplonk/shplonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/shplonk/shplonk_test.go b/ecc/bls24-317/shplonk/shplonk_test.go
index 0e49a01865..5f5eb5b05d 100644
--- a/ecc/bls24-317/shplonk/shplonk_test.go
+++ b/ecc/bls24-317/shplonk/shplonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/twistededwards/curve.go b/ecc/bls24-317/twistededwards/curve.go
index 7840ef8d97..952c388d69 100644
--- a/ecc/bls24-317/twistededwards/curve.go
+++ b/ecc/bls24-317/twistededwards/curve.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/twistededwards/doc.go b/ecc/bls24-317/twistededwards/doc.go
index 0a77cade57..e50b5bc91c 100644
--- a/ecc/bls24-317/twistededwards/doc.go
+++ b/ecc/bls24-317/twistededwards/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/twistededwards/eddsa/doc.go b/ecc/bls24-317/twistededwards/eddsa/doc.go
index adc990eae4..babd5b23ed 100644
--- a/ecc/bls24-317/twistededwards/eddsa/doc.go
+++ b/ecc/bls24-317/twistededwards/eddsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/twistededwards/eddsa/eddsa.go b/ecc/bls24-317/twistededwards/eddsa/eddsa.go
index 0019620804..f3fe4f8f88 100644
--- a/ecc/bls24-317/twistededwards/eddsa/eddsa.go
+++ b/ecc/bls24-317/twistededwards/eddsa/eddsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/twistededwards/eddsa/eddsa_test.go b/ecc/bls24-317/twistededwards/eddsa/eddsa_test.go
index 04d36aeb12..a045167a35 100644
--- a/ecc/bls24-317/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bls24-317/twistededwards/eddsa/eddsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/twistededwards/eddsa/marshal.go b/ecc/bls24-317/twistededwards/eddsa/marshal.go
index 3dcd026688..c5f2a6e909 100644
--- a/ecc/bls24-317/twistededwards/eddsa/marshal.go
+++ b/ecc/bls24-317/twistededwards/eddsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/twistededwards/point.go b/ecc/bls24-317/twistededwards/point.go
index cb16ff3442..26312f97f1 100644
--- a/ecc/bls24-317/twistededwards/point.go
+++ b/ecc/bls24-317/twistededwards/point.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/twistededwards/point_test.go b/ecc/bls24-317/twistededwards/point_test.go
index 0ad9b0b084..2019c5809e 100644
--- a/ecc/bls24-317/twistededwards/point_test.go
+++ b/ecc/bls24-317/twistededwards/point_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/bn254.go b/ecc/bn254/bn254.go
index 6c52a4c7f6..87c5ee74b9 100644
--- a/ecc/bn254/bn254.go
+++ b/ecc/bn254/bn254.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Package bn254 efficient elliptic curve, pairing and hash to curve implementation for bn254. This curve appears in
 // Ethereum pre-compiles as altbn128.
diff --git a/ecc/bn254/ecdsa/doc.go b/ecc/bn254/ecdsa/doc.go
index 5820113b67..0d2265c25a 100644
--- a/ecc/bn254/ecdsa/doc.go
+++ b/ecc/bn254/ecdsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/ecdsa/ecdsa.go b/ecc/bn254/ecdsa/ecdsa.go
index 5d9d9a8b2a..fbdd78ca48 100644
--- a/ecc/bn254/ecdsa/ecdsa.go
+++ b/ecc/bn254/ecdsa/ecdsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/ecdsa/ecdsa_test.go b/ecc/bn254/ecdsa/ecdsa_test.go
index 9c6b4d4993..086ae3c7ed 100644
--- a/ecc/bn254/ecdsa/ecdsa_test.go
+++ b/ecc/bn254/ecdsa/ecdsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/ecdsa/marshal.go b/ecc/bn254/ecdsa/marshal.go
index 57554a0b0b..bc3aecbd7c 100644
--- a/ecc/bn254/ecdsa/marshal.go
+++ b/ecc/bn254/ecdsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/ecdsa/marshal_test.go b/ecc/bn254/ecdsa/marshal_test.go
index 3cf033cab5..24508e4011 100644
--- a/ecc/bn254/ecdsa/marshal_test.go
+++ b/ecc/bn254/ecdsa/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fflonk/doc.go b/ecc/bn254/fflonk/doc.go
index b717383d87..67a8094e35 100644
--- a/ecc/bn254/fflonk/doc.go
+++ b/ecc/bn254/fflonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fflonk/example_test.go b/ecc/bn254/fflonk/example_test.go
index 9614b401a3..96c7f30f76 100644
--- a/ecc/bn254/fflonk/example_test.go
+++ b/ecc/bn254/fflonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fflonk/fflonk.go b/ecc/bn254/fflonk/fflonk.go
index fdd29ccf70..72f8efead6 100644
--- a/ecc/bn254/fflonk/fflonk.go
+++ b/ecc/bn254/fflonk/fflonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fflonk/fflonk_test.go b/ecc/bn254/fflonk/fflonk_test.go
index a75b371d42..c22fea4f11 100644
--- a/ecc/bn254/fflonk/fflonk_test.go
+++ b/ecc/bn254/fflonk/fflonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fflonk/marshal.go b/ecc/bn254/fflonk/marshal.go
index 8d08502778..c80e3c776d 100644
--- a/ecc/bn254/fflonk/marshal.go
+++ b/ecc/bn254/fflonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/arith.go b/ecc/bn254/fp/arith.go
index b202a1549a..bb63552f5a 100644
--- a/ecc/bn254/fp/arith.go
+++ b/ecc/bn254/fp/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/asm_adx.go b/ecc/bn254/fp/asm_adx.go
index fe25e82db2..75e92992fe 100644
--- a/ecc/bn254/fp/asm_adx.go
+++ b/ecc/bn254/fp/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/asm_avx.go b/ecc/bn254/fp/asm_avx.go
index fdb65bb8f2..aa233664d0 100644
--- a/ecc/bn254/fp/asm_avx.go
+++ b/ecc/bn254/fp/asm_avx.go
@@ -1,6 +1,6 @@
 //go:build !noavx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/asm_noadx.go b/ecc/bn254/fp/asm_noadx.go
index 95085a8e6f..304dfb7209 100644
--- a/ecc/bn254/fp/asm_noadx.go
+++ b/ecc/bn254/fp/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/asm_noavx.go b/ecc/bn254/fp/asm_noavx.go
index c5fec182cd..900dedbe8b 100644
--- a/ecc/bn254/fp/asm_noavx.go
+++ b/ecc/bn254/fp/asm_noavx.go
@@ -1,6 +1,6 @@
 //go:build noavx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/doc.go b/ecc/bn254/fp/doc.go
index 4319c7913d..5624ba2797 100644
--- a/ecc/bn254/fp/doc.go
+++ b/ecc/bn254/fp/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/element.go b/ecc/bn254/fp/element.go
index 313a1e3869..9b37dc541c 100644
--- a/ecc/bn254/fp/element.go
+++ b/ecc/bn254/fp/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/element_amd64.go b/ecc/bn254/fp/element_amd64.go
index e72f552ad9..9cee062e5b 100644
--- a/ecc/bn254/fp/element_amd64.go
+++ b/ecc/bn254/fp/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/element_amd64.s b/ecc/bn254/fp/element_amd64.s
index ed8a36e04d..a7c6ffae66 100644
--- a/ecc/bn254/fp/element_amd64.s
+++ b/ecc/bn254/fp/element_amd64.s
@@ -1,10 +1,10 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
-// We include the hash to force the Go compiler to recompile: 9425145785761608449
+// We include the hash to force the Go compiler to recompile: 14652627197992229521
 #include "../../../field/asm/element_4w_amd64.s"
 
diff --git a/ecc/bn254/fp/element_arm64.go b/ecc/bn254/fp/element_arm64.go
index 3eb868d38b..ed26d2b3d9 100644
--- a/ecc/bn254/fp/element_arm64.go
+++ b/ecc/bn254/fp/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/element_arm64.s b/ecc/bn254/fp/element_arm64.s
index a7bd036553..ef16eaba35 100644
--- a/ecc/bn254/fp/element_arm64.s
+++ b/ecc/bn254/fp/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/element_exp.go b/ecc/bn254/fp/element_exp.go
index 662e780e58..38eb2749af 100644
--- a/ecc/bn254/fp/element_exp.go
+++ b/ecc/bn254/fp/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/element_purego.go b/ecc/bn254/fp/element_purego.go
index 008cec50b2..861b453dfd 100644
--- a/ecc/bn254/fp/element_purego.go
+++ b/ecc/bn254/fp/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/element_test.go b/ecc/bn254/fp/element_test.go
index b49a4d6ffe..4b2af9d309 100644
--- a/ecc/bn254/fp/element_test.go
+++ b/ecc/bn254/fp/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/hash_to_field/doc.go b/ecc/bn254/fp/hash_to_field/doc.go
index bc05bf9bcd..113b4e6e69 100644
--- a/ecc/bn254/fp/hash_to_field/doc.go
+++ b/ecc/bn254/fp/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/hash_to_field/hash_to_field.go b/ecc/bn254/fp/hash_to_field/hash_to_field.go
index f229f83b36..f7b035d633 100644
--- a/ecc/bn254/fp/hash_to_field/hash_to_field.go
+++ b/ecc/bn254/fp/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/hash_to_field/hash_to_field_test.go b/ecc/bn254/fp/hash_to_field/hash_to_field_test.go
index 605f379235..ba809d498b 100644
--- a/ecc/bn254/fp/hash_to_field/hash_to_field_test.go
+++ b/ecc/bn254/fp/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/vector.go b/ecc/bn254/fp/vector.go
index ec52314aa7..ef60ed4b45 100644
--- a/ecc/bn254/fp/vector.go
+++ b/ecc/bn254/fp/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/vector_amd64.go b/ecc/bn254/fp/vector_amd64.go
index 39666a2df7..9e05e6b2f3 100644
--- a/ecc/bn254/fp/vector_amd64.go
+++ b/ecc/bn254/fp/vector_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/vector_purego.go b/ecc/bn254/fp/vector_purego.go
index 16afa898d4..6adeb1a8a2 100644
--- a/ecc/bn254/fp/vector_purego.go
+++ b/ecc/bn254/fp/vector_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || !amd64
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/vector_test.go b/ecc/bn254/fp/vector_test.go
index 06fe1084a8..e7185486cf 100644
--- a/ecc/bn254/fp/vector_test.go
+++ b/ecc/bn254/fp/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/arith.go b/ecc/bn254/fr/arith.go
index 9285041f4b..dbba8a9ae4 100644
--- a/ecc/bn254/fr/arith.go
+++ b/ecc/bn254/fr/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/asm_adx.go b/ecc/bn254/fr/asm_adx.go
index 9e7da5e865..9b970335f1 100644
--- a/ecc/bn254/fr/asm_adx.go
+++ b/ecc/bn254/fr/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/asm_avx.go b/ecc/bn254/fr/asm_avx.go
index d6d7d7f87a..2a0a166ed4 100644
--- a/ecc/bn254/fr/asm_avx.go
+++ b/ecc/bn254/fr/asm_avx.go
@@ -1,6 +1,6 @@
 //go:build !noavx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/asm_noadx.go b/ecc/bn254/fr/asm_noadx.go
index 3456158655..96741014f2 100644
--- a/ecc/bn254/fr/asm_noadx.go
+++ b/ecc/bn254/fr/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/asm_noavx.go b/ecc/bn254/fr/asm_noavx.go
index 4eb73e9a78..3cb6968fb8 100644
--- a/ecc/bn254/fr/asm_noavx.go
+++ b/ecc/bn254/fr/asm_noavx.go
@@ -1,6 +1,6 @@
 //go:build noavx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/doc.go b/ecc/bn254/fr/doc.go
index 759f5d2511..d2c6e01857 100644
--- a/ecc/bn254/fr/doc.go
+++ b/ecc/bn254/fr/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/element.go b/ecc/bn254/fr/element.go
index 589c9f99bb..8e59ea748f 100644
--- a/ecc/bn254/fr/element.go
+++ b/ecc/bn254/fr/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/element_amd64.go b/ecc/bn254/fr/element_amd64.go
index ca49d12590..4c3f2a8567 100644
--- a/ecc/bn254/fr/element_amd64.go
+++ b/ecc/bn254/fr/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/element_amd64.s b/ecc/bn254/fr/element_amd64.s
index ed8a36e04d..a7c6ffae66 100644
--- a/ecc/bn254/fr/element_amd64.s
+++ b/ecc/bn254/fr/element_amd64.s
@@ -1,10 +1,10 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
-// We include the hash to force the Go compiler to recompile: 9425145785761608449
+// We include the hash to force the Go compiler to recompile: 14652627197992229521
 #include "../../../field/asm/element_4w_amd64.s"
 
diff --git a/ecc/bn254/fr/element_arm64.go b/ecc/bn254/fr/element_arm64.go
index 7189fe30d5..2277914932 100644
--- a/ecc/bn254/fr/element_arm64.go
+++ b/ecc/bn254/fr/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/element_arm64.s b/ecc/bn254/fr/element_arm64.s
index a7bd036553..ef16eaba35 100644
--- a/ecc/bn254/fr/element_arm64.s
+++ b/ecc/bn254/fr/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/element_exp.go b/ecc/bn254/fr/element_exp.go
index d22db08600..6e87fa4f7e 100644
--- a/ecc/bn254/fr/element_exp.go
+++ b/ecc/bn254/fr/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/element_purego.go b/ecc/bn254/fr/element_purego.go
index 647d39dd42..70529c5ec8 100644
--- a/ecc/bn254/fr/element_purego.go
+++ b/ecc/bn254/fr/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/element_test.go b/ecc/bn254/fr/element_test.go
index 15785410c4..642d30347d 100644
--- a/ecc/bn254/fr/element_test.go
+++ b/ecc/bn254/fr/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/fft/bitreverse.go b/ecc/bn254/fr/fft/bitreverse.go
index b575154fa4..1299286f68 100644
--- a/ecc/bn254/fr/fft/bitreverse.go
+++ b/ecc/bn254/fr/fft/bitreverse.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/fft/bitreverse_test.go b/ecc/bn254/fr/fft/bitreverse_test.go
index 1c23996f51..28c14b4936 100644
--- a/ecc/bn254/fr/fft/bitreverse_test.go
+++ b/ecc/bn254/fr/fft/bitreverse_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/fft/doc.go b/ecc/bn254/fr/fft/doc.go
index 1ef04db2df..4cce0f9779 100644
--- a/ecc/bn254/fr/fft/doc.go
+++ b/ecc/bn254/fr/fft/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/fft/domain.go b/ecc/bn254/fr/fft/domain.go
index 48a84a9e1c..cf4c08e7c4 100644
--- a/ecc/bn254/fr/fft/domain.go
+++ b/ecc/bn254/fr/fft/domain.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/fft/domain_test.go b/ecc/bn254/fr/fft/domain_test.go
index d95288076c..e445d3cc12 100644
--- a/ecc/bn254/fr/fft/domain_test.go
+++ b/ecc/bn254/fr/fft/domain_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/fft/fft.go b/ecc/bn254/fr/fft/fft.go
index 6281c866aa..5b65603a62 100644
--- a/ecc/bn254/fr/fft/fft.go
+++ b/ecc/bn254/fr/fft/fft.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/fft/fft_test.go b/ecc/bn254/fr/fft/fft_test.go
index 9cfaf96110..758a257721 100644
--- a/ecc/bn254/fr/fft/fft_test.go
+++ b/ecc/bn254/fr/fft/fft_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/fft/options.go b/ecc/bn254/fr/fft/options.go
index 904036e7cc..9656a9e5d9 100644
--- a/ecc/bn254/fr/fft/options.go
+++ b/ecc/bn254/fr/fft/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/fri/doc.go b/ecc/bn254/fr/fri/doc.go
index 428dabf625..cea69fc79a 100644
--- a/ecc/bn254/fr/fri/doc.go
+++ b/ecc/bn254/fr/fri/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/fri/fri.go b/ecc/bn254/fr/fri/fri.go
index a76e40d4a3..f4443969ae 100644
--- a/ecc/bn254/fr/fri/fri.go
+++ b/ecc/bn254/fr/fri/fri.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/fri/fri_test.go b/ecc/bn254/fr/fri/fri_test.go
index d4629fd050..3e7f236f7c 100644
--- a/ecc/bn254/fr/fri/fri_test.go
+++ b/ecc/bn254/fr/fri/fri_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/generator.go b/ecc/bn254/fr/generator.go
index 5a6a0e9571..7997c96216 100644
--- a/ecc/bn254/fr/generator.go
+++ b/ecc/bn254/fr/generator.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/gkr/gkr.go b/ecc/bn254/fr/gkr/gkr.go
index 6b6e6c05a9..e52de1fc30 100644
--- a/ecc/bn254/fr/gkr/gkr.go
+++ b/ecc/bn254/fr/gkr/gkr.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/gkr/gkr_test.go b/ecc/bn254/fr/gkr/gkr_test.go
index b60faf98a1..cfd06a0aa7 100644
--- a/ecc/bn254/fr/gkr/gkr_test.go
+++ b/ecc/bn254/fr/gkr/gkr_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
@@ -325,7 +325,7 @@ func mimcCircuit(numRounds int) Circuit {
 
 func testMimc(t *testing.T, numRounds int, inputAssignments ...[]fr.Element) {
 	//TODO: Implement mimc correctly. Currently, the computation is mimc(a,b) = cipher( cipher( ... cipher(a, b), b) ..., b)
-	// @AlexandreBelling: Please explain the extra layers in https://github.com/ConsenSys/gkr-mimc/blob/81eada039ab4ed403b7726b535adb63026e8011f/examples/mimc.go#L10
+	// @AlexandreBelling: Please explain the extra layers in https://github.com/Consensys/gkr-mimc/blob/81eada039ab4ed403b7726b535adb63026e8011f/examples/mimc.go#L10
 
 	c := mimcCircuit(numRounds)
 
diff --git a/ecc/bn254/fr/hash_to_field/doc.go b/ecc/bn254/fr/hash_to_field/doc.go
index 6986d9ba80..cf89740488 100644
--- a/ecc/bn254/fr/hash_to_field/doc.go
+++ b/ecc/bn254/fr/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/hash_to_field/hash_to_field.go b/ecc/bn254/fr/hash_to_field/hash_to_field.go
index 6ead221a31..6753b391a1 100644
--- a/ecc/bn254/fr/hash_to_field/hash_to_field.go
+++ b/ecc/bn254/fr/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/hash_to_field/hash_to_field_test.go b/ecc/bn254/fr/hash_to_field/hash_to_field_test.go
index 895dc83d94..37e7db2dad 100644
--- a/ecc/bn254/fr/hash_to_field/hash_to_field_test.go
+++ b/ecc/bn254/fr/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/iop/doc.go b/ecc/bn254/fr/iop/doc.go
index ee3facf1e1..2ef06dfe1a 100644
--- a/ecc/bn254/fr/iop/doc.go
+++ b/ecc/bn254/fr/iop/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/iop/expressions.go b/ecc/bn254/fr/iop/expressions.go
index 3361af0357..396a25bc0f 100644
--- a/ecc/bn254/fr/iop/expressions.go
+++ b/ecc/bn254/fr/iop/expressions.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/iop/expressions_test.go b/ecc/bn254/fr/iop/expressions_test.go
index 4bb0851f0b..29a2a7ef10 100644
--- a/ecc/bn254/fr/iop/expressions_test.go
+++ b/ecc/bn254/fr/iop/expressions_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/iop/polynomial.go b/ecc/bn254/fr/iop/polynomial.go
index fa5310479b..4eb7e6bb8c 100644
--- a/ecc/bn254/fr/iop/polynomial.go
+++ b/ecc/bn254/fr/iop/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/iop/polynomial_test.go b/ecc/bn254/fr/iop/polynomial_test.go
index b1077bedab..8bce78d41b 100644
--- a/ecc/bn254/fr/iop/polynomial_test.go
+++ b/ecc/bn254/fr/iop/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/iop/quotient.go b/ecc/bn254/fr/iop/quotient.go
index 085f771af9..09c3d6681f 100644
--- a/ecc/bn254/fr/iop/quotient.go
+++ b/ecc/bn254/fr/iop/quotient.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/iop/quotient_test.go b/ecc/bn254/fr/iop/quotient_test.go
index 603a619d0e..c9df5e2971 100644
--- a/ecc/bn254/fr/iop/quotient_test.go
+++ b/ecc/bn254/fr/iop/quotient_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/iop/ratios.go b/ecc/bn254/fr/iop/ratios.go
index def50bc64a..1239a2ccf1 100644
--- a/ecc/bn254/fr/iop/ratios.go
+++ b/ecc/bn254/fr/iop/ratios.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/iop/ratios_test.go b/ecc/bn254/fr/iop/ratios_test.go
index a9a8a47a82..e7c8659ec1 100644
--- a/ecc/bn254/fr/iop/ratios_test.go
+++ b/ecc/bn254/fr/iop/ratios_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/iop/utils.go b/ecc/bn254/fr/iop/utils.go
index 44d187446b..674bb93184 100644
--- a/ecc/bn254/fr/iop/utils.go
+++ b/ecc/bn254/fr/iop/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/mimc/doc.go b/ecc/bn254/fr/mimc/doc.go
index cc7b101eb4..98aa3f8d81 100644
--- a/ecc/bn254/fr/mimc/doc.go
+++ b/ecc/bn254/fr/mimc/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/mimc/mimc.go b/ecc/bn254/fr/mimc/mimc.go
index 9a7619bb89..f58fc6ef3b 100644
--- a/ecc/bn254/fr/mimc/mimc.go
+++ b/ecc/bn254/fr/mimc/mimc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/mimc/options.go b/ecc/bn254/fr/mimc/options.go
index a53abb2def..ad4e60060e 100644
--- a/ecc/bn254/fr/mimc/options.go
+++ b/ecc/bn254/fr/mimc/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/pedersen/doc.go b/ecc/bn254/fr/pedersen/doc.go
index 62a62f179f..2e24034936 100644
--- a/ecc/bn254/fr/pedersen/doc.go
+++ b/ecc/bn254/fr/pedersen/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/pedersen/example_test.go b/ecc/bn254/fr/pedersen/example_test.go
index 6b46f1aafa..e31c8c6449 100644
--- a/ecc/bn254/fr/pedersen/example_test.go
+++ b/ecc/bn254/fr/pedersen/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/pedersen/pedersen.go b/ecc/bn254/fr/pedersen/pedersen.go
index ebbd9914ad..9b4e645cee 100644
--- a/ecc/bn254/fr/pedersen/pedersen.go
+++ b/ecc/bn254/fr/pedersen/pedersen.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
@@ -105,7 +105,7 @@ func (pk *ProvingKey) ProveKnowledge(values []fr.Element) (pok curve.G1Affine, e
 	}
 
 	// TODO @gbotrel this will spawn more than one task, see
-	// https://github.com/ConsenSys/gnark-crypto/issues/269
+	// https://github.com/Consensys/gnark-crypto/issues/269
 	config := ecc.MultiExpConfig{
 		NbTasks: 1, // TODO Experiment
 	}
@@ -123,7 +123,7 @@ func (pk *ProvingKey) Commit(values []fr.Element) (commitment curve.G1Affine, er
 	}
 
 	// TODO @gbotrel this will spawn more than one task, see
-	// https://github.com/ConsenSys/gnark-crypto/issues/269
+	// https://github.com/Consensys/gnark-crypto/issues/269
 	config := ecc.MultiExpConfig{
 		NbTasks: 1,
 	}
@@ -184,7 +184,7 @@ func BatchProve(pk []ProvingKey, values [][]fr.Element, combinationCoeff fr.Elem
 	}
 
 	// TODO @gbotrel this will spawn more than one task, see
-	// https://github.com/ConsenSys/gnark-crypto/issues/269
+	// https://github.com/Consensys/gnark-crypto/issues/269
 	config := ecc.MultiExpConfig{
 		NbTasks: 1,
 	}
diff --git a/ecc/bn254/fr/pedersen/pedersen_test.go b/ecc/bn254/fr/pedersen/pedersen_test.go
index b2f095f6e8..1c72af2a1e 100644
--- a/ecc/bn254/fr/pedersen/pedersen_test.go
+++ b/ecc/bn254/fr/pedersen/pedersen_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/permutation/doc.go b/ecc/bn254/fr/permutation/doc.go
index 5f346b5a53..e24cd82923 100644
--- a/ecc/bn254/fr/permutation/doc.go
+++ b/ecc/bn254/fr/permutation/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/permutation/permutation.go b/ecc/bn254/fr/permutation/permutation.go
index 42ced0634c..7bc72f1ff6 100644
--- a/ecc/bn254/fr/permutation/permutation.go
+++ b/ecc/bn254/fr/permutation/permutation.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/permutation/permutation_test.go b/ecc/bn254/fr/permutation/permutation_test.go
index 5745d7e922..33924e26ee 100644
--- a/ecc/bn254/fr/permutation/permutation_test.go
+++ b/ecc/bn254/fr/permutation/permutation_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/plookup/doc.go b/ecc/bn254/fr/plookup/doc.go
index d163104002..7a02c59719 100644
--- a/ecc/bn254/fr/plookup/doc.go
+++ b/ecc/bn254/fr/plookup/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/plookup/plookup_test.go b/ecc/bn254/fr/plookup/plookup_test.go
index 8af42ee374..e91a4ded4e 100644
--- a/ecc/bn254/fr/plookup/plookup_test.go
+++ b/ecc/bn254/fr/plookup/plookup_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/plookup/table.go b/ecc/bn254/fr/plookup/table.go
index 7cc0ecaf80..15728734c2 100644
--- a/ecc/bn254/fr/plookup/table.go
+++ b/ecc/bn254/fr/plookup/table.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/plookup/vector.go b/ecc/bn254/fr/plookup/vector.go
index cd9b2509ac..c1494d3f9a 100644
--- a/ecc/bn254/fr/plookup/vector.go
+++ b/ecc/bn254/fr/plookup/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/polynomial/doc.go b/ecc/bn254/fr/polynomial/doc.go
index 35b3f725c1..fd96328e8f 100644
--- a/ecc/bn254/fr/polynomial/doc.go
+++ b/ecc/bn254/fr/polynomial/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/polynomial/multilin.go b/ecc/bn254/fr/polynomial/multilin.go
index 0c10a86ee1..3399187752 100644
--- a/ecc/bn254/fr/polynomial/multilin.go
+++ b/ecc/bn254/fr/polynomial/multilin.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/polynomial/multilin_test.go b/ecc/bn254/fr/polynomial/multilin_test.go
index 1a32cc334a..7ce598505a 100644
--- a/ecc/bn254/fr/polynomial/multilin_test.go
+++ b/ecc/bn254/fr/polynomial/multilin_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/polynomial/polynomial.go b/ecc/bn254/fr/polynomial/polynomial.go
index fe096e5556..0b463ffab8 100644
--- a/ecc/bn254/fr/polynomial/polynomial.go
+++ b/ecc/bn254/fr/polynomial/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/polynomial/polynomial_test.go b/ecc/bn254/fr/polynomial/polynomial_test.go
index cd1c9219ee..76fad6fd40 100644
--- a/ecc/bn254/fr/polynomial/polynomial_test.go
+++ b/ecc/bn254/fr/polynomial/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/polynomial/pool.go b/ecc/bn254/fr/polynomial/pool.go
index 59b2e1868b..ada08b72e8 100644
--- a/ecc/bn254/fr/polynomial/pool.go
+++ b/ecc/bn254/fr/polynomial/pool.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/poseidon2/poseidon2.go b/ecc/bn254/fr/poseidon2/poseidon2.go
index c9b3e2d023..b781f9bb46 100644
--- a/ecc/bn254/fr/poseidon2/poseidon2.go
+++ b/ecc/bn254/fr/poseidon2/poseidon2.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/poseidon2/poseidon2_test.go b/ecc/bn254/fr/poseidon2/poseidon2_test.go
index ec371ab244..eb3c7c78e3 100644
--- a/ecc/bn254/fr/poseidon2/poseidon2_test.go
+++ b/ecc/bn254/fr/poseidon2/poseidon2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/sis/sis.go b/ecc/bn254/fr/sis/sis.go
index de608b9de7..fb4582c676 100644
--- a/ecc/bn254/fr/sis/sis.go
+++ b/ecc/bn254/fr/sis/sis.go
@@ -1,16 +1,5 @@
-// Copyright 2023 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package sis
 
diff --git a/ecc/bn254/fr/sis/sis_fft.go b/ecc/bn254/fr/sis/sis_fft.go
index 25ff7f8235..2ea3c6f4e7 100644
--- a/ecc/bn254/fr/sis/sis_fft.go
+++ b/ecc/bn254/fr/sis/sis_fft.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/sis/sis_test.go b/ecc/bn254/fr/sis/sis_test.go
index 24a14b46c9..8a2c55f892 100644
--- a/ecc/bn254/fr/sis/sis_test.go
+++ b/ecc/bn254/fr/sis/sis_test.go
@@ -1,16 +1,5 @@
-// Copyright 2023 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package sis
 
diff --git a/ecc/bn254/fr/sumcheck/sumcheck.go b/ecc/bn254/fr/sumcheck/sumcheck.go
index fea037b974..633d7c01c3 100644
--- a/ecc/bn254/fr/sumcheck/sumcheck.go
+++ b/ecc/bn254/fr/sumcheck/sumcheck.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/sumcheck/sumcheck_test.go b/ecc/bn254/fr/sumcheck/sumcheck_test.go
index 8330f3e7c6..4e50495ac8 100644
--- a/ecc/bn254/fr/sumcheck/sumcheck_test.go
+++ b/ecc/bn254/fr/sumcheck/sumcheck_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/tensor-commitment/commitment.go b/ecc/bn254/fr/tensor-commitment/commitment.go
index 923cbef2af..65542c5f40 100644
--- a/ecc/bn254/fr/tensor-commitment/commitment.go
+++ b/ecc/bn254/fr/tensor-commitment/commitment.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package tensorcommitment
 
diff --git a/ecc/bn254/fr/tensor-commitment/commitment_test.go b/ecc/bn254/fr/tensor-commitment/commitment_test.go
index a970a2dee2..fa5c43299a 100644
--- a/ecc/bn254/fr/tensor-commitment/commitment_test.go
+++ b/ecc/bn254/fr/tensor-commitment/commitment_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package tensorcommitment
 
diff --git a/ecc/bn254/fr/test_vector_utils/test_vector_utils.go b/ecc/bn254/fr/test_vector_utils/test_vector_utils.go
index 09087f9b03..581dd25889 100644
--- a/ecc/bn254/fr/test_vector_utils/test_vector_utils.go
+++ b/ecc/bn254/fr/test_vector_utils/test_vector_utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/vector.go b/ecc/bn254/fr/vector.go
index 8b59bd36e9..4654b1b2d3 100644
--- a/ecc/bn254/fr/vector.go
+++ b/ecc/bn254/fr/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/vector_amd64.go b/ecc/bn254/fr/vector_amd64.go
index b27679827c..a7dcec3b25 100644
--- a/ecc/bn254/fr/vector_amd64.go
+++ b/ecc/bn254/fr/vector_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/vector_purego.go b/ecc/bn254/fr/vector_purego.go
index 5973d16ce2..db43e73504 100644
--- a/ecc/bn254/fr/vector_purego.go
+++ b/ecc/bn254/fr/vector_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || !amd64
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/vector_test.go b/ecc/bn254/fr/vector_test.go
index a094bc0ac6..f6179e7824 100644
--- a/ecc/bn254/fr/vector_test.go
+++ b/ecc/bn254/fr/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/g1.go b/ecc/bn254/g1.go
index afddf318c2..b10c129683 100644
--- a/ecc/bn254/g1.go
+++ b/ecc/bn254/g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/g1_test.go b/ecc/bn254/g1_test.go
index 970369c503..1e95f6a6b5 100644
--- a/ecc/bn254/g1_test.go
+++ b/ecc/bn254/g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/g2.go b/ecc/bn254/g2.go
index 36b3168d1c..b89ec2f626 100644
--- a/ecc/bn254/g2.go
+++ b/ecc/bn254/g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/g2_test.go b/ecc/bn254/g2_test.go
index 5367b79b02..e1b5a712b5 100644
--- a/ecc/bn254/g2_test.go
+++ b/ecc/bn254/g2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/hash_to_g1.go b/ecc/bn254/hash_to_g1.go
index a1791f6e5a..bbc18d42b3 100644
--- a/ecc/bn254/hash_to_g1.go
+++ b/ecc/bn254/hash_to_g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/hash_to_g1_test.go b/ecc/bn254/hash_to_g1_test.go
index 3bb56740eb..e5915f4ab0 100644
--- a/ecc/bn254/hash_to_g1_test.go
+++ b/ecc/bn254/hash_to_g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/hash_to_g2.go b/ecc/bn254/hash_to_g2.go
index ae3dbfd41d..9c6cd9230e 100644
--- a/ecc/bn254/hash_to_g2.go
+++ b/ecc/bn254/hash_to_g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/hash_to_g2_test.go b/ecc/bn254/hash_to_g2_test.go
index 47700eb9e8..6b21f48a9d 100644
--- a/ecc/bn254/hash_to_g2_test.go
+++ b/ecc/bn254/hash_to_g2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/internal/fptower/asm.go b/ecc/bn254/internal/fptower/asm.go
index f1ff282d0b..7d64458b6c 100644
--- a/ecc/bn254/internal/fptower/asm.go
+++ b/ecc/bn254/internal/fptower/asm.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/internal/fptower/asm_noadx.go b/ecc/bn254/internal/fptower/asm_noadx.go
index 3885d93d55..28588f65a0 100644
--- a/ecc/bn254/internal/fptower/asm_noadx.go
+++ b/ecc/bn254/internal/fptower/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/internal/fptower/e12.go b/ecc/bn254/internal/fptower/e12.go
index 319c2c3462..043a8a4c85 100644
--- a/ecc/bn254/internal/fptower/e12.go
+++ b/ecc/bn254/internal/fptower/e12.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/internal/fptower/e12_test.go b/ecc/bn254/internal/fptower/e12_test.go
index b61d36078a..ab1bc05a1a 100644
--- a/ecc/bn254/internal/fptower/e12_test.go
+++ b/ecc/bn254/internal/fptower/e12_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/internal/fptower/e2.go b/ecc/bn254/internal/fptower/e2.go
index eacac97603..b0532223db 100644
--- a/ecc/bn254/internal/fptower/e2.go
+++ b/ecc/bn254/internal/fptower/e2.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/internal/fptower/e2_amd64.go b/ecc/bn254/internal/fptower/e2_amd64.go
index 4049fd2bed..c885a81a61 100644
--- a/ecc/bn254/internal/fptower/e2_amd64.go
+++ b/ecc/bn254/internal/fptower/e2_amd64.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/internal/fptower/e2_amd64.s b/ecc/bn254/internal/fptower/e2_amd64.s
index ce5a3624bc..f7d030d9dd 100644
--- a/ecc/bn254/internal/fptower/e2_amd64.s
+++ b/ecc/bn254/internal/fptower/e2_amd64.s
@@ -1,4 +1,4 @@
-// Copyright 2020 ConsenSys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 #include "textflag.h"
diff --git a/ecc/bn254/internal/fptower/e2_bn254.go b/ecc/bn254/internal/fptower/e2_bn254.go
index 87ab9d1caf..945fa1c761 100644
--- a/ecc/bn254/internal/fptower/e2_bn254.go
+++ b/ecc/bn254/internal/fptower/e2_bn254.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bn254/internal/fptower/e2_bn254_fallback.go b/ecc/bn254/internal/fptower/e2_bn254_fallback.go
index 467a96f77e..ffa25c7e1b 100644
--- a/ecc/bn254/internal/fptower/e2_bn254_fallback.go
+++ b/ecc/bn254/internal/fptower/e2_bn254_fallback.go
@@ -1,19 +1,8 @@
 //go:build !amd64
 // +build !amd64
 
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bn254/internal/fptower/e2_fallback.go b/ecc/bn254/internal/fptower/e2_fallback.go
index eaea355699..3dff96dcea 100644
--- a/ecc/bn254/internal/fptower/e2_fallback.go
+++ b/ecc/bn254/internal/fptower/e2_fallback.go
@@ -1,6 +1,6 @@
 //go:build !amd64
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/internal/fptower/e2_test.go b/ecc/bn254/internal/fptower/e2_test.go
index 808b48e27a..c28bfae171 100644
--- a/ecc/bn254/internal/fptower/e2_test.go
+++ b/ecc/bn254/internal/fptower/e2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/internal/fptower/e6.go b/ecc/bn254/internal/fptower/e6.go
index 5f2cca6625..a3bd71a6cc 100644
--- a/ecc/bn254/internal/fptower/e6.go
+++ b/ecc/bn254/internal/fptower/e6.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/internal/fptower/e6_test.go b/ecc/bn254/internal/fptower/e6_test.go
index a82cc881aa..a81a5daa05 100644
--- a/ecc/bn254/internal/fptower/e6_test.go
+++ b/ecc/bn254/internal/fptower/e6_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/internal/fptower/frobenius.go b/ecc/bn254/internal/fptower/frobenius.go
index 18d8fef960..4cfef6fa14 100644
--- a/ecc/bn254/internal/fptower/frobenius.go
+++ b/ecc/bn254/internal/fptower/frobenius.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bn254/internal/fptower/parameters.go b/ecc/bn254/internal/fptower/parameters.go
index 3859aeac76..e6d241b946 100644
--- a/ecc/bn254/internal/fptower/parameters.go
+++ b/ecc/bn254/internal/fptower/parameters.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bn254/kzg/doc.go b/ecc/bn254/kzg/doc.go
index 6c3454a2d9..226614bbdf 100644
--- a/ecc/bn254/kzg/doc.go
+++ b/ecc/bn254/kzg/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/kzg/kzg.go b/ecc/bn254/kzg/kzg.go
index 157accfa99..7ebc1c0627 100644
--- a/ecc/bn254/kzg/kzg.go
+++ b/ecc/bn254/kzg/kzg.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/kzg/kzg_test.go b/ecc/bn254/kzg/kzg_test.go
index ad94918d7e..e6fdcc7d58 100644
--- a/ecc/bn254/kzg/kzg_test.go
+++ b/ecc/bn254/kzg/kzg_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/kzg/marshal.go b/ecc/bn254/kzg/marshal.go
index 1953bd8cb9..3d7137a9a4 100644
--- a/ecc/bn254/kzg/marshal.go
+++ b/ecc/bn254/kzg/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/kzg/utils.go b/ecc/bn254/kzg/utils.go
index d14204dbd3..5f28c5b78e 100644
--- a/ecc/bn254/kzg/utils.go
+++ b/ecc/bn254/kzg/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/marshal.go b/ecc/bn254/marshal.go
index 95afd6bac0..4db3316aa7 100644
--- a/ecc/bn254/marshal.go
+++ b/ecc/bn254/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/marshal_test.go b/ecc/bn254/marshal_test.go
index b2ed1ba2c7..96978d256d 100644
--- a/ecc/bn254/marshal_test.go
+++ b/ecc/bn254/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/multiexp.go b/ecc/bn254/multiexp.go
index 46f12095e7..a9fc27c81b 100644
--- a/ecc/bn254/multiexp.go
+++ b/ecc/bn254/multiexp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/multiexp_affine.go b/ecc/bn254/multiexp_affine.go
index b3cc2d47a2..7d060d3d03 100644
--- a/ecc/bn254/multiexp_affine.go
+++ b/ecc/bn254/multiexp_affine.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
@@ -19,7 +19,7 @@ type batchOpG1Affine struct {
 // using affine coordinates for the buckets. To amortize the cost of the inverse in the affine addition
 // we use a batch affine addition.
 //
-// this is derived from a PR by 0x0ece : https://github.com/ConsenSys/gnark-crypto/pull/249
+// this is derived from a PR by 0x0ece : https://github.com/Consensys/gnark-crypto/pull/249
 // See Section 5.3: ia.cr/2022/1396
 func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP pG1Affine, TPP ppG1Affine, TQ qOpsG1Affine, TC cG1Affine](
 	chunk uint64,
@@ -346,7 +346,7 @@ type batchOpG2Affine struct {
 // using affine coordinates for the buckets. To amortize the cost of the inverse in the affine addition
 // we use a batch affine addition.
 //
-// this is derived from a PR by 0x0ece : https://github.com/ConsenSys/gnark-crypto/pull/249
+// this is derived from a PR by 0x0ece : https://github.com/Consensys/gnark-crypto/pull/249
 // See Section 5.3: ia.cr/2022/1396
 func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP pG2Affine, TPP ppG2Affine, TQ qOpsG2Affine, TC cG2Affine](
 	chunk uint64,
diff --git a/ecc/bn254/multiexp_jacobian.go b/ecc/bn254/multiexp_jacobian.go
index f1557637fe..4205b5620f 100644
--- a/ecc/bn254/multiexp_jacobian.go
+++ b/ecc/bn254/multiexp_jacobian.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/multiexp_test.go b/ecc/bn254/multiexp_test.go
index bbdc88d5ac..fb69e1db39 100644
--- a/ecc/bn254/multiexp_test.go
+++ b/ecc/bn254/multiexp_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/pairing.go b/ecc/bn254/pairing.go
index 675eebedf3..f0e843fd35 100644
--- a/ecc/bn254/pairing.go
+++ b/ecc/bn254/pairing.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package bn254
 
diff --git a/ecc/bn254/pairing_test.go b/ecc/bn254/pairing_test.go
index dd7fbfd2fa..abc290e42c 100644
--- a/ecc/bn254/pairing_test.go
+++ b/ecc/bn254/pairing_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/shplonk/doc.go b/ecc/bn254/shplonk/doc.go
index 17b34373c2..0367893999 100644
--- a/ecc/bn254/shplonk/doc.go
+++ b/ecc/bn254/shplonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/shplonk/example_test.go b/ecc/bn254/shplonk/example_test.go
index 4d0ce3c2d3..29fb75ad14 100644
--- a/ecc/bn254/shplonk/example_test.go
+++ b/ecc/bn254/shplonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/shplonk/marshal.go b/ecc/bn254/shplonk/marshal.go
index df73ab2bea..006769c68f 100644
--- a/ecc/bn254/shplonk/marshal.go
+++ b/ecc/bn254/shplonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
index 8335b78aa8..c732722145 100644
--- a/ecc/bn254/shplonk/shplonk.go
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/shplonk/shplonk_test.go b/ecc/bn254/shplonk/shplonk_test.go
index 7955cd7bfc..fd2be5987d 100644
--- a/ecc/bn254/shplonk/shplonk_test.go
+++ b/ecc/bn254/shplonk/shplonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/twistededwards/curve.go b/ecc/bn254/twistededwards/curve.go
index aaf24dd341..2721974834 100644
--- a/ecc/bn254/twistededwards/curve.go
+++ b/ecc/bn254/twistededwards/curve.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/twistededwards/doc.go b/ecc/bn254/twistededwards/doc.go
index 02a4aaf565..032ff269fe 100644
--- a/ecc/bn254/twistededwards/doc.go
+++ b/ecc/bn254/twistededwards/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/twistededwards/eddsa/doc.go b/ecc/bn254/twistededwards/eddsa/doc.go
index 1e50b3f6a9..12eebe5d29 100644
--- a/ecc/bn254/twistededwards/eddsa/doc.go
+++ b/ecc/bn254/twistededwards/eddsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/twistededwards/eddsa/eddsa.go b/ecc/bn254/twistededwards/eddsa/eddsa.go
index 0fae94c13e..fc1de34203 100644
--- a/ecc/bn254/twistededwards/eddsa/eddsa.go
+++ b/ecc/bn254/twistededwards/eddsa/eddsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/twistededwards/eddsa/eddsa_test.go b/ecc/bn254/twistededwards/eddsa/eddsa_test.go
index 0df6b846dc..16f6511f46 100644
--- a/ecc/bn254/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bn254/twistededwards/eddsa/eddsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/twistededwards/eddsa/marshal.go b/ecc/bn254/twistededwards/eddsa/marshal.go
index 997d632b52..4ab1f0b542 100644
--- a/ecc/bn254/twistededwards/eddsa/marshal.go
+++ b/ecc/bn254/twistededwards/eddsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/twistededwards/point.go b/ecc/bn254/twistededwards/point.go
index 981ce89b7b..c231cfa9e3 100644
--- a/ecc/bn254/twistededwards/point.go
+++ b/ecc/bn254/twistededwards/point.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/twistededwards/point_test.go b/ecc/bn254/twistededwards/point_test.go
index 80c0b1299d..767e56a70b 100644
--- a/ecc/bn254/twistededwards/point_test.go
+++ b/ecc/bn254/twistededwards/point_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/ecdsa/doc.go b/ecc/bw6-633/ecdsa/doc.go
index 59f91a57cd..933c753ea7 100644
--- a/ecc/bw6-633/ecdsa/doc.go
+++ b/ecc/bw6-633/ecdsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/ecdsa/ecdsa.go b/ecc/bw6-633/ecdsa/ecdsa.go
index 0f2f7593bb..24b909289d 100644
--- a/ecc/bw6-633/ecdsa/ecdsa.go
+++ b/ecc/bw6-633/ecdsa/ecdsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/ecdsa/ecdsa_test.go b/ecc/bw6-633/ecdsa/ecdsa_test.go
index 002945c411..f4090a3077 100644
--- a/ecc/bw6-633/ecdsa/ecdsa_test.go
+++ b/ecc/bw6-633/ecdsa/ecdsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/ecdsa/marshal.go b/ecc/bw6-633/ecdsa/marshal.go
index 8d78088705..0a348be708 100644
--- a/ecc/bw6-633/ecdsa/marshal.go
+++ b/ecc/bw6-633/ecdsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/ecdsa/marshal_test.go b/ecc/bw6-633/ecdsa/marshal_test.go
index 87f4dbed9d..c49a56e6c7 100644
--- a/ecc/bw6-633/ecdsa/marshal_test.go
+++ b/ecc/bw6-633/ecdsa/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fflonk/doc.go b/ecc/bw6-633/fflonk/doc.go
index b717383d87..67a8094e35 100644
--- a/ecc/bw6-633/fflonk/doc.go
+++ b/ecc/bw6-633/fflonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fflonk/example_test.go b/ecc/bw6-633/fflonk/example_test.go
index 7e1b0173af..2dfc9617b4 100644
--- a/ecc/bw6-633/fflonk/example_test.go
+++ b/ecc/bw6-633/fflonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fflonk/fflonk.go b/ecc/bw6-633/fflonk/fflonk.go
index c22d719fe7..dcc9c98c78 100644
--- a/ecc/bw6-633/fflonk/fflonk.go
+++ b/ecc/bw6-633/fflonk/fflonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fflonk/fflonk_test.go b/ecc/bw6-633/fflonk/fflonk_test.go
index d74bb16130..fa5630cf9b 100644
--- a/ecc/bw6-633/fflonk/fflonk_test.go
+++ b/ecc/bw6-633/fflonk/fflonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fflonk/marshal.go b/ecc/bw6-633/fflonk/marshal.go
index d30b5d7ac2..63c27aec6e 100644
--- a/ecc/bw6-633/fflonk/marshal.go
+++ b/ecc/bw6-633/fflonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/arith.go b/ecc/bw6-633/fp/arith.go
index b202a1549a..bb63552f5a 100644
--- a/ecc/bw6-633/fp/arith.go
+++ b/ecc/bw6-633/fp/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/asm_adx.go b/ecc/bw6-633/fp/asm_adx.go
index fe25e82db2..75e92992fe 100644
--- a/ecc/bw6-633/fp/asm_adx.go
+++ b/ecc/bw6-633/fp/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/asm_noadx.go b/ecc/bw6-633/fp/asm_noadx.go
index 95085a8e6f..304dfb7209 100644
--- a/ecc/bw6-633/fp/asm_noadx.go
+++ b/ecc/bw6-633/fp/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/bw6_utils.go b/ecc/bw6-633/fp/bw6_utils.go
index a62097b708..a661ec4154 100644
--- a/ecc/bw6-633/fp/bw6_utils.go
+++ b/ecc/bw6-633/fp/bw6_utils.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fp
 
diff --git a/ecc/bw6-633/fp/doc.go b/ecc/bw6-633/fp/doc.go
index f4bd26cf51..efda77a4cf 100644
--- a/ecc/bw6-633/fp/doc.go
+++ b/ecc/bw6-633/fp/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/element.go b/ecc/bw6-633/fp/element.go
index 021561c553..b976ed3eb0 100644
--- a/ecc/bw6-633/fp/element.go
+++ b/ecc/bw6-633/fp/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/element_amd64.go b/ecc/bw6-633/fp/element_amd64.go
index e72f552ad9..9cee062e5b 100644
--- a/ecc/bw6-633/fp/element_amd64.go
+++ b/ecc/bw6-633/fp/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/element_amd64.s b/ecc/bw6-633/fp/element_amd64.s
index 0db47520d3..76df6b685b 100644
--- a/ecc/bw6-633/fp/element_amd64.s
+++ b/ecc/bw6-633/fp/element_amd64.s
@@ -1,10 +1,10 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
-// We include the hash to force the Go compiler to recompile: 747913930085520082
+// We include the hash to force the Go compiler to recompile: 15320537321640126458
 #include "../../../field/asm/element_10w_amd64.s"
 
diff --git a/ecc/bw6-633/fp/element_arm64.go b/ecc/bw6-633/fp/element_arm64.go
index febbad8296..d0af52deaa 100644
--- a/ecc/bw6-633/fp/element_arm64.go
+++ b/ecc/bw6-633/fp/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/element_arm64.s b/ecc/bw6-633/fp/element_arm64.s
index 537ac0b636..39f3d76ae2 100644
--- a/ecc/bw6-633/fp/element_arm64.s
+++ b/ecc/bw6-633/fp/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/element_exp.go b/ecc/bw6-633/fp/element_exp.go
index 846338367d..21eef1d6c2 100644
--- a/ecc/bw6-633/fp/element_exp.go
+++ b/ecc/bw6-633/fp/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/element_purego.go b/ecc/bw6-633/fp/element_purego.go
index cabb8ff2b3..40e6af52e0 100644
--- a/ecc/bw6-633/fp/element_purego.go
+++ b/ecc/bw6-633/fp/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/element_test.go b/ecc/bw6-633/fp/element_test.go
index 33266dd93e..5ece775b31 100644
--- a/ecc/bw6-633/fp/element_test.go
+++ b/ecc/bw6-633/fp/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/hash_to_field/doc.go b/ecc/bw6-633/fp/hash_to_field/doc.go
index 4dee7c4096..fc145559ad 100644
--- a/ecc/bw6-633/fp/hash_to_field/doc.go
+++ b/ecc/bw6-633/fp/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/hash_to_field/hash_to_field.go b/ecc/bw6-633/fp/hash_to_field/hash_to_field.go
index 853d1a5aac..d5d745d725 100644
--- a/ecc/bw6-633/fp/hash_to_field/hash_to_field.go
+++ b/ecc/bw6-633/fp/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/hash_to_field/hash_to_field_test.go b/ecc/bw6-633/fp/hash_to_field/hash_to_field_test.go
index 8fc6ccdbe7..5f660415c4 100644
--- a/ecc/bw6-633/fp/hash_to_field/hash_to_field_test.go
+++ b/ecc/bw6-633/fp/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/vector.go b/ecc/bw6-633/fp/vector.go
index 05a1b66f95..58c3692973 100644
--- a/ecc/bw6-633/fp/vector.go
+++ b/ecc/bw6-633/fp/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/vector_purego.go b/ecc/bw6-633/fp/vector_purego.go
index 347b0df594..0cda361871 100644
--- a/ecc/bw6-633/fp/vector_purego.go
+++ b/ecc/bw6-633/fp/vector_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/vector_test.go b/ecc/bw6-633/fp/vector_test.go
index ac54705fea..3b2aa63de7 100644
--- a/ecc/bw6-633/fp/vector_test.go
+++ b/ecc/bw6-633/fp/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/arith.go b/ecc/bw6-633/fr/arith.go
index 9285041f4b..dbba8a9ae4 100644
--- a/ecc/bw6-633/fr/arith.go
+++ b/ecc/bw6-633/fr/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/asm_adx.go b/ecc/bw6-633/fr/asm_adx.go
index 9e7da5e865..9b970335f1 100644
--- a/ecc/bw6-633/fr/asm_adx.go
+++ b/ecc/bw6-633/fr/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/asm_noadx.go b/ecc/bw6-633/fr/asm_noadx.go
index 3456158655..96741014f2 100644
--- a/ecc/bw6-633/fr/asm_noadx.go
+++ b/ecc/bw6-633/fr/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/doc.go b/ecc/bw6-633/fr/doc.go
index a2b7cfd871..5adacadee4 100644
--- a/ecc/bw6-633/fr/doc.go
+++ b/ecc/bw6-633/fr/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/element.go b/ecc/bw6-633/fr/element.go
index d9671b7d08..7e16486ca6 100644
--- a/ecc/bw6-633/fr/element.go
+++ b/ecc/bw6-633/fr/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/element_amd64.go b/ecc/bw6-633/fr/element_amd64.go
index ca49d12590..4c3f2a8567 100644
--- a/ecc/bw6-633/fr/element_amd64.go
+++ b/ecc/bw6-633/fr/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/element_amd64.s b/ecc/bw6-633/fr/element_amd64.s
index 599977a11a..0f7e0b89ff 100644
--- a/ecc/bw6-633/fr/element_amd64.s
+++ b/ecc/bw6-633/fr/element_amd64.s
@@ -1,10 +1,10 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
-// We include the hash to force the Go compiler to recompile: 18184981773209750009
+// We include the hash to force the Go compiler to recompile: 4600622797032586825
 #include "../../../field/asm/element_5w_amd64.s"
 
diff --git a/ecc/bw6-633/fr/element_exp.go b/ecc/bw6-633/fr/element_exp.go
index 11528df7d0..7a9e0ec902 100644
--- a/ecc/bw6-633/fr/element_exp.go
+++ b/ecc/bw6-633/fr/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/element_purego.go b/ecc/bw6-633/fr/element_purego.go
index 7d2053163c..93d2bcac2d 100644
--- a/ecc/bw6-633/fr/element_purego.go
+++ b/ecc/bw6-633/fr/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || !amd64
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/element_test.go b/ecc/bw6-633/fr/element_test.go
index aec1350323..b9f7e8709d 100644
--- a/ecc/bw6-633/fr/element_test.go
+++ b/ecc/bw6-633/fr/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/fft/bitreverse.go b/ecc/bw6-633/fr/fft/bitreverse.go
index b495f43b30..d0c374f9b8 100644
--- a/ecc/bw6-633/fr/fft/bitreverse.go
+++ b/ecc/bw6-633/fr/fft/bitreverse.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/fft/bitreverse_test.go b/ecc/bw6-633/fr/fft/bitreverse_test.go
index c14e2905c3..1d94a1c6c6 100644
--- a/ecc/bw6-633/fr/fft/bitreverse_test.go
+++ b/ecc/bw6-633/fr/fft/bitreverse_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/fft/doc.go b/ecc/bw6-633/fr/fft/doc.go
index 1ef04db2df..4cce0f9779 100644
--- a/ecc/bw6-633/fr/fft/doc.go
+++ b/ecc/bw6-633/fr/fft/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/fft/domain.go b/ecc/bw6-633/fr/fft/domain.go
index e8c95c7bb8..a37f3d80f8 100644
--- a/ecc/bw6-633/fr/fft/domain.go
+++ b/ecc/bw6-633/fr/fft/domain.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/fft/domain_test.go b/ecc/bw6-633/fr/fft/domain_test.go
index d95288076c..e445d3cc12 100644
--- a/ecc/bw6-633/fr/fft/domain_test.go
+++ b/ecc/bw6-633/fr/fft/domain_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/fft/fft.go b/ecc/bw6-633/fr/fft/fft.go
index c4f306cbc1..24c93b2c24 100644
--- a/ecc/bw6-633/fr/fft/fft.go
+++ b/ecc/bw6-633/fr/fft/fft.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/fft/fft_test.go b/ecc/bw6-633/fr/fft/fft_test.go
index 6ff132f4db..f4cce97c61 100644
--- a/ecc/bw6-633/fr/fft/fft_test.go
+++ b/ecc/bw6-633/fr/fft/fft_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/fft/options.go b/ecc/bw6-633/fr/fft/options.go
index b7abd2878c..44dd664d89 100644
--- a/ecc/bw6-633/fr/fft/options.go
+++ b/ecc/bw6-633/fr/fft/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/fri/doc.go b/ecc/bw6-633/fr/fri/doc.go
index 428dabf625..cea69fc79a 100644
--- a/ecc/bw6-633/fr/fri/doc.go
+++ b/ecc/bw6-633/fr/fri/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/fri/fri.go b/ecc/bw6-633/fr/fri/fri.go
index c720a643fa..225b98655a 100644
--- a/ecc/bw6-633/fr/fri/fri.go
+++ b/ecc/bw6-633/fr/fri/fri.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/fri/fri_test.go b/ecc/bw6-633/fr/fri/fri_test.go
index 299f1b7187..336ee07c0b 100644
--- a/ecc/bw6-633/fr/fri/fri_test.go
+++ b/ecc/bw6-633/fr/fri/fri_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/generator.go b/ecc/bw6-633/fr/generator.go
index d18f530e8e..f7491984c9 100644
--- a/ecc/bw6-633/fr/generator.go
+++ b/ecc/bw6-633/fr/generator.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/gkr/gkr.go b/ecc/bw6-633/fr/gkr/gkr.go
index 5f251d6742..2f2b91b5ef 100644
--- a/ecc/bw6-633/fr/gkr/gkr.go
+++ b/ecc/bw6-633/fr/gkr/gkr.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/gkr/gkr_test.go b/ecc/bw6-633/fr/gkr/gkr_test.go
index 0c7fbc9cb6..5316f63c01 100644
--- a/ecc/bw6-633/fr/gkr/gkr_test.go
+++ b/ecc/bw6-633/fr/gkr/gkr_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
@@ -325,7 +325,7 @@ func mimcCircuit(numRounds int) Circuit {
 
 func testMimc(t *testing.T, numRounds int, inputAssignments ...[]fr.Element) {
 	//TODO: Implement mimc correctly. Currently, the computation is mimc(a,b) = cipher( cipher( ... cipher(a, b), b) ..., b)
-	// @AlexandreBelling: Please explain the extra layers in https://github.com/ConsenSys/gkr-mimc/blob/81eada039ab4ed403b7726b535adb63026e8011f/examples/mimc.go#L10
+	// @AlexandreBelling: Please explain the extra layers in https://github.com/Consensys/gkr-mimc/blob/81eada039ab4ed403b7726b535adb63026e8011f/examples/mimc.go#L10
 
 	c := mimcCircuit(numRounds)
 
diff --git a/ecc/bw6-633/fr/hash_to_field/doc.go b/ecc/bw6-633/fr/hash_to_field/doc.go
index 298175d9f9..bf75dbff35 100644
--- a/ecc/bw6-633/fr/hash_to_field/doc.go
+++ b/ecc/bw6-633/fr/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/hash_to_field/hash_to_field.go b/ecc/bw6-633/fr/hash_to_field/hash_to_field.go
index e504f76259..e8f300e1cb 100644
--- a/ecc/bw6-633/fr/hash_to_field/hash_to_field.go
+++ b/ecc/bw6-633/fr/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/hash_to_field/hash_to_field_test.go b/ecc/bw6-633/fr/hash_to_field/hash_to_field_test.go
index e5e9595d90..2beeea14db 100644
--- a/ecc/bw6-633/fr/hash_to_field/hash_to_field_test.go
+++ b/ecc/bw6-633/fr/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/iop/doc.go b/ecc/bw6-633/fr/iop/doc.go
index ee3facf1e1..2ef06dfe1a 100644
--- a/ecc/bw6-633/fr/iop/doc.go
+++ b/ecc/bw6-633/fr/iop/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/iop/expressions.go b/ecc/bw6-633/fr/iop/expressions.go
index 7d239194ca..ea9678075b 100644
--- a/ecc/bw6-633/fr/iop/expressions.go
+++ b/ecc/bw6-633/fr/iop/expressions.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/iop/expressions_test.go b/ecc/bw6-633/fr/iop/expressions_test.go
index ec0e96da8c..309b60bd44 100644
--- a/ecc/bw6-633/fr/iop/expressions_test.go
+++ b/ecc/bw6-633/fr/iop/expressions_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/iop/polynomial.go b/ecc/bw6-633/fr/iop/polynomial.go
index c496dcf9a5..0d5c2cf8a2 100644
--- a/ecc/bw6-633/fr/iop/polynomial.go
+++ b/ecc/bw6-633/fr/iop/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/iop/polynomial_test.go b/ecc/bw6-633/fr/iop/polynomial_test.go
index 08e97903aa..9ac04bf6f9 100644
--- a/ecc/bw6-633/fr/iop/polynomial_test.go
+++ b/ecc/bw6-633/fr/iop/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/iop/quotient.go b/ecc/bw6-633/fr/iop/quotient.go
index 8e4239ebdb..4420c026b2 100644
--- a/ecc/bw6-633/fr/iop/quotient.go
+++ b/ecc/bw6-633/fr/iop/quotient.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/iop/quotient_test.go b/ecc/bw6-633/fr/iop/quotient_test.go
index da0f0bfc41..629f0bf29f 100644
--- a/ecc/bw6-633/fr/iop/quotient_test.go
+++ b/ecc/bw6-633/fr/iop/quotient_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/iop/ratios.go b/ecc/bw6-633/fr/iop/ratios.go
index 876c380c94..97150f3f34 100644
--- a/ecc/bw6-633/fr/iop/ratios.go
+++ b/ecc/bw6-633/fr/iop/ratios.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/iop/ratios_test.go b/ecc/bw6-633/fr/iop/ratios_test.go
index 03c076bb75..1d6860c47b 100644
--- a/ecc/bw6-633/fr/iop/ratios_test.go
+++ b/ecc/bw6-633/fr/iop/ratios_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/iop/utils.go b/ecc/bw6-633/fr/iop/utils.go
index 5a4fb37c09..db5e837c70 100644
--- a/ecc/bw6-633/fr/iop/utils.go
+++ b/ecc/bw6-633/fr/iop/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/mimc/doc.go b/ecc/bw6-633/fr/mimc/doc.go
index cc7b101eb4..98aa3f8d81 100644
--- a/ecc/bw6-633/fr/mimc/doc.go
+++ b/ecc/bw6-633/fr/mimc/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/mimc/mimc.go b/ecc/bw6-633/fr/mimc/mimc.go
index cfa98c7a5c..3ed4a8a714 100644
--- a/ecc/bw6-633/fr/mimc/mimc.go
+++ b/ecc/bw6-633/fr/mimc/mimc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/mimc/options.go b/ecc/bw6-633/fr/mimc/options.go
index 6afaa999d2..9a6b28e3e3 100644
--- a/ecc/bw6-633/fr/mimc/options.go
+++ b/ecc/bw6-633/fr/mimc/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/pedersen/doc.go b/ecc/bw6-633/fr/pedersen/doc.go
index 62a62f179f..2e24034936 100644
--- a/ecc/bw6-633/fr/pedersen/doc.go
+++ b/ecc/bw6-633/fr/pedersen/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/pedersen/example_test.go b/ecc/bw6-633/fr/pedersen/example_test.go
index 5e32ec591f..c4a36efcc9 100644
--- a/ecc/bw6-633/fr/pedersen/example_test.go
+++ b/ecc/bw6-633/fr/pedersen/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/pedersen/pedersen.go b/ecc/bw6-633/fr/pedersen/pedersen.go
index acca5002c6..ac20e55e77 100644
--- a/ecc/bw6-633/fr/pedersen/pedersen.go
+++ b/ecc/bw6-633/fr/pedersen/pedersen.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
@@ -105,7 +105,7 @@ func (pk *ProvingKey) ProveKnowledge(values []fr.Element) (pok curve.G1Affine, e
 	}
 
 	// TODO @gbotrel this will spawn more than one task, see
-	// https://github.com/ConsenSys/gnark-crypto/issues/269
+	// https://github.com/Consensys/gnark-crypto/issues/269
 	config := ecc.MultiExpConfig{
 		NbTasks: 1, // TODO Experiment
 	}
@@ -123,7 +123,7 @@ func (pk *ProvingKey) Commit(values []fr.Element) (commitment curve.G1Affine, er
 	}
 
 	// TODO @gbotrel this will spawn more than one task, see
-	// https://github.com/ConsenSys/gnark-crypto/issues/269
+	// https://github.com/Consensys/gnark-crypto/issues/269
 	config := ecc.MultiExpConfig{
 		NbTasks: 1,
 	}
@@ -184,7 +184,7 @@ func BatchProve(pk []ProvingKey, values [][]fr.Element, combinationCoeff fr.Elem
 	}
 
 	// TODO @gbotrel this will spawn more than one task, see
-	// https://github.com/ConsenSys/gnark-crypto/issues/269
+	// https://github.com/Consensys/gnark-crypto/issues/269
 	config := ecc.MultiExpConfig{
 		NbTasks: 1,
 	}
diff --git a/ecc/bw6-633/fr/pedersen/pedersen_test.go b/ecc/bw6-633/fr/pedersen/pedersen_test.go
index 1de99bdbdb..3c263657c3 100644
--- a/ecc/bw6-633/fr/pedersen/pedersen_test.go
+++ b/ecc/bw6-633/fr/pedersen/pedersen_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/permutation/doc.go b/ecc/bw6-633/fr/permutation/doc.go
index 5f346b5a53..e24cd82923 100644
--- a/ecc/bw6-633/fr/permutation/doc.go
+++ b/ecc/bw6-633/fr/permutation/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/permutation/permutation.go b/ecc/bw6-633/fr/permutation/permutation.go
index 828b04c983..938ff17aed 100644
--- a/ecc/bw6-633/fr/permutation/permutation.go
+++ b/ecc/bw6-633/fr/permutation/permutation.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/permutation/permutation_test.go b/ecc/bw6-633/fr/permutation/permutation_test.go
index da06886a14..1d7a73d5b5 100644
--- a/ecc/bw6-633/fr/permutation/permutation_test.go
+++ b/ecc/bw6-633/fr/permutation/permutation_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/plookup/doc.go b/ecc/bw6-633/fr/plookup/doc.go
index d163104002..7a02c59719 100644
--- a/ecc/bw6-633/fr/plookup/doc.go
+++ b/ecc/bw6-633/fr/plookup/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/plookup/plookup_test.go b/ecc/bw6-633/fr/plookup/plookup_test.go
index 2d654beeaf..f081d33d5c 100644
--- a/ecc/bw6-633/fr/plookup/plookup_test.go
+++ b/ecc/bw6-633/fr/plookup/plookup_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/plookup/table.go b/ecc/bw6-633/fr/plookup/table.go
index 9863ccd2f4..221a50cfd3 100644
--- a/ecc/bw6-633/fr/plookup/table.go
+++ b/ecc/bw6-633/fr/plookup/table.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/plookup/vector.go b/ecc/bw6-633/fr/plookup/vector.go
index 25acc02ecb..e3a3351e8f 100644
--- a/ecc/bw6-633/fr/plookup/vector.go
+++ b/ecc/bw6-633/fr/plookup/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/polynomial/doc.go b/ecc/bw6-633/fr/polynomial/doc.go
index 35b3f725c1..fd96328e8f 100644
--- a/ecc/bw6-633/fr/polynomial/doc.go
+++ b/ecc/bw6-633/fr/polynomial/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/polynomial/multilin.go b/ecc/bw6-633/fr/polynomial/multilin.go
index 1b98d88c83..a271c88575 100644
--- a/ecc/bw6-633/fr/polynomial/multilin.go
+++ b/ecc/bw6-633/fr/polynomial/multilin.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/polynomial/multilin_test.go b/ecc/bw6-633/fr/polynomial/multilin_test.go
index f1b0c1f746..7b722b4c1f 100644
--- a/ecc/bw6-633/fr/polynomial/multilin_test.go
+++ b/ecc/bw6-633/fr/polynomial/multilin_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/polynomial/polynomial.go b/ecc/bw6-633/fr/polynomial/polynomial.go
index 1265961519..1c3ff26dfd 100644
--- a/ecc/bw6-633/fr/polynomial/polynomial.go
+++ b/ecc/bw6-633/fr/polynomial/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/polynomial/polynomial_test.go b/ecc/bw6-633/fr/polynomial/polynomial_test.go
index 75e6b9c7a0..5b1d24b09e 100644
--- a/ecc/bw6-633/fr/polynomial/polynomial_test.go
+++ b/ecc/bw6-633/fr/polynomial/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/polynomial/pool.go b/ecc/bw6-633/fr/polynomial/pool.go
index d58cb5d680..6382c3ea48 100644
--- a/ecc/bw6-633/fr/polynomial/pool.go
+++ b/ecc/bw6-633/fr/polynomial/pool.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/poseidon2/poseidon2.go b/ecc/bw6-633/fr/poseidon2/poseidon2.go
index d9583a8eb0..c4a9ccc8eb 100644
--- a/ecc/bw6-633/fr/poseidon2/poseidon2.go
+++ b/ecc/bw6-633/fr/poseidon2/poseidon2.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/poseidon2/poseidon2_test.go b/ecc/bw6-633/fr/poseidon2/poseidon2_test.go
index e601f0f082..b1e8913fd5 100644
--- a/ecc/bw6-633/fr/poseidon2/poseidon2_test.go
+++ b/ecc/bw6-633/fr/poseidon2/poseidon2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/sumcheck/sumcheck.go b/ecc/bw6-633/fr/sumcheck/sumcheck.go
index 192f993ce0..902757717f 100644
--- a/ecc/bw6-633/fr/sumcheck/sumcheck.go
+++ b/ecc/bw6-633/fr/sumcheck/sumcheck.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/sumcheck/sumcheck_test.go b/ecc/bw6-633/fr/sumcheck/sumcheck_test.go
index 4a7a939a41..1abeb3ea5b 100644
--- a/ecc/bw6-633/fr/sumcheck/sumcheck_test.go
+++ b/ecc/bw6-633/fr/sumcheck/sumcheck_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/test_vector_utils/test_vector_utils.go b/ecc/bw6-633/fr/test_vector_utils/test_vector_utils.go
index 48c3f18b7a..fda1206bc2 100644
--- a/ecc/bw6-633/fr/test_vector_utils/test_vector_utils.go
+++ b/ecc/bw6-633/fr/test_vector_utils/test_vector_utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/vector.go b/ecc/bw6-633/fr/vector.go
index 6f87987b48..53e5e4e49c 100644
--- a/ecc/bw6-633/fr/vector.go
+++ b/ecc/bw6-633/fr/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/vector_purego.go b/ecc/bw6-633/fr/vector_purego.go
index 3c81210b58..c26ef9f1bb 100644
--- a/ecc/bw6-633/fr/vector_purego.go
+++ b/ecc/bw6-633/fr/vector_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/vector_test.go b/ecc/bw6-633/fr/vector_test.go
index b7fd253809..22e0d1bb90 100644
--- a/ecc/bw6-633/fr/vector_test.go
+++ b/ecc/bw6-633/fr/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/g1.go b/ecc/bw6-633/g1.go
index 875a4c48cc..62917937bc 100644
--- a/ecc/bw6-633/g1.go
+++ b/ecc/bw6-633/g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/g1_test.go b/ecc/bw6-633/g1_test.go
index 69fc2bbf4f..ad2ec5789a 100644
--- a/ecc/bw6-633/g1_test.go
+++ b/ecc/bw6-633/g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/g2.go b/ecc/bw6-633/g2.go
index 63912e698f..bb5972f107 100644
--- a/ecc/bw6-633/g2.go
+++ b/ecc/bw6-633/g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/g2_test.go b/ecc/bw6-633/g2_test.go
index d69c0235d5..c36bcdbbe7 100644
--- a/ecc/bw6-633/g2_test.go
+++ b/ecc/bw6-633/g2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/hash_to_g1.go b/ecc/bw6-633/hash_to_g1.go
index caba82f431..7e2a7bb8da 100644
--- a/ecc/bw6-633/hash_to_g1.go
+++ b/ecc/bw6-633/hash_to_g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/hash_to_g1_test.go b/ecc/bw6-633/hash_to_g1_test.go
index 15201b3bc7..bcd21cb91d 100644
--- a/ecc/bw6-633/hash_to_g1_test.go
+++ b/ecc/bw6-633/hash_to_g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/hash_to_g2.go b/ecc/bw6-633/hash_to_g2.go
index b5b0fd99de..b08e142909 100644
--- a/ecc/bw6-633/hash_to_g2.go
+++ b/ecc/bw6-633/hash_to_g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/hash_to_g2_test.go b/ecc/bw6-633/hash_to_g2_test.go
index 020784d358..57fdc4b5b4 100644
--- a/ecc/bw6-633/hash_to_g2_test.go
+++ b/ecc/bw6-633/hash_to_g2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/internal/fptower/e3.go b/ecc/bw6-633/internal/fptower/e3.go
index 64f0bdb619..9f29bcb441 100644
--- a/ecc/bw6-633/internal/fptower/e3.go
+++ b/ecc/bw6-633/internal/fptower/e3.go
@@ -1,14 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bw6-633/internal/fptower/e6.go b/ecc/bw6-633/internal/fptower/e6.go
index a618ea2ef8..8b4e716395 100644
--- a/ecc/bw6-633/internal/fptower/e6.go
+++ b/ecc/bw6-633/internal/fptower/e6.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bw6-633/internal/fptower/e6_test.go b/ecc/bw6-633/internal/fptower/e6_test.go
index 7f8d04257d..9f7c1856f9 100644
--- a/ecc/bw6-633/internal/fptower/e6_test.go
+++ b/ecc/bw6-633/internal/fptower/e6_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bw6-633/internal/fptower/frobenius.go b/ecc/bw6-633/internal/fptower/frobenius.go
index e253da6344..6b5768cacf 100644
--- a/ecc/bw6-633/internal/fptower/frobenius.go
+++ b/ecc/bw6-633/internal/fptower/frobenius.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bw6-633/internal/fptower/parameters.go b/ecc/bw6-633/internal/fptower/parameters.go
index 308498b0c6..ced7fe6967 100644
--- a/ecc/bw6-633/internal/fptower/parameters.go
+++ b/ecc/bw6-633/internal/fptower/parameters.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bw6-633/kzg/doc.go b/ecc/bw6-633/kzg/doc.go
index 6c3454a2d9..226614bbdf 100644
--- a/ecc/bw6-633/kzg/doc.go
+++ b/ecc/bw6-633/kzg/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/kzg/kzg.go b/ecc/bw6-633/kzg/kzg.go
index b9fae65ab1..bc27742827 100644
--- a/ecc/bw6-633/kzg/kzg.go
+++ b/ecc/bw6-633/kzg/kzg.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/kzg/kzg_test.go b/ecc/bw6-633/kzg/kzg_test.go
index ac64838478..995877b769 100644
--- a/ecc/bw6-633/kzg/kzg_test.go
+++ b/ecc/bw6-633/kzg/kzg_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/kzg/marshal.go b/ecc/bw6-633/kzg/marshal.go
index f120926571..f14c91a860 100644
--- a/ecc/bw6-633/kzg/marshal.go
+++ b/ecc/bw6-633/kzg/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/kzg/utils.go b/ecc/bw6-633/kzg/utils.go
index 00006d1c20..1ead3e7c2e 100644
--- a/ecc/bw6-633/kzg/utils.go
+++ b/ecc/bw6-633/kzg/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/marshal.go b/ecc/bw6-633/marshal.go
index b10cc1b70a..edc60f546a 100644
--- a/ecc/bw6-633/marshal.go
+++ b/ecc/bw6-633/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/marshal_test.go b/ecc/bw6-633/marshal_test.go
index d68198dc29..9e44f97d3b 100644
--- a/ecc/bw6-633/marshal_test.go
+++ b/ecc/bw6-633/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/multiexp.go b/ecc/bw6-633/multiexp.go
index 37f75c2729..7bbf91d315 100644
--- a/ecc/bw6-633/multiexp.go
+++ b/ecc/bw6-633/multiexp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/multiexp_affine.go b/ecc/bw6-633/multiexp_affine.go
index 67c19aa4a2..d36e5040fa 100644
--- a/ecc/bw6-633/multiexp_affine.go
+++ b/ecc/bw6-633/multiexp_affine.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
@@ -18,7 +18,7 @@ type batchOpG1Affine struct {
 // using affine coordinates for the buckets. To amortize the cost of the inverse in the affine addition
 // we use a batch affine addition.
 //
-// this is derived from a PR by 0x0ece : https://github.com/ConsenSys/gnark-crypto/pull/249
+// this is derived from a PR by 0x0ece : https://github.com/Consensys/gnark-crypto/pull/249
 // See Section 5.3: ia.cr/2022/1396
 func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP pG1Affine, TPP ppG1Affine, TQ qOpsG1Affine, TC cG1Affine](
 	chunk uint64,
@@ -285,7 +285,7 @@ type batchOpG2Affine struct {
 // using affine coordinates for the buckets. To amortize the cost of the inverse in the affine addition
 // we use a batch affine addition.
 //
-// this is derived from a PR by 0x0ece : https://github.com/ConsenSys/gnark-crypto/pull/249
+// this is derived from a PR by 0x0ece : https://github.com/Consensys/gnark-crypto/pull/249
 // See Section 5.3: ia.cr/2022/1396
 func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP pG2Affine, TPP ppG2Affine, TQ qOpsG2Affine, TC cG2Affine](
 	chunk uint64,
diff --git a/ecc/bw6-633/multiexp_jacobian.go b/ecc/bw6-633/multiexp_jacobian.go
index ee53a3a060..f3caa67025 100644
--- a/ecc/bw6-633/multiexp_jacobian.go
+++ b/ecc/bw6-633/multiexp_jacobian.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/multiexp_test.go b/ecc/bw6-633/multiexp_test.go
index 0513c193c6..c8e312de6a 100644
--- a/ecc/bw6-633/multiexp_test.go
+++ b/ecc/bw6-633/multiexp_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/pairing.go b/ecc/bw6-633/pairing.go
index 5e8c3d9902..a898b72528 100644
--- a/ecc/bw6-633/pairing.go
+++ b/ecc/bw6-633/pairing.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package bw6633
 
diff --git a/ecc/bw6-633/pairing_test.go b/ecc/bw6-633/pairing_test.go
index 606068693e..a878c0e50f 100644
--- a/ecc/bw6-633/pairing_test.go
+++ b/ecc/bw6-633/pairing_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/shplonk/doc.go b/ecc/bw6-633/shplonk/doc.go
index 17b34373c2..0367893999 100644
--- a/ecc/bw6-633/shplonk/doc.go
+++ b/ecc/bw6-633/shplonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/shplonk/example_test.go b/ecc/bw6-633/shplonk/example_test.go
index fd6e34394e..57471ea4fb 100644
--- a/ecc/bw6-633/shplonk/example_test.go
+++ b/ecc/bw6-633/shplonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/shplonk/marshal.go b/ecc/bw6-633/shplonk/marshal.go
index ab4d61b642..abd3918e85 100644
--- a/ecc/bw6-633/shplonk/marshal.go
+++ b/ecc/bw6-633/shplonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/shplonk/shplonk.go b/ecc/bw6-633/shplonk/shplonk.go
index 925074f864..1b41c3adcd 100644
--- a/ecc/bw6-633/shplonk/shplonk.go
+++ b/ecc/bw6-633/shplonk/shplonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/shplonk/shplonk_test.go b/ecc/bw6-633/shplonk/shplonk_test.go
index aefbb8a6a3..bd6fa2f81b 100644
--- a/ecc/bw6-633/shplonk/shplonk_test.go
+++ b/ecc/bw6-633/shplonk/shplonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/twistededwards/curve.go b/ecc/bw6-633/twistededwards/curve.go
index 671cbc95ac..a5bd1b94f9 100644
--- a/ecc/bw6-633/twistededwards/curve.go
+++ b/ecc/bw6-633/twistededwards/curve.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/twistededwards/doc.go b/ecc/bw6-633/twistededwards/doc.go
index cdf5b586ff..59833f0b37 100644
--- a/ecc/bw6-633/twistededwards/doc.go
+++ b/ecc/bw6-633/twistededwards/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/twistededwards/eddsa/doc.go b/ecc/bw6-633/twistededwards/eddsa/doc.go
index 501d823f75..a92c9947a3 100644
--- a/ecc/bw6-633/twistededwards/eddsa/doc.go
+++ b/ecc/bw6-633/twistededwards/eddsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/twistededwards/eddsa/eddsa.go b/ecc/bw6-633/twistededwards/eddsa/eddsa.go
index 47ba6425b7..fca1faee82 100644
--- a/ecc/bw6-633/twistededwards/eddsa/eddsa.go
+++ b/ecc/bw6-633/twistededwards/eddsa/eddsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/twistededwards/eddsa/eddsa_test.go b/ecc/bw6-633/twistededwards/eddsa/eddsa_test.go
index de9fea0a8e..11dd10da30 100644
--- a/ecc/bw6-633/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bw6-633/twistededwards/eddsa/eddsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/twistededwards/eddsa/marshal.go b/ecc/bw6-633/twistededwards/eddsa/marshal.go
index 8c8dab8a85..c0d4f05feb 100644
--- a/ecc/bw6-633/twistededwards/eddsa/marshal.go
+++ b/ecc/bw6-633/twistededwards/eddsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/twistededwards/point.go b/ecc/bw6-633/twistededwards/point.go
index 0016475b23..f7a76239f3 100644
--- a/ecc/bw6-633/twistededwards/point.go
+++ b/ecc/bw6-633/twistededwards/point.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/twistededwards/point_test.go b/ecc/bw6-633/twistededwards/point_test.go
index fb8ec7efa8..7182cdd32d 100644
--- a/ecc/bw6-633/twistededwards/point_test.go
+++ b/ecc/bw6-633/twistededwards/point_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/ecdsa/doc.go b/ecc/bw6-761/ecdsa/doc.go
index 84fc6c059a..dd72153183 100644
--- a/ecc/bw6-761/ecdsa/doc.go
+++ b/ecc/bw6-761/ecdsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/ecdsa/ecdsa.go b/ecc/bw6-761/ecdsa/ecdsa.go
index ea3338651c..f452ce2164 100644
--- a/ecc/bw6-761/ecdsa/ecdsa.go
+++ b/ecc/bw6-761/ecdsa/ecdsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/ecdsa/ecdsa_test.go b/ecc/bw6-761/ecdsa/ecdsa_test.go
index 4c7dc6f362..d44c6052ae 100644
--- a/ecc/bw6-761/ecdsa/ecdsa_test.go
+++ b/ecc/bw6-761/ecdsa/ecdsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/ecdsa/marshal.go b/ecc/bw6-761/ecdsa/marshal.go
index e3d2d6dd35..aab61d03ab 100644
--- a/ecc/bw6-761/ecdsa/marshal.go
+++ b/ecc/bw6-761/ecdsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/ecdsa/marshal_test.go b/ecc/bw6-761/ecdsa/marshal_test.go
index e189bb247f..d0632664ad 100644
--- a/ecc/bw6-761/ecdsa/marshal_test.go
+++ b/ecc/bw6-761/ecdsa/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fflonk/doc.go b/ecc/bw6-761/fflonk/doc.go
index b717383d87..67a8094e35 100644
--- a/ecc/bw6-761/fflonk/doc.go
+++ b/ecc/bw6-761/fflonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fflonk/example_test.go b/ecc/bw6-761/fflonk/example_test.go
index 5576eeca34..22c353e4be 100644
--- a/ecc/bw6-761/fflonk/example_test.go
+++ b/ecc/bw6-761/fflonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fflonk/fflonk.go b/ecc/bw6-761/fflonk/fflonk.go
index e592fe11a4..e833ce793a 100644
--- a/ecc/bw6-761/fflonk/fflonk.go
+++ b/ecc/bw6-761/fflonk/fflonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fflonk/fflonk_test.go b/ecc/bw6-761/fflonk/fflonk_test.go
index f81e8fa0c9..371b281037 100644
--- a/ecc/bw6-761/fflonk/fflonk_test.go
+++ b/ecc/bw6-761/fflonk/fflonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fflonk/marshal.go b/ecc/bw6-761/fflonk/marshal.go
index 945cbeb7d5..29ab15ab97 100644
--- a/ecc/bw6-761/fflonk/marshal.go
+++ b/ecc/bw6-761/fflonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/arith.go b/ecc/bw6-761/fp/arith.go
index b202a1549a..bb63552f5a 100644
--- a/ecc/bw6-761/fp/arith.go
+++ b/ecc/bw6-761/fp/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/asm_adx.go b/ecc/bw6-761/fp/asm_adx.go
index fe25e82db2..75e92992fe 100644
--- a/ecc/bw6-761/fp/asm_adx.go
+++ b/ecc/bw6-761/fp/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/asm_noadx.go b/ecc/bw6-761/fp/asm_noadx.go
index 95085a8e6f..304dfb7209 100644
--- a/ecc/bw6-761/fp/asm_noadx.go
+++ b/ecc/bw6-761/fp/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/bw6_utils.go b/ecc/bw6-761/fp/bw6_utils.go
index 634b7861a2..f1359d951c 100644
--- a/ecc/bw6-761/fp/bw6_utils.go
+++ b/ecc/bw6-761/fp/bw6_utils.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fp
 
diff --git a/ecc/bw6-761/fp/doc.go b/ecc/bw6-761/fp/doc.go
index 79fbd8d702..c682d8d668 100644
--- a/ecc/bw6-761/fp/doc.go
+++ b/ecc/bw6-761/fp/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/element.go b/ecc/bw6-761/fp/element.go
index 3dbb53b4b7..82a4a111d7 100644
--- a/ecc/bw6-761/fp/element.go
+++ b/ecc/bw6-761/fp/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/element_amd64.go b/ecc/bw6-761/fp/element_amd64.go
index e72f552ad9..9cee062e5b 100644
--- a/ecc/bw6-761/fp/element_amd64.go
+++ b/ecc/bw6-761/fp/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/element_amd64.s b/ecc/bw6-761/fp/element_amd64.s
index b44c78d9ed..c50306bc8d 100644
--- a/ecc/bw6-761/fp/element_amd64.s
+++ b/ecc/bw6-761/fp/element_amd64.s
@@ -1,10 +1,10 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
-// We include the hash to force the Go compiler to recompile: 13892629867042773109
+// We include the hash to force the Go compiler to recompile: 9592094295531092101
 #include "../../../field/asm/element_12w_amd64.s"
 
diff --git a/ecc/bw6-761/fp/element_arm64.go b/ecc/bw6-761/fp/element_arm64.go
index cf4f884270..665fc7bf74 100644
--- a/ecc/bw6-761/fp/element_arm64.go
+++ b/ecc/bw6-761/fp/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/element_arm64.s b/ecc/bw6-761/fp/element_arm64.s
index 051a143619..e6d61fb12e 100644
--- a/ecc/bw6-761/fp/element_arm64.s
+++ b/ecc/bw6-761/fp/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/element_exp.go b/ecc/bw6-761/fp/element_exp.go
index 87e0135c53..f017426d0f 100644
--- a/ecc/bw6-761/fp/element_exp.go
+++ b/ecc/bw6-761/fp/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/element_purego.go b/ecc/bw6-761/fp/element_purego.go
index 0b478029e3..27bbd3ea4f 100644
--- a/ecc/bw6-761/fp/element_purego.go
+++ b/ecc/bw6-761/fp/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/element_test.go b/ecc/bw6-761/fp/element_test.go
index d57c1a4137..57f420e1e9 100644
--- a/ecc/bw6-761/fp/element_test.go
+++ b/ecc/bw6-761/fp/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/hash_to_field/doc.go b/ecc/bw6-761/fp/hash_to_field/doc.go
index 2248500dd4..9f9a0f60b2 100644
--- a/ecc/bw6-761/fp/hash_to_field/doc.go
+++ b/ecc/bw6-761/fp/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/hash_to_field/hash_to_field.go b/ecc/bw6-761/fp/hash_to_field/hash_to_field.go
index 4c3d232a30..ca34259946 100644
--- a/ecc/bw6-761/fp/hash_to_field/hash_to_field.go
+++ b/ecc/bw6-761/fp/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/hash_to_field/hash_to_field_test.go b/ecc/bw6-761/fp/hash_to_field/hash_to_field_test.go
index 9c54650caf..cc1be00fb8 100644
--- a/ecc/bw6-761/fp/hash_to_field/hash_to_field_test.go
+++ b/ecc/bw6-761/fp/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/vector.go b/ecc/bw6-761/fp/vector.go
index 18fd592d85..e312aebc6e 100644
--- a/ecc/bw6-761/fp/vector.go
+++ b/ecc/bw6-761/fp/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/vector_purego.go b/ecc/bw6-761/fp/vector_purego.go
index 347b0df594..0cda361871 100644
--- a/ecc/bw6-761/fp/vector_purego.go
+++ b/ecc/bw6-761/fp/vector_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/vector_test.go b/ecc/bw6-761/fp/vector_test.go
index 65e92b3d04..d1765ba9bc 100644
--- a/ecc/bw6-761/fp/vector_test.go
+++ b/ecc/bw6-761/fp/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/arith.go b/ecc/bw6-761/fr/arith.go
index 9285041f4b..dbba8a9ae4 100644
--- a/ecc/bw6-761/fr/arith.go
+++ b/ecc/bw6-761/fr/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/asm_adx.go b/ecc/bw6-761/fr/asm_adx.go
index 9e7da5e865..9b970335f1 100644
--- a/ecc/bw6-761/fr/asm_adx.go
+++ b/ecc/bw6-761/fr/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/asm_noadx.go b/ecc/bw6-761/fr/asm_noadx.go
index 3456158655..96741014f2 100644
--- a/ecc/bw6-761/fr/asm_noadx.go
+++ b/ecc/bw6-761/fr/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/doc.go b/ecc/bw6-761/fr/doc.go
index 6904be877b..277ef9945a 100644
--- a/ecc/bw6-761/fr/doc.go
+++ b/ecc/bw6-761/fr/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/element.go b/ecc/bw6-761/fr/element.go
index ebd218e002..98de557872 100644
--- a/ecc/bw6-761/fr/element.go
+++ b/ecc/bw6-761/fr/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/element_amd64.go b/ecc/bw6-761/fr/element_amd64.go
index ca49d12590..4c3f2a8567 100644
--- a/ecc/bw6-761/fr/element_amd64.go
+++ b/ecc/bw6-761/fr/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/element_amd64.s b/ecc/bw6-761/fr/element_amd64.s
index b73d1a484e..719aecfbe9 100644
--- a/ecc/bw6-761/fr/element_amd64.s
+++ b/ecc/bw6-761/fr/element_amd64.s
@@ -1,10 +1,10 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
-// We include the hash to force the Go compiler to recompile: 11124594824487954849
+// We include the hash to force the Go compiler to recompile: 18408829383245254329
 #include "../../../field/asm/element_6w_amd64.s"
 
diff --git a/ecc/bw6-761/fr/element_arm64.go b/ecc/bw6-761/fr/element_arm64.go
index e1d3e0bead..cde9727044 100644
--- a/ecc/bw6-761/fr/element_arm64.go
+++ b/ecc/bw6-761/fr/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/element_arm64.s b/ecc/bw6-761/fr/element_arm64.s
index 58d21358b0..b4dfd1612c 100644
--- a/ecc/bw6-761/fr/element_arm64.s
+++ b/ecc/bw6-761/fr/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/element_exp.go b/ecc/bw6-761/fr/element_exp.go
index c9df4d675c..73a46afaf0 100644
--- a/ecc/bw6-761/fr/element_exp.go
+++ b/ecc/bw6-761/fr/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/element_purego.go b/ecc/bw6-761/fr/element_purego.go
index 15fab63d4c..c4ef27e9a3 100644
--- a/ecc/bw6-761/fr/element_purego.go
+++ b/ecc/bw6-761/fr/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/element_test.go b/ecc/bw6-761/fr/element_test.go
index 8974a228ac..a01d11c9e7 100644
--- a/ecc/bw6-761/fr/element_test.go
+++ b/ecc/bw6-761/fr/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/fft/bitreverse.go b/ecc/bw6-761/fr/fft/bitreverse.go
index ec82646978..408320f032 100644
--- a/ecc/bw6-761/fr/fft/bitreverse.go
+++ b/ecc/bw6-761/fr/fft/bitreverse.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/fft/bitreverse_test.go b/ecc/bw6-761/fr/fft/bitreverse_test.go
index d32144152c..0206f2e5d2 100644
--- a/ecc/bw6-761/fr/fft/bitreverse_test.go
+++ b/ecc/bw6-761/fr/fft/bitreverse_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/fft/doc.go b/ecc/bw6-761/fr/fft/doc.go
index 1ef04db2df..4cce0f9779 100644
--- a/ecc/bw6-761/fr/fft/doc.go
+++ b/ecc/bw6-761/fr/fft/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/fft/domain.go b/ecc/bw6-761/fr/fft/domain.go
index e8d349dee2..189b5b1984 100644
--- a/ecc/bw6-761/fr/fft/domain.go
+++ b/ecc/bw6-761/fr/fft/domain.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/fft/domain_test.go b/ecc/bw6-761/fr/fft/domain_test.go
index d95288076c..e445d3cc12 100644
--- a/ecc/bw6-761/fr/fft/domain_test.go
+++ b/ecc/bw6-761/fr/fft/domain_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/fft/fft.go b/ecc/bw6-761/fr/fft/fft.go
index a7d6a44736..85b35a0639 100644
--- a/ecc/bw6-761/fr/fft/fft.go
+++ b/ecc/bw6-761/fr/fft/fft.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/fft/fft_test.go b/ecc/bw6-761/fr/fft/fft_test.go
index 4ba89f360b..81d4945ef2 100644
--- a/ecc/bw6-761/fr/fft/fft_test.go
+++ b/ecc/bw6-761/fr/fft/fft_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/fft/options.go b/ecc/bw6-761/fr/fft/options.go
index ec6214e752..a0fdb41944 100644
--- a/ecc/bw6-761/fr/fft/options.go
+++ b/ecc/bw6-761/fr/fft/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/fri/doc.go b/ecc/bw6-761/fr/fri/doc.go
index 428dabf625..cea69fc79a 100644
--- a/ecc/bw6-761/fr/fri/doc.go
+++ b/ecc/bw6-761/fr/fri/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/fri/fri.go b/ecc/bw6-761/fr/fri/fri.go
index d04ac242c9..9dce380ab0 100644
--- a/ecc/bw6-761/fr/fri/fri.go
+++ b/ecc/bw6-761/fr/fri/fri.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/fri/fri_test.go b/ecc/bw6-761/fr/fri/fri_test.go
index 2eb5fb3c29..95efe748ff 100644
--- a/ecc/bw6-761/fr/fri/fri_test.go
+++ b/ecc/bw6-761/fr/fri/fri_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/generator.go b/ecc/bw6-761/fr/generator.go
index 6399ad9926..ffa85ae746 100644
--- a/ecc/bw6-761/fr/generator.go
+++ b/ecc/bw6-761/fr/generator.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/gkr/gkr.go b/ecc/bw6-761/fr/gkr/gkr.go
index bd46e4abe1..eddfb771d5 100644
--- a/ecc/bw6-761/fr/gkr/gkr.go
+++ b/ecc/bw6-761/fr/gkr/gkr.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/gkr/gkr_test.go b/ecc/bw6-761/fr/gkr/gkr_test.go
index d3d18dfcba..1922eff6d8 100644
--- a/ecc/bw6-761/fr/gkr/gkr_test.go
+++ b/ecc/bw6-761/fr/gkr/gkr_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
@@ -325,7 +325,7 @@ func mimcCircuit(numRounds int) Circuit {
 
 func testMimc(t *testing.T, numRounds int, inputAssignments ...[]fr.Element) {
 	//TODO: Implement mimc correctly. Currently, the computation is mimc(a,b) = cipher( cipher( ... cipher(a, b), b) ..., b)
-	// @AlexandreBelling: Please explain the extra layers in https://github.com/ConsenSys/gkr-mimc/blob/81eada039ab4ed403b7726b535adb63026e8011f/examples/mimc.go#L10
+	// @AlexandreBelling: Please explain the extra layers in https://github.com/Consensys/gkr-mimc/blob/81eada039ab4ed403b7726b535adb63026e8011f/examples/mimc.go#L10
 
 	c := mimcCircuit(numRounds)
 
diff --git a/ecc/bw6-761/fr/hash_to_field/doc.go b/ecc/bw6-761/fr/hash_to_field/doc.go
index d03ec39735..504fadf149 100644
--- a/ecc/bw6-761/fr/hash_to_field/doc.go
+++ b/ecc/bw6-761/fr/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/hash_to_field/hash_to_field.go b/ecc/bw6-761/fr/hash_to_field/hash_to_field.go
index 0eda792a28..d941e2468b 100644
--- a/ecc/bw6-761/fr/hash_to_field/hash_to_field.go
+++ b/ecc/bw6-761/fr/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/hash_to_field/hash_to_field_test.go b/ecc/bw6-761/fr/hash_to_field/hash_to_field_test.go
index 731929288b..aa92379465 100644
--- a/ecc/bw6-761/fr/hash_to_field/hash_to_field_test.go
+++ b/ecc/bw6-761/fr/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/iop/doc.go b/ecc/bw6-761/fr/iop/doc.go
index ee3facf1e1..2ef06dfe1a 100644
--- a/ecc/bw6-761/fr/iop/doc.go
+++ b/ecc/bw6-761/fr/iop/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/iop/expressions.go b/ecc/bw6-761/fr/iop/expressions.go
index 72fbfd169f..ac0bd11bc8 100644
--- a/ecc/bw6-761/fr/iop/expressions.go
+++ b/ecc/bw6-761/fr/iop/expressions.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/iop/expressions_test.go b/ecc/bw6-761/fr/iop/expressions_test.go
index 51e837ead1..4874d59d49 100644
--- a/ecc/bw6-761/fr/iop/expressions_test.go
+++ b/ecc/bw6-761/fr/iop/expressions_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/iop/polynomial.go b/ecc/bw6-761/fr/iop/polynomial.go
index 0b72fe3c16..210e7a6b10 100644
--- a/ecc/bw6-761/fr/iop/polynomial.go
+++ b/ecc/bw6-761/fr/iop/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/iop/polynomial_test.go b/ecc/bw6-761/fr/iop/polynomial_test.go
index 5b6e5d5fd3..cee823decb 100644
--- a/ecc/bw6-761/fr/iop/polynomial_test.go
+++ b/ecc/bw6-761/fr/iop/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/iop/quotient.go b/ecc/bw6-761/fr/iop/quotient.go
index 1f90c46385..2c3f93e5e1 100644
--- a/ecc/bw6-761/fr/iop/quotient.go
+++ b/ecc/bw6-761/fr/iop/quotient.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/iop/quotient_test.go b/ecc/bw6-761/fr/iop/quotient_test.go
index e16d6dbf17..e3fc8147ec 100644
--- a/ecc/bw6-761/fr/iop/quotient_test.go
+++ b/ecc/bw6-761/fr/iop/quotient_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/iop/ratios.go b/ecc/bw6-761/fr/iop/ratios.go
index 4e38401ac0..c130c0ab53 100644
--- a/ecc/bw6-761/fr/iop/ratios.go
+++ b/ecc/bw6-761/fr/iop/ratios.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/iop/ratios_test.go b/ecc/bw6-761/fr/iop/ratios_test.go
index 78bf6823e1..259b0e65fe 100644
--- a/ecc/bw6-761/fr/iop/ratios_test.go
+++ b/ecc/bw6-761/fr/iop/ratios_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/iop/utils.go b/ecc/bw6-761/fr/iop/utils.go
index e061ac5f0f..eaf19d9f8e 100644
--- a/ecc/bw6-761/fr/iop/utils.go
+++ b/ecc/bw6-761/fr/iop/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/mimc/doc.go b/ecc/bw6-761/fr/mimc/doc.go
index cc7b101eb4..98aa3f8d81 100644
--- a/ecc/bw6-761/fr/mimc/doc.go
+++ b/ecc/bw6-761/fr/mimc/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/mimc/mimc.go b/ecc/bw6-761/fr/mimc/mimc.go
index 16c96957fd..2a0a323955 100644
--- a/ecc/bw6-761/fr/mimc/mimc.go
+++ b/ecc/bw6-761/fr/mimc/mimc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/mimc/options.go b/ecc/bw6-761/fr/mimc/options.go
index 347e79e576..67bf8506da 100644
--- a/ecc/bw6-761/fr/mimc/options.go
+++ b/ecc/bw6-761/fr/mimc/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/pedersen/doc.go b/ecc/bw6-761/fr/pedersen/doc.go
index 62a62f179f..2e24034936 100644
--- a/ecc/bw6-761/fr/pedersen/doc.go
+++ b/ecc/bw6-761/fr/pedersen/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/pedersen/example_test.go b/ecc/bw6-761/fr/pedersen/example_test.go
index 39ebdddb9f..6cfdf9cc00 100644
--- a/ecc/bw6-761/fr/pedersen/example_test.go
+++ b/ecc/bw6-761/fr/pedersen/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/pedersen/pedersen.go b/ecc/bw6-761/fr/pedersen/pedersen.go
index cef2884f62..78204513eb 100644
--- a/ecc/bw6-761/fr/pedersen/pedersen.go
+++ b/ecc/bw6-761/fr/pedersen/pedersen.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
@@ -105,7 +105,7 @@ func (pk *ProvingKey) ProveKnowledge(values []fr.Element) (pok curve.G1Affine, e
 	}
 
 	// TODO @gbotrel this will spawn more than one task, see
-	// https://github.com/ConsenSys/gnark-crypto/issues/269
+	// https://github.com/Consensys/gnark-crypto/issues/269
 	config := ecc.MultiExpConfig{
 		NbTasks: 1, // TODO Experiment
 	}
@@ -123,7 +123,7 @@ func (pk *ProvingKey) Commit(values []fr.Element) (commitment curve.G1Affine, er
 	}
 
 	// TODO @gbotrel this will spawn more than one task, see
-	// https://github.com/ConsenSys/gnark-crypto/issues/269
+	// https://github.com/Consensys/gnark-crypto/issues/269
 	config := ecc.MultiExpConfig{
 		NbTasks: 1,
 	}
@@ -184,7 +184,7 @@ func BatchProve(pk []ProvingKey, values [][]fr.Element, combinationCoeff fr.Elem
 	}
 
 	// TODO @gbotrel this will spawn more than one task, see
-	// https://github.com/ConsenSys/gnark-crypto/issues/269
+	// https://github.com/Consensys/gnark-crypto/issues/269
 	config := ecc.MultiExpConfig{
 		NbTasks: 1,
 	}
diff --git a/ecc/bw6-761/fr/pedersen/pedersen_test.go b/ecc/bw6-761/fr/pedersen/pedersen_test.go
index e36f0c4acc..95dcadf528 100644
--- a/ecc/bw6-761/fr/pedersen/pedersen_test.go
+++ b/ecc/bw6-761/fr/pedersen/pedersen_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/permutation/doc.go b/ecc/bw6-761/fr/permutation/doc.go
index 5f346b5a53..e24cd82923 100644
--- a/ecc/bw6-761/fr/permutation/doc.go
+++ b/ecc/bw6-761/fr/permutation/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/permutation/permutation.go b/ecc/bw6-761/fr/permutation/permutation.go
index 4846ce844d..9360d623f3 100644
--- a/ecc/bw6-761/fr/permutation/permutation.go
+++ b/ecc/bw6-761/fr/permutation/permutation.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/permutation/permutation_test.go b/ecc/bw6-761/fr/permutation/permutation_test.go
index 8dac14d91d..b06266ee8b 100644
--- a/ecc/bw6-761/fr/permutation/permutation_test.go
+++ b/ecc/bw6-761/fr/permutation/permutation_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/plookup/doc.go b/ecc/bw6-761/fr/plookup/doc.go
index d163104002..7a02c59719 100644
--- a/ecc/bw6-761/fr/plookup/doc.go
+++ b/ecc/bw6-761/fr/plookup/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/plookup/plookup_test.go b/ecc/bw6-761/fr/plookup/plookup_test.go
index 72da216a03..ba1c843af1 100644
--- a/ecc/bw6-761/fr/plookup/plookup_test.go
+++ b/ecc/bw6-761/fr/plookup/plookup_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/plookup/table.go b/ecc/bw6-761/fr/plookup/table.go
index ed0fd8ba76..1215d39f9d 100644
--- a/ecc/bw6-761/fr/plookup/table.go
+++ b/ecc/bw6-761/fr/plookup/table.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/plookup/vector.go b/ecc/bw6-761/fr/plookup/vector.go
index e136a5f3f8..f403607365 100644
--- a/ecc/bw6-761/fr/plookup/vector.go
+++ b/ecc/bw6-761/fr/plookup/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/polynomial/doc.go b/ecc/bw6-761/fr/polynomial/doc.go
index 35b3f725c1..fd96328e8f 100644
--- a/ecc/bw6-761/fr/polynomial/doc.go
+++ b/ecc/bw6-761/fr/polynomial/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/polynomial/multilin.go b/ecc/bw6-761/fr/polynomial/multilin.go
index 85015f1a34..bb658ae1a3 100644
--- a/ecc/bw6-761/fr/polynomial/multilin.go
+++ b/ecc/bw6-761/fr/polynomial/multilin.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/polynomial/multilin_test.go b/ecc/bw6-761/fr/polynomial/multilin_test.go
index 37d9d1d079..128f6197be 100644
--- a/ecc/bw6-761/fr/polynomial/multilin_test.go
+++ b/ecc/bw6-761/fr/polynomial/multilin_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/polynomial/polynomial.go b/ecc/bw6-761/fr/polynomial/polynomial.go
index 9e17273b00..a889bcb3b3 100644
--- a/ecc/bw6-761/fr/polynomial/polynomial.go
+++ b/ecc/bw6-761/fr/polynomial/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/polynomial/polynomial_test.go b/ecc/bw6-761/fr/polynomial/polynomial_test.go
index c51c6e41a4..db01a6842c 100644
--- a/ecc/bw6-761/fr/polynomial/polynomial_test.go
+++ b/ecc/bw6-761/fr/polynomial/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/polynomial/pool.go b/ecc/bw6-761/fr/polynomial/pool.go
index 41c1fa6041..b4c31a88b9 100644
--- a/ecc/bw6-761/fr/polynomial/pool.go
+++ b/ecc/bw6-761/fr/polynomial/pool.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/poseidon2/poseidon2.go b/ecc/bw6-761/fr/poseidon2/poseidon2.go
index ff49613b1a..2034e38169 100644
--- a/ecc/bw6-761/fr/poseidon2/poseidon2.go
+++ b/ecc/bw6-761/fr/poseidon2/poseidon2.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/poseidon2/poseidon2_test.go b/ecc/bw6-761/fr/poseidon2/poseidon2_test.go
index 11f1d7ed64..cd88f8b7b5 100644
--- a/ecc/bw6-761/fr/poseidon2/poseidon2_test.go
+++ b/ecc/bw6-761/fr/poseidon2/poseidon2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/sumcheck/sumcheck.go b/ecc/bw6-761/fr/sumcheck/sumcheck.go
index 64f3115343..ad97e14250 100644
--- a/ecc/bw6-761/fr/sumcheck/sumcheck.go
+++ b/ecc/bw6-761/fr/sumcheck/sumcheck.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/sumcheck/sumcheck_test.go b/ecc/bw6-761/fr/sumcheck/sumcheck_test.go
index eee8ae452c..40cfd15538 100644
--- a/ecc/bw6-761/fr/sumcheck/sumcheck_test.go
+++ b/ecc/bw6-761/fr/sumcheck/sumcheck_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/test_vector_utils/test_vector_utils.go b/ecc/bw6-761/fr/test_vector_utils/test_vector_utils.go
index 2005b5e824..27ac283790 100644
--- a/ecc/bw6-761/fr/test_vector_utils/test_vector_utils.go
+++ b/ecc/bw6-761/fr/test_vector_utils/test_vector_utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/vector.go b/ecc/bw6-761/fr/vector.go
index 5f5187cc51..3a2f40c1d1 100644
--- a/ecc/bw6-761/fr/vector.go
+++ b/ecc/bw6-761/fr/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/vector_purego.go b/ecc/bw6-761/fr/vector_purego.go
index 3c81210b58..c26ef9f1bb 100644
--- a/ecc/bw6-761/fr/vector_purego.go
+++ b/ecc/bw6-761/fr/vector_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/vector_test.go b/ecc/bw6-761/fr/vector_test.go
index a5369902cd..7d0a4162b1 100644
--- a/ecc/bw6-761/fr/vector_test.go
+++ b/ecc/bw6-761/fr/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/g1.go b/ecc/bw6-761/g1.go
index 8a4da31f52..8ac167f52e 100644
--- a/ecc/bw6-761/g1.go
+++ b/ecc/bw6-761/g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/g1_test.go b/ecc/bw6-761/g1_test.go
index bd42889c0f..6446bb30b9 100644
--- a/ecc/bw6-761/g1_test.go
+++ b/ecc/bw6-761/g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/g2.go b/ecc/bw6-761/g2.go
index 1edf22552c..608503f6c6 100644
--- a/ecc/bw6-761/g2.go
+++ b/ecc/bw6-761/g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/g2_test.go b/ecc/bw6-761/g2_test.go
index f3aec712c1..108d220cf7 100644
--- a/ecc/bw6-761/g2_test.go
+++ b/ecc/bw6-761/g2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/hash_to_g1.go b/ecc/bw6-761/hash_to_g1.go
index 54115d76f8..52491a7ebb 100644
--- a/ecc/bw6-761/hash_to_g1.go
+++ b/ecc/bw6-761/hash_to_g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/hash_to_g1_test.go b/ecc/bw6-761/hash_to_g1_test.go
index 59464b31d5..20a5d4dee5 100644
--- a/ecc/bw6-761/hash_to_g1_test.go
+++ b/ecc/bw6-761/hash_to_g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/hash_to_g2.go b/ecc/bw6-761/hash_to_g2.go
index 21acc97de8..6450a5be75 100644
--- a/ecc/bw6-761/hash_to_g2.go
+++ b/ecc/bw6-761/hash_to_g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/hash_to_g2_test.go b/ecc/bw6-761/hash_to_g2_test.go
index e891f374ae..daa6c09bb6 100644
--- a/ecc/bw6-761/hash_to_g2_test.go
+++ b/ecc/bw6-761/hash_to_g2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/internal/fptower/e3.go b/ecc/bw6-761/internal/fptower/e3.go
index e933a2825a..cd35eac1a3 100644
--- a/ecc/bw6-761/internal/fptower/e3.go
+++ b/ecc/bw6-761/internal/fptower/e3.go
@@ -1,14 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bw6-761/internal/fptower/e6.go b/ecc/bw6-761/internal/fptower/e6.go
index 508fc30690..84e5ce8160 100644
--- a/ecc/bw6-761/internal/fptower/e6.go
+++ b/ecc/bw6-761/internal/fptower/e6.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bw6-761/internal/fptower/e6_test.go b/ecc/bw6-761/internal/fptower/e6_test.go
index 1cf291d887..3a5f035bd6 100644
--- a/ecc/bw6-761/internal/fptower/e6_test.go
+++ b/ecc/bw6-761/internal/fptower/e6_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bw6-761/internal/fptower/frobenius.go b/ecc/bw6-761/internal/fptower/frobenius.go
index e18adf7e54..6c158728b9 100644
--- a/ecc/bw6-761/internal/fptower/frobenius.go
+++ b/ecc/bw6-761/internal/fptower/frobenius.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bw6-761/internal/fptower/parameters.go b/ecc/bw6-761/internal/fptower/parameters.go
index 8990cd62ea..fdef10fb91 100644
--- a/ecc/bw6-761/internal/fptower/parameters.go
+++ b/ecc/bw6-761/internal/fptower/parameters.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys AG
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
 
diff --git a/ecc/bw6-761/kzg/doc.go b/ecc/bw6-761/kzg/doc.go
index 6c3454a2d9..226614bbdf 100644
--- a/ecc/bw6-761/kzg/doc.go
+++ b/ecc/bw6-761/kzg/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/kzg/kzg.go b/ecc/bw6-761/kzg/kzg.go
index 5c61a6b1b7..f19397ef7a 100644
--- a/ecc/bw6-761/kzg/kzg.go
+++ b/ecc/bw6-761/kzg/kzg.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/kzg/kzg_test.go b/ecc/bw6-761/kzg/kzg_test.go
index 1fca86f6e6..d67540bd20 100644
--- a/ecc/bw6-761/kzg/kzg_test.go
+++ b/ecc/bw6-761/kzg/kzg_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/kzg/marshal.go b/ecc/bw6-761/kzg/marshal.go
index 86a5b42ae2..7aa04b5c73 100644
--- a/ecc/bw6-761/kzg/marshal.go
+++ b/ecc/bw6-761/kzg/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/kzg/utils.go b/ecc/bw6-761/kzg/utils.go
index 2e12e76bd0..42f8b42efb 100644
--- a/ecc/bw6-761/kzg/utils.go
+++ b/ecc/bw6-761/kzg/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/marshal.go b/ecc/bw6-761/marshal.go
index 5c57294e3b..ee4d185e2b 100644
--- a/ecc/bw6-761/marshal.go
+++ b/ecc/bw6-761/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/marshal_test.go b/ecc/bw6-761/marshal_test.go
index db3f7ad4e1..dde2f26b31 100644
--- a/ecc/bw6-761/marshal_test.go
+++ b/ecc/bw6-761/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/multiexp.go b/ecc/bw6-761/multiexp.go
index 1e87efcd61..507e7fa553 100644
--- a/ecc/bw6-761/multiexp.go
+++ b/ecc/bw6-761/multiexp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/multiexp_affine.go b/ecc/bw6-761/multiexp_affine.go
index 4a33d4fb0d..45826af9a8 100644
--- a/ecc/bw6-761/multiexp_affine.go
+++ b/ecc/bw6-761/multiexp_affine.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
@@ -18,7 +18,7 @@ type batchOpG1Affine struct {
 // using affine coordinates for the buckets. To amortize the cost of the inverse in the affine addition
 // we use a batch affine addition.
 //
-// this is derived from a PR by 0x0ece : https://github.com/ConsenSys/gnark-crypto/pull/249
+// this is derived from a PR by 0x0ece : https://github.com/Consensys/gnark-crypto/pull/249
 // See Section 5.3: ia.cr/2022/1396
 func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP pG1Affine, TPP ppG1Affine, TQ qOpsG1Affine, TC cG1Affine](
 	chunk uint64,
@@ -285,7 +285,7 @@ type batchOpG2Affine struct {
 // using affine coordinates for the buckets. To amortize the cost of the inverse in the affine addition
 // we use a batch affine addition.
 //
-// this is derived from a PR by 0x0ece : https://github.com/ConsenSys/gnark-crypto/pull/249
+// this is derived from a PR by 0x0ece : https://github.com/Consensys/gnark-crypto/pull/249
 // See Section 5.3: ia.cr/2022/1396
 func processChunkG2BatchAffine[BJE ibg2JacExtended, B ibG2Affine, BS bitSet, TP pG2Affine, TPP ppG2Affine, TQ qOpsG2Affine, TC cG2Affine](
 	chunk uint64,
diff --git a/ecc/bw6-761/multiexp_jacobian.go b/ecc/bw6-761/multiexp_jacobian.go
index abe9c17245..482a290b98 100644
--- a/ecc/bw6-761/multiexp_jacobian.go
+++ b/ecc/bw6-761/multiexp_jacobian.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/multiexp_test.go b/ecc/bw6-761/multiexp_test.go
index f212cd5a01..1afb6c9f68 100644
--- a/ecc/bw6-761/multiexp_test.go
+++ b/ecc/bw6-761/multiexp_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/pairing_test.go b/ecc/bw6-761/pairing_test.go
index c2946357d8..c1e639aa8d 100644
--- a/ecc/bw6-761/pairing_test.go
+++ b/ecc/bw6-761/pairing_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/shplonk/doc.go b/ecc/bw6-761/shplonk/doc.go
index 17b34373c2..0367893999 100644
--- a/ecc/bw6-761/shplonk/doc.go
+++ b/ecc/bw6-761/shplonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/shplonk/example_test.go b/ecc/bw6-761/shplonk/example_test.go
index 1206bccc1e..1f4faf86ab 100644
--- a/ecc/bw6-761/shplonk/example_test.go
+++ b/ecc/bw6-761/shplonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/shplonk/marshal.go b/ecc/bw6-761/shplonk/marshal.go
index be1e4acde3..1a12fe4d48 100644
--- a/ecc/bw6-761/shplonk/marshal.go
+++ b/ecc/bw6-761/shplonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/shplonk/shplonk.go b/ecc/bw6-761/shplonk/shplonk.go
index 19eb2433e5..7ad9e04699 100644
--- a/ecc/bw6-761/shplonk/shplonk.go
+++ b/ecc/bw6-761/shplonk/shplonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/shplonk/shplonk_test.go b/ecc/bw6-761/shplonk/shplonk_test.go
index ebc7a57517..4c0fe50bbf 100644
--- a/ecc/bw6-761/shplonk/shplonk_test.go
+++ b/ecc/bw6-761/shplonk/shplonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/twistededwards/curve.go b/ecc/bw6-761/twistededwards/curve.go
index bf0345c523..96b2881ed2 100644
--- a/ecc/bw6-761/twistededwards/curve.go
+++ b/ecc/bw6-761/twistededwards/curve.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/twistededwards/doc.go b/ecc/bw6-761/twistededwards/doc.go
index 3172ca7194..1b90b6805f 100644
--- a/ecc/bw6-761/twistededwards/doc.go
+++ b/ecc/bw6-761/twistededwards/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/twistededwards/eddsa/doc.go b/ecc/bw6-761/twistededwards/eddsa/doc.go
index 0aaf99ef4c..ae819082e3 100644
--- a/ecc/bw6-761/twistededwards/eddsa/doc.go
+++ b/ecc/bw6-761/twistededwards/eddsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/twistededwards/eddsa/eddsa.go b/ecc/bw6-761/twistededwards/eddsa/eddsa.go
index 1d464b279a..89ce193349 100644
--- a/ecc/bw6-761/twistededwards/eddsa/eddsa.go
+++ b/ecc/bw6-761/twistededwards/eddsa/eddsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/twistededwards/eddsa/eddsa_test.go b/ecc/bw6-761/twistededwards/eddsa/eddsa_test.go
index d85f4c6c51..d9b595e894 100644
--- a/ecc/bw6-761/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bw6-761/twistededwards/eddsa/eddsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/twistededwards/eddsa/marshal.go b/ecc/bw6-761/twistededwards/eddsa/marshal.go
index 9532895007..403e372609 100644
--- a/ecc/bw6-761/twistededwards/eddsa/marshal.go
+++ b/ecc/bw6-761/twistededwards/eddsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/twistededwards/point.go b/ecc/bw6-761/twistededwards/point.go
index 95af453d49..09af947b1f 100644
--- a/ecc/bw6-761/twistededwards/point.go
+++ b/ecc/bw6-761/twistededwards/point.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/twistededwards/point_test.go b/ecc/bw6-761/twistededwards/point_test.go
index b1e526022f..86a3737c0d 100644
--- a/ecc/bw6-761/twistededwards/point_test.go
+++ b/ecc/bw6-761/twistededwards/point_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/ecc.go b/ecc/ecc.go
index 9f927d5678..5c9b6b2b32 100644
--- a/ecc/ecc.go
+++ b/ecc/ecc.go
@@ -1,18 +1,5 @@
-/*
-Copyright © 2020 ConsenSys
-
-Licensed under the Apache License, Version 2.0 (the "License");
-you may not use this file except in compliance with the License.
-You may obtain a copy of the License at
-
-    http://www.apache.org/licenses/LICENSE-2.0
-
-Unless required by applicable law or agreed to in writing, software
-distributed under the License is distributed on an "AS IS" BASIS,
-WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-See the License for the specific language governing permissions and
-limitations under the License.
-*/
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Package ecc provides bls12-381, bls12-377, bn254, bw6-761, bls24-315, bls24-317, bw6-633, secp256k1 and stark-curve elliptic curves implementation (+pairing).
 //
diff --git a/ecc/secp256k1/ecdsa/doc.go b/ecc/secp256k1/ecdsa/doc.go
index a0ad0656cc..4bc6e71746 100644
--- a/ecc/secp256k1/ecdsa/doc.go
+++ b/ecc/secp256k1/ecdsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/ecdsa/ecdsa.go b/ecc/secp256k1/ecdsa/ecdsa.go
index dfba9976c2..b3ec2524a4 100644
--- a/ecc/secp256k1/ecdsa/ecdsa.go
+++ b/ecc/secp256k1/ecdsa/ecdsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/ecdsa/ecdsa_test.go b/ecc/secp256k1/ecdsa/ecdsa_test.go
index c3550765bd..7170cafd24 100644
--- a/ecc/secp256k1/ecdsa/ecdsa_test.go
+++ b/ecc/secp256k1/ecdsa/ecdsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/ecdsa/marshal.go b/ecc/secp256k1/ecdsa/marshal.go
index 7c297b6529..b82b22ddc1 100644
--- a/ecc/secp256k1/ecdsa/marshal.go
+++ b/ecc/secp256k1/ecdsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/ecdsa/marshal_test.go b/ecc/secp256k1/ecdsa/marshal_test.go
index 434a18c025..872b7f9a18 100644
--- a/ecc/secp256k1/ecdsa/marshal_test.go
+++ b/ecc/secp256k1/ecdsa/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fp/arith.go b/ecc/secp256k1/fp/arith.go
index b202a1549a..bb63552f5a 100644
--- a/ecc/secp256k1/fp/arith.go
+++ b/ecc/secp256k1/fp/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fp/doc.go b/ecc/secp256k1/fp/doc.go
index d5b439ad72..8e971a67c7 100644
--- a/ecc/secp256k1/fp/doc.go
+++ b/ecc/secp256k1/fp/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fp/element.go b/ecc/secp256k1/fp/element.go
index c98ef9e599..e7bb41de63 100644
--- a/ecc/secp256k1/fp/element.go
+++ b/ecc/secp256k1/fp/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fp/element_exp.go b/ecc/secp256k1/fp/element_exp.go
index 827dafc296..9acdd2b69e 100644
--- a/ecc/secp256k1/fp/element_exp.go
+++ b/ecc/secp256k1/fp/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fp/element_purego.go b/ecc/secp256k1/fp/element_purego.go
index fc9fec8677..7a22c54175 100644
--- a/ecc/secp256k1/fp/element_purego.go
+++ b/ecc/secp256k1/fp/element_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fp/element_test.go b/ecc/secp256k1/fp/element_test.go
index a29f105ef8..5ef370d1f1 100644
--- a/ecc/secp256k1/fp/element_test.go
+++ b/ecc/secp256k1/fp/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fp/vector.go b/ecc/secp256k1/fp/vector.go
index ec52314aa7..ef60ed4b45 100644
--- a/ecc/secp256k1/fp/vector.go
+++ b/ecc/secp256k1/fp/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fp/vector_purego.go b/ecc/secp256k1/fp/vector_purego.go
index 347b0df594..0cda361871 100644
--- a/ecc/secp256k1/fp/vector_purego.go
+++ b/ecc/secp256k1/fp/vector_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fp/vector_test.go b/ecc/secp256k1/fp/vector_test.go
index 06fe1084a8..e7185486cf 100644
--- a/ecc/secp256k1/fp/vector_test.go
+++ b/ecc/secp256k1/fp/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fr/arith.go b/ecc/secp256k1/fr/arith.go
index 9285041f4b..dbba8a9ae4 100644
--- a/ecc/secp256k1/fr/arith.go
+++ b/ecc/secp256k1/fr/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fr/doc.go b/ecc/secp256k1/fr/doc.go
index f440ce29b1..a03aa7a3d7 100644
--- a/ecc/secp256k1/fr/doc.go
+++ b/ecc/secp256k1/fr/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fr/element.go b/ecc/secp256k1/fr/element.go
index 8d0a11fd43..7041cca6cd 100644
--- a/ecc/secp256k1/fr/element.go
+++ b/ecc/secp256k1/fr/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fr/element_exp.go b/ecc/secp256k1/fr/element_exp.go
index f65be913cc..d508eb812d 100644
--- a/ecc/secp256k1/fr/element_exp.go
+++ b/ecc/secp256k1/fr/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fr/element_purego.go b/ecc/secp256k1/fr/element_purego.go
index 1e6c57d0f8..bdd8a849bb 100644
--- a/ecc/secp256k1/fr/element_purego.go
+++ b/ecc/secp256k1/fr/element_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fr/element_test.go b/ecc/secp256k1/fr/element_test.go
index 663205a9a8..dc51dce70d 100644
--- a/ecc/secp256k1/fr/element_test.go
+++ b/ecc/secp256k1/fr/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fr/vector.go b/ecc/secp256k1/fr/vector.go
index 8b59bd36e9..4654b1b2d3 100644
--- a/ecc/secp256k1/fr/vector.go
+++ b/ecc/secp256k1/fr/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fr/vector_purego.go b/ecc/secp256k1/fr/vector_purego.go
index 3c81210b58..c26ef9f1bb 100644
--- a/ecc/secp256k1/fr/vector_purego.go
+++ b/ecc/secp256k1/fr/vector_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fr/vector_test.go b/ecc/secp256k1/fr/vector_test.go
index a094bc0ac6..f6179e7824 100644
--- a/ecc/secp256k1/fr/vector_test.go
+++ b/ecc/secp256k1/fr/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/g1.go b/ecc/secp256k1/g1.go
index 123a7f69ea..e6aa66e1df 100644
--- a/ecc/secp256k1/g1.go
+++ b/ecc/secp256k1/g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/g1_test.go b/ecc/secp256k1/g1_test.go
index b57acc5635..d2050c04c6 100644
--- a/ecc/secp256k1/g1_test.go
+++ b/ecc/secp256k1/g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/hash_to_g1.go b/ecc/secp256k1/hash_to_g1.go
index 35a42ee2ff..4d0fc63aba 100644
--- a/ecc/secp256k1/hash_to_g1.go
+++ b/ecc/secp256k1/hash_to_g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/hash_to_g1_test.go b/ecc/secp256k1/hash_to_g1_test.go
index 37579c66fd..6e41450a0b 100644
--- a/ecc/secp256k1/hash_to_g1_test.go
+++ b/ecc/secp256k1/hash_to_g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/marshal.go b/ecc/secp256k1/marshal.go
index 8cca33d47d..061e8a5e37 100644
--- a/ecc/secp256k1/marshal.go
+++ b/ecc/secp256k1/marshal.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // FOO
 
diff --git a/ecc/secp256k1/marshal_test.go b/ecc/secp256k1/marshal_test.go
index 1cd3058deb..c51a86d091 100644
--- a/ecc/secp256k1/marshal_test.go
+++ b/ecc/secp256k1/marshal_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // FOO
 
diff --git a/ecc/secp256k1/multiexp.go b/ecc/secp256k1/multiexp.go
index 2ad970a1ed..10338357df 100644
--- a/ecc/secp256k1/multiexp.go
+++ b/ecc/secp256k1/multiexp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/multiexp_affine.go b/ecc/secp256k1/multiexp_affine.go
index c0e5d12e18..be8577bfa5 100644
--- a/ecc/secp256k1/multiexp_affine.go
+++ b/ecc/secp256k1/multiexp_affine.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
@@ -18,7 +18,7 @@ type batchOpG1Affine struct {
 // using affine coordinates for the buckets. To amortize the cost of the inverse in the affine addition
 // we use a batch affine addition.
 //
-// this is derived from a PR by 0x0ece : https://github.com/ConsenSys/gnark-crypto/pull/249
+// this is derived from a PR by 0x0ece : https://github.com/Consensys/gnark-crypto/pull/249
 // See Section 5.3: ia.cr/2022/1396
 func processChunkG1BatchAffine[BJE ibg1JacExtended, B ibG1Affine, BS bitSet, TP pG1Affine, TPP ppG1Affine, TQ qOpsG1Affine, TC cG1Affine](
 	chunk uint64,
diff --git a/ecc/secp256k1/multiexp_jacobian.go b/ecc/secp256k1/multiexp_jacobian.go
index 541fa208cd..a328744139 100644
--- a/ecc/secp256k1/multiexp_jacobian.go
+++ b/ecc/secp256k1/multiexp_jacobian.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/multiexp_test.go b/ecc/secp256k1/multiexp_test.go
index f30b924dd2..2d7881abe0 100644
--- a/ecc/secp256k1/multiexp_test.go
+++ b/ecc/secp256k1/multiexp_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/secp256k1.go b/ecc/secp256k1/secp256k1.go
index c315408371..7142e75571 100644
--- a/ecc/secp256k1/secp256k1.go
+++ b/ecc/secp256k1/secp256k1.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Package secp256k1 efficient elliptic curve implementation for secp256k1. This curve is defined in Standards for Efficient Cryptography (SEC) (Certicom Research, http://www.secg.org/sec2-v2.pdf) and appears in the Bitcoin and Ethereum ECDSA signatures.
 //
diff --git a/ecc/stark-curve/ecdsa/doc.go b/ecc/stark-curve/ecdsa/doc.go
index 599535ea05..6674a4ab62 100644
--- a/ecc/stark-curve/ecdsa/doc.go
+++ b/ecc/stark-curve/ecdsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/ecdsa/ecdsa.go b/ecc/stark-curve/ecdsa/ecdsa.go
index e43c51879a..589562b345 100644
--- a/ecc/stark-curve/ecdsa/ecdsa.go
+++ b/ecc/stark-curve/ecdsa/ecdsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/ecdsa/ecdsa_test.go b/ecc/stark-curve/ecdsa/ecdsa_test.go
index 30324ed6c3..61021d83c3 100644
--- a/ecc/stark-curve/ecdsa/ecdsa_test.go
+++ b/ecc/stark-curve/ecdsa/ecdsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/ecdsa/marshal.go b/ecc/stark-curve/ecdsa/marshal.go
index a838742bfa..26d82b5a55 100644
--- a/ecc/stark-curve/ecdsa/marshal.go
+++ b/ecc/stark-curve/ecdsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/ecdsa/marshal_test.go b/ecc/stark-curve/ecdsa/marshal_test.go
index 21a4d96b10..4429e18851 100644
--- a/ecc/stark-curve/ecdsa/marshal_test.go
+++ b/ecc/stark-curve/ecdsa/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/arith.go b/ecc/stark-curve/fp/arith.go
index b202a1549a..bb63552f5a 100644
--- a/ecc/stark-curve/fp/arith.go
+++ b/ecc/stark-curve/fp/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/asm_adx.go b/ecc/stark-curve/fp/asm_adx.go
index fe25e82db2..75e92992fe 100644
--- a/ecc/stark-curve/fp/asm_adx.go
+++ b/ecc/stark-curve/fp/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/asm_avx.go b/ecc/stark-curve/fp/asm_avx.go
index fdb65bb8f2..aa233664d0 100644
--- a/ecc/stark-curve/fp/asm_avx.go
+++ b/ecc/stark-curve/fp/asm_avx.go
@@ -1,6 +1,6 @@
 //go:build !noavx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/asm_noadx.go b/ecc/stark-curve/fp/asm_noadx.go
index 95085a8e6f..304dfb7209 100644
--- a/ecc/stark-curve/fp/asm_noadx.go
+++ b/ecc/stark-curve/fp/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/asm_noavx.go b/ecc/stark-curve/fp/asm_noavx.go
index c5fec182cd..900dedbe8b 100644
--- a/ecc/stark-curve/fp/asm_noavx.go
+++ b/ecc/stark-curve/fp/asm_noavx.go
@@ -1,6 +1,6 @@
 //go:build noavx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/doc.go b/ecc/stark-curve/fp/doc.go
index 4f31576c24..6c6ae3e577 100644
--- a/ecc/stark-curve/fp/doc.go
+++ b/ecc/stark-curve/fp/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/element.go b/ecc/stark-curve/fp/element.go
index 2c6fe84459..a0f588bc39 100644
--- a/ecc/stark-curve/fp/element.go
+++ b/ecc/stark-curve/fp/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/element_amd64.go b/ecc/stark-curve/fp/element_amd64.go
index e72f552ad9..9cee062e5b 100644
--- a/ecc/stark-curve/fp/element_amd64.go
+++ b/ecc/stark-curve/fp/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/element_amd64.s b/ecc/stark-curve/fp/element_amd64.s
index ed8a36e04d..a7c6ffae66 100644
--- a/ecc/stark-curve/fp/element_amd64.s
+++ b/ecc/stark-curve/fp/element_amd64.s
@@ -1,10 +1,10 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
-// We include the hash to force the Go compiler to recompile: 9425145785761608449
+// We include the hash to force the Go compiler to recompile: 14652627197992229521
 #include "../../../field/asm/element_4w_amd64.s"
 
diff --git a/ecc/stark-curve/fp/element_arm64.go b/ecc/stark-curve/fp/element_arm64.go
index eeeb12930d..3ed880d74f 100644
--- a/ecc/stark-curve/fp/element_arm64.go
+++ b/ecc/stark-curve/fp/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/element_arm64.s b/ecc/stark-curve/fp/element_arm64.s
index a7bd036553..ef16eaba35 100644
--- a/ecc/stark-curve/fp/element_arm64.s
+++ b/ecc/stark-curve/fp/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/element_exp.go b/ecc/stark-curve/fp/element_exp.go
index e2fddd105a..69e57afa05 100644
--- a/ecc/stark-curve/fp/element_exp.go
+++ b/ecc/stark-curve/fp/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/element_purego.go b/ecc/stark-curve/fp/element_purego.go
index 5062b3185a..425a7d564b 100644
--- a/ecc/stark-curve/fp/element_purego.go
+++ b/ecc/stark-curve/fp/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/element_test.go b/ecc/stark-curve/fp/element_test.go
index eab8b6eca3..2c47d8604b 100644
--- a/ecc/stark-curve/fp/element_test.go
+++ b/ecc/stark-curve/fp/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/vector.go b/ecc/stark-curve/fp/vector.go
index ec52314aa7..ef60ed4b45 100644
--- a/ecc/stark-curve/fp/vector.go
+++ b/ecc/stark-curve/fp/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/vector_amd64.go b/ecc/stark-curve/fp/vector_amd64.go
index 39666a2df7..9e05e6b2f3 100644
--- a/ecc/stark-curve/fp/vector_amd64.go
+++ b/ecc/stark-curve/fp/vector_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/vector_purego.go b/ecc/stark-curve/fp/vector_purego.go
index 16afa898d4..6adeb1a8a2 100644
--- a/ecc/stark-curve/fp/vector_purego.go
+++ b/ecc/stark-curve/fp/vector_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || !amd64
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/vector_test.go b/ecc/stark-curve/fp/vector_test.go
index 06fe1084a8..e7185486cf 100644
--- a/ecc/stark-curve/fp/vector_test.go
+++ b/ecc/stark-curve/fp/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/arith.go b/ecc/stark-curve/fr/arith.go
index 9285041f4b..dbba8a9ae4 100644
--- a/ecc/stark-curve/fr/arith.go
+++ b/ecc/stark-curve/fr/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/asm_adx.go b/ecc/stark-curve/fr/asm_adx.go
index 9e7da5e865..9b970335f1 100644
--- a/ecc/stark-curve/fr/asm_adx.go
+++ b/ecc/stark-curve/fr/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/asm_avx.go b/ecc/stark-curve/fr/asm_avx.go
index d6d7d7f87a..2a0a166ed4 100644
--- a/ecc/stark-curve/fr/asm_avx.go
+++ b/ecc/stark-curve/fr/asm_avx.go
@@ -1,6 +1,6 @@
 //go:build !noavx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/asm_noadx.go b/ecc/stark-curve/fr/asm_noadx.go
index 3456158655..96741014f2 100644
--- a/ecc/stark-curve/fr/asm_noadx.go
+++ b/ecc/stark-curve/fr/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/asm_noavx.go b/ecc/stark-curve/fr/asm_noavx.go
index 4eb73e9a78..3cb6968fb8 100644
--- a/ecc/stark-curve/fr/asm_noavx.go
+++ b/ecc/stark-curve/fr/asm_noavx.go
@@ -1,6 +1,6 @@
 //go:build noavx
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/doc.go b/ecc/stark-curve/fr/doc.go
index 7b99c5c2cc..3025d16c07 100644
--- a/ecc/stark-curve/fr/doc.go
+++ b/ecc/stark-curve/fr/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/element.go b/ecc/stark-curve/fr/element.go
index 68352c754d..7fa697492a 100644
--- a/ecc/stark-curve/fr/element.go
+++ b/ecc/stark-curve/fr/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/element_amd64.go b/ecc/stark-curve/fr/element_amd64.go
index ca49d12590..4c3f2a8567 100644
--- a/ecc/stark-curve/fr/element_amd64.go
+++ b/ecc/stark-curve/fr/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/element_amd64.s b/ecc/stark-curve/fr/element_amd64.s
index ed8a36e04d..a7c6ffae66 100644
--- a/ecc/stark-curve/fr/element_amd64.s
+++ b/ecc/stark-curve/fr/element_amd64.s
@@ -1,10 +1,10 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
-// We include the hash to force the Go compiler to recompile: 9425145785761608449
+// We include the hash to force the Go compiler to recompile: 14652627197992229521
 #include "../../../field/asm/element_4w_amd64.s"
 
diff --git a/ecc/stark-curve/fr/element_arm64.go b/ecc/stark-curve/fr/element_arm64.go
index 13632a244b..8e2641ede7 100644
--- a/ecc/stark-curve/fr/element_arm64.go
+++ b/ecc/stark-curve/fr/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/element_arm64.s b/ecc/stark-curve/fr/element_arm64.s
index a7bd036553..ef16eaba35 100644
--- a/ecc/stark-curve/fr/element_arm64.s
+++ b/ecc/stark-curve/fr/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/element_purego.go b/ecc/stark-curve/fr/element_purego.go
index 85a7015090..ebd6bca369 100644
--- a/ecc/stark-curve/fr/element_purego.go
+++ b/ecc/stark-curve/fr/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/element_test.go b/ecc/stark-curve/fr/element_test.go
index 78aa20965c..d217e25816 100644
--- a/ecc/stark-curve/fr/element_test.go
+++ b/ecc/stark-curve/fr/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/vector.go b/ecc/stark-curve/fr/vector.go
index 8b59bd36e9..4654b1b2d3 100644
--- a/ecc/stark-curve/fr/vector.go
+++ b/ecc/stark-curve/fr/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/vector_amd64.go b/ecc/stark-curve/fr/vector_amd64.go
index b27679827c..a7dcec3b25 100644
--- a/ecc/stark-curve/fr/vector_amd64.go
+++ b/ecc/stark-curve/fr/vector_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/vector_purego.go b/ecc/stark-curve/fr/vector_purego.go
index 5973d16ce2..db43e73504 100644
--- a/ecc/stark-curve/fr/vector_purego.go
+++ b/ecc/stark-curve/fr/vector_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || !amd64
 
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/vector_test.go b/ecc/stark-curve/fr/vector_test.go
index a094bc0ac6..f6179e7824 100644
--- a/ecc/stark-curve/fr/vector_test.go
+++ b/ecc/stark-curve/fr/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/g1.go b/ecc/stark-curve/g1.go
index b7ad98cd1b..3e2806a7df 100644
--- a/ecc/stark-curve/g1.go
+++ b/ecc/stark-curve/g1.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // FOO
 
diff --git a/ecc/stark-curve/g1_test.go b/ecc/stark-curve/g1_test.go
index 0e3373eb9f..768d07e76d 100644
--- a/ecc/stark-curve/g1_test.go
+++ b/ecc/stark-curve/g1_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // FOO
 
diff --git a/ecc/stark-curve/hash_to_g1.go b/ecc/stark-curve/hash_to_g1.go
index bc8273415d..701002df34 100644
--- a/ecc/stark-curve/hash_to_g1.go
+++ b/ecc/stark-curve/hash_to_g1.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // FOO
 
diff --git a/ecc/stark-curve/hash_to_g1_test.go b/ecc/stark-curve/hash_to_g1_test.go
index ae10337e68..7473b0d2cd 100644
--- a/ecc/stark-curve/hash_to_g1_test.go
+++ b/ecc/stark-curve/hash_to_g1_test.go
@@ -1,27 +1,17 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // FOO
 
 package starkcurve
 
 import (
+	"math/rand"
+	"testing"
+
 	"github.com/consensys/gnark-crypto/ecc/stark-curve/fp"
 	"github.com/leanovate/gopter"
 	"github.com/leanovate/gopter/prop"
-	"math/rand"
-	"testing"
 )
 
 func TestHashToFpG1(t *testing.T) {
diff --git a/ecc/stark-curve/marshal.go b/ecc/stark-curve/marshal.go
index f2c78c3e9b..ab1afc9184 100644
--- a/ecc/stark-curve/marshal.go
+++ b/ecc/stark-curve/marshal.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // FOO
 
diff --git a/ecc/stark-curve/marshal_test.go b/ecc/stark-curve/marshal_test.go
index a3a899a155..8e3e502335 100644
--- a/ecc/stark-curve/marshal_test.go
+++ b/ecc/stark-curve/marshal_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // FOO
 
diff --git a/ecc/stark-curve/stark_curve.go b/ecc/stark-curve/stark_curve.go
index c7ec96f8db..256ad02d03 100644
--- a/ecc/stark-curve/stark_curve.go
+++ b/ecc/stark-curve/stark_curve.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Package starkcurve efficient elliptic curve implementation for stark_curve. This is curve used in StarkNet: https://docs.starkware.co/starkex/crypto/stark-curve.html.
 //
diff --git a/fiat-shamir/transcript.go b/fiat-shamir/transcript.go
index a50f1ba657..b50df0f0da 100644
--- a/fiat-shamir/transcript.go
+++ b/fiat-shamir/transcript.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fiatshamir
 
diff --git a/fiat-shamir/transcript_test.go b/fiat-shamir/transcript_test.go
index 8451aae325..8232b6b90b 100644
--- a/fiat-shamir/transcript_test.go
+++ b/fiat-shamir/transcript_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fiatshamir
 
diff --git a/field/asm/element_10w_amd64.s b/field/asm/element_10w_amd64.s
index e5f10dca8c..c45206cc5c 100644
--- a/field/asm/element_10w_amd64.s
+++ b/field/asm/element_10w_amd64.s
@@ -409,7 +409,7 @@ TEXT ·mul(SB), $64-24
 
 	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
 	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
-	// See github.com/gnark-crypto/field/generator for more comments.
+	// See github.com/Consensys/gnark-crypto/field/generator for more comments.
 
 	NO_LOCAL_POINTERS
 	CMPB ·supportAdx(SB), $1
diff --git a/field/asm/element_12w_amd64.s b/field/asm/element_12w_amd64.s
index 52cf02adc1..9aa37956c0 100644
--- a/field/asm/element_12w_amd64.s
+++ b/field/asm/element_12w_amd64.s
@@ -473,7 +473,7 @@ TEXT ·mul(SB), $96-24
 
 	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
 	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
-	// See github.com/gnark-crypto/field/generator for more comments.
+	// See github.com/Consensys/gnark-crypto/field/generator for more comments.
 
 	NO_LOCAL_POINTERS
 	CMPB ·supportAdx(SB), $1
diff --git a/field/asm/element_4w_amd64.s b/field/asm/element_4w_amd64.s
index 6f62d63102..6d7a31b6a2 100644
--- a/field/asm/element_4w_amd64.s
+++ b/field/asm/element_4w_amd64.s
@@ -209,7 +209,7 @@ TEXT ·mul(SB), $24-24
 
 	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
 	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
-	// See github.com/gnark-crypto/field/generator for more comments.
+	// See github.com/Consensys/gnark-crypto/field/generator for more comments.
 
 	NO_LOCAL_POINTERS
 	CMPB ·supportAdx(SB), $1
diff --git a/field/asm/element_5w_amd64.s b/field/asm/element_5w_amd64.s
index b3ccd84b14..53a8c76771 100644
--- a/field/asm/element_5w_amd64.s
+++ b/field/asm/element_5w_amd64.s
@@ -250,7 +250,7 @@ TEXT ·mul(SB), $24-24
 
 	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
 	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
-	// See github.com/gnark-crypto/field/generator for more comments.
+	// See github.com/Consensys/gnark-crypto/field/generator for more comments.
 
 	NO_LOCAL_POINTERS
 	CMPB ·supportAdx(SB), $1
diff --git a/field/asm/element_6w_amd64.s b/field/asm/element_6w_amd64.s
index b8172b2870..1b4f66c04f 100644
--- a/field/asm/element_6w_amd64.s
+++ b/field/asm/element_6w_amd64.s
@@ -283,7 +283,7 @@ TEXT ·mul(SB), $24-24
 
 	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS"
 	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
-	// See github.com/gnark-crypto/field/generator for more comments.
+	// See github.com/Consensys/gnark-crypto/field/generator for more comments.
 
 	NO_LOCAL_POINTERS
 	CMPB ·supportAdx(SB), $1
diff --git a/field/babybear/arith.go b/field/babybear/arith.go
index 3dfd7e5ffe..10c487d46a 100644
--- a/field/babybear/arith.go
+++ b/field/babybear/arith.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/babybear/doc.go b/field/babybear/doc.go
index 76ec16e7d3..a0517f38d9 100644
--- a/field/babybear/doc.go
+++ b/field/babybear/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/element.go b/field/babybear/element.go
index fe21d3d87a..c0a64a1a10 100644
--- a/field/babybear/element.go
+++ b/field/babybear/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/element_exp.go b/field/babybear/element_exp.go
index 470040b7dd..b536f6ea6e 100644
--- a/field/babybear/element_exp.go
+++ b/field/babybear/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/element_purego.go b/field/babybear/element_purego.go
index f30766fdfe..19fe63b732 100644
--- a/field/babybear/element_purego.go
+++ b/field/babybear/element_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/element_test.go b/field/babybear/element_test.go
index ed2fe025d3..075793bf10 100644
--- a/field/babybear/element_test.go
+++ b/field/babybear/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/vector.go b/field/babybear/vector.go
index b9a91e68bc..dca652c999 100644
--- a/field/babybear/vector.go
+++ b/field/babybear/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/vector_purego.go b/field/babybear/vector_purego.go
index 296122be81..364c671c8a 100644
--- a/field/babybear/vector_purego.go
+++ b/field/babybear/vector_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/vector_test.go b/field/babybear/vector_test.go
index d7660863db..c05be2917f 100644
--- a/field/babybear/vector_test.go
+++ b/field/babybear/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/generator/asm/amd64/asm_macros.go b/field/generator/asm/amd64/asm_macros.go
index b2c6341cf5..c960713e2d 100644
--- a/field/generator/asm/amd64/asm_macros.go
+++ b/field/generator/asm/amd64/asm_macros.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package amd64
 
diff --git a/field/generator/asm/amd64/build.go b/field/generator/asm/amd64/build.go
index 40edcfc366..8372eebc1d 100644
--- a/field/generator/asm/amd64/build.go
+++ b/field/generator/asm/amd64/build.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Package amd64 contains syntactic sugar to generate amd64 assembly code
 package amd64
diff --git a/field/generator/asm/amd64/element_butterfly.go b/field/generator/asm/amd64/element_butterfly.go
index 8792b6dce3..6ada559b9a 100644
--- a/field/generator/asm/amd64/element_butterfly.go
+++ b/field/generator/asm/amd64/element_butterfly.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package amd64
 
diff --git a/field/generator/asm/amd64/element_frommont.go b/field/generator/asm/amd64/element_frommont.go
index de9d0e3c46..dc45d9c8da 100644
--- a/field/generator/asm/amd64/element_frommont.go
+++ b/field/generator/asm/amd64/element_frommont.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package amd64
 
@@ -32,7 +21,7 @@ func (f *FFAmd64) generateFromMont(forceADX bool) {
 	if f.NbWords <= 5 {
 		// when dynamic linking, R15 is clobbered by a global variable access
 		// this is a temporary workaround --> don't use R15 when we can avoid it.
-		// see https://github.com/ConsenSys/gnark-crypto/issues/113
+		// see https://github.com/Consensys/gnark-crypto/issues/113
 		reserved = append(reserved, amd64.R15)
 	}
 	registers := f.FnHeader("fromMont", stackSize, argSize, reserved...)
diff --git a/field/generator/asm/amd64/element_mul.go b/field/generator/asm/amd64/element_mul.go
index 55f816c267..59e3c5064a 100644
--- a/field/generator/asm/amd64/element_mul.go
+++ b/field/generator/asm/amd64/element_mul.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package amd64
 
@@ -187,7 +176,7 @@ func (f *FFAmd64) generateMul(forceADX bool) {
 	if f.NbWords <= 5 {
 		// when dynamic linking, R15 is clobbered by a global variable access
 		// this is a temporary workaround --> don't use R15 when we can avoid it.
-		// see https://github.com/ConsenSys/gnark-crypto/issues/113
+		// see https://github.com/Consensys/gnark-crypto/issues/113
 		reserved = append(reserved, amd64.R15)
 	}
 	registers := f.FnHeader("mul", stackSize, argSize, reserved...)
@@ -196,7 +185,7 @@ func (f *FFAmd64) generateMul(forceADX bool) {
 	f.WriteLn(`
 	// Algorithm 2 of "Faster Montgomery Multiplication and Multi-Scalar-Multiplication for SNARKS" 
 	// by Y. El Housni and G. Botrel https://doi.org/10.46586/tches.v2023.i3.504-521
-	// See github.com/gnark-crypto/field/generator for more comments.
+	// See github.com/Consensys/gnark-crypto/field/generator for more comments.
 	`)
 	if stackSize > 0 {
 		f.WriteLn("NO_LOCAL_POINTERS")
diff --git a/field/generator/asm/amd64/element_mul_constants.go b/field/generator/asm/amd64/element_mul_constants.go
index a73aa1b6a4..99e52dc16f 100644
--- a/field/generator/asm/amd64/element_mul_constants.go
+++ b/field/generator/asm/amd64/element_mul_constants.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package amd64
 
diff --git a/field/generator/asm/amd64/element_reduce.go b/field/generator/asm/amd64/element_reduce.go
index 70a566c3c8..c443140eba 100644
--- a/field/generator/asm/amd64/element_reduce.go
+++ b/field/generator/asm/amd64/element_reduce.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package amd64
 
diff --git a/field/generator/asm/amd64/element_vec.go b/field/generator/asm/amd64/element_vec.go
index c67137d6cb..b5de5e0c8e 100644
--- a/field/generator/asm/amd64/element_vec.go
+++ b/field/generator/asm/amd64/element_vec.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package amd64
 
diff --git a/field/generator/asm/arm64/element_mul.go b/field/generator/asm/arm64/element_mul.go
index 2a2de0ad0c..681e923ad7 100644
--- a/field/generator/asm/arm64/element_mul.go
+++ b/field/generator/asm/arm64/element_mul.go
@@ -1,16 +1,5 @@
-// Copyright 2022 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package arm64
 
diff --git a/field/generator/config/field_config.go b/field/generator/config/field_config.go
index 2d992db463..7810144356 100644
--- a/field/generator/config/field_config.go
+++ b/field/generator/config/field_config.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Package config provides Golang code generation for efficient field arithmetic operations.
 package config
diff --git a/field/generator/generator_test.go b/field/generator/generator_test.go
index ee5b5fafc0..f47d282aaa 100644
--- a/field/generator/generator_test.go
+++ b/field/generator/generator_test.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package generator
 
diff --git a/field/goff/cmd/errors.go b/field/goff/cmd/errors.go
index 6a0fa87fe5..c28c662d49 100644
--- a/field/goff/cmd/errors.go
+++ b/field/goff/cmd/errors.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package cmd
 
diff --git a/field/goff/cmd/root.go b/field/goff/cmd/root.go
index c2ae86809e..480c2345cf 100644
--- a/field/goff/cmd/root.go
+++ b/field/goff/cmd/root.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Package cmd is the CLI interface for goff
 package cmd
diff --git a/field/goff/cmd/version.go b/field/goff/cmd/version.go
index 149cd0dea8..1f32bf574a 100644
--- a/field/goff/cmd/version.go
+++ b/field/goff/cmd/version.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package cmd
 
diff --git a/field/goff/main.go b/field/goff/main.go
index 92cec47e52..0f3884e223 100644
--- a/field/goff/main.go
+++ b/field/goff/main.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Package goff (go finite field) is a library that generates fast field arithmetic code for a given modulus.
 //
diff --git a/field/goldilocks/arith.go b/field/goldilocks/arith.go
index 95d2a32596..fd46bf62a0 100644
--- a/field/goldilocks/arith.go
+++ b/field/goldilocks/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/doc.go b/field/goldilocks/doc.go
index 209714e87e..7ed505e777 100644
--- a/field/goldilocks/doc.go
+++ b/field/goldilocks/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/element.go b/field/goldilocks/element.go
index b707bcd996..5f5319330e 100644
--- a/field/goldilocks/element.go
+++ b/field/goldilocks/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/element_exp.go b/field/goldilocks/element_exp.go
index 2de013154a..676211d6b4 100644
--- a/field/goldilocks/element_exp.go
+++ b/field/goldilocks/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/element_purego.go b/field/goldilocks/element_purego.go
index aa6c1053f2..00d536c716 100644
--- a/field/goldilocks/element_purego.go
+++ b/field/goldilocks/element_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/element_test.go b/field/goldilocks/element_test.go
index e4c179aed6..e940b56092 100644
--- a/field/goldilocks/element_test.go
+++ b/field/goldilocks/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/vector.go b/field/goldilocks/vector.go
index 55f9cb5266..32ad268ee5 100644
--- a/field/goldilocks/vector.go
+++ b/field/goldilocks/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/vector_purego.go b/field/goldilocks/vector_purego.go
index c964b4150e..aadf02c291 100644
--- a/field/goldilocks/vector_purego.go
+++ b/field/goldilocks/vector_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/vector_test.go b/field/goldilocks/vector_test.go
index cecc96eb3a..96e735c8cd 100644
--- a/field/goldilocks/vector_test.go
+++ b/field/goldilocks/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/arith.go b/field/koalabear/arith.go
index 0252a5bd1e..f8ed8eb91f 100644
--- a/field/koalabear/arith.go
+++ b/field/koalabear/arith.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
 
diff --git a/field/koalabear/doc.go b/field/koalabear/doc.go
index 8b6839411f..b60c389776 100644
--- a/field/koalabear/doc.go
+++ b/field/koalabear/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/element.go b/field/koalabear/element.go
index 0549df00c4..42ed0ebe00 100644
--- a/field/koalabear/element.go
+++ b/field/koalabear/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/element_exp.go b/field/koalabear/element_exp.go
index ebf5ea1c26..3c2a3c72ba 100644
--- a/field/koalabear/element_exp.go
+++ b/field/koalabear/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/element_purego.go b/field/koalabear/element_purego.go
index 02f9da17d9..4ede470cca 100644
--- a/field/koalabear/element_purego.go
+++ b/field/koalabear/element_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/element_test.go b/field/koalabear/element_test.go
index d8670b0888..bea2f28ee3 100644
--- a/field/koalabear/element_test.go
+++ b/field/koalabear/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/vector.go b/field/koalabear/vector.go
index 0490927d51..725e065d16 100644
--- a/field/koalabear/vector.go
+++ b/field/koalabear/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/vector_purego.go b/field/koalabear/vector_purego.go
index 6e9b038922..e1dc6b8f81 100644
--- a/field/koalabear/vector_purego.go
+++ b/field/koalabear/vector_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/vector_test.go b/field/koalabear/vector_test.go
index 8f3c20664b..606366bb0c 100644
--- a/field/koalabear/vector_test.go
+++ b/field/koalabear/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/pool/pool.go b/field/pool/pool.go
index 6bb10bdbdc..373610588f 100644
--- a/field/pool/pool.go
+++ b/field/pool/pool.go
@@ -22,7 +22,7 @@ func (bigIntPool) Get() *big.Int {
 
 func (bigIntPool) Put(v *big.Int) {
 	if v == nil {
-		return // see https://github.com/ConsenSys/gnark-crypto/issues/316
+		return // see https://github.com/Consensys/gnark-crypto/issues/316
 	}
 	_bigIntPool.Put(v)
 }
diff --git a/go.mod b/go.mod
index ae2d6988c6..e52cac12d6 100644
--- a/go.mod
+++ b/go.mod
@@ -4,7 +4,7 @@ go 1.22
 
 require (
 	github.com/bits-and-blooms/bitset v1.14.2
-	github.com/consensys/bavard v0.1.23
+	github.com/consensys/bavard v0.1.24
 	github.com/leanovate/gopter v0.2.11
 	github.com/mmcloughlin/addchain v0.4.0
 	github.com/spf13/cobra v1.8.1
diff --git a/go.sum b/go.sum
index 9e1af01c23..4b478e8750 100644
--- a/go.sum
+++ b/go.sum
@@ -55,8 +55,8 @@ github.com/client9/misspell v0.3.4/go.mod h1:qj6jICC3Q7zFZvVWo7KLAzC3yx5G7kyvSDk
 github.com/cncf/udpa/go v0.0.0-20191209042840-269d4d468f6f/go.mod h1:M8M6+tZqaGXZJjfX53e64911xZQV5JYwmTeXPW+k8Sc=
 github.com/cncf/udpa/go v0.0.0-20200629203442-efcf912fb354/go.mod h1:WmhPx2Nbnhtbo57+VJT5O0JRkEi1Wbu0z5j0R8u5Hbk=
 github.com/cncf/udpa/go v0.0.0-20201120205902-5459f2c99403/go.mod h1:WmhPx2Nbnhtbo57+VJT5O0JRkEi1Wbu0z5j0R8u5Hbk=
-github.com/consensys/bavard v0.1.23 h1:EUMTIayTeUqb7tPy7n0IMrBM/GeEHGBSEkR8G5JE0po=
-github.com/consensys/bavard v0.1.23/go.mod h1:k/zVjHHC4B+PQy1Pg7fgvG3ALicQw540Crag8qx+dZs=
+github.com/consensys/bavard v0.1.24 h1:Lfe+bjYbpaoT7K5JTFoMi5wo9V4REGLvQQbHmatoN2I=
+github.com/consensys/bavard v0.1.24/go.mod h1:k/zVjHHC4B+PQy1Pg7fgvG3ALicQw540Crag8qx+dZs=
 github.com/coreos/go-semver v0.3.0/go.mod h1:nnelYz7RCh+5ahJtPPxZlU+153eP4D4r3EedlOD2RNk=
 github.com/coreos/go-systemd/v22 v22.3.2/go.mod h1:Y58oyj3AT4RCenI/lSvhwexgC+NSVTIJ3seZv2GcEnc=
 github.com/cpuguy83/go-md2man/v2 v2.0.0/go.mod h1:maD7wRr/U5Z6m/iR4s+kqSMx2CaBsrgA7czyZG/E6dU=
diff --git a/hash/hashes.go b/hash/hashes.go
index 56cc5d1b41..4388219c0b 100644
--- a/hash/hashes.go
+++ b/hash/hashes.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package hash
 
diff --git a/internal/generator/ecc/template/multiexp_affine.go.tmpl b/internal/generator/ecc/template/multiexp_affine.go.tmpl
index 4b3b732964..1c0bf7d325 100644
--- a/internal/generator/ecc/template/multiexp_affine.go.tmpl
+++ b/internal/generator/ecc/template/multiexp_affine.go.tmpl
@@ -31,7 +31,7 @@ type batchOp{{ $.TAffine }} struct {
 // using affine coordinates for the buckets. To amortize the cost of the inverse in the affine addition
 // we use a batch affine addition.
 //
-// this is derived from a PR by 0x0ece : https://github.com/ConsenSys/gnark-crypto/pull/249
+// this is derived from a PR by 0x0ece : https://github.com/Consensys/gnark-crypto/pull/249
 // See Section 5.3: ia.cr/2022/1396
 func processChunk{{ $.UPointName }}BatchAffine[BJE ib{{ $.TJacobianExtended }},B ib{{ $.TAffine }}, BS bitSet, TP p{{ $.TAffine }}, TPP pp{{ $.TAffine }}, TQ qOps{{ $.TAffine }}, TC c{{ $.TAffine}}](
 	 chunk uint64,
diff --git a/internal/generator/gkr/template/gkr.test.go.tmpl b/internal/generator/gkr/template/gkr.test.go.tmpl
index b553c23668..17d41fbb9b 100644
--- a/internal/generator/gkr/template/gkr.test.go.tmpl
+++ b/internal/generator/gkr/template/gkr.test.go.tmpl
@@ -326,7 +326,7 @@ func mimcCircuit(numRounds int) Circuit {
 
 func testMimc(t *testing.T, numRounds int, inputAssignments ...[]{{.ElementType}}) {
 	//TODO: Implement mimc correctly. Currently, the computation is mimc(a,b) = cipher( cipher( ... cipher(a, b), b) ..., b)
-	// @AlexandreBelling: Please explain the extra layers in https://github.com/ConsenSys/gkr-mimc/blob/81eada039ab4ed403b7726b535adb63026e8011f/examples/mimc.go#L10
+	// @AlexandreBelling: Please explain the extra layers in https://github.com/Consensys/gkr-mimc/blob/81eada039ab4ed403b7726b535adb63026e8011f/examples/mimc.go#L10
 
 	c := mimcCircuit(numRounds)
 
diff --git a/internal/generator/gkr/test_vectors/main.go b/internal/generator/gkr/test_vectors/main.go
index f4e6429e82..49ddf92414 100644
--- a/internal/generator/gkr/test_vectors/main.go
+++ b/internal/generator/gkr/test_vectors/main.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/internal/generator/pedersen/template/pedersen.go.tmpl b/internal/generator/pedersen/template/pedersen.go.tmpl
index 3497987dc0..f5f0df7e08 100644
--- a/internal/generator/pedersen/template/pedersen.go.tmpl
+++ b/internal/generator/pedersen/template/pedersen.go.tmpl
@@ -15,8 +15,8 @@ type ProvingKey struct {
 }
 
 type VerifyingKey struct {
-	G             curve.G2Affine
-	GSigmaNeg     curve.G2Affine // GSigmaNeg = G^{-σ}
+	G         curve.G2Affine
+	GSigmaNeg curve.G2Affine // GSigmaNeg = G^{-σ}
 }
 
 func randomFrSizedBytes() ([]byte, error) {
@@ -98,7 +98,7 @@ func (pk *ProvingKey) ProveKnowledge(values []fr.Element) (pok curve.G1Affine, e
 	}
 
 	// TODO @gbotrel this will spawn more than one task, see
-	// https://github.com/ConsenSys/gnark-crypto/issues/269
+	// https://github.com/Consensys/gnark-crypto/issues/269
 	config := ecc.MultiExpConfig{
 		NbTasks: 1, // TODO Experiment
 	}
@@ -116,7 +116,7 @@ func (pk *ProvingKey) Commit(values []fr.Element) (commitment curve.G1Affine, er
 	}
 
 	// TODO @gbotrel this will spawn more than one task, see
-	// https://github.com/ConsenSys/gnark-crypto/issues/269
+	// https://github.com/Consensys/gnark-crypto/issues/269
 	config := ecc.MultiExpConfig{
 		NbTasks: 1,
 	}
@@ -177,7 +177,7 @@ func BatchProve(pk []ProvingKey, values [][]fr.Element, combinationCoeff fr.Elem
 	}
 
 	// TODO @gbotrel this will spawn more than one task, see
-	// https://github.com/ConsenSys/gnark-crypto/issues/269
+	// https://github.com/Consensys/gnark-crypto/issues/269
 	config := ecc.MultiExpConfig{
 		NbTasks: 1,
 	}
diff --git a/internal/generator/test_vector_utils/small_rational/gkr/gkr.go b/internal/generator/test_vector_utils/small_rational/gkr/gkr.go
index a5bcb55b94..52e301df67 100644
--- a/internal/generator/test_vector_utils/small_rational/gkr/gkr.go
+++ b/internal/generator/test_vector_utils/small_rational/gkr/gkr.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/internal/generator/test_vector_utils/small_rational/polynomial/doc.go b/internal/generator/test_vector_utils/small_rational/polynomial/doc.go
index 35b3f725c1..fd96328e8f 100644
--- a/internal/generator/test_vector_utils/small_rational/polynomial/doc.go
+++ b/internal/generator/test_vector_utils/small_rational/polynomial/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/internal/generator/test_vector_utils/small_rational/polynomial/multilin.go b/internal/generator/test_vector_utils/small_rational/polynomial/multilin.go
index 20915de419..d3c0edc694 100644
--- a/internal/generator/test_vector_utils/small_rational/polynomial/multilin.go
+++ b/internal/generator/test_vector_utils/small_rational/polynomial/multilin.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/internal/generator/test_vector_utils/small_rational/polynomial/polynomial.go b/internal/generator/test_vector_utils/small_rational/polynomial/polynomial.go
index 2c76a20288..6b67eafada 100644
--- a/internal/generator/test_vector_utils/small_rational/polynomial/polynomial.go
+++ b/internal/generator/test_vector_utils/small_rational/polynomial/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/internal/generator/test_vector_utils/small_rational/polynomial/pool.go b/internal/generator/test_vector_utils/small_rational/polynomial/pool.go
index e9fc5204a2..9dbd98c86c 100644
--- a/internal/generator/test_vector_utils/small_rational/polynomial/pool.go
+++ b/internal/generator/test_vector_utils/small_rational/polynomial/pool.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck.go b/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck.go
index 61ed654aec..d5cd387d85 100644
--- a/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck.go
+++ b/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck_test.go b/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck_test.go
index 012aae6598..46acdcca1c 100644
--- a/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck_test.go
+++ b/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/internal/generator/test_vector_utils/small_rational/test_vector_utils/test_vector_utils.go b/internal/generator/test_vector_utils/small_rational/test_vector_utils/test_vector_utils.go
index 0432ac7bfc..273e1c537f 100644
--- a/internal/generator/test_vector_utils/small_rational/test_vector_utils/test_vector_utils.go
+++ b/internal/generator/test_vector_utils/small_rational/test_vector_utils/test_vector_utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020 Consensys Software Inc.
+// Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/internal/generator/tower/asm/amd64/e2.go b/internal/generator/tower/asm/amd64/e2.go
index e3564861a9..9f372f351a 100644
--- a/internal/generator/tower/asm/amd64/e2.go
+++ b/internal/generator/tower/asm/amd64/e2.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package amd64
 
@@ -44,7 +33,7 @@ func NewFq2Amd64(w io.Writer, F *field.FieldConfig, config config.Curve) *Fq2Amd
 
 // Generate ...
 func (fq2 *Fq2Amd64) Generate(forceADXCheck bool) error {
-	fq2.WriteLn(bavard.Apache2Header("ConsenSys Software Inc.", 2020))
+	fq2.WriteLn(bavard.Apache2Header("Consensys Software Inc.", 2020))
 
 	fq2.WriteLn("#include \"textflag.h\"")
 	fq2.WriteLn("#include \"funcdata.h\"")
diff --git a/internal/generator/tower/asm/amd64/e2_bls381.go b/internal/generator/tower/asm/amd64/e2_bls381.go
index d67663746e..54d49c65b2 100644
--- a/internal/generator/tower/asm/amd64/e2_bls381.go
+++ b/internal/generator/tower/asm/amd64/e2_bls381.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package amd64
 
diff --git a/internal/generator/tower/asm/amd64/e2_bn254.go b/internal/generator/tower/asm/amd64/e2_bn254.go
index c894c2c684..fed9e14a07 100644
--- a/internal/generator/tower/asm/amd64/e2_bn254.go
+++ b/internal/generator/tower/asm/amd64/e2_bn254.go
@@ -1,16 +1,5 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package amd64
 
diff --git a/signature/ecdsa/ecdsa.go b/signature/ecdsa/ecdsa.go
index 91bf8284b5..c21fecb8f6 100644
--- a/signature/ecdsa/ecdsa.go
+++ b/signature/ecdsa/ecdsa.go
@@ -1,18 +1,5 @@
-/*
-Copyright © 2020 ConsenSys
-
-Licensed under the Apache License, Version 2.0 (the "License");
-you may not use this file except in compliance with the License.
-You may obtain a copy of the License at
-
-    http://www.apache.org/licenses/LICENSE-2.0
-
-Unless required by applicable law or agreed to in writing, software
-distributed under the License is distributed on an "AS IS" BASIS,
-WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-See the License for the specific language governing permissions and
-limitations under the License.
-*/
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package ecdsa
 
diff --git a/signature/eddsa/eddsa.go b/signature/eddsa/eddsa.go
index 9df765f867..f17589ebb5 100644
--- a/signature/eddsa/eddsa.go
+++ b/signature/eddsa/eddsa.go
@@ -1,18 +1,5 @@
-/*
-Copyright © 2020 ConsenSys
-
-Licensed under the Apache License, Version 2.0 (the "License");
-you may not use this file except in compliance with the License.
-You may obtain a copy of the License at
-
-    http://www.apache.org/licenses/LICENSE-2.0
-
-Unless required by applicable law or agreed to in writing, software
-distributed under the License is distributed on an "AS IS" BASIS,
-WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-See the License for the specific language governing permissions and
-limitations under the License.
-*/
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package eddsa
 
diff --git a/signature/signature.go b/signature/signature.go
index 7fe8d78346..4a378a1d82 100644
--- a/signature/signature.go
+++ b/signature/signature.go
@@ -1,18 +1,5 @@
-/*
-Copyright © 2020 ConsenSys
-
-Licensed under the Apache License, Version 2.0 (the "License");
-you may not use this file except in compliance with the License.
-You may obtain a copy of the License at
-
-    http://www.apache.org/licenses/LICENSE-2.0
-
-Unless required by applicable law or agreed to in writing, software
-distributed under the License is distributed on an "AS IS" BASIS,
-WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-See the License for the specific language governing permissions and
-limitations under the License.
-*/
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Package signature defines interfaces for a Signer and a PublicKey similarly to go/crypto standard package.
 package signature

From 668229e7a423392f7195c2aed40ec7f4eba6fd0f Mon Sep 17 00:00:00 2001
From: Gautam Botrel <gautam.botrel@gmail.com>
Date: Tue, 10 Dec 2024 14:46:46 -0600
Subject: [PATCH 094/114] docs: update element package doc (#572)

---
 ecc/bls12-377/fp/doc.go                           |  8 ++++++--
 ecc/bls12-377/fr/doc.go                           |  8 ++++++--
 ecc/bls12-381/fp/doc.go                           |  8 ++++++--
 ecc/bls12-381/fr/doc.go                           |  8 ++++++--
 ecc/bls24-315/fp/doc.go                           |  8 ++++++--
 ecc/bls24-315/fr/doc.go                           |  8 ++++++--
 ecc/bls24-317/fp/doc.go                           |  8 ++++++--
 ecc/bls24-317/fr/doc.go                           |  8 ++++++--
 ecc/bn254/fp/doc.go                               |  8 ++++++--
 ecc/bn254/fr/doc.go                               |  8 ++++++--
 ecc/bw6-633/fp/doc.go                             |  8 ++++++--
 ecc/bw6-633/fr/doc.go                             |  8 ++++++--
 ecc/bw6-761/fp/doc.go                             |  8 ++++++--
 ecc/bw6-761/fr/doc.go                             |  8 ++++++--
 ecc/secp256k1/fp/doc.go                           |  8 ++++++--
 ecc/secp256k1/fr/doc.go                           |  8 ++++++--
 ecc/stark-curve/fp/doc.go                         |  8 ++++++--
 ecc/stark-curve/fr/doc.go                         |  8 ++++++--
 field/babybear/doc.go                             | 10 +++++++---
 field/generator/internal/templates/element/doc.go | 12 ++++++++----
 field/goldilocks/doc.go                           |  8 ++++++--
 field/koalabear/doc.go                            | 10 +++++++---
 22 files changed, 136 insertions(+), 48 deletions(-)

diff --git a/ecc/bls12-377/fp/doc.go b/ecc/bls12-377/fp/doc.go
index feeae6fb8f..9b31780d36 100644
--- a/ecc/bls12-377/fp/doc.go
+++ b/ecc/bls12-377/fp/doc.go
@@ -5,7 +5,9 @@
 
 // Package fp contains field arithmetic operations for modulus = 0x1ae3a4...000001.
 //
-// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@gnark/modular_multiplication)
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
+//
+// Additionally fp.Vector offers an API to manipulate []Element.
 //
 // The modulus is hardcoded in all the operations.
 //
@@ -38,5 +40,7 @@
 //
 // # Warning
 //
-// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+// There is no security guarantees such as constant time implementation or side-channel attack resistance.
+// This code is provided as-is. Partially audited, see https://github.com/Consensys/gnark/tree/master/audits
+// for more details.
 package fp
diff --git a/ecc/bls12-377/fr/doc.go b/ecc/bls12-377/fr/doc.go
index 0264190110..45501aa438 100644
--- a/ecc/bls12-377/fr/doc.go
+++ b/ecc/bls12-377/fr/doc.go
@@ -5,7 +5,9 @@
 
 // Package fr contains field arithmetic operations for modulus = 0x12ab65...000001.
 //
-// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@gnark/modular_multiplication)
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
+//
+// Additionally fr.Vector offers an API to manipulate []Element using AVX512 instructions if available.
 //
 // The modulus is hardcoded in all the operations.
 //
@@ -38,5 +40,7 @@
 //
 // # Warning
 //
-// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+// There is no security guarantees such as constant time implementation or side-channel attack resistance.
+// This code is provided as-is. Partially audited, see https://github.com/Consensys/gnark/tree/master/audits
+// for more details.
 package fr
diff --git a/ecc/bls12-381/fp/doc.go b/ecc/bls12-381/fp/doc.go
index 752d084ce1..1c2dab5466 100644
--- a/ecc/bls12-381/fp/doc.go
+++ b/ecc/bls12-381/fp/doc.go
@@ -5,7 +5,9 @@
 
 // Package fp contains field arithmetic operations for modulus = 0x1a0111...ffaaab.
 //
-// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@gnark/modular_multiplication)
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
+//
+// Additionally fp.Vector offers an API to manipulate []Element.
 //
 // The modulus is hardcoded in all the operations.
 //
@@ -38,5 +40,7 @@
 //
 // # Warning
 //
-// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+// There is no security guarantees such as constant time implementation or side-channel attack resistance.
+// This code is provided as-is. Partially audited, see https://github.com/Consensys/gnark/tree/master/audits
+// for more details.
 package fp
diff --git a/ecc/bls12-381/fr/doc.go b/ecc/bls12-381/fr/doc.go
index 09174a90f5..f7880aa698 100644
--- a/ecc/bls12-381/fr/doc.go
+++ b/ecc/bls12-381/fr/doc.go
@@ -5,7 +5,9 @@
 
 // Package fr contains field arithmetic operations for modulus = 0x73eda7...000001.
 //
-// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@gnark/modular_multiplication)
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
+//
+// Additionally fr.Vector offers an API to manipulate []Element using AVX512 instructions if available.
 //
 // The modulus is hardcoded in all the operations.
 //
@@ -38,5 +40,7 @@
 //
 // # Warning
 //
-// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+// There is no security guarantees such as constant time implementation or side-channel attack resistance.
+// This code is provided as-is. Partially audited, see https://github.com/Consensys/gnark/tree/master/audits
+// for more details.
 package fr
diff --git a/ecc/bls24-315/fp/doc.go b/ecc/bls24-315/fp/doc.go
index 3d963966ed..bb419e36d3 100644
--- a/ecc/bls24-315/fp/doc.go
+++ b/ecc/bls24-315/fp/doc.go
@@ -5,7 +5,9 @@
 
 // Package fp contains field arithmetic operations for modulus = 0x4c23a0...300001.
 //
-// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@gnark/modular_multiplication)
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
+//
+// Additionally fp.Vector offers an API to manipulate []Element.
 //
 // The modulus is hardcoded in all the operations.
 //
@@ -38,5 +40,7 @@
 //
 // # Warning
 //
-// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+// There is no security guarantees such as constant time implementation or side-channel attack resistance.
+// This code is provided as-is. Partially audited, see https://github.com/Consensys/gnark/tree/master/audits
+// for more details.
 package fp
diff --git a/ecc/bls24-315/fr/doc.go b/ecc/bls24-315/fr/doc.go
index cc2554feb3..ff95985edf 100644
--- a/ecc/bls24-315/fr/doc.go
+++ b/ecc/bls24-315/fr/doc.go
@@ -5,7 +5,9 @@
 
 // Package fr contains field arithmetic operations for modulus = 0x196dea...c00001.
 //
-// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@gnark/modular_multiplication)
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
+//
+// Additionally fr.Vector offers an API to manipulate []Element using AVX512 instructions if available.
 //
 // The modulus is hardcoded in all the operations.
 //
@@ -38,5 +40,7 @@
 //
 // # Warning
 //
-// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+// There is no security guarantees such as constant time implementation or side-channel attack resistance.
+// This code is provided as-is. Partially audited, see https://github.com/Consensys/gnark/tree/master/audits
+// for more details.
 package fr
diff --git a/ecc/bls24-317/fp/doc.go b/ecc/bls24-317/fp/doc.go
index 1e89d00a80..4fa34b745f 100644
--- a/ecc/bls24-317/fp/doc.go
+++ b/ecc/bls24-317/fp/doc.go
@@ -5,7 +5,9 @@
 
 // Package fp contains field arithmetic operations for modulus = 0x1058ca...ab2aab.
 //
-// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@gnark/modular_multiplication)
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
+//
+// Additionally fp.Vector offers an API to manipulate []Element.
 //
 // The modulus is hardcoded in all the operations.
 //
@@ -38,5 +40,7 @@
 //
 // # Warning
 //
-// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+// There is no security guarantees such as constant time implementation or side-channel attack resistance.
+// This code is provided as-is. Partially audited, see https://github.com/Consensys/gnark/tree/master/audits
+// for more details.
 package fp
diff --git a/ecc/bls24-317/fr/doc.go b/ecc/bls24-317/fr/doc.go
index 414b4e4577..16e760a47c 100644
--- a/ecc/bls24-317/fr/doc.go
+++ b/ecc/bls24-317/fr/doc.go
@@ -5,7 +5,9 @@
 
 // Package fr contains field arithmetic operations for modulus = 0x443f91...000001.
 //
-// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@gnark/modular_multiplication)
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
+//
+// Additionally fr.Vector offers an API to manipulate []Element using AVX512 instructions if available.
 //
 // The modulus is hardcoded in all the operations.
 //
@@ -38,5 +40,7 @@
 //
 // # Warning
 //
-// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+// There is no security guarantees such as constant time implementation or side-channel attack resistance.
+// This code is provided as-is. Partially audited, see https://github.com/Consensys/gnark/tree/master/audits
+// for more details.
 package fr
diff --git a/ecc/bn254/fp/doc.go b/ecc/bn254/fp/doc.go
index 5624ba2797..478c1f24dd 100644
--- a/ecc/bn254/fp/doc.go
+++ b/ecc/bn254/fp/doc.go
@@ -5,7 +5,9 @@
 
 // Package fp contains field arithmetic operations for modulus = 0x30644e...7cfd47.
 //
-// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@gnark/modular_multiplication)
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
+//
+// Additionally fp.Vector offers an API to manipulate []Element using AVX512 instructions if available.
 //
 // The modulus is hardcoded in all the operations.
 //
@@ -38,5 +40,7 @@
 //
 // # Warning
 //
-// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+// There is no security guarantees such as constant time implementation or side-channel attack resistance.
+// This code is provided as-is. Partially audited, see https://github.com/Consensys/gnark/tree/master/audits
+// for more details.
 package fp
diff --git a/ecc/bn254/fr/doc.go b/ecc/bn254/fr/doc.go
index d2c6e01857..0f4414a3a5 100644
--- a/ecc/bn254/fr/doc.go
+++ b/ecc/bn254/fr/doc.go
@@ -5,7 +5,9 @@
 
 // Package fr contains field arithmetic operations for modulus = 0x30644e...000001.
 //
-// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@gnark/modular_multiplication)
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
+//
+// Additionally fr.Vector offers an API to manipulate []Element using AVX512 instructions if available.
 //
 // The modulus is hardcoded in all the operations.
 //
@@ -38,5 +40,7 @@
 //
 // # Warning
 //
-// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+// There is no security guarantees such as constant time implementation or side-channel attack resistance.
+// This code is provided as-is. Partially audited, see https://github.com/Consensys/gnark/tree/master/audits
+// for more details.
 package fr
diff --git a/ecc/bw6-633/fp/doc.go b/ecc/bw6-633/fp/doc.go
index efda77a4cf..acb2269c30 100644
--- a/ecc/bw6-633/fp/doc.go
+++ b/ecc/bw6-633/fp/doc.go
@@ -5,7 +5,9 @@
 
 // Package fp contains field arithmetic operations for modulus = 0x126633...70000d.
 //
-// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@gnark/modular_multiplication)
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
+//
+// Additionally fp.Vector offers an API to manipulate []Element.
 //
 // The modulus is hardcoded in all the operations.
 //
@@ -38,5 +40,7 @@
 //
 // # Warning
 //
-// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+// There is no security guarantees such as constant time implementation or side-channel attack resistance.
+// This code is provided as-is. Partially audited, see https://github.com/Consensys/gnark/tree/master/audits
+// for more details.
 package fp
diff --git a/ecc/bw6-633/fr/doc.go b/ecc/bw6-633/fr/doc.go
index 5adacadee4..af16db2498 100644
--- a/ecc/bw6-633/fr/doc.go
+++ b/ecc/bw6-633/fr/doc.go
@@ -5,7 +5,9 @@
 
 // Package fr contains field arithmetic operations for modulus = 0x4c23a0...300001.
 //
-// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@gnark/modular_multiplication)
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
+//
+// Additionally fr.Vector offers an API to manipulate []Element.
 //
 // The modulus is hardcoded in all the operations.
 //
@@ -38,5 +40,7 @@
 //
 // # Warning
 //
-// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+// There is no security guarantees such as constant time implementation or side-channel attack resistance.
+// This code is provided as-is. Partially audited, see https://github.com/Consensys/gnark/tree/master/audits
+// for more details.
 package fr
diff --git a/ecc/bw6-761/fp/doc.go b/ecc/bw6-761/fp/doc.go
index c682d8d668..8b1c7f5d5e 100644
--- a/ecc/bw6-761/fp/doc.go
+++ b/ecc/bw6-761/fp/doc.go
@@ -5,7 +5,9 @@
 
 // Package fp contains field arithmetic operations for modulus = 0x122e82...00008b.
 //
-// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@gnark/modular_multiplication)
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
+//
+// Additionally fp.Vector offers an API to manipulate []Element.
 //
 // The modulus is hardcoded in all the operations.
 //
@@ -38,5 +40,7 @@
 //
 // # Warning
 //
-// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+// There is no security guarantees such as constant time implementation or side-channel attack resistance.
+// This code is provided as-is. Partially audited, see https://github.com/Consensys/gnark/tree/master/audits
+// for more details.
 package fp
diff --git a/ecc/bw6-761/fr/doc.go b/ecc/bw6-761/fr/doc.go
index 277ef9945a..d7af83c91e 100644
--- a/ecc/bw6-761/fr/doc.go
+++ b/ecc/bw6-761/fr/doc.go
@@ -5,7 +5,9 @@
 
 // Package fr contains field arithmetic operations for modulus = 0x1ae3a4...000001.
 //
-// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@gnark/modular_multiplication)
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
+//
+// Additionally fr.Vector offers an API to manipulate []Element.
 //
 // The modulus is hardcoded in all the operations.
 //
@@ -38,5 +40,7 @@
 //
 // # Warning
 //
-// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+// There is no security guarantees such as constant time implementation or side-channel attack resistance.
+// This code is provided as-is. Partially audited, see https://github.com/Consensys/gnark/tree/master/audits
+// for more details.
 package fr
diff --git a/ecc/secp256k1/fp/doc.go b/ecc/secp256k1/fp/doc.go
index 8e971a67c7..a7dfcff36c 100644
--- a/ecc/secp256k1/fp/doc.go
+++ b/ecc/secp256k1/fp/doc.go
@@ -5,7 +5,9 @@
 
 // Package fp contains field arithmetic operations for modulus = 0xffffff...fffc2f.
 //
-// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@gnark/modular_multiplication)
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
+//
+// Additionally fp.Vector offers an API to manipulate []Element.
 //
 // The modulus is hardcoded in all the operations.
 //
@@ -38,5 +40,7 @@
 //
 // # Warning
 //
-// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+// There is no security guarantees such as constant time implementation or side-channel attack resistance.
+// This code is provided as-is. Partially audited, see https://github.com/Consensys/gnark/tree/master/audits
+// for more details.
 package fp
diff --git a/ecc/secp256k1/fr/doc.go b/ecc/secp256k1/fr/doc.go
index a03aa7a3d7..5a59e09001 100644
--- a/ecc/secp256k1/fr/doc.go
+++ b/ecc/secp256k1/fr/doc.go
@@ -5,7 +5,9 @@
 
 // Package fr contains field arithmetic operations for modulus = 0xffffff...364141.
 //
-// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@gnark/modular_multiplication)
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
+//
+// Additionally fr.Vector offers an API to manipulate []Element.
 //
 // The modulus is hardcoded in all the operations.
 //
@@ -38,5 +40,7 @@
 //
 // # Warning
 //
-// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+// There is no security guarantees such as constant time implementation or side-channel attack resistance.
+// This code is provided as-is. Partially audited, see https://github.com/Consensys/gnark/tree/master/audits
+// for more details.
 package fr
diff --git a/ecc/stark-curve/fp/doc.go b/ecc/stark-curve/fp/doc.go
index 6c6ae3e577..b789d5224d 100644
--- a/ecc/stark-curve/fp/doc.go
+++ b/ecc/stark-curve/fp/doc.go
@@ -5,7 +5,9 @@
 
 // Package fp contains field arithmetic operations for modulus = 0x800000...000001.
 //
-// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@gnark/modular_multiplication)
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
+//
+// Additionally fp.Vector offers an API to manipulate []Element using AVX512 instructions if available.
 //
 // The modulus is hardcoded in all the operations.
 //
@@ -38,5 +40,7 @@
 //
 // # Warning
 //
-// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+// There is no security guarantees such as constant time implementation or side-channel attack resistance.
+// This code is provided as-is. Partially audited, see https://github.com/Consensys/gnark/tree/master/audits
+// for more details.
 package fp
diff --git a/ecc/stark-curve/fr/doc.go b/ecc/stark-curve/fr/doc.go
index 3025d16c07..483d069817 100644
--- a/ecc/stark-curve/fr/doc.go
+++ b/ecc/stark-curve/fr/doc.go
@@ -5,7 +5,9 @@
 
 // Package fr contains field arithmetic operations for modulus = 0x800000...c64d2f.
 //
-// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@gnark/modular_multiplication)
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
+//
+// Additionally fr.Vector offers an API to manipulate []Element using AVX512 instructions if available.
 //
 // The modulus is hardcoded in all the operations.
 //
@@ -38,5 +40,7 @@
 //
 // # Warning
 //
-// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+// There is no security guarantees such as constant time implementation or side-channel attack resistance.
+// This code is provided as-is. Partially audited, see https://github.com/Consensys/gnark/tree/master/audits
+// for more details.
 package fr
diff --git a/field/babybear/doc.go b/field/babybear/doc.go
index a0517f38d9..6a59371928 100644
--- a/field/babybear/doc.go
+++ b/field/babybear/doc.go
@@ -5,13 +5,15 @@
 
 // Package babybear contains field arithmetic operations for modulus = 0x78000001.
 //
-// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@gnark/modular_multiplication)
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
+//
+// Additionally babybear.Vector offers an API to manipulate []Element.
 //
 // The modulus is hardcoded in all the operations.
 //
 // Field elements are represented as an array, and assumed to be in Montgomery form in all methods:
 //
-//	type Element [1]uint64
+//	type Element [1]uint32
 //
 // # Usage
 //
@@ -38,5 +40,7 @@
 //
 // # Warning
 //
-// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+// There is no security guarantees such as constant time implementation or side-channel attack resistance.
+// This code is provided as-is. Partially audited, see https://github.com/Consensys/gnark/tree/master/audits
+// for more details.
 package babybear
diff --git a/field/generator/internal/templates/element/doc.go b/field/generator/internal/templates/element/doc.go
index 6b25db8755..8c6d17d357 100644
--- a/field/generator/internal/templates/element/doc.go
+++ b/field/generator/internal/templates/element/doc.go
@@ -3,12 +3,14 @@ package element
 const Doc = `
 // Package {{.PackageName}} contains field arithmetic operations for modulus = 0x{{shorten .ModulusHex}}.
 // 
-// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@gnark/modular_multiplication)
-// 
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x). 
+//
+// Additionally {{.PackageName}}.Vector offers an API to manipulate []{{.ElementName}}{{- if .GenerateVectorOpsAMD64}} using AVX512{{- if .GenerateVectorOpsARM64}}/NEON{{- end}} instructions if available{{- end}}.
+//
 // The modulus is hardcoded in all the operations.
 // 
 // Field elements are represented as an array, and assumed to be in Montgomery form in all methods:
-// 	type {{.ElementName}} [{{.NbWords}}]uint64
+// 	type {{.ElementName}} [{{.NbWords}}]{{.Word.TypeLower}}
 //
 // Usage
 //
@@ -33,6 +35,8 @@ const Doc = `
 //
 // Warning
 //
-// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+// There is no security guarantees such as constant time implementation or side-channel attack resistance.
+// This code is provided as-is. Partially audited, see https://github.com/Consensys/gnark/tree/master/audits
+// for more details.
 package {{.PackageName}}
 `
diff --git a/field/goldilocks/doc.go b/field/goldilocks/doc.go
index 7ed505e777..f122fa27df 100644
--- a/field/goldilocks/doc.go
+++ b/field/goldilocks/doc.go
@@ -5,7 +5,9 @@
 
 // Package goldilocks contains field arithmetic operations for modulus = 0xffffff...000001.
 //
-// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@gnark/modular_multiplication)
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
+//
+// Additionally goldilocks.Vector offers an API to manipulate []Element.
 //
 // The modulus is hardcoded in all the operations.
 //
@@ -38,5 +40,7 @@
 //
 // # Warning
 //
-// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+// There is no security guarantees such as constant time implementation or side-channel attack resistance.
+// This code is provided as-is. Partially audited, see https://github.com/Consensys/gnark/tree/master/audits
+// for more details.
 package goldilocks
diff --git a/field/koalabear/doc.go b/field/koalabear/doc.go
index b60c389776..4abddfb000 100644
--- a/field/koalabear/doc.go
+++ b/field/koalabear/doc.go
@@ -5,13 +5,15 @@
 
 // Package koalabear contains field arithmetic operations for modulus = 0x7f000001.
 //
-// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@gnark/modular_multiplication)
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
+//
+// Additionally koalabear.Vector offers an API to manipulate []Element.
 //
 // The modulus is hardcoded in all the operations.
 //
 // Field elements are represented as an array, and assumed to be in Montgomery form in all methods:
 //
-//	type Element [1]uint64
+//	type Element [1]uint32
 //
 // # Usage
 //
@@ -38,5 +40,7 @@
 //
 // # Warning
 //
-// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
+// There is no security guarantees such as constant time implementation or side-channel attack resistance.
+// This code is provided as-is. Partially audited, see https://github.com/Consensys/gnark/tree/master/audits
+// for more details.
 package koalabear

From be3c2bbb17242a9da48fbb52857f5ad9fc4ec38d Mon Sep 17 00:00:00 2001
From: Ivo Kubjas <ivo.kubjas@consensys.net>
Date: Wed, 11 Dec 2024 09:32:39 +0100
Subject: [PATCH 095/114] feat: hash registry with statestorer (#564)

Co-authored-by: AlexandreBelling <alexandrebelling8@gmail.com>
---
 ecc/bls12-377/fr/mimc/mimc.go                 |  42 +++++-
 ecc/bls12-377/fr/mimc/mimc_test.go            | 120 ++++++++++++++++++
 .../twistededwards/eddsa/eddsa_test.go        |   3 +-
 .../bandersnatch/eddsa/eddsa_test.go          |   3 +-
 ecc/bls12-381/fr/mimc/mimc.go                 |  42 +++++-
 ecc/bls12-381/fr/mimc/mimc_test.go            | 120 ++++++++++++++++++
 .../twistededwards/eddsa/eddsa_test.go        |   3 +-
 ecc/bls24-315/fr/mimc/mimc.go                 |  42 +++++-
 ecc/bls24-315/fr/mimc/mimc_test.go            | 120 ++++++++++++++++++
 .../twistededwards/eddsa/eddsa_test.go        |   3 +-
 ecc/bls24-317/fr/mimc/mimc.go                 |  42 +++++-
 ecc/bls24-317/fr/mimc/mimc_test.go            | 120 ++++++++++++++++++
 .../twistededwards/eddsa/eddsa_test.go        |   3 +-
 ecc/bn254/fr/mimc/mimc.go                     |  42 +++++-
 ecc/bn254/fr/mimc/mimc_test.go                |  47 +++++++
 ecc/bn254/twistededwards/eddsa/eddsa_test.go  |   3 +-
 ecc/bw6-633/fr/mimc/mimc.go                   |  42 +++++-
 ecc/bw6-633/fr/mimc/mimc_test.go              | 120 ++++++++++++++++++
 .../twistededwards/eddsa/eddsa_test.go        |   3 +-
 ecc/bw6-761/fr/mimc/mimc.go                   |  42 +++++-
 ecc/bw6-761/fr/mimc/mimc_test.go              | 120 ++++++++++++++++++
 .../twistededwards/eddsa/eddsa_test.go        |   3 +-
 hash/all/allhashes.go                         |  11 ++
 hash/doc.go                                   |  19 +++
 hash/hashes.go                                |  76 ++++++-----
 hash/interface.go                             |  16 +++
 .../generator/crypto/hash/mimc/generate.go    |  16 ++-
 .../crypto/hash/mimc/template/mimc.go.tmpl    |  42 +++++-
 .../mimc/template/tests/mimc_test.go.tmpl     | 114 +++++++++++++++++
 .../edwards/eddsa/template/eddsa.test.go.tmpl |   3 +-
 30 files changed, 1293 insertions(+), 89 deletions(-)
 create mode 100644 ecc/bls12-377/fr/mimc/mimc_test.go
 create mode 100644 ecc/bls12-381/fr/mimc/mimc_test.go
 create mode 100644 ecc/bls24-315/fr/mimc/mimc_test.go
 create mode 100644 ecc/bls24-317/fr/mimc/mimc_test.go
 create mode 100644 ecc/bw6-633/fr/mimc/mimc_test.go
 create mode 100644 ecc/bw6-761/fr/mimc/mimc_test.go
 create mode 100644 hash/all/allhashes.go
 create mode 100644 hash/interface.go
 create mode 100644 internal/generator/crypto/hash/mimc/template/tests/mimc_test.go.tmpl

diff --git a/ecc/bls12-377/fr/mimc/mimc.go b/ecc/bls12-377/fr/mimc/mimc.go
index 2855e3ab8e..43728abd36 100644
--- a/ecc/bls12-377/fr/mimc/mimc.go
+++ b/ecc/bls12-377/fr/mimc/mimc.go
@@ -7,14 +7,22 @@ package mimc
 
 import (
 	"errors"
-	"hash"
+	stdhash "hash"
+	"math/big"
+	"sync"
 
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
+	"github.com/consensys/gnark-crypto/hash"
+
 	"golang.org/x/crypto/sha3"
-	"math/big"
-	"sync"
 )
 
+func init() {
+	hash.RegisterHash(hash.MIMC_BLS12_377, func() stdhash.Hash {
+		return NewMiMC()
+	})
+}
+
 const (
 	mimcNbRounds = 62
 	seed         = "seed"   // seed to derive the constants
@@ -45,8 +53,8 @@ func GetConstants() []big.Int {
 	return res
 }
 
-// NewMiMC returns a MiMCImpl object, pure-go reference implementation
-func NewMiMC(opts ...Option) hash.Hash {
+// NewMiMC returns a MiMC implementation, pure Go reference implementation.
+func NewMiMC(opts ...Option) hash.StateStorer {
 	d := new(digest)
 	d.Reset()
 	cfg := mimcOptions(opts...)
@@ -193,3 +201,27 @@ func (d *digest) WriteString(rawBytes []byte) error {
 	}
 	return nil
 }
+
+// SetState manually sets the state of the hasher to an user-provided value. In
+// the context of MiMC, the method expects a byte slice of 32 elements.
+func (d *digest) SetState(newState []byte) error {
+
+	if len(newState) != 32 {
+		return errors.New("the mimc state expects a state of 32 bytes")
+	}
+
+	if err := d.h.SetBytesCanonical(newState); err != nil {
+		return errors.New("the provided newState does not represent a valid state")
+	}
+
+	d.data = nil
+
+	return nil
+}
+
+// State returns the internal state of the hasher
+func (d *digest) State() []byte {
+	_ = d.Sum(nil) // this flushes the hasher
+	b := d.h.Bytes()
+	return b[:]
+}
diff --git a/ecc/bls12-377/fr/mimc/mimc_test.go b/ecc/bls12-377/fr/mimc/mimc_test.go
new file mode 100644
index 0000000000..b018112257
--- /dev/null
+++ b/ecc/bls12-377/fr/mimc/mimc_test.go
@@ -0,0 +1,120 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package mimc_test
+
+import (
+	"bytes"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr/mimc"
+	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
+
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+func TestMiMCFiatShamir(t *testing.T) {
+	fs := fiatshamir.NewTranscript(mimc.NewMiMC(), "c0")
+	zero := make([]byte, mimc.BlockSize)
+	err := fs.Bind("c0", zero)
+	assert.NoError(t, err)
+	_, err = fs.ComputeChallenge("c0")
+	assert.NoError(t, err)
+}
+
+func TestByteOrder(t *testing.T) {
+	assert := require.New(t)
+
+	var buf [fr.Bytes]byte
+	// if the 31 first bytes are FF, it's a valid FF in little endian, but not in big endian
+	for i := 0; i < fr.Bytes-1; i++ {
+		buf[i] = 0xFF
+	}
+	_, err := fr.BigEndian.Element(&buf)
+	assert.Error(err)
+	_, err = fr.LittleEndian.Element(&buf)
+	assert.NoError(err)
+
+	{
+		// hashing buf with big endian should fail
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.BigEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.Error(err)
+	}
+
+	{
+		// hashing buf with little endian should succeed
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.LittleEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.NoError(err)
+	}
+
+	buf = [fr.Bytes]byte{}
+	// if the 31 bytes are FF, it's a valid FF in big endian, but not in little endian
+	for i := 1; i < fr.Bytes; i++ {
+		buf[i] = 0xFF
+	}
+	_, err = fr.BigEndian.Element(&buf)
+	assert.NoError(err)
+	_, err = fr.LittleEndian.Element(&buf)
+	assert.Error(err)
+
+	{
+		// hashing buf with big endian should succeed
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.BigEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.NoError(err)
+	}
+
+	{
+		// hashing buf with little endian should fail
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.LittleEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.Error(err)
+	}
+}
+
+func TestSetState(t *testing.T) {
+	// we use for hashing and retrieving the state
+	h1 := mimc.NewMiMC()
+	// only hashing
+	h2 := mimc.NewMiMC()
+	// we use for restoring from state
+	h3 := mimc.NewMiMC()
+
+	randInputs := make([]fr.Element, 10)
+	for i := range randInputs {
+		randInputs[i].SetRandom()
+	}
+
+	storedStates := make([][]byte, len(randInputs))
+
+	for i := range randInputs {
+		storedStates[i] = h1.State()
+
+		h1.Write(randInputs[i].Marshal())
+		h2.Write(randInputs[i].Marshal())
+	}
+	dgst1 := h1.Sum(nil)
+	dgst2 := h2.Sum(nil)
+	if !bytes.Equal(dgst1, dgst2) {
+		t.Fatal("hashes do not match")
+	}
+
+	for i := range storedStates {
+		if err := h3.SetState(storedStates[i]); err != nil {
+			t.Fatal(err)
+		}
+		for j := i; j < len(randInputs); j++ {
+			h3.Write(randInputs[j].Marshal())
+		}
+		dgst3 := h3.Sum(nil)
+		if !bytes.Equal(dgst1, dgst3) {
+			t.Fatal("hashes do not match")
+		}
+	}
+}
diff --git a/ecc/bls12-377/twistededwards/eddsa/eddsa_test.go b/ecc/bls12-377/twistededwards/eddsa/eddsa_test.go
index 09413696d2..4f79ebdf65 100644
--- a/ecc/bls12-377/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bls12-377/twistededwards/eddsa/eddsa_test.go
@@ -16,13 +16,14 @@ import (
 	"fmt"
 
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr/mimc"
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/twistededwards"
 	"github.com/consensys/gnark-crypto/hash"
 )
 
 func Example() {
 	// instantiate hash function
-	hFunc := hash.MIMC_BLS12_377.New()
+	hFunc := mimc.NewMiMC()
 
 	// create a eddsa key pair
 	privateKey, _ := GenerateKey(crand.Reader)
diff --git a/ecc/bls12-381/bandersnatch/eddsa/eddsa_test.go b/ecc/bls12-381/bandersnatch/eddsa/eddsa_test.go
index cccc545ff7..c53bfc6cc8 100644
--- a/ecc/bls12-381/bandersnatch/eddsa/eddsa_test.go
+++ b/ecc/bls12-381/bandersnatch/eddsa/eddsa_test.go
@@ -16,13 +16,14 @@ import (
 	"fmt"
 
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr/mimc"
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/twistededwards"
 	"github.com/consensys/gnark-crypto/hash"
 )
 
 func Example() {
 	// instantiate hash function
-	hFunc := hash.MIMC_BLS12_381.New()
+	hFunc := mimc.NewMiMC()
 
 	// create a eddsa key pair
 	privateKey, _ := GenerateKey(crand.Reader)
diff --git a/ecc/bls12-381/fr/mimc/mimc.go b/ecc/bls12-381/fr/mimc/mimc.go
index 59899b3e92..6db9581b75 100644
--- a/ecc/bls12-381/fr/mimc/mimc.go
+++ b/ecc/bls12-381/fr/mimc/mimc.go
@@ -7,14 +7,22 @@ package mimc
 
 import (
 	"errors"
-	"hash"
+	stdhash "hash"
+	"math/big"
+	"sync"
 
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
+	"github.com/consensys/gnark-crypto/hash"
+
 	"golang.org/x/crypto/sha3"
-	"math/big"
-	"sync"
 )
 
+func init() {
+	hash.RegisterHash(hash.MIMC_BLS12_381, func() stdhash.Hash {
+		return NewMiMC()
+	})
+}
+
 const (
 	mimcNbRounds = 111
 	seed         = "seed"   // seed to derive the constants
@@ -45,8 +53,8 @@ func GetConstants() []big.Int {
 	return res
 }
 
-// NewMiMC returns a MiMCImpl object, pure-go reference implementation
-func NewMiMC(opts ...Option) hash.Hash {
+// NewMiMC returns a MiMC implementation, pure Go reference implementation.
+func NewMiMC(opts ...Option) hash.StateStorer {
 	d := new(digest)
 	d.Reset()
 	cfg := mimcOptions(opts...)
@@ -191,3 +199,27 @@ func (d *digest) WriteString(rawBytes []byte) error {
 	}
 	return nil
 }
+
+// SetState manually sets the state of the hasher to an user-provided value. In
+// the context of MiMC, the method expects a byte slice of 32 elements.
+func (d *digest) SetState(newState []byte) error {
+
+	if len(newState) != 32 {
+		return errors.New("the mimc state expects a state of 32 bytes")
+	}
+
+	if err := d.h.SetBytesCanonical(newState); err != nil {
+		return errors.New("the provided newState does not represent a valid state")
+	}
+
+	d.data = nil
+
+	return nil
+}
+
+// State returns the internal state of the hasher
+func (d *digest) State() []byte {
+	_ = d.Sum(nil) // this flushes the hasher
+	b := d.h.Bytes()
+	return b[:]
+}
diff --git a/ecc/bls12-381/fr/mimc/mimc_test.go b/ecc/bls12-381/fr/mimc/mimc_test.go
new file mode 100644
index 0000000000..b8b94cc1ea
--- /dev/null
+++ b/ecc/bls12-381/fr/mimc/mimc_test.go
@@ -0,0 +1,120 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package mimc_test
+
+import (
+	"bytes"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr/mimc"
+	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
+
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+func TestMiMCFiatShamir(t *testing.T) {
+	fs := fiatshamir.NewTranscript(mimc.NewMiMC(), "c0")
+	zero := make([]byte, mimc.BlockSize)
+	err := fs.Bind("c0", zero)
+	assert.NoError(t, err)
+	_, err = fs.ComputeChallenge("c0")
+	assert.NoError(t, err)
+}
+
+func TestByteOrder(t *testing.T) {
+	assert := require.New(t)
+
+	var buf [fr.Bytes]byte
+	// if the 31 first bytes are FF, it's a valid FF in little endian, but not in big endian
+	for i := 0; i < fr.Bytes-1; i++ {
+		buf[i] = 0xFF
+	}
+	_, err := fr.BigEndian.Element(&buf)
+	assert.Error(err)
+	_, err = fr.LittleEndian.Element(&buf)
+	assert.NoError(err)
+
+	{
+		// hashing buf with big endian should fail
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.BigEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.Error(err)
+	}
+
+	{
+		// hashing buf with little endian should succeed
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.LittleEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.NoError(err)
+	}
+
+	buf = [fr.Bytes]byte{}
+	// if the 31 bytes are FF, it's a valid FF in big endian, but not in little endian
+	for i := 1; i < fr.Bytes; i++ {
+		buf[i] = 0xFF
+	}
+	_, err = fr.BigEndian.Element(&buf)
+	assert.NoError(err)
+	_, err = fr.LittleEndian.Element(&buf)
+	assert.Error(err)
+
+	{
+		// hashing buf with big endian should succeed
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.BigEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.NoError(err)
+	}
+
+	{
+		// hashing buf with little endian should fail
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.LittleEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.Error(err)
+	}
+}
+
+func TestSetState(t *testing.T) {
+	// we use for hashing and retrieving the state
+	h1 := mimc.NewMiMC()
+	// only hashing
+	h2 := mimc.NewMiMC()
+	// we use for restoring from state
+	h3 := mimc.NewMiMC()
+
+	randInputs := make([]fr.Element, 10)
+	for i := range randInputs {
+		randInputs[i].SetRandom()
+	}
+
+	storedStates := make([][]byte, len(randInputs))
+
+	for i := range randInputs {
+		storedStates[i] = h1.State()
+
+		h1.Write(randInputs[i].Marshal())
+		h2.Write(randInputs[i].Marshal())
+	}
+	dgst1 := h1.Sum(nil)
+	dgst2 := h2.Sum(nil)
+	if !bytes.Equal(dgst1, dgst2) {
+		t.Fatal("hashes do not match")
+	}
+
+	for i := range storedStates {
+		if err := h3.SetState(storedStates[i]); err != nil {
+			t.Fatal(err)
+		}
+		for j := i; j < len(randInputs); j++ {
+			h3.Write(randInputs[j].Marshal())
+		}
+		dgst3 := h3.Sum(nil)
+		if !bytes.Equal(dgst1, dgst3) {
+			t.Fatal("hashes do not match")
+		}
+	}
+}
diff --git a/ecc/bls12-381/twistededwards/eddsa/eddsa_test.go b/ecc/bls12-381/twistededwards/eddsa/eddsa_test.go
index cccc545ff7..c53bfc6cc8 100644
--- a/ecc/bls12-381/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bls12-381/twistededwards/eddsa/eddsa_test.go
@@ -16,13 +16,14 @@ import (
 	"fmt"
 
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr/mimc"
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/twistededwards"
 	"github.com/consensys/gnark-crypto/hash"
 )
 
 func Example() {
 	// instantiate hash function
-	hFunc := hash.MIMC_BLS12_381.New()
+	hFunc := mimc.NewMiMC()
 
 	// create a eddsa key pair
 	privateKey, _ := GenerateKey(crand.Reader)
diff --git a/ecc/bls24-315/fr/mimc/mimc.go b/ecc/bls24-315/fr/mimc/mimc.go
index c91ead0218..7f1ab7c7e8 100644
--- a/ecc/bls24-315/fr/mimc/mimc.go
+++ b/ecc/bls24-315/fr/mimc/mimc.go
@@ -7,14 +7,22 @@ package mimc
 
 import (
 	"errors"
-	"hash"
+	stdhash "hash"
+	"math/big"
+	"sync"
 
 	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
+	"github.com/consensys/gnark-crypto/hash"
+
 	"golang.org/x/crypto/sha3"
-	"math/big"
-	"sync"
 )
 
+func init() {
+	hash.RegisterHash(hash.MIMC_BLS24_315, func() stdhash.Hash {
+		return NewMiMC()
+	})
+}
+
 const (
 	mimcNbRounds = 109
 	seed         = "seed"   // seed to derive the constants
@@ -45,8 +53,8 @@ func GetConstants() []big.Int {
 	return res
 }
 
-// NewMiMC returns a MiMCImpl object, pure-go reference implementation
-func NewMiMC(opts ...Option) hash.Hash {
+// NewMiMC returns a MiMC implementation, pure Go reference implementation.
+func NewMiMC(opts ...Option) hash.StateStorer {
 	d := new(digest)
 	d.Reset()
 	cfg := mimcOptions(opts...)
@@ -191,3 +199,27 @@ func (d *digest) WriteString(rawBytes []byte) error {
 	}
 	return nil
 }
+
+// SetState manually sets the state of the hasher to an user-provided value. In
+// the context of MiMC, the method expects a byte slice of 32 elements.
+func (d *digest) SetState(newState []byte) error {
+
+	if len(newState) != 32 {
+		return errors.New("the mimc state expects a state of 32 bytes")
+	}
+
+	if err := d.h.SetBytesCanonical(newState); err != nil {
+		return errors.New("the provided newState does not represent a valid state")
+	}
+
+	d.data = nil
+
+	return nil
+}
+
+// State returns the internal state of the hasher
+func (d *digest) State() []byte {
+	_ = d.Sum(nil) // this flushes the hasher
+	b := d.h.Bytes()
+	return b[:]
+}
diff --git a/ecc/bls24-315/fr/mimc/mimc_test.go b/ecc/bls24-315/fr/mimc/mimc_test.go
new file mode 100644
index 0000000000..58aa9449fe
--- /dev/null
+++ b/ecc/bls24-315/fr/mimc/mimc_test.go
@@ -0,0 +1,120 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package mimc_test
+
+import (
+	"bytes"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr/mimc"
+	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
+
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+func TestMiMCFiatShamir(t *testing.T) {
+	fs := fiatshamir.NewTranscript(mimc.NewMiMC(), "c0")
+	zero := make([]byte, mimc.BlockSize)
+	err := fs.Bind("c0", zero)
+	assert.NoError(t, err)
+	_, err = fs.ComputeChallenge("c0")
+	assert.NoError(t, err)
+}
+
+func TestByteOrder(t *testing.T) {
+	assert := require.New(t)
+
+	var buf [fr.Bytes]byte
+	// if the 31 first bytes are FF, it's a valid FF in little endian, but not in big endian
+	for i := 0; i < fr.Bytes-1; i++ {
+		buf[i] = 0xFF
+	}
+	_, err := fr.BigEndian.Element(&buf)
+	assert.Error(err)
+	_, err = fr.LittleEndian.Element(&buf)
+	assert.NoError(err)
+
+	{
+		// hashing buf with big endian should fail
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.BigEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.Error(err)
+	}
+
+	{
+		// hashing buf with little endian should succeed
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.LittleEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.NoError(err)
+	}
+
+	buf = [fr.Bytes]byte{}
+	// if the 31 bytes are FF, it's a valid FF in big endian, but not in little endian
+	for i := 1; i < fr.Bytes; i++ {
+		buf[i] = 0xFF
+	}
+	_, err = fr.BigEndian.Element(&buf)
+	assert.NoError(err)
+	_, err = fr.LittleEndian.Element(&buf)
+	assert.Error(err)
+
+	{
+		// hashing buf with big endian should succeed
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.BigEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.NoError(err)
+	}
+
+	{
+		// hashing buf with little endian should fail
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.LittleEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.Error(err)
+	}
+}
+
+func TestSetState(t *testing.T) {
+	// we use for hashing and retrieving the state
+	h1 := mimc.NewMiMC()
+	// only hashing
+	h2 := mimc.NewMiMC()
+	// we use for restoring from state
+	h3 := mimc.NewMiMC()
+
+	randInputs := make([]fr.Element, 10)
+	for i := range randInputs {
+		randInputs[i].SetRandom()
+	}
+
+	storedStates := make([][]byte, len(randInputs))
+
+	for i := range randInputs {
+		storedStates[i] = h1.State()
+
+		h1.Write(randInputs[i].Marshal())
+		h2.Write(randInputs[i].Marshal())
+	}
+	dgst1 := h1.Sum(nil)
+	dgst2 := h2.Sum(nil)
+	if !bytes.Equal(dgst1, dgst2) {
+		t.Fatal("hashes do not match")
+	}
+
+	for i := range storedStates {
+		if err := h3.SetState(storedStates[i]); err != nil {
+			t.Fatal(err)
+		}
+		for j := i; j < len(randInputs); j++ {
+			h3.Write(randInputs[j].Marshal())
+		}
+		dgst3 := h3.Sum(nil)
+		if !bytes.Equal(dgst1, dgst3) {
+			t.Fatal("hashes do not match")
+		}
+	}
+}
diff --git a/ecc/bls24-315/twistededwards/eddsa/eddsa_test.go b/ecc/bls24-315/twistededwards/eddsa/eddsa_test.go
index a08863e866..3954c0a991 100644
--- a/ecc/bls24-315/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bls24-315/twistededwards/eddsa/eddsa_test.go
@@ -16,13 +16,14 @@ import (
 	"fmt"
 
 	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr/mimc"
 	"github.com/consensys/gnark-crypto/ecc/bls24-315/twistededwards"
 	"github.com/consensys/gnark-crypto/hash"
 )
 
 func Example() {
 	// instantiate hash function
-	hFunc := hash.MIMC_BLS24_315.New()
+	hFunc := mimc.NewMiMC()
 
 	// create a eddsa key pair
 	privateKey, _ := GenerateKey(crand.Reader)
diff --git a/ecc/bls24-317/fr/mimc/mimc.go b/ecc/bls24-317/fr/mimc/mimc.go
index 4e5a82ccf7..c4ca3df7c1 100644
--- a/ecc/bls24-317/fr/mimc/mimc.go
+++ b/ecc/bls24-317/fr/mimc/mimc.go
@@ -7,14 +7,22 @@ package mimc
 
 import (
 	"errors"
-	"hash"
+	stdhash "hash"
+	"math/big"
+	"sync"
 
 	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
+	"github.com/consensys/gnark-crypto/hash"
+
 	"golang.org/x/crypto/sha3"
-	"math/big"
-	"sync"
 )
 
+func init() {
+	hash.RegisterHash(hash.MIMC_BLS24_317, func() stdhash.Hash {
+		return NewMiMC()
+	})
+}
+
 const (
 	mimcNbRounds = 91
 	seed         = "seed"   // seed to derive the constants
@@ -45,8 +53,8 @@ func GetConstants() []big.Int {
 	return res
 }
 
-// NewMiMC returns a MiMCImpl object, pure-go reference implementation
-func NewMiMC(opts ...Option) hash.Hash {
+// NewMiMC returns a MiMC implementation, pure Go reference implementation.
+func NewMiMC(opts ...Option) hash.StateStorer {
 	d := new(digest)
 	d.Reset()
 	cfg := mimcOptions(opts...)
@@ -193,3 +201,27 @@ func (d *digest) WriteString(rawBytes []byte) error {
 	}
 	return nil
 }
+
+// SetState manually sets the state of the hasher to an user-provided value. In
+// the context of MiMC, the method expects a byte slice of 32 elements.
+func (d *digest) SetState(newState []byte) error {
+
+	if len(newState) != 32 {
+		return errors.New("the mimc state expects a state of 32 bytes")
+	}
+
+	if err := d.h.SetBytesCanonical(newState); err != nil {
+		return errors.New("the provided newState does not represent a valid state")
+	}
+
+	d.data = nil
+
+	return nil
+}
+
+// State returns the internal state of the hasher
+func (d *digest) State() []byte {
+	_ = d.Sum(nil) // this flushes the hasher
+	b := d.h.Bytes()
+	return b[:]
+}
diff --git a/ecc/bls24-317/fr/mimc/mimc_test.go b/ecc/bls24-317/fr/mimc/mimc_test.go
new file mode 100644
index 0000000000..54f4ce08aa
--- /dev/null
+++ b/ecc/bls24-317/fr/mimc/mimc_test.go
@@ -0,0 +1,120 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package mimc_test
+
+import (
+	"bytes"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr/mimc"
+	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
+
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+func TestMiMCFiatShamir(t *testing.T) {
+	fs := fiatshamir.NewTranscript(mimc.NewMiMC(), "c0")
+	zero := make([]byte, mimc.BlockSize)
+	err := fs.Bind("c0", zero)
+	assert.NoError(t, err)
+	_, err = fs.ComputeChallenge("c0")
+	assert.NoError(t, err)
+}
+
+func TestByteOrder(t *testing.T) {
+	assert := require.New(t)
+
+	var buf [fr.Bytes]byte
+	// if the 31 first bytes are FF, it's a valid FF in little endian, but not in big endian
+	for i := 0; i < fr.Bytes-1; i++ {
+		buf[i] = 0xFF
+	}
+	_, err := fr.BigEndian.Element(&buf)
+	assert.Error(err)
+	_, err = fr.LittleEndian.Element(&buf)
+	assert.NoError(err)
+
+	{
+		// hashing buf with big endian should fail
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.BigEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.Error(err)
+	}
+
+	{
+		// hashing buf with little endian should succeed
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.LittleEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.NoError(err)
+	}
+
+	buf = [fr.Bytes]byte{}
+	// if the 31 bytes are FF, it's a valid FF in big endian, but not in little endian
+	for i := 1; i < fr.Bytes; i++ {
+		buf[i] = 0xFF
+	}
+	_, err = fr.BigEndian.Element(&buf)
+	assert.NoError(err)
+	_, err = fr.LittleEndian.Element(&buf)
+	assert.Error(err)
+
+	{
+		// hashing buf with big endian should succeed
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.BigEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.NoError(err)
+	}
+
+	{
+		// hashing buf with little endian should fail
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.LittleEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.Error(err)
+	}
+}
+
+func TestSetState(t *testing.T) {
+	// we use for hashing and retrieving the state
+	h1 := mimc.NewMiMC()
+	// only hashing
+	h2 := mimc.NewMiMC()
+	// we use for restoring from state
+	h3 := mimc.NewMiMC()
+
+	randInputs := make([]fr.Element, 10)
+	for i := range randInputs {
+		randInputs[i].SetRandom()
+	}
+
+	storedStates := make([][]byte, len(randInputs))
+
+	for i := range randInputs {
+		storedStates[i] = h1.State()
+
+		h1.Write(randInputs[i].Marshal())
+		h2.Write(randInputs[i].Marshal())
+	}
+	dgst1 := h1.Sum(nil)
+	dgst2 := h2.Sum(nil)
+	if !bytes.Equal(dgst1, dgst2) {
+		t.Fatal("hashes do not match")
+	}
+
+	for i := range storedStates {
+		if err := h3.SetState(storedStates[i]); err != nil {
+			t.Fatal(err)
+		}
+		for j := i; j < len(randInputs); j++ {
+			h3.Write(randInputs[j].Marshal())
+		}
+		dgst3 := h3.Sum(nil)
+		if !bytes.Equal(dgst1, dgst3) {
+			t.Fatal("hashes do not match")
+		}
+	}
+}
diff --git a/ecc/bls24-317/twistededwards/eddsa/eddsa_test.go b/ecc/bls24-317/twistededwards/eddsa/eddsa_test.go
index a045167a35..dc56916881 100644
--- a/ecc/bls24-317/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bls24-317/twistededwards/eddsa/eddsa_test.go
@@ -16,13 +16,14 @@ import (
 	"fmt"
 
 	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
+	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr/mimc"
 	"github.com/consensys/gnark-crypto/ecc/bls24-317/twistededwards"
 	"github.com/consensys/gnark-crypto/hash"
 )
 
 func Example() {
 	// instantiate hash function
-	hFunc := hash.MIMC_BLS24_317.New()
+	hFunc := mimc.NewMiMC()
 
 	// create a eddsa key pair
 	privateKey, _ := GenerateKey(crand.Reader)
diff --git a/ecc/bn254/fr/mimc/mimc.go b/ecc/bn254/fr/mimc/mimc.go
index f58fc6ef3b..f7fde2955e 100644
--- a/ecc/bn254/fr/mimc/mimc.go
+++ b/ecc/bn254/fr/mimc/mimc.go
@@ -7,14 +7,22 @@ package mimc
 
 import (
 	"errors"
-	"hash"
+	stdhash "hash"
+	"math/big"
+	"sync"
 
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
+	"github.com/consensys/gnark-crypto/hash"
+
 	"golang.org/x/crypto/sha3"
-	"math/big"
-	"sync"
 )
 
+func init() {
+	hash.RegisterHash(hash.MIMC_BN254, func() stdhash.Hash {
+		return NewMiMC()
+	})
+}
+
 const (
 	mimcNbRounds = 110
 	seed         = "seed"   // seed to derive the constants
@@ -45,8 +53,8 @@ func GetConstants() []big.Int {
 	return res
 }
 
-// NewMiMC returns a MiMCImpl object, pure-go reference implementation
-func NewMiMC(opts ...Option) hash.Hash {
+// NewMiMC returns a MiMC implementation, pure Go reference implementation.
+func NewMiMC(opts ...Option) hash.StateStorer {
 	d := new(digest)
 	d.Reset()
 	cfg := mimcOptions(opts...)
@@ -191,3 +199,27 @@ func (d *digest) WriteString(rawBytes []byte) error {
 	}
 	return nil
 }
+
+// SetState manually sets the state of the hasher to an user-provided value. In
+// the context of MiMC, the method expects a byte slice of 32 elements.
+func (d *digest) SetState(newState []byte) error {
+
+	if len(newState) != 32 {
+		return errors.New("the mimc state expects a state of 32 bytes")
+	}
+
+	if err := d.h.SetBytesCanonical(newState); err != nil {
+		return errors.New("the provided newState does not represent a valid state")
+	}
+
+	d.data = nil
+
+	return nil
+}
+
+// State returns the internal state of the hasher
+func (d *digest) State() []byte {
+	_ = d.Sum(nil) // this flushes the hasher
+	b := d.h.Bytes()
+	return b[:]
+}
diff --git a/ecc/bn254/fr/mimc/mimc_test.go b/ecc/bn254/fr/mimc/mimc_test.go
index 73042f6c31..1c0a7e4c5f 100644
--- a/ecc/bn254/fr/mimc/mimc_test.go
+++ b/ecc/bn254/fr/mimc/mimc_test.go
@@ -1,11 +1,18 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
 package mimc_test
 
 import (
+	"bytes"
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr/mimc"
 	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
+
 	"github.com/stretchr/testify/assert"
 	"github.com/stretchr/testify/require"
 )
@@ -69,5 +76,45 @@ func TestByteOrder(t *testing.T) {
 		_, err := mimcHash.Write(buf[:])
 		assert.Error(err)
 	}
+}
+
+func TestSetState(t *testing.T) {
+	// we use for hashing and retrieving the state
+	h1 := mimc.NewMiMC()
+	// only hashing
+	h2 := mimc.NewMiMC()
+	// we use for restoring from state
+	h3 := mimc.NewMiMC()
+
+	randInputs := make([]fr.Element, 10)
+	for i := range randInputs {
+		randInputs[i].SetRandom()
+	}
 
+	storedStates := make([][]byte, len(randInputs))
+
+	for i := range randInputs {
+		storedStates[i] = h1.State()
+
+		h1.Write(randInputs[i].Marshal())
+		h2.Write(randInputs[i].Marshal())
+	}
+	dgst1 := h1.Sum(nil)
+	dgst2 := h2.Sum(nil)
+	if !bytes.Equal(dgst1, dgst2) {
+		t.Fatal("hashes do not match")
+	}
+
+	for i := range storedStates {
+		if err := h3.SetState(storedStates[i]); err != nil {
+			t.Fatal(err)
+		}
+		for j := i; j < len(randInputs); j++ {
+			h3.Write(randInputs[j].Marshal())
+		}
+		dgst3 := h3.Sum(nil)
+		if !bytes.Equal(dgst1, dgst3) {
+			t.Fatal("hashes do not match")
+		}
+	}
 }
diff --git a/ecc/bn254/twistededwards/eddsa/eddsa_test.go b/ecc/bn254/twistededwards/eddsa/eddsa_test.go
index 16f6511f46..f817340864 100644
--- a/ecc/bn254/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bn254/twistededwards/eddsa/eddsa_test.go
@@ -16,13 +16,14 @@ import (
 	"fmt"
 
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
+	"github.com/consensys/gnark-crypto/ecc/bn254/fr/mimc"
 	"github.com/consensys/gnark-crypto/ecc/bn254/twistededwards"
 	"github.com/consensys/gnark-crypto/hash"
 )
 
 func Example() {
 	// instantiate hash function
-	hFunc := hash.MIMC_BN254.New()
+	hFunc := mimc.NewMiMC()
 
 	// create a eddsa key pair
 	privateKey, _ := GenerateKey(crand.Reader)
diff --git a/ecc/bw6-633/fr/mimc/mimc.go b/ecc/bw6-633/fr/mimc/mimc.go
index 3ed4a8a714..f9665cf347 100644
--- a/ecc/bw6-633/fr/mimc/mimc.go
+++ b/ecc/bw6-633/fr/mimc/mimc.go
@@ -7,14 +7,22 @@ package mimc
 
 import (
 	"errors"
-	"hash"
+	stdhash "hash"
+	"math/big"
+	"sync"
 
 	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
+	"github.com/consensys/gnark-crypto/hash"
+
 	"golang.org/x/crypto/sha3"
-	"math/big"
-	"sync"
 )
 
+func init() {
+	hash.RegisterHash(hash.MIMC_BW6_633, func() stdhash.Hash {
+		return NewMiMC()
+	})
+}
+
 const (
 	mimcNbRounds = 136
 	seed         = "seed"   // seed to derive the constants
@@ -45,8 +53,8 @@ func GetConstants() []big.Int {
 	return res
 }
 
-// NewMiMC returns a MiMCImpl object, pure-go reference implementation
-func NewMiMC(opts ...Option) hash.Hash {
+// NewMiMC returns a MiMC implementation, pure Go reference implementation.
+func NewMiMC(opts ...Option) hash.StateStorer {
 	d := new(digest)
 	d.Reset()
 	cfg := mimcOptions(opts...)
@@ -191,3 +199,27 @@ func (d *digest) WriteString(rawBytes []byte) error {
 	}
 	return nil
 }
+
+// SetState manually sets the state of the hasher to an user-provided value. In
+// the context of MiMC, the method expects a byte slice of 32 elements.
+func (d *digest) SetState(newState []byte) error {
+
+	if len(newState) != 40 {
+		return errors.New("the mimc state expects a state of 40 bytes")
+	}
+
+	if err := d.h.SetBytesCanonical(newState); err != nil {
+		return errors.New("the provided newState does not represent a valid state")
+	}
+
+	d.data = nil
+
+	return nil
+}
+
+// State returns the internal state of the hasher
+func (d *digest) State() []byte {
+	_ = d.Sum(nil) // this flushes the hasher
+	b := d.h.Bytes()
+	return b[:]
+}
diff --git a/ecc/bw6-633/fr/mimc/mimc_test.go b/ecc/bw6-633/fr/mimc/mimc_test.go
new file mode 100644
index 0000000000..f896dd8e3b
--- /dev/null
+++ b/ecc/bw6-633/fr/mimc/mimc_test.go
@@ -0,0 +1,120 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package mimc_test
+
+import (
+	"bytes"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
+	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr/mimc"
+	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
+
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+func TestMiMCFiatShamir(t *testing.T) {
+	fs := fiatshamir.NewTranscript(mimc.NewMiMC(), "c0")
+	zero := make([]byte, mimc.BlockSize)
+	err := fs.Bind("c0", zero)
+	assert.NoError(t, err)
+	_, err = fs.ComputeChallenge("c0")
+	assert.NoError(t, err)
+}
+
+func TestByteOrder(t *testing.T) {
+	assert := require.New(t)
+
+	var buf [fr.Bytes]byte
+	// if the 39 first bytes are FF, it's a valid FF in little endian, but not in big endian
+	for i := 0; i < fr.Bytes-1; i++ {
+		buf[i] = 0xFF
+	}
+	_, err := fr.BigEndian.Element(&buf)
+	assert.Error(err)
+	_, err = fr.LittleEndian.Element(&buf)
+	assert.NoError(err)
+
+	{
+		// hashing buf with big endian should fail
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.BigEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.Error(err)
+	}
+
+	{
+		// hashing buf with little endian should succeed
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.LittleEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.NoError(err)
+	}
+
+	buf = [fr.Bytes]byte{}
+	// if the 39 bytes are FF, it's a valid FF in big endian, but not in little endian
+	for i := 1; i < fr.Bytes; i++ {
+		buf[i] = 0xFF
+	}
+	_, err = fr.BigEndian.Element(&buf)
+	assert.NoError(err)
+	_, err = fr.LittleEndian.Element(&buf)
+	assert.Error(err)
+
+	{
+		// hashing buf with big endian should succeed
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.BigEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.NoError(err)
+	}
+
+	{
+		// hashing buf with little endian should fail
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.LittleEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.Error(err)
+	}
+}
+
+func TestSetState(t *testing.T) {
+	// we use for hashing and retrieving the state
+	h1 := mimc.NewMiMC()
+	// only hashing
+	h2 := mimc.NewMiMC()
+	// we use for restoring from state
+	h3 := mimc.NewMiMC()
+
+	randInputs := make([]fr.Element, 10)
+	for i := range randInputs {
+		randInputs[i].SetRandom()
+	}
+
+	storedStates := make([][]byte, len(randInputs))
+
+	for i := range randInputs {
+		storedStates[i] = h1.State()
+
+		h1.Write(randInputs[i].Marshal())
+		h2.Write(randInputs[i].Marshal())
+	}
+	dgst1 := h1.Sum(nil)
+	dgst2 := h2.Sum(nil)
+	if !bytes.Equal(dgst1, dgst2) {
+		t.Fatal("hashes do not match")
+	}
+
+	for i := range storedStates {
+		if err := h3.SetState(storedStates[i]); err != nil {
+			t.Fatal(err)
+		}
+		for j := i; j < len(randInputs); j++ {
+			h3.Write(randInputs[j].Marshal())
+		}
+		dgst3 := h3.Sum(nil)
+		if !bytes.Equal(dgst1, dgst3) {
+			t.Fatal("hashes do not match")
+		}
+	}
+}
diff --git a/ecc/bw6-633/twistededwards/eddsa/eddsa_test.go b/ecc/bw6-633/twistededwards/eddsa/eddsa_test.go
index 11dd10da30..6ffff698d8 100644
--- a/ecc/bw6-633/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bw6-633/twistededwards/eddsa/eddsa_test.go
@@ -16,13 +16,14 @@ import (
 	"fmt"
 
 	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
+	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr/mimc"
 	"github.com/consensys/gnark-crypto/ecc/bw6-633/twistededwards"
 	"github.com/consensys/gnark-crypto/hash"
 )
 
 func Example() {
 	// instantiate hash function
-	hFunc := hash.MIMC_BW6_633.New()
+	hFunc := mimc.NewMiMC()
 
 	// create a eddsa key pair
 	privateKey, _ := GenerateKey(crand.Reader)
diff --git a/ecc/bw6-761/fr/mimc/mimc.go b/ecc/bw6-761/fr/mimc/mimc.go
index 2a0a323955..c77a4a9698 100644
--- a/ecc/bw6-761/fr/mimc/mimc.go
+++ b/ecc/bw6-761/fr/mimc/mimc.go
@@ -7,14 +7,22 @@ package mimc
 
 import (
 	"errors"
-	"hash"
+	stdhash "hash"
+	"math/big"
+	"sync"
 
 	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
+	"github.com/consensys/gnark-crypto/hash"
+
 	"golang.org/x/crypto/sha3"
-	"math/big"
-	"sync"
 )
 
+func init() {
+	hash.RegisterHash(hash.MIMC_BW6_761, func() stdhash.Hash {
+		return NewMiMC()
+	})
+}
+
 const (
 	mimcNbRounds = 163
 	seed         = "seed"   // seed to derive the constants
@@ -45,8 +53,8 @@ func GetConstants() []big.Int {
 	return res
 }
 
-// NewMiMC returns a MiMCImpl object, pure-go reference implementation
-func NewMiMC(opts ...Option) hash.Hash {
+// NewMiMC returns a MiMC implementation, pure Go reference implementation.
+func NewMiMC(opts ...Option) hash.StateStorer {
 	d := new(digest)
 	d.Reset()
 	cfg := mimcOptions(opts...)
@@ -191,3 +199,27 @@ func (d *digest) WriteString(rawBytes []byte) error {
 	}
 	return nil
 }
+
+// SetState manually sets the state of the hasher to an user-provided value. In
+// the context of MiMC, the method expects a byte slice of 32 elements.
+func (d *digest) SetState(newState []byte) error {
+
+	if len(newState) != 48 {
+		return errors.New("the mimc state expects a state of 48 bytes")
+	}
+
+	if err := d.h.SetBytesCanonical(newState); err != nil {
+		return errors.New("the provided newState does not represent a valid state")
+	}
+
+	d.data = nil
+
+	return nil
+}
+
+// State returns the internal state of the hasher
+func (d *digest) State() []byte {
+	_ = d.Sum(nil) // this flushes the hasher
+	b := d.h.Bytes()
+	return b[:]
+}
diff --git a/ecc/bw6-761/fr/mimc/mimc_test.go b/ecc/bw6-761/fr/mimc/mimc_test.go
new file mode 100644
index 0000000000..f40411068f
--- /dev/null
+++ b/ecc/bw6-761/fr/mimc/mimc_test.go
@@ -0,0 +1,120 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package mimc_test
+
+import (
+	"bytes"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
+	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr/mimc"
+	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
+
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+func TestMiMCFiatShamir(t *testing.T) {
+	fs := fiatshamir.NewTranscript(mimc.NewMiMC(), "c0")
+	zero := make([]byte, mimc.BlockSize)
+	err := fs.Bind("c0", zero)
+	assert.NoError(t, err)
+	_, err = fs.ComputeChallenge("c0")
+	assert.NoError(t, err)
+}
+
+func TestByteOrder(t *testing.T) {
+	assert := require.New(t)
+
+	var buf [fr.Bytes]byte
+	// if the 47 first bytes are FF, it's a valid FF in little endian, but not in big endian
+	for i := 0; i < fr.Bytes-1; i++ {
+		buf[i] = 0xFF
+	}
+	_, err := fr.BigEndian.Element(&buf)
+	assert.Error(err)
+	_, err = fr.LittleEndian.Element(&buf)
+	assert.NoError(err)
+
+	{
+		// hashing buf with big endian should fail
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.BigEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.Error(err)
+	}
+
+	{
+		// hashing buf with little endian should succeed
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.LittleEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.NoError(err)
+	}
+
+	buf = [fr.Bytes]byte{}
+	// if the 47 bytes are FF, it's a valid FF in big endian, but not in little endian
+	for i := 1; i < fr.Bytes; i++ {
+		buf[i] = 0xFF
+	}
+	_, err = fr.BigEndian.Element(&buf)
+	assert.NoError(err)
+	_, err = fr.LittleEndian.Element(&buf)
+	assert.Error(err)
+
+	{
+		// hashing buf with big endian should succeed
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.BigEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.NoError(err)
+	}
+
+	{
+		// hashing buf with little endian should fail
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.LittleEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.Error(err)
+	}
+}
+
+func TestSetState(t *testing.T) {
+	// we use for hashing and retrieving the state
+	h1 := mimc.NewMiMC()
+	// only hashing
+	h2 := mimc.NewMiMC()
+	// we use for restoring from state
+	h3 := mimc.NewMiMC()
+
+	randInputs := make([]fr.Element, 10)
+	for i := range randInputs {
+		randInputs[i].SetRandom()
+	}
+
+	storedStates := make([][]byte, len(randInputs))
+
+	for i := range randInputs {
+		storedStates[i] = h1.State()
+
+		h1.Write(randInputs[i].Marshal())
+		h2.Write(randInputs[i].Marshal())
+	}
+	dgst1 := h1.Sum(nil)
+	dgst2 := h2.Sum(nil)
+	if !bytes.Equal(dgst1, dgst2) {
+		t.Fatal("hashes do not match")
+	}
+
+	for i := range storedStates {
+		if err := h3.SetState(storedStates[i]); err != nil {
+			t.Fatal(err)
+		}
+		for j := i; j < len(randInputs); j++ {
+			h3.Write(randInputs[j].Marshal())
+		}
+		dgst3 := h3.Sum(nil)
+		if !bytes.Equal(dgst1, dgst3) {
+			t.Fatal("hashes do not match")
+		}
+	}
+}
diff --git a/ecc/bw6-761/twistededwards/eddsa/eddsa_test.go b/ecc/bw6-761/twistededwards/eddsa/eddsa_test.go
index d9b595e894..905eca2e21 100644
--- a/ecc/bw6-761/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bw6-761/twistededwards/eddsa/eddsa_test.go
@@ -16,13 +16,14 @@ import (
 	"fmt"
 
 	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
+	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr/mimc"
 	"github.com/consensys/gnark-crypto/ecc/bw6-761/twistededwards"
 	"github.com/consensys/gnark-crypto/hash"
 )
 
 func Example() {
 	// instantiate hash function
-	hFunc := hash.MIMC_BW6_761.New()
+	hFunc := mimc.NewMiMC()
 
 	// create a eddsa key pair
 	privateKey, _ := GenerateKey(crand.Reader)
diff --git a/hash/all/allhashes.go b/hash/all/allhashes.go
new file mode 100644
index 0000000000..cb7b5947e3
--- /dev/null
+++ b/hash/all/allhashes.go
@@ -0,0 +1,11 @@
+package all
+
+import (
+	_ "github.com/consensys/gnark-crypto/ecc/bls12-377/fr/mimc"
+	_ "github.com/consensys/gnark-crypto/ecc/bls12-381/fr/mimc"
+	_ "github.com/consensys/gnark-crypto/ecc/bls24-315/fr/mimc"
+	_ "github.com/consensys/gnark-crypto/ecc/bls24-317/fr/mimc"
+	_ "github.com/consensys/gnark-crypto/ecc/bn254/fr/mimc"
+	_ "github.com/consensys/gnark-crypto/ecc/bw6-633/fr/mimc"
+	_ "github.com/consensys/gnark-crypto/ecc/bw6-761/fr/mimc"
+)
diff --git a/hash/doc.go b/hash/doc.go
index faefa0669e..b1ed8c91c3 100644
--- a/hash/doc.go
+++ b/hash/doc.go
@@ -1,5 +1,24 @@
 // Package hash provides MiMC hash function defined over implemented curves
 //
+// This package is kept for backwards compatibility. The recommended way to
+// initialize hash function is to directly use the constructors in the
+// corresponding packages (e.g. ecc/bn254/fr/mimc). Using the direct
+// constructors allows to apply options for altering the hash function behavior
+// (endianness, input splicing etc.) and returns more specific types with
+// additional methods.
+//
+// See [Importing hash functions] below for more information.
+//
+// # Importing hash functions
+//
+// The package follows registration pattern for importing hash functions. To
+// import all known hash functions in gnark-crypto, import the
+// [github.com/consensys/gnark-crypto/hash/all] package in your code. To import
+// only a specific hash, then import the corresponding package directly, e.g.
+// [github.com/consensys/gnark-crypto/ecc/bn254/fr/mimc]. The import format should be:
+//
+//	import _ "github.com/consensys/gnark-crypto/ecc/bn254/fr/mimc"
+//
 // # Length extension attack
 //
 // The MiMC hash function is vulnerable to a length extension attack. For
diff --git a/hash/hashes.go b/hash/hashes.go
index 4388219c0b..ee88d158e4 100644
--- a/hash/hashes.go
+++ b/hash/hashes.go
@@ -4,17 +4,22 @@
 package hash
 
 import (
+	"fmt"
 	"hash"
-
-	bls377 "github.com/consensys/gnark-crypto/ecc/bls12-377/fr/mimc"
-	bls381 "github.com/consensys/gnark-crypto/ecc/bls12-381/fr/mimc"
-	bls315 "github.com/consensys/gnark-crypto/ecc/bls24-315/fr/mimc"
-	bls317 "github.com/consensys/gnark-crypto/ecc/bls24-317/fr/mimc"
-	bn254 "github.com/consensys/gnark-crypto/ecc/bn254/fr/mimc"
-	bw633 "github.com/consensys/gnark-crypto/ecc/bw6-633/fr/mimc"
-	bw761 "github.com/consensys/gnark-crypto/ecc/bw6-761/fr/mimc"
+	"strings"
 )
 
+var hashes = make([]func() hash.Hash, maxHash)
+
+// RegisterHash registers a new hash function constructor. Should be called in
+// the init function of the hash package.
+//
+// To register all known hash functions in gnark-crypto, import the
+// [github.com/consensys/gnark-crypto/hash/all] package in your code.
+func RegisterHash(h Hash, new func() hash.Hash) {
+	hashes[h] = new
+}
+
 // Hash defines an unique identifier for a hash function.
 type Hash uint
 
@@ -33,6 +38,8 @@ const (
 	MIMC_BLS24_317
 	// MIMC_BW6_633 is the MiMC hash function for the BW6-633 curve.
 	MIMC_BW6_633
+
+	maxHash
 )
 
 // size of digests in bytes
@@ -46,26 +53,21 @@ var digestSize = []uint8{
 	MIMC_BW6_633:   80,
 }
 
-// New initializes the hash function.
+// New initializes the hash function. This is a convenience function which does
+// not allow setting hash-specific options.
 func (m Hash) New() hash.Hash {
-	switch m {
-	case MIMC_BN254:
-		return bn254.NewMiMC()
-	case MIMC_BLS12_381:
-		return bls381.NewMiMC()
-	case MIMC_BLS12_377:
-		return bls377.NewMiMC()
-	case MIMC_BW6_761:
-		return bw761.NewMiMC()
-	case MIMC_BLS24_315:
-		return bls315.NewMiMC()
-	case MIMC_BLS24_317:
-		return bls317.NewMiMC()
-	case MIMC_BW6_633:
-		return bw633.NewMiMC()
-	default:
-		panic("Unknown mimc ID")
+	if m < maxHash {
+		f := hashes[m]
+		if f != nil {
+			return f()
+		}
 	}
+	pkgname, _ := strings.CutPrefix(m.String(), "MIMC_")
+	pkgname = strings.ToLower(pkgname)
+	pkgname = strings.ReplaceAll(pkgname, "_", "-")
+	msg := fmt.Sprintf(`requested hash function #%s not registered. Import the corresponding package to register it:
+	import _ "github.com/consensys/gnark-crypto/ecc/%s/fr/mimc"`, m.String(), pkgname)
+	panic(msg)
 }
 
 // String returns the unique identifier of the hash function.
@@ -74,24 +76,28 @@ func (m Hash) String() string {
 	case MIMC_BN254:
 		return "MIMC_BN254"
 	case MIMC_BLS12_381:
-		return "MIMC_BLS381"
+		return "MIMC_BLS12_381"
 	case MIMC_BLS12_377:
-		return "MIMC_BLS377"
+		return "MIMC_BLS12_377"
 	case MIMC_BW6_761:
-		return "MIMC_BW761"
+		return "MIMC_BW6_761"
 	case MIMC_BLS24_315:
-		return "MIMC_BLS315"
+		return "MIMC_BLS24_315"
 	case MIMC_BLS24_317:
-		return "MIMC_BLS317"
+		return "MIMC_BLS24_317"
 	case MIMC_BW6_633:
-		return "MIMC_BW633"
+		return "MIMC_BW6_633"
 	default:
-		panic("Unknown mimc ID")
+		return "unknown hash function"
 	}
 }
 
-// Size returns the size of the digest of
-// the corresponding hash function
+// Available returns true if the hash function is available.
+func (m Hash) Available() bool {
+	return m < maxHash && hashes[m] != nil
+}
+
+// Size returns the size of the digest of the corresponding hash function
 func (m Hash) Size() int {
 	return int(digestSize[m])
 }
diff --git a/hash/interface.go b/hash/interface.go
new file mode 100644
index 0000000000..5b2c3063b4
--- /dev/null
+++ b/hash/interface.go
@@ -0,0 +1,16 @@
+package hash
+
+import "hash"
+
+// StateStorer allows to store and retrieve the state of a hash function.
+type StateStorer interface {
+	hash.Hash
+
+	// State retrieves the current state of the hash function. Calling this
+	// method should not destroy the current state and allow continue the use of
+	// the current hasher.
+	State() []byte
+	// SetState sets the state of the hash function from a previously stored
+	// state retrieved using [StateStorer.State] method.
+	SetState(state []byte) error
+}
diff --git a/internal/generator/crypto/hash/mimc/generate.go b/internal/generator/crypto/hash/mimc/generate.go
index 3783931ba0..58dc7fb099 100644
--- a/internal/generator/crypto/hash/mimc/generate.go
+++ b/internal/generator/crypto/hash/mimc/generate.go
@@ -1,7 +1,7 @@
 package mimc
 
 import (
-	"os"
+	"fmt"
 	"path/filepath"
 
 	"github.com/consensys/bavard"
@@ -16,9 +16,15 @@ func Generate(conf config.Curve, baseDir string, bgen *bavard.BatchGenerator) er
 		{File: filepath.Join(baseDir, "mimc.go"), Templates: []string{"mimc.go.tmpl"}},
 		{File: filepath.Join(baseDir, "options.go"), Templates: []string{"options.go.tmpl"}},
 	}
-	os.Remove(filepath.Join(baseDir, "utils.go"))
-	os.Remove(filepath.Join(baseDir, "utils_test.go"))
-
-	return bgen.Generate(conf, conf.Package, "./crypto/hash/mimc/template", entries...)
+	entriesTest := []bavard.Entry{
+		{File: filepath.Join(baseDir, "mimc_test.go"), Templates: []string{"tests/mimc_test.go.tmpl"}},
+	}
 
+	if err := bgen.Generate(conf, conf.Package, "./crypto/hash/mimc/template", entries...); err != nil {
+		return fmt.Errorf("generate package: %w", err)
+	}
+	if err := bgen.Generate(conf, "mimc_test", "./crypto/hash/mimc/template", entriesTest...); err != nil {
+		return fmt.Errorf("generate tests: %w", err)
+	}
+	return nil
 }
diff --git a/internal/generator/crypto/hash/mimc/template/mimc.go.tmpl b/internal/generator/crypto/hash/mimc/template/mimc.go.tmpl
index 69d0434980..a50dc24c1c 100644
--- a/internal/generator/crypto/hash/mimc/template/mimc.go.tmpl
+++ b/internal/generator/crypto/hash/mimc/template/mimc.go.tmpl
@@ -1,13 +1,21 @@
 import (
 	"errors"
-	"hash"
-
+	stdhash "hash"
 	"math/big"
+	"sync"
+
+	"github.com/consensys/gnark-crypto/hash"
 	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/fr"
+
 	"golang.org/x/crypto/sha3"
-	"sync"
 )
 
+func init() {
+	hash.RegisterHash(hash.MIMC_{{ .EnumID }}, func() stdhash.Hash {
+		return NewMiMC()
+	})
+}
+
 const (
 {{ if eq .Name "bn254" }}
 	mimcNbRounds = 110
@@ -54,8 +62,8 @@ func GetConstants() []big.Int {
 	return res
 }
 
-// NewMiMC returns a MiMCImpl object, pure-go reference implementation
-func NewMiMC(opts ...Option) hash.Hash {
+// NewMiMC returns a MiMC implementation, pure Go reference implementation.
+func NewMiMC(opts ...Option) hash.StateStorer {
 	d := new(digest)
 	d.Reset()
 	cfg := mimcOptions(opts...)
@@ -244,3 +252,27 @@ func (d *digest) WriteString(rawBytes []byte) error {
 	}
 	return nil
 }
+
+// SetState manually sets the state of the hasher to an user-provided value. In
+// the context of MiMC, the method expects a byte slice of 32 elements.
+func  (d *digest) SetState(newState []byte) error {
+	
+	if len(newState) != {{ .Fr.NbBytes }} {
+		return errors.New("the mimc state expects a state of {{ .Fr.NbBytes }} bytes")
+	}
+
+	if err := d.h.SetBytesCanonical(newState); err != nil {
+		return errors.New("the provided newState does not represent a valid state")
+	}
+
+	d.data = nil
+
+	return nil
+}
+
+// State returns the internal state of the hasher
+func (d *digest) State() []byte {
+	_ = d.Sum(nil) // this flushes the hasher
+	b := d.h.Bytes()
+	return b[:]
+}
\ No newline at end of file
diff --git a/internal/generator/crypto/hash/mimc/template/tests/mimc_test.go.tmpl b/internal/generator/crypto/hash/mimc/template/tests/mimc_test.go.tmpl
new file mode 100644
index 0000000000..fa99cdd4f6
--- /dev/null
+++ b/internal/generator/crypto/hash/mimc/template/tests/mimc_test.go.tmpl
@@ -0,0 +1,114 @@
+import (
+	"bytes"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc/{{.Name}}/fr"
+	"github.com/consensys/gnark-crypto/ecc/{{.Name}}/fr/mimc"
+	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
+
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+func TestMiMCFiatShamir(t *testing.T) {
+	fs := fiatshamir.NewTranscript(mimc.NewMiMC(), "c0")
+	zero := make([]byte, mimc.BlockSize)
+	err := fs.Bind("c0", zero)
+	assert.NoError(t, err)
+	_, err = fs.ComputeChallenge("c0")
+	assert.NoError(t, err)
+}
+
+func TestByteOrder(t *testing.T) {
+	assert := require.New(t)
+
+	var buf [fr.Bytes]byte
+	// if the {{ sub .Fr.NbBytes 1 }} first bytes are FF, it's a valid FF in little endian, but not in big endian
+	for i := 0; i < fr.Bytes-1; i++ {
+		buf[i] = 0xFF
+	}
+	_, err := fr.BigEndian.Element(&buf)
+	assert.Error(err)
+	_, err = fr.LittleEndian.Element(&buf)
+	assert.NoError(err)
+
+	{
+		// hashing buf with big endian should fail
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.BigEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.Error(err)
+	}
+
+	{
+		// hashing buf with little endian should succeed
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.LittleEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.NoError(err)
+	}
+
+	buf = [fr.Bytes]byte{}
+	// if the {{ sub .Fr.NbBytes 1 }} bytes are FF, it's a valid FF in big endian, but not in little endian
+	for i := 1; i < fr.Bytes; i++ {
+		buf[i] = 0xFF
+	}
+	_, err = fr.BigEndian.Element(&buf)
+	assert.NoError(err)
+	_, err = fr.LittleEndian.Element(&buf)
+	assert.Error(err)
+
+	{
+		// hashing buf with big endian should succeed
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.BigEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.NoError(err)
+	}
+
+	{
+		// hashing buf with little endian should fail
+		mimcHash := mimc.NewMiMC(mimc.WithByteOrder(fr.LittleEndian))
+		_, err := mimcHash.Write(buf[:])
+		assert.Error(err)
+	}
+}
+
+func TestSetState(t *testing.T) {
+	// we use for hashing and retrieving the state
+	h1 := mimc.NewMiMC()
+	// only hashing
+	h2 := mimc.NewMiMC()
+	// we use for restoring from state
+	h3 := mimc.NewMiMC()
+
+	randInputs := make([]fr.Element, 10)
+	for i := range randInputs {
+		randInputs[i].SetRandom()
+	}
+
+	storedStates := make([][]byte, len(randInputs))
+
+
+	for i := range randInputs {
+		storedStates[i] = h1.State()
+
+		h1.Write(randInputs[i].Marshal())
+		h2.Write(randInputs[i].Marshal())
+	}
+	dgst1 := h1.Sum(nil)
+	dgst2 := h2.Sum(nil)
+	if !bytes.Equal(dgst1, dgst2) {
+		t.Fatal("hashes do not match")
+	}
+
+	for i := range storedStates {
+		if err := h3.SetState(storedStates[i]); err != nil {
+			t.Fatal(err)
+		}
+		for j := i; j < len(randInputs); j++ {
+			h3.Write(randInputs[j].Marshal())
+		}
+		dgst3 := h3.Sum(nil)
+		if !bytes.Equal(dgst1, dgst3) {
+			t.Fatal("hashes do not match")
+		}
+	}
+}
diff --git a/internal/generator/edwards/eddsa/template/eddsa.test.go.tmpl b/internal/generator/edwards/eddsa/template/eddsa.test.go.tmpl
index bdc6fdf7b4..86fcd599b2 100644
--- a/internal/generator/edwards/eddsa/template/eddsa.test.go.tmpl
+++ b/internal/generator/edwards/eddsa/template/eddsa.test.go.tmpl
@@ -11,12 +11,13 @@ import (
 	"github.com/consensys/gnark-crypto/hash"
 	"github.com/consensys/gnark-crypto/ecc/{{.Name}}/twistededwards"
 	"github.com/consensys/gnark-crypto/ecc/{{.Name}}/fr"
+	"github.com/consensys/gnark-crypto/ecc/{{.Name}}/fr/mimc"
 )
 
 
 func Example() {
 	// instantiate hash function
-	hFunc := hash.MIMC_{{ .EnumID }}.New()
+	hFunc := mimc.NewMiMC()
 
 	// create a eddsa key pair
 	privateKey, _ := GenerateKey(crand.Reader)

From afee1955665fe5f0d0fb78955a1fba9835ff7675 Mon Sep 17 00:00:00 2001
From: ThomasPiellard <thomas.piellard@consensys.net>
Date: Fri, 13 Dec 2024 23:33:22 +0100
Subject: [PATCH 096/114] feat: restored fft (#574)

Co-authored-by: Gautam Botrel <gautam.botrel@gmail.com>
---
 field/babybear/fft/bitreverse.go              | 563 ++++++++++++++++++
 field/babybear/fft/bitreverse_test.go         | 102 ++++
 field/babybear/fft/doc.go                     |   8 +
 field/babybear/fft/domain.go                  | 317 ++++++++++
 field/babybear/fft/domain_test.go             |  36 ++
 field/babybear/fft/fft.go                     | 410 +++++++++++++
 field/babybear/fft/fft_test.go                | 318 ++++++++++
 field/babybear/fft/options.go                 |  92 +++
 field/babybear/generator.go                   |  36 ++
 field/generator/asm/amd64/build.go            |   2 +-
 field/generator/asm/arm64/build.go            |   2 +-
 field/generator/config/asm_config.go          |   6 +
 field/generator/config/extension.go           |  10 +-
 field/generator/config/fft_config.go          |  25 +
 field/generator/config/field_config.go        |  32 +-
 field/generator/config/field_test.go          |  12 +-
 field/generator/generator.go                  | 338 +++--------
 field/generator/generator_asm.go              | 143 +++++
 field/generator/generator_fft.go              | 231 +++++++
 field/generator/generator_field.go            | 203 +++++++
 field/generator/generator_test.go             |  13 +-
 .../templates/fft}/bitreverse.go.tmpl         |  33 +-
 .../internal/templates/fft}/doc.go.tmpl       |   0
 .../internal/templates/fft}/domain.go.tmpl    |  86 ++-
 .../internal/templates/fft}/fft.go.tmpl       |  63 +-
 .../templates/fft/fr.generator.go.tmpl        |  29 +
 .../internal/templates/fft}/fuzz.go.tmpl      |   6 +-
 .../internal/templates/fft}/options.go.tmpl   |   9 +-
 .../templates/fft}/tests/bitreverse.go.tmpl   |  24 +-
 .../templates/fft}/tests/domain.go.tmpl       |   0
 .../internal/templates/fft}/tests/fft.go.tmpl |  40 +-
 .../templates/fft}/tests/fuzz.go.tmpl         |   0
 field/generator/options.go                    |  46 ++
 field/goff/cmd/root.go                        |  15 +-
 field/goldilocks/fft/bitreverse.go            | 563 ++++++++++++++++++
 field/goldilocks/fft/bitreverse_test.go       | 102 ++++
 field/goldilocks/fft/doc.go                   |   8 +
 field/goldilocks/fft/domain.go                | 317 ++++++++++
 field/goldilocks/fft/domain_test.go           |  36 ++
 field/goldilocks/fft/fft.go                   | 410 +++++++++++++
 field/goldilocks/fft/fft_test.go              | 318 ++++++++++
 field/goldilocks/fft/options.go               |  92 +++
 field/goldilocks/generator.go                 |  36 ++
 field/internal/main.go                        |   5 +-
 field/koalabear/fft/bitreverse.go             | 563 ++++++++++++++++++
 field/koalabear/fft/bitreverse_test.go        | 102 ++++
 field/koalabear/fft/doc.go                    |   8 +
 field/koalabear/fft/domain.go                 | 317 ++++++++++
 field/koalabear/fft/domain_test.go            |  36 ++
 field/koalabear/fft/fft.go                    | 410 +++++++++++++
 field/koalabear/fft/fft_test.go               | 318 ++++++++++
 field/koalabear/fft/options.go                |  92 +++
 field/koalabear/generator.go                  |  36 ++
 internal/generator/config/curve.go            |   4 +-
 internal/generator/config/hash_to_curve.go    |   6 +-
 internal/generator/fft/generate.go            |  76 ---
 .../fft/template/fr.generator.go.tmpl         |  48 --
 .../generator/fft/template/imports.go.tmpl    |  43 --
 internal/generator/main.go                    |  33 +-
 internal/generator/tower/asm/amd64/e2.go      |   4 +-
 60 files changed, 6594 insertions(+), 639 deletions(-)
 create mode 100644 field/babybear/fft/bitreverse.go
 create mode 100644 field/babybear/fft/bitreverse_test.go
 create mode 100644 field/babybear/fft/doc.go
 create mode 100644 field/babybear/fft/domain.go
 create mode 100644 field/babybear/fft/domain_test.go
 create mode 100644 field/babybear/fft/fft.go
 create mode 100644 field/babybear/fft/fft_test.go
 create mode 100644 field/babybear/fft/options.go
 create mode 100644 field/babybear/generator.go
 create mode 100644 field/generator/config/asm_config.go
 create mode 100644 field/generator/config/fft_config.go
 create mode 100644 field/generator/generator_asm.go
 create mode 100644 field/generator/generator_fft.go
 create mode 100644 field/generator/generator_field.go
 rename {internal/generator/fft/template => field/generator/internal/templates/fft}/bitreverse.go.tmpl (90%)
 rename {internal/generator/fft/template => field/generator/internal/templates/fft}/doc.go.tmpl (100%)
 rename {internal/generator/fft/template => field/generator/internal/templates/fft}/domain.go.tmpl (76%)
 rename {internal/generator/fft/template => field/generator/internal/templates/fft}/fft.go.tmpl (84%)
 create mode 100644 field/generator/internal/templates/fft/fr.generator.go.tmpl
 rename {internal/generator/fft/template => field/generator/internal/templates/fft}/fuzz.go.tmpl (89%)
 rename {internal/generator/fft/template => field/generator/internal/templates/fft}/options.go.tmpl (91%)
 rename {internal/generator/fft/template => field/generator/internal/templates/fft}/tests/bitreverse.go.tmpl (74%)
 rename {internal/generator/fft/template => field/generator/internal/templates/fft}/tests/domain.go.tmpl (100%)
 rename {internal/generator/fft/template => field/generator/internal/templates/fft}/tests/fft.go.tmpl (86%)
 rename {internal/generator/fft/template => field/generator/internal/templates/fft}/tests/fuzz.go.tmpl (100%)
 create mode 100644 field/generator/options.go
 create mode 100644 field/goldilocks/fft/bitreverse.go
 create mode 100644 field/goldilocks/fft/bitreverse_test.go
 create mode 100644 field/goldilocks/fft/doc.go
 create mode 100644 field/goldilocks/fft/domain.go
 create mode 100644 field/goldilocks/fft/domain_test.go
 create mode 100644 field/goldilocks/fft/fft.go
 create mode 100644 field/goldilocks/fft/fft_test.go
 create mode 100644 field/goldilocks/fft/options.go
 create mode 100644 field/goldilocks/generator.go
 create mode 100644 field/koalabear/fft/bitreverse.go
 create mode 100644 field/koalabear/fft/bitreverse_test.go
 create mode 100644 field/koalabear/fft/doc.go
 create mode 100644 field/koalabear/fft/domain.go
 create mode 100644 field/koalabear/fft/domain_test.go
 create mode 100644 field/koalabear/fft/fft.go
 create mode 100644 field/koalabear/fft/fft_test.go
 create mode 100644 field/koalabear/fft/options.go
 create mode 100644 field/koalabear/generator.go
 delete mode 100644 internal/generator/fft/generate.go
 delete mode 100644 internal/generator/fft/template/fr.generator.go.tmpl
 delete mode 100644 internal/generator/fft/template/imports.go.tmpl

diff --git a/field/babybear/fft/bitreverse.go b/field/babybear/fft/bitreverse.go
new file mode 100644
index 0000000000..164ee25831
--- /dev/null
+++ b/field/babybear/fft/bitreverse.go
@@ -0,0 +1,563 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fft
+
+import (
+	"math/bits"
+	"runtime"
+
+	"github.com/consensys/gnark-crypto/field/babybear"
+)
+
+// BitReverse applies the bit-reversal permutation to v.
+// len(v) must be a power of 2
+func BitReverse(v []babybear.Element) {
+	n := uint64(len(v))
+	if bits.OnesCount64(n) != 1 {
+		panic("len(a) must be a power of 2")
+	}
+
+	if runtime.GOARCH == "arm64" {
+		bitReverseNaive(v)
+	} else {
+		bitReverseCobra(v)
+	}
+}
+
+// bitReverseNaive applies the bit-reversal permutation to v.
+// len(v) must be a power of 2
+func bitReverseNaive(v []babybear.Element) {
+	n := uint64(len(v))
+	nn := uint64(64 - bits.TrailingZeros64(n))
+
+	for i := uint64(0); i < n; i++ {
+		iRev := bits.Reverse64(i) >> nn
+		if iRev > i {
+			v[i], v[iRev] = v[iRev], v[i]
+		}
+	}
+}
+
+// bitReverseCobraInPlace applies the bit-reversal permutation to v.
+// len(v) must be a power of 2
+// This is derived from:
+//
+//   - Towards an Optimal Bit-Reversal Permutation Program
+//     Larry Carter and Kang Su Gatlin, 1998
+//     https://csaws.cs.technion.ac.il/~itai/Courses/Cache/bit.pdf
+//
+//   - Practically efficient methods for performing bit-reversed
+//     permutation in C++11 on the x86-64 architecture
+//     Knauth, Adas, Whitfield, Wang, Ickler, Conrad, Serang, 2017
+//     https://arxiv.org/pdf/1708.01873.pdf
+//
+//   - and more specifically, constantine implementation:
+//     https://github.com/mratsim/constantine/blob/d51699248db04e29c7b1ad97e0bafa1499db00b5/constantine/math/polynomials/fft.nim#L205
+//     by Mamy Ratsimbazafy (@mratsim).
+func bitReverseCobraInPlace(v []babybear.Element) {
+	logN := uint64(bits.Len64(uint64(len(v))) - 1)
+	logTileSize := deriveLogTileSize(logN)
+	logBLen := logN - 2*logTileSize
+	bLen := uint64(1) << logBLen
+	bShift := logBLen + logTileSize
+	tileSize := uint64(1) << logTileSize
+
+	// rough idea;
+	// bit reversal permutation naive implementation may have some cache associativity issues,
+	// since we are accessing elements by strides of powers of 2.
+	// on large inputs, this is noticeable and can be improved by using a t buffer.
+	// idea is for t buffer to be small enough to fit in cache.
+	// in the first inner loop, we copy the elements of v into t in a bit-reversed order.
+	// in the subsequent inner loops, accesses have much better cache locality than the naive implementation.
+	// hence even if we apparently do more work (swaps / copies), we are faster.
+	//
+	// on arm64 (and particularly on M1 macs), this is not noticeable, and the naive implementation is faster,
+	// in most cases.
+	// on x86 (and particularly on aws hpc6a) this is noticeable, and the t buffer implementation is faster (up to 3x).
+	//
+	// optimal choice for the tile size is cache dependent; in theory, we want the t buffer to fit in the L1 cache;
+	// in practice, a common size for L1 is 64kb, a field element is 32bytes or more.
+	// hence we can fit 2k elements in the L1 cache, which corresponds to a tile size of 2**5 with some margin for cache conflicts.
+	//
+	// for most sizes of interest, this tile size choice doesn't yield good results;
+	// we find that a tile size of 2**9 gives best results for input sizes from 2**21 up to 2**27+.
+	t := make([]babybear.Element, tileSize*tileSize)
+
+	// see https://csaws.cs.technion.ac.il/~itai/Courses/Cache/bit.pdf
+	// for a detailed explanation of the algorithm.
+	for b := uint64(0); b < bLen; b++ {
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := (bits.Reverse64(a) >> (64 - logTileSize)) << logTileSize
+			for c := uint64(0); c < tileSize; c++ {
+				idx := (a << bShift) | (b << logTileSize) | c
+				t[aRev|c] = v[idx]
+			}
+		}
+
+		bRev := (bits.Reverse64(b) >> (64 - logBLen)) << logTileSize
+
+		for c := uint64(0); c < tileSize; c++ {
+			cRev := ((bits.Reverse64(c) >> (64 - logTileSize)) << bShift) | bRev
+			for aRev := uint64(0); aRev < tileSize; aRev++ {
+				a := bits.Reverse64(aRev) >> (64 - logTileSize)
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idxRev], t[tIdx] = t[tIdx], v[idxRev]
+				}
+			}
+		}
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := bits.Reverse64(a) >> (64 - logTileSize)
+			for c := uint64(0); c < tileSize; c++ {
+				cRev := (bits.Reverse64(c) >> (64 - logTileSize)) << bShift
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | bRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idx], t[tIdx] = t[tIdx], v[idx]
+				}
+			}
+		}
+	}
+}
+
+func bitReverseCobra(v []babybear.Element) {
+	switch len(v) {
+	case 1 << 21:
+		bitReverseCobraInPlace_9_21(v)
+	case 1 << 22:
+		bitReverseCobraInPlace_9_22(v)
+	case 1 << 23:
+		bitReverseCobraInPlace_9_23(v)
+	case 1 << 24:
+		bitReverseCobraInPlace_9_24(v)
+	case 1 << 25:
+		bitReverseCobraInPlace_9_25(v)
+	case 1 << 26:
+		bitReverseCobraInPlace_9_26(v)
+	case 1 << 27:
+		bitReverseCobraInPlace_9_27(v)
+	default:
+		if len(v) > 1<<27 {
+			bitReverseCobraInPlace(v)
+		} else {
+			bitReverseNaive(v)
+		}
+	}
+}
+
+func deriveLogTileSize(logN uint64) uint64 {
+	q := uint64(9) // see bitReverseCobraInPlace for more details
+
+	for int(logN)-int(2*q) <= 0 {
+		q--
+	}
+
+	return q
+}
+
+// bitReverseCobraInPlace_9_21 applies the bit-reversal permutation to v.
+// len(v) must be 1 << 21.
+// see bitReverseCobraInPlace for more details; this function is specialized for 9,
+// as it declares the t buffer and various constants statically for performance.
+func bitReverseCobraInPlace_9_21(v []babybear.Element) {
+	const (
+		logTileSize = uint64(9)
+		tileSize    = uint64(1) << logTileSize
+		logN        = 21
+		logBLen     = logN - 2*logTileSize
+		bShift      = logBLen + logTileSize
+		bLen        = uint64(1) << logBLen
+	)
+
+	var t [tileSize * tileSize]babybear.Element
+
+	for b := uint64(0); b < bLen; b++ {
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := (bits.Reverse64(a) >> 55) << logTileSize
+			for c := uint64(0); c < tileSize; c++ {
+				idx := (a << bShift) | (b << logTileSize) | c
+				t[aRev|c] = v[idx]
+			}
+		}
+
+		bRev := (bits.Reverse64(b) >> (64 - logBLen)) << logTileSize
+
+		for c := uint64(0); c < tileSize; c++ {
+			cRev := ((bits.Reverse64(c) >> 55) << bShift) | bRev
+			for aRev := uint64(0); aRev < tileSize; aRev++ {
+				a := bits.Reverse64(aRev) >> 55
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idxRev], t[tIdx] = t[tIdx], v[idxRev]
+				}
+			}
+		}
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := bits.Reverse64(a) >> 55
+			for c := uint64(0); c < tileSize; c++ {
+				cRev := (bits.Reverse64(c) >> 55) << bShift
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | bRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idx], t[tIdx] = t[tIdx], v[idx]
+				}
+			}
+		}
+	}
+
+}
+
+// bitReverseCobraInPlace_9_22 applies the bit-reversal permutation to v.
+// len(v) must be 1 << 22.
+// see bitReverseCobraInPlace for more details; this function is specialized for 9,
+// as it declares the t buffer and various constants statically for performance.
+func bitReverseCobraInPlace_9_22(v []babybear.Element) {
+	const (
+		logTileSize = uint64(9)
+		tileSize    = uint64(1) << logTileSize
+		logN        = 22
+		logBLen     = logN - 2*logTileSize
+		bShift      = logBLen + logTileSize
+		bLen        = uint64(1) << logBLen
+	)
+
+	var t [tileSize * tileSize]babybear.Element
+
+	for b := uint64(0); b < bLen; b++ {
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := (bits.Reverse64(a) >> 55) << logTileSize
+			for c := uint64(0); c < tileSize; c++ {
+				idx := (a << bShift) | (b << logTileSize) | c
+				t[aRev|c] = v[idx]
+			}
+		}
+
+		bRev := (bits.Reverse64(b) >> (64 - logBLen)) << logTileSize
+
+		for c := uint64(0); c < tileSize; c++ {
+			cRev := ((bits.Reverse64(c) >> 55) << bShift) | bRev
+			for aRev := uint64(0); aRev < tileSize; aRev++ {
+				a := bits.Reverse64(aRev) >> 55
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idxRev], t[tIdx] = t[tIdx], v[idxRev]
+				}
+			}
+		}
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := bits.Reverse64(a) >> 55
+			for c := uint64(0); c < tileSize; c++ {
+				cRev := (bits.Reverse64(c) >> 55) << bShift
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | bRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idx], t[tIdx] = t[tIdx], v[idx]
+				}
+			}
+		}
+	}
+
+}
+
+// bitReverseCobraInPlace_9_23 applies the bit-reversal permutation to v.
+// len(v) must be 1 << 23.
+// see bitReverseCobraInPlace for more details; this function is specialized for 9,
+// as it declares the t buffer and various constants statically for performance.
+func bitReverseCobraInPlace_9_23(v []babybear.Element) {
+	const (
+		logTileSize = uint64(9)
+		tileSize    = uint64(1) << logTileSize
+		logN        = 23
+		logBLen     = logN - 2*logTileSize
+		bShift      = logBLen + logTileSize
+		bLen        = uint64(1) << logBLen
+	)
+
+	var t [tileSize * tileSize]babybear.Element
+
+	for b := uint64(0); b < bLen; b++ {
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := (bits.Reverse64(a) >> 55) << logTileSize
+			for c := uint64(0); c < tileSize; c++ {
+				idx := (a << bShift) | (b << logTileSize) | c
+				t[aRev|c] = v[idx]
+			}
+		}
+
+		bRev := (bits.Reverse64(b) >> (64 - logBLen)) << logTileSize
+
+		for c := uint64(0); c < tileSize; c++ {
+			cRev := ((bits.Reverse64(c) >> 55) << bShift) | bRev
+			for aRev := uint64(0); aRev < tileSize; aRev++ {
+				a := bits.Reverse64(aRev) >> 55
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idxRev], t[tIdx] = t[tIdx], v[idxRev]
+				}
+			}
+		}
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := bits.Reverse64(a) >> 55
+			for c := uint64(0); c < tileSize; c++ {
+				cRev := (bits.Reverse64(c) >> 55) << bShift
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | bRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idx], t[tIdx] = t[tIdx], v[idx]
+				}
+			}
+		}
+	}
+
+}
+
+// bitReverseCobraInPlace_9_24 applies the bit-reversal permutation to v.
+// len(v) must be 1 << 24.
+// see bitReverseCobraInPlace for more details; this function is specialized for 9,
+// as it declares the t buffer and various constants statically for performance.
+func bitReverseCobraInPlace_9_24(v []babybear.Element) {
+	const (
+		logTileSize = uint64(9)
+		tileSize    = uint64(1) << logTileSize
+		logN        = 24
+		logBLen     = logN - 2*logTileSize
+		bShift      = logBLen + logTileSize
+		bLen        = uint64(1) << logBLen
+	)
+
+	var t [tileSize * tileSize]babybear.Element
+
+	for b := uint64(0); b < bLen; b++ {
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := (bits.Reverse64(a) >> 55) << logTileSize
+			for c := uint64(0); c < tileSize; c++ {
+				idx := (a << bShift) | (b << logTileSize) | c
+				t[aRev|c] = v[idx]
+			}
+		}
+
+		bRev := (bits.Reverse64(b) >> (64 - logBLen)) << logTileSize
+
+		for c := uint64(0); c < tileSize; c++ {
+			cRev := ((bits.Reverse64(c) >> 55) << bShift) | bRev
+			for aRev := uint64(0); aRev < tileSize; aRev++ {
+				a := bits.Reverse64(aRev) >> 55
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idxRev], t[tIdx] = t[tIdx], v[idxRev]
+				}
+			}
+		}
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := bits.Reverse64(a) >> 55
+			for c := uint64(0); c < tileSize; c++ {
+				cRev := (bits.Reverse64(c) >> 55) << bShift
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | bRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idx], t[tIdx] = t[tIdx], v[idx]
+				}
+			}
+		}
+	}
+
+}
+
+// bitReverseCobraInPlace_9_25 applies the bit-reversal permutation to v.
+// len(v) must be 1 << 25.
+// see bitReverseCobraInPlace for more details; this function is specialized for 9,
+// as it declares the t buffer and various constants statically for performance.
+func bitReverseCobraInPlace_9_25(v []babybear.Element) {
+	const (
+		logTileSize = uint64(9)
+		tileSize    = uint64(1) << logTileSize
+		logN        = 25
+		logBLen     = logN - 2*logTileSize
+		bShift      = logBLen + logTileSize
+		bLen        = uint64(1) << logBLen
+	)
+
+	var t [tileSize * tileSize]babybear.Element
+
+	for b := uint64(0); b < bLen; b++ {
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := (bits.Reverse64(a) >> 55) << logTileSize
+			for c := uint64(0); c < tileSize; c++ {
+				idx := (a << bShift) | (b << logTileSize) | c
+				t[aRev|c] = v[idx]
+			}
+		}
+
+		bRev := (bits.Reverse64(b) >> (64 - logBLen)) << logTileSize
+
+		for c := uint64(0); c < tileSize; c++ {
+			cRev := ((bits.Reverse64(c) >> 55) << bShift) | bRev
+			for aRev := uint64(0); aRev < tileSize; aRev++ {
+				a := bits.Reverse64(aRev) >> 55
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idxRev], t[tIdx] = t[tIdx], v[idxRev]
+				}
+			}
+		}
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := bits.Reverse64(a) >> 55
+			for c := uint64(0); c < tileSize; c++ {
+				cRev := (bits.Reverse64(c) >> 55) << bShift
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | bRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idx], t[tIdx] = t[tIdx], v[idx]
+				}
+			}
+		}
+	}
+
+}
+
+// bitReverseCobraInPlace_9_26 applies the bit-reversal permutation to v.
+// len(v) must be 1 << 26.
+// see bitReverseCobraInPlace for more details; this function is specialized for 9,
+// as it declares the t buffer and various constants statically for performance.
+func bitReverseCobraInPlace_9_26(v []babybear.Element) {
+	const (
+		logTileSize = uint64(9)
+		tileSize    = uint64(1) << logTileSize
+		logN        = 26
+		logBLen     = logN - 2*logTileSize
+		bShift      = logBLen + logTileSize
+		bLen        = uint64(1) << logBLen
+	)
+
+	var t [tileSize * tileSize]babybear.Element
+
+	for b := uint64(0); b < bLen; b++ {
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := (bits.Reverse64(a) >> 55) << logTileSize
+			for c := uint64(0); c < tileSize; c++ {
+				idx := (a << bShift) | (b << logTileSize) | c
+				t[aRev|c] = v[idx]
+			}
+		}
+
+		bRev := (bits.Reverse64(b) >> (64 - logBLen)) << logTileSize
+
+		for c := uint64(0); c < tileSize; c++ {
+			cRev := ((bits.Reverse64(c) >> 55) << bShift) | bRev
+			for aRev := uint64(0); aRev < tileSize; aRev++ {
+				a := bits.Reverse64(aRev) >> 55
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idxRev], t[tIdx] = t[tIdx], v[idxRev]
+				}
+			}
+		}
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := bits.Reverse64(a) >> 55
+			for c := uint64(0); c < tileSize; c++ {
+				cRev := (bits.Reverse64(c) >> 55) << bShift
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | bRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idx], t[tIdx] = t[tIdx], v[idx]
+				}
+			}
+		}
+	}
+
+}
+
+// bitReverseCobraInPlace_9_27 applies the bit-reversal permutation to v.
+// len(v) must be 1 << 27.
+// see bitReverseCobraInPlace for more details; this function is specialized for 9,
+// as it declares the t buffer and various constants statically for performance.
+func bitReverseCobraInPlace_9_27(v []babybear.Element) {
+	const (
+		logTileSize = uint64(9)
+		tileSize    = uint64(1) << logTileSize
+		logN        = 27
+		logBLen     = logN - 2*logTileSize
+		bShift      = logBLen + logTileSize
+		bLen        = uint64(1) << logBLen
+	)
+
+	var t [tileSize * tileSize]babybear.Element
+
+	for b := uint64(0); b < bLen; b++ {
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := (bits.Reverse64(a) >> 55) << logTileSize
+			for c := uint64(0); c < tileSize; c++ {
+				idx := (a << bShift) | (b << logTileSize) | c
+				t[aRev|c] = v[idx]
+			}
+		}
+
+		bRev := (bits.Reverse64(b) >> (64 - logBLen)) << logTileSize
+
+		for c := uint64(0); c < tileSize; c++ {
+			cRev := ((bits.Reverse64(c) >> 55) << bShift) | bRev
+			for aRev := uint64(0); aRev < tileSize; aRev++ {
+				a := bits.Reverse64(aRev) >> 55
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idxRev], t[tIdx] = t[tIdx], v[idxRev]
+				}
+			}
+		}
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := bits.Reverse64(a) >> 55
+			for c := uint64(0); c < tileSize; c++ {
+				cRev := (bits.Reverse64(c) >> 55) << bShift
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | bRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idx], t[tIdx] = t[tIdx], v[idx]
+				}
+			}
+		}
+	}
+
+}
diff --git a/field/babybear/fft/bitreverse_test.go b/field/babybear/fft/bitreverse_test.go
new file mode 100644
index 0000000000..ec29679866
--- /dev/null
+++ b/field/babybear/fft/bitreverse_test.go
@@ -0,0 +1,102 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fft
+
+import (
+	"fmt"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/field/babybear"
+)
+
+type bitReverseVariant struct {
+	name string
+	buf  []babybear.Element
+	fn   func([]babybear.Element)
+}
+
+const maxSizeBitReverse = 1 << 23
+
+var bitReverse = []bitReverseVariant{
+	{name: "bitReverseNaive", buf: make([]babybear.Element, maxSizeBitReverse), fn: bitReverseNaive},
+	{name: "BitReverse", buf: make([]babybear.Element, maxSizeBitReverse), fn: BitReverse},
+	{name: "bitReverseCobraInPlace", buf: make([]babybear.Element, maxSizeBitReverse), fn: bitReverseCobraInPlace},
+}
+
+func TestBitReverse(t *testing.T) {
+
+	// generate a random []babybear.Element array of size 2**20
+	pol := make([]babybear.Element, maxSizeBitReverse)
+	one := babybear.One()
+	pol[0].SetRandom()
+	for i := 1; i < maxSizeBitReverse; i++ {
+		pol[i].Add(&pol[i-1], &one)
+	}
+
+	// for each size, check that all the bitReverse functions fn compute the same result.
+	for size := 2; size <= maxSizeBitReverse; size <<= 1 {
+
+		// copy pol into the buffers
+		for _, data := range bitReverse {
+			copy(data.buf, pol[:size])
+		}
+
+		// compute bit reverse shuffling
+		for _, data := range bitReverse {
+			data.fn(data.buf[:size])
+		}
+
+		// all bitReverse.buf should hold the same result
+		for i := 0; i < size; i++ {
+			for j := 1; j < len(bitReverse); j++ {
+				if !bitReverse[0].buf[i].Equal(&bitReverse[j].buf[i]) {
+					t.Fatalf("bitReverse %s and %s do not compute the same result", bitReverse[0].name, bitReverse[j].name)
+				}
+			}
+		}
+
+		// bitReverse back should be identity
+		for _, data := range bitReverse {
+			data.fn(data.buf[:size])
+		}
+
+		for i := 0; i < size; i++ {
+			for j := 1; j < len(bitReverse); j++ {
+				if !bitReverse[0].buf[i].Equal(&bitReverse[j].buf[i]) {
+					t.Fatalf("(fn-1) bitReverse %s and %s do not compute the same result", bitReverse[0].name, bitReverse[j].name)
+				}
+			}
+		}
+	}
+
+}
+
+func BenchmarkBitReverse(b *testing.B) {
+	// generate a random []babybear.Element array of size 2**22
+	pol := make([]babybear.Element, maxSizeBitReverse)
+	one := babybear.One()
+	pol[0].SetRandom()
+	for i := 1; i < maxSizeBitReverse; i++ {
+		pol[i].Add(&pol[i-1], &one)
+	}
+
+	// copy pol into the buffers
+	for _, data := range bitReverse {
+		copy(data.buf, pol[:maxSizeBitReverse])
+	}
+
+	// benchmark for each size, each bitReverse function
+	for size := 1 << 18; size <= maxSizeBitReverse; size <<= 1 {
+		for _, data := range bitReverse {
+			b.Run(fmt.Sprintf("name=%s/size=%d", data.name, size), func(b *testing.B) {
+				b.ResetTimer()
+				for j := 0; j < b.N; j++ {
+					data.fn(data.buf[:size])
+				}
+			})
+		}
+	}
+}
diff --git a/field/babybear/fft/doc.go b/field/babybear/fft/doc.go
new file mode 100644
index 0000000000..4cce0f9779
--- /dev/null
+++ b/field/babybear/fft/doc.go
@@ -0,0 +1,8 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// Package fft provides in-place discrete Fourier transform on powers-of-two subgroups
+// of 𝔽ᵣˣ (the multiplicative group (ℤ/rℤ, x) ).
+package fft
diff --git a/field/babybear/fft/domain.go b/field/babybear/fft/domain.go
new file mode 100644
index 0000000000..dc0f897185
--- /dev/null
+++ b/field/babybear/fft/domain.go
@@ -0,0 +1,317 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fft
+
+import (
+	"encoding/binary"
+	"errors"
+	"io"
+	"math/big"
+	"math/bits"
+	"runtime"
+	"sync"
+
+	"github.com/consensys/gnark-crypto/field/babybear"
+
+	"github.com/consensys/gnark-crypto/ecc"
+)
+
+// Domain with a power of 2 cardinality
+// compute a field element of order 2x and store it in FinerGenerator
+// all other values can be derived from x, GeneratorSqrt
+type Domain struct {
+	Cardinality            uint64
+	CardinalityInv         babybear.Element
+	Generator              babybear.Element
+	GeneratorInv           babybear.Element
+	FrMultiplicativeGen    babybear.Element // generator of Fr*
+	FrMultiplicativeGenInv babybear.Element
+
+	// this is set with the WithoutPrecompute option;
+	// if true, the domain does some pre-computation and stores it.
+	// if false, the FFT will compute the twiddles on the fly (this is less CPU efficient, but uses less memory)
+	withPrecompute bool
+
+	// the following slices are not serialized and are (re)computed through domain.preComputeTwiddles()
+
+	// twiddles factor for the FFT using Generator for each stage of the recursive FFT
+	twiddles [][]babybear.Element
+
+	// twiddles factor for the FFT using GeneratorInv for each stage of the recursive FFT
+	twiddlesInv [][]babybear.Element
+
+	// we precompute these mostly to avoid the memory intensive bit reverse permutation in the groth16.Prover
+
+	// cosetTable u*<1,g,..,g^(n-1)>
+	cosetTable []babybear.Element
+
+	// cosetTable[i][j] = domain.Generator(i-th)SqrtInv ^ j
+	cosetTableInv []babybear.Element
+}
+
+// GeneratorFullMultiplicativeGroup returns a generator of 𝔽ᵣˣ
+func GeneratorFullMultiplicativeGroup() babybear.Element {
+	var res babybear.Element
+
+	res.SetUint64(31)
+
+	return res
+}
+
+// NewDomain returns a subgroup with a power of 2 cardinality
+// cardinality >= m
+// shift: when specified, it's the element by which the set of root of unity is shifted.
+func NewDomain(m uint64, opts ...DomainOption) *Domain {
+	opt := domainOptions(opts...)
+	domain := &Domain{}
+	x := ecc.NextPowerOfTwo(m)
+	domain.Cardinality = uint64(x)
+	domain.FrMultiplicativeGen = GeneratorFullMultiplicativeGroup()
+
+	if opt.shift != nil {
+		domain.FrMultiplicativeGen.Set(opt.shift)
+	}
+	domain.FrMultiplicativeGenInv.Inverse(&domain.FrMultiplicativeGen)
+
+	var err error
+	domain.Generator, err = Generator(m)
+	if err != nil {
+		panic(err)
+	}
+	domain.GeneratorInv.Inverse(&domain.Generator)
+	domain.CardinalityInv.SetUint64(uint64(x)).Inverse(&domain.CardinalityInv)
+
+	// twiddle factors
+	domain.withPrecompute = opt.withPrecompute
+	if domain.withPrecompute {
+		domain.preComputeTwiddles()
+	}
+
+	return domain
+}
+
+// Generator returns a generator for Z/2^(log(m))Z
+// or an error if m is too big (required root of unity doesn't exist)
+func Generator(m uint64) (babybear.Element, error) {
+	return babybear.Generator(m)
+}
+
+// Twiddles returns the twiddles factor for the FFT using Generator for each stage of the recursive FFT
+// or an error if the domain was created with the WithoutPrecompute option
+func (d *Domain) Twiddles() ([][]babybear.Element, error) {
+	if d.twiddles == nil {
+		return nil, errors.New("twiddles not precomputed")
+	}
+	return d.twiddles, nil
+}
+
+// TwiddlesInv returns the twiddles factor for the FFT using GeneratorInv for each stage of the recursive FFT
+// or an error if the domain was created with the WithoutPrecompute option
+func (d *Domain) TwiddlesInv() ([][]babybear.Element, error) {
+	if d.twiddlesInv == nil {
+		return nil, errors.New("twiddles not precomputed")
+	}
+	return d.twiddlesInv, nil
+}
+
+// CosetTable returns the cosetTable u*<1,g,..,g^(n-1)>
+// or an error if the domain was created with the WithoutPrecompute option
+func (d *Domain) CosetTable() ([]babybear.Element, error) {
+	if d.cosetTable == nil {
+		return nil, errors.New("cosetTable not precomputed")
+	}
+	return d.cosetTable, nil
+}
+
+// CosetTableInv returns the cosetTableInv u*<1,g,..,g^(n-1)>
+// or an error if the domain was created with the WithoutPrecompute option
+func (d *Domain) CosetTableInv() ([]babybear.Element, error) {
+	if d.cosetTableInv == nil {
+		return nil, errors.New("cosetTableInv not precomputed")
+	}
+	return d.cosetTableInv, nil
+}
+
+func (d *Domain) preComputeTwiddles() {
+
+	// nb fft stages
+	nbStages := uint64(bits.TrailingZeros64(d.Cardinality))
+
+	d.twiddles = make([][]babybear.Element, nbStages)
+	d.twiddlesInv = make([][]babybear.Element, nbStages)
+	d.cosetTable = make([]babybear.Element, d.Cardinality)
+	d.cosetTableInv = make([]babybear.Element, d.Cardinality)
+
+	var wg sync.WaitGroup
+
+	expTable := func(sqrt babybear.Element, t []babybear.Element) {
+		BuildExpTable(sqrt, t)
+		wg.Done()
+	}
+
+	wg.Add(4)
+	go func() {
+		buildTwiddles(d.twiddles, d.Generator, nbStages)
+		wg.Done()
+	}()
+	go func() {
+		buildTwiddles(d.twiddlesInv, d.GeneratorInv, nbStages)
+		wg.Done()
+	}()
+	go expTable(d.FrMultiplicativeGen, d.cosetTable)
+	go expTable(d.FrMultiplicativeGenInv, d.cosetTableInv)
+
+	wg.Wait()
+
+}
+
+func buildTwiddles(t [][]babybear.Element, omega babybear.Element, nbStages uint64) {
+	if nbStages == 0 {
+		return
+	}
+	if len(t) != int(nbStages) {
+		panic("invalid twiddle table")
+	}
+	// we just compute the first stage
+	t[0] = make([]babybear.Element, 1+(1<<(nbStages-1)))
+	BuildExpTable(omega, t[0])
+
+	// for the next stages, we just iterate on the first stage with larger stride
+	for i := uint64(1); i < nbStages; i++ {
+		t[i] = make([]babybear.Element, 1+(1<<(nbStages-i-1)))
+		k := 0
+		for j := 0; j < len(t[i]); j++ {
+			t[i][j] = t[0][k]
+			k += 1 << i
+		}
+	}
+
+}
+
+// BuildExpTable precomputes the first n powers of w in parallel
+// table[0] = w^0
+// table[1] = w^1
+// ...
+func BuildExpTable(w babybear.Element, table []babybear.Element) {
+	table[0].SetOne()
+	n := len(table)
+
+	// see if it makes sense to parallelize exp tables pre-computation
+	interval := 0
+	if runtime.NumCPU() >= 4 {
+		interval = (n - 1) / (runtime.NumCPU() / 4)
+	}
+
+	// this ratio roughly correspond to the number of multiplication one can do in place of a Exp operation
+	// TODO @gbotrel revisit this; Exps in this context will be by a "small power of 2" so faster than this ref ratio.
+	const ratioExpMul = 6000 / 17
+
+	if interval < ratioExpMul {
+		precomputeExpTableChunk(w, 1, table[1:])
+		return
+	}
+
+	// we parallelize
+	var wg sync.WaitGroup
+	for i := 1; i < n; i += interval {
+		start := i
+		end := i + interval
+		if end > n {
+			end = n
+		}
+		wg.Add(1)
+		go func() {
+			precomputeExpTableChunk(w, uint64(start), table[start:end])
+			wg.Done()
+		}()
+	}
+	wg.Wait()
+}
+
+func precomputeExpTableChunk(w babybear.Element, power uint64, table []babybear.Element) {
+
+	// this condition ensures that creating a domain of size 1 with cosets don't fail
+	if len(table) > 0 {
+		table[0].Exp(w, new(big.Int).SetUint64(power))
+		for i := 1; i < len(table); i++ {
+			table[i].Mul(&table[i-1], &w)
+		}
+	}
+}
+
+// WriteTo writes a binary representation of the domain (without the precomputed twiddle factors)
+// to the provided writer
+func (d *Domain) WriteTo(w io.Writer) (int64, error) {
+	// note to stay retro compatible with previous version using ecc/encoder, we encode as:
+	// d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute
+
+	var written int64
+	var err error
+
+	err = binary.Write(w, binary.BigEndian, d.Cardinality)
+	if err != nil {
+		return written, err
+	}
+	written += 8
+
+	toEncode := []*babybear.Element{&d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
+	for _, v := range toEncode {
+		buf := v.Bytes()
+		_, err = w.Write(buf[:])
+		if err != nil {
+			return written, err
+		}
+		written += babybear.Bytes
+	}
+
+	err = binary.Write(w, binary.BigEndian, d.withPrecompute)
+	if err != nil {
+		return written, err
+	}
+	written += 1
+
+	return written, nil
+}
+
+// ReadFrom attempts to decode a domain from Reader
+func (d *Domain) ReadFrom(r io.Reader) (int64, error) {
+
+	var read int64
+	var err error
+
+	err = binary.Read(r, binary.BigEndian, &d.Cardinality)
+	if err != nil {
+		return read, err
+	}
+	read += 8
+
+	toDecode := []*babybear.Element{&d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
+
+	for _, v := range toDecode {
+		var buf [babybear.Bytes]byte
+		_, err = r.Read(buf[:])
+		if err != nil {
+			return read, err
+		}
+		read += babybear.Bytes
+		*v, err = babybear.BigEndian.Element(&buf)
+		if err != nil {
+			return read, err
+		}
+	}
+
+	err = binary.Read(r, binary.BigEndian, &d.withPrecompute)
+	if err != nil {
+		return read, err
+	}
+	read += 1
+
+	if d.withPrecompute {
+		d.preComputeTwiddles()
+	}
+
+	return read, nil
+}
diff --git a/field/babybear/fft/domain_test.go b/field/babybear/fft/domain_test.go
new file mode 100644
index 0000000000..e445d3cc12
--- /dev/null
+++ b/field/babybear/fft/domain_test.go
@@ -0,0 +1,36 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fft
+
+import (
+	"bytes"
+	"reflect"
+	"testing"
+)
+
+func TestDomainSerialization(t *testing.T) {
+
+	domain := NewDomain(1 << 6)
+	var reconstructed Domain
+
+	var buf bytes.Buffer
+	written, err := domain.WriteTo(&buf)
+	if err != nil {
+		t.Fatal(err)
+	}
+	var read int64
+	read, err = reconstructed.ReadFrom(&buf)
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	if written != read {
+		t.Fatal("didn't read as many bytes as we wrote")
+	}
+	if !reflect.DeepEqual(domain, &reconstructed) {
+		t.Fatal("Domain.SetBytes(Bytes()) failed")
+	}
+}
diff --git a/field/babybear/fft/fft.go b/field/babybear/fft/fft.go
new file mode 100644
index 0000000000..bb69c72330
--- /dev/null
+++ b/field/babybear/fft/fft.go
@@ -0,0 +1,410 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fft
+
+import (
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/internal/parallel"
+	"math/big"
+	"math/bits"
+
+	"github.com/consensys/gnark-crypto/field/babybear"
+)
+
+// Decimation is used in the FFT call to select decimation in time or in frequency
+type Decimation uint8
+
+const (
+	DIT Decimation = iota
+	DIF
+)
+
+// parallelize threshold for a single butterfly op, if the fft stage is not parallelized already
+const butterflyThreshold = 16
+
+// FFT computes (recursively) the discrete Fourier transform of a and stores the result in a
+// if decimation == DIT (decimation in time), the input must be in bit-reversed order
+// if decimation == DIF (decimation in frequency), the output will be in bit-reversed order
+func (domain *Domain) FFT(a []babybear.Element, decimation Decimation, opts ...Option) {
+
+	opt := fftOptions(opts...)
+
+	// find the stage where we should stop spawning go routines in our recursive calls
+	// (ie when we have as many go routines running as we have available CPUs)
+	maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks)))
+	if opt.nbTasks == 1 {
+		maxSplits = -1
+	}
+
+	// if coset != 0, scale by coset table
+	if opt.coset {
+		if decimation == DIT {
+			// scale by coset table (in bit reversed order)
+			cosetTable := domain.cosetTable
+			if !domain.withPrecompute {
+				// we need to build the full table or do a bit reverse dance.
+				cosetTable = make([]babybear.Element, len(a))
+				BuildExpTable(domain.FrMultiplicativeGen, cosetTable)
+			}
+			parallel.Execute(len(a), func(start, end int) {
+				n := uint64(len(a))
+				nn := uint64(64 - bits.TrailingZeros64(n))
+				for i := start; i < end; i++ {
+					irev := int(bits.Reverse64(uint64(i)) >> nn)
+					a[i].Mul(&a[i], &cosetTable[irev])
+				}
+			}, opt.nbTasks)
+		} else {
+			if domain.withPrecompute {
+				parallel.Execute(len(a), func(start, end int) {
+					for i := start; i < end; i++ {
+						a[i].Mul(&a[i], &domain.cosetTable[i])
+					}
+				}, opt.nbTasks)
+			} else {
+				c := domain.FrMultiplicativeGen
+				parallel.Execute(len(a), func(start, end int) {
+					var at babybear.Element
+					at.Exp(c, big.NewInt(int64(start)))
+					for i := start; i < end; i++ {
+						a[i].Mul(&a[i], &at)
+						at.Mul(&at, &c)
+					}
+				}, opt.nbTasks)
+			}
+
+		}
+	}
+
+	twiddles := domain.twiddles
+	twiddlesStartStage := 0
+	if !domain.withPrecompute {
+		twiddlesStartStage = 3
+		nbStages := int(bits.TrailingZeros64(domain.Cardinality))
+		if nbStages-twiddlesStartStage > 0 {
+			twiddles = make([][]babybear.Element, nbStages-twiddlesStartStage)
+			w := domain.Generator
+			w.Exp(w, big.NewInt(int64(1<<twiddlesStartStage)))
+			buildTwiddles(twiddles, w, uint64(nbStages-twiddlesStartStage))
+		} // else, we don't need twiddles
+	}
+
+	switch decimation {
+	case DIF:
+		difFFT(a, domain.Generator, twiddles, twiddlesStartStage, 0, maxSplits, nil, opt.nbTasks)
+	case DIT:
+		ditFFT(a, domain.Generator, twiddles, twiddlesStartStage, 0, maxSplits, nil, opt.nbTasks)
+	default:
+		panic("not implemented")
+	}
+}
+
+// FFTInverse computes (recursively) the inverse discrete Fourier transform of a and stores the result in a
+// if decimation == DIT (decimation in time), the input must be in bit-reversed order
+// if decimation == DIF (decimation in frequency), the output will be in bit-reversed order
+// coset sets the shift of the fft (0 = no shift, standard fft)
+// len(a) must be a power of 2, and w must be a len(a)th root of unity in field F.
+func (domain *Domain) FFTInverse(a []babybear.Element, decimation Decimation, opts ...Option) {
+	opt := fftOptions(opts...)
+
+	// find the stage where we should stop spawning go routines in our recursive calls
+	// (ie when we have as many go routines running as we have available CPUs)
+	maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks)))
+	if opt.nbTasks == 1 {
+		maxSplits = -1
+	}
+
+	twiddlesInv := domain.twiddlesInv
+	twiddlesStartStage := 0
+	if !domain.withPrecompute {
+		twiddlesStartStage = 3
+		nbStages := int(bits.TrailingZeros64(domain.Cardinality))
+		if nbStages-twiddlesStartStage > 0 {
+			twiddlesInv = make([][]babybear.Element, nbStages-twiddlesStartStage)
+			w := domain.GeneratorInv
+			w.Exp(w, big.NewInt(int64(1<<twiddlesStartStage)))
+			buildTwiddles(twiddlesInv, w, uint64(nbStages-twiddlesStartStage))
+		} // else, we don't need twiddles
+	}
+
+	switch decimation {
+	case DIF:
+		difFFT(a, domain.GeneratorInv, twiddlesInv, twiddlesStartStage, 0, maxSplits, nil, opt.nbTasks)
+	case DIT:
+		ditFFT(a, domain.GeneratorInv, twiddlesInv, twiddlesStartStage, 0, maxSplits, nil, opt.nbTasks)
+	default:
+		panic("not implemented")
+	}
+
+	// scale by CardinalityInv
+	if !opt.coset {
+		parallel.Execute(len(a), func(start, end int) {
+			for i := start; i < end; i++ {
+				a[i].Mul(&a[i], &domain.CardinalityInv)
+			}
+		}, opt.nbTasks)
+		return
+	}
+
+	if decimation == DIT {
+		if domain.withPrecompute {
+			parallel.Execute(len(a), func(start, end int) {
+				for i := start; i < end; i++ {
+					a[i].Mul(&a[i], &domain.cosetTableInv[i]).
+						Mul(&a[i], &domain.CardinalityInv)
+				}
+			}, opt.nbTasks)
+		} else {
+			c := domain.FrMultiplicativeGenInv
+			parallel.Execute(len(a), func(start, end int) {
+				var at babybear.Element
+				at.Exp(c, big.NewInt(int64(start)))
+				at.Mul(&at, &domain.CardinalityInv)
+				for i := start; i < end; i++ {
+					a[i].Mul(&a[i], &at)
+					at.Mul(&at, &c)
+				}
+			}, opt.nbTasks)
+		}
+		return
+	}
+
+	// decimation == DIF, need to access coset table in bit reversed order.
+	cosetTableInv := domain.cosetTableInv
+	if !domain.withPrecompute {
+		// we need to build the full table or do a bit reverse dance.
+		cosetTableInv = make([]babybear.Element, len(a))
+		BuildExpTable(domain.FrMultiplicativeGenInv, cosetTableInv)
+	}
+	parallel.Execute(len(a), func(start, end int) {
+		n := uint64(len(a))
+		nn := uint64(64 - bits.TrailingZeros64(n))
+		for i := start; i < end; i++ {
+			irev := int(bits.Reverse64(uint64(i)) >> nn)
+			a[i].Mul(&a[i], &cosetTableInv[irev]).
+				Mul(&a[i], &domain.CardinalityInv)
+		}
+	}, opt.nbTasks)
+
+}
+
+func difFFT(a []babybear.Element, w babybear.Element, twiddles [][]babybear.Element, twiddlesStartStage, stage, maxSplits int, chDone chan struct{}, nbTasks int) {
+	if chDone != nil {
+		defer close(chDone)
+	}
+
+	n := len(a)
+	if n == 1 {
+		return
+	} else if n == 256 && stage >= twiddlesStartStage {
+		kerDIFNP_256(a, twiddles, stage-twiddlesStartStage)
+		return
+	}
+	m := n >> 1
+
+	parallelButterfly := (m > butterflyThreshold) && (stage < maxSplits)
+
+	if stage < twiddlesStartStage {
+		if parallelButterfly {
+			w := w
+			parallel.Execute(m, func(start, end int) {
+				if start == 0 {
+					babybear.Butterfly(&a[0], &a[m])
+					start++
+				}
+				var at babybear.Element
+				at.Exp(w, big.NewInt(int64(start)))
+				innerDIFWithoutTwiddles(a, at, w, start, end, m)
+			}, nbTasks/(1<<(stage))) // 1 << stage == estimated used CPUs
+		} else {
+			innerDIFWithoutTwiddles(a, w, w, 0, m, m)
+		}
+		// compute next twiddle
+		w.Square(&w)
+	} else {
+		if parallelButterfly {
+			parallel.Execute(m, func(start, end int) {
+				innerDIFWithTwiddles(a, twiddles[stage-twiddlesStartStage], start, end, m)
+			}, nbTasks/(1<<(stage)))
+		} else {
+			innerDIFWithTwiddles(a, twiddles[stage-twiddlesStartStage], 0, m, m)
+		}
+	}
+
+	if m == 1 {
+		return
+	}
+
+	nextStage := stage + 1
+	if stage < maxSplits {
+		chDone := make(chan struct{}, 1)
+		go difFFT(a[m:n], w, twiddles, twiddlesStartStage, nextStage, maxSplits, chDone, nbTasks)
+		difFFT(a[0:m], w, twiddles, twiddlesStartStage, nextStage, maxSplits, nil, nbTasks)
+		<-chDone
+	} else {
+		difFFT(a[0:m], w, twiddles, twiddlesStartStage, nextStage, maxSplits, nil, nbTasks)
+		difFFT(a[m:n], w, twiddles, twiddlesStartStage, nextStage, maxSplits, nil, nbTasks)
+	}
+
+}
+
+func innerDIFWithTwiddles(a []babybear.Element, twiddles []babybear.Element, start, end, m int) {
+	if start == 0 {
+		babybear.Butterfly(&a[0], &a[m])
+		start++
+	}
+	for i := start; i < end; i++ {
+		babybear.Butterfly(&a[i], &a[i+m])
+		a[i+m].Mul(&a[i+m], &twiddles[i])
+	}
+}
+
+func innerDIFWithoutTwiddles(a []babybear.Element, at, w babybear.Element, start, end, m int) {
+	if start == 0 {
+		babybear.Butterfly(&a[0], &a[m])
+		start++
+	}
+	for i := start; i < end; i++ {
+		babybear.Butterfly(&a[i], &a[i+m])
+		a[i+m].Mul(&a[i+m], &at)
+		at.Mul(&at, &w)
+	}
+}
+
+func ditFFT(a []babybear.Element, w babybear.Element, twiddles [][]babybear.Element, twiddlesStartStage, stage, maxSplits int, chDone chan struct{}, nbTasks int) {
+	if chDone != nil {
+		defer close(chDone)
+	}
+	n := len(a)
+	if n == 1 {
+		return
+	} else if n == 256 && stage >= twiddlesStartStage {
+		kerDITNP_256(a, twiddles, stage-twiddlesStartStage)
+		return
+	}
+	m := n >> 1
+
+	nextStage := stage + 1
+	nextW := w
+	nextW.Square(&nextW)
+
+	if stage < maxSplits {
+		// that's the only time we fire go routines
+		chDone := make(chan struct{}, 1)
+		go ditFFT(a[m:], nextW, twiddles, twiddlesStartStage, nextStage, maxSplits, chDone, nbTasks)
+		ditFFT(a[0:m], nextW, twiddles, twiddlesStartStage, nextStage, maxSplits, nil, nbTasks)
+		<-chDone
+	} else {
+		ditFFT(a[0:m], nextW, twiddles, twiddlesStartStage, nextStage, maxSplits, nil, nbTasks)
+		ditFFT(a[m:n], nextW, twiddles, twiddlesStartStage, nextStage, maxSplits, nil, nbTasks)
+	}
+
+	parallelButterfly := (m > butterflyThreshold) && (stage < maxSplits)
+
+	if stage < twiddlesStartStage {
+		// we need to compute the twiddles for this stage on the fly.
+		if parallelButterfly {
+			w := w
+			parallel.Execute(m, func(start, end int) {
+				if start == 0 {
+					babybear.Butterfly(&a[0], &a[m])
+					start++
+				}
+				var at babybear.Element
+				at.Exp(w, big.NewInt(int64(start)))
+				innerDITWithoutTwiddles(a, at, w, start, end, m)
+			}, nbTasks/(1<<(stage))) // 1 << stage == estimated used CPUs
+
+		} else {
+			innerDITWithoutTwiddles(a, w, w, 0, m, m)
+		}
+		return
+	}
+	if parallelButterfly {
+		parallel.Execute(m, func(start, end int) {
+			innerDITWithTwiddles(a, twiddles[stage-twiddlesStartStage], start, end, m)
+		}, nbTasks/(1<<(stage)))
+	} else {
+		innerDITWithTwiddles(a, twiddles[stage-twiddlesStartStage], 0, m, m)
+	}
+}
+
+func innerDITWithTwiddles(a []babybear.Element, twiddles []babybear.Element, start, end, m int) {
+	if start == 0 {
+		babybear.Butterfly(&a[0], &a[m])
+		start++
+	}
+	for i := start; i < end; i++ {
+		a[i+m].Mul(&a[i+m], &twiddles[i])
+		babybear.Butterfly(&a[i], &a[i+m])
+	}
+}
+
+func innerDITWithoutTwiddles(a []babybear.Element, at, w babybear.Element, start, end, m int) {
+	if start == 0 {
+		babybear.Butterfly(&a[0], &a[m])
+		start++
+	}
+	for i := start; i < end; i++ {
+		a[i+m].Mul(&a[i+m], &at)
+		babybear.Butterfly(&a[i], &a[i+m])
+		at.Mul(&at, &w)
+	}
+}
+
+func kerDIFNP_256(a []babybear.Element, twiddles [][]babybear.Element, stage int) {
+	// code unrolled & generated by internal/generator/fft/template/fft.go.tmpl
+
+	innerDIFWithTwiddles(a[:256], twiddles[stage+0], 0, 128, 128)
+	for offset := 0; offset < 256; offset += 128 {
+		innerDIFWithTwiddles(a[offset:offset+128], twiddles[stage+1], 0, 64, 64)
+	}
+	for offset := 0; offset < 256; offset += 64 {
+		innerDIFWithTwiddles(a[offset:offset+64], twiddles[stage+2], 0, 32, 32)
+	}
+	for offset := 0; offset < 256; offset += 32 {
+		innerDIFWithTwiddles(a[offset:offset+32], twiddles[stage+3], 0, 16, 16)
+	}
+	for offset := 0; offset < 256; offset += 16 {
+		innerDIFWithTwiddles(a[offset:offset+16], twiddles[stage+4], 0, 8, 8)
+	}
+	for offset := 0; offset < 256; offset += 8 {
+		innerDIFWithTwiddles(a[offset:offset+8], twiddles[stage+5], 0, 4, 4)
+	}
+	for offset := 0; offset < 256; offset += 4 {
+		innerDIFWithTwiddles(a[offset:offset+4], twiddles[stage+6], 0, 2, 2)
+	}
+	for offset := 0; offset < 256; offset += 2 {
+		babybear.Butterfly(&a[offset], &a[offset+1])
+	}
+}
+
+func kerDITNP_256(a []babybear.Element, twiddles [][]babybear.Element, stage int) {
+	// code unrolled & generated by internal/generator/fft/template/fft.go.tmpl
+
+	for offset := 0; offset < 256; offset += 2 {
+		babybear.Butterfly(&a[offset], &a[offset+1])
+	}
+	for offset := 0; offset < 256; offset += 4 {
+		innerDITWithTwiddles(a[offset:offset+4], twiddles[stage+6], 0, 2, 2)
+	}
+	for offset := 0; offset < 256; offset += 8 {
+		innerDITWithTwiddles(a[offset:offset+8], twiddles[stage+5], 0, 4, 4)
+	}
+	for offset := 0; offset < 256; offset += 16 {
+		innerDITWithTwiddles(a[offset:offset+16], twiddles[stage+4], 0, 8, 8)
+	}
+	for offset := 0; offset < 256; offset += 32 {
+		innerDITWithTwiddles(a[offset:offset+32], twiddles[stage+3], 0, 16, 16)
+	}
+	for offset := 0; offset < 256; offset += 64 {
+		innerDITWithTwiddles(a[offset:offset+64], twiddles[stage+2], 0, 32, 32)
+	}
+	for offset := 0; offset < 256; offset += 128 {
+		innerDITWithTwiddles(a[offset:offset+128], twiddles[stage+1], 0, 64, 64)
+	}
+	innerDITWithTwiddles(a[:256], twiddles[stage+0], 0, 128, 128)
+}
diff --git a/field/babybear/fft/fft_test.go b/field/babybear/fft/fft_test.go
new file mode 100644
index 0000000000..b8619c1ccf
--- /dev/null
+++ b/field/babybear/fft/fft_test.go
@@ -0,0 +1,318 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fft
+
+import (
+	"math/big"
+	"strconv"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/field/babybear"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/gen"
+	"github.com/leanovate/gopter/prop"
+
+	"fmt"
+)
+
+func TestFFT(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	parameters.MinSuccessfulTests = 5
+	properties := gopter.NewProperties(parameters)
+
+	for maxSize := 2; maxSize <= 1<<10; maxSize <<= 1 {
+
+		domainWithPrecompute := NewDomain(uint64(maxSize))
+		domainWithoutPrecompute := NewDomain(uint64(maxSize), WithoutPrecompute())
+
+		for domainName, domain := range map[string]*Domain{
+			"with precompute":    domainWithPrecompute,
+			"without precompute": domainWithoutPrecompute,
+		} {
+			domainName := domainName
+			domain := domain
+			t.Logf("domain: %s", domainName)
+			properties.Property("DIF FFT should be consistent with dual basis", prop.ForAll(
+
+				// checks that a random evaluation of a dual function eval(gen**ithpower) is consistent with the FFT result
+				func(ithpower int) bool {
+
+					pol := make([]babybear.Element, maxSize)
+					backupPol := make([]babybear.Element, maxSize)
+
+					for i := 0; i < maxSize; i++ {
+						pol[i].SetRandom()
+					}
+					copy(backupPol, pol)
+
+					domain.FFT(pol, DIF)
+					BitReverse(pol)
+
+					sample := domain.Generator
+					sample.Exp(sample, big.NewInt(int64(ithpower)))
+
+					eval := evaluatePolynomial(backupPol, sample)
+
+					return eval.Equal(&pol[ithpower])
+
+				},
+				gen.IntRange(0, maxSize-1),
+			))
+
+			properties.Property("DIF FFT on cosets should be consistent with dual basis", prop.ForAll(
+
+				// checks that a random evaluation of a dual function eval(gen**ithpower) is consistent with the FFT result
+				func(ithpower int) bool {
+
+					pol := make([]babybear.Element, maxSize)
+					backupPol := make([]babybear.Element, maxSize)
+
+					for i := 0; i < maxSize; i++ {
+						pol[i].SetRandom()
+					}
+					copy(backupPol, pol)
+
+					domain.FFT(pol, DIF, OnCoset())
+					BitReverse(pol)
+
+					sample := domain.Generator
+					sample.Exp(sample, big.NewInt(int64(ithpower))).
+						Mul(&sample, &domain.FrMultiplicativeGen)
+
+					eval := evaluatePolynomial(backupPol, sample)
+
+					return eval.Equal(&pol[ithpower])
+
+				},
+				gen.IntRange(0, maxSize-1),
+			))
+
+			properties.Property("DIT FFT should be consistent with dual basis", prop.ForAll(
+
+				// checks that a random evaluation of a dual function eval(gen**ithpower) is consistent with the FFT result
+				func(ithpower int) bool {
+
+					pol := make([]babybear.Element, maxSize)
+					backupPol := make([]babybear.Element, maxSize)
+
+					for i := 0; i < maxSize; i++ {
+						pol[i].SetRandom()
+					}
+					copy(backupPol, pol)
+
+					BitReverse(pol)
+					domain.FFT(pol, DIT)
+
+					sample := domain.Generator
+					sample.Exp(sample, big.NewInt(int64(ithpower)))
+
+					eval := evaluatePolynomial(backupPol, sample)
+
+					return eval.Equal(&pol[ithpower])
+
+				},
+				gen.IntRange(0, maxSize-1),
+			))
+
+			properties.Property("bitReverse(DIF FFT(DIT FFT (bitReverse))))==id", prop.ForAll(
+
+				func() bool {
+
+					pol := make([]babybear.Element, maxSize)
+					backupPol := make([]babybear.Element, maxSize)
+
+					for i := 0; i < maxSize; i++ {
+						pol[i].SetRandom()
+					}
+					copy(backupPol, pol)
+
+					BitReverse(pol)
+					domain.FFT(pol, DIT)
+					domain.FFTInverse(pol, DIF)
+					BitReverse(pol)
+
+					check := true
+					for i := 0; i < len(pol); i++ {
+						check = check && pol[i].Equal(&backupPol[i])
+					}
+					return check
+				},
+			))
+
+			for nbCosets := 2; nbCosets < 5; nbCosets++ {
+				properties.Property(fmt.Sprintf("bitReverse(DIF FFT(DIT FFT (bitReverse))))==id on %d cosets", nbCosets), prop.ForAll(
+
+					func() bool {
+
+						pol := make([]babybear.Element, maxSize)
+						backupPol := make([]babybear.Element, maxSize)
+
+						for i := 0; i < maxSize; i++ {
+							pol[i].SetRandom()
+						}
+						copy(backupPol, pol)
+
+						check := true
+
+						for i := 1; i <= nbCosets; i++ {
+
+							BitReverse(pol)
+							domain.FFT(pol, DIT, OnCoset())
+							domain.FFTInverse(pol, DIF, OnCoset())
+							BitReverse(pol)
+
+							for i := 0; i < len(pol); i++ {
+								check = check && pol[i].Equal(&backupPol[i])
+							}
+						}
+
+						return check
+					},
+				))
+			}
+
+			properties.Property("DIT FFT(DIF FFT)==id", prop.ForAll(
+
+				func() bool {
+
+					pol := make([]babybear.Element, maxSize)
+					backupPol := make([]babybear.Element, maxSize)
+
+					for i := 0; i < maxSize; i++ {
+						pol[i].SetRandom()
+					}
+					copy(backupPol, pol)
+
+					domain.FFTInverse(pol, DIF)
+					domain.FFT(pol, DIT)
+
+					check := true
+					for i := 0; i < len(pol); i++ {
+						check = check && (pol[i] == backupPol[i])
+					}
+					return check
+				},
+			))
+
+			properties.Property("DIT FFT(DIF FFT)==id on cosets", prop.ForAll(
+
+				func() bool {
+
+					pol := make([]babybear.Element, maxSize)
+					backupPol := make([]babybear.Element, maxSize)
+
+					for i := 0; i < maxSize; i++ {
+						pol[i].SetRandom()
+					}
+					copy(backupPol, pol)
+
+					domain.FFTInverse(pol, DIF, OnCoset())
+					domain.FFT(pol, DIT, OnCoset())
+
+					for i := 0; i < len(pol); i++ {
+						if !(pol[i].Equal(&backupPol[i])) {
+							return false
+						}
+					}
+
+					// compute with nbTasks == 1
+					domain.FFTInverse(pol, DIF, OnCoset(), WithNbTasks(1))
+					domain.FFT(pol, DIT, OnCoset(), WithNbTasks(1))
+
+					for i := 0; i < len(pol); i++ {
+						if !(pol[i].Equal(&backupPol[i])) {
+							return false
+						}
+					}
+
+					return true
+				},
+			))
+		}
+		properties.TestingRun(t, gopter.ConsoleReporter(false))
+	}
+
+}
+
+// --------------------------------------------------------------------
+// benches
+
+func BenchmarkFFT(b *testing.B) {
+
+	const maxSize = 1 << 20
+
+	pol := make([]babybear.Element, maxSize)
+	pol[0].SetRandom()
+	for i := 1; i < maxSize; i++ {
+		pol[i] = pol[i-1]
+	}
+
+	for i := 8; i < 20; i++ {
+		sizeDomain := 1 << i
+		b.Run("fft 2**"+strconv.Itoa(i)+"bits", func(b *testing.B) {
+			domain := NewDomain(uint64(sizeDomain))
+			b.ResetTimer()
+			for j := 0; j < b.N; j++ {
+				domain.FFT(pol[:sizeDomain], DIT)
+			}
+		})
+		b.Run("fft 2**"+strconv.Itoa(i)+"bits (coset)", func(b *testing.B) {
+			domain := NewDomain(uint64(sizeDomain))
+			b.ResetTimer()
+			for j := 0; j < b.N; j++ {
+				domain.FFT(pol[:sizeDomain], DIT, OnCoset())
+			}
+		})
+	}
+
+}
+
+func BenchmarkFFTDITCosetReference(b *testing.B) {
+	const maxSize = 1 << 20
+
+	pol := make([]babybear.Element, maxSize)
+	pol[0].SetRandom()
+	for i := 1; i < maxSize; i++ {
+		pol[i] = pol[i-1]
+	}
+
+	domain := NewDomain(maxSize)
+
+	b.ResetTimer()
+	for j := 0; j < b.N; j++ {
+		domain.FFT(pol, DIT, OnCoset())
+	}
+}
+
+func BenchmarkFFTDIFReference(b *testing.B) {
+	const maxSize = 1 << 20
+
+	pol := make([]babybear.Element, maxSize)
+	pol[0].SetRandom()
+	for i := 1; i < maxSize; i++ {
+		pol[i] = pol[i-1]
+	}
+
+	domain := NewDomain(maxSize)
+
+	b.ResetTimer()
+	for j := 0; j < b.N; j++ {
+		domain.FFT(pol, DIF)
+	}
+}
+
+func evaluatePolynomial(pol []babybear.Element, val babybear.Element) babybear.Element {
+	var acc, res, tmp babybear.Element
+	res.Set(&pol[0])
+	acc.Set(&val)
+	for i := 1; i < len(pol); i++ {
+		tmp.Mul(&acc, &pol[i])
+		res.Add(&res, &tmp)
+		acc.Mul(&acc, &val)
+	}
+	return res
+}
diff --git a/field/babybear/fft/options.go b/field/babybear/fft/options.go
new file mode 100644
index 0000000000..ef1ded416b
--- /dev/null
+++ b/field/babybear/fft/options.go
@@ -0,0 +1,92 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fft
+
+import (
+	"runtime"
+
+	"github.com/consensys/gnark-crypto/field/babybear"
+)
+
+// Option defines option for altering the behavior of FFT methods.
+// See the descriptions of functions returning instances of this type for
+// particular options.
+type Option func(*fftConfig)
+
+type fftConfig struct {
+	coset   bool
+	nbTasks int
+}
+
+// OnCoset if provided, FFT(a) returns the evaluation of a on a coset.
+func OnCoset() Option {
+	return func(opt *fftConfig) {
+		opt.coset = true
+	}
+}
+
+// WithNbTasks sets the max number of task (go routine) to spawn. Must be between 1 and 512.
+func WithNbTasks(nbTasks int) Option {
+	if nbTasks < 1 {
+		nbTasks = 1
+	} else if nbTasks > 512 {
+		nbTasks = 512
+	}
+	return func(opt *fftConfig) {
+		opt.nbTasks = nbTasks
+	}
+}
+
+// default options
+func fftOptions(opts ...Option) fftConfig {
+	// apply options
+	opt := fftConfig{
+		coset:   false,
+		nbTasks: runtime.NumCPU(),
+	}
+	for _, option := range opts {
+		option(&opt)
+	}
+	return opt
+}
+
+// DomainOption defines option for altering the definition of the FFT domain
+// See the descriptions of functions returning instances of this type for
+// particular options.
+type DomainOption func(*domainConfig)
+
+type domainConfig struct {
+	shift          *babybear.Element
+	withPrecompute bool
+}
+
+// WithShift sets the FrMultiplicativeGen of the domain.
+// Default is generator of the largest 2-adic subgroup.
+func WithShift(shift babybear.Element) DomainOption {
+	return func(opt *domainConfig) {
+		opt.shift = new(babybear.Element).Set(&shift)
+	}
+}
+
+// WithoutPrecompute disables precomputation of twiddles in the domain.
+// When this option is set, FFTs will be slower, but will use less memory.
+func WithoutPrecompute() DomainOption {
+	return func(opt *domainConfig) {
+		opt.withPrecompute = false
+	}
+}
+
+// default options
+func domainOptions(opts ...DomainOption) domainConfig {
+	// apply options
+	opt := domainConfig{
+		withPrecompute: true,
+	}
+	for _, option := range opts {
+		option(&opt)
+	}
+	return opt
+}
diff --git a/field/babybear/generator.go b/field/babybear/generator.go
new file mode 100644
index 0000000000..18d6198950
--- /dev/null
+++ b/field/babybear/generator.go
@@ -0,0 +1,36 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package babybear
+
+import (
+	"fmt"
+	"math/big"
+	"math/bits"
+
+	"github.com/consensys/gnark-crypto/ecc"
+)
+
+// Generator returns a generator for Z/2^(log(m))Z
+// or an error if m is too big (required root of unity doesn't exist)
+func Generator(m uint64) (Element, error) {
+	x := ecc.NextPowerOfTwo(m)
+
+	var rootOfUnity Element
+
+	rootOfUnity.SetString("440564289")
+	const maxOrderRoot uint64 = 27
+
+	// find generator for Z/2^(log(m))Z
+	logx := uint64(bits.TrailingZeros64(x))
+	if logx > maxOrderRoot {
+		return Element{}, fmt.Errorf("m (%d) is too big: the required root of unity does not exist", m)
+	}
+
+	expo := uint64(1 << (maxOrderRoot - logx))
+	var generator Element
+	generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x
+	return generator, nil
+}
diff --git a/field/generator/asm/amd64/build.go b/field/generator/asm/amd64/build.go
index 8372eebc1d..7b99c3cbfe 100644
--- a/field/generator/asm/amd64/build.go
+++ b/field/generator/asm/amd64/build.go
@@ -213,7 +213,7 @@ func (f *FFAmd64) mu() string {
 	return "$const_mu"
 }
 
-func GenerateFieldWrapper(w io.Writer, F *config.FieldConfig, asmDirBuildPath, asmDirIncludePath string) error {
+func GenerateFieldWrapper(w io.Writer, F *config.Field, asmDirBuildPath, asmDirIncludePath string) error {
 	// for each field we generate the defines for the modulus and the montgomery constant
 	f := NewFFAmd64(w, F.NbWords)
 
diff --git a/field/generator/asm/arm64/build.go b/field/generator/asm/arm64/build.go
index 1752dae187..93170d5c75 100644
--- a/field/generator/asm/arm64/build.go
+++ b/field/generator/asm/arm64/build.go
@@ -52,7 +52,7 @@ type FFArm64 struct {
 	mDefines             map[string]defineFn
 }
 
-func GenerateFieldWrapper(w io.Writer, F *config.FieldConfig, asmDirBuildPath, asmDirIncludePath string) error {
+func GenerateFieldWrapper(w io.Writer, F *config.Field, asmDirBuildPath, asmDirIncludePath string) error {
 	// for each field we generate the defines for the modulus and the montgomery constant
 	f := NewFFArm64(w, F.NbWords)
 
diff --git a/field/generator/config/asm_config.go b/field/generator/config/asm_config.go
new file mode 100644
index 0000000000..b7e998e322
--- /dev/null
+++ b/field/generator/config/asm_config.go
@@ -0,0 +1,6 @@
+package config
+
+type Assembly struct {
+	BuildDir   string
+	IncludeDir string
+}
diff --git a/field/generator/config/extension.go b/field/generator/config/extension.go
index 53221f89c3..4247db68ae 100644
--- a/field/generator/config/extension.go
+++ b/field/generator/config/extension.go
@@ -6,13 +6,13 @@ type Element []big.Int
 
 // Extension is a simple radical extension, obtained by adjoining ⁿ√α to Fp
 type Extension struct {
-	Base   *FieldConfig //Fp
-	Size   big.Int      //q
-	Degree int          //n such that q = pⁿ TODO: Make uint8 so forced to be positive and small
-	RootOf int64        //α
+	Base   *Field  //Fp
+	Size   big.Int //q
+	Degree int     //n such that q = pⁿ TODO: Make uint8 so forced to be positive and small
+	RootOf int64   //α
 }
 
-func NewTower(base *FieldConfig, degree uint8, rootOf int64) Extension {
+func NewTower(base *Field, degree uint8, rootOf int64) Extension {
 	ret := Extension{
 		Degree: int(degree),
 		RootOf: rootOf,
diff --git a/field/generator/config/fft_config.go b/field/generator/config/fft_config.go
new file mode 100644
index 0000000000..e36d38aa0d
--- /dev/null
+++ b/field/generator/config/fft_config.go
@@ -0,0 +1,25 @@
+package config
+
+type FFT struct {
+	// TODO this should be in the finite field package API
+	GeneratorFullMultiplicativeGroup uint64 // generator of \mathbb{F}_r^{*}
+
+	// TODO should be generated by goff
+	GeneratorMaxTwoAdicSubgroup string // generator of the maximum subgroup of size 2^<something>
+
+	// TODO should be generated by goff
+	LogTwoOrderMaxTwoAdicSubgroup string // log_2 of the max order of the max two adic subgroup
+
+}
+
+// NewFFTConfig returns a data structure with needed information to generate apis for the FFT
+func NewConfig(
+	genFullMultiplicativeGroup uint64,
+	generatorMaxTwoAdicSubgroup,
+	logTwoOrderMaxTwoAdicSubgroup string) FFT {
+	return FFT{
+		GeneratorFullMultiplicativeGroup: genFullMultiplicativeGroup,
+		GeneratorMaxTwoAdicSubgroup:      generatorMaxTwoAdicSubgroup,
+		LogTwoOrderMaxTwoAdicSubgroup:    logTwoOrderMaxTwoAdicSubgroup,
+	}
+}
diff --git a/field/generator/config/field_config.go b/field/generator/config/field_config.go
index 7810144356..a1c8e30fa5 100644
--- a/field/generator/config/field_config.go
+++ b/field/generator/config/field_config.go
@@ -20,8 +20,8 @@ var (
 	errParseModulus = errors.New("can't parse modulus")
 )
 
-// FieldConfig precomputed values used in template for code generation of field element APIs
-type FieldConfig struct {
+// Field precomputed values used in template for code generation of field element APIs
+type Field struct {
 	PackageName               string
 	ElementName               string
 	ModulusBig                *big.Int
@@ -85,7 +85,7 @@ type Word struct {
 // NewFieldConfig returns a data structure with needed information to generate apis for field element
 //
 // See field/generator package
-func NewFieldConfig(packageName, elementName, modulus string, useAddChain bool) (*FieldConfig, error) {
+func NewFieldConfig(packageName, elementName, modulus string, useAddChain bool) (*Field, error) {
 	// parse modulus
 	var bModulus big.Int
 	if _, ok := bModulus.SetString(modulus, 0); !ok {
@@ -93,7 +93,7 @@ func NewFieldConfig(packageName, elementName, modulus string, useAddChain bool)
 	}
 
 	// field info
-	F := &FieldConfig{
+	F := &Field{
 		PackageName: packageName,
 		ElementName: elementName,
 		Modulus:     bModulus.Text(10),
@@ -289,6 +289,12 @@ func NewFieldConfig(packageName, elementName, modulus string, useAddChain bool)
 	// moduli that meet the condition F.NoCarry
 	// asm code generation for moduli with more than 6 words can be optimized further
 	F.GenerateOpsAMD64 = F.NoCarry && F.NbWords <= 12 && F.NbWords > 1
+	if F.NbWords == 4 && F.GenerateOpsAMD64 && F.NbBits <= 225 {
+		// 4 words field with 225 bits or less have no vector ops
+		// for now since we generate both in same file we disable
+		// TODO @gbotrel
+		F.GenerateOpsAMD64 = false
+	}
 	F.GenerateVectorOpsAMD64 = F.GenerateOpsAMD64 && F.NbWords == 4 && F.NbBits > 225
 	F.GenerateOpsARM64 = F.GenerateOpsAMD64 && (F.NbWords%2 == 0)
 	F.GenerateVectorOpsARM64 = false
@@ -354,7 +360,7 @@ func extendedEuclideanAlgo(r, q, rInv, qInv *big.Int) {
 
 // StringToMont takes an element written in string form, and returns it in Montgomery form
 // Useful for hard-coding in implementation field elements from standards documents
-func (f *FieldConfig) StringToMont(str string) big.Int {
+func (f *Field) StringToMont(str string) big.Int {
 
 	var i big.Int
 	i.SetString(str, 0)
@@ -363,14 +369,14 @@ func (f *FieldConfig) StringToMont(str string) big.Int {
 	return i
 }
 
-func (f *FieldConfig) ToMont(nonMont big.Int) big.Int {
+func (f *Field) ToMont(nonMont big.Int) big.Int {
 	var mont big.Int
 	mont.Lsh(&nonMont, uint(f.NbWords)*uint(f.Word.BitSize))
 	mont.Mod(&mont, f.ModulusBig)
 	return mont
 }
 
-func (f *FieldConfig) FromMont(nonMont *big.Int, mont *big.Int) *FieldConfig {
+func (f *Field) FromMont(nonMont *big.Int, mont *big.Int) *Field {
 
 	if f.NbWords == 0 {
 		nonMont.SetInt64(0)
@@ -384,7 +390,7 @@ func (f *FieldConfig) FromMont(nonMont *big.Int, mont *big.Int) *FieldConfig {
 	return f
 }
 
-func (f *FieldConfig) Exp(res *big.Int, x *big.Int, pow *big.Int) *FieldConfig {
+func (f *Field) Exp(res *big.Int, x *big.Int, pow *big.Int) *Field {
 	res.SetInt64(1)
 
 	for i := pow.BitLen() - 1; ; {
@@ -405,7 +411,7 @@ func (f *FieldConfig) Exp(res *big.Int, x *big.Int, pow *big.Int) *FieldConfig {
 	return f
 }
 
-func (f *FieldConfig) halve(res *big.Int, x *big.Int) {
+func (f *Field) halve(res *big.Int, x *big.Int) {
 	var z big.Int
 	if x.Bit(0) == 0 {
 		z.Set(x)
@@ -415,17 +421,17 @@ func (f *FieldConfig) halve(res *big.Int, x *big.Int) {
 	res.Rsh(&z, 1)
 }
 
-func (f *FieldConfig) Mul(z *big.Int, x *big.Int, y *big.Int) *FieldConfig {
+func (f *Field) Mul(z *big.Int, x *big.Int, y *big.Int) *Field {
 	z.Mul(x, y).Mod(z, f.ModulusBig)
 	return f
 }
 
-func (f *FieldConfig) Add(z *big.Int, x *big.Int, y *big.Int) *FieldConfig {
+func (f *Field) Add(z *big.Int, x *big.Int, y *big.Int) *Field {
 	z.Add(x, y).Mod(z, f.ModulusBig)
 	return f
 }
 
-func (f *FieldConfig) ToMontSlice(x []big.Int) []big.Int {
+func (f *Field) ToMontSlice(x []big.Int) []big.Int {
 	z := make(Element, len(x))
 	for i := 0; i < len(x); i++ {
 		z[i] = f.ToMont(x[i])
@@ -448,7 +454,7 @@ func CoordNameForExtensionDegree(degree uint8) string {
 	panic(fmt.Sprint("unknown extension degree", degree))
 }
 
-func (f *FieldConfig) WriteElement(element Element) string {
+func (f *Field) WriteElement(element Element) string {
 	var builder strings.Builder
 
 	builder.WriteString("{")
diff --git a/field/generator/config/field_test.go b/field/generator/config/field_test.go
index 6b668b60cd..abf31bb397 100644
--- a/field/generator/config/field_test.go
+++ b/field/generator/config/field_test.go
@@ -25,7 +25,7 @@ func TestIntToMont(t *testing.T) {
 	genF := genField(t)
 
 	properties.Property("must recover initial non-montgomery value by repeated halving", prop.ForAll(
-		func(f *FieldConfig, ib [][]uint8) (bool, error) {
+		func(f *Field, ib [][]uint8) (bool, error) {
 
 			var i big.Int
 			i.SetBytes(ib[0])
@@ -40,7 +40,7 @@ func TestIntToMont(t *testing.T) {
 	))
 
 	properties.Property("turning R into montgomery form must match the R value from field", prop.ForAll(
-		func(f *FieldConfig) (bool, error) {
+		func(f *Field) (bool, error) {
 			// test if using the same R
 			r := big.NewInt(1)
 			r.Lsh(r, uint(f.Word.BitSize)*uint(f.NbWords))
@@ -64,7 +64,7 @@ func TestBigIntMatchUint64Slice(t *testing.T) {
 	genF := genField(t)
 
 	properties.Property("random big.int must match uint64 slice made out of .Bytes()", prop.ForAll(
-		func(f *FieldConfig, ib [][]uint8) (bool, error) {
+		func(f *Field, ib [][]uint8) (bool, error) {
 
 			var i big.Int
 			i.SetBytes(ib[0])
@@ -85,7 +85,7 @@ func TestBigIntMatchUint64Slice(t *testing.T) {
 func TestQuadExtensionMul(t *testing.T) {
 	t.Parallel()
 
-	verifyMul := func(base *FieldConfig, x8Slice [][]uint8, y8Slice [][]uint8) (bool, error) {
+	verifyMul := func(base *Field, x8Slice [][]uint8, y8Slice [][]uint8) (bool, error) {
 		var nonRes big.Int
 		base.FromMont(&nonRes, &base.NonResidue)
 		if !nonRes.IsInt64() {
@@ -199,7 +199,7 @@ func uint8SliceSliceToBigIntSlice(f *Extension, in [][]uint8) []big.Int {
 func genField(t *testing.T) gopter.Gen {
 	return func(genParams *gopter.GenParameters) *gopter.GenResult {
 
-		genField := func() *FieldConfig {
+		genField := func() *Field {
 
 			nbWords := minNbWords + mrand.Intn(maxNbWords-minNbWords) //#nosec G404 -- This is a false positive
 			bitLen := nbWords*64 - mrand.Intn(64)                     //#nosec G404 -- This is a false positive
@@ -213,7 +213,7 @@ func genField(t *testing.T) gopter.Gen {
 				t.Error(err)
 			}
 
-			var field *FieldConfig
+			var field *Field
 			field, err = NewFieldConfig("dummy", "DummyElement", "0x"+modulus.Text(16), false)
 
 			if err == nil {
diff --git a/field/generator/generator.go b/field/generator/generator.go
index 388eb0cd49..4feac2c76b 100644
--- a/field/generator/generator.go
+++ b/field/generator/generator.go
@@ -2,327 +2,145 @@ package generator
 
 import (
 	"fmt"
-	"hash/fnv"
 	"os"
 	"os/exec"
 	"path/filepath"
 	"strings"
-	"text/template"
 
-	"github.com/consensys/bavard"
-	"github.com/consensys/gnark-crypto/field/generator/asm/amd64"
-	"github.com/consensys/gnark-crypto/field/generator/asm/arm64"
 	"github.com/consensys/gnark-crypto/field/generator/config"
-	"github.com/consensys/gnark-crypto/field/generator/internal/addchain"
-	"github.com/consensys/gnark-crypto/field/generator/internal/templates/element"
-	"golang.org/x/sync/errgroup"
 )
 
-// GenerateFF will generate go (and .s) files in outputDir for modulus (in base 10)
-//
-// Example usage
-//
-//	fp, _ = config.NewField("fp", "Element", fpModulus")
-//	generator.GenerateFF(fp, filepath.Join(baseDir, "fp"))
-func GenerateFF(F *config.FieldConfig, outputDir, asmDirBuildPath, asmDirIncludePath string) error {
-	// source file templates
-	sourceFiles := []string{
-		element.Base,
-		element.Reduce,
-		element.Exp,
-		element.Conv,
-		element.MulDoc,
-		element.MulCIOS,
-		element.MulNoCarry,
-		element.Sqrt,
-		element.Inverse,
-		element.BigNum,
-	}
-
-	// test file templates
-	testFiles := []string{
-		element.MulCIOS,
-		element.MulNoCarry,
-		element.Reduce,
-		element.Test,
-		element.InverseTests,
-	}
-	funcs := template.FuncMap{}
-	if F.UseAddChain {
-		for _, f := range addchain.Functions {
-			funcs[f.Name] = f.Func
-		}
-	}
-
-	os.Remove(filepath.Join(outputDir, "vector_arm64.go"))
-	os.Remove(filepath.Join(outputDir, "exp.go"))
-
-	funcs["shorten"] = shorten
-	funcs["ltu64"] = func(a, b uint64) bool {
-		return a < b
-	}
-
-	generate := func(suffix string, templates []string, opts ...option) func() error {
-		opt := generateOptions(opts...)
-		if opt.skip {
-			return func() error { return nil }
-		}
-		return func() error {
-			bavardOpts := []func(*bavard.Bavard) error{
-				bavard.Apache2("Consensys Software Inc.", 2020),
-				bavard.GeneratedBy("consensys/gnark-crypto"),
-				bavard.Funcs(funcs),
-			}
-			if !strings.HasSuffix(suffix, ".s") {
-				bavardOpts = append(bavardOpts, bavard.Package(F.PackageName))
-			}
-			if opt.buildTag != "" {
-				bavardOpts = append(bavardOpts, bavard.BuildTag(opt.buildTag))
-			}
-			if suffix == ".go" {
-				suffix = filepath.Join(outputDir, suffix)
-			} else {
-				suffix = filepath.Join(outputDir, suffix)
-			}
+func GenerateFF(F *config.Field, outputDir string, options ...Option) error {
 
-			tmplData := any(F)
-			if opt.tmplData != nil {
-				tmplData = opt.tmplData
-			}
+	// default config
+	cfg := generatorOptions(options...)
 
-			return bavard.GenerateFromString(suffix, templates, tmplData, bavardOpts...)
-		}
-	}
-
-	// generate asm files;
-	// couple of cases;
-	// 1. we generate arm64 and amd64
-	// 2. we generate only amd64
-	// 3. we generate only purego
-
-	// sanity check
-	if (F.GenerateOpsARM64 && !F.GenerateOpsAMD64) ||
-		(F.GenerateVectorOpsAMD64 && !F.GenerateOpsAMD64) ||
-		(F.GenerateVectorOpsARM64 && !F.GenerateOpsARM64) {
-		panic("not implemented.")
-	}
-
-	// get hash of the common asm files to force compiler to recompile in case of changes.
-	var amd64d, arm64d ASMWrapperData
+	// generate asm
+	// note: we need to do that before the fields, as the fields will include a hash of the (shared)
+	// asm files to force a recompile of the field package if the asm files have changed
+	var hashArm64, hashAMD64 string
 	var err error
-
-	if F.GenerateOpsAMD64 {
-		amd64d, err = hashAndInclude(asmDirBuildPath, asmDirIncludePath, amd64.ElementASMFileName, F.NbWords)
+	if cfg.HasArm64() {
+		hashArm64, err = generateARM64(F, cfg.asmConfig)
 		if err != nil {
 			return err
 		}
 	}
 
-	if F.GenerateOpsARM64 {
-		arm64d, err = hashAndInclude(asmDirBuildPath, asmDirIncludePath, arm64.ElementASMFileName, F.NbWords)
+	if cfg.HasAMD64() {
+		hashAMD64, err = generateAMD64(F, cfg.asmConfig)
 		if err != nil {
 			return err
 		}
 	}
 
-	// purego files have no build tags if we don't generate asm
-	pureGoBuildTag := "purego || (!amd64 && !arm64)"
-	if !F.GenerateOpsAMD64 && !F.GenerateOpsARM64 {
-		pureGoBuildTag = ""
-	} else if !F.GenerateOpsARM64 {
-		pureGoBuildTag = "purego || (!amd64)"
-	}
-	pureGoVectorBuildTag := "purego || (!amd64 && !arm64)"
-	if !F.GenerateVectorOpsAMD64 && !F.GenerateVectorOpsARM64 {
-		pureGoVectorBuildTag = ""
-	} else if !F.GenerateVectorOpsARM64 {
-		pureGoVectorBuildTag = "purego || (!amd64)"
+	// generate field
+	if err := generateField(F, outputDir, cfg.asmConfig.IncludeDir, hashArm64, hashAMD64); err != nil {
+		return err
 	}
 
-	var g errgroup.Group
-
-	g.Go(generate("element.go", sourceFiles))
-	g.Go(generate("doc.go", []string{element.Doc}))
-	g.Go(generate("vector.go", []string{element.Vector}))
-	g.Go(generate("arith.go", []string{element.Arith}, Only(!F.F31)))
-	g.Go(generate("element_test.go", testFiles))
-	g.Go(generate("vector_test.go", []string{element.TestVector}))
-
-	g.Go(generate("element_amd64.s", []string{element.IncludeASM}, Only(F.GenerateOpsAMD64), WithBuildTag("!purego"), WithData(amd64d)))
-	g.Go(generate("element_arm64.s", []string{element.IncludeASM}, Only(F.GenerateOpsARM64), WithBuildTag("!purego"), WithData(arm64d)))
-
-	g.Go(generate("element_amd64.go", []string{element.OpsAMD64, element.MulDoc}, Only(F.GenerateOpsAMD64), WithBuildTag("!purego")))
-	g.Go(generate("element_arm64.go", []string{element.OpsARM64, element.MulNoCarry, element.Reduce}, Only(F.GenerateOpsARM64), WithBuildTag("!purego")))
-
-	g.Go(generate("element_purego.go", []string{element.OpsNoAsm, element.MulCIOS, element.MulNoCarry, element.Reduce, element.MulDoc}, WithBuildTag(pureGoBuildTag)))
-
-	g.Go(generate("vector_amd64.go", []string{element.VectorOpsAmd64}, Only(F.GenerateVectorOpsAMD64), WithBuildTag("!purego")))
-	g.Go(generate("vector_arm64.go", []string{element.VectorOpsArm64}, Only(F.GenerateVectorOpsARM64), WithBuildTag("!purego")))
-
-	g.Go(generate("vector_purego.go", []string{element.VectorOpsPureGo}, WithBuildTag(pureGoVectorBuildTag)))
-
-	g.Go(generate("asm_adx.go", []string{element.Asm}, Only(F.GenerateOpsAMD64), WithBuildTag("!noadx")))
-	g.Go(generate("asm_noadx.go", []string{element.AsmNoAdx}, Only(F.GenerateOpsAMD64), WithBuildTag("noadx")))
-	g.Go(generate("asm_avx.go", []string{element.Avx}, Only(F.GenerateVectorOpsAMD64), WithBuildTag("!noavx")))
-	g.Go(generate("asm_noavx.go", []string{element.NoAvx}, Only(F.GenerateVectorOpsAMD64), WithBuildTag("noavx")))
-
-	if F.UseAddChain {
-		g.Go(generate("element_exp.go", []string{element.FixedExp}))
+	// generate fft
+	if cfg.HasFFT() {
+		if err := generateFFT(F, cfg.fftConfig, outputDir); err != nil {
+			return err
+		}
 	}
 
-	if err := g.Wait(); err != nil {
-		return err
-	}
+	return runFormatters(outputDir)
+}
 
+func runFormatters(outputDir string) error {
+	var out strings.Builder
 	{
 		// run go fmt on whole directory
 		cmd := exec.Command("gofmt", "-s", "-w", outputDir)
-		cmd.Stdout = os.Stdout
-		cmd.Stderr = os.Stderr
+		cmd.Stdout = &out
+		cmd.Stderr = &out
 		if err := cmd.Run(); err != nil {
-			return err
+			return fmt.Errorf("gofmt failed: %v\n%s", err, out.String())
 		}
 	}
 	{
 		// run asmfmt on whole directory
 		cmd := exec.Command("asmfmt", "-w", outputDir)
-		cmd.Stdout = os.Stdout
-		cmd.Stderr = os.Stderr
+		cmd.Stdout = &out
+		cmd.Stderr = &out
 		if err := cmd.Run(); err != nil {
-			return err
+			return fmt.Errorf("asmfmt failed: %v\n%s", err, out.String())
 		}
 	}
-
 	return nil
 }
 
-type ASMWrapperData struct {
-	IncludePath string
-	Hash        string
-}
-
-func hashAndInclude(asmDirBuildPath, asmDirIncludePath, fileName string, nbWords int) (data ASMWrapperData, err error) {
-	fileName = fmt.Sprintf(fileName, nbWords)
-	// we hash the file content and include the hash in comment of the generated file
-	// to force the Go compiler to recompile the file if the content has changed
-	fData, err := os.ReadFile(filepath.Join(asmDirBuildPath, fileName))
-	if err != nil {
-		return ASMWrapperData{}, err
-	}
-	// hash the file using FNV
-	hasher := fnv.New64()
-	hasher.Write(fData)
-	hash64 := hasher.Sum64()
-
-	hash := fmt.Sprintf("%d", hash64)
-	includePath := filepath.Join(asmDirIncludePath, fileName)
-	// on windows, we replace the "\" by "/"
-	if filepath.Separator == '\\' {
-		includePath = strings.ReplaceAll(includePath, "\\", "/")
-	}
-
-	return ASMWrapperData{
-		IncludePath: includePath,
-		Hash:        hash,
-	}, nil
-
-}
-
-func shorten(input string) string {
-	const maxLen = 15
-	if len(input) > maxLen {
-		return input[:6] + "..." + input[len(input)-6:]
+func runASMFormatter(file string) error {
+	var out strings.Builder
+	{
+		// run asmfmt on whole directory
+		cmd := exec.Command("asmfmt", "-w", file)
+		cmd.Stdout = &out
+		cmd.Stderr = &out
+		if err := cmd.Run(); err != nil {
+			return fmt.Errorf("asmfmt failed: %v\n%s", err, out.String())
+		}
 	}
-	return input
+	return nil
 }
 
-func GenerateARM64(nbWords int, asmDir string, hasVector bool) error {
-	os.MkdirAll(asmDir, 0755)
-	pathSrc := filepath.Join(asmDir, fmt.Sprintf(arm64.ElementASMFileName, nbWords))
-
-	fmt.Println("generating", pathSrc)
-	f, err := os.Create(pathSrc)
+func getImportPath(dir string) (string, error) {
+	// get absolute path for dir
+	dir, err := filepath.Abs(dir)
 	if err != nil {
-		return err
-	}
-
-	if err := arm64.GenerateCommonASM(f, nbWords, hasVector); err != nil {
-		_ = f.Close()
-		return err
-	}
-	_ = f.Close()
-
-	// run asmfmt
-	// run go fmt on whole directory
-	cmd := exec.Command("asmfmt", "-w", pathSrc)
-	cmd.Stdout = os.Stdout
-	cmd.Stderr = os.Stderr
-	if err := cmd.Run(); err != nil {
-		return err
+		return "", fmt.Errorf("error getting absolute path: %w", err)
 	}
 
-	return nil
-}
-
-func GenerateAMD64(nbWords int, asmDir string, hasVector bool) error {
-	os.MkdirAll(asmDir, 0755)
-	pathSrc := filepath.Join(asmDir, fmt.Sprintf(amd64.ElementASMFileName, nbWords))
-
-	fmt.Println("generating", pathSrc)
-	f, err := os.Create(pathSrc)
+	modDir, err := findGoMod(dir)
 	if err != nil {
-		return err
+		return "", fmt.Errorf("error finding go.mod: %w", err)
 	}
 
-	if err := amd64.GenerateCommonASM(f, nbWords, hasVector); err != nil {
-		_ = f.Close()
-		return err
+	modulePath, err := getModulePath(modDir)
+	if err != nil {
+		return "", fmt.Errorf("error reading module path: %w", err)
 	}
-	_ = f.Close()
 
-	// run asmfmt
-	// run go fmt on whole directory
-	cmd := exec.Command("asmfmt", "-w", pathSrc)
-	cmd.Stdout = os.Stdout
-	cmd.Stderr = os.Stderr
-	if err := cmd.Run(); err != nil {
-		return err
+	relPath, err := filepath.Rel(modDir, dir)
+	if err != nil {
+		return "", fmt.Errorf("error computing relative path: %w", err)
 	}
 
-	return nil
-}
-
-type option func(*generateConfig)
-type generateConfig struct {
-	buildTag string
-	skip     bool
-	tmplData any
-}
-
-func WithBuildTag(buildTag string) option {
-	return func(opt *generateConfig) {
-		opt.buildTag = buildTag
+	// Handle the case where the directory is the module root
+	if relPath == "." {
+		return modulePath, nil
 	}
+	return modulePath + "/" + filepath.ToSlash(relPath), nil
 }
 
-func Only(condition bool) option {
-	return func(opt *generateConfig) {
-		opt.skip = !condition
+// findGoMod ascends the directory tree to locate the go.mod file.
+func findGoMod(dir string) (string, error) {
+	for {
+		if _, err := os.Stat(filepath.Join(dir, "go.mod")); err == nil {
+			return dir, nil
+		}
+		newDir := filepath.Dir(dir)
+		if newDir == dir {
+			return "", fmt.Errorf("no go.mod found up to root")
+		}
+		dir = newDir
 	}
 }
 
-func WithData(data any) option {
-	return func(opt *generateConfig) {
-		opt.tmplData = data
+// getModulePath extracts the module path from the go.mod file.
+func getModulePath(modDir string) (string, error) {
+	content, err := os.ReadFile(filepath.Join(modDir, "go.mod"))
+	if err != nil {
+		return "", fmt.Errorf("error reading go.mod: %w", err)
 	}
-}
 
-// default options
-func generateOptions(opts ...option) generateConfig {
-	// apply options
-	opt := generateConfig{}
-	for _, option := range opts {
-		option(&opt)
+	for _, line := range strings.Split(string(content), "\n") {
+		line = strings.TrimSpace(line)
+		if strings.HasPrefix(line, "module ") {
+			return strings.TrimPrefix(line, "module "), nil
+		}
 	}
-	return opt
+	return "", fmt.Errorf("module declaration not found in go.mod")
 }
diff --git a/field/generator/generator_asm.go b/field/generator/generator_asm.go
new file mode 100644
index 0000000000..8726ac7d78
--- /dev/null
+++ b/field/generator/generator_asm.go
@@ -0,0 +1,143 @@
+package generator
+
+import (
+	"fmt"
+	"hash/fnv"
+	"os"
+	"path/filepath"
+	"strings"
+	"sync"
+
+	"github.com/consensys/gnark-crypto/field/generator/asm/amd64"
+	"github.com/consensys/gnark-crypto/field/generator/asm/arm64"
+	"github.com/consensys/gnark-crypto/field/generator/config"
+)
+
+var (
+	mARM64    sync.Map
+	mAMD64    sync.Map
+	lockARM64 sync.Mutex
+	lockAMD64 sync.Mutex
+)
+
+// generateARM64 generates the assembly file for ARM64
+// it formats it and returns a hash of the file
+// this is safe to run concurrently
+func generateARM64(F *config.Field, asm *config.Assembly) (string, error) {
+	if !F.GenerateOpsARM64 {
+		return "", nil
+	}
+
+	os.MkdirAll(asm.BuildDir, 0755)
+	pathSrc := filepath.Join(asm.BuildDir, fmt.Sprintf(arm64.ElementASMFileName, F.NbWords))
+
+	hash, ok := mARM64.Load(pathSrc)
+	if ok {
+		return hash.(string), nil
+	}
+	lockARM64.Lock()
+	defer lockARM64.Unlock()
+
+	fmt.Println("generating", pathSrc)
+	f, err := os.Create(pathSrc)
+	if err != nil {
+		return "", err
+	}
+
+	if err := arm64.GenerateCommonASM(f, F.NbWords, F.GenerateVectorOpsARM64); err != nil {
+		_ = f.Close()
+		return "", err
+	}
+	_ = f.Close()
+
+	if err := runASMFormatter(pathSrc); err != nil {
+		return "", err
+	}
+
+	toReturn, err := hashFile(pathSrc)
+	if err != nil {
+		return "", err
+	}
+
+	mARM64.Store(pathSrc, toReturn)
+	return toReturn, nil
+}
+
+// generateAMD64 generates the assembly file for AMD64
+// it formats it and returns a hash of the file
+// this is safe to run concurrently
+func generateAMD64(F *config.Field, asm *config.Assembly) (string, error) {
+	if !F.GenerateOpsAMD64 {
+		return "", nil
+	}
+	os.MkdirAll(asm.BuildDir, 0755)
+	pathSrc := filepath.Join(asm.BuildDir, fmt.Sprintf(amd64.ElementASMFileName, F.NbWords))
+
+	hash, ok := mAMD64.Load(pathSrc)
+	if ok {
+		return hash.(string), nil
+	}
+	lockAMD64.Lock()
+	defer lockAMD64.Unlock()
+
+	fmt.Println("generating", pathSrc)
+	f, err := os.Create(pathSrc)
+	if err != nil {
+		return "", err
+	}
+
+	if err := amd64.GenerateCommonASM(f, F.NbWords, F.GenerateVectorOpsAMD64); err != nil {
+		_ = f.Close()
+		return "", err
+	}
+	_ = f.Close()
+
+	if err := runASMFormatter(pathSrc); err != nil {
+		return "", err
+	}
+
+	toReturn, err := hashFile(pathSrc)
+	if err != nil {
+		return "", err
+	}
+
+	mAMD64.Store(pathSrc, toReturn)
+
+	return toReturn, nil
+}
+
+type ASMWrapperData struct {
+	IncludePath string
+	Hash        string
+}
+
+func hashFile(filePath string) (string, error) {
+	// we hash the file content and include the hash in comment of the generated file
+	// to force the Go compiler to recompile the file if the content has changed
+	fData, err := os.ReadFile(filePath)
+	if err != nil {
+		return "", err
+	}
+	// hash the file using FNV
+	hasher := fnv.New64()
+	hasher.Write(fData)
+	hash64 := hasher.Sum64()
+
+	return fmt.Sprintf("%d", hash64), nil
+}
+
+func newASMWrapperData(hash, asmDirIncludePath, fileName string, nbWords int) (data ASMWrapperData, err error) {
+	fileName = fmt.Sprintf(fileName, nbWords)
+
+	includePath := filepath.Join(asmDirIncludePath, fileName)
+	// on windows, we replace the "\" by "/"
+	if filepath.Separator == '\\' {
+		includePath = strings.ReplaceAll(includePath, "\\", "/")
+	}
+
+	return ASMWrapperData{
+		IncludePath: includePath,
+		Hash:        hash,
+	}, nil
+
+}
diff --git a/field/generator/generator_fft.go b/field/generator/generator_fft.go
new file mode 100644
index 0000000000..72ef9aa42d
--- /dev/null
+++ b/field/generator/generator_fft.go
@@ -0,0 +1,231 @@
+package generator
+
+import (
+	"errors"
+	"fmt"
+	"math/bits"
+	"os"
+	"path/filepath"
+	"strings"
+
+	"github.com/consensys/bavard"
+	"github.com/consensys/gnark-crypto/field/generator/config"
+	eccconfig "github.com/consensys/gnark-crypto/internal/generator/config"
+)
+
+func generateFFT(F *config.Field, fft *config.FFT, outputDir string) error {
+
+	if fft.GeneratorFullMultiplicativeGroup == 0 || fft.GeneratorMaxTwoAdicSubgroup == "" {
+		// try to populate ourselves
+		// TODO @gbotrel right now hardcoded lookup tables, we should do better.
+		data, ok := fftConfigs[F.Modulus]
+		if !ok {
+			return fmt.Errorf("no fft config for modulus %s", F.Modulus)
+		}
+		fft = &data
+	}
+
+	fieldImportPath, err := getImportPath(outputDir)
+	if err != nil {
+		return err
+	}
+	data := &fftTemplateData{
+		FFT:              *fft,
+		FieldPackagePath: fieldImportPath,
+		FF:               F.PackageName,
+		Package:          "fft",
+	}
+	outputDir = filepath.Join(outputDir, "fft")
+
+	entries := []bavard.Entry{
+		{File: filepath.Join(outputDir, "doc.go"), Templates: []string{"doc.go.tmpl"}},
+		{File: filepath.Join(outputDir, "domain_test.go"), Templates: []string{"tests/domain.go.tmpl"}},
+		{File: filepath.Join(outputDir, "domain.go"), Templates: []string{"domain.go.tmpl"}},
+		{File: filepath.Join(outputDir, "fft_test.go"), Templates: []string{"tests/fft.go.tmpl"}},
+		{File: filepath.Join(outputDir, "bitreverse_test.go"), Templates: []string{"tests/bitreverse.go.tmpl"}},
+		{File: filepath.Join(outputDir, "fft.go"), Templates: []string{"fft.go.tmpl"}},
+		{File: filepath.Join(outputDir, "bitreverse.go"), Templates: []string{"bitreverse.go.tmpl"}},
+		{File: filepath.Join(outputDir, "options.go"), Templates: []string{"options.go.tmpl"}},
+	}
+
+	funcs := make(map[string]interface{})
+	funcs["bitReverse"] = func(n, i int64) uint64 {
+		nn := uint64(64 - bits.TrailingZeros64(uint64(n)))
+		r := make([]uint64, n)
+		for i := 0; i < len(r); i++ {
+			r[i] = uint64(i)
+		}
+		for i := 0; i < len(r); i++ {
+			irev := bits.Reverse64(r[i]) >> nn
+			if irev > uint64(i) {
+				r[i], r[irev] = r[irev], r[i]
+			}
+		}
+		return r[i]
+	}
+	funcs["reverseBits"] = func(x, n any) uint64 {
+		return bits.Reverse64(anyToUint64(x)) >> anyToUint64(n)
+	}
+	funcs["shl"] = func(x, n any) uint64 {
+		return anyToUint64(x) << anyToUint64(n)
+	}
+	funcs["logicalOr"] = func(x, y any) uint64 {
+		return anyToUint64(x) | anyToUint64(y)
+	}
+
+	bavardOpts := []func(*bavard.Bavard) error{bavard.Funcs(funcs)}
+
+	bgen := bavard.NewBatchGenerator("Consensys Software Inc.", 2020, "consensys/gnark-crypto")
+
+	fftTemplatesRootDir, err := findTemplatesRootDir()
+	if err != nil {
+		return err
+	}
+	fftTemplatesRootDir = filepath.Join(fftTemplatesRootDir, "fft")
+
+	if err := bgen.GenerateWithOptions(data, data.Package, fftTemplatesRootDir, bavardOpts, entries...); err != nil {
+		return err
+	}
+
+	// put the generator in the parent dir (fr)
+	// TODO this should be in goff
+	entries = []bavard.Entry{
+		{File: filepath.Join(outputDir, "../generator.go"), Templates: []string{"fr.generator.go.tmpl"}},
+	}
+	fieldNameSplitted := strings.Split(data.FieldPackagePath, "/")
+	fieldName := fieldNameSplitted[len(fieldNameSplitted)-1]
+	if err := bgen.GenerateWithOptions(data, fieldName, fftTemplatesRootDir, bavardOpts, entries...); err != nil {
+		return err
+	}
+
+	return runFormatters(outputDir)
+}
+
+type fftTemplateData struct {
+	config.FFT
+
+	// Package name of the generated package
+	Package string
+
+	// ImportPathFiniteField path to the finite field package
+	FieldPackagePath string
+
+	// FF the name of the package corresponding to the finite field
+	FF string
+}
+
+func findTemplatesRootDir() (string, error) {
+	// walks through the directory tree to find the templates root dir;
+	// we find the dir with go.mod file, then go up to field/generator/internal/templates
+	// this is a bit hacky, but it works
+
+	// find the dir with go.mod file
+	dir, err := os.Getwd()
+	if err != nil {
+		return "", err
+	}
+
+	for {
+		if _, err := os.Stat(filepath.Join(dir, "go.mod")); err == nil {
+			break
+		}
+		dir = filepath.Dir(dir)
+		if dir == "/" || dir == "." {
+			return "", errors.New("could not find templates root dir")
+		}
+	}
+
+	return filepath.Join(dir, "field/generator/internal/templates"), nil
+
+}
+
+func anyToUint64(x any) uint64 {
+	switch v := x.(type) {
+	case int:
+		return uint64(v)
+	case int64:
+		return uint64(v)
+	case uint64:
+		return v
+	default:
+		panic("unknown type")
+	}
+}
+
+var fftConfigs map[string]config.FFT
+
+func init() {
+	fftConfigs = make(map[string]config.FFT)
+
+	// TODO @gbotrel temporary
+	// bls12-377
+	fftConfigs[eccconfig.BLS12_377.FrModulus] = config.NewConfig(
+		22,
+		"8065159656716812877374967518403273466521432693661810619979959746626482506078",
+		"47",
+	)
+
+	// bls12-381
+	fftConfigs[eccconfig.BLS12_381.FrModulus] = (config.NewConfig(
+		7,
+		"10238227357739495823651030575849232062558860180284477541189508159991286009131",
+		"32",
+	))
+
+	// bn254
+	fftConfigs[eccconfig.BN254.FrModulus] = (config.NewConfig(
+		5,
+		"19103219067921713944291392827692070036145651957329286315305642004821462161904",
+		"28",
+	))
+
+	// bw6-761
+	fftConfigs[eccconfig.BW6_761.FrModulus] = (config.NewConfig(
+		15,
+		"32863578547254505029601261939868325669770508939375122462904745766352256812585773382134936404344547323199885654433",
+		"46",
+	))
+
+	// bw6-633
+	fftConfigs[eccconfig.BW6_633.FrModulus] = (config.NewConfig(
+		13,
+		"4991787701895089137426454739366935169846548798279261157172811661565882460884369603588700158257",
+		"20",
+	))
+
+	// bls24-315
+	fftConfigs[eccconfig.BLS24_315.FrModulus] = (config.NewConfig(
+		7,
+		"1792993287828780812362846131493071959406149719416102105453370749552622525216",
+		"22",
+	))
+
+	// bls24-317
+	fftConfigs[eccconfig.BLS24_317.FrModulus] = (config.NewConfig(
+		7,
+		"16532287748948254263922689505213135976137839535221842169193829039521719560631",
+		"60",
+	))
+
+	// goldilocks
+	fftConfigs["18446744069414584321"] = (config.NewConfig(
+		7,
+		"1753635133440165772",
+		"32",
+	))
+
+	// koala bear
+	fftConfigs["2130706433"] = (config.NewConfig(
+		3,
+		"1791270792",
+		"24",
+	))
+
+	// baby bear
+	fftConfigs["2013265921"] = (config.NewConfig(
+		31,
+		"440564289",
+		"27",
+	))
+
+}
diff --git a/field/generator/generator_field.go b/field/generator/generator_field.go
new file mode 100644
index 0000000000..64111c325f
--- /dev/null
+++ b/field/generator/generator_field.go
@@ -0,0 +1,203 @@
+package generator
+
+import (
+	"path/filepath"
+	"strings"
+	"text/template"
+
+	"github.com/consensys/bavard"
+	"github.com/consensys/gnark-crypto/field/generator/asm/amd64"
+	"github.com/consensys/gnark-crypto/field/generator/asm/arm64"
+	"github.com/consensys/gnark-crypto/field/generator/config"
+	"github.com/consensys/gnark-crypto/field/generator/internal/addchain"
+	"github.com/consensys/gnark-crypto/field/generator/internal/templates/element"
+	"golang.org/x/sync/errgroup"
+)
+
+func generateField(F *config.Field, outputDir, asmDirIncludePath, hashArm64, hashAMD64 string) error {
+
+	// source file templates
+	sourceFiles := []string{
+		element.Base,
+		element.Reduce,
+		element.Exp,
+		element.Conv,
+		element.MulDoc,
+		element.MulCIOS,
+		element.MulNoCarry,
+		element.Sqrt,
+		element.Inverse,
+		element.BigNum,
+	}
+
+	// test file templates
+	testFiles := []string{
+		element.MulCIOS,
+		element.MulNoCarry,
+		element.Reduce,
+		element.Test,
+		element.InverseTests,
+	}
+	funcs := template.FuncMap{}
+	if F.UseAddChain {
+		for _, f := range addchain.Functions {
+			funcs[f.Name] = f.Func
+		}
+	}
+
+	funcs["shorten"] = func(input string) string {
+		if len(input) > 15 {
+			return input[:6] + "..." + input[len(input)-6:]
+		}
+		return input
+	}
+
+	funcs["ltu64"] = func(a, b uint64) bool {
+		return a < b
+	}
+
+	generate := func(suffix string, templates []string, opts ...fieldOption) func() error {
+		opt := fieldOptions(opts...)
+		if opt.skip {
+			return func() error { return nil }
+		}
+		return func() error {
+			bavardOpts := []func(*bavard.Bavard) error{
+				bavard.Apache2("Consensys Software Inc.", 2020),
+				bavard.GeneratedBy("consensys/gnark-crypto"),
+				bavard.Funcs(funcs),
+			}
+			if !strings.HasSuffix(suffix, ".s") {
+				bavardOpts = append(bavardOpts, bavard.Package(F.PackageName))
+			}
+			if opt.buildTag != "" {
+				bavardOpts = append(bavardOpts, bavard.BuildTag(opt.buildTag))
+			}
+			if suffix == ".go" {
+				suffix = filepath.Join(outputDir, suffix)
+			} else {
+				suffix = filepath.Join(outputDir, suffix)
+			}
+
+			tmplData := any(F)
+			if opt.tmplData != nil {
+				tmplData = opt.tmplData
+			}
+
+			return bavard.GenerateFromString(suffix, templates, tmplData, bavardOpts...)
+		}
+	}
+
+	// generate asm files;
+	// couple of cases;
+	// 1. we generate arm64 and amd64
+	// 2. we generate only amd64
+	// 3. we generate only purego
+
+	// sanity check
+	if (F.GenerateOpsARM64 && !F.GenerateOpsAMD64) ||
+		(F.GenerateVectorOpsAMD64 && !F.GenerateOpsAMD64) ||
+		(F.GenerateVectorOpsARM64 && !F.GenerateOpsARM64) {
+		panic("not implemented.")
+	}
+
+	// get hash of the common asm files to force compiler to recompile in case of changes.
+	var amd64d, arm64d ASMWrapperData
+	var err error
+
+	if F.GenerateOpsAMD64 {
+		amd64d, err = newASMWrapperData(hashAMD64, asmDirIncludePath, amd64.ElementASMFileName, F.NbWords)
+		if err != nil {
+			return err
+		}
+	}
+
+	if F.GenerateOpsARM64 {
+		arm64d, err = newASMWrapperData(hashArm64, asmDirIncludePath, arm64.ElementASMFileName, F.NbWords)
+		if err != nil {
+			return err
+		}
+	}
+
+	// purego files have no build tags if we don't generate asm
+	pureGoBuildTag := "purego || (!amd64 && !arm64)"
+	if !F.GenerateOpsAMD64 && !F.GenerateOpsARM64 {
+		pureGoBuildTag = ""
+	} else if !F.GenerateOpsARM64 {
+		pureGoBuildTag = "purego || (!amd64)"
+	}
+	pureGoVectorBuildTag := "purego || (!amd64 && !arm64)"
+	if !F.GenerateVectorOpsAMD64 && !F.GenerateVectorOpsARM64 {
+		pureGoVectorBuildTag = ""
+	} else if !F.GenerateVectorOpsARM64 {
+		pureGoVectorBuildTag = "purego || (!amd64)"
+	}
+
+	var g errgroup.Group
+
+	g.Go(generate("element.go", sourceFiles))
+	g.Go(generate("doc.go", []string{element.Doc}))
+	g.Go(generate("vector.go", []string{element.Vector}))
+	g.Go(generate("arith.go", []string{element.Arith}, only(!F.F31)))
+	g.Go(generate("element_test.go", testFiles))
+	g.Go(generate("vector_test.go", []string{element.TestVector}))
+
+	g.Go(generate("element_amd64.s", []string{element.IncludeASM}, only(F.GenerateOpsAMD64), withBuildTag("!purego"), withData(amd64d)))
+	g.Go(generate("element_arm64.s", []string{element.IncludeASM}, only(F.GenerateOpsARM64), withBuildTag("!purego"), withData(arm64d)))
+
+	g.Go(generate("element_amd64.go", []string{element.OpsAMD64, element.MulDoc}, only(F.GenerateOpsAMD64), withBuildTag("!purego")))
+	g.Go(generate("element_arm64.go", []string{element.OpsARM64, element.MulNoCarry, element.Reduce}, only(F.GenerateOpsARM64), withBuildTag("!purego")))
+
+	g.Go(generate("element_purego.go", []string{element.OpsNoAsm, element.MulCIOS, element.MulNoCarry, element.Reduce, element.MulDoc}, withBuildTag(pureGoBuildTag)))
+
+	g.Go(generate("vector_amd64.go", []string{element.VectorOpsAmd64}, only(F.GenerateVectorOpsAMD64), withBuildTag("!purego")))
+	g.Go(generate("vector_arm64.go", []string{element.VectorOpsArm64}, only(F.GenerateVectorOpsARM64), withBuildTag("!purego")))
+
+	g.Go(generate("vector_purego.go", []string{element.VectorOpsPureGo}, withBuildTag(pureGoVectorBuildTag)))
+
+	g.Go(generate("asm_adx.go", []string{element.Asm}, only(F.GenerateOpsAMD64), withBuildTag("!noadx")))
+	g.Go(generate("asm_noadx.go", []string{element.AsmNoAdx}, only(F.GenerateOpsAMD64), withBuildTag("noadx")))
+	g.Go(generate("asm_avx.go", []string{element.Avx}, only(F.GenerateVectorOpsAMD64), withBuildTag("!noavx")))
+	g.Go(generate("asm_noavx.go", []string{element.NoAvx}, only(F.GenerateVectorOpsAMD64), withBuildTag("noavx")))
+
+	if F.UseAddChain {
+		g.Go(generate("element_exp.go", []string{element.FixedExp}))
+	}
+
+	return g.Wait()
+}
+
+type fieldOption func(*fieldConfig)
+type fieldConfig struct {
+	buildTag string
+	skip     bool
+	tmplData any
+}
+
+func withBuildTag(buildTag string) fieldOption {
+	return func(opt *fieldConfig) {
+		opt.buildTag = buildTag
+	}
+}
+
+func only(condition bool) fieldOption {
+	return func(opt *fieldConfig) {
+		opt.skip = !condition
+	}
+}
+
+func withData(data any) fieldOption {
+	return func(opt *fieldConfig) {
+		opt.tmplData = data
+	}
+}
+
+// default options
+func fieldOptions(opts ...fieldOption) fieldConfig {
+	// apply options
+	opt := fieldConfig{}
+	for _, option := range opts {
+		option(&opt)
+	}
+	return opt
+}
diff --git a/field/generator/generator_test.go b/field/generator/generator_test.go
index f47d282aaa..95e28701c2 100644
--- a/field/generator/generator_test.go
+++ b/field/generator/generator_test.go
@@ -13,6 +13,7 @@ import (
 	"strings"
 	"testing"
 
+	"github.com/consensys/gnark-crypto/field/generator/config"
 	field "github.com/consensys/gnark-crypto/field/generator/config"
 	"github.com/stretchr/testify/require"
 	"golang.org/x/sync/errgroup"
@@ -68,21 +69,13 @@ func TestIntegration(t *testing.T) {
 	moduli["e_nocarry_edge_0127"] = "170141183460469231731687303715884105727"
 	moduli["e_nocarry_edge_1279"] = "10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729087"
 
-	assert.NoError(GenerateAMD64(2, asmDir, false))
-	assert.NoError(GenerateAMD64(3, asmDir, false))
-	assert.NoError(GenerateAMD64(7, asmDir, false))
-	assert.NoError(GenerateAMD64(8, asmDir, false))
-
-	assert.NoError(GenerateARM64(2, asmDir, false))
-	assert.NoError(GenerateARM64(8, asmDir, false))
-
 	for elementName, modulus := range moduli {
-		var fIntegration *field.FieldConfig
+		var fIntegration *field.Field
 		// generate field
 		childDir := filepath.Join(rootDir, elementName)
 		fIntegration, err = field.NewFieldConfig("integration", elementName, modulus, false)
 		assert.NoError(err)
-		assert.NoError(GenerateFF(fIntegration, childDir, asmDir, asmDirIncludePath))
+		assert.NoError(GenerateFF(fIntegration, childDir, WithASM(&config.Assembly{BuildDir: asmDir, IncludeDir: asmDirIncludePath})))
 	}
 
 	// run go test
diff --git a/internal/generator/fft/template/bitreverse.go.tmpl b/field/generator/internal/templates/fft/bitreverse.go.tmpl
similarity index 90%
rename from internal/generator/fft/template/bitreverse.go.tmpl
rename to field/generator/internal/templates/fft/bitreverse.go.tmpl
index 62d777389f..2f05849b78 100644
--- a/internal/generator/fft/template/bitreverse.go.tmpl
+++ b/field/generator/internal/templates/fft/bitreverse.go.tmpl
@@ -1,12 +1,13 @@
 import (
 	"math/bits"
 	"runtime"
-	{{ template "import_fr" . }}
+	
+	"{{ .FieldPackagePath }}"
 )
 
 // BitReverse applies the bit-reversal permutation to v.
 // len(v) must be a power of 2
-func BitReverse(v []fr.Element) {
+func BitReverse(v []{{ .FF }}.Element) {
 	n := uint64(len(v))
 	if bits.OnesCount64(n) != 1 {
 		panic("len(a) must be a power of 2")
@@ -21,7 +22,7 @@ func BitReverse(v []fr.Element) {
 
 // bitReverseNaive applies the bit-reversal permutation to v.
 // len(v) must be a power of 2
-func bitReverseNaive(v []fr.Element) {
+func bitReverseNaive(v []{{ .FF }}.Element) {
 	n := uint64(len(v))
 	nn := uint64(64 - bits.TrailingZeros64(n))
 
@@ -51,7 +52,7 @@ func bitReverseNaive(v []fr.Element) {
 //	 https://github.com/mratsim/constantine/blob/d51699248db04e29c7b1ad97e0bafa1499db00b5/constantine/math/polynomials/fft.nim#L205
 // 	 by Mamy Ratsimbazafy (@mratsim).
 //
-func bitReverseCobraInPlace(v []fr.Element) {
+func bitReverseCobraInPlace(v []{{ .FF }}.Element) {
 	logN := uint64(bits.Len64(uint64(len(v))) - 1)
 	logTileSize := deriveLogTileSize(logN)
 	logBLen := logN - 2*logTileSize
@@ -78,7 +79,7 @@ func bitReverseCobraInPlace(v []fr.Element) {
 	//
 	// for most sizes of interest, this tile size choice doesn't yield good results;
 	// we find that a tile size of 2**9 gives best results for input sizes from 2**21 up to 2**27+.
-	t := make([]fr.Element, tileSize*tileSize)
+	t := make([]{{ .FF }}.Element, tileSize*tileSize)
 
 
 	// see https://csaws.cs.technion.ac.il/~itai/Courses/Cache/bit.pdf
@@ -124,7 +125,7 @@ func bitReverseCobraInPlace(v []fr.Element) {
 }
 
 
-func bitReverseCobra(v []fr.Element) {
+func bitReverseCobra(v []{{ .FF }}.Element) {
 	switch len(v) {
 	case 1 << 21:
 		bitReverseCobraInPlace_9_21(v)
@@ -161,22 +162,22 @@ func deriveLogTileSize(logN uint64) uint64 {
 }
 
 
-{{bitReverseCobraInPlace 9 21}}
-{{bitReverseCobraInPlace 9 22}}
-{{bitReverseCobraInPlace 9 23}}
-{{bitReverseCobraInPlace 9 24}}
-{{bitReverseCobraInPlace 9 25}}
-{{bitReverseCobraInPlace 9 26}}
-{{bitReverseCobraInPlace 9 27}}
+{{bitReverseCobraInPlace 9 21 $.FF }}
+{{bitReverseCobraInPlace 9 22 $.FF }}
+{{bitReverseCobraInPlace 9 23 $.FF }}
+{{bitReverseCobraInPlace 9 24 $.FF }}
+{{bitReverseCobraInPlace 9 25 $.FF }}
+{{bitReverseCobraInPlace 9 26 $.FF }}
+{{bitReverseCobraInPlace 9 27 $.FF }}
 
 
-{{define "bitReverseCobraInPlace logTileSize logN"}}
+{{define "bitReverseCobraInPlace logTileSize logN FF"}}
 
 // bitReverseCobraInPlace_{{.logTileSize}}_{{.logN}} applies the bit-reversal permutation to v.
 // len(v) must be 1 << {{.logN}}.
 // see bitReverseCobraInPlace for more details; this function is specialized for {{.logTileSize}},
 // as it declares the t buffer and various constants statically for performance.
-func bitReverseCobraInPlace_{{.logTileSize}}_{{.logN}}(v []fr.Element) {
+func bitReverseCobraInPlace_{{.logTileSize}}_{{.logN}}(v []{{ .FF }}.Element) {
 	const (
 		logTileSize = uint64({{.logTileSize}})
 		tileSize = uint64(1) << logTileSize
@@ -186,7 +187,7 @@ func bitReverseCobraInPlace_{{.logTileSize}}_{{.logN}}(v []fr.Element) {
 		bLen = uint64(1) << logBLen
 	)
 
-	var t [tileSize * tileSize]fr.Element
+	var t [tileSize * tileSize]{{ .FF }}.Element
 	{{$k := sub 64  .logTileSize}}
 	{{$l := .logTileSize}}
 	{{$tileSize := shl 1 .logTileSize}}
diff --git a/internal/generator/fft/template/doc.go.tmpl b/field/generator/internal/templates/fft/doc.go.tmpl
similarity index 100%
rename from internal/generator/fft/template/doc.go.tmpl
rename to field/generator/internal/templates/fft/doc.go.tmpl
diff --git a/internal/generator/fft/template/domain.go.tmpl b/field/generator/internal/templates/fft/domain.go.tmpl
similarity index 76%
rename from internal/generator/fft/template/domain.go.tmpl
rename to field/generator/internal/templates/fft/domain.go.tmpl
index 59a87a6c19..fd54a6f49d 100644
--- a/internal/generator/fft/template/domain.go.tmpl
+++ b/field/generator/internal/templates/fft/domain.go.tmpl
@@ -7,7 +7,7 @@ import (
 	"errors"
 	"encoding/binary"
 
-	{{ template "import_fr" . }}
+	"{{ .FieldPackagePath }}"
 
 	"github.com/consensys/gnark-crypto/ecc"
 )
@@ -17,11 +17,11 @@ import (
 // all other values can be derived from x, GeneratorSqrt
 type Domain struct {
 	Cardinality             uint64
-	CardinalityInv          fr.Element
-	Generator               fr.Element
-	GeneratorInv            fr.Element
-	FrMultiplicativeGen     fr.Element // generator of Fr*
-	FrMultiplicativeGenInv  fr.Element
+	CardinalityInv          {{ .FF }}.Element
+	Generator               {{ .FF }}.Element
+	GeneratorInv            {{ .FF }}.Element
+	FrMultiplicativeGen     {{ .FF }}.Element // generator of Fr*
+	FrMultiplicativeGenInv  {{ .FF }}.Element
 
 	// this is set with the WithoutPrecompute option;
 	// if true, the domain does some pre-computation and stores it.
@@ -31,38 +31,26 @@ type Domain struct {
 	// the following slices are not serialized and are (re)computed through domain.preComputeTwiddles()
 
 	// twiddles factor for the FFT using Generator for each stage of the recursive FFT
-	twiddles [][]fr.Element
+	twiddles [][]{{ .FF }}.Element
 
 	// twiddles factor for the FFT using GeneratorInv for each stage of the recursive FFT
-	twiddlesInv [][]fr.Element
+	twiddlesInv [][]{{ .FF }}.Element
 
 	// we precompute these mostly to avoid the memory intensive bit reverse permutation in the groth16.Prover
 
 	// cosetTable u*<1,g,..,g^(n-1)>
-	cosetTable         []fr.Element
+	cosetTable         []{{ .FF }}.Element
 
 	// cosetTable[i][j] = domain.Generator(i-th)SqrtInv ^ j
-	cosetTableInv         []fr.Element
+	cosetTableInv         []{{ .FF }}.Element
 }
 
 // GeneratorFullMultiplicativeGroup returns a generator of 𝔽ᵣˣ
-func GeneratorFullMultiplicativeGroup() fr.Element {
-	var res fr.Element
-	{{if eq .Name "bls12-377"}}
-        res.SetUint64(22)
-	{{else if eq .Name "bls12-381"}}
-        res.SetUint64(7)
-	{{else if eq .Name "bn254"}}
-        res.SetUint64(5)
-	{{else if eq .Name "bw6-761"}}
-        res.SetUint64(15)
-    {{else if eq .Name "bw6-633"}}
-        res.SetUint64(13)
-	{{else if eq .Name "bls24-315"}}
-        res.SetUint64(7)
-	{{else if eq .Name "bls24-317"}}
-        res.SetUint64(7)
-	{{end}}
+func GeneratorFullMultiplicativeGroup() {{ .FF }}.Element {
+	var res {{ .FF }}.Element
+	
+	res.SetUint64({{ .GeneratorFullMultiplicativeGroup }})
+
 	return res
 }
 
@@ -100,13 +88,13 @@ func NewDomain(m uint64, opts ...DomainOption) *Domain {
 
 // Generator returns a generator for Z/2^(log(m))Z
 // or an error if m is too big (required root of unity doesn't exist)
-func Generator(m uint64) (fr.Element, error) {
-	return fr.Generator(m)
+func Generator(m uint64) ({{ .FF }}.Element, error) {
+	return {{ .FF }}.Generator(m)
 }
 
 // Twiddles returns the twiddles factor for the FFT using Generator for each stage of the recursive FFT
 // or an error if the domain was created with the WithoutPrecompute option
-func (d *Domain) Twiddles() ([][]fr.Element, error) {
+func (d *Domain) Twiddles() ([][]{{ .FF }}.Element, error) {
 	if d.twiddles == nil {
 		return nil, errors.New("twiddles not precomputed")
 	}
@@ -115,7 +103,7 @@ func (d *Domain) Twiddles() ([][]fr.Element, error) {
 
 // TwiddlesInv returns the twiddles factor for the FFT using GeneratorInv for each stage of the recursive FFT
 // or an error if the domain was created with the WithoutPrecompute option
-func (d *Domain) TwiddlesInv() ([][]fr.Element, error) {
+func (d *Domain) TwiddlesInv() ([][]{{ .FF }}.Element, error) {
 	if d.twiddlesInv == nil {
 		return nil, errors.New("twiddles not precomputed")
 	}
@@ -124,7 +112,7 @@ func (d *Domain) TwiddlesInv() ([][]fr.Element, error) {
 
 // CosetTable returns the cosetTable u*<1,g,..,g^(n-1)>
 // or an error if the domain was created with the WithoutPrecompute option
-func (d *Domain) CosetTable() ([]fr.Element, error) {
+func (d *Domain) CosetTable() ([]{{ .FF }}.Element, error) {
 	if d.cosetTable == nil {
 		return nil, errors.New("cosetTable not precomputed")
 	}
@@ -133,7 +121,7 @@ func (d *Domain) CosetTable() ([]fr.Element, error) {
 
 // CosetTableInv returns the cosetTableInv u*<1,g,..,g^(n-1)>
 // or an error if the domain was created with the WithoutPrecompute option
-func (d *Domain) CosetTableInv() ([]fr.Element, error) {
+func (d *Domain) CosetTableInv() ([]{{ .FF }}.Element, error) {
 	if d.cosetTableInv == nil {
 		return nil, errors.New("cosetTableInv not precomputed")
 	}
@@ -147,14 +135,14 @@ func (d *Domain) preComputeTwiddles() {
 	// nb fft stages
 	nbStages := uint64(bits.TrailingZeros64(d.Cardinality))
 
-	d.twiddles = make([][]fr.Element, nbStages)
-	d.twiddlesInv = make([][]fr.Element, nbStages)
-	d.cosetTable = make([]fr.Element, d.Cardinality)
-	d.cosetTableInv = make([]fr.Element, d.Cardinality)
+	d.twiddles = make([][]{{ .FF }}.Element, nbStages)
+	d.twiddlesInv = make([][]{{ .FF }}.Element, nbStages)
+	d.cosetTable = make([]{{ .FF }}.Element, d.Cardinality)
+	d.cosetTableInv = make([]{{ .FF }}.Element, d.Cardinality)
 
 	var wg sync.WaitGroup
 
-	expTable := func(sqrt fr.Element, t []fr.Element) {
+	expTable := func(sqrt {{ .FF }}.Element, t []{{ .FF }}.Element) {
 		BuildExpTable(sqrt, t)
 		wg.Done()
 	}
@@ -175,7 +163,7 @@ func (d *Domain) preComputeTwiddles() {
 
 }
 
-func buildTwiddles(t [][]fr.Element, omega fr.Element,nbStages uint64) {
+func buildTwiddles(t [][]{{ .FF }}.Element, omega {{ .FF }}.Element,nbStages uint64) {
 	if nbStages == 0 {
 		return
 	}
@@ -183,12 +171,12 @@ func buildTwiddles(t [][]fr.Element, omega fr.Element,nbStages uint64) {
 		panic("invalid twiddle table")
 	}
 	// we just compute the first stage
-	t[0] = make([]fr.Element, 1+(1<<(nbStages-1)))
+	t[0] = make([]{{ .FF }}.Element, 1+(1<<(nbStages-1)))
 	BuildExpTable(omega, t[0])
 
 	// for the next stages, we just iterate on the first stage with larger stride
 	for i := uint64(1); i < nbStages; i++ {
-		t[i] = make([]fr.Element, 1+(1<<(nbStages-i-1)))
+		t[i] = make([]{{ .FF }}.Element, 1+(1<<(nbStages-i-1)))
 		k := 0
 		for j := 0; j < len(t[i]); j++ {
 			t[i][j] = t[0][k]
@@ -202,7 +190,7 @@ func buildTwiddles(t [][]fr.Element, omega fr.Element,nbStages uint64) {
 // table[0] = w^0
 // table[1] = w^1
 // ...
-func BuildExpTable(w fr.Element, table []fr.Element) {
+func BuildExpTable(w {{ .FF }}.Element, table []{{ .FF }}.Element) {
 	table[0].SetOne()
 	n := len(table)
 
@@ -238,7 +226,7 @@ func BuildExpTable(w fr.Element, table []fr.Element) {
 	wg.Wait()
 }
 
-func precomputeExpTableChunk(w fr.Element, power uint64, table []fr.Element) {
+func precomputeExpTableChunk(w {{ .FF }}.Element, power uint64, table []{{ .FF }}.Element) {
 
 	// this condition ensures that creating a domain of size 1 with cosets don't fail
 	if len(table) > 0 {
@@ -264,14 +252,14 @@ func (d *Domain) WriteTo(w io.Writer) (int64, error) {
 	}
 	written += 8
 
-	toEncode := []*fr.Element{ &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
+	toEncode := []*{{ .FF }}.Element{ &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
 	for _, v := range toEncode {
 		buf := v.Bytes()
 		_, err = w.Write(buf[:])
 		if err != nil {
 			return written, err
 		}
-		written += fr.Bytes
+		written += {{ .FF }}.Bytes
 	}
 
 	err = binary.Write(w, binary.BigEndian, d.withPrecompute)
@@ -295,16 +283,16 @@ func (d *Domain) ReadFrom(r io.Reader) (int64, error) {
 	}
 	read += 8
 
-	toDecode := []*fr.Element{&d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
+	toDecode := []*{{ .FF }}.Element{&d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
 
 	for _, v := range toDecode {
-		var buf [fr.Bytes]byte
+		var buf [{{ .FF }}.Bytes]byte
 		_, err = r.Read(buf[:])
 		if err != nil {
 			return read, err
 		}
-		read += fr.Bytes
-		*v, err = fr.BigEndian.Element(&buf)
+		read += {{ .FF }}.Bytes
+		*v, err = {{ .FF }}.BigEndian.Element(&buf)
 		if err != nil {
 			return read, err
 		}
diff --git a/internal/generator/fft/template/fft.go.tmpl b/field/generator/internal/templates/fft/fft.go.tmpl
similarity index 84%
rename from internal/generator/fft/template/fft.go.tmpl
rename to field/generator/internal/templates/fft/fft.go.tmpl
index 71baed1fe7..b143e0c969 100644
--- a/internal/generator/fft/template/fft.go.tmpl
+++ b/field/generator/internal/templates/fft/fft.go.tmpl
@@ -3,7 +3,8 @@ import (
 	"github.com/consensys/gnark-crypto/ecc"
 	"github.com/consensys/gnark-crypto/internal/parallel"
 	"math/big"
-	{{ template "import_fr" . }}
+	
+	"{{ .FieldPackagePath }}"
 )
 
 {{- /* these params set the size of the kernel we generate & unroll */}}
@@ -24,7 +25,7 @@ const butterflyThreshold = 16
 // FFT computes (recursively) the discrete Fourier transform of a and stores the result in a
 // if decimation == DIT (decimation in time), the input must be in bit-reversed order
 // if decimation == DIF (decimation in frequency), the output will be in bit-reversed order
-func (domain *Domain) FFT(a []fr.Element, decimation Decimation, opts ...Option) {
+func (domain *Domain) FFT(a []{{ .FF }}.Element, decimation Decimation, opts ...Option) {
 
 	opt := fftOptions(opts...)
 
@@ -42,7 +43,7 @@ func (domain *Domain) FFT(a []fr.Element, decimation Decimation, opts ...Option)
 			cosetTable := domain.cosetTable
 			if !domain.withPrecompute {
 				// we need to build the full table or do a bit reverse dance.
-				cosetTable = make([]fr.Element, len(a))
+				cosetTable = make([]{{ .FF }}.Element, len(a))
 				BuildExpTable(domain.FrMultiplicativeGen, cosetTable)
 			}
 			parallel.Execute(len(a), func(start, end int) {
@@ -63,7 +64,7 @@ func (domain *Domain) FFT(a []fr.Element, decimation Decimation, opts ...Option)
 			} else {
 				c := domain.FrMultiplicativeGen
 				parallel.Execute(len(a), func(start, end int) {
-					var at fr.Element
+					var at {{ .FF }}.Element
 					at.Exp(c, big.NewInt(int64(start)))
 					for i := start; i < end; i++ {
 						a[i].Mul(&a[i], &at)
@@ -81,7 +82,7 @@ func (domain *Domain) FFT(a []fr.Element, decimation Decimation, opts ...Option)
 		twiddlesStartStage = 3
 		nbStages := int(bits.TrailingZeros64(domain.Cardinality))
 		if nbStages - twiddlesStartStage > 0 {
-			twiddles = make([][]fr.Element, nbStages - twiddlesStartStage)
+			twiddles = make([][]{{ .FF }}.Element, nbStages - twiddlesStartStage)
 			w := domain.Generator
 			w.Exp(w, big.NewInt(int64(1 << twiddlesStartStage)))
 			buildTwiddles(twiddles, w, uint64(nbStages - twiddlesStartStage))
@@ -105,7 +106,7 @@ func (domain *Domain) FFT(a []fr.Element, decimation Decimation, opts ...Option)
 // if decimation == DIF (decimation in frequency), the output will be in bit-reversed order
 // coset sets the shift of the fft (0 = no shift, standard fft)
 // len(a) must be a power of 2, and w must be a len(a)th root of unity in field F.
-func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, opts ...Option) {
+func (domain *Domain) FFTInverse(a []{{ .FF }}.Element, decimation Decimation, opts ...Option) {
 	opt := fftOptions(opts...)
 
 	// find the stage where we should stop spawning go routines in our recursive calls
@@ -121,7 +122,7 @@ func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, opts ...
 		twiddlesStartStage = 3
 		nbStages := int(bits.TrailingZeros64(domain.Cardinality))
 		if nbStages - twiddlesStartStage > 0 {
-			twiddlesInv = make([][]fr.Element, nbStages - twiddlesStartStage)
+			twiddlesInv = make([][]{{ .FF }}.Element, nbStages - twiddlesStartStage)
 			w := domain.GeneratorInv
 			w.Exp(w, big.NewInt(int64(1 << twiddlesStartStage)))
 			buildTwiddles(twiddlesInv, w, uint64(nbStages - twiddlesStartStage))
@@ -159,7 +160,7 @@ func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, opts ...
 		} else {
 			c := domain.FrMultiplicativeGenInv
 			parallel.Execute(len(a), func(start, end int) {
-				var at fr.Element
+				var at {{ .FF }}.Element
 				at.Exp(c, big.NewInt(int64(start)))
 				at.Mul(&at, &domain.CardinalityInv)
 				for i := start; i < end; i++ {
@@ -175,7 +176,7 @@ func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, opts ...
 	cosetTableInv := domain.cosetTableInv
 	if !domain.withPrecompute {
 		// we need to build the full table or do a bit reverse dance.
-		cosetTableInv = make([]fr.Element, len(a))
+		cosetTableInv = make([]{{ .FF }}.Element, len(a))
 		BuildExpTable(domain.FrMultiplicativeGenInv, cosetTableInv)
 	}
 	parallel.Execute(len(a), func(start, end int) {
@@ -190,7 +191,7 @@ func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, opts ...
 
 }
 
-func difFFT(a []fr.Element, w fr.Element, twiddles [][]fr.Element, twiddlesStartStage, stage, maxSplits int, chDone chan struct{}, nbTasks int) {
+func difFFT(a []{{ .FF }}.Element, w {{ .FF }}.Element, twiddles [][]{{ .FF }}.Element, twiddlesStartStage, stage, maxSplits int, chDone chan struct{}, nbTasks int) {
 	if chDone != nil {
 		defer close(chDone)
 	}
@@ -211,10 +212,10 @@ func difFFT(a []fr.Element, w fr.Element, twiddles [][]fr.Element, twiddlesStart
 			w := w
 			parallel.Execute(m, func(start, end int) {
 				if start == 0 {
-					fr.Butterfly(&a[0], &a[m])
+					{{ .FF }}.Butterfly(&a[0], &a[m])
 					start++
 				}
-				var at fr.Element
+				var at {{ .FF }}.Element
 				at.Exp(w, big.NewInt(int64(start)))
 				innerDIFWithoutTwiddles(a, at,w, start, end, m)
 			}, nbTasks / (1 << (stage))) // 1 << stage == estimated used CPUs
@@ -251,31 +252,31 @@ func difFFT(a []fr.Element, w fr.Element, twiddles [][]fr.Element, twiddlesStart
 }
 
 
-func innerDIFWithTwiddles(a []fr.Element, twiddles []fr.Element, start, end, m int) {
+func innerDIFWithTwiddles(a []{{ .FF }}.Element, twiddles []{{ .FF }}.Element, start, end, m int) {
 	if start == 0 {
-		fr.Butterfly(&a[0], &a[m])
+		{{ .FF }}.Butterfly(&a[0], &a[m])
 		start++
 	}
 	for i := start; i < end; i++ {
-		fr.Butterfly(&a[i], &a[i+m])
+		{{ .FF }}.Butterfly(&a[i], &a[i+m])
 		a[i+m].Mul(&a[i+m], &twiddles[i])
 	}
 }
 
-func innerDIFWithoutTwiddles(a []fr.Element, at, w fr.Element, start, end, m int) {
+func innerDIFWithoutTwiddles(a []{{ .FF }}.Element, at, w {{ .FF }}.Element, start, end, m int) {
 	if start == 0 {
-		fr.Butterfly(&a[0], &a[m])
+		{{ .FF }}.Butterfly(&a[0], &a[m])
 		start++
 	}
 	for i := start; i < end; i++ {
-		fr.Butterfly(&a[i], &a[i+m])
+		{{ .FF }}.Butterfly(&a[i], &a[i+m])
 		a[i+m].Mul(&a[i+m], &at)
 		at.Mul(&at, &w)
 	}
 }
 
 
-func ditFFT(a []fr.Element, w fr.Element, twiddles [][]fr.Element, twiddlesStartStage, stage, maxSplits int, chDone chan struct{}, nbTasks int) {
+func ditFFT(a []{{ .FF }}.Element, w {{ .FF }}.Element, twiddles [][]{{ .FF }}.Element, twiddlesStartStage, stage, maxSplits int, chDone chan struct{}, nbTasks int) {
 	if chDone != nil {
 		defer close(chDone)
 	}
@@ -311,10 +312,10 @@ func ditFFT(a []fr.Element, w fr.Element, twiddles [][]fr.Element, twiddlesStart
 			w := w
 			parallel.Execute(m, func(start, end int) {
 				if start == 0 {
-					fr.Butterfly(&a[0], &a[m])
+					{{ .FF }}.Butterfly(&a[0], &a[m])
 					start++
 				}
-				var at fr.Element
+				var at {{ .FF }}.Element
 				at.Exp(w, big.NewInt(int64(start)))
 				innerDITWithoutTwiddles(a, at,w, start, end, m)
 			}, nbTasks / (1 << (stage))) // 1 << stage == estimated used CPUs
@@ -334,32 +335,32 @@ func ditFFT(a []fr.Element, w fr.Element, twiddles [][]fr.Element, twiddlesStart
 }
 
 
-func innerDITWithTwiddles(a []fr.Element, twiddles []fr.Element, start, end, m int) {
+func innerDITWithTwiddles(a []{{ .FF }}.Element, twiddles []{{ .FF }}.Element, start, end, m int) {
 	if start == 0 {
-		fr.Butterfly(&a[0], &a[m])
+		{{ .FF }}.Butterfly(&a[0], &a[m])
 		start++
 	}
 	for i := start; i < end; i++ {
 		a[i+m].Mul(&a[i+m], &twiddles[i])
-		fr.Butterfly(&a[i], &a[i+m])
+		{{ .FF }}.Butterfly(&a[i], &a[i+m])
 	}
 }
 
-func innerDITWithoutTwiddles(a []fr.Element, at, w fr.Element, start, end, m int) {
+func innerDITWithoutTwiddles(a []{{ .FF }}.Element, at, w {{ .FF }}.Element, start, end, m int) {
 	if start == 0 {
-		fr.Butterfly(&a[0], &a[m])
+		{{ .FF }}.Butterfly(&a[0], &a[m])
 		start++
 	}
 	for i := start; i < end; i++ {
 		a[i+m].Mul(&a[i+m], &at)
-		fr.Butterfly(&a[i], &a[i+m])
+		{{ .FF }}.Butterfly(&a[i], &a[i+m])
 		at.Mul(&at, &w)
 	}
 }
 
 
 
-func kerDIFNP_{{$sizeKernel}}(a []fr.Element, twiddles [][]fr.Element, stage int) {
+func kerDIFNP_{{$sizeKernel}}(a []{{ .FF }}.Element, twiddles [][]{{ .FF }}.Element, stage int) {
 	// code unrolled & generated by internal/generator/fft/template/fft.go.tmpl
 
 	{{ $n := shl 1 $sizeKernelLog2}}
@@ -374,7 +375,7 @@ func kerDIFNP_{{$sizeKernel}}(a []fr.Element, twiddles [][]fr.Element, stage int
 		{{- else}}
 			for offset := 0; offset < {{$bound}}; offset += {{$n}} {
 				{{- if eq $m 1}}
-					fr.Butterfly(&a[offset], &a[offset+1])
+					{{ $.FF }}.Butterfly(&a[offset], &a[offset+1])
 				{{- else}}
 					innerDIFWithTwiddles(a[offset:offset + {{$n}}], twiddles[stage + {{$step}}], 0, {{$m}}, {{$m}})
 				{{- end}}
@@ -388,7 +389,7 @@ func kerDIFNP_{{$sizeKernel}}(a []fr.Element, twiddles [][]fr.Element, stage int
 }
 
 
-func kerDITNP_{{$sizeKernel}}(a []fr.Element, twiddles [][]fr.Element, stage int) {
+func kerDITNP_{{$sizeKernel}}(a []{{ .FF }}.Element, twiddles [][]{{ .FF }}.Element, stage int) {
 	// code unrolled & generated by internal/generator/fft/template/fft.go.tmpl
 
 	{{ $n := 2}}
@@ -403,7 +404,7 @@ func kerDITNP_{{$sizeKernel}}(a []fr.Element, twiddles [][]fr.Element, stage int
 		{{- else}}
 			for offset := 0; offset < {{$bound}}; offset += {{$n}} {
 				{{- if eq $m 1}}
-					fr.Butterfly(&a[offset], &a[offset+1])
+					{{ $.FF }}.Butterfly(&a[offset], &a[offset+1])
 				{{- else}}
 					innerDITWithTwiddles(a[offset:offset + {{$n}}], twiddles[stage + {{$step}}], 0, {{$m}}, {{$m}})
 				{{- end}}
diff --git a/field/generator/internal/templates/fft/fr.generator.go.tmpl b/field/generator/internal/templates/fft/fr.generator.go.tmpl
new file mode 100644
index 0000000000..790f7f083a
--- /dev/null
+++ b/field/generator/internal/templates/fft/fr.generator.go.tmpl
@@ -0,0 +1,29 @@
+import (
+	"fmt"
+	"math/big"
+	"math/bits"
+
+	"github.com/consensys/gnark-crypto/ecc"
+)
+
+// Generator returns a generator for Z/2^(log(m))Z
+// or an error if m is too big (required root of unity doesn't exist)
+func Generator(m uint64) (Element, error) {
+	x := ecc.NextPowerOfTwo(m)
+
+	var rootOfUnity Element
+	
+    rootOfUnity.SetString("{{ .GeneratorMaxTwoAdicSubgroup }}")
+    const maxOrderRoot uint64 = {{ .LogTwoOrderMaxTwoAdicSubgroup }}
+
+	// find generator for Z/2^(log(m))Z
+	logx := uint64(bits.TrailingZeros64(x))
+	if logx > maxOrderRoot {
+		return Element{}, fmt.Errorf("m (%d) is too big: the required root of unity does not exist", m)
+	}
+
+	expo := uint64(1 << (maxOrderRoot - logx))
+	var generator Element
+	generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x
+	return generator, nil
+}
\ No newline at end of file
diff --git a/internal/generator/fft/template/fuzz.go.tmpl b/field/generator/internal/templates/fft/fuzz.go.tmpl
similarity index 89%
rename from internal/generator/fft/template/fuzz.go.tmpl
rename to field/generator/internal/templates/fft/fuzz.go.tmpl
index f417cdd8be..5818d0ce11 100644
--- a/internal/generator/fft/template/fuzz.go.tmpl
+++ b/field/generator/internal/templates/fft/fuzz.go.tmpl
@@ -2,7 +2,7 @@ import (
 	"bytes"
     "fmt"
     "github.com/consensys/gnark-crypto/ecc"
-    {{ template "import_fr" . }}
+    "{{ .FieldPackagePath }}"
 )
 
 const (
@@ -24,8 +24,8 @@ func Fuzz(data []byte) int {
         size = 1 << 15
     }
     paddedSize := ecc.NextPowerOfTwo(uint64(size))
-    p1 := make([]fr.Element, paddedSize)
-    p2 := make([]fr.Element, paddedSize)
+    p1 := make([]{{ .FF }}.Element, paddedSize)
+    p2 := make([]{{ .FF }}.Element, paddedSize)
     for i := 0; i < len(p1); i++ {
         p1[i].SetRawBytes(r)
     }
diff --git a/internal/generator/fft/template/options.go.tmpl b/field/generator/internal/templates/fft/options.go.tmpl
similarity index 91%
rename from internal/generator/fft/template/options.go.tmpl
rename to field/generator/internal/templates/fft/options.go.tmpl
index 1eb8407e0a..6e57878ec4 100644
--- a/internal/generator/fft/template/options.go.tmpl
+++ b/field/generator/internal/templates/fft/options.go.tmpl
@@ -1,6 +1,7 @@
 import (
 	"runtime"
-	{{ template "import_fr" . }}
+	
+	"{{ .FieldPackagePath }}"
 )
 
 // Option defines option for altering the behavior of FFT methods.
@@ -51,15 +52,15 @@ func fftOptions(opts ...Option) fftConfig {
 type DomainOption func(*domainConfig)
 
 type domainConfig struct {
-	shift    *fr.Element
+	shift    *{{ .FF }}.Element
 	withPrecompute bool
 }
 
 // WithShift sets the FrMultiplicativeGen of the domain.
 // Default is generator of the largest 2-adic subgroup.
-func WithShift(shift fr.Element) DomainOption {
+func WithShift(shift {{ .FF }}.Element) DomainOption {
 	return func(opt *domainConfig) {
-		opt.shift = new(fr.Element).Set(&shift)
+		opt.shift = new({{ .FF }}.Element).Set(&shift)
 	}
 }
 
diff --git a/internal/generator/fft/template/tests/bitreverse.go.tmpl b/field/generator/internal/templates/fft/tests/bitreverse.go.tmpl
similarity index 74%
rename from internal/generator/fft/template/tests/bitreverse.go.tmpl
rename to field/generator/internal/templates/fft/tests/bitreverse.go.tmpl
index 2f70e73bb8..8fa5f711c4 100644
--- a/internal/generator/fft/template/tests/bitreverse.go.tmpl
+++ b/field/generator/internal/templates/fft/tests/bitreverse.go.tmpl
@@ -2,14 +2,14 @@ import (
 	"fmt"
 	"testing"
 
-	{{ template "import_fr" . }}
+	"{{ .FieldPackagePath }}"
 )
 
 
 type bitReverseVariant struct {
 	name string
-	buf  []fr.Element
-	fn   func([]fr.Element)
+	buf  []{{ .FF }}.Element
+	fn   func([]{{ .FF }}.Element)
 }
 
 
@@ -17,16 +17,16 @@ type bitReverseVariant struct {
 const maxSizeBitReverse = 1 << 23
 
 var bitReverse = []bitReverseVariant{
-	{name: "bitReverseNaive", buf: make([]fr.Element, maxSizeBitReverse), fn: bitReverseNaive},
-	{name: "BitReverse", buf: make([]fr.Element, maxSizeBitReverse), fn: BitReverse},
-	{name: "bitReverseCobraInPlace", buf: make([]fr.Element, maxSizeBitReverse), fn: bitReverseCobraInPlace},
+	{name: "bitReverseNaive", buf: make([]{{ .FF }}.Element, maxSizeBitReverse), fn: bitReverseNaive},
+	{name: "BitReverse", buf: make([]{{ .FF }}.Element, maxSizeBitReverse), fn: BitReverse},
+	{name: "bitReverseCobraInPlace", buf: make([]{{ .FF }}.Element, maxSizeBitReverse), fn: bitReverseCobraInPlace},
 }
 
 func TestBitReverse(t *testing.T) {
 
-	// generate a random []fr.Element array of size 2**20
-	pol := make([]fr.Element, maxSizeBitReverse)
-	one := fr.One()
+	// generate a random []{{ .FF }}.Element array of size 2**20
+	pol := make([]{{ .FF }}.Element, maxSizeBitReverse)
+	one := {{ .FF }}.One()
 	pol[0].SetRandom()
 	for i := 1; i < maxSizeBitReverse; i++ {
 		pol[i].Add(&pol[i-1], &one)
@@ -71,9 +71,9 @@ func TestBitReverse(t *testing.T) {
 }
 
 func BenchmarkBitReverse(b *testing.B) {
-	// generate a random []fr.Element array of size 2**22
-	pol := make([]fr.Element, maxSizeBitReverse)
-	one := fr.One()
+	// generate a random []{{ .FF }}.Element array of size 2**22
+	pol := make([]{{ .FF }}.Element, maxSizeBitReverse)
+	one := {{ .FF }}.One()
 	pol[0].SetRandom()
 	for i := 1; i < maxSizeBitReverse; i++ {
 		pol[i].Add(&pol[i-1], &one)
diff --git a/internal/generator/fft/template/tests/domain.go.tmpl b/field/generator/internal/templates/fft/tests/domain.go.tmpl
similarity index 100%
rename from internal/generator/fft/template/tests/domain.go.tmpl
rename to field/generator/internal/templates/fft/tests/domain.go.tmpl
diff --git a/internal/generator/fft/template/tests/fft.go.tmpl b/field/generator/internal/templates/fft/tests/fft.go.tmpl
similarity index 86%
rename from internal/generator/fft/template/tests/fft.go.tmpl
rename to field/generator/internal/templates/fft/tests/fft.go.tmpl
index 73b22993b2..4500234956 100644
--- a/internal/generator/fft/template/tests/fft.go.tmpl
+++ b/field/generator/internal/templates/fft/tests/fft.go.tmpl
@@ -3,7 +3,7 @@ import (
 	"testing"
 	"strconv"
 
-	{{ template "import_fr" . }}
+	"{{ .FieldPackagePath }}"
 
 	"github.com/leanovate/gopter"
 	"github.com/leanovate/gopter/prop"
@@ -36,8 +36,8 @@ func TestFFT(t *testing.T) {
 				// checks that a random evaluation of a dual function eval(gen**ithpower) is consistent with the FFT result
 				func(ithpower int) bool {
 
-					pol := make([]fr.Element, maxSize)
-					backupPol := make([]fr.Element, maxSize)
+					pol := make([]{{ .FF }}.Element, maxSize)
+					backupPol := make([]{{ .FF }}.Element, maxSize)
 
 					for i := 0; i < maxSize; i++ {
 						pol[i].SetRandom()
@@ -65,8 +65,8 @@ func TestFFT(t *testing.T) {
 				// checks that a random evaluation of a dual function eval(gen**ithpower) is consistent with the FFT result
 				func(ithpower int) bool {
 
-					pol := make([]fr.Element, maxSize)
-					backupPol := make([]fr.Element, maxSize)
+					pol := make([]{{ .FF }}.Element, maxSize)
+					backupPol := make([]{{ .FF }}.Element, maxSize)
 
 					for i := 0; i < maxSize; i++ {
 						pol[i].SetRandom()
@@ -93,8 +93,8 @@ func TestFFT(t *testing.T) {
 				// checks that a random evaluation of a dual function eval(gen**ithpower) is consistent with the FFT result
 				func(ithpower int) bool {
 
-					pol := make([]fr.Element, maxSize)
-					backupPol := make([]fr.Element, maxSize)
+					pol := make([]{{ .FF }}.Element, maxSize)
+					backupPol := make([]{{ .FF }}.Element, maxSize)
 
 					for i := 0; i < maxSize; i++ {
 						pol[i].SetRandom()
@@ -119,8 +119,8 @@ func TestFFT(t *testing.T) {
 
 				func() bool {
 
-					pol := make([]fr.Element, maxSize)
-					backupPol := make([]fr.Element, maxSize)
+					pol := make([]{{ .FF }}.Element, maxSize)
+					backupPol := make([]{{ .FF }}.Element, maxSize)
 
 					for i := 0; i < maxSize; i++ {
 						pol[i].SetRandom()
@@ -145,8 +145,8 @@ func TestFFT(t *testing.T) {
 
 					func() bool {
 
-						pol := make([]fr.Element, maxSize)
-						backupPol := make([]fr.Element, maxSize)
+						pol := make([]{{ .FF }}.Element, maxSize)
+						backupPol := make([]{{ .FF }}.Element, maxSize)
 
 						for i := 0; i < maxSize; i++ {
 							pol[i].SetRandom()
@@ -176,8 +176,8 @@ func TestFFT(t *testing.T) {
 
 				func() bool {
 
-					pol := make([]fr.Element, maxSize)
-					backupPol := make([]fr.Element, maxSize)
+					pol := make([]{{ .FF }}.Element, maxSize)
+					backupPol := make([]{{ .FF }}.Element, maxSize)
 
 					for i := 0; i < maxSize; i++ {
 						pol[i].SetRandom()
@@ -200,8 +200,8 @@ func TestFFT(t *testing.T) {
 
 				func() bool {
 
-					pol := make([]fr.Element, maxSize)
-					backupPol := make([]fr.Element, maxSize)
+					pol := make([]{{ .FF }}.Element, maxSize)
+					backupPol := make([]{{ .FF }}.Element, maxSize)
 
 					for i := 0; i < maxSize; i++ {
 						pol[i].SetRandom()
@@ -243,7 +243,7 @@ func BenchmarkFFT(b *testing.B) {
 
 	const maxSize = 1 << 20
 
-	pol := make([]fr.Element, maxSize)
+	pol := make([]{{ .FF }}.Element, maxSize)
 	pol[0].SetRandom()
 	for i := 1; i < maxSize; i++ {
 		pol[i] = pol[i-1]
@@ -272,7 +272,7 @@ func BenchmarkFFT(b *testing.B) {
 func BenchmarkFFTDITCosetReference(b *testing.B) {
 	const maxSize = 1 << 20
 
-	pol := make([]fr.Element, maxSize)
+	pol := make([]{{ .FF }}.Element, maxSize)
 	pol[0].SetRandom()
 	for i := 1; i < maxSize; i++ {
 		pol[i] = pol[i-1]
@@ -289,7 +289,7 @@ func BenchmarkFFTDITCosetReference(b *testing.B) {
 func BenchmarkFFTDIFReference(b *testing.B) {
 	const maxSize = 1 << 20
 
-	pol := make([]fr.Element, maxSize)
+	pol := make([]{{ .FF }}.Element, maxSize)
 	pol[0].SetRandom()
 	for i := 1; i < maxSize; i++ {
 		pol[i] = pol[i-1]
@@ -303,8 +303,8 @@ func BenchmarkFFTDIFReference(b *testing.B) {
 	}
 }
 
-func evaluatePolynomial(pol []fr.Element, val fr.Element) fr.Element {
-	var acc, res, tmp fr.Element
+func evaluatePolynomial(pol []{{ .FF }}.Element, val {{ .FF }}.Element) {{ .FF }}.Element {
+	var acc, res, tmp {{ .FF }}.Element
 	res.Set(&pol[0])
 	acc.Set(&val)
 	for i := 1; i < len(pol); i++ {
diff --git a/internal/generator/fft/template/tests/fuzz.go.tmpl b/field/generator/internal/templates/fft/tests/fuzz.go.tmpl
similarity index 100%
rename from internal/generator/fft/template/tests/fuzz.go.tmpl
rename to field/generator/internal/templates/fft/tests/fuzz.go.tmpl
diff --git a/field/generator/options.go b/field/generator/options.go
new file mode 100644
index 0000000000..e89e8b1ad1
--- /dev/null
+++ b/field/generator/options.go
@@ -0,0 +1,46 @@
+package generator
+
+import (
+	"github.com/consensys/gnark-crypto/field/generator/config"
+)
+
+type Option func(*generatorConfig)
+
+type generatorConfig struct {
+	fftConfig *config.FFT
+	asmConfig *config.Assembly
+}
+
+func (cfg *generatorConfig) HasFFT() bool {
+	return cfg.fftConfig != nil
+}
+
+func (cfg *generatorConfig) HasArm64() bool {
+	return cfg.asmConfig != nil
+}
+
+func (cfg *generatorConfig) HasAMD64() bool {
+	return cfg.asmConfig != nil
+}
+
+func WithFFT(cfg *config.FFT) Option {
+	return func(opt *generatorConfig) {
+		opt.fftConfig = cfg
+	}
+}
+
+func WithASM(cfg *config.Assembly) Option {
+	return func(opt *generatorConfig) {
+		opt.asmConfig = cfg
+	}
+}
+
+// default options
+func generatorOptions(opts ...Option) generatorConfig {
+	// apply options
+	opt := generatorConfig{}
+	for _, option := range opts {
+		option(&opt)
+	}
+	return opt
+}
diff --git a/field/goff/cmd/root.go b/field/goff/cmd/root.go
index 480c2345cf..bf2d859fad 100644
--- a/field/goff/cmd/root.go
+++ b/field/goff/cmd/root.go
@@ -12,6 +12,7 @@ import (
 	"strings"
 
 	"github.com/consensys/gnark-crypto/field/generator"
+	"github.com/consensys/gnark-crypto/field/generator/config"
 	field "github.com/consensys/gnark-crypto/field/generator/config"
 	"github.com/spf13/cobra"
 )
@@ -62,20 +63,8 @@ func cmdGenerate(cmd *cobra.Command, args []string) {
 	}
 
 	asmDir := filepath.Join(fOutputDir, "asm")
-	if F.GenerateOpsAMD64 {
-		if err := generator.GenerateAMD64(F.NbWords, asmDir, F.GenerateVectorOpsAMD64); err != nil {
-			fmt.Printf("\n%s\n", err.Error())
-			os.Exit(-1)
-		}
-	}
-	if F.GenerateOpsARM64 {
-		if err := generator.GenerateARM64(F.NbWords, asmDir, F.GenerateVectorOpsARM64); err != nil {
-			fmt.Printf("\n%s\n", err.Error())
-			os.Exit(-1)
-		}
-	}
 
-	if err := generator.GenerateFF(F, fOutputDir, asmDir, "asm"); err != nil {
+	if err := generator.GenerateFF(F, fOutputDir, generator.WithASM(&config.Assembly{BuildDir: asmDir, IncludeDir: "asm"})); err != nil {
 		fmt.Printf("\n%s\n", err.Error())
 		os.Exit(-1)
 	}
diff --git a/field/goldilocks/fft/bitreverse.go b/field/goldilocks/fft/bitreverse.go
new file mode 100644
index 0000000000..4e0f7bd962
--- /dev/null
+++ b/field/goldilocks/fft/bitreverse.go
@@ -0,0 +1,563 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fft
+
+import (
+	"math/bits"
+	"runtime"
+
+	"github.com/consensys/gnark-crypto/field/goldilocks"
+)
+
+// BitReverse applies the bit-reversal permutation to v.
+// len(v) must be a power of 2
+func BitReverse(v []goldilocks.Element) {
+	n := uint64(len(v))
+	if bits.OnesCount64(n) != 1 {
+		panic("len(a) must be a power of 2")
+	}
+
+	if runtime.GOARCH == "arm64" {
+		bitReverseNaive(v)
+	} else {
+		bitReverseCobra(v)
+	}
+}
+
+// bitReverseNaive applies the bit-reversal permutation to v.
+// len(v) must be a power of 2
+func bitReverseNaive(v []goldilocks.Element) {
+	n := uint64(len(v))
+	nn := uint64(64 - bits.TrailingZeros64(n))
+
+	for i := uint64(0); i < n; i++ {
+		iRev := bits.Reverse64(i) >> nn
+		if iRev > i {
+			v[i], v[iRev] = v[iRev], v[i]
+		}
+	}
+}
+
+// bitReverseCobraInPlace applies the bit-reversal permutation to v.
+// len(v) must be a power of 2
+// This is derived from:
+//
+//   - Towards an Optimal Bit-Reversal Permutation Program
+//     Larry Carter and Kang Su Gatlin, 1998
+//     https://csaws.cs.technion.ac.il/~itai/Courses/Cache/bit.pdf
+//
+//   - Practically efficient methods for performing bit-reversed
+//     permutation in C++11 on the x86-64 architecture
+//     Knauth, Adas, Whitfield, Wang, Ickler, Conrad, Serang, 2017
+//     https://arxiv.org/pdf/1708.01873.pdf
+//
+//   - and more specifically, constantine implementation:
+//     https://github.com/mratsim/constantine/blob/d51699248db04e29c7b1ad97e0bafa1499db00b5/constantine/math/polynomials/fft.nim#L205
+//     by Mamy Ratsimbazafy (@mratsim).
+func bitReverseCobraInPlace(v []goldilocks.Element) {
+	logN := uint64(bits.Len64(uint64(len(v))) - 1)
+	logTileSize := deriveLogTileSize(logN)
+	logBLen := logN - 2*logTileSize
+	bLen := uint64(1) << logBLen
+	bShift := logBLen + logTileSize
+	tileSize := uint64(1) << logTileSize
+
+	// rough idea;
+	// bit reversal permutation naive implementation may have some cache associativity issues,
+	// since we are accessing elements by strides of powers of 2.
+	// on large inputs, this is noticeable and can be improved by using a t buffer.
+	// idea is for t buffer to be small enough to fit in cache.
+	// in the first inner loop, we copy the elements of v into t in a bit-reversed order.
+	// in the subsequent inner loops, accesses have much better cache locality than the naive implementation.
+	// hence even if we apparently do more work (swaps / copies), we are faster.
+	//
+	// on arm64 (and particularly on M1 macs), this is not noticeable, and the naive implementation is faster,
+	// in most cases.
+	// on x86 (and particularly on aws hpc6a) this is noticeable, and the t buffer implementation is faster (up to 3x).
+	//
+	// optimal choice for the tile size is cache dependent; in theory, we want the t buffer to fit in the L1 cache;
+	// in practice, a common size for L1 is 64kb, a field element is 32bytes or more.
+	// hence we can fit 2k elements in the L1 cache, which corresponds to a tile size of 2**5 with some margin for cache conflicts.
+	//
+	// for most sizes of interest, this tile size choice doesn't yield good results;
+	// we find that a tile size of 2**9 gives best results for input sizes from 2**21 up to 2**27+.
+	t := make([]goldilocks.Element, tileSize*tileSize)
+
+	// see https://csaws.cs.technion.ac.il/~itai/Courses/Cache/bit.pdf
+	// for a detailed explanation of the algorithm.
+	for b := uint64(0); b < bLen; b++ {
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := (bits.Reverse64(a) >> (64 - logTileSize)) << logTileSize
+			for c := uint64(0); c < tileSize; c++ {
+				idx := (a << bShift) | (b << logTileSize) | c
+				t[aRev|c] = v[idx]
+			}
+		}
+
+		bRev := (bits.Reverse64(b) >> (64 - logBLen)) << logTileSize
+
+		for c := uint64(0); c < tileSize; c++ {
+			cRev := ((bits.Reverse64(c) >> (64 - logTileSize)) << bShift) | bRev
+			for aRev := uint64(0); aRev < tileSize; aRev++ {
+				a := bits.Reverse64(aRev) >> (64 - logTileSize)
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idxRev], t[tIdx] = t[tIdx], v[idxRev]
+				}
+			}
+		}
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := bits.Reverse64(a) >> (64 - logTileSize)
+			for c := uint64(0); c < tileSize; c++ {
+				cRev := (bits.Reverse64(c) >> (64 - logTileSize)) << bShift
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | bRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idx], t[tIdx] = t[tIdx], v[idx]
+				}
+			}
+		}
+	}
+}
+
+func bitReverseCobra(v []goldilocks.Element) {
+	switch len(v) {
+	case 1 << 21:
+		bitReverseCobraInPlace_9_21(v)
+	case 1 << 22:
+		bitReverseCobraInPlace_9_22(v)
+	case 1 << 23:
+		bitReverseCobraInPlace_9_23(v)
+	case 1 << 24:
+		bitReverseCobraInPlace_9_24(v)
+	case 1 << 25:
+		bitReverseCobraInPlace_9_25(v)
+	case 1 << 26:
+		bitReverseCobraInPlace_9_26(v)
+	case 1 << 27:
+		bitReverseCobraInPlace_9_27(v)
+	default:
+		if len(v) > 1<<27 {
+			bitReverseCobraInPlace(v)
+		} else {
+			bitReverseNaive(v)
+		}
+	}
+}
+
+func deriveLogTileSize(logN uint64) uint64 {
+	q := uint64(9) // see bitReverseCobraInPlace for more details
+
+	for int(logN)-int(2*q) <= 0 {
+		q--
+	}
+
+	return q
+}
+
+// bitReverseCobraInPlace_9_21 applies the bit-reversal permutation to v.
+// len(v) must be 1 << 21.
+// see bitReverseCobraInPlace for more details; this function is specialized for 9,
+// as it declares the t buffer and various constants statically for performance.
+func bitReverseCobraInPlace_9_21(v []goldilocks.Element) {
+	const (
+		logTileSize = uint64(9)
+		tileSize    = uint64(1) << logTileSize
+		logN        = 21
+		logBLen     = logN - 2*logTileSize
+		bShift      = logBLen + logTileSize
+		bLen        = uint64(1) << logBLen
+	)
+
+	var t [tileSize * tileSize]goldilocks.Element
+
+	for b := uint64(0); b < bLen; b++ {
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := (bits.Reverse64(a) >> 55) << logTileSize
+			for c := uint64(0); c < tileSize; c++ {
+				idx := (a << bShift) | (b << logTileSize) | c
+				t[aRev|c] = v[idx]
+			}
+		}
+
+		bRev := (bits.Reverse64(b) >> (64 - logBLen)) << logTileSize
+
+		for c := uint64(0); c < tileSize; c++ {
+			cRev := ((bits.Reverse64(c) >> 55) << bShift) | bRev
+			for aRev := uint64(0); aRev < tileSize; aRev++ {
+				a := bits.Reverse64(aRev) >> 55
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idxRev], t[tIdx] = t[tIdx], v[idxRev]
+				}
+			}
+		}
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := bits.Reverse64(a) >> 55
+			for c := uint64(0); c < tileSize; c++ {
+				cRev := (bits.Reverse64(c) >> 55) << bShift
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | bRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idx], t[tIdx] = t[tIdx], v[idx]
+				}
+			}
+		}
+	}
+
+}
+
+// bitReverseCobraInPlace_9_22 applies the bit-reversal permutation to v.
+// len(v) must be 1 << 22.
+// see bitReverseCobraInPlace for more details; this function is specialized for 9,
+// as it declares the t buffer and various constants statically for performance.
+func bitReverseCobraInPlace_9_22(v []goldilocks.Element) {
+	const (
+		logTileSize = uint64(9)
+		tileSize    = uint64(1) << logTileSize
+		logN        = 22
+		logBLen     = logN - 2*logTileSize
+		bShift      = logBLen + logTileSize
+		bLen        = uint64(1) << logBLen
+	)
+
+	var t [tileSize * tileSize]goldilocks.Element
+
+	for b := uint64(0); b < bLen; b++ {
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := (bits.Reverse64(a) >> 55) << logTileSize
+			for c := uint64(0); c < tileSize; c++ {
+				idx := (a << bShift) | (b << logTileSize) | c
+				t[aRev|c] = v[idx]
+			}
+		}
+
+		bRev := (bits.Reverse64(b) >> (64 - logBLen)) << logTileSize
+
+		for c := uint64(0); c < tileSize; c++ {
+			cRev := ((bits.Reverse64(c) >> 55) << bShift) | bRev
+			for aRev := uint64(0); aRev < tileSize; aRev++ {
+				a := bits.Reverse64(aRev) >> 55
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idxRev], t[tIdx] = t[tIdx], v[idxRev]
+				}
+			}
+		}
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := bits.Reverse64(a) >> 55
+			for c := uint64(0); c < tileSize; c++ {
+				cRev := (bits.Reverse64(c) >> 55) << bShift
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | bRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idx], t[tIdx] = t[tIdx], v[idx]
+				}
+			}
+		}
+	}
+
+}
+
+// bitReverseCobraInPlace_9_23 applies the bit-reversal permutation to v.
+// len(v) must be 1 << 23.
+// see bitReverseCobraInPlace for more details; this function is specialized for 9,
+// as it declares the t buffer and various constants statically for performance.
+func bitReverseCobraInPlace_9_23(v []goldilocks.Element) {
+	const (
+		logTileSize = uint64(9)
+		tileSize    = uint64(1) << logTileSize
+		logN        = 23
+		logBLen     = logN - 2*logTileSize
+		bShift      = logBLen + logTileSize
+		bLen        = uint64(1) << logBLen
+	)
+
+	var t [tileSize * tileSize]goldilocks.Element
+
+	for b := uint64(0); b < bLen; b++ {
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := (bits.Reverse64(a) >> 55) << logTileSize
+			for c := uint64(0); c < tileSize; c++ {
+				idx := (a << bShift) | (b << logTileSize) | c
+				t[aRev|c] = v[idx]
+			}
+		}
+
+		bRev := (bits.Reverse64(b) >> (64 - logBLen)) << logTileSize
+
+		for c := uint64(0); c < tileSize; c++ {
+			cRev := ((bits.Reverse64(c) >> 55) << bShift) | bRev
+			for aRev := uint64(0); aRev < tileSize; aRev++ {
+				a := bits.Reverse64(aRev) >> 55
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idxRev], t[tIdx] = t[tIdx], v[idxRev]
+				}
+			}
+		}
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := bits.Reverse64(a) >> 55
+			for c := uint64(0); c < tileSize; c++ {
+				cRev := (bits.Reverse64(c) >> 55) << bShift
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | bRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idx], t[tIdx] = t[tIdx], v[idx]
+				}
+			}
+		}
+	}
+
+}
+
+// bitReverseCobraInPlace_9_24 applies the bit-reversal permutation to v.
+// len(v) must be 1 << 24.
+// see bitReverseCobraInPlace for more details; this function is specialized for 9,
+// as it declares the t buffer and various constants statically for performance.
+func bitReverseCobraInPlace_9_24(v []goldilocks.Element) {
+	const (
+		logTileSize = uint64(9)
+		tileSize    = uint64(1) << logTileSize
+		logN        = 24
+		logBLen     = logN - 2*logTileSize
+		bShift      = logBLen + logTileSize
+		bLen        = uint64(1) << logBLen
+	)
+
+	var t [tileSize * tileSize]goldilocks.Element
+
+	for b := uint64(0); b < bLen; b++ {
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := (bits.Reverse64(a) >> 55) << logTileSize
+			for c := uint64(0); c < tileSize; c++ {
+				idx := (a << bShift) | (b << logTileSize) | c
+				t[aRev|c] = v[idx]
+			}
+		}
+
+		bRev := (bits.Reverse64(b) >> (64 - logBLen)) << logTileSize
+
+		for c := uint64(0); c < tileSize; c++ {
+			cRev := ((bits.Reverse64(c) >> 55) << bShift) | bRev
+			for aRev := uint64(0); aRev < tileSize; aRev++ {
+				a := bits.Reverse64(aRev) >> 55
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idxRev], t[tIdx] = t[tIdx], v[idxRev]
+				}
+			}
+		}
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := bits.Reverse64(a) >> 55
+			for c := uint64(0); c < tileSize; c++ {
+				cRev := (bits.Reverse64(c) >> 55) << bShift
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | bRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idx], t[tIdx] = t[tIdx], v[idx]
+				}
+			}
+		}
+	}
+
+}
+
+// bitReverseCobraInPlace_9_25 applies the bit-reversal permutation to v.
+// len(v) must be 1 << 25.
+// see bitReverseCobraInPlace for more details; this function is specialized for 9,
+// as it declares the t buffer and various constants statically for performance.
+func bitReverseCobraInPlace_9_25(v []goldilocks.Element) {
+	const (
+		logTileSize = uint64(9)
+		tileSize    = uint64(1) << logTileSize
+		logN        = 25
+		logBLen     = logN - 2*logTileSize
+		bShift      = logBLen + logTileSize
+		bLen        = uint64(1) << logBLen
+	)
+
+	var t [tileSize * tileSize]goldilocks.Element
+
+	for b := uint64(0); b < bLen; b++ {
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := (bits.Reverse64(a) >> 55) << logTileSize
+			for c := uint64(0); c < tileSize; c++ {
+				idx := (a << bShift) | (b << logTileSize) | c
+				t[aRev|c] = v[idx]
+			}
+		}
+
+		bRev := (bits.Reverse64(b) >> (64 - logBLen)) << logTileSize
+
+		for c := uint64(0); c < tileSize; c++ {
+			cRev := ((bits.Reverse64(c) >> 55) << bShift) | bRev
+			for aRev := uint64(0); aRev < tileSize; aRev++ {
+				a := bits.Reverse64(aRev) >> 55
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idxRev], t[tIdx] = t[tIdx], v[idxRev]
+				}
+			}
+		}
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := bits.Reverse64(a) >> 55
+			for c := uint64(0); c < tileSize; c++ {
+				cRev := (bits.Reverse64(c) >> 55) << bShift
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | bRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idx], t[tIdx] = t[tIdx], v[idx]
+				}
+			}
+		}
+	}
+
+}
+
+// bitReverseCobraInPlace_9_26 applies the bit-reversal permutation to v.
+// len(v) must be 1 << 26.
+// see bitReverseCobraInPlace for more details; this function is specialized for 9,
+// as it declares the t buffer and various constants statically for performance.
+func bitReverseCobraInPlace_9_26(v []goldilocks.Element) {
+	const (
+		logTileSize = uint64(9)
+		tileSize    = uint64(1) << logTileSize
+		logN        = 26
+		logBLen     = logN - 2*logTileSize
+		bShift      = logBLen + logTileSize
+		bLen        = uint64(1) << logBLen
+	)
+
+	var t [tileSize * tileSize]goldilocks.Element
+
+	for b := uint64(0); b < bLen; b++ {
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := (bits.Reverse64(a) >> 55) << logTileSize
+			for c := uint64(0); c < tileSize; c++ {
+				idx := (a << bShift) | (b << logTileSize) | c
+				t[aRev|c] = v[idx]
+			}
+		}
+
+		bRev := (bits.Reverse64(b) >> (64 - logBLen)) << logTileSize
+
+		for c := uint64(0); c < tileSize; c++ {
+			cRev := ((bits.Reverse64(c) >> 55) << bShift) | bRev
+			for aRev := uint64(0); aRev < tileSize; aRev++ {
+				a := bits.Reverse64(aRev) >> 55
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idxRev], t[tIdx] = t[tIdx], v[idxRev]
+				}
+			}
+		}
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := bits.Reverse64(a) >> 55
+			for c := uint64(0); c < tileSize; c++ {
+				cRev := (bits.Reverse64(c) >> 55) << bShift
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | bRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idx], t[tIdx] = t[tIdx], v[idx]
+				}
+			}
+		}
+	}
+
+}
+
+// bitReverseCobraInPlace_9_27 applies the bit-reversal permutation to v.
+// len(v) must be 1 << 27.
+// see bitReverseCobraInPlace for more details; this function is specialized for 9,
+// as it declares the t buffer and various constants statically for performance.
+func bitReverseCobraInPlace_9_27(v []goldilocks.Element) {
+	const (
+		logTileSize = uint64(9)
+		tileSize    = uint64(1) << logTileSize
+		logN        = 27
+		logBLen     = logN - 2*logTileSize
+		bShift      = logBLen + logTileSize
+		bLen        = uint64(1) << logBLen
+	)
+
+	var t [tileSize * tileSize]goldilocks.Element
+
+	for b := uint64(0); b < bLen; b++ {
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := (bits.Reverse64(a) >> 55) << logTileSize
+			for c := uint64(0); c < tileSize; c++ {
+				idx := (a << bShift) | (b << logTileSize) | c
+				t[aRev|c] = v[idx]
+			}
+		}
+
+		bRev := (bits.Reverse64(b) >> (64 - logBLen)) << logTileSize
+
+		for c := uint64(0); c < tileSize; c++ {
+			cRev := ((bits.Reverse64(c) >> 55) << bShift) | bRev
+			for aRev := uint64(0); aRev < tileSize; aRev++ {
+				a := bits.Reverse64(aRev) >> 55
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idxRev], t[tIdx] = t[tIdx], v[idxRev]
+				}
+			}
+		}
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := bits.Reverse64(a) >> 55
+			for c := uint64(0); c < tileSize; c++ {
+				cRev := (bits.Reverse64(c) >> 55) << bShift
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | bRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idx], t[tIdx] = t[tIdx], v[idx]
+				}
+			}
+		}
+	}
+
+}
diff --git a/field/goldilocks/fft/bitreverse_test.go b/field/goldilocks/fft/bitreverse_test.go
new file mode 100644
index 0000000000..11bb9f440b
--- /dev/null
+++ b/field/goldilocks/fft/bitreverse_test.go
@@ -0,0 +1,102 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fft
+
+import (
+	"fmt"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/field/goldilocks"
+)
+
+type bitReverseVariant struct {
+	name string
+	buf  []goldilocks.Element
+	fn   func([]goldilocks.Element)
+}
+
+const maxSizeBitReverse = 1 << 23
+
+var bitReverse = []bitReverseVariant{
+	{name: "bitReverseNaive", buf: make([]goldilocks.Element, maxSizeBitReverse), fn: bitReverseNaive},
+	{name: "BitReverse", buf: make([]goldilocks.Element, maxSizeBitReverse), fn: BitReverse},
+	{name: "bitReverseCobraInPlace", buf: make([]goldilocks.Element, maxSizeBitReverse), fn: bitReverseCobraInPlace},
+}
+
+func TestBitReverse(t *testing.T) {
+
+	// generate a random []goldilocks.Element array of size 2**20
+	pol := make([]goldilocks.Element, maxSizeBitReverse)
+	one := goldilocks.One()
+	pol[0].SetRandom()
+	for i := 1; i < maxSizeBitReverse; i++ {
+		pol[i].Add(&pol[i-1], &one)
+	}
+
+	// for each size, check that all the bitReverse functions fn compute the same result.
+	for size := 2; size <= maxSizeBitReverse; size <<= 1 {
+
+		// copy pol into the buffers
+		for _, data := range bitReverse {
+			copy(data.buf, pol[:size])
+		}
+
+		// compute bit reverse shuffling
+		for _, data := range bitReverse {
+			data.fn(data.buf[:size])
+		}
+
+		// all bitReverse.buf should hold the same result
+		for i := 0; i < size; i++ {
+			for j := 1; j < len(bitReverse); j++ {
+				if !bitReverse[0].buf[i].Equal(&bitReverse[j].buf[i]) {
+					t.Fatalf("bitReverse %s and %s do not compute the same result", bitReverse[0].name, bitReverse[j].name)
+				}
+			}
+		}
+
+		// bitReverse back should be identity
+		for _, data := range bitReverse {
+			data.fn(data.buf[:size])
+		}
+
+		for i := 0; i < size; i++ {
+			for j := 1; j < len(bitReverse); j++ {
+				if !bitReverse[0].buf[i].Equal(&bitReverse[j].buf[i]) {
+					t.Fatalf("(fn-1) bitReverse %s and %s do not compute the same result", bitReverse[0].name, bitReverse[j].name)
+				}
+			}
+		}
+	}
+
+}
+
+func BenchmarkBitReverse(b *testing.B) {
+	// generate a random []goldilocks.Element array of size 2**22
+	pol := make([]goldilocks.Element, maxSizeBitReverse)
+	one := goldilocks.One()
+	pol[0].SetRandom()
+	for i := 1; i < maxSizeBitReverse; i++ {
+		pol[i].Add(&pol[i-1], &one)
+	}
+
+	// copy pol into the buffers
+	for _, data := range bitReverse {
+		copy(data.buf, pol[:maxSizeBitReverse])
+	}
+
+	// benchmark for each size, each bitReverse function
+	for size := 1 << 18; size <= maxSizeBitReverse; size <<= 1 {
+		for _, data := range bitReverse {
+			b.Run(fmt.Sprintf("name=%s/size=%d", data.name, size), func(b *testing.B) {
+				b.ResetTimer()
+				for j := 0; j < b.N; j++ {
+					data.fn(data.buf[:size])
+				}
+			})
+		}
+	}
+}
diff --git a/field/goldilocks/fft/doc.go b/field/goldilocks/fft/doc.go
new file mode 100644
index 0000000000..4cce0f9779
--- /dev/null
+++ b/field/goldilocks/fft/doc.go
@@ -0,0 +1,8 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// Package fft provides in-place discrete Fourier transform on powers-of-two subgroups
+// of 𝔽ᵣˣ (the multiplicative group (ℤ/rℤ, x) ).
+package fft
diff --git a/field/goldilocks/fft/domain.go b/field/goldilocks/fft/domain.go
new file mode 100644
index 0000000000..cbde6c90e3
--- /dev/null
+++ b/field/goldilocks/fft/domain.go
@@ -0,0 +1,317 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fft
+
+import (
+	"encoding/binary"
+	"errors"
+	"io"
+	"math/big"
+	"math/bits"
+	"runtime"
+	"sync"
+
+	"github.com/consensys/gnark-crypto/field/goldilocks"
+
+	"github.com/consensys/gnark-crypto/ecc"
+)
+
+// Domain with a power of 2 cardinality
+// compute a field element of order 2x and store it in FinerGenerator
+// all other values can be derived from x, GeneratorSqrt
+type Domain struct {
+	Cardinality            uint64
+	CardinalityInv         goldilocks.Element
+	Generator              goldilocks.Element
+	GeneratorInv           goldilocks.Element
+	FrMultiplicativeGen    goldilocks.Element // generator of Fr*
+	FrMultiplicativeGenInv goldilocks.Element
+
+	// this is set with the WithoutPrecompute option;
+	// if true, the domain does some pre-computation and stores it.
+	// if false, the FFT will compute the twiddles on the fly (this is less CPU efficient, but uses less memory)
+	withPrecompute bool
+
+	// the following slices are not serialized and are (re)computed through domain.preComputeTwiddles()
+
+	// twiddles factor for the FFT using Generator for each stage of the recursive FFT
+	twiddles [][]goldilocks.Element
+
+	// twiddles factor for the FFT using GeneratorInv for each stage of the recursive FFT
+	twiddlesInv [][]goldilocks.Element
+
+	// we precompute these mostly to avoid the memory intensive bit reverse permutation in the groth16.Prover
+
+	// cosetTable u*<1,g,..,g^(n-1)>
+	cosetTable []goldilocks.Element
+
+	// cosetTable[i][j] = domain.Generator(i-th)SqrtInv ^ j
+	cosetTableInv []goldilocks.Element
+}
+
+// GeneratorFullMultiplicativeGroup returns a generator of 𝔽ᵣˣ
+func GeneratorFullMultiplicativeGroup() goldilocks.Element {
+	var res goldilocks.Element
+
+	res.SetUint64(7)
+
+	return res
+}
+
+// NewDomain returns a subgroup with a power of 2 cardinality
+// cardinality >= m
+// shift: when specified, it's the element by which the set of root of unity is shifted.
+func NewDomain(m uint64, opts ...DomainOption) *Domain {
+	opt := domainOptions(opts...)
+	domain := &Domain{}
+	x := ecc.NextPowerOfTwo(m)
+	domain.Cardinality = uint64(x)
+	domain.FrMultiplicativeGen = GeneratorFullMultiplicativeGroup()
+
+	if opt.shift != nil {
+		domain.FrMultiplicativeGen.Set(opt.shift)
+	}
+	domain.FrMultiplicativeGenInv.Inverse(&domain.FrMultiplicativeGen)
+
+	var err error
+	domain.Generator, err = Generator(m)
+	if err != nil {
+		panic(err)
+	}
+	domain.GeneratorInv.Inverse(&domain.Generator)
+	domain.CardinalityInv.SetUint64(uint64(x)).Inverse(&domain.CardinalityInv)
+
+	// twiddle factors
+	domain.withPrecompute = opt.withPrecompute
+	if domain.withPrecompute {
+		domain.preComputeTwiddles()
+	}
+
+	return domain
+}
+
+// Generator returns a generator for Z/2^(log(m))Z
+// or an error if m is too big (required root of unity doesn't exist)
+func Generator(m uint64) (goldilocks.Element, error) {
+	return goldilocks.Generator(m)
+}
+
+// Twiddles returns the twiddles factor for the FFT using Generator for each stage of the recursive FFT
+// or an error if the domain was created with the WithoutPrecompute option
+func (d *Domain) Twiddles() ([][]goldilocks.Element, error) {
+	if d.twiddles == nil {
+		return nil, errors.New("twiddles not precomputed")
+	}
+	return d.twiddles, nil
+}
+
+// TwiddlesInv returns the twiddles factor for the FFT using GeneratorInv for each stage of the recursive FFT
+// or an error if the domain was created with the WithoutPrecompute option
+func (d *Domain) TwiddlesInv() ([][]goldilocks.Element, error) {
+	if d.twiddlesInv == nil {
+		return nil, errors.New("twiddles not precomputed")
+	}
+	return d.twiddlesInv, nil
+}
+
+// CosetTable returns the cosetTable u*<1,g,..,g^(n-1)>
+// or an error if the domain was created with the WithoutPrecompute option
+func (d *Domain) CosetTable() ([]goldilocks.Element, error) {
+	if d.cosetTable == nil {
+		return nil, errors.New("cosetTable not precomputed")
+	}
+	return d.cosetTable, nil
+}
+
+// CosetTableInv returns the cosetTableInv u*<1,g,..,g^(n-1)>
+// or an error if the domain was created with the WithoutPrecompute option
+func (d *Domain) CosetTableInv() ([]goldilocks.Element, error) {
+	if d.cosetTableInv == nil {
+		return nil, errors.New("cosetTableInv not precomputed")
+	}
+	return d.cosetTableInv, nil
+}
+
+func (d *Domain) preComputeTwiddles() {
+
+	// nb fft stages
+	nbStages := uint64(bits.TrailingZeros64(d.Cardinality))
+
+	d.twiddles = make([][]goldilocks.Element, nbStages)
+	d.twiddlesInv = make([][]goldilocks.Element, nbStages)
+	d.cosetTable = make([]goldilocks.Element, d.Cardinality)
+	d.cosetTableInv = make([]goldilocks.Element, d.Cardinality)
+
+	var wg sync.WaitGroup
+
+	expTable := func(sqrt goldilocks.Element, t []goldilocks.Element) {
+		BuildExpTable(sqrt, t)
+		wg.Done()
+	}
+
+	wg.Add(4)
+	go func() {
+		buildTwiddles(d.twiddles, d.Generator, nbStages)
+		wg.Done()
+	}()
+	go func() {
+		buildTwiddles(d.twiddlesInv, d.GeneratorInv, nbStages)
+		wg.Done()
+	}()
+	go expTable(d.FrMultiplicativeGen, d.cosetTable)
+	go expTable(d.FrMultiplicativeGenInv, d.cosetTableInv)
+
+	wg.Wait()
+
+}
+
+func buildTwiddles(t [][]goldilocks.Element, omega goldilocks.Element, nbStages uint64) {
+	if nbStages == 0 {
+		return
+	}
+	if len(t) != int(nbStages) {
+		panic("invalid twiddle table")
+	}
+	// we just compute the first stage
+	t[0] = make([]goldilocks.Element, 1+(1<<(nbStages-1)))
+	BuildExpTable(omega, t[0])
+
+	// for the next stages, we just iterate on the first stage with larger stride
+	for i := uint64(1); i < nbStages; i++ {
+		t[i] = make([]goldilocks.Element, 1+(1<<(nbStages-i-1)))
+		k := 0
+		for j := 0; j < len(t[i]); j++ {
+			t[i][j] = t[0][k]
+			k += 1 << i
+		}
+	}
+
+}
+
+// BuildExpTable precomputes the first n powers of w in parallel
+// table[0] = w^0
+// table[1] = w^1
+// ...
+func BuildExpTable(w goldilocks.Element, table []goldilocks.Element) {
+	table[0].SetOne()
+	n := len(table)
+
+	// see if it makes sense to parallelize exp tables pre-computation
+	interval := 0
+	if runtime.NumCPU() >= 4 {
+		interval = (n - 1) / (runtime.NumCPU() / 4)
+	}
+
+	// this ratio roughly correspond to the number of multiplication one can do in place of a Exp operation
+	// TODO @gbotrel revisit this; Exps in this context will be by a "small power of 2" so faster than this ref ratio.
+	const ratioExpMul = 6000 / 17
+
+	if interval < ratioExpMul {
+		precomputeExpTableChunk(w, 1, table[1:])
+		return
+	}
+
+	// we parallelize
+	var wg sync.WaitGroup
+	for i := 1; i < n; i += interval {
+		start := i
+		end := i + interval
+		if end > n {
+			end = n
+		}
+		wg.Add(1)
+		go func() {
+			precomputeExpTableChunk(w, uint64(start), table[start:end])
+			wg.Done()
+		}()
+	}
+	wg.Wait()
+}
+
+func precomputeExpTableChunk(w goldilocks.Element, power uint64, table []goldilocks.Element) {
+
+	// this condition ensures that creating a domain of size 1 with cosets don't fail
+	if len(table) > 0 {
+		table[0].Exp(w, new(big.Int).SetUint64(power))
+		for i := 1; i < len(table); i++ {
+			table[i].Mul(&table[i-1], &w)
+		}
+	}
+}
+
+// WriteTo writes a binary representation of the domain (without the precomputed twiddle factors)
+// to the provided writer
+func (d *Domain) WriteTo(w io.Writer) (int64, error) {
+	// note to stay retro compatible with previous version using ecc/encoder, we encode as:
+	// d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute
+
+	var written int64
+	var err error
+
+	err = binary.Write(w, binary.BigEndian, d.Cardinality)
+	if err != nil {
+		return written, err
+	}
+	written += 8
+
+	toEncode := []*goldilocks.Element{&d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
+	for _, v := range toEncode {
+		buf := v.Bytes()
+		_, err = w.Write(buf[:])
+		if err != nil {
+			return written, err
+		}
+		written += goldilocks.Bytes
+	}
+
+	err = binary.Write(w, binary.BigEndian, d.withPrecompute)
+	if err != nil {
+		return written, err
+	}
+	written += 1
+
+	return written, nil
+}
+
+// ReadFrom attempts to decode a domain from Reader
+func (d *Domain) ReadFrom(r io.Reader) (int64, error) {
+
+	var read int64
+	var err error
+
+	err = binary.Read(r, binary.BigEndian, &d.Cardinality)
+	if err != nil {
+		return read, err
+	}
+	read += 8
+
+	toDecode := []*goldilocks.Element{&d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
+
+	for _, v := range toDecode {
+		var buf [goldilocks.Bytes]byte
+		_, err = r.Read(buf[:])
+		if err != nil {
+			return read, err
+		}
+		read += goldilocks.Bytes
+		*v, err = goldilocks.BigEndian.Element(&buf)
+		if err != nil {
+			return read, err
+		}
+	}
+
+	err = binary.Read(r, binary.BigEndian, &d.withPrecompute)
+	if err != nil {
+		return read, err
+	}
+	read += 1
+
+	if d.withPrecompute {
+		d.preComputeTwiddles()
+	}
+
+	return read, nil
+}
diff --git a/field/goldilocks/fft/domain_test.go b/field/goldilocks/fft/domain_test.go
new file mode 100644
index 0000000000..e445d3cc12
--- /dev/null
+++ b/field/goldilocks/fft/domain_test.go
@@ -0,0 +1,36 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fft
+
+import (
+	"bytes"
+	"reflect"
+	"testing"
+)
+
+func TestDomainSerialization(t *testing.T) {
+
+	domain := NewDomain(1 << 6)
+	var reconstructed Domain
+
+	var buf bytes.Buffer
+	written, err := domain.WriteTo(&buf)
+	if err != nil {
+		t.Fatal(err)
+	}
+	var read int64
+	read, err = reconstructed.ReadFrom(&buf)
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	if written != read {
+		t.Fatal("didn't read as many bytes as we wrote")
+	}
+	if !reflect.DeepEqual(domain, &reconstructed) {
+		t.Fatal("Domain.SetBytes(Bytes()) failed")
+	}
+}
diff --git a/field/goldilocks/fft/fft.go b/field/goldilocks/fft/fft.go
new file mode 100644
index 0000000000..ab9ff0135c
--- /dev/null
+++ b/field/goldilocks/fft/fft.go
@@ -0,0 +1,410 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fft
+
+import (
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/internal/parallel"
+	"math/big"
+	"math/bits"
+
+	"github.com/consensys/gnark-crypto/field/goldilocks"
+)
+
+// Decimation is used in the FFT call to select decimation in time or in frequency
+type Decimation uint8
+
+const (
+	DIT Decimation = iota
+	DIF
+)
+
+// parallelize threshold for a single butterfly op, if the fft stage is not parallelized already
+const butterflyThreshold = 16
+
+// FFT computes (recursively) the discrete Fourier transform of a and stores the result in a
+// if decimation == DIT (decimation in time), the input must be in bit-reversed order
+// if decimation == DIF (decimation in frequency), the output will be in bit-reversed order
+func (domain *Domain) FFT(a []goldilocks.Element, decimation Decimation, opts ...Option) {
+
+	opt := fftOptions(opts...)
+
+	// find the stage where we should stop spawning go routines in our recursive calls
+	// (ie when we have as many go routines running as we have available CPUs)
+	maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks)))
+	if opt.nbTasks == 1 {
+		maxSplits = -1
+	}
+
+	// if coset != 0, scale by coset table
+	if opt.coset {
+		if decimation == DIT {
+			// scale by coset table (in bit reversed order)
+			cosetTable := domain.cosetTable
+			if !domain.withPrecompute {
+				// we need to build the full table or do a bit reverse dance.
+				cosetTable = make([]goldilocks.Element, len(a))
+				BuildExpTable(domain.FrMultiplicativeGen, cosetTable)
+			}
+			parallel.Execute(len(a), func(start, end int) {
+				n := uint64(len(a))
+				nn := uint64(64 - bits.TrailingZeros64(n))
+				for i := start; i < end; i++ {
+					irev := int(bits.Reverse64(uint64(i)) >> nn)
+					a[i].Mul(&a[i], &cosetTable[irev])
+				}
+			}, opt.nbTasks)
+		} else {
+			if domain.withPrecompute {
+				parallel.Execute(len(a), func(start, end int) {
+					for i := start; i < end; i++ {
+						a[i].Mul(&a[i], &domain.cosetTable[i])
+					}
+				}, opt.nbTasks)
+			} else {
+				c := domain.FrMultiplicativeGen
+				parallel.Execute(len(a), func(start, end int) {
+					var at goldilocks.Element
+					at.Exp(c, big.NewInt(int64(start)))
+					for i := start; i < end; i++ {
+						a[i].Mul(&a[i], &at)
+						at.Mul(&at, &c)
+					}
+				}, opt.nbTasks)
+			}
+
+		}
+	}
+
+	twiddles := domain.twiddles
+	twiddlesStartStage := 0
+	if !domain.withPrecompute {
+		twiddlesStartStage = 3
+		nbStages := int(bits.TrailingZeros64(domain.Cardinality))
+		if nbStages-twiddlesStartStage > 0 {
+			twiddles = make([][]goldilocks.Element, nbStages-twiddlesStartStage)
+			w := domain.Generator
+			w.Exp(w, big.NewInt(int64(1<<twiddlesStartStage)))
+			buildTwiddles(twiddles, w, uint64(nbStages-twiddlesStartStage))
+		} // else, we don't need twiddles
+	}
+
+	switch decimation {
+	case DIF:
+		difFFT(a, domain.Generator, twiddles, twiddlesStartStage, 0, maxSplits, nil, opt.nbTasks)
+	case DIT:
+		ditFFT(a, domain.Generator, twiddles, twiddlesStartStage, 0, maxSplits, nil, opt.nbTasks)
+	default:
+		panic("not implemented")
+	}
+}
+
+// FFTInverse computes (recursively) the inverse discrete Fourier transform of a and stores the result in a
+// if decimation == DIT (decimation in time), the input must be in bit-reversed order
+// if decimation == DIF (decimation in frequency), the output will be in bit-reversed order
+// coset sets the shift of the fft (0 = no shift, standard fft)
+// len(a) must be a power of 2, and w must be a len(a)th root of unity in field F.
+func (domain *Domain) FFTInverse(a []goldilocks.Element, decimation Decimation, opts ...Option) {
+	opt := fftOptions(opts...)
+
+	// find the stage where we should stop spawning go routines in our recursive calls
+	// (ie when we have as many go routines running as we have available CPUs)
+	maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks)))
+	if opt.nbTasks == 1 {
+		maxSplits = -1
+	}
+
+	twiddlesInv := domain.twiddlesInv
+	twiddlesStartStage := 0
+	if !domain.withPrecompute {
+		twiddlesStartStage = 3
+		nbStages := int(bits.TrailingZeros64(domain.Cardinality))
+		if nbStages-twiddlesStartStage > 0 {
+			twiddlesInv = make([][]goldilocks.Element, nbStages-twiddlesStartStage)
+			w := domain.GeneratorInv
+			w.Exp(w, big.NewInt(int64(1<<twiddlesStartStage)))
+			buildTwiddles(twiddlesInv, w, uint64(nbStages-twiddlesStartStage))
+		} // else, we don't need twiddles
+	}
+
+	switch decimation {
+	case DIF:
+		difFFT(a, domain.GeneratorInv, twiddlesInv, twiddlesStartStage, 0, maxSplits, nil, opt.nbTasks)
+	case DIT:
+		ditFFT(a, domain.GeneratorInv, twiddlesInv, twiddlesStartStage, 0, maxSplits, nil, opt.nbTasks)
+	default:
+		panic("not implemented")
+	}
+
+	// scale by CardinalityInv
+	if !opt.coset {
+		parallel.Execute(len(a), func(start, end int) {
+			for i := start; i < end; i++ {
+				a[i].Mul(&a[i], &domain.CardinalityInv)
+			}
+		}, opt.nbTasks)
+		return
+	}
+
+	if decimation == DIT {
+		if domain.withPrecompute {
+			parallel.Execute(len(a), func(start, end int) {
+				for i := start; i < end; i++ {
+					a[i].Mul(&a[i], &domain.cosetTableInv[i]).
+						Mul(&a[i], &domain.CardinalityInv)
+				}
+			}, opt.nbTasks)
+		} else {
+			c := domain.FrMultiplicativeGenInv
+			parallel.Execute(len(a), func(start, end int) {
+				var at goldilocks.Element
+				at.Exp(c, big.NewInt(int64(start)))
+				at.Mul(&at, &domain.CardinalityInv)
+				for i := start; i < end; i++ {
+					a[i].Mul(&a[i], &at)
+					at.Mul(&at, &c)
+				}
+			}, opt.nbTasks)
+		}
+		return
+	}
+
+	// decimation == DIF, need to access coset table in bit reversed order.
+	cosetTableInv := domain.cosetTableInv
+	if !domain.withPrecompute {
+		// we need to build the full table or do a bit reverse dance.
+		cosetTableInv = make([]goldilocks.Element, len(a))
+		BuildExpTable(domain.FrMultiplicativeGenInv, cosetTableInv)
+	}
+	parallel.Execute(len(a), func(start, end int) {
+		n := uint64(len(a))
+		nn := uint64(64 - bits.TrailingZeros64(n))
+		for i := start; i < end; i++ {
+			irev := int(bits.Reverse64(uint64(i)) >> nn)
+			a[i].Mul(&a[i], &cosetTableInv[irev]).
+				Mul(&a[i], &domain.CardinalityInv)
+		}
+	}, opt.nbTasks)
+
+}
+
+func difFFT(a []goldilocks.Element, w goldilocks.Element, twiddles [][]goldilocks.Element, twiddlesStartStage, stage, maxSplits int, chDone chan struct{}, nbTasks int) {
+	if chDone != nil {
+		defer close(chDone)
+	}
+
+	n := len(a)
+	if n == 1 {
+		return
+	} else if n == 256 && stage >= twiddlesStartStage {
+		kerDIFNP_256(a, twiddles, stage-twiddlesStartStage)
+		return
+	}
+	m := n >> 1
+
+	parallelButterfly := (m > butterflyThreshold) && (stage < maxSplits)
+
+	if stage < twiddlesStartStage {
+		if parallelButterfly {
+			w := w
+			parallel.Execute(m, func(start, end int) {
+				if start == 0 {
+					goldilocks.Butterfly(&a[0], &a[m])
+					start++
+				}
+				var at goldilocks.Element
+				at.Exp(w, big.NewInt(int64(start)))
+				innerDIFWithoutTwiddles(a, at, w, start, end, m)
+			}, nbTasks/(1<<(stage))) // 1 << stage == estimated used CPUs
+		} else {
+			innerDIFWithoutTwiddles(a, w, w, 0, m, m)
+		}
+		// compute next twiddle
+		w.Square(&w)
+	} else {
+		if parallelButterfly {
+			parallel.Execute(m, func(start, end int) {
+				innerDIFWithTwiddles(a, twiddles[stage-twiddlesStartStage], start, end, m)
+			}, nbTasks/(1<<(stage)))
+		} else {
+			innerDIFWithTwiddles(a, twiddles[stage-twiddlesStartStage], 0, m, m)
+		}
+	}
+
+	if m == 1 {
+		return
+	}
+
+	nextStage := stage + 1
+	if stage < maxSplits {
+		chDone := make(chan struct{}, 1)
+		go difFFT(a[m:n], w, twiddles, twiddlesStartStage, nextStage, maxSplits, chDone, nbTasks)
+		difFFT(a[0:m], w, twiddles, twiddlesStartStage, nextStage, maxSplits, nil, nbTasks)
+		<-chDone
+	} else {
+		difFFT(a[0:m], w, twiddles, twiddlesStartStage, nextStage, maxSplits, nil, nbTasks)
+		difFFT(a[m:n], w, twiddles, twiddlesStartStage, nextStage, maxSplits, nil, nbTasks)
+	}
+
+}
+
+func innerDIFWithTwiddles(a []goldilocks.Element, twiddles []goldilocks.Element, start, end, m int) {
+	if start == 0 {
+		goldilocks.Butterfly(&a[0], &a[m])
+		start++
+	}
+	for i := start; i < end; i++ {
+		goldilocks.Butterfly(&a[i], &a[i+m])
+		a[i+m].Mul(&a[i+m], &twiddles[i])
+	}
+}
+
+func innerDIFWithoutTwiddles(a []goldilocks.Element, at, w goldilocks.Element, start, end, m int) {
+	if start == 0 {
+		goldilocks.Butterfly(&a[0], &a[m])
+		start++
+	}
+	for i := start; i < end; i++ {
+		goldilocks.Butterfly(&a[i], &a[i+m])
+		a[i+m].Mul(&a[i+m], &at)
+		at.Mul(&at, &w)
+	}
+}
+
+func ditFFT(a []goldilocks.Element, w goldilocks.Element, twiddles [][]goldilocks.Element, twiddlesStartStage, stage, maxSplits int, chDone chan struct{}, nbTasks int) {
+	if chDone != nil {
+		defer close(chDone)
+	}
+	n := len(a)
+	if n == 1 {
+		return
+	} else if n == 256 && stage >= twiddlesStartStage {
+		kerDITNP_256(a, twiddles, stage-twiddlesStartStage)
+		return
+	}
+	m := n >> 1
+
+	nextStage := stage + 1
+	nextW := w
+	nextW.Square(&nextW)
+
+	if stage < maxSplits {
+		// that's the only time we fire go routines
+		chDone := make(chan struct{}, 1)
+		go ditFFT(a[m:], nextW, twiddles, twiddlesStartStage, nextStage, maxSplits, chDone, nbTasks)
+		ditFFT(a[0:m], nextW, twiddles, twiddlesStartStage, nextStage, maxSplits, nil, nbTasks)
+		<-chDone
+	} else {
+		ditFFT(a[0:m], nextW, twiddles, twiddlesStartStage, nextStage, maxSplits, nil, nbTasks)
+		ditFFT(a[m:n], nextW, twiddles, twiddlesStartStage, nextStage, maxSplits, nil, nbTasks)
+	}
+
+	parallelButterfly := (m > butterflyThreshold) && (stage < maxSplits)
+
+	if stage < twiddlesStartStage {
+		// we need to compute the twiddles for this stage on the fly.
+		if parallelButterfly {
+			w := w
+			parallel.Execute(m, func(start, end int) {
+				if start == 0 {
+					goldilocks.Butterfly(&a[0], &a[m])
+					start++
+				}
+				var at goldilocks.Element
+				at.Exp(w, big.NewInt(int64(start)))
+				innerDITWithoutTwiddles(a, at, w, start, end, m)
+			}, nbTasks/(1<<(stage))) // 1 << stage == estimated used CPUs
+
+		} else {
+			innerDITWithoutTwiddles(a, w, w, 0, m, m)
+		}
+		return
+	}
+	if parallelButterfly {
+		parallel.Execute(m, func(start, end int) {
+			innerDITWithTwiddles(a, twiddles[stage-twiddlesStartStage], start, end, m)
+		}, nbTasks/(1<<(stage)))
+	} else {
+		innerDITWithTwiddles(a, twiddles[stage-twiddlesStartStage], 0, m, m)
+	}
+}
+
+func innerDITWithTwiddles(a []goldilocks.Element, twiddles []goldilocks.Element, start, end, m int) {
+	if start == 0 {
+		goldilocks.Butterfly(&a[0], &a[m])
+		start++
+	}
+	for i := start; i < end; i++ {
+		a[i+m].Mul(&a[i+m], &twiddles[i])
+		goldilocks.Butterfly(&a[i], &a[i+m])
+	}
+}
+
+func innerDITWithoutTwiddles(a []goldilocks.Element, at, w goldilocks.Element, start, end, m int) {
+	if start == 0 {
+		goldilocks.Butterfly(&a[0], &a[m])
+		start++
+	}
+	for i := start; i < end; i++ {
+		a[i+m].Mul(&a[i+m], &at)
+		goldilocks.Butterfly(&a[i], &a[i+m])
+		at.Mul(&at, &w)
+	}
+}
+
+func kerDIFNP_256(a []goldilocks.Element, twiddles [][]goldilocks.Element, stage int) {
+	// code unrolled & generated by internal/generator/fft/template/fft.go.tmpl
+
+	innerDIFWithTwiddles(a[:256], twiddles[stage+0], 0, 128, 128)
+	for offset := 0; offset < 256; offset += 128 {
+		innerDIFWithTwiddles(a[offset:offset+128], twiddles[stage+1], 0, 64, 64)
+	}
+	for offset := 0; offset < 256; offset += 64 {
+		innerDIFWithTwiddles(a[offset:offset+64], twiddles[stage+2], 0, 32, 32)
+	}
+	for offset := 0; offset < 256; offset += 32 {
+		innerDIFWithTwiddles(a[offset:offset+32], twiddles[stage+3], 0, 16, 16)
+	}
+	for offset := 0; offset < 256; offset += 16 {
+		innerDIFWithTwiddles(a[offset:offset+16], twiddles[stage+4], 0, 8, 8)
+	}
+	for offset := 0; offset < 256; offset += 8 {
+		innerDIFWithTwiddles(a[offset:offset+8], twiddles[stage+5], 0, 4, 4)
+	}
+	for offset := 0; offset < 256; offset += 4 {
+		innerDIFWithTwiddles(a[offset:offset+4], twiddles[stage+6], 0, 2, 2)
+	}
+	for offset := 0; offset < 256; offset += 2 {
+		goldilocks.Butterfly(&a[offset], &a[offset+1])
+	}
+}
+
+func kerDITNP_256(a []goldilocks.Element, twiddles [][]goldilocks.Element, stage int) {
+	// code unrolled & generated by internal/generator/fft/template/fft.go.tmpl
+
+	for offset := 0; offset < 256; offset += 2 {
+		goldilocks.Butterfly(&a[offset], &a[offset+1])
+	}
+	for offset := 0; offset < 256; offset += 4 {
+		innerDITWithTwiddles(a[offset:offset+4], twiddles[stage+6], 0, 2, 2)
+	}
+	for offset := 0; offset < 256; offset += 8 {
+		innerDITWithTwiddles(a[offset:offset+8], twiddles[stage+5], 0, 4, 4)
+	}
+	for offset := 0; offset < 256; offset += 16 {
+		innerDITWithTwiddles(a[offset:offset+16], twiddles[stage+4], 0, 8, 8)
+	}
+	for offset := 0; offset < 256; offset += 32 {
+		innerDITWithTwiddles(a[offset:offset+32], twiddles[stage+3], 0, 16, 16)
+	}
+	for offset := 0; offset < 256; offset += 64 {
+		innerDITWithTwiddles(a[offset:offset+64], twiddles[stage+2], 0, 32, 32)
+	}
+	for offset := 0; offset < 256; offset += 128 {
+		innerDITWithTwiddles(a[offset:offset+128], twiddles[stage+1], 0, 64, 64)
+	}
+	innerDITWithTwiddles(a[:256], twiddles[stage+0], 0, 128, 128)
+}
diff --git a/field/goldilocks/fft/fft_test.go b/field/goldilocks/fft/fft_test.go
new file mode 100644
index 0000000000..f5d88e02a4
--- /dev/null
+++ b/field/goldilocks/fft/fft_test.go
@@ -0,0 +1,318 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fft
+
+import (
+	"math/big"
+	"strconv"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/field/goldilocks"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/gen"
+	"github.com/leanovate/gopter/prop"
+
+	"fmt"
+)
+
+func TestFFT(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	parameters.MinSuccessfulTests = 5
+	properties := gopter.NewProperties(parameters)
+
+	for maxSize := 2; maxSize <= 1<<10; maxSize <<= 1 {
+
+		domainWithPrecompute := NewDomain(uint64(maxSize))
+		domainWithoutPrecompute := NewDomain(uint64(maxSize), WithoutPrecompute())
+
+		for domainName, domain := range map[string]*Domain{
+			"with precompute":    domainWithPrecompute,
+			"without precompute": domainWithoutPrecompute,
+		} {
+			domainName := domainName
+			domain := domain
+			t.Logf("domain: %s", domainName)
+			properties.Property("DIF FFT should be consistent with dual basis", prop.ForAll(
+
+				// checks that a random evaluation of a dual function eval(gen**ithpower) is consistent with the FFT result
+				func(ithpower int) bool {
+
+					pol := make([]goldilocks.Element, maxSize)
+					backupPol := make([]goldilocks.Element, maxSize)
+
+					for i := 0; i < maxSize; i++ {
+						pol[i].SetRandom()
+					}
+					copy(backupPol, pol)
+
+					domain.FFT(pol, DIF)
+					BitReverse(pol)
+
+					sample := domain.Generator
+					sample.Exp(sample, big.NewInt(int64(ithpower)))
+
+					eval := evaluatePolynomial(backupPol, sample)
+
+					return eval.Equal(&pol[ithpower])
+
+				},
+				gen.IntRange(0, maxSize-1),
+			))
+
+			properties.Property("DIF FFT on cosets should be consistent with dual basis", prop.ForAll(
+
+				// checks that a random evaluation of a dual function eval(gen**ithpower) is consistent with the FFT result
+				func(ithpower int) bool {
+
+					pol := make([]goldilocks.Element, maxSize)
+					backupPol := make([]goldilocks.Element, maxSize)
+
+					for i := 0; i < maxSize; i++ {
+						pol[i].SetRandom()
+					}
+					copy(backupPol, pol)
+
+					domain.FFT(pol, DIF, OnCoset())
+					BitReverse(pol)
+
+					sample := domain.Generator
+					sample.Exp(sample, big.NewInt(int64(ithpower))).
+						Mul(&sample, &domain.FrMultiplicativeGen)
+
+					eval := evaluatePolynomial(backupPol, sample)
+
+					return eval.Equal(&pol[ithpower])
+
+				},
+				gen.IntRange(0, maxSize-1),
+			))
+
+			properties.Property("DIT FFT should be consistent with dual basis", prop.ForAll(
+
+				// checks that a random evaluation of a dual function eval(gen**ithpower) is consistent with the FFT result
+				func(ithpower int) bool {
+
+					pol := make([]goldilocks.Element, maxSize)
+					backupPol := make([]goldilocks.Element, maxSize)
+
+					for i := 0; i < maxSize; i++ {
+						pol[i].SetRandom()
+					}
+					copy(backupPol, pol)
+
+					BitReverse(pol)
+					domain.FFT(pol, DIT)
+
+					sample := domain.Generator
+					sample.Exp(sample, big.NewInt(int64(ithpower)))
+
+					eval := evaluatePolynomial(backupPol, sample)
+
+					return eval.Equal(&pol[ithpower])
+
+				},
+				gen.IntRange(0, maxSize-1),
+			))
+
+			properties.Property("bitReverse(DIF FFT(DIT FFT (bitReverse))))==id", prop.ForAll(
+
+				func() bool {
+
+					pol := make([]goldilocks.Element, maxSize)
+					backupPol := make([]goldilocks.Element, maxSize)
+
+					for i := 0; i < maxSize; i++ {
+						pol[i].SetRandom()
+					}
+					copy(backupPol, pol)
+
+					BitReverse(pol)
+					domain.FFT(pol, DIT)
+					domain.FFTInverse(pol, DIF)
+					BitReverse(pol)
+
+					check := true
+					for i := 0; i < len(pol); i++ {
+						check = check && pol[i].Equal(&backupPol[i])
+					}
+					return check
+				},
+			))
+
+			for nbCosets := 2; nbCosets < 5; nbCosets++ {
+				properties.Property(fmt.Sprintf("bitReverse(DIF FFT(DIT FFT (bitReverse))))==id on %d cosets", nbCosets), prop.ForAll(
+
+					func() bool {
+
+						pol := make([]goldilocks.Element, maxSize)
+						backupPol := make([]goldilocks.Element, maxSize)
+
+						for i := 0; i < maxSize; i++ {
+							pol[i].SetRandom()
+						}
+						copy(backupPol, pol)
+
+						check := true
+
+						for i := 1; i <= nbCosets; i++ {
+
+							BitReverse(pol)
+							domain.FFT(pol, DIT, OnCoset())
+							domain.FFTInverse(pol, DIF, OnCoset())
+							BitReverse(pol)
+
+							for i := 0; i < len(pol); i++ {
+								check = check && pol[i].Equal(&backupPol[i])
+							}
+						}
+
+						return check
+					},
+				))
+			}
+
+			properties.Property("DIT FFT(DIF FFT)==id", prop.ForAll(
+
+				func() bool {
+
+					pol := make([]goldilocks.Element, maxSize)
+					backupPol := make([]goldilocks.Element, maxSize)
+
+					for i := 0; i < maxSize; i++ {
+						pol[i].SetRandom()
+					}
+					copy(backupPol, pol)
+
+					domain.FFTInverse(pol, DIF)
+					domain.FFT(pol, DIT)
+
+					check := true
+					for i := 0; i < len(pol); i++ {
+						check = check && (pol[i] == backupPol[i])
+					}
+					return check
+				},
+			))
+
+			properties.Property("DIT FFT(DIF FFT)==id on cosets", prop.ForAll(
+
+				func() bool {
+
+					pol := make([]goldilocks.Element, maxSize)
+					backupPol := make([]goldilocks.Element, maxSize)
+
+					for i := 0; i < maxSize; i++ {
+						pol[i].SetRandom()
+					}
+					copy(backupPol, pol)
+
+					domain.FFTInverse(pol, DIF, OnCoset())
+					domain.FFT(pol, DIT, OnCoset())
+
+					for i := 0; i < len(pol); i++ {
+						if !(pol[i].Equal(&backupPol[i])) {
+							return false
+						}
+					}
+
+					// compute with nbTasks == 1
+					domain.FFTInverse(pol, DIF, OnCoset(), WithNbTasks(1))
+					domain.FFT(pol, DIT, OnCoset(), WithNbTasks(1))
+
+					for i := 0; i < len(pol); i++ {
+						if !(pol[i].Equal(&backupPol[i])) {
+							return false
+						}
+					}
+
+					return true
+				},
+			))
+		}
+		properties.TestingRun(t, gopter.ConsoleReporter(false))
+	}
+
+}
+
+// --------------------------------------------------------------------
+// benches
+
+func BenchmarkFFT(b *testing.B) {
+
+	const maxSize = 1 << 20
+
+	pol := make([]goldilocks.Element, maxSize)
+	pol[0].SetRandom()
+	for i := 1; i < maxSize; i++ {
+		pol[i] = pol[i-1]
+	}
+
+	for i := 8; i < 20; i++ {
+		sizeDomain := 1 << i
+		b.Run("fft 2**"+strconv.Itoa(i)+"bits", func(b *testing.B) {
+			domain := NewDomain(uint64(sizeDomain))
+			b.ResetTimer()
+			for j := 0; j < b.N; j++ {
+				domain.FFT(pol[:sizeDomain], DIT)
+			}
+		})
+		b.Run("fft 2**"+strconv.Itoa(i)+"bits (coset)", func(b *testing.B) {
+			domain := NewDomain(uint64(sizeDomain))
+			b.ResetTimer()
+			for j := 0; j < b.N; j++ {
+				domain.FFT(pol[:sizeDomain], DIT, OnCoset())
+			}
+		})
+	}
+
+}
+
+func BenchmarkFFTDITCosetReference(b *testing.B) {
+	const maxSize = 1 << 20
+
+	pol := make([]goldilocks.Element, maxSize)
+	pol[0].SetRandom()
+	for i := 1; i < maxSize; i++ {
+		pol[i] = pol[i-1]
+	}
+
+	domain := NewDomain(maxSize)
+
+	b.ResetTimer()
+	for j := 0; j < b.N; j++ {
+		domain.FFT(pol, DIT, OnCoset())
+	}
+}
+
+func BenchmarkFFTDIFReference(b *testing.B) {
+	const maxSize = 1 << 20
+
+	pol := make([]goldilocks.Element, maxSize)
+	pol[0].SetRandom()
+	for i := 1; i < maxSize; i++ {
+		pol[i] = pol[i-1]
+	}
+
+	domain := NewDomain(maxSize)
+
+	b.ResetTimer()
+	for j := 0; j < b.N; j++ {
+		domain.FFT(pol, DIF)
+	}
+}
+
+func evaluatePolynomial(pol []goldilocks.Element, val goldilocks.Element) goldilocks.Element {
+	var acc, res, tmp goldilocks.Element
+	res.Set(&pol[0])
+	acc.Set(&val)
+	for i := 1; i < len(pol); i++ {
+		tmp.Mul(&acc, &pol[i])
+		res.Add(&res, &tmp)
+		acc.Mul(&acc, &val)
+	}
+	return res
+}
diff --git a/field/goldilocks/fft/options.go b/field/goldilocks/fft/options.go
new file mode 100644
index 0000000000..2ebef76ee5
--- /dev/null
+++ b/field/goldilocks/fft/options.go
@@ -0,0 +1,92 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fft
+
+import (
+	"runtime"
+
+	"github.com/consensys/gnark-crypto/field/goldilocks"
+)
+
+// Option defines option for altering the behavior of FFT methods.
+// See the descriptions of functions returning instances of this type for
+// particular options.
+type Option func(*fftConfig)
+
+type fftConfig struct {
+	coset   bool
+	nbTasks int
+}
+
+// OnCoset if provided, FFT(a) returns the evaluation of a on a coset.
+func OnCoset() Option {
+	return func(opt *fftConfig) {
+		opt.coset = true
+	}
+}
+
+// WithNbTasks sets the max number of task (go routine) to spawn. Must be between 1 and 512.
+func WithNbTasks(nbTasks int) Option {
+	if nbTasks < 1 {
+		nbTasks = 1
+	} else if nbTasks > 512 {
+		nbTasks = 512
+	}
+	return func(opt *fftConfig) {
+		opt.nbTasks = nbTasks
+	}
+}
+
+// default options
+func fftOptions(opts ...Option) fftConfig {
+	// apply options
+	opt := fftConfig{
+		coset:   false,
+		nbTasks: runtime.NumCPU(),
+	}
+	for _, option := range opts {
+		option(&opt)
+	}
+	return opt
+}
+
+// DomainOption defines option for altering the definition of the FFT domain
+// See the descriptions of functions returning instances of this type for
+// particular options.
+type DomainOption func(*domainConfig)
+
+type domainConfig struct {
+	shift          *goldilocks.Element
+	withPrecompute bool
+}
+
+// WithShift sets the FrMultiplicativeGen of the domain.
+// Default is generator of the largest 2-adic subgroup.
+func WithShift(shift goldilocks.Element) DomainOption {
+	return func(opt *domainConfig) {
+		opt.shift = new(goldilocks.Element).Set(&shift)
+	}
+}
+
+// WithoutPrecompute disables precomputation of twiddles in the domain.
+// When this option is set, FFTs will be slower, but will use less memory.
+func WithoutPrecompute() DomainOption {
+	return func(opt *domainConfig) {
+		opt.withPrecompute = false
+	}
+}
+
+// default options
+func domainOptions(opts ...DomainOption) domainConfig {
+	// apply options
+	opt := domainConfig{
+		withPrecompute: true,
+	}
+	for _, option := range opts {
+		option(&opt)
+	}
+	return opt
+}
diff --git a/field/goldilocks/generator.go b/field/goldilocks/generator.go
new file mode 100644
index 0000000000..799abb8d58
--- /dev/null
+++ b/field/goldilocks/generator.go
@@ -0,0 +1,36 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package goldilocks
+
+import (
+	"fmt"
+	"math/big"
+	"math/bits"
+
+	"github.com/consensys/gnark-crypto/ecc"
+)
+
+// Generator returns a generator for Z/2^(log(m))Z
+// or an error if m is too big (required root of unity doesn't exist)
+func Generator(m uint64) (Element, error) {
+	x := ecc.NextPowerOfTwo(m)
+
+	var rootOfUnity Element
+
+	rootOfUnity.SetString("1753635133440165772")
+	const maxOrderRoot uint64 = 32
+
+	// find generator for Z/2^(log(m))Z
+	logx := uint64(bits.TrailingZeros64(x))
+	if logx > maxOrderRoot {
+		return Element{}, fmt.Errorf("m (%d) is too big: the required root of unity does not exist", m)
+	}
+
+	expo := uint64(1 << (maxOrderRoot - logx))
+	var generator Element
+	generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x
+	return generator, nil
+}
diff --git a/field/internal/main.go b/field/internal/main.go
index b495d394e5..ce7631131a 100644
--- a/field/internal/main.go
+++ b/field/internal/main.go
@@ -28,7 +28,10 @@ func main() {
 		if err != nil {
 			panic(err)
 		}
-		if err := generator.GenerateFF(fc, filepath.Join("..", f.name), "", ""); err != nil {
+		if err := generator.GenerateFF(fc, filepath.Join("..", f.name),
+			generator.WithASM(&config.Assembly{BuildDir: "../asm", IncludeDir: "../asm"}),
+			generator.WithFFT(&config.FFT{}), // TODO @gbotrel
+		); err != nil {
 			panic(err)
 		}
 		fmt.Println("successfully generated", f.name, "field")
diff --git a/field/koalabear/fft/bitreverse.go b/field/koalabear/fft/bitreverse.go
new file mode 100644
index 0000000000..5604c76673
--- /dev/null
+++ b/field/koalabear/fft/bitreverse.go
@@ -0,0 +1,563 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fft
+
+import (
+	"math/bits"
+	"runtime"
+
+	"github.com/consensys/gnark-crypto/field/koalabear"
+)
+
+// BitReverse applies the bit-reversal permutation to v.
+// len(v) must be a power of 2
+func BitReverse(v []koalabear.Element) {
+	n := uint64(len(v))
+	if bits.OnesCount64(n) != 1 {
+		panic("len(a) must be a power of 2")
+	}
+
+	if runtime.GOARCH == "arm64" {
+		bitReverseNaive(v)
+	} else {
+		bitReverseCobra(v)
+	}
+}
+
+// bitReverseNaive applies the bit-reversal permutation to v.
+// len(v) must be a power of 2
+func bitReverseNaive(v []koalabear.Element) {
+	n := uint64(len(v))
+	nn := uint64(64 - bits.TrailingZeros64(n))
+
+	for i := uint64(0); i < n; i++ {
+		iRev := bits.Reverse64(i) >> nn
+		if iRev > i {
+			v[i], v[iRev] = v[iRev], v[i]
+		}
+	}
+}
+
+// bitReverseCobraInPlace applies the bit-reversal permutation to v.
+// len(v) must be a power of 2
+// This is derived from:
+//
+//   - Towards an Optimal Bit-Reversal Permutation Program
+//     Larry Carter and Kang Su Gatlin, 1998
+//     https://csaws.cs.technion.ac.il/~itai/Courses/Cache/bit.pdf
+//
+//   - Practically efficient methods for performing bit-reversed
+//     permutation in C++11 on the x86-64 architecture
+//     Knauth, Adas, Whitfield, Wang, Ickler, Conrad, Serang, 2017
+//     https://arxiv.org/pdf/1708.01873.pdf
+//
+//   - and more specifically, constantine implementation:
+//     https://github.com/mratsim/constantine/blob/d51699248db04e29c7b1ad97e0bafa1499db00b5/constantine/math/polynomials/fft.nim#L205
+//     by Mamy Ratsimbazafy (@mratsim).
+func bitReverseCobraInPlace(v []koalabear.Element) {
+	logN := uint64(bits.Len64(uint64(len(v))) - 1)
+	logTileSize := deriveLogTileSize(logN)
+	logBLen := logN - 2*logTileSize
+	bLen := uint64(1) << logBLen
+	bShift := logBLen + logTileSize
+	tileSize := uint64(1) << logTileSize
+
+	// rough idea;
+	// bit reversal permutation naive implementation may have some cache associativity issues,
+	// since we are accessing elements by strides of powers of 2.
+	// on large inputs, this is noticeable and can be improved by using a t buffer.
+	// idea is for t buffer to be small enough to fit in cache.
+	// in the first inner loop, we copy the elements of v into t in a bit-reversed order.
+	// in the subsequent inner loops, accesses have much better cache locality than the naive implementation.
+	// hence even if we apparently do more work (swaps / copies), we are faster.
+	//
+	// on arm64 (and particularly on M1 macs), this is not noticeable, and the naive implementation is faster,
+	// in most cases.
+	// on x86 (and particularly on aws hpc6a) this is noticeable, and the t buffer implementation is faster (up to 3x).
+	//
+	// optimal choice for the tile size is cache dependent; in theory, we want the t buffer to fit in the L1 cache;
+	// in practice, a common size for L1 is 64kb, a field element is 32bytes or more.
+	// hence we can fit 2k elements in the L1 cache, which corresponds to a tile size of 2**5 with some margin for cache conflicts.
+	//
+	// for most sizes of interest, this tile size choice doesn't yield good results;
+	// we find that a tile size of 2**9 gives best results for input sizes from 2**21 up to 2**27+.
+	t := make([]koalabear.Element, tileSize*tileSize)
+
+	// see https://csaws.cs.technion.ac.il/~itai/Courses/Cache/bit.pdf
+	// for a detailed explanation of the algorithm.
+	for b := uint64(0); b < bLen; b++ {
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := (bits.Reverse64(a) >> (64 - logTileSize)) << logTileSize
+			for c := uint64(0); c < tileSize; c++ {
+				idx := (a << bShift) | (b << logTileSize) | c
+				t[aRev|c] = v[idx]
+			}
+		}
+
+		bRev := (bits.Reverse64(b) >> (64 - logBLen)) << logTileSize
+
+		for c := uint64(0); c < tileSize; c++ {
+			cRev := ((bits.Reverse64(c) >> (64 - logTileSize)) << bShift) | bRev
+			for aRev := uint64(0); aRev < tileSize; aRev++ {
+				a := bits.Reverse64(aRev) >> (64 - logTileSize)
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idxRev], t[tIdx] = t[tIdx], v[idxRev]
+				}
+			}
+		}
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := bits.Reverse64(a) >> (64 - logTileSize)
+			for c := uint64(0); c < tileSize; c++ {
+				cRev := (bits.Reverse64(c) >> (64 - logTileSize)) << bShift
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | bRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idx], t[tIdx] = t[tIdx], v[idx]
+				}
+			}
+		}
+	}
+}
+
+func bitReverseCobra(v []koalabear.Element) {
+	switch len(v) {
+	case 1 << 21:
+		bitReverseCobraInPlace_9_21(v)
+	case 1 << 22:
+		bitReverseCobraInPlace_9_22(v)
+	case 1 << 23:
+		bitReverseCobraInPlace_9_23(v)
+	case 1 << 24:
+		bitReverseCobraInPlace_9_24(v)
+	case 1 << 25:
+		bitReverseCobraInPlace_9_25(v)
+	case 1 << 26:
+		bitReverseCobraInPlace_9_26(v)
+	case 1 << 27:
+		bitReverseCobraInPlace_9_27(v)
+	default:
+		if len(v) > 1<<27 {
+			bitReverseCobraInPlace(v)
+		} else {
+			bitReverseNaive(v)
+		}
+	}
+}
+
+func deriveLogTileSize(logN uint64) uint64 {
+	q := uint64(9) // see bitReverseCobraInPlace for more details
+
+	for int(logN)-int(2*q) <= 0 {
+		q--
+	}
+
+	return q
+}
+
+// bitReverseCobraInPlace_9_21 applies the bit-reversal permutation to v.
+// len(v) must be 1 << 21.
+// see bitReverseCobraInPlace for more details; this function is specialized for 9,
+// as it declares the t buffer and various constants statically for performance.
+func bitReverseCobraInPlace_9_21(v []koalabear.Element) {
+	const (
+		logTileSize = uint64(9)
+		tileSize    = uint64(1) << logTileSize
+		logN        = 21
+		logBLen     = logN - 2*logTileSize
+		bShift      = logBLen + logTileSize
+		bLen        = uint64(1) << logBLen
+	)
+
+	var t [tileSize * tileSize]koalabear.Element
+
+	for b := uint64(0); b < bLen; b++ {
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := (bits.Reverse64(a) >> 55) << logTileSize
+			for c := uint64(0); c < tileSize; c++ {
+				idx := (a << bShift) | (b << logTileSize) | c
+				t[aRev|c] = v[idx]
+			}
+		}
+
+		bRev := (bits.Reverse64(b) >> (64 - logBLen)) << logTileSize
+
+		for c := uint64(0); c < tileSize; c++ {
+			cRev := ((bits.Reverse64(c) >> 55) << bShift) | bRev
+			for aRev := uint64(0); aRev < tileSize; aRev++ {
+				a := bits.Reverse64(aRev) >> 55
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idxRev], t[tIdx] = t[tIdx], v[idxRev]
+				}
+			}
+		}
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := bits.Reverse64(a) >> 55
+			for c := uint64(0); c < tileSize; c++ {
+				cRev := (bits.Reverse64(c) >> 55) << bShift
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | bRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idx], t[tIdx] = t[tIdx], v[idx]
+				}
+			}
+		}
+	}
+
+}
+
+// bitReverseCobraInPlace_9_22 applies the bit-reversal permutation to v.
+// len(v) must be 1 << 22.
+// see bitReverseCobraInPlace for more details; this function is specialized for 9,
+// as it declares the t buffer and various constants statically for performance.
+func bitReverseCobraInPlace_9_22(v []koalabear.Element) {
+	const (
+		logTileSize = uint64(9)
+		tileSize    = uint64(1) << logTileSize
+		logN        = 22
+		logBLen     = logN - 2*logTileSize
+		bShift      = logBLen + logTileSize
+		bLen        = uint64(1) << logBLen
+	)
+
+	var t [tileSize * tileSize]koalabear.Element
+
+	for b := uint64(0); b < bLen; b++ {
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := (bits.Reverse64(a) >> 55) << logTileSize
+			for c := uint64(0); c < tileSize; c++ {
+				idx := (a << bShift) | (b << logTileSize) | c
+				t[aRev|c] = v[idx]
+			}
+		}
+
+		bRev := (bits.Reverse64(b) >> (64 - logBLen)) << logTileSize
+
+		for c := uint64(0); c < tileSize; c++ {
+			cRev := ((bits.Reverse64(c) >> 55) << bShift) | bRev
+			for aRev := uint64(0); aRev < tileSize; aRev++ {
+				a := bits.Reverse64(aRev) >> 55
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idxRev], t[tIdx] = t[tIdx], v[idxRev]
+				}
+			}
+		}
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := bits.Reverse64(a) >> 55
+			for c := uint64(0); c < tileSize; c++ {
+				cRev := (bits.Reverse64(c) >> 55) << bShift
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | bRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idx], t[tIdx] = t[tIdx], v[idx]
+				}
+			}
+		}
+	}
+
+}
+
+// bitReverseCobraInPlace_9_23 applies the bit-reversal permutation to v.
+// len(v) must be 1 << 23.
+// see bitReverseCobraInPlace for more details; this function is specialized for 9,
+// as it declares the t buffer and various constants statically for performance.
+func bitReverseCobraInPlace_9_23(v []koalabear.Element) {
+	const (
+		logTileSize = uint64(9)
+		tileSize    = uint64(1) << logTileSize
+		logN        = 23
+		logBLen     = logN - 2*logTileSize
+		bShift      = logBLen + logTileSize
+		bLen        = uint64(1) << logBLen
+	)
+
+	var t [tileSize * tileSize]koalabear.Element
+
+	for b := uint64(0); b < bLen; b++ {
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := (bits.Reverse64(a) >> 55) << logTileSize
+			for c := uint64(0); c < tileSize; c++ {
+				idx := (a << bShift) | (b << logTileSize) | c
+				t[aRev|c] = v[idx]
+			}
+		}
+
+		bRev := (bits.Reverse64(b) >> (64 - logBLen)) << logTileSize
+
+		for c := uint64(0); c < tileSize; c++ {
+			cRev := ((bits.Reverse64(c) >> 55) << bShift) | bRev
+			for aRev := uint64(0); aRev < tileSize; aRev++ {
+				a := bits.Reverse64(aRev) >> 55
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idxRev], t[tIdx] = t[tIdx], v[idxRev]
+				}
+			}
+		}
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := bits.Reverse64(a) >> 55
+			for c := uint64(0); c < tileSize; c++ {
+				cRev := (bits.Reverse64(c) >> 55) << bShift
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | bRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idx], t[tIdx] = t[tIdx], v[idx]
+				}
+			}
+		}
+	}
+
+}
+
+// bitReverseCobraInPlace_9_24 applies the bit-reversal permutation to v.
+// len(v) must be 1 << 24.
+// see bitReverseCobraInPlace for more details; this function is specialized for 9,
+// as it declares the t buffer and various constants statically for performance.
+func bitReverseCobraInPlace_9_24(v []koalabear.Element) {
+	const (
+		logTileSize = uint64(9)
+		tileSize    = uint64(1) << logTileSize
+		logN        = 24
+		logBLen     = logN - 2*logTileSize
+		bShift      = logBLen + logTileSize
+		bLen        = uint64(1) << logBLen
+	)
+
+	var t [tileSize * tileSize]koalabear.Element
+
+	for b := uint64(0); b < bLen; b++ {
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := (bits.Reverse64(a) >> 55) << logTileSize
+			for c := uint64(0); c < tileSize; c++ {
+				idx := (a << bShift) | (b << logTileSize) | c
+				t[aRev|c] = v[idx]
+			}
+		}
+
+		bRev := (bits.Reverse64(b) >> (64 - logBLen)) << logTileSize
+
+		for c := uint64(0); c < tileSize; c++ {
+			cRev := ((bits.Reverse64(c) >> 55) << bShift) | bRev
+			for aRev := uint64(0); aRev < tileSize; aRev++ {
+				a := bits.Reverse64(aRev) >> 55
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idxRev], t[tIdx] = t[tIdx], v[idxRev]
+				}
+			}
+		}
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := bits.Reverse64(a) >> 55
+			for c := uint64(0); c < tileSize; c++ {
+				cRev := (bits.Reverse64(c) >> 55) << bShift
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | bRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idx], t[tIdx] = t[tIdx], v[idx]
+				}
+			}
+		}
+	}
+
+}
+
+// bitReverseCobraInPlace_9_25 applies the bit-reversal permutation to v.
+// len(v) must be 1 << 25.
+// see bitReverseCobraInPlace for more details; this function is specialized for 9,
+// as it declares the t buffer and various constants statically for performance.
+func bitReverseCobraInPlace_9_25(v []koalabear.Element) {
+	const (
+		logTileSize = uint64(9)
+		tileSize    = uint64(1) << logTileSize
+		logN        = 25
+		logBLen     = logN - 2*logTileSize
+		bShift      = logBLen + logTileSize
+		bLen        = uint64(1) << logBLen
+	)
+
+	var t [tileSize * tileSize]koalabear.Element
+
+	for b := uint64(0); b < bLen; b++ {
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := (bits.Reverse64(a) >> 55) << logTileSize
+			for c := uint64(0); c < tileSize; c++ {
+				idx := (a << bShift) | (b << logTileSize) | c
+				t[aRev|c] = v[idx]
+			}
+		}
+
+		bRev := (bits.Reverse64(b) >> (64 - logBLen)) << logTileSize
+
+		for c := uint64(0); c < tileSize; c++ {
+			cRev := ((bits.Reverse64(c) >> 55) << bShift) | bRev
+			for aRev := uint64(0); aRev < tileSize; aRev++ {
+				a := bits.Reverse64(aRev) >> 55
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idxRev], t[tIdx] = t[tIdx], v[idxRev]
+				}
+			}
+		}
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := bits.Reverse64(a) >> 55
+			for c := uint64(0); c < tileSize; c++ {
+				cRev := (bits.Reverse64(c) >> 55) << bShift
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | bRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idx], t[tIdx] = t[tIdx], v[idx]
+				}
+			}
+		}
+	}
+
+}
+
+// bitReverseCobraInPlace_9_26 applies the bit-reversal permutation to v.
+// len(v) must be 1 << 26.
+// see bitReverseCobraInPlace for more details; this function is specialized for 9,
+// as it declares the t buffer and various constants statically for performance.
+func bitReverseCobraInPlace_9_26(v []koalabear.Element) {
+	const (
+		logTileSize = uint64(9)
+		tileSize    = uint64(1) << logTileSize
+		logN        = 26
+		logBLen     = logN - 2*logTileSize
+		bShift      = logBLen + logTileSize
+		bLen        = uint64(1) << logBLen
+	)
+
+	var t [tileSize * tileSize]koalabear.Element
+
+	for b := uint64(0); b < bLen; b++ {
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := (bits.Reverse64(a) >> 55) << logTileSize
+			for c := uint64(0); c < tileSize; c++ {
+				idx := (a << bShift) | (b << logTileSize) | c
+				t[aRev|c] = v[idx]
+			}
+		}
+
+		bRev := (bits.Reverse64(b) >> (64 - logBLen)) << logTileSize
+
+		for c := uint64(0); c < tileSize; c++ {
+			cRev := ((bits.Reverse64(c) >> 55) << bShift) | bRev
+			for aRev := uint64(0); aRev < tileSize; aRev++ {
+				a := bits.Reverse64(aRev) >> 55
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idxRev], t[tIdx] = t[tIdx], v[idxRev]
+				}
+			}
+		}
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := bits.Reverse64(a) >> 55
+			for c := uint64(0); c < tileSize; c++ {
+				cRev := (bits.Reverse64(c) >> 55) << bShift
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | bRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idx], t[tIdx] = t[tIdx], v[idx]
+				}
+			}
+		}
+	}
+
+}
+
+// bitReverseCobraInPlace_9_27 applies the bit-reversal permutation to v.
+// len(v) must be 1 << 27.
+// see bitReverseCobraInPlace for more details; this function is specialized for 9,
+// as it declares the t buffer and various constants statically for performance.
+func bitReverseCobraInPlace_9_27(v []koalabear.Element) {
+	const (
+		logTileSize = uint64(9)
+		tileSize    = uint64(1) << logTileSize
+		logN        = 27
+		logBLen     = logN - 2*logTileSize
+		bShift      = logBLen + logTileSize
+		bLen        = uint64(1) << logBLen
+	)
+
+	var t [tileSize * tileSize]koalabear.Element
+
+	for b := uint64(0); b < bLen; b++ {
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := (bits.Reverse64(a) >> 55) << logTileSize
+			for c := uint64(0); c < tileSize; c++ {
+				idx := (a << bShift) | (b << logTileSize) | c
+				t[aRev|c] = v[idx]
+			}
+		}
+
+		bRev := (bits.Reverse64(b) >> (64 - logBLen)) << logTileSize
+
+		for c := uint64(0); c < tileSize; c++ {
+			cRev := ((bits.Reverse64(c) >> 55) << bShift) | bRev
+			for aRev := uint64(0); aRev < tileSize; aRev++ {
+				a := bits.Reverse64(aRev) >> 55
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idxRev], t[tIdx] = t[tIdx], v[idxRev]
+				}
+			}
+		}
+
+		for a := uint64(0); a < tileSize; a++ {
+			aRev := bits.Reverse64(a) >> 55
+			for c := uint64(0); c < tileSize; c++ {
+				cRev := (bits.Reverse64(c) >> 55) << bShift
+				idx := (a << bShift) | (b << logTileSize) | c
+				idxRev := cRev | bRev | aRev
+				if idx < idxRev {
+					tIdx := (aRev << logTileSize) | c
+					v[idx], t[tIdx] = t[tIdx], v[idx]
+				}
+			}
+		}
+	}
+
+}
diff --git a/field/koalabear/fft/bitreverse_test.go b/field/koalabear/fft/bitreverse_test.go
new file mode 100644
index 0000000000..732831a20a
--- /dev/null
+++ b/field/koalabear/fft/bitreverse_test.go
@@ -0,0 +1,102 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fft
+
+import (
+	"fmt"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/field/koalabear"
+)
+
+type bitReverseVariant struct {
+	name string
+	buf  []koalabear.Element
+	fn   func([]koalabear.Element)
+}
+
+const maxSizeBitReverse = 1 << 23
+
+var bitReverse = []bitReverseVariant{
+	{name: "bitReverseNaive", buf: make([]koalabear.Element, maxSizeBitReverse), fn: bitReverseNaive},
+	{name: "BitReverse", buf: make([]koalabear.Element, maxSizeBitReverse), fn: BitReverse},
+	{name: "bitReverseCobraInPlace", buf: make([]koalabear.Element, maxSizeBitReverse), fn: bitReverseCobraInPlace},
+}
+
+func TestBitReverse(t *testing.T) {
+
+	// generate a random []koalabear.Element array of size 2**20
+	pol := make([]koalabear.Element, maxSizeBitReverse)
+	one := koalabear.One()
+	pol[0].SetRandom()
+	for i := 1; i < maxSizeBitReverse; i++ {
+		pol[i].Add(&pol[i-1], &one)
+	}
+
+	// for each size, check that all the bitReverse functions fn compute the same result.
+	for size := 2; size <= maxSizeBitReverse; size <<= 1 {
+
+		// copy pol into the buffers
+		for _, data := range bitReverse {
+			copy(data.buf, pol[:size])
+		}
+
+		// compute bit reverse shuffling
+		for _, data := range bitReverse {
+			data.fn(data.buf[:size])
+		}
+
+		// all bitReverse.buf should hold the same result
+		for i := 0; i < size; i++ {
+			for j := 1; j < len(bitReverse); j++ {
+				if !bitReverse[0].buf[i].Equal(&bitReverse[j].buf[i]) {
+					t.Fatalf("bitReverse %s and %s do not compute the same result", bitReverse[0].name, bitReverse[j].name)
+				}
+			}
+		}
+
+		// bitReverse back should be identity
+		for _, data := range bitReverse {
+			data.fn(data.buf[:size])
+		}
+
+		for i := 0; i < size; i++ {
+			for j := 1; j < len(bitReverse); j++ {
+				if !bitReverse[0].buf[i].Equal(&bitReverse[j].buf[i]) {
+					t.Fatalf("(fn-1) bitReverse %s and %s do not compute the same result", bitReverse[0].name, bitReverse[j].name)
+				}
+			}
+		}
+	}
+
+}
+
+func BenchmarkBitReverse(b *testing.B) {
+	// generate a random []koalabear.Element array of size 2**22
+	pol := make([]koalabear.Element, maxSizeBitReverse)
+	one := koalabear.One()
+	pol[0].SetRandom()
+	for i := 1; i < maxSizeBitReverse; i++ {
+		pol[i].Add(&pol[i-1], &one)
+	}
+
+	// copy pol into the buffers
+	for _, data := range bitReverse {
+		copy(data.buf, pol[:maxSizeBitReverse])
+	}
+
+	// benchmark for each size, each bitReverse function
+	for size := 1 << 18; size <= maxSizeBitReverse; size <<= 1 {
+		for _, data := range bitReverse {
+			b.Run(fmt.Sprintf("name=%s/size=%d", data.name, size), func(b *testing.B) {
+				b.ResetTimer()
+				for j := 0; j < b.N; j++ {
+					data.fn(data.buf[:size])
+				}
+			})
+		}
+	}
+}
diff --git a/field/koalabear/fft/doc.go b/field/koalabear/fft/doc.go
new file mode 100644
index 0000000000..4cce0f9779
--- /dev/null
+++ b/field/koalabear/fft/doc.go
@@ -0,0 +1,8 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// Package fft provides in-place discrete Fourier transform on powers-of-two subgroups
+// of 𝔽ᵣˣ (the multiplicative group (ℤ/rℤ, x) ).
+package fft
diff --git a/field/koalabear/fft/domain.go b/field/koalabear/fft/domain.go
new file mode 100644
index 0000000000..7f13919e7b
--- /dev/null
+++ b/field/koalabear/fft/domain.go
@@ -0,0 +1,317 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fft
+
+import (
+	"encoding/binary"
+	"errors"
+	"io"
+	"math/big"
+	"math/bits"
+	"runtime"
+	"sync"
+
+	"github.com/consensys/gnark-crypto/field/koalabear"
+
+	"github.com/consensys/gnark-crypto/ecc"
+)
+
+// Domain with a power of 2 cardinality
+// compute a field element of order 2x and store it in FinerGenerator
+// all other values can be derived from x, GeneratorSqrt
+type Domain struct {
+	Cardinality            uint64
+	CardinalityInv         koalabear.Element
+	Generator              koalabear.Element
+	GeneratorInv           koalabear.Element
+	FrMultiplicativeGen    koalabear.Element // generator of Fr*
+	FrMultiplicativeGenInv koalabear.Element
+
+	// this is set with the WithoutPrecompute option;
+	// if true, the domain does some pre-computation and stores it.
+	// if false, the FFT will compute the twiddles on the fly (this is less CPU efficient, but uses less memory)
+	withPrecompute bool
+
+	// the following slices are not serialized and are (re)computed through domain.preComputeTwiddles()
+
+	// twiddles factor for the FFT using Generator for each stage of the recursive FFT
+	twiddles [][]koalabear.Element
+
+	// twiddles factor for the FFT using GeneratorInv for each stage of the recursive FFT
+	twiddlesInv [][]koalabear.Element
+
+	// we precompute these mostly to avoid the memory intensive bit reverse permutation in the groth16.Prover
+
+	// cosetTable u*<1,g,..,g^(n-1)>
+	cosetTable []koalabear.Element
+
+	// cosetTable[i][j] = domain.Generator(i-th)SqrtInv ^ j
+	cosetTableInv []koalabear.Element
+}
+
+// GeneratorFullMultiplicativeGroup returns a generator of 𝔽ᵣˣ
+func GeneratorFullMultiplicativeGroup() koalabear.Element {
+	var res koalabear.Element
+
+	res.SetUint64(3)
+
+	return res
+}
+
+// NewDomain returns a subgroup with a power of 2 cardinality
+// cardinality >= m
+// shift: when specified, it's the element by which the set of root of unity is shifted.
+func NewDomain(m uint64, opts ...DomainOption) *Domain {
+	opt := domainOptions(opts...)
+	domain := &Domain{}
+	x := ecc.NextPowerOfTwo(m)
+	domain.Cardinality = uint64(x)
+	domain.FrMultiplicativeGen = GeneratorFullMultiplicativeGroup()
+
+	if opt.shift != nil {
+		domain.FrMultiplicativeGen.Set(opt.shift)
+	}
+	domain.FrMultiplicativeGenInv.Inverse(&domain.FrMultiplicativeGen)
+
+	var err error
+	domain.Generator, err = Generator(m)
+	if err != nil {
+		panic(err)
+	}
+	domain.GeneratorInv.Inverse(&domain.Generator)
+	domain.CardinalityInv.SetUint64(uint64(x)).Inverse(&domain.CardinalityInv)
+
+	// twiddle factors
+	domain.withPrecompute = opt.withPrecompute
+	if domain.withPrecompute {
+		domain.preComputeTwiddles()
+	}
+
+	return domain
+}
+
+// Generator returns a generator for Z/2^(log(m))Z
+// or an error if m is too big (required root of unity doesn't exist)
+func Generator(m uint64) (koalabear.Element, error) {
+	return koalabear.Generator(m)
+}
+
+// Twiddles returns the twiddles factor for the FFT using Generator for each stage of the recursive FFT
+// or an error if the domain was created with the WithoutPrecompute option
+func (d *Domain) Twiddles() ([][]koalabear.Element, error) {
+	if d.twiddles == nil {
+		return nil, errors.New("twiddles not precomputed")
+	}
+	return d.twiddles, nil
+}
+
+// TwiddlesInv returns the twiddles factor for the FFT using GeneratorInv for each stage of the recursive FFT
+// or an error if the domain was created with the WithoutPrecompute option
+func (d *Domain) TwiddlesInv() ([][]koalabear.Element, error) {
+	if d.twiddlesInv == nil {
+		return nil, errors.New("twiddles not precomputed")
+	}
+	return d.twiddlesInv, nil
+}
+
+// CosetTable returns the cosetTable u*<1,g,..,g^(n-1)>
+// or an error if the domain was created with the WithoutPrecompute option
+func (d *Domain) CosetTable() ([]koalabear.Element, error) {
+	if d.cosetTable == nil {
+		return nil, errors.New("cosetTable not precomputed")
+	}
+	return d.cosetTable, nil
+}
+
+// CosetTableInv returns the cosetTableInv u*<1,g,..,g^(n-1)>
+// or an error if the domain was created with the WithoutPrecompute option
+func (d *Domain) CosetTableInv() ([]koalabear.Element, error) {
+	if d.cosetTableInv == nil {
+		return nil, errors.New("cosetTableInv not precomputed")
+	}
+	return d.cosetTableInv, nil
+}
+
+func (d *Domain) preComputeTwiddles() {
+
+	// nb fft stages
+	nbStages := uint64(bits.TrailingZeros64(d.Cardinality))
+
+	d.twiddles = make([][]koalabear.Element, nbStages)
+	d.twiddlesInv = make([][]koalabear.Element, nbStages)
+	d.cosetTable = make([]koalabear.Element, d.Cardinality)
+	d.cosetTableInv = make([]koalabear.Element, d.Cardinality)
+
+	var wg sync.WaitGroup
+
+	expTable := func(sqrt koalabear.Element, t []koalabear.Element) {
+		BuildExpTable(sqrt, t)
+		wg.Done()
+	}
+
+	wg.Add(4)
+	go func() {
+		buildTwiddles(d.twiddles, d.Generator, nbStages)
+		wg.Done()
+	}()
+	go func() {
+		buildTwiddles(d.twiddlesInv, d.GeneratorInv, nbStages)
+		wg.Done()
+	}()
+	go expTable(d.FrMultiplicativeGen, d.cosetTable)
+	go expTable(d.FrMultiplicativeGenInv, d.cosetTableInv)
+
+	wg.Wait()
+
+}
+
+func buildTwiddles(t [][]koalabear.Element, omega koalabear.Element, nbStages uint64) {
+	if nbStages == 0 {
+		return
+	}
+	if len(t) != int(nbStages) {
+		panic("invalid twiddle table")
+	}
+	// we just compute the first stage
+	t[0] = make([]koalabear.Element, 1+(1<<(nbStages-1)))
+	BuildExpTable(omega, t[0])
+
+	// for the next stages, we just iterate on the first stage with larger stride
+	for i := uint64(1); i < nbStages; i++ {
+		t[i] = make([]koalabear.Element, 1+(1<<(nbStages-i-1)))
+		k := 0
+		for j := 0; j < len(t[i]); j++ {
+			t[i][j] = t[0][k]
+			k += 1 << i
+		}
+	}
+
+}
+
+// BuildExpTable precomputes the first n powers of w in parallel
+// table[0] = w^0
+// table[1] = w^1
+// ...
+func BuildExpTable(w koalabear.Element, table []koalabear.Element) {
+	table[0].SetOne()
+	n := len(table)
+
+	// see if it makes sense to parallelize exp tables pre-computation
+	interval := 0
+	if runtime.NumCPU() >= 4 {
+		interval = (n - 1) / (runtime.NumCPU() / 4)
+	}
+
+	// this ratio roughly correspond to the number of multiplication one can do in place of a Exp operation
+	// TODO @gbotrel revisit this; Exps in this context will be by a "small power of 2" so faster than this ref ratio.
+	const ratioExpMul = 6000 / 17
+
+	if interval < ratioExpMul {
+		precomputeExpTableChunk(w, 1, table[1:])
+		return
+	}
+
+	// we parallelize
+	var wg sync.WaitGroup
+	for i := 1; i < n; i += interval {
+		start := i
+		end := i + interval
+		if end > n {
+			end = n
+		}
+		wg.Add(1)
+		go func() {
+			precomputeExpTableChunk(w, uint64(start), table[start:end])
+			wg.Done()
+		}()
+	}
+	wg.Wait()
+}
+
+func precomputeExpTableChunk(w koalabear.Element, power uint64, table []koalabear.Element) {
+
+	// this condition ensures that creating a domain of size 1 with cosets don't fail
+	if len(table) > 0 {
+		table[0].Exp(w, new(big.Int).SetUint64(power))
+		for i := 1; i < len(table); i++ {
+			table[i].Mul(&table[i-1], &w)
+		}
+	}
+}
+
+// WriteTo writes a binary representation of the domain (without the precomputed twiddle factors)
+// to the provided writer
+func (d *Domain) WriteTo(w io.Writer) (int64, error) {
+	// note to stay retro compatible with previous version using ecc/encoder, we encode as:
+	// d.Cardinality, &d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv, &d.withPrecompute
+
+	var written int64
+	var err error
+
+	err = binary.Write(w, binary.BigEndian, d.Cardinality)
+	if err != nil {
+		return written, err
+	}
+	written += 8
+
+	toEncode := []*koalabear.Element{&d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
+	for _, v := range toEncode {
+		buf := v.Bytes()
+		_, err = w.Write(buf[:])
+		if err != nil {
+			return written, err
+		}
+		written += koalabear.Bytes
+	}
+
+	err = binary.Write(w, binary.BigEndian, d.withPrecompute)
+	if err != nil {
+		return written, err
+	}
+	written += 1
+
+	return written, nil
+}
+
+// ReadFrom attempts to decode a domain from Reader
+func (d *Domain) ReadFrom(r io.Reader) (int64, error) {
+
+	var read int64
+	var err error
+
+	err = binary.Read(r, binary.BigEndian, &d.Cardinality)
+	if err != nil {
+		return read, err
+	}
+	read += 8
+
+	toDecode := []*koalabear.Element{&d.CardinalityInv, &d.Generator, &d.GeneratorInv, &d.FrMultiplicativeGen, &d.FrMultiplicativeGenInv}
+
+	for _, v := range toDecode {
+		var buf [koalabear.Bytes]byte
+		_, err = r.Read(buf[:])
+		if err != nil {
+			return read, err
+		}
+		read += koalabear.Bytes
+		*v, err = koalabear.BigEndian.Element(&buf)
+		if err != nil {
+			return read, err
+		}
+	}
+
+	err = binary.Read(r, binary.BigEndian, &d.withPrecompute)
+	if err != nil {
+		return read, err
+	}
+	read += 1
+
+	if d.withPrecompute {
+		d.preComputeTwiddles()
+	}
+
+	return read, nil
+}
diff --git a/field/koalabear/fft/domain_test.go b/field/koalabear/fft/domain_test.go
new file mode 100644
index 0000000000..e445d3cc12
--- /dev/null
+++ b/field/koalabear/fft/domain_test.go
@@ -0,0 +1,36 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fft
+
+import (
+	"bytes"
+	"reflect"
+	"testing"
+)
+
+func TestDomainSerialization(t *testing.T) {
+
+	domain := NewDomain(1 << 6)
+	var reconstructed Domain
+
+	var buf bytes.Buffer
+	written, err := domain.WriteTo(&buf)
+	if err != nil {
+		t.Fatal(err)
+	}
+	var read int64
+	read, err = reconstructed.ReadFrom(&buf)
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	if written != read {
+		t.Fatal("didn't read as many bytes as we wrote")
+	}
+	if !reflect.DeepEqual(domain, &reconstructed) {
+		t.Fatal("Domain.SetBytes(Bytes()) failed")
+	}
+}
diff --git a/field/koalabear/fft/fft.go b/field/koalabear/fft/fft.go
new file mode 100644
index 0000000000..5e63e1954a
--- /dev/null
+++ b/field/koalabear/fft/fft.go
@@ -0,0 +1,410 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fft
+
+import (
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/internal/parallel"
+	"math/big"
+	"math/bits"
+
+	"github.com/consensys/gnark-crypto/field/koalabear"
+)
+
+// Decimation is used in the FFT call to select decimation in time or in frequency
+type Decimation uint8
+
+const (
+	DIT Decimation = iota
+	DIF
+)
+
+// parallelize threshold for a single butterfly op, if the fft stage is not parallelized already
+const butterflyThreshold = 16
+
+// FFT computes (recursively) the discrete Fourier transform of a and stores the result in a
+// if decimation == DIT (decimation in time), the input must be in bit-reversed order
+// if decimation == DIF (decimation in frequency), the output will be in bit-reversed order
+func (domain *Domain) FFT(a []koalabear.Element, decimation Decimation, opts ...Option) {
+
+	opt := fftOptions(opts...)
+
+	// find the stage where we should stop spawning go routines in our recursive calls
+	// (ie when we have as many go routines running as we have available CPUs)
+	maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks)))
+	if opt.nbTasks == 1 {
+		maxSplits = -1
+	}
+
+	// if coset != 0, scale by coset table
+	if opt.coset {
+		if decimation == DIT {
+			// scale by coset table (in bit reversed order)
+			cosetTable := domain.cosetTable
+			if !domain.withPrecompute {
+				// we need to build the full table or do a bit reverse dance.
+				cosetTable = make([]koalabear.Element, len(a))
+				BuildExpTable(domain.FrMultiplicativeGen, cosetTable)
+			}
+			parallel.Execute(len(a), func(start, end int) {
+				n := uint64(len(a))
+				nn := uint64(64 - bits.TrailingZeros64(n))
+				for i := start; i < end; i++ {
+					irev := int(bits.Reverse64(uint64(i)) >> nn)
+					a[i].Mul(&a[i], &cosetTable[irev])
+				}
+			}, opt.nbTasks)
+		} else {
+			if domain.withPrecompute {
+				parallel.Execute(len(a), func(start, end int) {
+					for i := start; i < end; i++ {
+						a[i].Mul(&a[i], &domain.cosetTable[i])
+					}
+				}, opt.nbTasks)
+			} else {
+				c := domain.FrMultiplicativeGen
+				parallel.Execute(len(a), func(start, end int) {
+					var at koalabear.Element
+					at.Exp(c, big.NewInt(int64(start)))
+					for i := start; i < end; i++ {
+						a[i].Mul(&a[i], &at)
+						at.Mul(&at, &c)
+					}
+				}, opt.nbTasks)
+			}
+
+		}
+	}
+
+	twiddles := domain.twiddles
+	twiddlesStartStage := 0
+	if !domain.withPrecompute {
+		twiddlesStartStage = 3
+		nbStages := int(bits.TrailingZeros64(domain.Cardinality))
+		if nbStages-twiddlesStartStage > 0 {
+			twiddles = make([][]koalabear.Element, nbStages-twiddlesStartStage)
+			w := domain.Generator
+			w.Exp(w, big.NewInt(int64(1<<twiddlesStartStage)))
+			buildTwiddles(twiddles, w, uint64(nbStages-twiddlesStartStage))
+		} // else, we don't need twiddles
+	}
+
+	switch decimation {
+	case DIF:
+		difFFT(a, domain.Generator, twiddles, twiddlesStartStage, 0, maxSplits, nil, opt.nbTasks)
+	case DIT:
+		ditFFT(a, domain.Generator, twiddles, twiddlesStartStage, 0, maxSplits, nil, opt.nbTasks)
+	default:
+		panic("not implemented")
+	}
+}
+
+// FFTInverse computes (recursively) the inverse discrete Fourier transform of a and stores the result in a
+// if decimation == DIT (decimation in time), the input must be in bit-reversed order
+// if decimation == DIF (decimation in frequency), the output will be in bit-reversed order
+// coset sets the shift of the fft (0 = no shift, standard fft)
+// len(a) must be a power of 2, and w must be a len(a)th root of unity in field F.
+func (domain *Domain) FFTInverse(a []koalabear.Element, decimation Decimation, opts ...Option) {
+	opt := fftOptions(opts...)
+
+	// find the stage where we should stop spawning go routines in our recursive calls
+	// (ie when we have as many go routines running as we have available CPUs)
+	maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks)))
+	if opt.nbTasks == 1 {
+		maxSplits = -1
+	}
+
+	twiddlesInv := domain.twiddlesInv
+	twiddlesStartStage := 0
+	if !domain.withPrecompute {
+		twiddlesStartStage = 3
+		nbStages := int(bits.TrailingZeros64(domain.Cardinality))
+		if nbStages-twiddlesStartStage > 0 {
+			twiddlesInv = make([][]koalabear.Element, nbStages-twiddlesStartStage)
+			w := domain.GeneratorInv
+			w.Exp(w, big.NewInt(int64(1<<twiddlesStartStage)))
+			buildTwiddles(twiddlesInv, w, uint64(nbStages-twiddlesStartStage))
+		} // else, we don't need twiddles
+	}
+
+	switch decimation {
+	case DIF:
+		difFFT(a, domain.GeneratorInv, twiddlesInv, twiddlesStartStage, 0, maxSplits, nil, opt.nbTasks)
+	case DIT:
+		ditFFT(a, domain.GeneratorInv, twiddlesInv, twiddlesStartStage, 0, maxSplits, nil, opt.nbTasks)
+	default:
+		panic("not implemented")
+	}
+
+	// scale by CardinalityInv
+	if !opt.coset {
+		parallel.Execute(len(a), func(start, end int) {
+			for i := start; i < end; i++ {
+				a[i].Mul(&a[i], &domain.CardinalityInv)
+			}
+		}, opt.nbTasks)
+		return
+	}
+
+	if decimation == DIT {
+		if domain.withPrecompute {
+			parallel.Execute(len(a), func(start, end int) {
+				for i := start; i < end; i++ {
+					a[i].Mul(&a[i], &domain.cosetTableInv[i]).
+						Mul(&a[i], &domain.CardinalityInv)
+				}
+			}, opt.nbTasks)
+		} else {
+			c := domain.FrMultiplicativeGenInv
+			parallel.Execute(len(a), func(start, end int) {
+				var at koalabear.Element
+				at.Exp(c, big.NewInt(int64(start)))
+				at.Mul(&at, &domain.CardinalityInv)
+				for i := start; i < end; i++ {
+					a[i].Mul(&a[i], &at)
+					at.Mul(&at, &c)
+				}
+			}, opt.nbTasks)
+		}
+		return
+	}
+
+	// decimation == DIF, need to access coset table in bit reversed order.
+	cosetTableInv := domain.cosetTableInv
+	if !domain.withPrecompute {
+		// we need to build the full table or do a bit reverse dance.
+		cosetTableInv = make([]koalabear.Element, len(a))
+		BuildExpTable(domain.FrMultiplicativeGenInv, cosetTableInv)
+	}
+	parallel.Execute(len(a), func(start, end int) {
+		n := uint64(len(a))
+		nn := uint64(64 - bits.TrailingZeros64(n))
+		for i := start; i < end; i++ {
+			irev := int(bits.Reverse64(uint64(i)) >> nn)
+			a[i].Mul(&a[i], &cosetTableInv[irev]).
+				Mul(&a[i], &domain.CardinalityInv)
+		}
+	}, opt.nbTasks)
+
+}
+
+func difFFT(a []koalabear.Element, w koalabear.Element, twiddles [][]koalabear.Element, twiddlesStartStage, stage, maxSplits int, chDone chan struct{}, nbTasks int) {
+	if chDone != nil {
+		defer close(chDone)
+	}
+
+	n := len(a)
+	if n == 1 {
+		return
+	} else if n == 256 && stage >= twiddlesStartStage {
+		kerDIFNP_256(a, twiddles, stage-twiddlesStartStage)
+		return
+	}
+	m := n >> 1
+
+	parallelButterfly := (m > butterflyThreshold) && (stage < maxSplits)
+
+	if stage < twiddlesStartStage {
+		if parallelButterfly {
+			w := w
+			parallel.Execute(m, func(start, end int) {
+				if start == 0 {
+					koalabear.Butterfly(&a[0], &a[m])
+					start++
+				}
+				var at koalabear.Element
+				at.Exp(w, big.NewInt(int64(start)))
+				innerDIFWithoutTwiddles(a, at, w, start, end, m)
+			}, nbTasks/(1<<(stage))) // 1 << stage == estimated used CPUs
+		} else {
+			innerDIFWithoutTwiddles(a, w, w, 0, m, m)
+		}
+		// compute next twiddle
+		w.Square(&w)
+	} else {
+		if parallelButterfly {
+			parallel.Execute(m, func(start, end int) {
+				innerDIFWithTwiddles(a, twiddles[stage-twiddlesStartStage], start, end, m)
+			}, nbTasks/(1<<(stage)))
+		} else {
+			innerDIFWithTwiddles(a, twiddles[stage-twiddlesStartStage], 0, m, m)
+		}
+	}
+
+	if m == 1 {
+		return
+	}
+
+	nextStage := stage + 1
+	if stage < maxSplits {
+		chDone := make(chan struct{}, 1)
+		go difFFT(a[m:n], w, twiddles, twiddlesStartStage, nextStage, maxSplits, chDone, nbTasks)
+		difFFT(a[0:m], w, twiddles, twiddlesStartStage, nextStage, maxSplits, nil, nbTasks)
+		<-chDone
+	} else {
+		difFFT(a[0:m], w, twiddles, twiddlesStartStage, nextStage, maxSplits, nil, nbTasks)
+		difFFT(a[m:n], w, twiddles, twiddlesStartStage, nextStage, maxSplits, nil, nbTasks)
+	}
+
+}
+
+func innerDIFWithTwiddles(a []koalabear.Element, twiddles []koalabear.Element, start, end, m int) {
+	if start == 0 {
+		koalabear.Butterfly(&a[0], &a[m])
+		start++
+	}
+	for i := start; i < end; i++ {
+		koalabear.Butterfly(&a[i], &a[i+m])
+		a[i+m].Mul(&a[i+m], &twiddles[i])
+	}
+}
+
+func innerDIFWithoutTwiddles(a []koalabear.Element, at, w koalabear.Element, start, end, m int) {
+	if start == 0 {
+		koalabear.Butterfly(&a[0], &a[m])
+		start++
+	}
+	for i := start; i < end; i++ {
+		koalabear.Butterfly(&a[i], &a[i+m])
+		a[i+m].Mul(&a[i+m], &at)
+		at.Mul(&at, &w)
+	}
+}
+
+func ditFFT(a []koalabear.Element, w koalabear.Element, twiddles [][]koalabear.Element, twiddlesStartStage, stage, maxSplits int, chDone chan struct{}, nbTasks int) {
+	if chDone != nil {
+		defer close(chDone)
+	}
+	n := len(a)
+	if n == 1 {
+		return
+	} else if n == 256 && stage >= twiddlesStartStage {
+		kerDITNP_256(a, twiddles, stage-twiddlesStartStage)
+		return
+	}
+	m := n >> 1
+
+	nextStage := stage + 1
+	nextW := w
+	nextW.Square(&nextW)
+
+	if stage < maxSplits {
+		// that's the only time we fire go routines
+		chDone := make(chan struct{}, 1)
+		go ditFFT(a[m:], nextW, twiddles, twiddlesStartStage, nextStage, maxSplits, chDone, nbTasks)
+		ditFFT(a[0:m], nextW, twiddles, twiddlesStartStage, nextStage, maxSplits, nil, nbTasks)
+		<-chDone
+	} else {
+		ditFFT(a[0:m], nextW, twiddles, twiddlesStartStage, nextStage, maxSplits, nil, nbTasks)
+		ditFFT(a[m:n], nextW, twiddles, twiddlesStartStage, nextStage, maxSplits, nil, nbTasks)
+	}
+
+	parallelButterfly := (m > butterflyThreshold) && (stage < maxSplits)
+
+	if stage < twiddlesStartStage {
+		// we need to compute the twiddles for this stage on the fly.
+		if parallelButterfly {
+			w := w
+			parallel.Execute(m, func(start, end int) {
+				if start == 0 {
+					koalabear.Butterfly(&a[0], &a[m])
+					start++
+				}
+				var at koalabear.Element
+				at.Exp(w, big.NewInt(int64(start)))
+				innerDITWithoutTwiddles(a, at, w, start, end, m)
+			}, nbTasks/(1<<(stage))) // 1 << stage == estimated used CPUs
+
+		} else {
+			innerDITWithoutTwiddles(a, w, w, 0, m, m)
+		}
+		return
+	}
+	if parallelButterfly {
+		parallel.Execute(m, func(start, end int) {
+			innerDITWithTwiddles(a, twiddles[stage-twiddlesStartStage], start, end, m)
+		}, nbTasks/(1<<(stage)))
+	} else {
+		innerDITWithTwiddles(a, twiddles[stage-twiddlesStartStage], 0, m, m)
+	}
+}
+
+func innerDITWithTwiddles(a []koalabear.Element, twiddles []koalabear.Element, start, end, m int) {
+	if start == 0 {
+		koalabear.Butterfly(&a[0], &a[m])
+		start++
+	}
+	for i := start; i < end; i++ {
+		a[i+m].Mul(&a[i+m], &twiddles[i])
+		koalabear.Butterfly(&a[i], &a[i+m])
+	}
+}
+
+func innerDITWithoutTwiddles(a []koalabear.Element, at, w koalabear.Element, start, end, m int) {
+	if start == 0 {
+		koalabear.Butterfly(&a[0], &a[m])
+		start++
+	}
+	for i := start; i < end; i++ {
+		a[i+m].Mul(&a[i+m], &at)
+		koalabear.Butterfly(&a[i], &a[i+m])
+		at.Mul(&at, &w)
+	}
+}
+
+func kerDIFNP_256(a []koalabear.Element, twiddles [][]koalabear.Element, stage int) {
+	// code unrolled & generated by internal/generator/fft/template/fft.go.tmpl
+
+	innerDIFWithTwiddles(a[:256], twiddles[stage+0], 0, 128, 128)
+	for offset := 0; offset < 256; offset += 128 {
+		innerDIFWithTwiddles(a[offset:offset+128], twiddles[stage+1], 0, 64, 64)
+	}
+	for offset := 0; offset < 256; offset += 64 {
+		innerDIFWithTwiddles(a[offset:offset+64], twiddles[stage+2], 0, 32, 32)
+	}
+	for offset := 0; offset < 256; offset += 32 {
+		innerDIFWithTwiddles(a[offset:offset+32], twiddles[stage+3], 0, 16, 16)
+	}
+	for offset := 0; offset < 256; offset += 16 {
+		innerDIFWithTwiddles(a[offset:offset+16], twiddles[stage+4], 0, 8, 8)
+	}
+	for offset := 0; offset < 256; offset += 8 {
+		innerDIFWithTwiddles(a[offset:offset+8], twiddles[stage+5], 0, 4, 4)
+	}
+	for offset := 0; offset < 256; offset += 4 {
+		innerDIFWithTwiddles(a[offset:offset+4], twiddles[stage+6], 0, 2, 2)
+	}
+	for offset := 0; offset < 256; offset += 2 {
+		koalabear.Butterfly(&a[offset], &a[offset+1])
+	}
+}
+
+func kerDITNP_256(a []koalabear.Element, twiddles [][]koalabear.Element, stage int) {
+	// code unrolled & generated by internal/generator/fft/template/fft.go.tmpl
+
+	for offset := 0; offset < 256; offset += 2 {
+		koalabear.Butterfly(&a[offset], &a[offset+1])
+	}
+	for offset := 0; offset < 256; offset += 4 {
+		innerDITWithTwiddles(a[offset:offset+4], twiddles[stage+6], 0, 2, 2)
+	}
+	for offset := 0; offset < 256; offset += 8 {
+		innerDITWithTwiddles(a[offset:offset+8], twiddles[stage+5], 0, 4, 4)
+	}
+	for offset := 0; offset < 256; offset += 16 {
+		innerDITWithTwiddles(a[offset:offset+16], twiddles[stage+4], 0, 8, 8)
+	}
+	for offset := 0; offset < 256; offset += 32 {
+		innerDITWithTwiddles(a[offset:offset+32], twiddles[stage+3], 0, 16, 16)
+	}
+	for offset := 0; offset < 256; offset += 64 {
+		innerDITWithTwiddles(a[offset:offset+64], twiddles[stage+2], 0, 32, 32)
+	}
+	for offset := 0; offset < 256; offset += 128 {
+		innerDITWithTwiddles(a[offset:offset+128], twiddles[stage+1], 0, 64, 64)
+	}
+	innerDITWithTwiddles(a[:256], twiddles[stage+0], 0, 128, 128)
+}
diff --git a/field/koalabear/fft/fft_test.go b/field/koalabear/fft/fft_test.go
new file mode 100644
index 0000000000..1d447f2bdf
--- /dev/null
+++ b/field/koalabear/fft/fft_test.go
@@ -0,0 +1,318 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fft
+
+import (
+	"math/big"
+	"strconv"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/field/koalabear"
+
+	"github.com/leanovate/gopter"
+	"github.com/leanovate/gopter/gen"
+	"github.com/leanovate/gopter/prop"
+
+	"fmt"
+)
+
+func TestFFT(t *testing.T) {
+	parameters := gopter.DefaultTestParameters()
+	parameters.MinSuccessfulTests = 5
+	properties := gopter.NewProperties(parameters)
+
+	for maxSize := 2; maxSize <= 1<<10; maxSize <<= 1 {
+
+		domainWithPrecompute := NewDomain(uint64(maxSize))
+		domainWithoutPrecompute := NewDomain(uint64(maxSize), WithoutPrecompute())
+
+		for domainName, domain := range map[string]*Domain{
+			"with precompute":    domainWithPrecompute,
+			"without precompute": domainWithoutPrecompute,
+		} {
+			domainName := domainName
+			domain := domain
+			t.Logf("domain: %s", domainName)
+			properties.Property("DIF FFT should be consistent with dual basis", prop.ForAll(
+
+				// checks that a random evaluation of a dual function eval(gen**ithpower) is consistent with the FFT result
+				func(ithpower int) bool {
+
+					pol := make([]koalabear.Element, maxSize)
+					backupPol := make([]koalabear.Element, maxSize)
+
+					for i := 0; i < maxSize; i++ {
+						pol[i].SetRandom()
+					}
+					copy(backupPol, pol)
+
+					domain.FFT(pol, DIF)
+					BitReverse(pol)
+
+					sample := domain.Generator
+					sample.Exp(sample, big.NewInt(int64(ithpower)))
+
+					eval := evaluatePolynomial(backupPol, sample)
+
+					return eval.Equal(&pol[ithpower])
+
+				},
+				gen.IntRange(0, maxSize-1),
+			))
+
+			properties.Property("DIF FFT on cosets should be consistent with dual basis", prop.ForAll(
+
+				// checks that a random evaluation of a dual function eval(gen**ithpower) is consistent with the FFT result
+				func(ithpower int) bool {
+
+					pol := make([]koalabear.Element, maxSize)
+					backupPol := make([]koalabear.Element, maxSize)
+
+					for i := 0; i < maxSize; i++ {
+						pol[i].SetRandom()
+					}
+					copy(backupPol, pol)
+
+					domain.FFT(pol, DIF, OnCoset())
+					BitReverse(pol)
+
+					sample := domain.Generator
+					sample.Exp(sample, big.NewInt(int64(ithpower))).
+						Mul(&sample, &domain.FrMultiplicativeGen)
+
+					eval := evaluatePolynomial(backupPol, sample)
+
+					return eval.Equal(&pol[ithpower])
+
+				},
+				gen.IntRange(0, maxSize-1),
+			))
+
+			properties.Property("DIT FFT should be consistent with dual basis", prop.ForAll(
+
+				// checks that a random evaluation of a dual function eval(gen**ithpower) is consistent with the FFT result
+				func(ithpower int) bool {
+
+					pol := make([]koalabear.Element, maxSize)
+					backupPol := make([]koalabear.Element, maxSize)
+
+					for i := 0; i < maxSize; i++ {
+						pol[i].SetRandom()
+					}
+					copy(backupPol, pol)
+
+					BitReverse(pol)
+					domain.FFT(pol, DIT)
+
+					sample := domain.Generator
+					sample.Exp(sample, big.NewInt(int64(ithpower)))
+
+					eval := evaluatePolynomial(backupPol, sample)
+
+					return eval.Equal(&pol[ithpower])
+
+				},
+				gen.IntRange(0, maxSize-1),
+			))
+
+			properties.Property("bitReverse(DIF FFT(DIT FFT (bitReverse))))==id", prop.ForAll(
+
+				func() bool {
+
+					pol := make([]koalabear.Element, maxSize)
+					backupPol := make([]koalabear.Element, maxSize)
+
+					for i := 0; i < maxSize; i++ {
+						pol[i].SetRandom()
+					}
+					copy(backupPol, pol)
+
+					BitReverse(pol)
+					domain.FFT(pol, DIT)
+					domain.FFTInverse(pol, DIF)
+					BitReverse(pol)
+
+					check := true
+					for i := 0; i < len(pol); i++ {
+						check = check && pol[i].Equal(&backupPol[i])
+					}
+					return check
+				},
+			))
+
+			for nbCosets := 2; nbCosets < 5; nbCosets++ {
+				properties.Property(fmt.Sprintf("bitReverse(DIF FFT(DIT FFT (bitReverse))))==id on %d cosets", nbCosets), prop.ForAll(
+
+					func() bool {
+
+						pol := make([]koalabear.Element, maxSize)
+						backupPol := make([]koalabear.Element, maxSize)
+
+						for i := 0; i < maxSize; i++ {
+							pol[i].SetRandom()
+						}
+						copy(backupPol, pol)
+
+						check := true
+
+						for i := 1; i <= nbCosets; i++ {
+
+							BitReverse(pol)
+							domain.FFT(pol, DIT, OnCoset())
+							domain.FFTInverse(pol, DIF, OnCoset())
+							BitReverse(pol)
+
+							for i := 0; i < len(pol); i++ {
+								check = check && pol[i].Equal(&backupPol[i])
+							}
+						}
+
+						return check
+					},
+				))
+			}
+
+			properties.Property("DIT FFT(DIF FFT)==id", prop.ForAll(
+
+				func() bool {
+
+					pol := make([]koalabear.Element, maxSize)
+					backupPol := make([]koalabear.Element, maxSize)
+
+					for i := 0; i < maxSize; i++ {
+						pol[i].SetRandom()
+					}
+					copy(backupPol, pol)
+
+					domain.FFTInverse(pol, DIF)
+					domain.FFT(pol, DIT)
+
+					check := true
+					for i := 0; i < len(pol); i++ {
+						check = check && (pol[i] == backupPol[i])
+					}
+					return check
+				},
+			))
+
+			properties.Property("DIT FFT(DIF FFT)==id on cosets", prop.ForAll(
+
+				func() bool {
+
+					pol := make([]koalabear.Element, maxSize)
+					backupPol := make([]koalabear.Element, maxSize)
+
+					for i := 0; i < maxSize; i++ {
+						pol[i].SetRandom()
+					}
+					copy(backupPol, pol)
+
+					domain.FFTInverse(pol, DIF, OnCoset())
+					domain.FFT(pol, DIT, OnCoset())
+
+					for i := 0; i < len(pol); i++ {
+						if !(pol[i].Equal(&backupPol[i])) {
+							return false
+						}
+					}
+
+					// compute with nbTasks == 1
+					domain.FFTInverse(pol, DIF, OnCoset(), WithNbTasks(1))
+					domain.FFT(pol, DIT, OnCoset(), WithNbTasks(1))
+
+					for i := 0; i < len(pol); i++ {
+						if !(pol[i].Equal(&backupPol[i])) {
+							return false
+						}
+					}
+
+					return true
+				},
+			))
+		}
+		properties.TestingRun(t, gopter.ConsoleReporter(false))
+	}
+
+}
+
+// --------------------------------------------------------------------
+// benches
+
+func BenchmarkFFT(b *testing.B) {
+
+	const maxSize = 1 << 20
+
+	pol := make([]koalabear.Element, maxSize)
+	pol[0].SetRandom()
+	for i := 1; i < maxSize; i++ {
+		pol[i] = pol[i-1]
+	}
+
+	for i := 8; i < 20; i++ {
+		sizeDomain := 1 << i
+		b.Run("fft 2**"+strconv.Itoa(i)+"bits", func(b *testing.B) {
+			domain := NewDomain(uint64(sizeDomain))
+			b.ResetTimer()
+			for j := 0; j < b.N; j++ {
+				domain.FFT(pol[:sizeDomain], DIT)
+			}
+		})
+		b.Run("fft 2**"+strconv.Itoa(i)+"bits (coset)", func(b *testing.B) {
+			domain := NewDomain(uint64(sizeDomain))
+			b.ResetTimer()
+			for j := 0; j < b.N; j++ {
+				domain.FFT(pol[:sizeDomain], DIT, OnCoset())
+			}
+		})
+	}
+
+}
+
+func BenchmarkFFTDITCosetReference(b *testing.B) {
+	const maxSize = 1 << 20
+
+	pol := make([]koalabear.Element, maxSize)
+	pol[0].SetRandom()
+	for i := 1; i < maxSize; i++ {
+		pol[i] = pol[i-1]
+	}
+
+	domain := NewDomain(maxSize)
+
+	b.ResetTimer()
+	for j := 0; j < b.N; j++ {
+		domain.FFT(pol, DIT, OnCoset())
+	}
+}
+
+func BenchmarkFFTDIFReference(b *testing.B) {
+	const maxSize = 1 << 20
+
+	pol := make([]koalabear.Element, maxSize)
+	pol[0].SetRandom()
+	for i := 1; i < maxSize; i++ {
+		pol[i] = pol[i-1]
+	}
+
+	domain := NewDomain(maxSize)
+
+	b.ResetTimer()
+	for j := 0; j < b.N; j++ {
+		domain.FFT(pol, DIF)
+	}
+}
+
+func evaluatePolynomial(pol []koalabear.Element, val koalabear.Element) koalabear.Element {
+	var acc, res, tmp koalabear.Element
+	res.Set(&pol[0])
+	acc.Set(&val)
+	for i := 1; i < len(pol); i++ {
+		tmp.Mul(&acc, &pol[i])
+		res.Add(&res, &tmp)
+		acc.Mul(&acc, &val)
+	}
+	return res
+}
diff --git a/field/koalabear/fft/options.go b/field/koalabear/fft/options.go
new file mode 100644
index 0000000000..c146ac1123
--- /dev/null
+++ b/field/koalabear/fft/options.go
@@ -0,0 +1,92 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package fft
+
+import (
+	"runtime"
+
+	"github.com/consensys/gnark-crypto/field/koalabear"
+)
+
+// Option defines option for altering the behavior of FFT methods.
+// See the descriptions of functions returning instances of this type for
+// particular options.
+type Option func(*fftConfig)
+
+type fftConfig struct {
+	coset   bool
+	nbTasks int
+}
+
+// OnCoset if provided, FFT(a) returns the evaluation of a on a coset.
+func OnCoset() Option {
+	return func(opt *fftConfig) {
+		opt.coset = true
+	}
+}
+
+// WithNbTasks sets the max number of task (go routine) to spawn. Must be between 1 and 512.
+func WithNbTasks(nbTasks int) Option {
+	if nbTasks < 1 {
+		nbTasks = 1
+	} else if nbTasks > 512 {
+		nbTasks = 512
+	}
+	return func(opt *fftConfig) {
+		opt.nbTasks = nbTasks
+	}
+}
+
+// default options
+func fftOptions(opts ...Option) fftConfig {
+	// apply options
+	opt := fftConfig{
+		coset:   false,
+		nbTasks: runtime.NumCPU(),
+	}
+	for _, option := range opts {
+		option(&opt)
+	}
+	return opt
+}
+
+// DomainOption defines option for altering the definition of the FFT domain
+// See the descriptions of functions returning instances of this type for
+// particular options.
+type DomainOption func(*domainConfig)
+
+type domainConfig struct {
+	shift          *koalabear.Element
+	withPrecompute bool
+}
+
+// WithShift sets the FrMultiplicativeGen of the domain.
+// Default is generator of the largest 2-adic subgroup.
+func WithShift(shift koalabear.Element) DomainOption {
+	return func(opt *domainConfig) {
+		opt.shift = new(koalabear.Element).Set(&shift)
+	}
+}
+
+// WithoutPrecompute disables precomputation of twiddles in the domain.
+// When this option is set, FFTs will be slower, but will use less memory.
+func WithoutPrecompute() DomainOption {
+	return func(opt *domainConfig) {
+		opt.withPrecompute = false
+	}
+}
+
+// default options
+func domainOptions(opts ...DomainOption) domainConfig {
+	// apply options
+	opt := domainConfig{
+		withPrecompute: true,
+	}
+	for _, option := range opts {
+		option(&opt)
+	}
+	return opt
+}
diff --git a/field/koalabear/generator.go b/field/koalabear/generator.go
new file mode 100644
index 0000000000..dd5bbb97e9
--- /dev/null
+++ b/field/koalabear/generator.go
@@ -0,0 +1,36 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package koalabear
+
+import (
+	"fmt"
+	"math/big"
+	"math/bits"
+
+	"github.com/consensys/gnark-crypto/ecc"
+)
+
+// Generator returns a generator for Z/2^(log(m))Z
+// or an error if m is too big (required root of unity doesn't exist)
+func Generator(m uint64) (Element, error) {
+	x := ecc.NextPowerOfTwo(m)
+
+	var rootOfUnity Element
+
+	rootOfUnity.SetString("1791270792")
+	const maxOrderRoot uint64 = 24
+
+	// find generator for Z/2^(log(m))Z
+	logx := uint64(bits.TrailingZeros64(x))
+	if logx > maxOrderRoot {
+		return Element{}, fmt.Errorf("m (%d) is too big: the required root of unity does not exist", m)
+	}
+
+	expo := uint64(1 << (maxOrderRoot - logx))
+	var generator Element
+	generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x
+	return generator, nil
+}
diff --git a/internal/generator/config/curve.go b/internal/generator/config/curve.go
index 0c55a6a976..c490a1143c 100644
--- a/internal/generator/config/curve.go
+++ b/internal/generator/config/curve.go
@@ -15,8 +15,8 @@ type Curve struct {
 	FpModulus    string
 	FrModulus    string
 
-	Fp           *config.FieldConfig
-	Fr           *config.FieldConfig
+	Fp           *config.Field
+	Fr           *config.Field
 	FpUnusedBits int
 
 	FpInfo, FrInfo Field
diff --git a/internal/generator/config/hash_to_curve.go b/internal/generator/config/hash_to_curve.go
index cb7c5b9142..27a3a86229 100644
--- a/internal/generator/config/hash_to_curve.go
+++ b/internal/generator/config/hash_to_curve.go
@@ -26,7 +26,7 @@ type RationalPolynomial struct {
 }
 
 type HashSuite interface {
-	GetInfo(baseField *field.FieldConfig, g *Point, name string) HashSuiteInfo
+	GetInfo(baseField *field.Field, g *Point, name string) HashSuiteInfo
 }
 
 type HashSuiteSswu struct {
@@ -54,7 +54,7 @@ type HashSuiteSvdw struct {
 	c4 []string
 }
 
-func (parameters *HashSuiteSvdw) GetInfo(baseField *field.FieldConfig, g *Point, name string) HashSuiteInfo {
+func (parameters *HashSuiteSvdw) GetInfo(baseField *field.Field, g *Point, name string) HashSuiteInfo {
 	f := field.NewTower(baseField, g.CoordExtDegree, g.CoordExtRoot)
 	c := []field.Element{
 		field.NewElement(parameters.z),
@@ -74,7 +74,7 @@ func (parameters *HashSuiteSvdw) GetInfo(baseField *field.FieldConfig, g *Point,
 	}
 }
 
-func (suite *HashSuiteSswu) GetInfo(baseField *field.FieldConfig, g *Point, name string) HashSuiteInfo {
+func (suite *HashSuiteSswu) GetInfo(baseField *field.Field, g *Point, name string) HashSuiteInfo {
 
 	f := field.NewTower(baseField, g.CoordExtDegree, g.CoordExtRoot)
 	fieldSizeMod256 := uint8(f.Size.Bits()[0])
diff --git a/internal/generator/fft/generate.go b/internal/generator/fft/generate.go
deleted file mode 100644
index 1ccc35c74d..0000000000
--- a/internal/generator/fft/generate.go
+++ /dev/null
@@ -1,76 +0,0 @@
-package fft
-
-import (
-	"math/bits"
-	"path/filepath"
-
-	"github.com/consensys/bavard"
-	"github.com/consensys/gnark-crypto/internal/generator/config"
-)
-
-func Generate(conf config.Curve, baseDir string, bgen *bavard.BatchGenerator) error {
-
-	conf.Package = "fft"
-
-	entries := []bavard.Entry{
-		{File: filepath.Join(baseDir, "doc.go"), Templates: []string{"doc.go.tmpl"}},
-		{File: filepath.Join(baseDir, "domain_test.go"), Templates: []string{"tests/domain.go.tmpl", "imports.go.tmpl"}},
-		{File: filepath.Join(baseDir, "domain.go"), Templates: []string{"domain.go.tmpl", "imports.go.tmpl"}},
-		{File: filepath.Join(baseDir, "fft_test.go"), Templates: []string{"tests/fft.go.tmpl", "imports.go.tmpl"}},
-		{File: filepath.Join(baseDir, "bitreverse_test.go"), Templates: []string{"tests/bitreverse.go.tmpl", "imports.go.tmpl"}},
-		{File: filepath.Join(baseDir, "fft.go"), Templates: []string{"fft.go.tmpl", "imports.go.tmpl"}},
-		{File: filepath.Join(baseDir, "bitreverse.go"), Templates: []string{"bitreverse.go.tmpl", "imports.go.tmpl"}},
-		{File: filepath.Join(baseDir, "options.go"), Templates: []string{"options.go.tmpl", "imports.go.tmpl"}},
-	}
-
-	funcs := make(map[string]interface{})
-	funcs["bitReverse"] = func(n, i int64) uint64 {
-		nn := uint64(64 - bits.TrailingZeros64(uint64(n)))
-		r := make([]uint64, n)
-		for i := 0; i < len(r); i++ {
-			r[i] = uint64(i)
-		}
-		for i := 0; i < len(r); i++ {
-			irev := bits.Reverse64(r[i]) >> nn
-			if irev > uint64(i) {
-				r[i], r[irev] = r[irev], r[i]
-			}
-		}
-		return r[i]
-	}
-	funcs["reverseBits"] = func(x, n any) uint64 {
-		return bits.Reverse64(anyToUint64(x)) >> anyToUint64(n)
-	}
-	funcs["shl"] = func(x, n any) uint64 {
-		return anyToUint64(x) << anyToUint64(n)
-	}
-	funcs["logicalOr"] = func(x, y any) uint64 {
-		return anyToUint64(x) | anyToUint64(y)
-	}
-
-	bavardOpts := []func(*bavard.Bavard) error{bavard.Funcs(funcs)}
-
-	if err := bgen.GenerateWithOptions(conf, conf.Package, "./fft/template/", bavardOpts, entries...); err != nil {
-		return err
-	}
-
-	// put the generator in the parent dir (fr)
-	frDir := filepath.Dir(baseDir)
-	entries = []bavard.Entry{
-		{File: filepath.Join(frDir, "generator.go"), Templates: []string{"fr.generator.go.tmpl"}},
-	}
-	return bgen.GenerateWithOptions(conf, "fr", "./fft/template/", bavardOpts, entries...)
-}
-
-func anyToUint64(x any) uint64 {
-	switch v := x.(type) {
-	case int:
-		return uint64(v)
-	case int64:
-		return uint64(v)
-	case uint64:
-		return v
-	default:
-		panic("unknown type")
-	}
-}
diff --git a/internal/generator/fft/template/fr.generator.go.tmpl b/internal/generator/fft/template/fr.generator.go.tmpl
deleted file mode 100644
index 3cfaef1026..0000000000
--- a/internal/generator/fft/template/fr.generator.go.tmpl
+++ /dev/null
@@ -1,48 +0,0 @@
-import (
-	"fmt"
-	"math/big"
-	"math/bits"
-
-	"github.com/consensys/gnark-crypto/ecc"
-)
-
-// Generator returns a generator for Z/2^(log(m))Z
-// or an error if m is too big (required root of unity doesn't exist)
-func Generator(m uint64) (Element, error) {
-	x := ecc.NextPowerOfTwo(m)
-
-	var rootOfUnity Element
-	{{if eq .Name "bls12-377"}}
-		rootOfUnity.SetString("8065159656716812877374967518403273466521432693661810619979959746626482506078")
-		const maxOrderRoot uint64 = 47
-	{{else if eq .Name "bls12-381"}}
-		rootOfUnity.SetString("10238227357739495823651030575849232062558860180284477541189508159991286009131")
-		const maxOrderRoot uint64 = 32
-	{{else if eq .Name "bn254"}}
-		rootOfUnity.SetString("19103219067921713944291392827692070036145651957329286315305642004821462161904")
-		const maxOrderRoot uint64 = 28
-	{{else if eq .Name "bw6-761"}}
-		rootOfUnity.SetString("32863578547254505029601261939868325669770508939375122462904745766352256812585773382134936404344547323199885654433")
-		const maxOrderRoot uint64 = 46
-    {{else if eq .Name "bw6-633"}}
-		rootOfUnity.SetString("4991787701895089137426454739366935169846548798279261157172811661565882460884369603588700158257")
-		const maxOrderRoot uint64 = 20
-	{{else if eq .Name "bls24-315"}}
-		rootOfUnity.SetString("1792993287828780812362846131493071959406149719416102105453370749552622525216")
-       const maxOrderRoot uint64 = 22
-	{{else if eq .Name "bls24-317"}}
-		rootOfUnity.SetString("16532287748948254263922689505213135976137839535221842169193829039521719560631")
-       const maxOrderRoot uint64 = 60
-	{{end}}
-
-	// find generator for Z/2^(log(m))Z
-	logx := uint64(bits.TrailingZeros64(x))
-	if logx > maxOrderRoot {
-		return Element{}, fmt.Errorf("m (%d) is too big: the required root of unity does not exist", m)
-	}
-
-	expo := uint64(1 << (maxOrderRoot - logx))
-	var generator Element
-	generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x
-	return generator, nil
-}
diff --git a/internal/generator/fft/template/imports.go.tmpl b/internal/generator/fft/template/imports.go.tmpl
deleted file mode 100644
index c8d1a96222..0000000000
--- a/internal/generator/fft/template/imports.go.tmpl
+++ /dev/null
@@ -1,43 +0,0 @@
-{{ define "import_fr" }}
-
-{{ if eq .Name "bls12-377"}}
-	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
-{{ else if eq .Name "bls12-381"}}
-	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
-{{ else if eq .Name "bn254"}}
-	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
-{{ else if eq .Name "bw6-761"}}
-	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
-{{ else if eq .Name "bw6-633"}}
-	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
-{{ else if eq .Name "bls24-315"}}
-	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
-{{ else if eq .Name "bls24-317"}}
-	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
-{{ else if eq .Name "secp256k1"}}
-	"github.com/consensys/gnark-crypto/ecc/secp256k1/fr"
-{{end}}
-
-{{end}}
-
-{{ define "import_curve" }}
-{{if eq .Name "bls12-377"}}
-	curve "github.com/consensys/gnark-crypto/ecc/bls12-377"
-{{else if eq .Name "bls12-381"}}
-	curve "github.com/consensys/gnark-crypto/ecc/bls12-381"
-{{else if eq .Name "bn254"}}
-	curve "github.com/consensys/gnark-crypto/ecc/bn254"
-{{else if eq .Name "bw6-761"}}
-	curve "github.com/consensys/gnark-crypto/ecc/bw6-761"
-{{else if eq .Name "bw6-633"}}
-	curve "github.com/consensys/gnark-crypto/ecc/bw6-633"
-{{ else if eq .Name "bls24-315"}}
-	curve "github.com/consensys/gnark-crypto/ecc/bls24-315"
-{{ else if eq .Name "bls24-317"}}
-	curve "github.com/consensys/gnark-crypto/ecc/bls24-317"
-{{ else if eq .Name "secp256k1"}}
-	curve "github.com/consensys/gnark-crypto/ecc/secp256k1"
-{{end}}
-
-
-{{end}}
diff --git a/internal/generator/main.go b/internal/generator/main.go
index 76467b4d7e..619314f630 100644
--- a/internal/generator/main.go
+++ b/internal/generator/main.go
@@ -9,7 +9,7 @@ import (
 
 	"github.com/consensys/bavard"
 	"github.com/consensys/gnark-crypto/field/generator"
-	field "github.com/consensys/gnark-crypto/field/generator/config"
+	fieldConfig "github.com/consensys/gnark-crypto/field/generator/config"
 	"github.com/consensys/gnark-crypto/internal/generator/config"
 	"github.com/consensys/gnark-crypto/internal/generator/crypto/hash/mimc"
 	"github.com/consensys/gnark-crypto/internal/generator/crypto/hash/poseidon2"
@@ -18,7 +18,6 @@ import (
 	"github.com/consensys/gnark-crypto/internal/generator/edwards"
 	"github.com/consensys/gnark-crypto/internal/generator/edwards/eddsa"
 	"github.com/consensys/gnark-crypto/internal/generator/fflonk"
-	"github.com/consensys/gnark-crypto/internal/generator/fft"
 	fri "github.com/consensys/gnark-crypto/internal/generator/fri/template"
 	"github.com/consensys/gnark-crypto/internal/generator/gkr"
 	"github.com/consensys/gnark-crypto/internal/generator/hash_to_field"
@@ -52,17 +51,10 @@ func main() {
 	asmDirBuildPath := filepath.Join(baseDir, "field", "asm")
 	asmDirIncludePath := filepath.Join(baseDir, "..", "field", "asm")
 
-	// generate common assembly files depending on field number of words
-	assertNoError(generator.GenerateAMD64(4, asmDirBuildPath, true))
-	assertNoError(generator.GenerateAMD64(5, asmDirBuildPath, false))
-	assertNoError(generator.GenerateAMD64(6, asmDirBuildPath, false))
-	assertNoError(generator.GenerateAMD64(10, asmDirBuildPath, false))
-	assertNoError(generator.GenerateAMD64(12, asmDirBuildPath, false))
-
-	assertNoError(generator.GenerateARM64(4, asmDirBuildPath, false))
-	assertNoError(generator.GenerateARM64(6, asmDirBuildPath, false))
-	assertNoError(generator.GenerateARM64(10, asmDirBuildPath, false))
-	assertNoError(generator.GenerateARM64(12, asmDirBuildPath, false))
+	asmConfig := &fieldConfig.Assembly{BuildDir: asmDirBuildPath, IncludeDir: asmDirIncludePath}
+	// this enable the generation of fft functions;
+	// the parameters are hard coded in a lookup table for now for the modulus we use.
+	fftConfig := &fieldConfig.FFT{}
 
 	var wg sync.WaitGroup
 	for _, conf := range config.Curves {
@@ -73,18 +65,22 @@ func main() {
 
 			var err error
 
-			conf.Fp, err = field.NewFieldConfig("fp", "Element", conf.FpModulus, true)
+			conf.Fp, err = fieldConfig.NewFieldConfig("fp", "Element", conf.FpModulus, true)
 			assertNoError(err)
 
-			conf.Fr, err = field.NewFieldConfig("fr", "Element", conf.FrModulus, !conf.Equal(config.STARK_CURVE))
+			conf.Fr, err = fieldConfig.NewFieldConfig("fr", "Element", conf.FrModulus, !conf.Equal(config.STARK_CURVE))
 			assertNoError(err)
 
 			curveDir := filepath.Join(baseDir, "ecc", conf.Name)
 
 			conf.FpUnusedBits = 64 - (conf.Fp.NbBits % 64)
 
-			assertNoError(generator.GenerateFF(conf.Fr, filepath.Join(curveDir, "fr"), asmDirBuildPath, asmDirIncludePath))
-			assertNoError(generator.GenerateFF(conf.Fp, filepath.Join(curveDir, "fp"), asmDirBuildPath, asmDirIncludePath))
+			if !(conf.Equal(config.STARK_CURVE) || conf.Equal(config.SECP256K1)) {
+				assertNoError(generator.GenerateFF(conf.Fr, filepath.Join(curveDir, "fr"), generator.WithASM(asmConfig), generator.WithFFT(fftConfig)))
+			} else {
+				assertNoError(generator.GenerateFF(conf.Fr, filepath.Join(curveDir, "fr"), generator.WithASM(asmConfig)))
+			}
+			assertNoError(generator.GenerateFF(conf.Fp, filepath.Join(curveDir, "fp"), generator.WithASM(asmConfig)))
 
 			// generate ecdsa
 			assertNoError(ecdsa.Generate(conf, curveDir, bgen))
@@ -109,9 +105,6 @@ func main() {
 			// generate fri on fr
 			assertNoError(fri.Generate(conf, filepath.Join(curveDir, "fr", "fri"), bgen))
 
-			// generate fft on fr
-			assertNoError(fft.Generate(conf, filepath.Join(curveDir, "fr", "fft"), bgen))
-
 			if conf.Equal(config.BN254) || conf.Equal(config.BLS12_377) {
 				assertNoError(sis.Generate(conf, filepath.Join(curveDir, "fr", "sis"), bgen))
 			}
diff --git a/internal/generator/tower/asm/amd64/e2.go b/internal/generator/tower/asm/amd64/e2.go
index 9f372f351a..e61b127ded 100644
--- a/internal/generator/tower/asm/amd64/e2.go
+++ b/internal/generator/tower/asm/amd64/e2.go
@@ -18,11 +18,11 @@ type Fq2Amd64 struct {
 	*amd64.FFAmd64
 	config config.Curve
 	w      io.Writer
-	F      *field.FieldConfig
+	F      *field.Field
 }
 
 // NewFq2Amd64 ...
-func NewFq2Amd64(w io.Writer, F *field.FieldConfig, config config.Curve) *Fq2Amd64 {
+func NewFq2Amd64(w io.Writer, F *field.Field, config config.Curve) *Fq2Amd64 {
 	return &Fq2Amd64{
 		amd64.NewFFAmd64(w, F.NbWords),
 		config,

From b998989abdbec3eb5d4fc8f7bd460352a1ccffbd Mon Sep 17 00:00:00 2001
From: Gautam Botrel <gautam.botrel@gmail.com>
Date: Tue, 17 Dec 2024 07:13:46 -0600
Subject: [PATCH 097/114] feat: generate uint32 arith only for babybear and
 koalabear (#577)

---
 field/generator/config/field_config.go |  5 ++++-
 field/generator/generator_asm.go       | 10 ++++++++--
 field/generator/options.go             |  8 +++++---
 3 files changed, 17 insertions(+), 6 deletions(-)

diff --git a/field/generator/config/field_config.go b/field/generator/config/field_config.go
index a1c8e30fa5..e05a51ca48 100644
--- a/field/generator/config/field_config.go
+++ b/field/generator/config/field_config.go
@@ -103,7 +103,10 @@ func NewFieldConfig(packageName, elementName, modulus string, useAddChain bool)
 	}
 	// pre compute field constants
 	F.NbBits = bModulus.BitLen()
-	F.F31 = F.NbBits <= 31
+	// note: here we set F31 only for BabyBear and KoalaBear;
+	// we could do uint32 bit size for all fields with NbBits <= 31, but we keep it as is for now
+	// to avoid breaking changes
+	F.F31 = F.ModulusHex == "7f000001" || F.ModulusHex == "78000001" // F.NbBits <= 31
 	F.NbWords = len(bModulus.Bits())
 	F.NbWordsLastIndex = F.NbWords - 1
 
diff --git a/field/generator/generator_asm.go b/field/generator/generator_asm.go
index 8726ac7d78..a242433a3c 100644
--- a/field/generator/generator_asm.go
+++ b/field/generator/generator_asm.go
@@ -28,7 +28,10 @@ func generateARM64(F *config.Field, asm *config.Assembly) (string, error) {
 		return "", nil
 	}
 
-	os.MkdirAll(asm.BuildDir, 0755)
+	err := os.MkdirAll(asm.BuildDir, 0755)
+	if err != nil {
+		return "", fmt.Errorf("failed to create directory %s: %w", asm.BuildDir, err)
+	}
 	pathSrc := filepath.Join(asm.BuildDir, fmt.Sprintf(arm64.ElementASMFileName, F.NbWords))
 
 	hash, ok := mARM64.Load(pathSrc)
@@ -70,7 +73,10 @@ func generateAMD64(F *config.Field, asm *config.Assembly) (string, error) {
 	if !F.GenerateOpsAMD64 {
 		return "", nil
 	}
-	os.MkdirAll(asm.BuildDir, 0755)
+	err := os.MkdirAll(asm.BuildDir, 0755)
+	if err != nil {
+		return "", fmt.Errorf("failed to create directory %s: %w", asm.BuildDir, err)
+	}
 	pathSrc := filepath.Join(asm.BuildDir, fmt.Sprintf(amd64.ElementASMFileName, F.NbWords))
 
 	hash, ok := mAMD64.Load(pathSrc)
diff --git a/field/generator/options.go b/field/generator/options.go
index e89e8b1ad1..71f7ee0212 100644
--- a/field/generator/options.go
+++ b/field/generator/options.go
@@ -16,11 +16,11 @@ func (cfg *generatorConfig) HasFFT() bool {
 }
 
 func (cfg *generatorConfig) HasArm64() bool {
-	return cfg.asmConfig != nil
+	return cfg.asmConfig != nil && cfg.asmConfig.BuildDir != ""
 }
 
 func (cfg *generatorConfig) HasAMD64() bool {
-	return cfg.asmConfig != nil
+	return cfg.asmConfig != nil && cfg.asmConfig.BuildDir != ""
 }
 
 func WithFFT(cfg *config.FFT) Option {
@@ -38,7 +38,9 @@ func WithASM(cfg *config.Assembly) Option {
 // default options
 func generatorOptions(opts ...Option) generatorConfig {
 	// apply options
-	opt := generatorConfig{}
+	opt := generatorConfig{
+		asmConfig: &config.Assembly{},
+	}
 	for _, option := range opts {
 		option(&opt)
 	}

From 810063550bd41835cc019e677f7108bbc7b9f4bb Mon Sep 17 00:00:00 2001
From: "dependabot[bot]" <49699333+dependabot[bot]@users.noreply.github.com>
Date: Tue, 17 Dec 2024 14:43:52 +0100
Subject: [PATCH 098/114] build(deps): bump golang.org/x/crypto from 0.26.0 to
 0.31.0 (#579)

Signed-off-by: dependabot[bot] <support@github.com>
Co-authored-by: dependabot[bot] <49699333+dependabot[bot]@users.noreply.github.com>
---
 go.mod | 4 ++--
 go.sum | 8 ++++----
 2 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/go.mod b/go.mod
index e52cac12d6..226897a8a9 100644
--- a/go.mod
+++ b/go.mod
@@ -9,9 +9,9 @@ require (
 	github.com/mmcloughlin/addchain v0.4.0
 	github.com/spf13/cobra v1.8.1
 	github.com/stretchr/testify v1.9.0
-	golang.org/x/crypto v0.26.0
+	golang.org/x/crypto v0.31.0
 	golang.org/x/sync v0.1.0
-	golang.org/x/sys v0.24.0
+	golang.org/x/sys v0.28.0
 	gopkg.in/yaml.v2 v2.4.0
 )
 
diff --git a/go.sum b/go.sum
index 4b478e8750..5ff805b862 100644
--- a/go.sum
+++ b/go.sum
@@ -281,8 +281,8 @@ golang.org/x/crypto v0.0.0-20191011191535-87dc89f01550/go.mod h1:yigFU9vqHzYiE8U
 golang.org/x/crypto v0.0.0-20200622213623-75b288015ac9/go.mod h1:LzIPMQfyMNhhGPhUkYOs5KpL4U8rLKemX1yGLhDgUto=
 golang.org/x/crypto v0.0.0-20210711020723-a769d52b0f97/go.mod h1:GvvjBRRGRdwPK5ydBHafDWAxML/pGHZbMvKqRZ5+Abc=
 golang.org/x/crypto v0.0.0-20210921155107-089bfa567519/go.mod h1:GvvjBRRGRdwPK5ydBHafDWAxML/pGHZbMvKqRZ5+Abc=
-golang.org/x/crypto v0.26.0 h1:RrRspgV4mU+YwB4FYnuBoKsUapNIL5cohGAmSH3azsw=
-golang.org/x/crypto v0.26.0/go.mod h1:GY7jblb9wI+FOo5y8/S2oY4zWP07AkOJ4+jxCqdqn54=
+golang.org/x/crypto v0.31.0 h1:ihbySMvVjLAeSH1IbfcRTkD/iNscyz8rGzjF/E5hV6U=
+golang.org/x/crypto v0.31.0/go.mod h1:kDsLvtWBEx7MV9tJOj9bnXsPbxwJQ6csT/x4KIN4Ssk=
 golang.org/x/exp v0.0.0-20190121172915-509febef88a4/go.mod h1:CJ0aWSM057203Lf6IL+f9T1iT9GByDxfZKAQTCR3kQA=
 golang.org/x/exp v0.0.0-20190306152737-a1d7652674e8/go.mod h1:CJ0aWSM057203Lf6IL+f9T1iT9GByDxfZKAQTCR3kQA=
 golang.org/x/exp v0.0.0-20190510132918-efd6b22b2522/go.mod h1:ZjyILWgesfNpC6sMxTJOJm9Kp84zZh5NQWvqDGG3Qr8=
@@ -434,8 +434,8 @@ golang.org/x/sys v0.0.0-20220520151302-bc2c85ada10a/go.mod h1:oPkhp1MJrh7nUepCBc
 golang.org/x/sys v0.0.0-20220722155257-8c9f86f7a55f/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
 golang.org/x/sys v0.5.0/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
 golang.org/x/sys v0.6.0/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
-golang.org/x/sys v0.24.0 h1:Twjiwq9dn6R1fQcyiK+wQyHWfaz/BJB+YIpzU/Cv3Xg=
-golang.org/x/sys v0.24.0/go.mod h1:/VUhepiaJMQUp4+oa/7Zr1D23ma6VTLIYjOOTFZPUcA=
+golang.org/x/sys v0.28.0 h1:Fksou7UEQUWlKvIdsqzJmUmCX3cZuD2+P3XyyzwMhlA=
+golang.org/x/sys v0.28.0/go.mod h1:/VUhepiaJMQUp4+oa/7Zr1D23ma6VTLIYjOOTFZPUcA=
 golang.org/x/term v0.0.0-20201126162022-7de9c90e9dd1/go.mod h1:bj7SfCRtBDWHUb9snDiAeCFNEtKQo2Wmx5Cou7ajbmo=
 golang.org/x/term v0.0.0-20210927222741-03fcf44c2211/go.mod h1:jbD1KX2456YbFQfuXm/mYQcufACuNUgVhRMnK/tPxf8=
 golang.org/x/term v0.5.0/go.mod h1:jMB1sMXY+tzblOD4FWmEbocvup2/aLOaQEp7JmGp78k=

From cb03f64f5329d53a49a4402fc67d4c6c7b621e3c Mon Sep 17 00:00:00 2001
From: Gautam Botrel <gautam.botrel@gmail.com>
Date: Thu, 19 Dec 2024 10:29:27 -0600
Subject: [PATCH 099/114] perf: adds avx512 vector ops for koalabear and
 babybear fields (#568)

---
 field/asm/element_31b_amd64.s                 | 228 +++++++++
 field/babybear/arith.go                       |  49 --
 field/babybear/asm_avx.go                     |  15 +
 field/babybear/asm_noavx.go                   |  10 +
 field/babybear/doc.go                         |   2 +-
 field/babybear/element_amd64.s                |  10 +
 field/babybear/vector_amd64.go                | 192 +++++++
 field/babybear/vector_purego.go               |   2 +
 field/generator/asm/amd64/build.go            |  98 ++--
 .../{element_vec.go => element_vec_4words.go} |  10 +-
 field/generator/asm/amd64/element_vec_F31.go  | 470 ++++++++++++++++++
 field/generator/asm/arm64/build.go            |  62 +--
 field/generator/config/field_config.go        |   4 +-
 field/generator/generator.go                  |   6 +-
 field/generator/generator_asm.go              |  11 +-
 field/generator/generator_field.go            |  24 +-
 .../internal/templates/element/asm.go         |   2 +-
 .../templates/element/vector_ops_asm.go       | 190 +++++++
 field/internal/main.go                        |   5 +-
 field/koalabear/arith.go                      |  49 --
 field/koalabear/asm_avx.go                    |  15 +
 field/koalabear/asm_noavx.go                  |  10 +
 field/koalabear/doc.go                        |   2 +-
 field/koalabear/element_amd64.s               |  10 +
 field/koalabear/vector_amd64.go               | 192 +++++++
 field/koalabear/vector_purego.go              |   2 +
 26 files changed, 1441 insertions(+), 229 deletions(-)
 create mode 100644 field/asm/element_31b_amd64.s
 delete mode 100644 field/babybear/arith.go
 create mode 100644 field/babybear/asm_avx.go
 create mode 100644 field/babybear/asm_noavx.go
 create mode 100644 field/babybear/element_amd64.s
 create mode 100644 field/babybear/vector_amd64.go
 rename field/generator/asm/amd64/{element_vec.go => element_vec_4words.go} (99%)
 create mode 100644 field/generator/asm/amd64/element_vec_F31.go
 delete mode 100644 field/koalabear/arith.go
 create mode 100644 field/koalabear/asm_avx.go
 create mode 100644 field/koalabear/asm_noavx.go
 create mode 100644 field/koalabear/element_amd64.s
 create mode 100644 field/koalabear/vector_amd64.go

diff --git a/field/asm/element_31b_amd64.s b/field/asm/element_31b_amd64.s
new file mode 100644
index 0000000000..82451ced17
--- /dev/null
+++ b/field/asm/element_31b_amd64.s
@@ -0,0 +1,228 @@
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+#include "textflag.h"
+#include "funcdata.h"
+#include "go_asm.h"
+
+// addVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] + b[0...n]
+// n is the number of blocks of 16 elements to process
+TEXT ·addVec(SB), NOSPLIT, $0-32
+	MOVD         $const_q, AX
+	VPBROADCASTD AX, Z3
+	MOVQ         res+0(FP), CX
+	MOVQ         a+8(FP), AX
+	MOVQ         b+16(FP), DX
+	MOVQ         n+24(FP), BX
+
+loop_1:
+	TESTQ     BX, BX
+	JEQ       done_2     // n == 0, we are done
+	VMOVDQU32 0(AX), Z0
+	VMOVDQU32 0(DX), Z1
+	VPADDD    Z0, Z1, Z0 // a = a + b
+	VPSUBD    Z3, Z0, Z2 // t = a - q
+	VPMINUD   Z0, Z2, Z1 // b = min(t, a)
+	VMOVDQU32 Z1, 0(CX)  // res = b
+
+	// increment pointers to visit next element
+	ADDQ $64, AX
+	ADDQ $64, DX
+	ADDQ $64, CX
+	DECQ BX      // decrement n
+	JMP  loop_1
+
+done_2:
+	RET
+
+// subVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] - b[0...n]
+// n is the number of blocks of 16 elements to process
+TEXT ·subVec(SB), NOSPLIT, $0-32
+	MOVD         $const_q, AX
+	VPBROADCASTD AX, Z3
+	MOVQ         res+0(FP), CX
+	MOVQ         a+8(FP), AX
+	MOVQ         b+16(FP), DX
+	MOVQ         n+24(FP), BX
+
+loop_3:
+	TESTQ     BX, BX
+	JEQ       done_4     // n == 0, we are done
+	VMOVDQU32 0(AX), Z0
+	VMOVDQU32 0(DX), Z1
+	VPSUBD    Z1, Z0, Z0 // a = a - b
+	VPADDD    Z3, Z0, Z2 // t = a + q
+	VPMINUD   Z0, Z2, Z1 // b = min(t, a)
+	VMOVDQU32 Z1, 0(CX)  // res = b
+
+	// increment pointers to visit next element
+	ADDQ $64, AX
+	ADDQ $64, DX
+	ADDQ $64, CX
+	DECQ BX      // decrement n
+	JMP  loop_3
+
+done_4:
+	RET
+
+// sumVec(res *uint64, a *[]uint32, n uint64) res = sum(a[0...n])
+// n is the number of blocks of 16 elements to process
+TEXT ·sumVec(SB), NOSPLIT, $0-24
+
+	// We load 8 31bits values at a time and accumulate them into an accumulator of
+	// 8 quadwords (64bits). The caller then needs to reduce the result mod q.
+	// We can safely accumulate ~2**33 31bits values into a single accumulator.
+	// That gives us a maximum of 2**33 * 8 = 2**36 31bits values to sum safely.
+
+	MOVQ      t+0(FP), R15
+	MOVQ      a+8(FP), R14
+	MOVQ      n+16(FP), CX
+	VXORPS    Z2, Z2, Z2   // acc1 = 0
+	VMOVDQA64 Z2, Z3       // acc2 = 0
+
+loop_5:
+	TESTQ     CX, CX
+	JEQ       done_6      // n == 0, we are done
+	VPMOVZXDQ 0(R14), Z0  // load 8 31bits values in a1
+	VPMOVZXDQ 32(R14), Z1 // load 8 31bits values in a2
+	VPADDQ    Z0, Z2, Z2  // acc1 += a1
+	VPADDQ    Z1, Z3, Z3  // acc2 += a2
+
+	// increment pointers to visit next element
+	ADDQ $64, R14
+	DECQ CX       // decrement n
+	JMP  loop_5
+
+done_6:
+	VPADDQ    Z2, Z3, Z2 // acc1 += acc2
+	VMOVDQU64 Z2, 0(R15) // res = acc1
+	RET
+
+// mulVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] * b[0...n]
+// n is the number of blocks of 8 elements to process
+TEXT ·mulVec(SB), NOSPLIT, $0-32
+	MOVD         $const_q, AX
+	VPBROADCASTQ AX, Z3
+	MOVD         $const_qInvNeg, AX
+	VPBROADCASTQ AX, Z4
+
+	// Create mask for low dword in each qword
+	VPCMPEQB  Y0, Y0, Y0
+	VPMOVZXDQ Y0, Z6
+	MOVQ      res+0(FP), CX
+	MOVQ      a+8(FP), AX
+	MOVQ      b+16(FP), DX
+	MOVQ      n+24(FP), BX
+
+loop_7:
+	TESTQ     BX, BX
+	JEQ       done_8      // n == 0, we are done
+	VPMOVZXDQ 0(AX), Z0
+	VPMOVZXDQ 0(DX), Z1
+	VPMULUDQ  Z0, Z1, Z2  // P = a * b
+	VPANDQ    Z6, Z2, Z5  // m = uint32(P)
+	VPMULUDQ  Z5, Z4, Z5  // m = m * qInvNeg
+	VPANDQ    Z6, Z5, Z5  // m = uint32(m)
+	VPMULUDQ  Z5, Z3, Z5  // m = m * q
+	VPADDQ    Z2, Z5, Z2  // P = P + m
+	VPSRLQ    $32, Z2, Z2 // P = P >> 32
+	VPSUBD    Z3, Z2, Z5  // PL = P - q
+	VPMINUD   Z2, Z5, Z2  // P = min(P, PL)
+	VPMOVQD   Z2, 0(CX)   // res = P
+
+	// increment pointers to visit next element
+	ADDQ $32, AX
+	ADDQ $32, DX
+	ADDQ $32, CX
+	DECQ BX      // decrement n
+	JMP  loop_7
+
+done_8:
+	RET
+
+// scalarMulVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] * b
+// n is the number of blocks of 8 elements to process
+TEXT ·scalarMulVec(SB), NOSPLIT, $0-32
+	MOVD         $const_q, AX
+	VPBROADCASTQ AX, Z3
+	MOVD         $const_qInvNeg, AX
+	VPBROADCASTQ AX, Z4
+
+	// Create mask for low dword in each qword
+	VPCMPEQB     Y0, Y0, Y0
+	VPMOVZXDQ    Y0, Z6
+	MOVQ         res+0(FP), CX
+	MOVQ         a+8(FP), AX
+	MOVQ         b+16(FP), DX
+	MOVQ         n+24(FP), BX
+	VPBROADCASTD 0(DX), Z1
+
+loop_9:
+	TESTQ     BX, BX
+	JEQ       done_10     // n == 0, we are done
+	VPMOVZXDQ 0(AX), Z0
+	VPMULUDQ  Z0, Z1, Z2  // P = a * b
+	VPANDQ    Z6, Z2, Z5  // m = uint32(P)
+	VPMULUDQ  Z5, Z4, Z5  // m = m * qInvNeg
+	VPANDQ    Z6, Z5, Z5  // m = uint32(m)
+	VPMULUDQ  Z5, Z3, Z5  // m = m * q
+	VPADDQ    Z2, Z5, Z2  // P = P + m
+	VPSRLQ    $32, Z2, Z2 // P = P >> 32
+	VPSUBD    Z3, Z2, Z5  // PL = P - q
+	VPMINUD   Z2, Z5, Z2  // P = min(P, PL)
+	VPMOVQD   Z2, 0(CX)   // res = P
+
+	// increment pointers to visit next element
+	ADDQ $32, AX
+	ADDQ $32, CX
+	DECQ BX      // decrement n
+	JMP  loop_9
+
+done_10:
+	RET
+
+// innerProdVec(t *uint64, a,b *[]uint32, n uint64) res = sum(a[0...n] * b[0...n])
+// n is the number of blocks of 8 elements to process
+TEXT ·innerProdVec(SB), NOSPLIT, $0-32
+
+	// Similar to mulVec; we do most of the montgomery multiplication but don't do
+	// the final reduction. We accumulate the result like in sumVec and let the caller
+	// reduce mod q.
+
+	MOVD         $const_q, AX
+	VPBROADCASTQ AX, Z3
+	MOVD         $const_qInvNeg, AX
+	VPBROADCASTQ AX, Z4
+
+	// Create mask for low dword in each qword
+	VPCMPEQB  Y0, Y0, Y0
+	VPMOVZXDQ Y0, Z6
+	VXORPS    Z2, Z2, Z2    // acc = 0
+	MOVQ      t+0(FP), CX
+	MOVQ      a+8(FP), R14
+	MOVQ      b+16(FP), R15
+	MOVQ      n+24(FP), BX
+
+loop_11:
+	TESTQ     BX, BX
+	JEQ       done_12     // n == 0, we are done
+	VPMOVZXDQ 0(R14), Z0
+	VPMOVZXDQ 0(R15), Z1
+	VPMULUDQ  Z0, Z1, Z7  // P = a * b
+	VPANDQ    Z6, Z7, Z5  // m = uint32(P)
+	VPMULUDQ  Z5, Z4, Z5  // m = m * qInvNeg
+	VPANDQ    Z6, Z5, Z5  // m = uint32(m)
+	VPMULUDQ  Z5, Z3, Z5  // m = m * q
+	VPADDQ    Z7, Z5, Z7  // P = P + m
+	VPSRLQ    $32, Z7, Z7 // P = P >> 32
+
+	// accumulate P into acc, P is in [0, 2q] on 32bits max
+	VPADDQ Z7, Z2, Z2 // acc += P
+
+	// increment pointers to visit next element
+	ADDQ $32, R14
+	ADDQ $32, R15
+	DECQ BX       // decrement n
+	JMP  loop_11
+
+done_12:
+	VMOVDQU64 Z2, 0(CX) // res = acc
+	RET
diff --git a/field/babybear/arith.go b/field/babybear/arith.go
deleted file mode 100644
index 10c487d46a..0000000000
--- a/field/babybear/arith.go
+++ /dev/null
@@ -1,49 +0,0 @@
-// Copyright 2020-2024 Consensys Software Inc.
-// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
-
-// Code generated by consensys/gnark-crypto DO NOT EDIT
-
-package babybear
-
-import (
-	"math/bits"
-)
-
-// madd0 hi = a*b + c (discards lo bits)
-func madd0(a, b, c uint64) (hi uint64) {
-	var carry, lo uint64
-	hi, lo = bits.Mul64(a, b)
-	_, carry = bits.Add64(lo, c, 0)
-	hi, _ = bits.Add64(hi, 0, carry)
-	return
-}
-
-// madd1 hi, lo = a*b + c
-func madd1(a, b, c uint64) (hi uint64, lo uint64) {
-	var carry uint64
-	hi, lo = bits.Mul64(a, b)
-	lo, carry = bits.Add64(lo, c, 0)
-	hi, _ = bits.Add64(hi, 0, carry)
-	return
-}
-
-// madd2 hi, lo = a*b + c + d
-func madd2(a, b, c, d uint64) (hi uint64, lo uint64) {
-	var carry uint64
-	hi, lo = bits.Mul64(a, b)
-	c, carry = bits.Add64(c, d, 0)
-	hi, _ = bits.Add64(hi, 0, carry)
-	lo, carry = bits.Add64(lo, c, 0)
-	hi, _ = bits.Add64(hi, 0, carry)
-	return
-}
-
-func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) {
-	var carry uint64
-	hi, lo = bits.Mul64(a, b)
-	c, carry = bits.Add64(c, d, 0)
-	hi, _ = bits.Add64(hi, 0, carry)
-	lo, carry = bits.Add64(lo, c, 0)
-	hi, _ = bits.Add64(hi, e, carry)
-	return
-}
diff --git a/field/babybear/asm_avx.go b/field/babybear/asm_avx.go
new file mode 100644
index 0000000000..a8a213182a
--- /dev/null
+++ b/field/babybear/asm_avx.go
@@ -0,0 +1,15 @@
+//go:build !noavx
+
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package babybear
+
+import "golang.org/x/sys/cpu"
+
+var (
+	supportAvx512 = cpu.X86.HasAVX512 && cpu.X86.HasAVX512DQ
+	_             = supportAvx512
+)
diff --git a/field/babybear/asm_noavx.go b/field/babybear/asm_noavx.go
new file mode 100644
index 0000000000..00d2951e19
--- /dev/null
+++ b/field/babybear/asm_noavx.go
@@ -0,0 +1,10 @@
+//go:build noavx
+
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package babybear
+
+const supportAvx512 = false
diff --git a/field/babybear/doc.go b/field/babybear/doc.go
index 6a59371928..e134942b43 100644
--- a/field/babybear/doc.go
+++ b/field/babybear/doc.go
@@ -7,7 +7,7 @@
 //
 // The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
 //
-// Additionally babybear.Vector offers an API to manipulate []Element.
+// Additionally babybear.Vector offers an API to manipulate []Element using AVX512 instructions if available.
 //
 // The modulus is hardcoded in all the operations.
 //
diff --git a/field/babybear/element_amd64.s b/field/babybear/element_amd64.s
new file mode 100644
index 0000000000..11676c6f04
--- /dev/null
+++ b/field/babybear/element_amd64.s
@@ -0,0 +1,10 @@
+//go:build  !purego
+
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 17349933987904761959
+#include "../asm/element_31b_amd64.s"
+
diff --git a/field/babybear/vector_amd64.go b/field/babybear/vector_amd64.go
new file mode 100644
index 0000000000..2ace506476
--- /dev/null
+++ b/field/babybear/vector_amd64.go
@@ -0,0 +1,192 @@
+//go:build !purego
+
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package babybear
+
+//go:noescape
+func addVec(res, a, b *Element, n uint64)
+
+//go:noescape
+func subVec(res, a, b *Element, n uint64)
+
+//go:noescape
+func sumVec(t *uint64, a *Element, n uint64)
+
+//go:noescape
+func mulVec(res, a, b *Element, n uint64)
+
+//go:noescape
+func scalarMulVec(res, a, b *Element, n uint64)
+
+//go:noescape
+func innerProdVec(t *uint64, a, b *Element, n uint64)
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Add: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	if !supportAvx512 {
+		// call addVecGeneric
+		addVecGeneric(*vector, a, b)
+		return
+	}
+
+	const blockSize = 16
+	addVec(&(*vector)[0], &a[0], &b[0], n/blockSize)
+	if n%blockSize != 0 {
+		// call addVecGeneric on the rest
+		start := n - n%blockSize
+		addVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Sub: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	if !supportAvx512 {
+		// call subVecGeneric
+		subVecGeneric(*vector, a, b)
+		return
+	}
+
+	const blockSize = 16
+	subVec(&(*vector)[0], &a[0], &b[0], n/blockSize)
+	if n%blockSize != 0 {
+		// call subVecGeneric on the rest
+		start := n - n%blockSize
+		subVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	if len(a) != len(*vector) {
+		panic("vector.ScalarMul: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	if !supportAvx512 {
+		// call scalarMulVecGeneric
+		scalarMulVecGeneric(*vector, a, b)
+		return
+	}
+
+	const blockSize = 8
+	scalarMulVec(&(*vector)[0], &a[0], b, n/blockSize)
+	if n%blockSize != 0 {
+		// call scalarMulVecGeneric on the rest
+		start := n - n%blockSize
+		scalarMulVecGeneric((*vector)[start:], a[start:], b)
+	}
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	if !supportAvx512 {
+		// call sumVecGeneric
+		sumVecGeneric(&res, *vector)
+		return
+	}
+
+	const blockSize = 16
+	var t [8]uint64 // stores the accumulators (not reduced mod q)
+	sumVec(&t[0], &(*vector)[0], n/blockSize)
+	// we reduce the accumulators mod q and add to res
+	var v Element
+	for i := 0; i < 8; i++ {
+		t[i] %= q
+		v[0] = uint32(t[i])
+		res.Add(&res, &v)
+	}
+	if n%blockSize != 0 {
+		// call sumVecGeneric on the rest
+		start := n - n%blockSize
+		sumVecGeneric(&res, (*vector)[start:])
+	}
+
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	if n != uint64(len(other)) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	if !supportAvx512 {
+		// call innerProductVecGeneric
+		innerProductVecGeneric(&res, *vector, other)
+		return
+	}
+
+	const blockSize = 8
+	var t [8]uint64 // stores the accumulators (not reduced mod q)
+	innerProdVec(&t[0], &(*vector)[0], &other[0], n/blockSize)
+	// we reduce the accumulators mod q and add to res
+	var v Element
+	for i := 0; i < 8; i++ {
+		t[i] %= q
+		v[0] = uint32(t[i])
+		res.Add(&res, &v)
+	}
+	if n%blockSize != 0 {
+		// call innerProductVecGeneric on the rest
+		start := n - n%blockSize
+		innerProductVecGeneric(&res, (*vector)[start:], other[start:])
+	}
+
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	if !supportAvx512 {
+		// call mulVecGeneric
+		mulVecGeneric(*vector, a, b)
+		return
+	}
+
+	const blockSize = 8
+	mulVec(&(*vector)[0], &a[0], &b[0], n/blockSize)
+	if n%blockSize != 0 {
+		// call mulVecGeneric on the rest
+		start := n - n%blockSize
+		mulVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+}
diff --git a/field/babybear/vector_purego.go b/field/babybear/vector_purego.go
index 364c671c8a..3d9177a0ef 100644
--- a/field/babybear/vector_purego.go
+++ b/field/babybear/vector_purego.go
@@ -1,3 +1,5 @@
+//go:build purego || !amd64
+
 // Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
diff --git a/field/generator/asm/amd64/build.go b/field/generator/asm/amd64/build.go
index 7b99c3cbfe..3cce93670d 100644
--- a/field/generator/asm/amd64/build.go
+++ b/field/generator/asm/amd64/build.go
@@ -6,20 +6,13 @@ package amd64
 
 import (
 	"fmt"
-	"hash/fnv"
 	"io"
-	"os"
-	"path/filepath"
 	"strings"
 
 	"github.com/consensys/bavard/amd64"
-	"github.com/consensys/gnark-crypto/field/generator/config"
 )
 
 const SmallModulus = 6
-const (
-	ElementASMFileName = "element_%dw_amd64.s"
-)
 
 func NewFFAmd64(w io.Writer, nbWords int) *FFAmd64 {
 	F := &FFAmd64{
@@ -213,49 +206,9 @@ func (f *FFAmd64) mu() string {
 	return "$const_mu"
 }
 
-func GenerateFieldWrapper(w io.Writer, F *config.Field, asmDirBuildPath, asmDirIncludePath string) error {
-	// for each field we generate the defines for the modulus and the montgomery constant
-	f := NewFFAmd64(w, F.NbWords)
-
-	// we add the defines first, then the common asm, then the global variable section
-	// to enable correct compilations with #include in order.
-	f.WriteLn("")
-
-	hashAndInclude := func(fileName string) error {
-		// we hash the file content and include the hash in comment of the generated file
-		// to force the Go compiler to recompile the file if the content has changed
-		fData, err := os.ReadFile(filepath.Join(asmDirBuildPath, fileName))
-		if err != nil {
-			return err
-		}
-		// hash the file using FNV
-		hasher := fnv.New64()
-		hasher.Write(fData)
-		hash := hasher.Sum64()
-
-		f.WriteLn("// Code generated by gnark-crypto/generator. DO NOT EDIT.")
-		f.WriteLn(fmt.Sprintf("// We include the hash to force the Go compiler to recompile: %d", hash))
-		includePath := filepath.Join(asmDirIncludePath, fileName)
-		// on windows, we replace the "\" by "/"
-		if filepath.Separator == '\\' {
-			includePath = strings.ReplaceAll(includePath, "\\", "/")
-		}
-		f.WriteLn(fmt.Sprintf("#include \"%s\"\n", includePath))
-
-		return nil
-	}
-
-	toInclude := fmt.Sprintf(ElementASMFileName, F.NbWords)
-	if err := hashAndInclude(toInclude); err != nil {
-		return err
-	}
-
-	return nil
-}
-
 // GenerateCommonASM generates assembly code for the base field provided to goff
 // see internal/templates/ops*
-func GenerateCommonASM(w io.Writer, nbWords int, hasVector bool) error {
+func GenerateCommonASM(w io.Writer, nbWords, nbBits int, hasVector bool) error {
 	f := NewFFAmd64(w, nbWords)
 	f.Comment("Code generated by gnark-crypto/generator. DO NOT EDIT.")
 
@@ -264,6 +217,16 @@ func GenerateCommonASM(w io.Writer, nbWords int, hasVector bool) error {
 	f.WriteLn("#include \"go_asm.h\"")
 	f.WriteLn("")
 
+	if nbWords == 1 {
+		if nbBits == 31 {
+			return GenerateF31ASM(f, hasVector)
+		} else {
+			fmt.Printf("nbWords: %d, nbBits: %d\n", nbWords, nbBits)
+			panic("not implemented")
+		}
+
+	}
+
 	f.GenerateReduceDefine()
 
 	// reduce
@@ -288,13 +251,40 @@ func GenerateCommonASM(w io.Writer, nbWords int, hasVector bool) error {
 		f.Comment("Vector operations are partially derived from Dag Arne Osvik's work in github.com/a16z/vectorized-fields")
 		f.WriteLn("")
 
-		f.generateAddVec()
-		f.generateSubVec()
-		f.generateSumVec()
-		f.generateInnerProduct()
-		f.generateMulVec("scalarMulVec")
-		f.generateMulVec("mulVec")
+		f.generateAddVecW4()
+		f.generateSubVecW4()
+		f.generateSumVecW4()
+		f.generateInnerProductW4()
+		f.generateMulVecW4("scalarMulVec")
+		f.generateMulVecW4("mulVec")
+	}
+
+	return nil
+}
+
+func GenerateF31ASM(f *FFAmd64, hasVector bool) error {
+	if !hasVector {
+		return nil // nothing for now.
 	}
 
+	f.generateAddVecF31()
+	f.generateSubVecF31()
+	f.generateSumVecF31()
+	f.generateMulVecF31()
+	f.generateScalarMulVecF31()
+	f.generateInnerProdVecF31()
+
 	return nil
 }
+
+func ElementASMFileName(nbWords, nbBits int) string {
+	const nameW1 = "element_%db_amd64.s"
+	const nameWN = "element_%dw_amd64.s"
+	if nbWords == 1 {
+		if nbBits >= 32 {
+			panic("not implemented")
+		}
+		return fmt.Sprintf(nameW1, 31)
+	}
+	return fmt.Sprintf(nameWN, nbWords)
+}
diff --git a/field/generator/asm/amd64/element_vec.go b/field/generator/asm/amd64/element_vec_4words.go
similarity index 99%
rename from field/generator/asm/amd64/element_vec.go
rename to field/generator/asm/amd64/element_vec_4words.go
index b5de5e0c8e..14ac51f8ab 100644
--- a/field/generator/asm/amd64/element_vec.go
+++ b/field/generator/asm/amd64/element_vec_4words.go
@@ -12,7 +12,7 @@ import (
 
 // addVec res = a + b
 // func addVec(res, a, b *{{.ElementName}}, n uint64)
-func (f *FFAmd64) generateAddVec() {
+func (f *FFAmd64) generateAddVecW4() {
 	f.Comment("addVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] + b[0...n]")
 
 	const argSize = 4 * 8
@@ -74,7 +74,7 @@ func (f *FFAmd64) generateAddVec() {
 
 // subVec res = a - b
 // func subVec(res, a, b *{{.ElementName}}, n uint64)
-func (f *FFAmd64) generateSubVec() {
+func (f *FFAmd64) generateSubVecW4() {
 	f.Comment("subVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] - b[0...n]")
 
 	const argSize = 4 * 8
@@ -149,7 +149,7 @@ func (f *FFAmd64) generateSubVec() {
 }
 
 // sumVec res = sum(a[0...n])
-func (f *FFAmd64) generateSumVec() {
+func (f *FFAmd64) generateSumVecW4() {
 	f.Comment("sumVec(res, a *Element, n uint64) res = sum(a[0...n])")
 
 	const argSize = 3 * 8
@@ -441,7 +441,7 @@ func (f *FFAmd64) generateSumVec() {
 	f.Push(&registers, w0l, w1l, w2l, w3l, w3h)
 }
 
-func (f *FFAmd64) generateInnerProduct() {
+func (f *FFAmd64) generateInnerProductW4() {
 	f.Comment("innerProdVec(res, a,b *Element, n uint64) res = sum(a[0...n] * b[0...n])")
 
 	const argSize = 4 * 8
@@ -811,7 +811,7 @@ func (f *FFAmd64) generateInnerProduct() {
 	f.RET()
 }
 
-func (f *FFAmd64) generateMulVec(funcName string) {
+func (f *FFAmd64) generateMulVecW4(funcName string) {
 	scalarMul := funcName != "mulVec"
 
 	const argSize = 5 * 8
diff --git a/field/generator/asm/amd64/element_vec_F31.go b/field/generator/asm/amd64/element_vec_F31.go
new file mode 100644
index 0000000000..1d13fd5d4d
--- /dev/null
+++ b/field/generator/asm/amd64/element_vec_F31.go
@@ -0,0 +1,470 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package amd64
+
+import (
+	"github.com/consensys/bavard/amd64"
+)
+
+func (f *FFAmd64) generateAddVecF31() {
+	f.Comment("addVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] + b[0...n]")
+	f.Comment("n is the number of blocks of 16 elements to process")
+
+	const argSize = 4 * 8
+	stackSize := f.StackSize(f.NbWords*2+4, 0, 0)
+	registers := f.FnHeader("addVec", stackSize, argSize)
+	defer f.AssertCleanStack(stackSize, 0)
+
+	// registers & labels we need
+	addrA := f.Pop(&registers)
+	addrB := f.Pop(&registers)
+	addrRes := f.Pop(&registers)
+	len := f.Pop(&registers)
+
+	// AVX512 registers
+	a := amd64.Register("Z0")
+	b := amd64.Register("Z1")
+	t := amd64.Register("Z2")
+	q := amd64.Register("Z3")
+
+	// load q in Z3
+	f.WriteLn("MOVD $const_q, AX")
+	f.VPBROADCASTD("AX", q)
+
+	loop := f.NewLabel("loop")
+	done := f.NewLabel("done")
+
+	// load arguments
+	f.MOVQ("res+0(FP)", addrRes)
+	f.MOVQ("a+8(FP)", addrA)
+	f.MOVQ("b+16(FP)", addrB)
+	f.MOVQ("n+24(FP)", len)
+
+	f.LABEL(loop)
+
+	f.TESTQ(len, len)
+	f.JEQ(done, "n == 0, we are done")
+
+	// a = a + b
+	f.VMOVDQU32(addrA.At(0), a)
+	f.VMOVDQU32(addrB.At(0), b)
+	f.VPADDD(a, b, a, "a = a + b")
+	// t = a - q
+	f.VPSUBD(q, a, t, "t = a - q")
+	// b = min(t, a)
+	f.VPMINUD(a, t, b, "b = min(t, a)")
+
+	// move b to res
+	f.VMOVDQU32(b, addrRes.At(0), "res = b")
+
+	f.Comment("increment pointers to visit next element")
+	f.ADDQ("$64", addrA)
+	f.ADDQ("$64", addrB)
+	f.ADDQ("$64", addrRes)
+	f.DECQ(len, "decrement n")
+	f.JMP(loop)
+
+	f.LABEL(done)
+
+	f.RET()
+
+	f.Push(&registers, addrA, addrB, addrRes, len)
+
+}
+
+func (f *FFAmd64) generateSubVecF31() {
+	f.Comment("subVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] - b[0...n]")
+	f.Comment("n is the number of blocks of 16 elements to process")
+
+	const argSize = 4 * 8
+	stackSize := f.StackSize(f.NbWords*2+4, 0, 0)
+	registers := f.FnHeader("subVec", stackSize, argSize)
+	defer f.AssertCleanStack(stackSize, 0)
+
+	// registers & labels we need
+	addrA := f.Pop(&registers)
+	addrB := f.Pop(&registers)
+	addrRes := f.Pop(&registers)
+	len := f.Pop(&registers)
+
+	// AVX512 registers
+	a := amd64.Register("Z0")
+	b := amd64.Register("Z1")
+	t := amd64.Register("Z2")
+	q := amd64.Register("Z3")
+
+	// load q in Z3
+	f.WriteLn("MOVD $const_q, AX")
+	f.VPBROADCASTD("AX", q)
+
+	loop := f.NewLabel("loop")
+	done := f.NewLabel("done")
+
+	// load arguments
+	f.MOVQ("res+0(FP)", addrRes)
+	f.MOVQ("a+8(FP)", addrA)
+	f.MOVQ("b+16(FP)", addrB)
+	f.MOVQ("n+24(FP)", len)
+
+	f.LABEL(loop)
+
+	f.TESTQ(len, len)
+	f.JEQ(done, "n == 0, we are done")
+
+	// a = a - b
+	f.VMOVDQU32(addrA.At(0), a)
+	f.VMOVDQU32(addrB.At(0), b)
+
+	f.VPSUBD(b, a, a, "a = a - b")
+
+	// t = a + q
+	f.VPADDD(q, a, t, "t = a + q")
+
+	// b = min(t, a)
+	f.VPMINUD(a, t, b, "b = min(t, a)")
+
+	// move b to res
+	f.VMOVDQU32(b, addrRes.At(0), "res = b")
+
+	f.Comment("increment pointers to visit next element")
+	f.ADDQ("$64", addrA)
+	f.ADDQ("$64", addrB)
+	f.ADDQ("$64", addrRes)
+	f.DECQ(len, "decrement n")
+	f.JMP(loop)
+
+	f.LABEL(done)
+
+	f.RET()
+
+	f.Push(&registers, addrA, addrB, addrRes, len)
+
+}
+
+// sumVec res = sum(a[0...n])
+func (f *FFAmd64) generateSumVecF31() {
+	f.Comment("sumVec(res *uint64, a *[]uint32, n uint64) res = sum(a[0...n])")
+	f.Comment("n is the number of blocks of 16 elements to process")
+	const argSize = 3 * 8
+	stackSize := f.StackSize(f.NbWords*3+2, 0, 0)
+	registers := f.FnHeader("sumVec", stackSize, argSize, amd64.DX, amd64.AX)
+	defer f.AssertCleanStack(stackSize, 0)
+
+	f.WriteLn(`
+	// We load 8 31bits values at a time and accumulate them into an accumulator of
+	// 8 quadwords (64bits). The caller then needs to reduce the result mod q.
+	// We can safely accumulate ~2**33 31bits values into a single accumulator.
+	// That gives us a maximum of 2**33 * 8 = 2**36 31bits values to sum safely.
+	`)
+
+	// registers & labels we need
+	addrA := f.Pop(&registers)
+	addrT := f.Pop(&registers)
+	len := f.Pop(&registers)
+
+	// AVX512 registers
+	a1 := amd64.Register("Z0")
+	a2 := amd64.Register("Z1")
+	acc1 := amd64.Register("Z2")
+	acc2 := amd64.Register("Z3")
+
+	loop := f.NewLabel("loop")
+	done := f.NewLabel("done")
+
+	// load arguments
+	f.MOVQ("t+0(FP)", addrT)
+	f.MOVQ("a+8(FP)", addrA)
+	f.MOVQ("n+16(FP)", len)
+
+	// zeroize the accumulators
+	f.VXORPS(acc1, acc1, acc1, "acc1 = 0")
+	f.VMOVDQA64(acc1, acc2, "acc2 = 0")
+
+	f.LABEL(loop)
+
+	f.TESTQ(len, len)
+	f.JEQ(done, "n == 0, we are done")
+
+	// 1 cache line is typically 64 bytes, so we maintain 2 accumulators
+	f.VPMOVZXDQ(addrA.At(0), a1, "load 8 31bits values in a1")
+	f.VPMOVZXDQ(addrA.At(4), a2, "load 8 31bits values in a2")
+
+	f.VPADDQ(a1, acc1, acc1, "acc1 += a1")
+	f.VPADDQ(a2, acc2, acc2, "acc2 += a2")
+
+	f.Comment("increment pointers to visit next element")
+	f.ADDQ("$64", addrA)
+	f.DECQ(len, "decrement n")
+	f.JMP(loop)
+
+	f.LABEL(done)
+
+	// store t into res
+	f.VPADDQ(acc1, acc2, acc1, "acc1 += acc2")
+	f.VMOVDQU64(acc1, addrT.At(0), "res = acc1")
+
+	f.RET()
+
+	f.Push(&registers, addrA, addrT, len)
+}
+
+// mulVec res = a * b
+func (f *FFAmd64) generateMulVecF31() {
+	f.Comment("mulVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] * b[0...n]")
+	f.Comment("n is the number of blocks of 8 elements to process")
+	const argSize = 4 * 8
+	stackSize := f.StackSize(f.NbWords*2+4, 0, 0)
+	registers := f.FnHeader("mulVec", stackSize, argSize)
+	defer f.AssertCleanStack(stackSize, 0)
+
+	// registers & labels we need
+	addrA := f.Pop(&registers)
+	addrB := f.Pop(&registers)
+	addrRes := f.Pop(&registers)
+	len := f.Pop(&registers)
+
+	// AVX512 registers
+	a := amd64.Register("Z0")
+	b := amd64.Register("Z1")
+	P := amd64.Register("Z2")
+	q := amd64.Register("Z3")
+	qInvNeg := amd64.Register("Z4")
+	PL := amd64.Register("Z5")
+	LSW := amd64.Register("Z6")
+
+	// load q in Z3
+	f.WriteLn("MOVD $const_q, AX")
+	f.VPBROADCASTQ("AX", q)
+	f.WriteLn("MOVD $const_qInvNeg, AX")
+	f.VPBROADCASTQ("AX", qInvNeg)
+
+	f.Comment("Create mask for low dword in each qword")
+	f.VPCMPEQB("Y0", "Y0", "Y0")
+	f.VPMOVZXDQ("Y0", LSW)
+
+	loop := f.NewLabel("loop")
+	done := f.NewLabel("done")
+
+	// load arguments
+	f.MOVQ("res+0(FP)", addrRes)
+	f.MOVQ("a+8(FP)", addrA)
+	f.MOVQ("b+16(FP)", addrB)
+	f.MOVQ("n+24(FP)", len)
+
+	f.LABEL(loop)
+
+	f.TESTQ(len, len)
+	f.JEQ(done, "n == 0, we are done")
+
+	// a = a * b
+	f.VPMOVZXDQ(addrA.At(0), a)
+	f.VPMOVZXDQ(addrB.At(0), b)
+	f.VPMULUDQ(a, b, P, "P = a * b")
+	f.VPANDQ(LSW, P, PL, "m = uint32(P)")
+	f.VPMULUDQ(PL, qInvNeg, PL, "m = m * qInvNeg")
+	f.VPANDQ(LSW, PL, PL, "m = uint32(m)")
+	f.VPMULUDQ(PL, q, PL, "m = m * q")
+	f.VPADDQ(P, PL, P, "P = P + m")
+	f.VPSRLQ("$32", P, P, "P = P >> 32")
+
+	f.VPSUBD(q, P, PL, "PL = P - q")
+	f.VPMINUD(P, PL, P, "P = min(P, PL)")
+
+	// move P to res
+	f.VPMOVQD(P, addrRes.At(0), "res = P")
+
+	f.Comment("increment pointers to visit next element")
+	f.ADDQ("$32", addrA)
+	f.ADDQ("$32", addrB)
+	f.ADDQ("$32", addrRes)
+	f.DECQ(len, "decrement n")
+	f.JMP(loop)
+
+	f.LABEL(done)
+
+	f.RET()
+
+	f.Push(&registers, addrA, addrB, addrRes, len)
+
+}
+
+// scalarMulVec res = a * b
+func (f *FFAmd64) generateScalarMulVecF31() {
+	f.Comment("scalarMulVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] * b")
+	f.Comment("n is the number of blocks of 8 elements to process")
+	const argSize = 4 * 8
+	stackSize := f.StackSize(f.NbWords*2+4, 0, 0)
+	registers := f.FnHeader("scalarMulVec", stackSize, argSize)
+	defer f.AssertCleanStack(stackSize, 0)
+
+	// registers & labels we need
+	addrA := f.Pop(&registers)
+	addrB := f.Pop(&registers)
+	addrRes := f.Pop(&registers)
+	len := f.Pop(&registers)
+
+	// AVX512 registers
+	a := amd64.Register("Z0")
+	b := amd64.Register("Z1")
+	P := amd64.Register("Z2")
+	q := amd64.Register("Z3")
+	qInvNeg := amd64.Register("Z4")
+	PL := amd64.Register("Z5")
+	LSW := amd64.Register("Z6")
+
+	// load q in Z3
+	f.WriteLn("MOVD $const_q, AX")
+	f.VPBROADCASTQ("AX", q)
+	f.WriteLn("MOVD $const_qInvNeg, AX")
+	f.VPBROADCASTQ("AX", qInvNeg)
+
+	f.Comment("Create mask for low dword in each qword")
+	f.VPCMPEQB("Y0", "Y0", "Y0")
+	f.VPMOVZXDQ("Y0", LSW)
+
+	loop := f.NewLabel("loop")
+	done := f.NewLabel("done")
+
+	// load arguments
+	f.MOVQ("res+0(FP)", addrRes)
+	f.MOVQ("a+8(FP)", addrA)
+	f.MOVQ("b+16(FP)", addrB)
+	f.MOVQ("n+24(FP)", len)
+
+	f.VPBROADCASTD(addrB.At(0), b)
+
+	f.LABEL(loop)
+
+	f.TESTQ(len, len)
+	f.JEQ(done, "n == 0, we are done")
+
+	// a = a * b
+	f.VPMOVZXDQ(addrA.At(0), a)
+
+	f.VPMULUDQ(a, b, P, "P = a * b")
+	f.VPANDQ(LSW, P, PL, "m = uint32(P)")
+	f.VPMULUDQ(PL, qInvNeg, PL, "m = m * qInvNeg")
+	f.VPANDQ(LSW, PL, PL, "m = uint32(m)")
+	f.VPMULUDQ(PL, q, PL, "m = m * q")
+	f.VPADDQ(P, PL, P, "P = P + m")
+	f.VPSRLQ("$32", P, P, "P = P >> 32")
+
+	f.VPSUBD(q, P, PL, "PL = P - q")
+	f.VPMINUD(P, PL, P, "P = min(P, PL)")
+
+	// move P to res
+	f.VPMOVQD(P, addrRes.At(0), "res = P")
+
+	f.Comment("increment pointers to visit next element")
+	f.ADDQ("$32", addrA)
+	f.ADDQ("$32", addrRes)
+	f.DECQ(len, "decrement n")
+	f.JMP(loop)
+
+	f.LABEL(done)
+
+	f.RET()
+
+	f.Push(&registers, addrA, addrB, addrRes, len)
+}
+
+// innerProdVec res = sum(a * b)
+func (f *FFAmd64) generateInnerProdVecF31() {
+	f.Comment("innerProdVec(t *uint64, a,b *[]uint32, n uint64) res = sum(a[0...n] * b[0...n])")
+	f.Comment("n is the number of blocks of 8 elements to process")
+	const argSize = 4 * 8
+	stackSize := f.StackSize(f.NbWords*4+2, 0, 0)
+	registers := f.FnHeader("innerProdVec", stackSize, argSize, amd64.DX, amd64.AX)
+	defer f.AssertCleanStack(stackSize, 0)
+
+	f.WriteLn(`
+	// Similar to mulVec; we do most of the montgomery multiplication but don't do
+	// the final reduction. We accumulate the result like in sumVec and let the caller
+	// reduce mod q.
+	`)
+
+	// registers & labels we need
+	addrA := f.Pop(&registers)
+	addrB := f.Pop(&registers)
+	addrT := f.Pop(&registers)
+	len := f.Pop(&registers)
+
+	// AVX512 registers
+	a := amd64.Register("Z0")
+	b := amd64.Register("Z1")
+	acc := amd64.Register("Z2")
+	q := amd64.Register("Z3")
+	qInvNeg := amd64.Register("Z4")
+	PL := amd64.Register("Z5")
+	LSW := amd64.Register("Z6")
+	P := amd64.Register("Z7")
+
+	loop := f.NewLabel("loop")
+	done := f.NewLabel("done")
+
+	f.WriteLn("MOVD $const_q, AX")
+	f.VPBROADCASTQ("AX", q)
+	f.WriteLn("MOVD $const_qInvNeg, AX")
+	f.VPBROADCASTQ("AX", qInvNeg)
+
+	f.Comment("Create mask for low dword in each qword")
+	f.VPCMPEQB("Y0", "Y0", "Y0")
+	f.VPMOVZXDQ("Y0", LSW)
+
+	// zeroize the accumulators
+	f.VXORPS(acc, acc, acc, "acc = 0")
+
+	// load arguments
+	f.MOVQ("t+0(FP)", addrT)
+	f.MOVQ("a+8(FP)", addrA)
+	f.MOVQ("b+16(FP)", addrB)
+	f.MOVQ("n+24(FP)", len)
+
+	f.LABEL(loop)
+
+	f.TESTQ(len, len)
+	f.JEQ(done, "n == 0, we are done")
+
+	f.VPMOVZXDQ(addrA.At(0), a)
+	f.VPMOVZXDQ(addrB.At(0), b)
+
+	f.VPMULUDQ(a, b, P, "P = a * b")
+	f.VPANDQ(LSW, P, PL, "m = uint32(P)")
+	f.VPMULUDQ(PL, qInvNeg, PL, "m = m * qInvNeg")
+	f.VPANDQ(LSW, PL, PL, "m = uint32(m)")
+	f.VPMULUDQ(PL, q, PL, "m = m * q")
+	f.VPADDQ(P, PL, P, "P = P + m")
+	f.VPSRLQ("$32", P, P, "P = P >> 32")
+
+	// we can accumulate ~2**32 32bits values into a single accumulator without overflow;
+	// that gives us a maximum of 2**32 * 8 = 2**35 32bits values to sum safely.
+	f.Comment("accumulate P into acc, P is in [0, 2q] on 32bits max")
+	f.VPADDQ(P, acc, acc, "acc += P")
+
+	f.Comment("increment pointers to visit next element")
+	f.ADDQ("$32", addrA)
+	f.ADDQ("$32", addrB)
+	f.DECQ(len, "decrement n")
+	f.JMP(loop)
+
+	f.LABEL(done)
+
+	// store t into res
+	f.VMOVDQU64(acc, addrT.At(0), "res = acc")
+
+	f.RET()
+
+	f.Push(&registers, addrA, addrT, len)
+}
diff --git a/field/generator/asm/arm64/build.go b/field/generator/asm/arm64/build.go
index 93170d5c75..c0d617410a 100644
--- a/field/generator/asm/arm64/build.go
+++ b/field/generator/asm/arm64/build.go
@@ -2,18 +2,10 @@ package arm64
 
 import (
 	"fmt"
-	"hash/fnv"
 	"io"
-	"os"
-	"path/filepath"
 	"strings"
 
 	"github.com/consensys/bavard/arm64"
-	"github.com/consensys/gnark-crypto/field/generator/config"
-)
-
-const (
-	ElementASMFileName = "element_%dw_arm64.s"
 )
 
 type defineFn func(args ...arm64.Register)
@@ -52,49 +44,9 @@ type FFArm64 struct {
 	mDefines             map[string]defineFn
 }
 
-func GenerateFieldWrapper(w io.Writer, F *config.Field, asmDirBuildPath, asmDirIncludePath string) error {
-	// for each field we generate the defines for the modulus and the montgomery constant
-	f := NewFFArm64(w, F.NbWords)
-
-	// we add the defines first, then the common asm, then the global variable section
-	// to enable correct compilations with #include in order.
-	f.WriteLn("")
-
-	hashAndInclude := func(fileName string) error {
-		// we hash the file content and include the hash in comment of the generated file
-		// to force the Go compiler to recompile the file if the content has changed
-		fData, err := os.ReadFile(filepath.Join(asmDirBuildPath, fileName))
-		if err != nil {
-			return err
-		}
-		// hash the file using FNV
-		hasher := fnv.New64()
-		hasher.Write(fData)
-		hash := hasher.Sum64()
-
-		f.WriteLn("// Code generated by gnark-crypto/generator. DO NOT EDIT.")
-		f.WriteLn(fmt.Sprintf("// We include the hash to force the Go compiler to recompile: %d", hash))
-		includePath := filepath.Join(asmDirIncludePath, fileName)
-		// on windows, we replace the "\" by "/"
-		if filepath.Separator == '\\' {
-			includePath = strings.ReplaceAll(includePath, "\\", "/")
-		}
-		f.WriteLn(fmt.Sprintf("#include \"%s\"\n", includePath))
-
-		return nil
-	}
-
-	toInclude := fmt.Sprintf(ElementASMFileName, F.NbWords)
-	if err := hashAndInclude(toInclude); err != nil {
-		return err
-	}
-
-	return nil
-}
-
 // GenerateCommonASM generates assembly code for the base field provided to goff
 // see internal/templates/ops*
-func GenerateCommonASM(w io.Writer, nbWords int, hasVector bool) error {
+func GenerateCommonASM(w io.Writer, nbWords, nbBits int, hasVector bool) error {
 	f := NewFFArm64(w, nbWords)
 	f.Comment("Code generated by gnark-crypto/generator. DO NOT EDIT.")
 
@@ -253,6 +205,14 @@ func (f *FFArm64) qInv0() string {
 	return "$const_qInvNeg"
 }
 
-func (f *FFArm64) qi(i int) string {
-	return fmt.Sprintf("$const_q%d", i)
+func ElementASMFileName(nbWords, nbBits int) string {
+	const nameW1 = "element_%db_arm64.s"
+	const nameWN = "element_%dw_arm64.s"
+	if nbWords == 1 {
+		if nbBits >= 32 {
+			panic("not implemented")
+		}
+		return fmt.Sprintf(nameW1, 31)
+	}
+	return fmt.Sprintf(nameWN, nbWords)
 }
diff --git a/field/generator/config/field_config.go b/field/generator/config/field_config.go
index e05a51ca48..aa96da2fbe 100644
--- a/field/generator/config/field_config.go
+++ b/field/generator/config/field_config.go
@@ -291,14 +291,14 @@ func NewFieldConfig(packageName, elementName, modulus string, useAddChain bool)
 	// note: to simplify output files generated, we generated ASM code only for
 	// moduli that meet the condition F.NoCarry
 	// asm code generation for moduli with more than 6 words can be optimized further
-	F.GenerateOpsAMD64 = F.NoCarry && F.NbWords <= 12 && F.NbWords > 1
+	F.GenerateOpsAMD64 = F.F31 || (F.NoCarry && F.NbWords <= 12 && F.NbWords > 1)
 	if F.NbWords == 4 && F.GenerateOpsAMD64 && F.NbBits <= 225 {
 		// 4 words field with 225 bits or less have no vector ops
 		// for now since we generate both in same file we disable
 		// TODO @gbotrel
 		F.GenerateOpsAMD64 = false
 	}
-	F.GenerateVectorOpsAMD64 = F.GenerateOpsAMD64 && F.NbWords == 4 && F.NbBits > 225
+	F.GenerateVectorOpsAMD64 = F.F31 || (F.GenerateOpsAMD64 && F.NbWords == 4 && F.NbBits > 225)
 	F.GenerateOpsARM64 = F.GenerateOpsAMD64 && (F.NbWords%2 == 0)
 	F.GenerateVectorOpsARM64 = false
 
diff --git a/field/generator/generator.go b/field/generator/generator.go
index 4feac2c76b..29943ef6e4 100644
--- a/field/generator/generator.go
+++ b/field/generator/generator.go
@@ -35,7 +35,11 @@ func GenerateFF(F *config.Field, outputDir string, options ...Option) error {
 	}
 
 	// generate field
-	if err := generateField(F, outputDir, cfg.asmConfig.IncludeDir, hashArm64, hashAMD64); err != nil {
+	asmIncludeDir := ""
+	if cfg.HasArm64() || cfg.HasAMD64() {
+		asmIncludeDir = cfg.asmConfig.IncludeDir
+	}
+	if err := generateField(F, outputDir, asmIncludeDir, hashArm64, hashAMD64); err != nil {
 		return err
 	}
 
diff --git a/field/generator/generator_asm.go b/field/generator/generator_asm.go
index a242433a3c..829f8d8fe2 100644
--- a/field/generator/generator_asm.go
+++ b/field/generator/generator_asm.go
@@ -32,7 +32,7 @@ func generateARM64(F *config.Field, asm *config.Assembly) (string, error) {
 	if err != nil {
 		return "", fmt.Errorf("failed to create directory %s: %w", asm.BuildDir, err)
 	}
-	pathSrc := filepath.Join(asm.BuildDir, fmt.Sprintf(arm64.ElementASMFileName, F.NbWords))
+	pathSrc := filepath.Join(asm.BuildDir, arm64.ElementASMFileName(F.NbWords, F.NbBits))
 
 	hash, ok := mARM64.Load(pathSrc)
 	if ok {
@@ -47,7 +47,7 @@ func generateARM64(F *config.Field, asm *config.Assembly) (string, error) {
 		return "", err
 	}
 
-	if err := arm64.GenerateCommonASM(f, F.NbWords, F.GenerateVectorOpsARM64); err != nil {
+	if err := arm64.GenerateCommonASM(f, F.NbWords, F.NbBits, F.GenerateVectorOpsARM64); err != nil {
 		_ = f.Close()
 		return "", err
 	}
@@ -77,7 +77,7 @@ func generateAMD64(F *config.Field, asm *config.Assembly) (string, error) {
 	if err != nil {
 		return "", fmt.Errorf("failed to create directory %s: %w", asm.BuildDir, err)
 	}
-	pathSrc := filepath.Join(asm.BuildDir, fmt.Sprintf(amd64.ElementASMFileName, F.NbWords))
+	pathSrc := filepath.Join(asm.BuildDir, amd64.ElementASMFileName(F.NbWords, F.NbBits))
 
 	hash, ok := mAMD64.Load(pathSrc)
 	if ok {
@@ -92,7 +92,7 @@ func generateAMD64(F *config.Field, asm *config.Assembly) (string, error) {
 		return "", err
 	}
 
-	if err := amd64.GenerateCommonASM(f, F.NbWords, F.GenerateVectorOpsAMD64); err != nil {
+	if err := amd64.GenerateCommonASM(f, F.NbWords, F.NbBits, F.GenerateVectorOpsAMD64); err != nil {
 		_ = f.Close()
 		return "", err
 	}
@@ -132,8 +132,7 @@ func hashFile(filePath string) (string, error) {
 	return fmt.Sprintf("%d", hash64), nil
 }
 
-func newASMWrapperData(hash, asmDirIncludePath, fileName string, nbWords int) (data ASMWrapperData, err error) {
-	fileName = fmt.Sprintf(fileName, nbWords)
+func newASMWrapperData(hash, asmDirIncludePath, fileName string) (data ASMWrapperData, err error) {
 
 	includePath := filepath.Join(asmDirIncludePath, fileName)
 	// on windows, we replace the "\" by "/"
diff --git a/field/generator/generator_field.go b/field/generator/generator_field.go
index 64111c325f..7e8b27cc10 100644
--- a/field/generator/generator_field.go
+++ b/field/generator/generator_field.go
@@ -106,14 +106,14 @@ func generateField(F *config.Field, outputDir, asmDirIncludePath, hashArm64, has
 	var err error
 
 	if F.GenerateOpsAMD64 {
-		amd64d, err = newASMWrapperData(hashAMD64, asmDirIncludePath, amd64.ElementASMFileName, F.NbWords)
+		amd64d, err = newASMWrapperData(hashAMD64, asmDirIncludePath, amd64.ElementASMFileName(F.NbWords, F.NbBits))
 		if err != nil {
 			return err
 		}
 	}
 
 	if F.GenerateOpsARM64 {
-		arm64d, err = newASMWrapperData(hashArm64, asmDirIncludePath, arm64.ElementASMFileName, F.NbWords)
+		arm64d, err = newASMWrapperData(hashArm64, asmDirIncludePath, arm64.ElementASMFileName(F.NbWords, F.NbBits))
 		if err != nil {
 			return err
 		}
@@ -126,6 +126,7 @@ func generateField(F *config.Field, outputDir, asmDirIncludePath, hashArm64, has
 	} else if !F.GenerateOpsARM64 {
 		pureGoBuildTag = "purego || (!amd64)"
 	}
+
 	pureGoVectorBuildTag := "purego || (!amd64 && !arm64)"
 	if !F.GenerateVectorOpsAMD64 && !F.GenerateVectorOpsARM64 {
 		pureGoVectorBuildTag = ""
@@ -133,6 +134,11 @@ func generateField(F *config.Field, outputDir, asmDirIncludePath, hashArm64, has
 		pureGoVectorBuildTag = "purego || (!amd64)"
 	}
 
+	if F.F31 {
+		pureGoBuildTag = "" // always generate pure go for F31
+		pureGoVectorBuildTag = "purego || (!amd64)"
+	}
+
 	var g errgroup.Group
 
 	g.Go(generate("element.go", sourceFiles))
@@ -145,18 +151,20 @@ func generateField(F *config.Field, outputDir, asmDirIncludePath, hashArm64, has
 	g.Go(generate("element_amd64.s", []string{element.IncludeASM}, only(F.GenerateOpsAMD64), withBuildTag("!purego"), withData(amd64d)))
 	g.Go(generate("element_arm64.s", []string{element.IncludeASM}, only(F.GenerateOpsARM64), withBuildTag("!purego"), withData(arm64d)))
 
-	g.Go(generate("element_amd64.go", []string{element.OpsAMD64, element.MulDoc}, only(F.GenerateOpsAMD64), withBuildTag("!purego")))
-	g.Go(generate("element_arm64.go", []string{element.OpsARM64, element.MulNoCarry, element.Reduce}, only(F.GenerateOpsARM64), withBuildTag("!purego")))
+	g.Go(generate("element_amd64.go", []string{element.OpsAMD64, element.MulDoc}, only(!F.F31 && F.GenerateOpsAMD64), withBuildTag("!purego")))
+	g.Go(generate("element_arm64.go", []string{element.OpsARM64, element.MulNoCarry, element.Reduce}, only(!F.F31 && F.GenerateOpsARM64), withBuildTag("!purego")))
 
 	g.Go(generate("element_purego.go", []string{element.OpsNoAsm, element.MulCIOS, element.MulNoCarry, element.Reduce, element.MulDoc}, withBuildTag(pureGoBuildTag)))
 
-	g.Go(generate("vector_amd64.go", []string{element.VectorOpsAmd64}, only(F.GenerateVectorOpsAMD64), withBuildTag("!purego")))
-	g.Go(generate("vector_arm64.go", []string{element.VectorOpsArm64}, only(F.GenerateVectorOpsARM64), withBuildTag("!purego")))
+	g.Go(generate("vector_amd64.go", []string{element.VectorOpsAmd64}, only(!F.F31 && F.GenerateVectorOpsAMD64), withBuildTag("!purego")))
+	g.Go(generate("vector_arm64.go", []string{element.VectorOpsArm64}, only(!F.F31 && F.GenerateVectorOpsARM64), withBuildTag("!purego")))
+
+	g.Go(generate("vector_amd64.go", []string{element.VectorOpsAmd64F31}, only(F.F31 && F.GenerateVectorOpsAMD64), withBuildTag("!purego")))
 
 	g.Go(generate("vector_purego.go", []string{element.VectorOpsPureGo}, withBuildTag(pureGoVectorBuildTag)))
 
-	g.Go(generate("asm_adx.go", []string{element.Asm}, only(F.GenerateOpsAMD64), withBuildTag("!noadx")))
-	g.Go(generate("asm_noadx.go", []string{element.AsmNoAdx}, only(F.GenerateOpsAMD64), withBuildTag("noadx")))
+	g.Go(generate("asm_adx.go", []string{element.Asm}, only(!F.F31 && F.GenerateOpsAMD64), withBuildTag("!noadx")))
+	g.Go(generate("asm_noadx.go", []string{element.AsmNoAdx}, only(!F.F31 && F.GenerateOpsAMD64), withBuildTag("noadx")))
 	g.Go(generate("asm_avx.go", []string{element.Avx}, only(F.GenerateVectorOpsAMD64), withBuildTag("!noavx")))
 	g.Go(generate("asm_noavx.go", []string{element.NoAvx}, only(F.GenerateVectorOpsAMD64), withBuildTag("noavx")))
 
diff --git a/field/generator/internal/templates/element/asm.go b/field/generator/internal/templates/element/asm.go
index ed7fac7b40..53cadbc0a8 100644
--- a/field/generator/internal/templates/element/asm.go
+++ b/field/generator/internal/templates/element/asm.go
@@ -14,7 +14,7 @@ const Avx = `
 import 	"golang.org/x/sys/cpu"
 
 var (
-	supportAvx512 = supportAdx && cpu.X86.HasAVX512 && cpu.X86.HasAVX512DQ
+	supportAvx512 = {{- if not .F31 }}supportAdx && {{- end}}cpu.X86.HasAVX512 && cpu.X86.HasAVX512DQ
 	_ = supportAvx512
 )
 `
diff --git a/field/generator/internal/templates/element/vector_ops_asm.go b/field/generator/internal/templates/element/vector_ops_asm.go
index e4de4f1b27..aa00830dfd 100644
--- a/field/generator/internal/templates/element/vector_ops_asm.go
+++ b/field/generator/internal/templates/element/vector_ops_asm.go
@@ -145,3 +145,193 @@ func mulVec(res, a, b *{{.ElementName}}, n uint64, qInvNeg uint64)
 `
 
 const VectorOpsArm64 = VectorOpsPureGo
+
+const VectorOpsAmd64F31 = `
+
+//go:noescape
+func addVec(res, a, b *{{.ElementName}}, n uint64)
+
+//go:noescape
+func subVec(res, a, b *{{.ElementName}}, n uint64)
+
+//go:noescape
+func sumVec(t *uint64, a *{{.ElementName}}, n uint64)
+
+//go:noescape
+func mulVec(res, a, b *{{.ElementName}}, n uint64)
+
+//go:noescape
+func scalarMulVec(res, a, b *{{.ElementName}}, n uint64)
+
+//go:noescape
+func innerProdVec(t *uint64, a, b *{{.ElementName}}, n uint64)
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Add: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	if !supportAvx512 {
+		// call addVecGeneric
+		addVecGeneric(*vector, a, b)
+		return
+	}
+
+	const blockSize = 16
+	addVec(&(*vector)[0], &a[0], &b[0], n/blockSize)
+	if n % blockSize != 0 {
+		// call addVecGeneric on the rest
+		start := n - n % blockSize
+		addVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Sub: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	if !supportAvx512 {
+		// call subVecGeneric
+		subVecGeneric(*vector, a, b)
+		return
+	}
+
+	const blockSize = 16
+	subVec(&(*vector)[0], &a[0], &b[0], n/blockSize)
+	if n % blockSize != 0 {
+		// call subVecGeneric on the rest
+		start := n - n % blockSize
+		subVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *{{.ElementName}}) {
+	if len(a) != len(*vector) {
+		panic("vector.ScalarMul: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	if !supportAvx512 {
+		// call scalarMulVecGeneric
+		scalarMulVecGeneric(*vector, a, b)
+		return
+	}
+
+	const blockSize = 8
+	scalarMulVec(&(*vector)[0], &a[0], b, n/blockSize)
+	if n % blockSize != 0 {
+		// call scalarMulVecGeneric on the rest
+		start := n - n % blockSize
+		scalarMulVecGeneric((*vector)[start:], a[start:], b)
+	}
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res {{.ElementName}}) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	if !supportAvx512 {
+		// call sumVecGeneric
+		sumVecGeneric(&res, *vector)
+		return
+	}
+
+	const blockSize = 16
+	var t [8]uint64 // stores the accumulators (not reduced mod q)
+	sumVec(&t[0], &(*vector)[0], n/blockSize)
+	// we reduce the accumulators mod q and add to res
+	var v {{.ElementName}}
+	for i := 0; i < 8; i++ {
+		t[i] %= q
+		v[0] = uint32(t[i])
+		res.Add(&res, &v)
+	}
+	if n % blockSize != 0 {
+		// call sumVecGeneric on the rest
+		start := n - n % blockSize
+		sumVecGeneric(&res, (*vector)[start:])
+	}
+
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res {{.ElementName}}) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	if n != uint64(len(other)) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	if !supportAvx512 {
+		// call innerProductVecGeneric
+		innerProductVecGeneric(&res, *vector, other)
+		return
+	}
+
+	const blockSize = 8
+	var t [8]uint64 // stores the accumulators (not reduced mod q)
+	innerProdVec(&t[0], &(*vector)[0], &other[0], n/blockSize)
+	// we reduce the accumulators mod q and add to res
+	var v {{.ElementName}}
+	for i := 0; i < 8; i++ {
+		t[i] %= q
+		v[0] = uint32(t[i])
+		res.Add(&res, &v)
+	}
+	if n % blockSize != 0 {
+		// call innerProductVecGeneric on the rest
+		start := n - n % blockSize
+		innerProductVecGeneric(&res, (*vector)[start:], other[start:])
+	}
+
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	if !supportAvx512 {
+		// call mulVecGeneric
+		mulVecGeneric(*vector, a, b)
+		return
+	}
+
+	const blockSize = 8
+	mulVec(&(*vector)[0], &a[0], &b[0], n/blockSize)
+	if n % blockSize != 0 {
+		// call mulVecGeneric on the rest
+		start := n - n % blockSize
+		mulVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+}
+
+
+
+`
diff --git a/field/internal/main.go b/field/internal/main.go
index ce7631131a..d2dcc7294f 100644
--- a/field/internal/main.go
+++ b/field/internal/main.go
@@ -23,13 +23,16 @@ func main() {
 		{"babybear", "0x78000001"},  // 2^31 - 2^27 + 1 ==> 2-adicity 27
 	}
 
+	// generate assembly
+	asmDirIncludePath := filepath.Join("..", "asm")
+
 	for _, f := range fields {
 		fc, err := config.NewFieldConfig(f.name, "Element", f.modulus, true)
 		if err != nil {
 			panic(err)
 		}
 		if err := generator.GenerateFF(fc, filepath.Join("..", f.name),
-			generator.WithASM(&config.Assembly{BuildDir: "../asm", IncludeDir: "../asm"}),
+			generator.WithASM(&config.Assembly{BuildDir: asmDirIncludePath, IncludeDir: asmDirIncludePath}),
 			generator.WithFFT(&config.FFT{}), // TODO @gbotrel
 		); err != nil {
 			panic(err)
diff --git a/field/koalabear/arith.go b/field/koalabear/arith.go
deleted file mode 100644
index f8ed8eb91f..0000000000
--- a/field/koalabear/arith.go
+++ /dev/null
@@ -1,49 +0,0 @@
-// Copyright 2020-2024 Consensys Software Inc.
-// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
-
-// Code generated by consensys/gnark-crypto DO NOT EDIT
-
-package koalabear
-
-import (
-	"math/bits"
-)
-
-// madd0 hi = a*b + c (discards lo bits)
-func madd0(a, b, c uint64) (hi uint64) {
-	var carry, lo uint64
-	hi, lo = bits.Mul64(a, b)
-	_, carry = bits.Add64(lo, c, 0)
-	hi, _ = bits.Add64(hi, 0, carry)
-	return
-}
-
-// madd1 hi, lo = a*b + c
-func madd1(a, b, c uint64) (hi uint64, lo uint64) {
-	var carry uint64
-	hi, lo = bits.Mul64(a, b)
-	lo, carry = bits.Add64(lo, c, 0)
-	hi, _ = bits.Add64(hi, 0, carry)
-	return
-}
-
-// madd2 hi, lo = a*b + c + d
-func madd2(a, b, c, d uint64) (hi uint64, lo uint64) {
-	var carry uint64
-	hi, lo = bits.Mul64(a, b)
-	c, carry = bits.Add64(c, d, 0)
-	hi, _ = bits.Add64(hi, 0, carry)
-	lo, carry = bits.Add64(lo, c, 0)
-	hi, _ = bits.Add64(hi, 0, carry)
-	return
-}
-
-func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) {
-	var carry uint64
-	hi, lo = bits.Mul64(a, b)
-	c, carry = bits.Add64(c, d, 0)
-	hi, _ = bits.Add64(hi, 0, carry)
-	lo, carry = bits.Add64(lo, c, 0)
-	hi, _ = bits.Add64(hi, e, carry)
-	return
-}
diff --git a/field/koalabear/asm_avx.go b/field/koalabear/asm_avx.go
new file mode 100644
index 0000000000..85e3e37582
--- /dev/null
+++ b/field/koalabear/asm_avx.go
@@ -0,0 +1,15 @@
+//go:build !noavx
+
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package koalabear
+
+import "golang.org/x/sys/cpu"
+
+var (
+	supportAvx512 = cpu.X86.HasAVX512 && cpu.X86.HasAVX512DQ
+	_             = supportAvx512
+)
diff --git a/field/koalabear/asm_noavx.go b/field/koalabear/asm_noavx.go
new file mode 100644
index 0000000000..cdd0d205b3
--- /dev/null
+++ b/field/koalabear/asm_noavx.go
@@ -0,0 +1,10 @@
+//go:build noavx
+
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package koalabear
+
+const supportAvx512 = false
diff --git a/field/koalabear/doc.go b/field/koalabear/doc.go
index 4abddfb000..60c2390f6a 100644
--- a/field/koalabear/doc.go
+++ b/field/koalabear/doc.go
@@ -7,7 +7,7 @@
 //
 // The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
 //
-// Additionally koalabear.Vector offers an API to manipulate []Element.
+// Additionally koalabear.Vector offers an API to manipulate []Element using AVX512 instructions if available.
 //
 // The modulus is hardcoded in all the operations.
 //
diff --git a/field/koalabear/element_amd64.s b/field/koalabear/element_amd64.s
new file mode 100644
index 0000000000..11676c6f04
--- /dev/null
+++ b/field/koalabear/element_amd64.s
@@ -0,0 +1,10 @@
+//go:build  !purego
+
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 17349933987904761959
+#include "../asm/element_31b_amd64.s"
+
diff --git a/field/koalabear/vector_amd64.go b/field/koalabear/vector_amd64.go
new file mode 100644
index 0000000000..cc80c68d04
--- /dev/null
+++ b/field/koalabear/vector_amd64.go
@@ -0,0 +1,192 @@
+//go:build !purego
+
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package koalabear
+
+//go:noescape
+func addVec(res, a, b *Element, n uint64)
+
+//go:noescape
+func subVec(res, a, b *Element, n uint64)
+
+//go:noescape
+func sumVec(t *uint64, a *Element, n uint64)
+
+//go:noescape
+func mulVec(res, a, b *Element, n uint64)
+
+//go:noescape
+func scalarMulVec(res, a, b *Element, n uint64)
+
+//go:noescape
+func innerProdVec(t *uint64, a, b *Element, n uint64)
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Add: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	if !supportAvx512 {
+		// call addVecGeneric
+		addVecGeneric(*vector, a, b)
+		return
+	}
+
+	const blockSize = 16
+	addVec(&(*vector)[0], &a[0], &b[0], n/blockSize)
+	if n%blockSize != 0 {
+		// call addVecGeneric on the rest
+		start := n - n%blockSize
+		addVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Sub: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	if !supportAvx512 {
+		// call subVecGeneric
+		subVecGeneric(*vector, a, b)
+		return
+	}
+
+	const blockSize = 16
+	subVec(&(*vector)[0], &a[0], &b[0], n/blockSize)
+	if n%blockSize != 0 {
+		// call subVecGeneric on the rest
+		start := n - n%blockSize
+		subVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+}
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	if len(a) != len(*vector) {
+		panic("vector.ScalarMul: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	if !supportAvx512 {
+		// call scalarMulVecGeneric
+		scalarMulVecGeneric(*vector, a, b)
+		return
+	}
+
+	const blockSize = 8
+	scalarMulVec(&(*vector)[0], &a[0], b, n/blockSize)
+	if n%blockSize != 0 {
+		// call scalarMulVecGeneric on the rest
+		start := n - n%blockSize
+		scalarMulVecGeneric((*vector)[start:], a[start:], b)
+	}
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	if !supportAvx512 {
+		// call sumVecGeneric
+		sumVecGeneric(&res, *vector)
+		return
+	}
+
+	const blockSize = 16
+	var t [8]uint64 // stores the accumulators (not reduced mod q)
+	sumVec(&t[0], &(*vector)[0], n/blockSize)
+	// we reduce the accumulators mod q and add to res
+	var v Element
+	for i := 0; i < 8; i++ {
+		t[i] %= q
+		v[0] = uint32(t[i])
+		res.Add(&res, &v)
+	}
+	if n%blockSize != 0 {
+		// call sumVecGeneric on the rest
+		start := n - n%blockSize
+		sumVecGeneric(&res, (*vector)[start:])
+	}
+
+	return
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+	if n != uint64(len(other)) {
+		panic("vector.InnerProduct: vectors don't have the same length")
+	}
+	if !supportAvx512 {
+		// call innerProductVecGeneric
+		innerProductVecGeneric(&res, *vector, other)
+		return
+	}
+
+	const blockSize = 8
+	var t [8]uint64 // stores the accumulators (not reduced mod q)
+	innerProdVec(&t[0], &(*vector)[0], &other[0], n/blockSize)
+	// we reduce the accumulators mod q and add to res
+	var v Element
+	for i := 0; i < 8; i++ {
+		t[i] %= q
+		v[0] = uint32(t[i])
+		res.Add(&res, &v)
+	}
+	if n%blockSize != 0 {
+		// call innerProductVecGeneric on the rest
+		start := n - n%blockSize
+		innerProductVecGeneric(&res, (*vector)[start:], other[start:])
+	}
+
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Mul: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+	if !supportAvx512 {
+		// call mulVecGeneric
+		mulVecGeneric(*vector, a, b)
+		return
+	}
+
+	const blockSize = 8
+	mulVec(&(*vector)[0], &a[0], &b[0], n/blockSize)
+	if n%blockSize != 0 {
+		// call mulVecGeneric on the rest
+		start := n - n%blockSize
+		mulVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+}
diff --git a/field/koalabear/vector_purego.go b/field/koalabear/vector_purego.go
index e1dc6b8f81..c96e144f86 100644
--- a/field/koalabear/vector_purego.go
+++ b/field/koalabear/vector_purego.go
@@ -1,3 +1,5 @@
+//go:build purego || !amd64
+
 // Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 

From 97d69dcde082a20847e16ba29bce35e9bfde0261 Mon Sep 17 00:00:00 2001
From: ThomasPiellard <thomas.piellard@consensys.net>
Date: Thu, 19 Dec 2024 18:15:16 +0100
Subject: [PATCH 100/114] feat: restored sis (#583)

Co-authored-by: Gautam Botrel <gautam.botrel@gmail.com>
---
 ecc/bls12-377/fr/sis/sis.go                   |     94 +-
 ecc/bls12-377/fr/sis/sis_test.go              |    334 +-
 ecc/bls12-377/fr/sis/test_cases.json          | 117317 +--------------
 ecc/bn254/fr/sis/sis.go                       |     92 +-
 ecc/bn254/fr/sis/sis_test.go                  |    306 +-
 ecc/bn254/fr/sis/test_cases.json              | 117317 +--------------
 field/babybear/sis/sis.go                     |    468 +
 field/babybear/sis/sis.py                     |    254 +
 field/babybear/sis/sis_fft.go                 |    556 +
 field/babybear/sis/sis_test.go                |    488 +
 field/babybear/sis/test_cases.json            |     86 +
 field/generator/generator.go                  |      7 +
 field/generator/generator_fft.go              |     30 +-
 field/generator/generator_sis.go              |     53 +
 .../internal/templates/sis/fft.go.tmpl        |     82 +
 .../internal/templates/sis/sis.go.tmpl        |    472 +
 .../internal/templates/sis/sis.test.go.tmpl   |    481 +
 field/generator/options.go                    |     11 +
 field/goldilocks/sis/sis.go                   |    468 +
 field/goldilocks/sis/sis.py                   |    253 +
 field/goldilocks/sis/sis_fft.go               |    556 +
 field/goldilocks/sis/sis_test.go              |    488 +
 field/goldilocks/sis/test_cases.json          |     86 +
 field/internal/main.go                        |      1 +
 field/koalabear/sis/sis.go                    |    468 +
 field/koalabear/sis/sis_fft.go                |    556 +
 field/koalabear/sis/sis_test.go               |    488 +
 field/koalabear/sis/test_cases.json           |     86 +
 internal/generator/main.go                    |      9 +-
 29 files changed, 7091 insertions(+), 234816 deletions(-)
 create mode 100644 field/babybear/sis/sis.go
 create mode 100644 field/babybear/sis/sis.py
 create mode 100644 field/babybear/sis/sis_fft.go
 create mode 100644 field/babybear/sis/sis_test.go
 create mode 100644 field/babybear/sis/test_cases.json
 create mode 100644 field/generator/generator_sis.go
 create mode 100644 field/generator/internal/templates/sis/fft.go.tmpl
 create mode 100644 field/generator/internal/templates/sis/sis.go.tmpl
 create mode 100644 field/generator/internal/templates/sis/sis.test.go.tmpl
 create mode 100644 field/goldilocks/sis/sis.go
 create mode 100644 field/goldilocks/sis/sis.py
 create mode 100644 field/goldilocks/sis/sis_fft.go
 create mode 100644 field/goldilocks/sis/sis_test.go
 create mode 100644 field/goldilocks/sis/test_cases.json
 create mode 100644 field/koalabear/sis/sis.go
 create mode 100644 field/koalabear/sis/sis_fft.go
 create mode 100644 field/koalabear/sis/sis_test.go
 create mode 100644 field/koalabear/sis/test_cases.json

diff --git a/ecc/bls12-377/fr/sis/sis.go b/ecc/bls12-377/fr/sis/sis.go
index d07717f8d3..f05720aa86 100644
--- a/ecc/bls12-377/fr/sis/sis.go
+++ b/ecc/bls12-377/fr/sis/sis.go
@@ -1,6 +1,8 @@
 // Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
 package sis
 
 import (
@@ -8,7 +10,6 @@ import (
 	"encoding/binary"
 	"errors"
 	"hash"
-	"math/big"
 	"math/bits"
 
 	"github.com/bits-and-blooms/bitset"
@@ -99,10 +100,10 @@ func NewRSis(seed int64, logTwoDegree, logTwoBound, maxNbElementsToHash int) (*R
 	}
 
 	// domains (shift is √{gen} )
-	var shift fr.Element
-	shift.SetString("8065159656716812877374967518403273466521432693661810619979959746626482506078") // -> 2^47-th root of unity of bls12377
-	e := int64(1 << (47 - (logTwoDegree + 1)))
-	shift.Exp(shift, big.NewInt(e))
+	shift, err := fr.Generator(uint64(2 * degree))
+	if err != nil {
+		return nil, err
+	}
 
 	r := &RSis{
 		LogTwoBound:         logTwoBound,
@@ -168,9 +169,10 @@ func (r *RSis) Sum(b []byte) []byte {
 	m := r.bufM
 	mValues := r.bufMValues
 
-	if fastPath {
-		// fast path.
-		limbDecomposeBytes8_64(buf, m, mValues)
+	if r.LogTwoBound < 8 && (8%r.LogTwoBound == 0) {
+		limbDecomposeBytesSmallBound(buf, m, r.LogTwoBound, r.Degree, mValues)
+	} else if r.LogTwoBound >= 8 && (fr.Bytes*8)%r.LogTwoBound == 0 {
+		limbDecomposeBytesMiddleBound(buf, m, r.LogTwoBound, r.Degree, mValues)
 	} else {
 		limbDecomposeBytes(buf, m, r.LogTwoBound, r.Degree, mValues)
 	}
@@ -322,11 +324,76 @@ func LimbDecomposeBytes(buf []byte, m fr.Vector, logTwoBound int) {
 	limbDecomposeBytes(buf, m, logTwoBound, 0, nil)
 }
 
+// decomposes m as by taking chunks of logTwoBound bits at a time. The buffer is interpreted like this:
+// [0xa,        ..            , 0x1 | 0xa ... ]
+//
+//	<- #bytes in a field element ->
+//	<-0xa is the MSB, 0x1 the LSB->
+//	<-we read this chunk from right
+//	   			to left 	 	 ->
+//
+// This function is called when logTwoBound divides the number of bits used to represent a
+// fr element.
+// From a slice of field elements m:=[a_0, a_1, ...]
+// Doing h.Sum(h.Write([Marshal[a_i] for i in len(m)])) is the same than
+// writing the a_i in little endian, and then taking logTwoBound bits at a time.
+//
+// ex: m := [0x1, 0x3]
+// in the hash buffer, it is interpreted like that as a stream of bits:
+// [100...0 110...0] corresponding to [0x1, 0x3] in little endian, so first bit = LSbit
+// then the stream of bits is splitted in chunks of logTwoBound bits.
+//
+// This function is called when logTwoBound divides 8.
+func limbDecomposeBytesSmallBound(buf []byte, m fr.Vector, logTwoBound, degree int, mValues *bitset.BitSet) {
+	mask := byte((1 << logTwoBound) - 1)
+	nbChunksPerBytes := 8 / logTwoBound
+	nbFieldsElmts := len(buf) / fr.Bytes
+	for i := 0; i < nbFieldsElmts; i++ {
+		for j := fr.Bytes - 1; j >= 0; j-- {
+			curByte := buf[i*fr.Bytes+j]
+			curPos := i*fr.Bytes*nbChunksPerBytes + (fr.Bytes-1-j)*nbChunksPerBytes
+			for k := 0; k < nbChunksPerBytes; k++ {
+
+				m[curPos+k][0] = uint64((curByte >> (k * logTwoBound)) & mask)
+
+				// Check if mPos is zero and mark as non-zero in the bitset if not
+				if m[curPos+k][0] != 0 && mValues != nil {
+					mValues.Set(uint((curPos + k) / degree))
+				}
+			}
+		}
+	}
+}
+
+// limbDecomposeBytesMiddleBound same function than limbDecomposeBytesSmallBound, but logTwoBound is
+// a multiple of 8, and divides the number of bits of the fields.
+func limbDecomposeBytesMiddleBound(buf []byte, m fr.Vector, logTwoBound, degree int, mValues *bitset.BitSet) {
+	nbFieldsElmts := len(buf) / fr.Bytes
+	nbChunksPerElements := fr.Bytes * 8 / logTwoBound
+	nbBytesInChunk := logTwoBound / 8
+	curElmt := 0
+	for i := 0; i < nbFieldsElmts; i++ {
+		for j := nbChunksPerElements; j > 0; j-- {
+			curPos := i*fr.Bytes + j*nbBytesInChunk
+			for k := 1; k <= nbBytesInChunk; k++ {
+
+				m[curElmt][0] |= (uint64(buf[curPos-k]) << ((k - 1) * 8))
+
+			}
+			// Check if mPos is zero and mark as non-zero in the bitset if not
+			if m[curElmt][0] != 0 && mValues != nil {
+				mValues.Set(uint((curElmt) / degree))
+			}
+			curElmt += 1
+		}
+	}
+}
+
 // Split an slice of bytes representing an array of serialized field element in
 // big-endian form into an array of limbs representing the same field elements
 // in little-endian form. Namely, if our field is represented with 64 bits and we
 // have the following field element 0x0123456789abcdef (0 being the most significant
-// character and and f being the least significant one) and our norm bound is
+// character and and f being the least significant one) and our log norm bound is
 // 16 (so 1 hex character = 1 limb). The function assigns the values of m to [f, e,
 // d, c, b, a, ..., 3, 2, 1, 0]. m should be preallocated and zeroized. mValues is
 // an optional bitSet. If provided, it must be empty. The function will set bit "i"
@@ -339,9 +406,9 @@ func limbDecomposeBytes(buf []byte, m fr.Vector, logTwoBound, degree int, mValue
 	// bitwise decomposition of the buffer, in order to build m (the vector to hash)
 	// as a list of polynomials, whose coefficients are less than r.B bits long.
 	// Say buf=[0xbe,0x0f]. As a stream of bits it is interpreted like this:
-	// 10111110 00001111. BitAt(0)=1 (=leftmost bit), bitAt(1)=0 (=second leftmost bit), etc.
+	// 10111110 00001111. getIthBit(0)=1 (=leftmost bit), getIthBit(1)=0 (=second leftmost bit), etc.
 	nbBits := len(buf) * 8
-	bitAt := func(i int) uint8 {
+	getIthBit := func(i int) uint8 {
 		k := i / 8
 		if k >= len(buf) {
 			return 0
@@ -363,7 +430,8 @@ func limbDecomposeBytes(buf []byte, m fr.Vector, logTwoBound, degree int, mValue
 			// and set the bits from LSB to MSB.
 			at := fieldStart + fr.Bytes*8 - bitInField - 1
 
-			m[mPos][0] |= uint64(bitAt(at)) << j
+			m[mPos][0] |= uint64(getIthBit(at) << j)
+
 			bitInField++
 
 			// Check if mPos is zero and mark as non-zero in the bitset if not
@@ -388,7 +456,9 @@ func limbDecomposeBytes8_64(buf []byte, m fr.Vector, mValues *bitset.BitSet) {
 
 	for startPos := fr.Bytes - 1; startPos < len(buf); startPos += fr.Bytes {
 		for i := startPos; i >= startPos-fr.Bytes+1; i-- {
+
 			m[j][0] = uint64(buf[i])
+
 			if m[j][0] != 0 {
 				mValues.Set(uint(j / degree))
 			}
diff --git a/ecc/bls12-377/fr/sis/sis_test.go b/ecc/bls12-377/fr/sis/sis_test.go
index 73e26a32a2..92834d50c4 100644
--- a/ecc/bls12-377/fr/sis/sis_test.go
+++ b/ecc/bls12-377/fr/sis/sis_test.go
@@ -1,6 +1,8 @@
 // Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
 package sis
 
 import (
@@ -19,7 +21,6 @@ import (
 	"github.com/bits-and-blooms/bitset"
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr/fft"
-	"github.com/stretchr/testify/assert"
 	"github.com/stretchr/testify/require"
 )
 
@@ -38,7 +39,7 @@ var params128Bits []sisParams = []sisParams{
 }
 
 type TestCases struct {
-	Inputs  [][]fr.Element `json:"inputs"`
+	Inputs  []fr.Element `json:"inputs"`
 	Entries []struct {
 		Params struct {
 			Seed                int64 `json:"seed"`
@@ -46,7 +47,7 @@ type TestCases struct {
 			LogTwoBound         int   `json:"logTwoBound"`
 			MaxNbElementsToHash int   `json:"maxNbElementsToHash"`
 		} `json:"params"`
-		Expected [][]fr.Element `json:"expected"`
+		Expected []fr.Element `json:"expected"`
 	} `json:"entries"`
 }
 
@@ -63,7 +64,10 @@ func TestReference(t *testing.T) {
 	err = json.Unmarshal(data, &testCases)
 	assert.NoError(err, "reading test cases failed")
 
+	inputs := testCases.Inputs
+
 	for testCaseID, testCase := range testCases.Entries {
+
 		// create the SIS instance
 		sis, err := NewRSis(testCase.Params.Seed, testCase.Params.LogTwoDegree, testCase.Params.LogTwoBound, testCase.Params.MaxNbElementsToHash)
 		assert.NoError(err)
@@ -71,188 +75,167 @@ func TestReference(t *testing.T) {
 		// key generation same than in sage
 		makeKeyDeterministic(t, sis, testCase.Params.Seed)
 
-		for i, in := range testCases.Inputs {
-			sis.Reset()
-
-			// hash test case entry input and compare with expected (computed by sage)
-			got, err := sis.Hash(in)
-			assert.NoError(err)
-			if len(testCase.Expected[i]) == 0 {
-				for _, e := range got {
-					assert.True(e.IsZero(), "mismatch between reference test and computed value")
-				}
-			} else {
-				assert.EqualValues(
-					testCase.Expected[i], got,
-					"mismatch between reference test and computed value (testcase %v - input n° %v)",
-					testCaseID, i,
-				)
-			}
+		sis.Reset()
 
-			// ensure max nb elements to hash has no incidence on result.
-			if len(in) < testCase.Params.MaxNbElementsToHash {
-				sis2, err := NewRSis(testCase.Params.Seed, testCase.Params.LogTwoDegree, testCase.Params.LogTwoBound, len(in))
-				assert.NoError(err)
-				makeKeyDeterministic(t, sis2, testCase.Params.Seed)
-
-				got2, err := sis2.Hash(in)
-				assert.NoError(err)
-				if len(testCase.Expected[i]) == 0 {
-					for _, e := range got2 {
-						assert.True(e.IsZero(), "mismatch between reference test and computed value")
-					}
-				} else {
-					assert.EqualValues(got, got2, "max nb elements to hash change SIS result")
-				}
-			}
+		// hash test case entry input and compare with expected (computed by sage)
+		goHash, err := sis.Hash(inputs)
+		assert.NoError(err)
+
+		assert.EqualValues(
+			testCase.Expected, goHash,
+			"mismatch between reference test and computed value (testcase %v)",
+			testCaseID,
+		)
 
-		}
 	}
 
 }
 
-func TestMulMod(t *testing.T) {
+func TestLimbDecomposeBytesMiddleBound(t *testing.T) {
 
-	size := 4
+	var montConstant fr.Element
+	var bMontConstant big.Int
+	bMontConstant.SetUint64(1)
+	bMontConstant.Lsh(&bMontConstant, fr.Bytes*8)
+	montConstant.SetBigInt(&bMontConstant)
 
-	p := make([]fr.Element, size)
-	p[0].SetString("2389")
-	p[1].SetString("987192")
-	p[2].SetString("623")
-	p[3].SetString("91")
+	nbElmts := 10
+	a := make([]fr.Element, nbElmts)
+	for i := 0; i < nbElmts; i++ {
+		a[i].SetUint64(33)
+	}
+	var buf bytes.Buffer
+	for i := 0; i < nbElmts; i++ {
+		buf.Write(a[i].Marshal())
+	}
 
-	q := make([]fr.Element, size)
-	q[0].SetString("76755")
-	q[1].SetString("232893720")
-	q[2].SetString("989273")
-	q[3].SetString("675273")
+	logTwoBound := 8
 
-	// creation of the domain. Note that the value of the shift is purely arbitrary
-	// and random.
-	var shift fr.Element
-	shift.SetString("19540430494807482326159819597004422086093766032135589407132600596362845576832")
-	domain := fft.NewDomain(uint64(size), fft.WithShift(shift))
+	for cc := 0; cc < 3; cc++ {
+		m := make(fr.Vector, nbElmts*fr.Bytes*8/logTwoBound)
+		limbDecomposeBytesMiddleBound(buf.Bytes(), m, logTwoBound, 4, nil)
 
-	// mul mod
-	domain.FFT(p, fft.DIF, fft.OnCoset())
-	domain.FFT(q, fft.DIF, fft.OnCoset())
-	r := mulMod(p, q)
-	domain.FFTInverse(r, fft.DIT, fft.OnCoset())
+		for i := 0; i < len(m); i++ {
+			m[i].Mul(&m[i], &montConstant)
+		}
 
-	// expected result
-	expectedr := make([]fr.Element, 4)
-	expectedr[0].SetString("1612335717510792699655803640368030375030102334758014597273992900671209760644")
-	expectedr[1].SetString("7801939531701554412773487946871330804032103116849274522170062191886789772982")
-	expectedr[2].SetString("3958508915483304256780311126107405810447277056055916093890488600778971951103")
-	expectedr[3].SetString("1123315390878")
+		var x fr.Element
+		x.SetUint64(1 << logTwoBound)
 
-	for i := 0; i < 4; i++ {
-		assert.Equal(t, expectedr[i].String(), r[i].String())
+		coeffsPerFieldsElmt := fr.Bytes * 8 / logTwoBound
+		for i := 0; i < nbElmts; i++ {
+			r := eval(m[i*coeffsPerFieldsElmt:(i+1)*coeffsPerFieldsElmt], x)
+			if !r.Equal(&a[i]) {
+				t.Fatal("limbDecomposeBytes failed")
+			}
+		}
+		logTwoBound *= 2
 	}
+
 }
 
-// Test the fact that the limb decomposition allows obtaining the original
-// field element by evaluating the polynomial whose the coeffiients are the
-// limbs.
-func TestLimbDecomposition(t *testing.T) {
+func TestLimbDecomposeBytesSmallBound(t *testing.T) {
 
-	// Skipping the test for 32 bits
-	if bits.UintSize == 32 {
-		t.Skip("skipping this test in 32bit.")
-	}
+	var montConstant fr.Element
+	var bMontConstant big.Int
+	bMontConstant.SetUint64(1)
+	bMontConstant.Lsh(&bMontConstant, fr.Bytes*8)
+	montConstant.SetBigInt(&bMontConstant)
 
-	testcases := []struct {
-		logTwoDegree, logTwoBound int
-		vec                       fr.Vector
-	}{
-		{
-			logTwoDegree: 4,
-			logTwoBound:  4,
-			vec:          fr.Vector{fr.One()},
-		},
-		{
-			logTwoDegree: 4,
-			logTwoBound:  4,
-			vec:          fr.Vector{fr.NewElement(2)},
-		},
-		{
-			logTwoDegree: 4,
-			logTwoBound:  4,
-			vec:          fr.Vector{fr.NewElement(1 << 32), fr.NewElement(2), fr.NewElement(1)},
-		},
-		{
-			logTwoDegree: 4,
-			logTwoBound:  16,
-			vec:          fr.Vector{fr.One()},
-		},
-		{
-			logTwoDegree: 4,
-			logTwoBound:  16,
-			vec:          fr.Vector{fr.NewElement(2)},
-		},
-		{
-			logTwoDegree: 4,
-			logTwoBound:  16,
-			vec:          fr.Vector{fr.NewElement(1 << 32), fr.NewElement(2), fr.NewElement(1)},
-		},
+	nbElmts := 10
+	a := make([]fr.Element, nbElmts)
+	for i := 0; i < nbElmts; i++ {
+		a[i].SetRandom()
+	}
+	var buf bytes.Buffer
+	for i := 0; i < nbElmts; i++ {
+		buf.Write(a[i].Marshal())
 	}
 
-	for i, testcase := range testcases {
+	logTwoBound := 2
 
-		t.Run(fmt.Sprintf("testcase-%v", i), func(t *testing.T) {
+	for cc := 0; cc < 3; cc++ {
 
-			t.Logf("testcase %v", testcase)
+		m := make(fr.Vector, nbElmts*fr.Bytes*8/logTwoBound)
+		m2 := make(fr.Vector, nbElmts*fr.Bytes*8/logTwoBound)
 
-			sis, _ := NewRSis(0, testcase.logTwoDegree, testcase.logTwoBound, 3)
+		// the limbs are set as is, they are NOT converted in Montgomery form
+		limbDecomposeBytes(buf.Bytes(), m, logTwoBound, 4, nil)
+		limbDecomposeBytesSmallBound(buf.Bytes(), m2, logTwoBound, 4, nil)
 
-			// clean the sis hasher
-			sis.bufMValues.ClearAll()
-			for i := 0; i < len(sis.bufM); i++ {
-				sis.bufM[i].SetZero()
-			}
-			for i := 0; i < len(sis.bufRes); i++ {
-				sis.bufRes[i].SetZero()
+		for i := 0; i < len(m); i++ {
+			m[i].Mul(&m[i], &montConstant)
+			m2[i].Mul(&m2[i], &montConstant)
+		}
+		var x fr.Element
+		x.SetUint64(1 << logTwoBound)
+
+		coeffsPerFieldsElmt := fr.Bytes * 8 / logTwoBound
+		for i := 0; i < nbElmts; i++ {
+			r := eval(m[i*coeffsPerFieldsElmt:(i+1)*coeffsPerFieldsElmt], x)
+			if !r.Equal(&a[i]) {
+				t.Fatal("limbDecomposeBytes failed")
 			}
-
-			buf := bytes.Buffer{}
-			for _, x := range testcase.vec {
-				xBytes := x.Bytes()
-				buf.Write(xBytes[:])
+			r = eval(m2[i*coeffsPerFieldsElmt:(i+1)*coeffsPerFieldsElmt], x)
+			if !r.Equal(&a[i]) {
+				t.Fatal("limbDecomposeBytesSmallBound failed")
 			}
+		}
+		logTwoBound *= 2
+	}
 
-			limbDecomposeBytes(buf.Bytes(), sis.bufM, sis.LogTwoBound, sis.Degree, sis.bufMValues)
+}
 
-			// Just to test, this does not return panic
-			dummyBuffer := make(fr.Vector, 192)
-			LimbDecomposeBytes(buf.Bytes(), dummyBuffer, sis.LogTwoBound)
+func eval(p []fr.Element, x fr.Element) fr.Element {
+	var res fr.Element
+	for i := len(p) - 1; i >= 0; i-- {
+		res.Mul(&res, &x).Add(&res, &p[i])
+	}
+	return res
+}
 
-			// b is a field element representing the max norm bound
-			// used for limb splitting the input field elements.
-			b := fr.NewElement(1 << sis.LogTwoBound)
-			numLimbsPerField := fr.Bytes * 8 / sis.LogTwoBound
+func TestMulMod(t *testing.T) {
 
-			// Compute r (corresponds to the Montgommery constant)
-			var r fr.Element
-			r.SetString("6014086494747379908336260804527802945383293308637734276299549080986809532403")
+	size := 4
 
-			// Attempt to recompose the entry #i in the test-case
-			for i := range testcase.vec {
-				// allegedly corresponds to the limbs of the entry i
-				subRes := sis.bufM[i*numLimbsPerField : (i+1)*numLimbsPerField]
+	p := make([]fr.Element, size)
+	q := make([]fr.Element, size)
+	pCopy := make([]fr.Element, size)
+	qCopy := make([]fr.Element, size)
+	for i := 0; i < size; i++ {
+		p[i].SetRandom()
+		pCopy[i].Set(&p[i])
+		q[i].SetRandom()
+		qCopy[i].Set(&q[i])
+	}
 
-				// performs a Horner evaluation of subres by b
-				var y fr.Element
-				for j := numLimbsPerField - 1; j >= 0; j-- {
-					y.Mul(&y, &b)
-					y.Add(&y, &subRes[j])
-				}
+	// creation of the domain
+	shift, err := fr.Generator(uint64(2 * size))
+	if err != nil {
+		t.Fatal(err)
+	}
+	var g fr.Element
+	g.Square(&shift)
+	domain := fft.NewDomain(uint64(size), fft.WithShift(shift))
 
-				y.Mul(&y, &r)
-				require.Equal(t, testcase.vec[i].String(), y.String(), "the subRes was %v", subRes)
-			}
-		})
+	// mul mod
+	domain.FFT(p, fft.DIF, fft.OnCoset())
+	domain.FFT(q, fft.DIF, fft.OnCoset())
+	r := mulMod(p, q)
+	domain.FFTInverse(r, fft.DIT, fft.OnCoset())
 
+	// manually check the product on the zeroes of X^4+1
+	for i := 0; i < 4; i++ {
+		u := eval(pCopy, shift)
+		v := eval(qCopy, shift)
+		w := eval(r, shift)
+		u.Mul(&u, &v)
+		if !w.Equal(&u) {
+			t.Fatal("mul mol failed")
+		}
+		shift.Mul(&shift, &g)
 	}
+
 }
 
 func makeKeyDeterministic(t *testing.T, sis *RSis, _seed int64) {
@@ -313,6 +296,51 @@ func estimateSisTheory(p sisParams) float64 {
 	return float64(r)
 }
 
+func BenchmarkDecomposition(b *testing.B) {
+
+	nbElmts := 1000
+	a := make([]fr.Element, nbElmts)
+	for i := 0; i < nbElmts; i++ {
+		a[i].SetRandom()
+	}
+	var buf bytes.Buffer
+	for i := 0; i < nbElmts; i++ {
+		buf.Write(a[i].Marshal())
+	}
+	logTwoBound := 4
+	m := make(fr.Vector, nbElmts*fr.Bytes*8/logTwoBound)
+
+	b.Run(fmt.Sprintf("limbDecomposeBytes logTwoBound=%d", logTwoBound), func(b *testing.B) {
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			limbDecomposeBytes(buf.Bytes(), m, logTwoBound, 4, nil)
+		}
+	})
+
+	b.Run(fmt.Sprintf("limbDecomposeByteSmallBound logTwoBound=%d", logTwoBound), func(b *testing.B) {
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			limbDecomposeBytesSmallBound(buf.Bytes(), m, logTwoBound, 4, nil)
+		}
+	})
+
+	logTwoBound = 16
+	b.Run(fmt.Sprintf("limbDecomposeBytes logTwoBound=%d", logTwoBound), func(b *testing.B) {
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			limbDecomposeBytes(buf.Bytes(), m, logTwoBound, 4, nil)
+		}
+	})
+
+	b.Run(fmt.Sprintf("limbDecomposeByteSmallBound logTwoBound=%d", logTwoBound), func(b *testing.B) {
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			limbDecomposeBytesMiddleBound(buf.Bytes(), m, logTwoBound, 4, nil)
+		}
+	})
+
+}
+
 func BenchmarkSIS(b *testing.B) {
 
 	// max nb field elements to hash
@@ -415,7 +443,7 @@ func TestLimbDecompositionFastPath(t *testing.T) {
 		nValues := bitset.New(uint(size))
 
 		// Generate a random buffer
-		_, err := rand.Read(buf) //#nosec G404 weak rng is fine here
+		_, err := rand.Read(buf)
 		assert.NoError(err)
 
 		limbDecomposeBytes8_64(buf, m, mValues)
@@ -432,9 +460,7 @@ func TestLimbDecompositionFastPath(t *testing.T) {
 func TestUnrolledFFT(t *testing.T) {
 
 	var shift fr.Element
-	shift.SetString("8065159656716812877374967518403273466521432693661810619979959746626482506078") // -> 2^47-th root of unity of bls12377
-	e := int64(1 << (47 - (6 + 1)))
-	shift.Exp(shift, big.NewInt(e))
+	shift.SetRandom()
 
 	const size = 64
 	assert := require.New(t)
diff --git a/ecc/bls12-377/fr/sis/test_cases.json b/ecc/bls12-377/fr/sis/test_cases.json
index 4d2a45dca6..b6324c8dcc 100644
--- a/ecc/bls12-377/fr/sis/test_cases.json
+++ b/ecc/bls12-377/fr/sis/test_cases.json
@@ -1,117269 +1,86 @@
 {
     "inputs": [
-        [
-            "0x12ab655e9a2ca55660b44d1e5c37b00159aa76fed00000010a117ffffffffffd"
-        ],
-        [
-            "0x1"
-        ],
-        [
-            "0x2a",
-            "0x1f40"
-        ],
-        [
-            "0x1",
-            "0x2",
-            "0x0",
-            "0x12ab655e9a2ca55660b44d1e5c37b00159aa76fed00000010a11800000000000"
-        ],
-        [
-            "0x1",
-            "0x0"
-        ],
-        [
-            "0x0",
-            "0x1"
-        ],
-        [
-            "0x0"
-        ],
-        [
-            "0x0",
-            "0x0",
-            "0x0",
-            "0x0"
-        ],
-        [
-            "0x0",
-            "0x0",
-            "0x1f40",
-            "0x0"
-        ],
-        [],
-        [
-            "0xffce5e50681376dae465b351bffd139699af26a3d8a64b41a23f4d1a5e026e8"
-        ],
-        [
-            "0x10cea286017ba10212f690149c7465bda7a72fbf67824d3053ed4cd15bb8d494",
-            "0xc1979d0b4c6fc8fbd9babbad732a1f5674aedd7b850cd3b9c5a584ca477584f"
-        ],
-        [
-            "0x192eaacad9d72da189f7cc8f20ea26cdfd9fa6a559d4bab7b9f467a12524fc8",
-            "0xb8eb490ff132bd4675a7c7b4bdf6e5f67986e8562bc27eff1b69bda303fdf59",
-            "0x9aa71656fc7a584649fddcdbc4abc32d9d0b622c5a1c98deb79702a0efc53aa"
-        ],
-        [
-            "0x70285f380d0885b53fdcd9b318ed35e2eb62064640a7a423cfdcf5f8c494ceb",
-            "0x58754e1df07a23a46381aad9178b87cf86f73f364fc02a0a012b3108b10f15b",
-            "0x1182083951d7072bfe3cbcfa9553b61fe93c5641e053c95c9731a5b76d616d75",
-            "0x7187949cbdefc0849f63c9f3ef6e1d313fdfde0fdd18b1ea14d4b0515a6c76d"
-        ],
-        [
-            "0x3c0915ec789b095eb729cdebbeada2850ffde50acafb7d9456c63ea9e6978cf",
-            "0x481f60fac771d05cbb1a169dc7a8fd0eea0df5510ac67a0010885fb796baef5",
-            "0xfba2950f71375c84b2308634fd0c780249ae4f9c0d9c6321b514521e75e45ae",
-            "0xbe623fa7ef255d0a8db09449b52854afa6593d5df0760f9c7834b8871aa3c2",
-            "0x12766513abb7af501b0b7ed6e85ee9ecd8be5e408286a95c5609c622e9e124be"
-        ],
-        [
-            "0x114b89700e94de2c57514a1c58f4def4c9a44d46ec3c0c4dba8bc4203445f6fe",
-            "0x10a13712ca464069796adda69af88f46080f8deb571c10fc6f9fb27a327c467c",
-            "0x1bd9ad15fa63fe9de7d11a91b4ecf0f63a04bffca3bbf0394270ee5d65a4df7",
-            "0xdffa88f673746f0bcf536765f7cb96168a865c9dea9223ff7581a01a58b3f90",
-            "0x7e671ae93df3b73a9bc2c2cbbdb4785f6a28270be489e032729d3c4dd0bb317",
-            "0x506753d1afd246cd7de09bc7fbf75bbdc338b9da6f3f24e081b1f3d2b9ab83e"
-        ],
-        [
-            "0x1f135791a50dcb194daa7be42737930149cab7b661df0b057e8da51568da19d",
-            "0x106cda0c22db6bb2e8998cbe7d42659062d8ce2330f9c4f120a1fe87a488d94e",
-            "0x1059f68b2fbe9be91c2c6710c7f9aa98a176d2796100735d73149e73cdae46e7",
-            "0x57c03d12e6c87148f1fc2e27758299c0baf30786c13048abff33e90d8405ce1",
-            "0xf5d3e5c53b5b9e156f77dbb3b2d75cb7db33cc9c89a397f835f6b6804d759a1",
-            "0x7a4f2b0f32e02a64babfe51d5173ab9e265afa04fd3a74a42b1f6891f2c6a09",
-            "0x7eccb14817400fb4a9bafd1f5b3b6efc5e3674ae80f30bdb5f9238b01176d65"
-        ],
-        [
-            "0x119568cb3f0e1b28c92b93c98b49cd51e6996249d9b8663117af1ae8a60eb642",
-            "0xe7fa3d0ede91ede40baba910f897fbaf309aa29aa71f0add6fabee16496e073",
-            "0x11e5a0ed5d3a6f4265adb831309168f120f96834a1b100ca18c688f41d0e1801",
-            "0x3c480689fc73bb123439b398fb710d56dad75d9665b7f2b79ba78f1a2313f28",
-            "0x126ff937e9b62b1b90b0ccd82d330370694c12f25a9250b74f99c98d11012d76",
-            "0xd4f5e73be61f972b6d611cc60a1f77d61988f259d612647bf7f690f7d5a415c",
-            "0x101672a8ed1ffe009eb4e53cd08ae929c274a526f618406a0e03cbb6aaaf61ab",
-            "0x5d8ae026e2b58f3fa3182c444977c1ab9fa781ce86927e37ce439c7452898c0"
-        ],
-        [
-            "0x1013a463532aa518a84326f034411cc097e799a7ebc495c70dadae1b5ad65ef2",
-            "0xcd0d8de0d9d8bb93864fd8524d7f953a939c633f5cb24fa99b20015255288f3",
-            "0xc0d4c30741d55b3e244a4192e63411e686488860341ff0775030c299f16a431",
-            "0xe19b2f03c10c9d5872d664727f909af19195c38d13dd22da8a6134782f481be",
-            "0x5592e1a389fe35a0bfafa388da2cd27ed276f7410fcb6918f1c7e7fa224fe59",
-            "0x65e85b963a5898d33f7c4c5274eca25064ae47b05a5d13f9ddfd77cd4a5a13e",
-            "0x8d44e2938fa646f351ac111908be79008f13dd1d6c6bd0559b90913c79d8290",
-            "0xc7dcccca6570c28997725e1937cf8c13adbfdfe040cd2541694e5732458d81c",
-            "0x576f0d89cb4c75eb93a9d7c9fa95a8bc655e430ddee119dcc5fb10990e8bd33"
-        ]
-    ],
+        "5", 
+        "25", 
+        "125", 
+        "625", 
+        "3125", 
+        "15625", 
+        "78125", 
+        "390625", 
+        "1953125", 
+        "9765625"
+    ], 
     "entries": [
         {
-            "params": {
-                "seed": 5,
-                "logTwoDegree": 2,
-                "logTwoBound": 3,
-                "maxNbElementsToHash": 10
-            },
             "expected": [
-                [
-                    "0x1b7a4764b392865400172b98c318c1cb8368de744a129b5d0df2eb0f90e1b52",
-                    "0x77beee76ef338018ec14f070abb3a2a315960b07ef1eb3d8d32ee3a08837f4f",
-                    "0x64a72f0fc50108d08fedb95a525c91d99c84a655844dd0d4c9dfd362c8a2e6e",
-                    "0x107fae934f57c4a012e6d6ac3ee7766127fd1de1f179a5b2256720908104d1c4"
-                ],
-                [
-                    "0x5c9317a5a644ef910fa91e64643029bf75666a44ce4b368f7b8978cba550c28",
-                    "0xdf60f5c9c9330f6038a23a857057131b3c6c513d2558538ea8c4cbe324e2fe1",
-                    "0x711958703e8ec0c3b585f9a3ab347e15650128f12ca3e0f429adc58d0e2e27e",
-                    "0x384705bb697de3694a80334b262e82225355bbc576f1aba40703e67269f6503"
-                ],
-                [
-                    "0x321503108148809e0bcf9722508c69f8c66d00197abebee542400ebdf66fcad",
-                    "0x93091c5a0b7dc312ee69fe1f4ab0f72a1353336d18d208fe66e13dae6aa2f5e",
-                    "0xa02806d1be774bbd2ffa307e81816acf416bd94c7119ae9840868bdaf4398d6",
-                    "0x7cdf3d078577a040ea28f9089bb54b309c369c531108647567702522198b528"
-                ],
-                [
-                    "0x41b4801915e75261244ec1642b6a5b76d2eb65af48f50360f0d6ce91a9755c4",
-                    "0x65ee2e9f6f580015536ab6e824a63f2761c1883c2d0a4d2be5f48978051ebef",
-                    "0x278ad622bba9a12aa261a1607d822517de852ecd5142a3cb8ec57cf9573f3e4",
-                    "0xde405acfc5e80fff93b5a4381b9205395d38009ec680b34523192f97100397a"
-                ],
-                [
-                    "0x5c9317a5a644ef910fa91e64643029bf75666a44ce4b368f7b8978cba550c28",
-                    "0xdf60f5c9c9330f6038a23a857057131b3c6c513d2558538ea8c4cbe324e2fe1",
-                    "0x711958703e8ec0c3b585f9a3ab347e15650128f12ca3e0f429adc58d0e2e27e",
-                    "0x384705bb697de3694a80334b262e82225355bbc576f1aba40703e67269f6503"
-                ],
-                [
-                    "0xff6bf2802ac2eaa1239c6837fc09cfabfa82c21b9b8dfa4f695be964293c389",
-                    "0x23a5bad799331c41c05aea222825525c519aaa2ba97bf6bb0d077c9c8956613",
-                    "0xe900e83d9bfe9be48505238af06549805e7c9f3111dd47f110ed8f1c2e73432",
-                    "0x590a66b9cdcdda5e0ee5c2e56140ea802264f4b02c51d65512e5e66aa85d1f9"
-                ],
-                [],
-                [],
-                [
-                    "0x108bc0648805ba2cf26a78afeed99d0df50f870f759b19379a85ec41ef04b79c",
-                    "0xc4f16124ebd6f7b3abb98e8a2bb4721f68e47187995d2374d0c788d3029e49c",
-                    "0x11cf8df64a5cb72ebac09cc539a4b933cfa9a51227ca18cfc452186056739f07",
-                    "0x36cfbeec34b6ecb8e07dc95d041dd1d959fb875ee4d13684171bd562b3268c4"
-                ],
-                [],
-                [
-                    "0x111b709999d32d928017d7eb759c5c2cab59fcc4a682b0b463206a832cfdd40b",
-                    "0x93a5870efbf7ca5631d58e5862328ad3bcfd7730b2669f5c928a33f41fc9c4",
-                    "0x453490444624c753d20bfda42629859740247bbd56528deefb968f65c1cd10c",
-                    "0x8efa0f6671dd4da27038d6bb442e79587ac1cdf1f457cfe433c762e922648a6"
-                ],
-                [
-                    "0x6cf249451e21e2c2d62c5722b2635c6c36aa8e62210b5b254e5556e98881d60",
-                    "0x54906ca070c38f598a073596d9659bfa3c77f22cd8edacfe274fa0056d67d3a",
-                    "0x11c62c61368ff0275ac5a4a93067e4d53c8417e99c8d871f67b2e56b298ff8d2",
-                    "0x656a860d5b9818a1c85f7d997440c036acac1ffd30c150b8cb292b9e5d10c9e"
-                ],
-                [
-                    "0x1478017c56f244a341d3975235a4457fc1d6b7b16128afa3c04f2642e8c38c",
-                    "0x126d6ea75adf4a3b4c0bed9064db0794f6765a7cd82218eed95e18bb0e33f163",
-                    "0xf3444831f75c0a3b3ad84776698c78412d4c27f316283d74e2af849c4a5b0b8",
-                    "0x45a07001013e04d3cd528496859051195047a8b07e62ea42f0e9997ff8a7708"
-                ],
-                [
-                    "0x48352c97ad45bbb11978d2576ee2f8f690e1b391ef9352d3377e2ebecea7e59",
-                    "0x397063dba8d006b00adcd33922d99f7c0fcfbc7402d6505304aef55dcbb2a10",
-                    "0x5b12283693bbc829f15d413bddb6378177232296eae4364120cf5bf42e2637",
-                    "0x380a392f3a9508344c3d9c5154dec18af0a7d49ff1ed32e6119acd8b2bce22d"
-                ],
-                [
-                    "0xdc0bd1db49dcb59b3a0ce7008ce1c1fd3cfd39acd880742e521a3bc0b3cead4",
-                    "0xa607a35e0f4755d0964c78150bc0eec15a79f60c3307e46fa1f4bf17388c2ec",
-                    "0x1b95a19fb47b0c5065ca4e89ff0a48a367d6adc4d6ae0a0556a6811bb7df83e",
-                    "0x84802e118a3e977fe9cc2002faf8fe8a7a54f69dc0d0fa2177f910b57f074dc"
-                ],
-                [
-                    "0x7a8163302960fadcc694ac337bf8e163a49c285ab93f81eb491ce97a6f8fe0e",
-                    "0xe41303810f7e20b33b3d7d101deb44323594cfd0059345426dfd8e51d2d1cbf",
-                    "0xcdde27434c0a34bb174bf3225c074802674301df61e68f4c1713cb357622f88",
-                    "0x6fa33a15d8dea083eccf40c51941fedff9e50c44ad76351bbcf38e5f63ded40"
-                ],
-                [
-                    "0x97f357307e3f4b6fb1573ac1619ba966232bc102e62b3bf4043641940a05413",
-                    "0xd974f4fcb5c98453340f5e253981a54c01d7708b1e5c6d8a48bff96b41cd02d",
-                    "0x2f6bb15cc5d387b89236c800fc08ed765162a2062dc5cae9059ce5ea782d051",
-                    "0x11d3f27fb44e09d6f55e5409e932d730def6113598870ba0c6a0883012fb7740"
-                ],
-                [
-                    "0x29f8365666f747e1c992d95e8f47b91f5eaf5d94e10dc056b0f27779eff5adb",
-                    "0xdfb7ba9a31170bdcaeec51bf85f7edeeef01996267c97fb0d8e1e28138d3608",
-                    "0xcd7dc40636044ddf4192d48a9a52992cace8d6fd6d428f27c842a878702e1e8",
-                    "0x7b8103a051e155edd05433c18852f364e8066339c03338a0a20119347ea7618"
-                ],
-                [
-                    "0x112d44f6becb495ce368b4f18961a73f03dede32c519e3378ce90257218e437f",
-                    "0x915f5adc6d20589d1779286e8540554445571adeb4e6fac1c9df9e715e6eb98",
-                    "0x1ba864532dc4d54e4c469706f819d87ac19dfc7f47000811515c9a1174ea00b",
-                    "0x1a6b1f1fa2b0be62b7050d737e5d9e262ff3fb05a025c986a9752f2da990529"
-                ]
-            ]
-        },
-        {
+                "3078320190771076262412873347051737190533757156987186234683795634861248119986", 
+                "5722601819712865833063992565453245209633789585987183895205076391281570131548", 
+                "4520975219946485001694103770581698444755978549980127415852238695379721685115", 
+                "7050003880324188466537429486029383228122772145772231365546122143186583597939"
+            ], 
             "params": {
-                "seed": 5,
-                "logTwoDegree": 4,
-                "logTwoBound": 3,
-                "maxNbElementsToHash": 10
-            },
-            "expected": [
-                [
-                    "0x27c859c68cea50d412ab8b7c569b978365e00f904040aa42fb4b609d76b033c",
-                    "0x35c608a8e421d0f4d475d9bf9259286b5e1047ba7b52fe53bc097ec61ecebfb",
-                    "0x862a22cbdb12433dc059b74b61006540e0d6a1c7bfc566741ed61d72de7b304",
-                    "0x3e9667d4e310e46696fd22d7433607cd9208f2b1e9a4558a979e20912f79d68",
-                    "0x255db53cd109c9bdbaff9938e4f601ac90c8d58804b81686d025b18fbdeed39",
-                    "0x446140d3af52ae358f55016d80e77411cb2bdf89150b60f53acc5304c709333",
-                    "0x55c4c4229f26ce3ab989599a4551fbf31e4dc9b3a99072d8b539f85d16ae7dc",
-                    "0x44e3c94c43e86991bd359bd39e73b24b0cb903c9bd622be6ecb624755f71901",
-                    "0xef788687f4beae8f625a7bc44df875b031350696b56518d627e36c88ac451ec",
-                    "0x9aba92fffeef54a79d0aad57249cfd24f6a89af41062c722f7a656e7289323e",
-                    "0xf28905abfefe47128cfb5d154918e5cf0cdd366d4956fdd41194a0494511ca0",
-                    "0xd1763c3bd8cf4289c4d858fa3fb2383a1d491e99fee1a3f84b61ccc8ab69468",
-                    "0x855314ac31bb7579ebf5d0478b849c017abff2b88e533b86a7bbdb9a310b2b8",
-                    "0x200369d0984172d720cc934982f0a638010719ad04e9409fbf906420f2e976c",
-                    "0xe33113024a317b68d46ccec273cddf2c237d86441b069ee5e43ecf1b3151fa1",
-                    "0x100a817ac2d1f9d65dcc8a2084f782c39c19d632a6302d01cc393839896367fc"
-                ],
-                [
-                    "0x5c9317a5a644ef910fa91e64643029bf75666a44ce4b368f7b8978cba550c28",
-                    "0xdf60f5c9c9330f6038a23a857057131b3c6c513d2558538ea8c4cbe324e2fe1",
-                    "0x711958703e8ec0c3b585f9a3ab347e15650128f12ca3e0f429adc58d0e2e27e",
-                    "0x384705bb697de3694a80334b262e82225355bbc576f1aba40703e67269f6503",
-                    "0x835a26bdcb09c0858ef9e6119e3d862a42f8b38039ccea97818067298502e7c",
-                    "0x7032d776c976f0a8c6895f11e4ed69a073b216213472fa2e2d832b70e7b4b4d",
-                    "0xb8971f1d440747065a3362101e51c89cd94b42983654946e3cfe646e9a189af",
-                    "0x304828cb8eaec61f2c453976d1cfee5f5c4a6d85a91d2e0062bab8aa32a730c",
-                    "0x53a73cc414e34c54eaf88b8b35c5740ff5c75d5fbc20ab329328b719d7968a0",
-                    "0x10f48b90dd48db89818753d5500ce8921ffd60e7ba7d2150eb859c532cd78737",
-                    "0x111a93e38b9947cd59b698de259728191d5d76356037d500e53dc3afef0a5ac1",
-                    "0xf789c9481317bada709c22cb9ae11acf8203d4f00fca97876d01e85f4f94fa9",
-                    "0xdd4f8a67d020b1e83f4a045a69c86dd108cab0fd3f6a62a63e5ecb2886bccac",
-                    "0xa126ee57a5eb173bdcc7bf721cdd7d95b78af39f2e57c8c522875bef16c5a5c",
-                    "0x41d479dfe37d18ba23c7c5e7e62af585425b4f877107141da329aae1dd9d8fc",
-                    "0xa523bdd07a1e6d18b122ad3ddda3854a177ce776bce4ca42edd9a8f7ac9f095"
-                ],
-                [
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-                    "0xd8f1ad24abd98d868ce88b82e5fa2602f5368ba91a52ddcb81c51de21c5489f"
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-                    "0xd29bf23e95e8bca42e21f8335f08f365bab904569d070e8c0512b9059cfe9bb",
-                    "0x29ec59cbdecfb4b34062f81d9202bd73b9d0496f79ae26bab2324fc7d41617d",
-                    "0x760dbb11b79ce45aa89a9db2d064175742cc13eac60c249dbe9ed5199bb4ee0",
-                    "0x17c4d20b3fec25c3edc94d89e4b2e34182c336c75a9bd8f0c914f3244592d7d",
-                    "0x38194140403faf7751ee7cb91042d228d24c8411d62f3c8c6661df6bed59c5c",
-                    "0x75cac9d1b5b5287d29980eb11f958405ba406754f77afc8645546c1530a8101",
-                    "0xe002602afd7fbfaa0b51ee001bf7077e94eccfcd286c1c11458366450f76995",
-                    "0xdc67a4511c90127ab0a2e66ca0c81105a2bfce5c2cb004f34c6b5d6df16bbd2",
-                    "0x207936ccfe2a2ae659d63ccfe6814265074f9ad17c3331d1ef7dcf5fcdfea78",
-                    "0x4c2e3b6b283053c769f44d9dc3f6e93b069d1152ad02cd065678fd4644050ca",
-                    "0xbf34a4714ae88ee35d885fd4bdaf20d1c4a63bd9d968bf3cd8b95d7c2e90ce9",
-                    "0x2b39e61a757ce2f39f79d169089e59d8209778c9cda3f2a17ca381ec2242863",
-                    "0x1214da3f49a4ac11da32da5d8f35d4af8217e74238706beb03550a0c4263958b",
-                    "0x7f37c6749c55f975dd1e8ef5a9277165a9bd6f2d672df0e356504ad073ec969",
-                    "0x99ebe640762c0015e88f785fc4a48d50518f5e07e9b0208129ed6f29abb7e30"
-                ]
-            ]
-        },
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 2
+            }
+        }, 
         {
-            "params": {
-                "seed": 5,
-                "logTwoDegree": 4,
-                "logTwoBound": 4,
-                "maxNbElementsToHash": 10
-            },
             "expected": [
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-                    "0xd4758f7a9af3771909a7c8431fe78074fe3850c577aaf1403f9525bfe38650c",
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-                    "0x12824bf2ab3718747544054a273ce6fd9f6687e39a7ca8b98fb957e7216560e0",
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-                    "0x1af5e501b0cd9d40d1d858f050b96461bcf6493a4b59f0233762ed1a2187cf2"
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-                    "0xdcfb3faa6f255429c06d5d8517ce0835c833f1ced220e7d8e2e127b7928774b",
-                    "0xc41168fb4b56f41ab4775aa6b5313b47c413eadbe1797bdf83901e444ce583f",
-                    "0xeeb1afc0826c36baae3755c1bf2a470e8a6ddd8745ccab947bd0d1cd9622aaf",
-                    "0x6f51e8d71b16b95d854f32cc2cfb37f6d8a06c9e393202e74124674f542e0f",
-                    "0xa8cf05db6ca6591af36a6f6232ba1436b480de8ec344ae5eab2b208f1169b51",
-                    "0x3774305973e411185f7c3ae0d7d1ea246fc06a7c64a3e56b99fe985eb8df62d",
-                    "0x4d1d78aafe1a00cad6f543b975105decf3a6305dafd7c1d28ce8eee6573ee4f",
-                    "0x10f8ae9229d6ddcf0053b830102d6573d726e18433b0bb14151c5dfdbe40b91",
-                    "0x90bd766a9fc749b6abdd0eaaa3fd28cbcfd8dc2086702bb2cfaa07b6d7abd3e",
-                    "0x7a9c622d3444ae6abb5f8551c53d3bb1f9baa7b0afb4d3f90b864cf7d8a367a",
-                    "0x51937a7486c27a4baaf334fac581be596caefd89d8a8ecdf45740eb4945fa23",
-                    "0xfc747fb47a87020e6dd0f0374e20f8e4d2bedec85cc85415421bbb56c709ed1"
-                ],
-                [
-                    "0xc30af117a421a6be8a34d31eefa625b7915bc6e7fcafa0eacb571a38a4e4146",
-                    "0xcbf8acc1641c4140e7d83cc08549bf49ab2a211abb27e1286e0b454de3e7330",
-                    "0xa5759a3b2c50353b512d1f9df3525e64ccfd1d9a618bddde471d74606419dde",
-                    "0x2e6098944b34e24c20aedf63215c8cb776d38328462f027cca907fa9a0740a6",
-                    "0x70404dcdab9f763f5e5f682b0db2af38f2e34dcf462480ce0850614860e8d83",
-                    "0x10aa4137d325c8ad2a5dc72741a30a0347ca71d0573bc45a4c76f2becb81f911",
-                    "0x4423969818b388ddefd1b82b4af92f575b26a63713d79bc52cfebbbcec7ea17",
-                    "0x120fd7e634f85efa5ac1a82d577808d13f3b3c2427af6661d000df91c04316af",
-                    "0x9c55eeabc6efbf0f5a55ae270687f2d29b9994a992753738d9dc7926a90ec1b",
-                    "0xc20dee2ab6c53335a79324e752a4c82e325d7ae44530b74e795849c861cfc1d",
-                    "0xb2c69384c5df93bd499b4c4eb5b39686913cde78bee659616a97f1121edd5c8",
-                    "0xa58dfd54126615c892977b8271df555d262ecd84c7bbd2beabe7bbe1f056d4a",
-                    "0x88a5ee217bff7c6dac2a98f0d5ce9496e185100893919c17caf023875c9fc9b",
-                    "0xe0c97f9b48bbcfbe507870e2c82f9f391efe4ecd29d032d090a2daa8e690388",
-                    "0x4244291ee47ffd8e5079b036ccb1da5249389f7fed98836dc4743a176e17ab0",
-                    "0x34a319bc51dd45ac9f204bd6402d0915f032d7f963e137d241c0bfdbefd553f"
-                ]
-            ]
-        },
-        {
+                "2299542015288307956558364039061873631490919342272584797523675030775062718862", 
+                "14932832174090352428924927870700305089009956568077435631000559610052431588", 
+                "7233535885147252397062964264366959924650260371246848761281868739353860587981", 
+                "1759568569393991896322194380438707338663648355408975713999300578069388282124"
+            ], 
             "params": {
-                "seed": 5,
-                "logTwoDegree": 5,
-                "logTwoBound": 4,
-                "maxNbElementsToHash": 10
-            },
-            "expected": [
-                [
-                    "0x183e84a95614a7fe4e8445f6d8e3d5f643886d786ca1b7061c8d84ba488c59d",
-                    "0x6c598f3b4b7e18f92a230fb5f7a610ef748013b83133354b2aff6ad17c6a2e2",
-                    "0xb4dbe829c110653f1b6043924c09fd77d92fdee5499f871d1dce01142ee78c",
-                    "0xfb5c919b1f040507b0a372c5a2889c2a2a7d9e9011b97ae2dfa2ea0bde5cde4",
-                    "0xc7248080dd44cf9da62e5eb18bde2e78ba900daa51c1239e3cc0b18239cffde",
-                    "0x5585e7ef4572cdc79bd5dcce2280285f0e1802fff11f1ef0c134066dc1eb0af",
-                    "0xc9307dc26cdfa52abd7076a9d4224c1c3adbc52f04219e248c366f3bd36603b",
-                    "0x70c21f67b618202c1eb1a8430426942d00edf4ae97948d78fdf829efc552d4",
-                    "0x6015fe92c8bb2c99e5e7673deca41a8f1f35f8d3d29c018084c13f71c8c3403",
-                    "0xd646c61baec0d0284658a646e3d989068c6ba931a7cba2c32035bfb480b0c38",
-                    "0x1946cea1bbad0c3c58c71aebf12ab4c31a749200c01ec1c39b4182357215322",
-                    "0xffd0b0948d03d525fc16f9254a2808e9554aaa9fd2f1ebed8db0813c7af636e",
-                    "0xc067de83a0efb697480b8d16e631eefe9ac49ec42b7fb854d74c9477925026d",
-                    "0x9792b5f17013d7a5c50aec941867b54d4adc073b21c29fe31f3cd7dede551c6",
-                    "0x91e0a0814a30bd1fb38c04f6ec00e585b6c9f42e50ca452da8811b7143b0d1d",
-                    "0xece8c2b280decba8207cfade84697356f4cbd4b854aac01ee4752a3c7415833",
-                    "0x8a04cded0a63a760cbea13513f2baf226d3c7f8ae70b68d8b01b0a6a0d80dd8",
-                    "0xf6594008ec81897bcc3990e78d95cfa0f237b557273b44de315667cc542117c",
-                    "0xfc4c5c2536e3585af6ddf6325d97279b4973a1a2f3a76470de61dac42ad9b0",
-                    "0x61b735dc103a4818ff9ec454b87ec114431854797d87a8615400006219709ff",
-                    "0x6da999ed5e97cbcb140d41e115459ce3cef6bf0e05573d2830b1358bc966b45",
-                    "0xead4bf95ad541b70435a564c2a32ff2e2d132856ad3e0483796c95b2daf8290",
-                    "0x417878216bf7dc1ea9e833e94a7bad86ad54af9375d658e8e081ccfb979cf4d",
-                    "0xa9b0c8f56b6ba5c0d82690d8f87cd2818bc4042e0b24559664108de491aed1a",
-                    "0x114c5ded08d252c5ec96f31696e054519df4e483546a71bb96b3ee01e6f34f44",
-                    "0xc338d593cbb03794c86b2c8bad48431d451e037adee987f12c21154f42f497a",
-                    "0x75dad63223b20ced1269a0b7699ec81d766b76940c7f52cd944fb705489c7da",
-                    "0x1f0df300072411dacb6ac60980e44df8071ae11e831c10303053343dd363807",
-                    "0xe2b63d5e3c11ffbe5b2c8d0a10f3a79f689e6eb94814c571492a4f0a4e889f9",
-                    "0xc88d00ce739f553fb573e71aa83080f8df5e77fa50f9055cdc5959eaba073cd",
-                    "0xb6465ae79b4c6abe2cafeb776feb397308beb4af644e551680fe218e3bcb15a",
-                    "0x7e4afa656aa0dfff9ca13dc96434c639e3ac25755149f7e601202252168a4ae"
-                ],
-                [
-                    "0x5c9317a5a644ef910fa91e64643029bf75666a44ce4b368f7b8978cba550c28",
-                    "0xdf60f5c9c9330f6038a23a857057131b3c6c513d2558538ea8c4cbe324e2fe1",
-                    "0x711958703e8ec0c3b585f9a3ab347e15650128f12ca3e0f429adc58d0e2e27e",
-                    "0x384705bb697de3694a80334b262e82225355bbc576f1aba40703e67269f6503",
-                    "0x835a26bdcb09c0858ef9e6119e3d862a42f8b38039ccea97818067298502e7c",
-                    "0x7032d776c976f0a8c6895f11e4ed69a073b216213472fa2e2d832b70e7b4b4d",
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-                    "0x9915b9b76a13a6e4c0939f26c137bc4730480c42b2c3b7c5d35a641043a609",
-                    "0xf45f63b76c50625347007844ac9c51fbf691c2b53b88478b74347e2263c1d0",
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-                    "0x9fca38ef455ed01febc5d898dfe81ed73887fc840910d9e37f916df4297c0b9",
-                    "0xff41a17f7afe71afcf69ee030bc419f29fda903c582396e9338a375008c6993",
-                    "0x724f04528186c321a29254c88c3a7ea427a2c7528f2385b4b766ad38ca7883",
-                    "0x10db8170abcf3f63816cf65d1ac0da75e110e7ff77514d69ceed7abb89720024",
-                    "0x87fbcc3cd6450ac34b8b48ef6b317c5507a11539e57559f7d5197c0a868a2e8",
-                    "0x2ece61abd58c0498d67a42e3ea8f821df1471f40c0bf9f31516069d4418ab4a",
-                    "0xf48bd121dd315581838d64597025ccb78236318a82f25486332089402b9cd0",
-                    "0x19fd2363b13bbee8230ee51ebf22bd520d5ea14c879f196be8f6e662d805454",
-                    "0xc33b30172cb41370b55417371cf4f55fe32dd90c49730b39662bc2e29e9597c",
-                    "0x8eaaa915e258c41b559a6ab34d84bc99b8f77b3d9bdd69c42ca9012ec550298",
-                    "0x6ed7cd3fa9546af14480d52cff52fb9b4b46780b80cc6787755b12b67aba81b",
-                    "0x30dd385acb96e7bc8a98b5fb9df095c4dad4c48dd7ced3e69f143e48aad7be6",
-                    "0xc1efec0c3a48c4eaf45050992b31c00c2db8d4d78a0e360b7b88992f3789ca4",
-                    "0xe83ce771be518a7e09c94db2d8554ee354b1f86cd95774f0a5b19500ceadee5",
-                    "0xf254ff677d7b3cf494f6d7055ea6e270db28d7f2f819f1a9d0f2fca2b0c66b",
-                    "0xf0590aa0d5dfa39ba870f6c20053c7d94d9f2eeb8488f2bf8a9f306dc6b7317",
-                    "0xf70f63f1e634a3f3824c15d9ad54e517d557b4904facab5e3fbc5a78f35eaa4",
-                    "0x590bbc3dbb4dbfaa5675808e5e996ce96fe1ad8adaae3bdf6893d9d40766bfc"
-                ]
-            ]
-        },
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 4
+            }
+        }, 
         {
-            "params": {
-                "seed": 5,
-                "logTwoDegree": 6,
-                "logTwoBound": 5,
-                "maxNbElementsToHash": 10
-            },
             "expected": [
-                [
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-                    "0xa7b5252e28ea14e170914c6cf93093ef468d2a2cc5d519d556e2bb4f8647355",
-                    "0x519cc4ff4cb30b6c5506483a9f0377e6aca90db4844caf893b5e4e37a15626f",
-                    "0x21e4c8efd9f89921cc5bcd76539ea00b2ed3a120b8000ce87a62bbade80cead",
-                    "0xe3f6582f30fa25d195109caeebc174b570d71a3c5d1ca3ae8433cabfcdf970",
-                    "0xa3876d9da21e268ed93166c863ece4c053ad405e06ccfd38c208474f2564a5e",
-                    "0x10fdcad4af859fe66014235438b7e1c693dadeaef444b8aedf8be9e0a94ed276",
-                    "0x3aea85939baccec14d8cd6c7a6526ad22fdc6f9db615fa7345fdfaa2b7883c6",
-                    "0x641662f860401ccb39b695a35c54349612d8c4bf86e36c36dfd098fab2da78",
-                    "0x33c7418b9a6638c8a6bc0edf9714047bbc181dd38503e8a2781455e394eeba",
-                    "0x1195c3c1e111525cbc901d2fcb79e5ab124b0d1229ed445e6809f664ee3f9385",
-                    "0x86af082b6b300727e334c237cea5e3577944ea95a4773621171a9a798523646",
-                    "0xa2511885ee3a51019a0d15f484a20818f38f8804f8596293b6c3b7362b52b91",
-                    "0x67b200b1670d74d4c696c5510f8a3afb5c7081b255c2afbb02421e409490d9e",
-                    "0x5e454e3fb0eab798bc6474b7a27f8b86afa9fd129db41fde26c05a615edcfe2",
-                    "0x127db4ace1e78da315104318ef8300574633898ff09cfea95e20ae8f720e7881",
-                    "0x122acbd3868be52eed241eb4b86e62458e89aa3e55c16ed12f9711a4019f7ed4",
-                    "0x9bfa2db177d5b92054ff2e2046988a5642336a7b3a0ef83a06940c4ba485200",
-                    "0x86d221915504c6154b117d26af659519ce63124d62bf824afb23af270acd219",
-                    "0xa7f116c431cc7db2162423b6d34c81c8f06af38b66a049f49e22bf5be34233c",
-                    "0x37bd8c143feadac51d9915eb60504cdf125148e2901a16457916e2be2cde613",
-                    "0x11873f3815415f3b2f2a93b3cbfc95d59f5f03e5a754f22a9c3995c7f9afb173",
-                    "0xabee77cbbf6ea8bb6521e6dc7a79873f245a76cb4a5fc8796c2ac816cd4595e",
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-                    "0x113b4c606967a8e8a5e37892b6e8df054e1b63eab43f31aa0a4e2e6967a2a85b",
-                    "0x32508a7788b3aa6d87d31dd5216f9dbd88791893e55ed49e9eca0f72b70e9d5",
-                    "0xbf12bbaea8ed6a6db142803d05c8fae8f2e574c76cfc47fee9974f0df465c26",
-                    "0x877bddd92a06e1652cb12658b6d5888a361fe06d3fd7f9641e3c06912d004bd",
-                    "0x6b7763f7d9c727330b76440a24598af1fb3084a6f7710f97bcfb768b6bb7fe",
-                    "0x1297867593dff427b07cf7e409323e77e65d15ad452c054598e5f4d278f58eda",
-                    "0xb3d9ee390f13b2be6ceb0e0805dc0a2c5d9142ee3fad056a65711b60fe0f4ac",
-                    "0x110e5a3a2cb5aece57d2899b54a254ac0077575c035864ee1a5000b3aaa138d1",
-                    "0xa00405d0bcfe353a449294f5f6a889e2fe1f8607539e6bcbb83b51318860c8a",
-                    "0xa525b13dc42a1ae6f12edbb778f844b8b7175cb1218f83e47b614036c462d8e",
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-                    "0xe42fc906ec9416aa434731bd1684b5e4334c1cd287597958ad2a6d457f129a5",
-                    "0xdcc580bcecf85b8ba22ed87eea58d6329c5225d3c523b3d95c5b89c7127ec67",
-                    "0xad08079b553a9849068e2d5780999a37c93cd447785fa46e5333924a9585ad9",
-                    "0x8aacd918e0f00e097ffb7d4fe498b0e88c40ab46d72d58b95e3b1fac0de6c5",
-                    "0xd5751eaaeffce98fedd9aa116506f0c1165e2134f92852ed2e412b5cae98578",
-                    "0x1145da2a9c93da68b41f3406d1d37093419c975573288d263f05ef091a1e432b",
-                    "0x1200b662e634863496e82d0b446df82c931d8f6e33f001fe4f0f0798c310c22b",
-                    "0xb04f726861372e21564e56f8775954e0d5336629c8bb2db96de8e3beea50d7b",
-                    "0x9f4b30aebfd1370f70631606b4fd1b2da738374790f29066e66ac2cff84c527",
-                    "0xafada425af7eaf71f770324102eb0cb3d8d0e8f02edbfdcd74475713135071b",
-                    "0x9023c59df7d93da197fd70abdc48ceb87426588a703c4832874d3067e25d579",
-                    "0x763fa3eed306ef5623247253667ffb119a4fdc48e32b806dc20ea1a7214cbdc",
-                    "0x7a8d694db913d7d855a318a3647e07575de2025f833f63ccbdc408e74c71274",
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-                    "0x107c65f15e21c16975de28b262b1bcb426083b42b6c850f901c3ce7ddf5cd0d4",
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-                    "0x1c79a7916f2a532c089dc3e10c887de546daebb2d7028837e08e531e08f0559",
-                    "0xce7730bbdc4de1f89568fb673ee5b37b5f7538460cc9205ae7968abfb1a5d1c",
-                    "0x3377ab8b45f4842951c310fd5a79c0cb1782d15be8c848c87dbd063443cc92d",
-                    "0x7dbc09cae4978f34db63d45f64d558eb16d72eebfdaf995de7a51b876c798c0",
-                    "0x84580cca74813a3b314edb5c50dd5d2240bbd736ead6d0118d0c4ccc104a296",
-                    "0x1620754b33a4e0d90bdedca8beb03199247e26008a7363757e951fe05d0d209",
-                    "0xb72b418edc08254cc00bc895ad35da2b3be4c9b9e1a856bea680ec60433e49d",
-                    "0xa58e6f58fcc036bdf149a4397a020c78530d27db18c19ebcd5485c08483aa5d",
-                    "0xa5ed139dc2e5944b1867d794915124f730b0c5f1876e65aafa6ffeeede6c3f4",
-                    "0x3fba26d8b4a04460acb7fd09c11da545583f622f9503a11588e1ac2eeb66ec9",
-                    "0x54bb9c4e3bffefee48778af907d0e9be534060d3765168f7eec17982b686912",
-                    "0x112012e1156a72b7ccb06772864bb0ce4f81bddb9001d60846559703616a3603",
-                    "0xeefbdc0acf36a445ad0837844ec39661050f759c026ec941d6c0b36c67dec9d",
-                    "0x5ab1553568877fc810475e0db37b0f3242a40865feb8717ee5624983a2896c6",
-                    "0xa73e2fd081f0394b88ac8e9a21da7cdd2db4ef1543af2459c17f8eccb7e3a5e",
-                    "0xa7158031eb9f9f8960a6337829aee7ef1afaf07354e4006fa8301f24d7a3523",
-                    "0x789541cfb2fc21bf698c7d9a0520abca76dc73b95356c1b407b4c055604d473",
-                    "0x1164d8a921760a4ec52ca2fe10df28eae3e9c129e63424d82e27be4942512cf5",
-                    "0xa55b194265b85fb9618d07a3e996e8c474d3c986b9240bb8a9f6ce0306adc23",
-                    "0x79c28b4937dcfd4fd589cb0951823e0db228b424ba1e37204d7848a3a12a3a0",
-                    "0xde1a936ee3c83587c8740278648dc62e91cca0f71f734a1323fe9fccae7b285",
-                    "0x77a3852648eca85e5f68f722b0c8aa2f3820b03f77d4f7e180963eb1a401f34",
-                    "0xa7ca6b941bedba2eec723d552af65a40f93e3ed9cbcc4125a3c778ff1230f69",
-                    "0x511d996424f19fecf074b9cb81c65b260d9d9a283eaaf78f43b564aab310b53",
-                    "0xfa5c15bff6ddfcd31b668665164b3beb8dcfae3911132b64736f6a3c962841c",
-                    "0x5e3c8c3de5391f5a31813585b2b294b0983dc14a6d513f352a071483bc2946d",
-                    "0xb28a3799876a27eb7ca5b8439939fbc43d1dd208662e33f33a3371e5a98e35f",
-                    "0x902dd0a927defc963f48797030c3c4f6873c399c04e364deb2c20ef9d28d464",
-                    "0x4ace5f6c577c3d9182628640aab1f21904c54801e60e45565ae927ca217ed0f",
-                    "0x10c46f26a3f32c6e8068eaed23e0eff53f5976772bd95efaa28f43efa4b5f3c0",
-                    "0x15eb241407404f51804d58bc004586c40d28d959b9d15dd14d8d6ad688c300",
-                    "0x2a3301e9d73308485dbeddbc3f2e6957fba68f04aa05cab1577d91ebae20270",
-                    "0x109809a2afe0a723bde9186c6b80cd5a636f5d2dc54eb65584896d7491be9195",
-                    "0xc08ddb302ab39812c8518e2840ad8fee0aea2c0b5de096240488174d37bf4df",
-                    "0x26e2f3e76046e3a2bf83cd6d7f7e82539603aa66dbe5a7d030177c5f4556227",
-                    "0x2f3306abdb50e5ca842502892df1181b033b35f877f35e989c772f4f245a7fc",
-                    "0x655d51c84ac3c5382d3e0320f1779265eb410f4404c80437a55caacb27845b8",
-                    "0x608623b2ec1e9f636e6194e5719edb67749440bff4b2f4c3847f2e675c5633d",
-                    "0x443e63e6f5d269816725a3f7ac8cac7f19ea344be592c1d6587acbb0fb99970",
-                    "0xfcea546e566dc4f13cddfe8848b16ea272b8d8eeaaaa4a103c679456388b279",
-                    "0x77182c9d354baeb74830a1e6ec460f54bafd0554d7f7884594b722297d07bf",
-                    "0xa2957ddf0364a0a346acbea7be5931398bcc05f8beafd64049252c78f0a6271"
-                ]
-            ]
-        },
-        {
+                "4350576149771551611219207265205854355662122459345445035725765564897087286207", 
+                "5194668121908679018796438272367959962134017757764111600596380114707652814588", 
+                "5627264133846894265194482571773797655570000001334400910313928056946338473909", 
+                "27575157476448708348562273940820210103976480498063724672134383293314039718"
+            ], 
             "params": {
-                "seed": 5,
-                "logTwoDegree": 10,
-                "logTwoBound": 6,
-                "maxNbElementsToHash": 10
-            },
-            "expected": [
-                [
-                    "0xc643a981a9cf693706978383788ad022f7f41e327f5c5e06480adc8f8b69853",
-                    "0x48766a4d65ff2a06e97c9e08ada208c37492123a2bc51e6ffce369174072ac7",
-                    "0x1c6177153d3cca5b32c669e2d717a6e51e9d9fd5fa83f94badd620441537f9b",
-                    "0x70ea53072071b4f405f06583c1b2dca3f1c1570ffdcbeb4d1e3484daed180e1",
-                    "0x9637a5acac4a89c3e60f33025829ba0f6e47a0bde863d5ac3840429e03dbb34",
-                    "0x3f34acfda25d323dc62acfb7b7fda17801f3256dec840c93db0f437e87d7635",
-                    "0x1e3c113ad76a62c75e56304a4d8fe5b4840cf928902d246532b0a0bbc8fd68c",
-                    "0x4115675c042738c25f2ace6733d0b2814eeace6983c08fd8b1581468ee42155",
-                    "0x592173242889b481e0d6d7af4cef47e303fd5fb0fa62172472fb982e4bb12c",
-                    "0xbd483251447553dc02ca35f04dd7b8083f1a0acb56d7d7720affb0b89cf648d",
-                    "0xc48ed07a54c97a22d461c42b624a472378dd5f7aaa16b583d59a8184afd5919",
-                    "0x11ab80e48111b8c43ad59da3071b1c37512f8a1835d37635b578ea1cebd9d4b0",
-                    "0x5624a7785bd528e1b1ead54aac1e71b8844f725e7c0df164da39a0757895041",
-                    "0xe9950007bc7f1d0765f9dd8f4bee577884051faad70ba28ba44675ab1575d82",
-                    "0xb707a41264b0cbb91ee00abe39e1666db29a6c3f3ac9c59ea2990806cf88d15",
-                    "0x5807b2011b565e7fe3179ff06e1055e4f0889489773e3a090f96d9745c12208",
-                    "0x6802fad274d0490d5315e144ff7f082e51d69a2a3756a7eb5c2886d5df5246c",
-                    "0x32ba7f9fe3a1d2df15f17533b987386f1090ddf77cc108c3a7ea8259bda273a",
-                    "0x91a973084b7cadd4e950699f27f41d2b2432da5abcd4468ef68e9c0cab469f3",
-                    "0x272c8ba0b20618223f15fc2dfc82ff43390c19eab9c1fadf8857cb5afd69a77",
-                    "0xf5b7365561b6fb5248f3f94d503eeafef73dce44a37831fb8c8331caa5703d6",
-                    "0xd146399afd53f73bcb6d127ade9dc8e0c8762a5f43904fb96a2f102c76c92b6",
-                    "0xa920523a28d3bbe8c78b2d87d1928c5a9a4d1c845dd910fbb312ee29a8a2f0f",
-                    "0x52f4795f0e1d1a579415d649e62c215b7c8af0273ecb53ab648035f23006ea",
-                    "0xcfdf080aa53d8e14a64a2998476be9eea1816d66e5d10b54b3fd739019fd3a6",
-                    "0x2bd43d133c9f271b71ecbc66e6cfed124679129206042db1c8efdc60ad089d1",
-                    "0x56b84a1b69185959a4801aaa7f99601874d651f8ed0397c109ffcc6ea7eb8a0",
-                    "0x12a8a64cd05ab388c5b5afac234adde479d4461f0205c24238a6a8a715c981cc",
-                    "0xcd7baf0122e4993d750ee4a03bc91b564dd961e3e5f04126b8c4afac549db4e",
-                    "0x7bbff2b3fd6d654f1c6167e32129f4c204d22259c10d49f212ea52ff651d9d9",
-                    "0x1c47ef30628062474b411d0d060b12dd4f0dcad590abe05e46966deeaddb0e9",
-                    "0x33b03e6211bdd53d14fd7bc6a1690484559208a3bf142d996a91a241f9c7e62",
-                    "0x98ea9f5fcda1e1e3e39f7f83c14375fae714a2bf31a00a6c17ed0d42e33bb4b",
-                    "0xabfd1ac742e09e6d18e019a0b4ea6bbe3cc44fa32fdeb3a18dc3bd13a512b9f",
-                    "0x4eeae6d7f1cd9664a482c0e30a7df3c1e6b3277c79fb6dda039e2181527b9dd",
-                    "0x8ed710e0feae756d759f793b20a5b05511cd9bfe53bfe543895598b807a01f7",
-                    "0x1168bd0902641c384b1a9308fe340c3b10e7556c66c4368fd7c9e1572a549951",
-                    "0xcf0df2c217f3cc2fb76ec358749e3da36bdbba0bd6e5d1a0ddfed30c6a46acc",
-                    "0x6ce52132105063f91b5d0b9ca353110bff6f7ad8414917eb637f69cccea5720",
-                    "0x105cc0bb5a4f6a8442cc5b7c6b0dd246b0cb3e4d64e13a14eb80632334266d7a",
-                    "0x2d69518166eb2fd4d87275a56ee9df562dda526c645bec28fa13f0db358ca29",
-                    "0x98d0dd1831e33f4a130ed0d32cc26f7efbb38f36dfb28a3c8635b04d5b7b13b",
-                    "0x103816a822f088dbabd00be143e963677bbefd9afa1323027149897981eee122",
-                    "0xd169ca1dbd5edbb52ac22665a6b0df09acdf69e54118ecb6edd3f67238c086e",
-                    "0x4f27a85c2e26f2d640e006f39e6cb3edf3feb528b96cf15b207b1563c0614f9",
-                    "0x58bc298cb4f9eac98adee3cb76d5d3b86a2f931afa9767ad47cfef44dba5a27",
-                    "0xd382945c9c3da884d7a60c789dd87a12352dbc5b3e562a9c708a49aa84424cc",
-                    "0x5c69d4cd90e4270753b3629904418f9c3680bd0cf8ebdd3328d6447b2255e3e",
-                    "0x3956c8c4d44ae69f05e7bec3e7b36b461efbe852c46c67e0d33fc46f78770a9",
-                    "0x749a51c16737836235fe3c68c0866cf18f32ac10b9fb151a7933d5c155245ed",
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-                    "0xf649bcf9f70a26c3c0010122ac95424f7b58355fa0c965532114bfe4c78e639",
-                    "0x33de68b9136a67a6b455aa48294cf83c27970865e4586fd9089602c9420e635",
-                    "0x17de11fce5f5122d1afb4743bb63fd2b71a1ec6b7bccd6b7088e74b510c446f",
-                    "0xb2dc4f373741433397cc13812c83a721e0fea620d97d5284e9b7f125d833550",
-                    "0x571632004f67725e3e047a2c3224075e40640d20571f72c7c552f1f058eebcb",
-                    "0xa601a2dcc33d3da3628a52f36cf11090387a73a3e4f77a94e404c414b7ef6ec",
-                    "0xaa26048b14d8eec5723d655a1e4ec1918807274ae699baa0c572e4467037348",
-                    "0x109dc00c605c383ddb9414c6f65c428999591e22d394887f3da5a9f22dbd858d",
-                    "0x809533a7a4a95e7235cd6beb25343600bbb8c6cee219a2fa9a17ca7aee6644d",
-                    "0x960e3c7e763f4f7ec09425ef36cead67d32b2a1628057514d9537bea71064bc",
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-                    "0x1b4c8eea4cd700cd89235bfa573108739fda626f4ce2a09ccb29dcea7cf17f8",
-                    "0x11bcc6f149f4d5e2250e06cbbff7699f64f108f76486eb4a7d8be6acc28fddf7",
-                    "0xb357cbd879fcd19ef353c88cd0ce2dcaf980fc2c2e5b211263f6f607706295",
-                    "0xbc8a9cf2f55c980c3410cf24eef773474bd07f4ee2c290d2afcc7dd908879a",
-                    "0x710539cdf9ab347d0eef6c2c4b1139b522f59154a7a39a9174aa10e0ff0c469",
-                    "0x1169cdd32ad8c9164018993e7ef4fbbd32708a50ab8377f3142af07ce81c1f06",
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-                    "0xdbedb0a2ed5371409f2ba151605386c7ed162d951c95879a3b0383bb2f8e244",
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-                    "0x53c3fe3bc34782dd798293c1cea1a04de0030b3af4e103b3ff3e7c6efd96c91",
-                    "0xdc0417369f03bd23d5842fb3f7d2fda162c3e33749b715b8fc56546c1c3b33f",
-                    "0x22c2d29182eec48e804d9a42d02e85bf2cef7673487ac9566949a4a43f99f2",
-                    "0x88c1f38e8b588cc109cd3baeae17a30914cc0e4a3b1d80cb02aae3f480fcb33",
-                    "0xfc34e830deb8d33184ae47106864c715175c1e34a46337c434a37b47acd3265",
-                    "0xd3466cf834242a018ea2a0ca61ad7cec5efe485de84a3ee9dfbf1d97bd74692",
-                    "0x114e8ef4a9edc7fd8f7a2d953c918e8750cbad4548ac0dd7fabcbda20ddc5df6",
-                    "0xe5fe83ac05fabd63aae903e7a39bfec40cc8b35ec6464d46e2122904f8acff2",
-                    "0xded59118e64b16ab7b23500e030d57b6dcc0d95b526f6f8dfdaab071505664e",
-                    "0x19a388d94b4d1847c95f5be2db46c51a9b2117d2f448d0ea2a1730d6b19fea7",
-                    "0xc8393be5c37960b532d0bd1009fbeec617cc5f732b67edfda9442b671abec9a",
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-                    "0x3dc931300702b2214775758bada24326f73a7e585b3902ac5e88da0dd6abd7b",
-                    "0x82ad6fa3c574557d1b2b8aa4da0e7fb7fe604a999f3526be820e7f7d660adb6",
-                    "0xee58f39f479fc79298e2bd3823cf012988f2114baa551c1fcdea4fb6ea5681f",
-                    "0x6b5b1409263687ac928b1eaab57aaae2e3b099c985b4385cb13fb28bec03697",
-                    "0x1a86aec9c430a0b73213ea8562c51c1ea376104a43dbd218aa96164db7abe65",
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-                    "0x70f877caab7092c2d3e8b0fc50668ae2197d24badbc49db9721be29f5155ce8",
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-                    "0x10f1ccc0cdd795bf673d3764fc112316af441cd91c6944aadfec241bab1d8d58",
-                    "0xdede81b26b14152eda274928d9831a7ab0e9ff429dcf4f3df800d25a9fa57d4",
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-                    "0x8a8973a67c27db130b289f70cc56165fe086e551a069ca726bdac923385c316",
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-                    "0xc20b6495b25e4083bdc9a6d7283d275067b6337e5eaf056b9342a4ea6b6c0cd",
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-                    "0xec1863389310f8f1008aaf53e2fd5c4a012592181ff6e0a092f653b9117c2ce",
-                    "0xddd7044de49beb91679fbac54892a499b71ec6572830592d9b0a2094a823128",
-                    "0xd524f573d8360e9c2cf1029e2741ae57dbe650064447a9a2b3b5da097b9311d",
-                    "0xe5a0a07b53188b48fe5f6c8d11d859d8f6d7da0800cd06abe9efc03440af8c2",
-                    "0xc18d4c36a0ea056176fea1e640affb36fc61bb1abac42b9b760f08e1a6775f9",
-                    "0xc39b7bfd4f320f1cdc704d774401345ef5058951255e5e4e4203601e7d8ed9b",
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-                    "0x10f984665c2c478d3dd662387fc68330a48b6cef0c19594f9fa4b619137dadba",
-                    "0xd9e9e7ad9058ada47eb0e6a5f0fc5d9aa216ebe2181a2578d135d0ca122ca0f",
-                    "0x82a86a60f0079c344e393ca8298fb50c31a95ec78d779c8dc92fa92710496b",
-                    "0xf7e0e9191b26766cceed5ee39faf10353d1779f0eb8f6a5aa51a3a4ae8358b9",
-                    "0xdc829f657430efe4586e02c86425be6a5ff6e4664bc610c7bd5bcf286412315",
-                    "0x123caa53af0a81e15e573255e0aa60ee8b70ad0e5b4646b1e2804d566c856fda",
-                    "0x117b7e10c764de7ba555b36fcc8d771b56f5726d37af1304c738b80a43c0a465",
-                    "0xecf0bd37a1eaf2bb5437614c6fc77033ffd9ecc494867588b09a9989392352",
-                    "0x9d48de061184bc673fb7a61c2e9842e1c00104260bfb873ceb9eeb9aeb305ae",
-                    "0x17489b5618c9f38ed9a487b0a903c95f4c4047c0707f84e50d6a8e45da8c6ed",
-                    "0xd026030b7fc5f4d033faa7ab9bfd6ae3ce584fc1a72a7252777f47f9e3ad2d1",
-                    "0x98a3362424c20555e6c42157324cf0454f7d8b79e8d6a4206e6322dfaba802d",
-                    "0xf3200abe60a657f3cb067264c45cbbda0dfe4d7dc8aa684afa26eb22b0f1e4b",
-                    "0x89fea945752f4229d6ac029252e8e42bda82ff3b5673654d1a4cce52658a935",
-                    "0xa0ae5c7d68f21b84baef337c379cc7494157ef8532a17e55c1dfdcc7fd48276",
-                    "0x2c130b6e8ce32050b012d675bd0e7935fbcaeae824656e1afc491be38fdd254",
-                    "0xc90f968958d3ca5540dd2c8a673f623311fb1222e1101b0297d0e18538a544e",
-                    "0x1b245f6fd13cfbd495dc035199ab1f4b03ed8d385d7e8c692f8dde814ceeb32",
-                    "0xdd09caab683b53bb767748fcfe26a69beb820c94a2b92101c5371ff0074517c",
-                    "0xacc420815b078f59ba5f3f3fabe10e9d88388e4a6ab5616f5b294a1e8aa83cf",
-                    "0x979109fe0ad29c19666b776e7031809a20089cb825efde7aaba803c54ca1461",
-                    "0xd0d11c36ee40654feb312367376e1efa4fc797a201bc3359d210134ba5c5fff",
-                    "0x10118a5de1bf083b717b0366ddf899c98773dff2efe17bf965f0ce664a630ba1",
-                    "0x4ee1e2ec7979b9f67a5aa2e735befc29ac43310945c29888f9b778874bef436",
-                    "0x623411e82b57f4fe5e29f90404ce740bdc772c3dcc50b4f195107e8c5cd8e5a",
-                    "0x127a6341cc4b5570f922acf7c2eb7c08580a0552409e0da642d78c9a57e842c7",
-                    "0xdb52d14367e8af0a5e947220f6ec3198a5e8a271bc03d1ed11ae3cd91fa944b",
-                    "0xec7291e45d49521efb90f5814f395fb096515150d43adb53bcb3ede3a9d19f1",
-                    "0x5276f17b6ce01188d9f23b6d6505d0717b45983db45518db425293fe9ecd429",
-                    "0x45516fdd374c199e7ab0a08fe9dc622fd02406a8d15c286696e2c3942bb7308",
-                    "0x1445750b073c748037a8f5e13f7df2a7a0683db44a8fb2acbd352a73f7146f0",
-                    "0x2aa8b186d3b93837155005f778b34490333d961cea5313ae2f2443de6d8a850",
-                    "0x134ced89665733cb05043dc6a402fcca7a16ac32a9fe29e826da5c593651a30",
-                    "0x1007e420652a93c90eea4695a3dfdf046ab7cfa181cf72acb59c43151c9ebc1",
-                    "0xd9a627d6cccc1621171e49f3707ccfd99615447e19011f0c6050228722d10d8",
-                    "0x90579785857f6ccb7f642e9ba3e09a6c9b22f1ae9d8e86c4155e98d5d564db4",
-                    "0x71d3f5cf520ec86e08dcf84b0b71df659238d794844f6fa01ed3e0e64d1acd3",
-                    "0x39e8990ed55e3d8faf5c7c8e052317c075df9d4e28a58e53a2d5a92245cc067",
-                    "0x106595726daa8dd4ddae20c400da2122745c83de977a227007059f4645dc312",
-                    "0x67107403048bd4c2c3c976727f0eb7ce76a9e41b9eab7f96f5962ed2e79b143",
-                    "0xe23d21c528b6f38adb9337f06e591eec09e99e8d1e0c9412a44b87e6bf15a3b",
-                    "0xb38cda31e26523f5803632221de04823c8c0fe0c62ab82920e06592652e6324",
-                    "0xb77594f9ad76eb2a001f6abc8f32e7ab47d0e207248708cb5c2a00cb5209de9",
-                    "0x1b2c4196400622e6b6f2de3f6d14bf6d1efc99d649d94d524cbe084039a8c86"
-                ]
-            ]
-        },
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 8
+            }
+        }, 
         {
-            "params": {
-                "seed": 5,
-                "logTwoDegree": 11,
-                "logTwoBound": 7,
-                "maxNbElementsToHash": 10
-            },
             "expected": [
-                [
-                    "0x76c8729ad7cb4a21d127d19b63f1e9bedc92e75fd1c54c3bbbc96afe7038ca7",
-                    "0x3386f3acc32e25516c7300e4cdb9f3c831795d02935025c7614b2fb74ceab92",
-                    "0xba0bc875b90325274d05df0d24ee81c5dc1029855e5f8666beb320ff864520c",
-                    "0xd5c671f403fe07ec4e99fa3149e644e6fa3300b8b72082dd005ee8e20bf1043",
-                    "0x4e9e08770089c13677c869d12984531d2a101076c6e6903fed96ec18ca35202",
-                    "0x13669f45d3aa363cba7e5498edef687f46bf765d2555cb98ccadc3b0cbfab32",
-                    "0xa96b9fd1239284e030418073ed7173f9fdef215adb59a17832f3ad53fbfc639",
-                    "0x4f927fbe6204a03131e36f8888289d4b43c410103228ae9cd86f93ced999f6e",
-                    "0x112626b4ed083d107d858aa23a573ecd7bcf67a96e3cb5942943450ffe474967",
-                    "0xf5f563faf73b36636c3b577ade2091a4e0caef72e9e84808eafc8e0ecd3d942",
-                    "0x53ac9630aa2de6b3adf98e997c8043b8fecc14cacc605bb5411c08646311a83",
-                    "0x11fe05ad0dcf2a1c21cda047d1fb48200493fcd10d385fd0b1e90ba4e17aa813",
-                    "0x21bbf0eeec87cd414cc8598170a3c5f6b53da75912e0b8de773d10761468d6b",
-                    "0xee5c5f64ac1d5c53310ced2a1b3743781d20859fecb561d2506cc774f96f6b4",
-                    "0x69042a3b2277cdcd65918541bc7ae76c9a2f5eb11776dc8f13e11c6cd28a58c",
-                    "0xbdcd1d7b47a0e1c5d53f11a9a731d86f1c44826058a1917d452f496e71536fe",
-                    "0x108f6a7631790dbb6affe9a2402edc12d65a94b5e04fea2c127467b3e89fcab3",
-                    "0x8e63bfb57d1622355be2a4c1077a10b98aa10944e1287e0503c8b613dc6a159",
-                    "0x33d7d9fbaa0d59889c875359df0014e29a6cec0f2744203e7c7c5748f6a50da",
-                    "0xce2bbd1973e133a53d3c4d48eb127f03531052ce9dd9d787e390baf56b0f419",
-                    "0x8a3ff947c501050cfe7bce86254a53840f9e8912372db25867d8868e56af6c",
-                    "0x8df6eb2598ae71c38062bd41a3bc4d28c55216dc2ad4a32fec4bb3bb75ed3d8",
-                    "0x4dbc0fa061fc263cdb9d8cfec3be9ec5b83cc77f3d021d7d30e001794f188c5",
-                    "0xfdbc19e94057214a3961c1bb68d3b50a46f5e0d3ccac30576d1d6db910719d7",
-                    "0x3bd1849e1612ac333da01868bcb1f0c2e88063469b527ee768d471fb9466c5",
-                    "0x654ec5933b7f2803c6770d362ad3f75af89ba357917235a7488a1a1f82359a5",
-                    "0x35c53495e8d4e8630d41131af2555db5befa476b73d221cf78a256d6ac4c0fc",
-                    "0x1210dcf3c2f1e17547404f317c4491d6c5fbbd80f09b7e5e06b6dcbe4ff49ad2",
-                    "0x51f641de3f54b7ab9c6b492a323993d3d02e19efb8fd12d57f53f47ae59c7f3",
-                    "0xe5af80af01e269f32fd1f328af0f6673d5998be73e667a584d95c772a6a7ab2",
-                    "0x9bf76c798203ecd335c892b5c00e8c4babfc78e0b187369a1ff8bdbe92095ff",
-                    "0x6350f3dd0fc8332406fe80e970d64fcb0cd6e45a30df3e0406f261ab367e1ef",
-                    "0x49a4c5f34d6c93a8a9f471be6daaaeddf4870ba6f349bb28b4c290daa7aa982",
-                    "0xf20e5e74cd87bb4282cefc34fad06840f4767d5160cf02d61a5792c7485cfc5",
-                    "0xebd1617df46c44e5c04707722b91940025ced7e9b9d5a5fd56e0dc567315179",
-                    "0x85c8e7314f6f35453d10ab3a1e90dbf42708839cad142065e7c0bbe12c92952",
-                    "0x5db03fafd2dc7c924c3bd2d697bf5b1fffd7a3a7d91a84328ca4c583cfd91bf",
-                    "0x390f8ed56d9babfcf595590f03c384d83012913811a454fd7e444f6e268b28f",
-                    "0xd72887c1af2b73b7bfa9ba40c07abc50e9cb6d26dafef3894ddfa84acdc2e53",
-                    "0x1150847b8a94c9bfa3f3fdb2d212229d8a3a147759f5e7a10f629bcc6f299811",
-                    "0xff50197ecccdc177febe02d9880ec23d55df2ad57f42759d2ea0087cbb33f2f",
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-                    "0x935735485749453a781f8d825cfd9824373373f5b372c7a70f717259fad3302",
-                    "0x126e2f109a930f024194111b74caccaad73e7ff23e3a98932129a2f1eb7bad88",
-                    "0x4e9c4dcf01e0099821bb6e5195c585f03447ca5f5bffce2d366dcbe1a55eee5",
-                    "0xe87c5f1086f21f6a21c2a050d42a8ad4628ce37c0a7bbcc80ff010894a82c2b",
-                    "0xa48d46dead84343c64cdfb869c74bf17d25a9d5b1c5ee883cfb9dad95b741f8",
-                    "0xab433390aeb2f9951323951e94b3b3921d7ea210fb50ba14480519d049f695b",
-                    "0xd9d170b136a3b7db6fd8966a76e314a30602d4843065767ec7430bb76ecdb15",
-                    "0x6647e3858e361fddbfe5cbd6aef6d3c39ad5d101b66fcd9b6870da8a87c2903",
-                    "0x6bfac249ba2915efb1c3154d5544db551c499a4d9dcce645b3ac07dbb630a80",
-                    "0xeaa6afd27a6e176e48a55dce956e342d619df6799ac0536c52090a8ca372ac0",
-                    "0xaff749f16632cb24eb133bb6d33eb8cb5a0af7124ded1d3ca0d2a15a6888f09",
-                    "0x99ec86011d6aa23ca1a52e2b1a42b9070e67982d0b08ce7c1e3cd408e7818e1",
-                    "0xc99c3db973d8bd135fd9a8238cd5e2064ac21aeaca51349db73f1b3841240c",
-                    "0x11c86afbac1b4621366cb175404bc20a6751ff7591b7780037e55f1fe7af2775",
-                    "0x11b1bdd6ec75f982a600726c970fa48a542df5ce4a23779579c835bd26f8eb2f",
-                    "0x7d8d4a5acfe0a60cfcbbc55e07973883ef9c062600721c0dbdfd67cce656fbb",
-                    "0x1158c821b0d7e979763f6b58eec6de87fafcb1f3ff8838abfe3a1be80ad4f0aa",
-                    "0x251b3cc9271c16519c8de7b445b9bbbc93c0fada72a8cf96ee47f2f9ba7374",
-                    "0x886c8fe1fa904f746b8e632b3e8095c23086b3216408e2b2232d5899b1247ea",
-                    "0x121dfbc3fb9c92237bf66437290cb544ab594a8943a48aa4ee8f56a9089467d",
-                    "0x562182f9b3f0ba52f84f6fe7b4b1fb4d64b390cd40cd66acef2510ea26d934c",
-                    "0xcf52119791b776ee1143e20022398dcfd146cdb62d985d8332285969da9ef3e",
-                    "0x21b7ce7d576d01fb41db8e7e92d3537aff4cfb1a0f5ea2278b865fac6faac1f",
-                    "0xdb574a96e681dc1356a4e2c892771428eaa1253157aec57bd889ff6ae722e90",
-                    "0x11e9a6c0635d3d45015f501fec48acfdb2d73cca2e64d09c58ef65655cc3494f",
-                    "0xc18594b5000a9d26523364f8a032d86a4a051e53c19863b6f7efbe29ccc3ef5",
-                    "0x92509c9dedb5853b0800075d1ee63d22de3ed7935227420931198ce39c41bc7",
-                    "0xe4ad7d57d0c3db8189fa7592343851c9932bf59fd07810f656f18717d4175ee",
-                    "0x2c6e3dceb94eb71dbb7a6aa5e25de69685ff78abc980da00a23cc52483082cf"
-                ]
-            ]
-        },
-        {
+                "1098214087705584201028990279934649779177338882271963760347384798718201351976", 
+                "5840556312695378082480546769349838360321356495169693994360721592312337970436", 
+                "502346333244351887108168429833529195005523926949517499908945345870158134515", 
+                "2519454607714422385904965998366856792820612859011611269024027962032393129493"
+            ], 
             "params": {
-                "seed": 5,
-                "logTwoDegree": 12,
-                "logTwoBound": 7,
-                "maxNbElementsToHash": 10
-            },
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 16
+            }
+        }, 
+        {
             "expected": [
-                [
-                    "0x1b883281ab6f9ebd5a87ebfe41d429868ca2a89833b6ad1907f72c906feca0e",
-                    "0xcd04a9a089126e94a598a27a3c38bb88141c244807790c23ef625b5a718bffb",
-                    "0x5827acf8f552855766aa014a7bc110e10ff1981d0be4a6555874ffd29b17c5c",
-                    "0x112a4ded5a5514c69dcc527e6f9d1fbe0bff7da238069557df80d15ea8be9ca9",
-                    "0x4cef1a6a8481616eecc017d08cd76cdb7524abcd72bad230bb602aeb3103093",
-                    "0x74ce5edad5437c472e5c416d4f0cfaa89e5f6d58d20366f86b8d85ff9ad08",
-                    "0x82a0ff916d3f6618b1a29b4309e2b01c4433e6776c82d996b62fb2792e4ce60",
-                    "0xd20e0c0c9adee75c3adefee2d77856de7c15eab8cfdf0d1823412614a8e7c29",
-                    "0xbad33b7d7fee6804060e79c4c54f9fabbc8fe358f5d1989cac63c74a7d33317",
-                    "0x7eb7db6763021f31e3ccd794f61acdaea5407fe92a41539f23ed9267460f901",
-                    "0x3cb20802b88390cb15fbcf0eab4dcec2249d6aab61f35ce0caca05c12961757",
-                    "0xeda95b40e20356c9dc93c4711d78aba747cf8fcf98528a456b729c9f386787",
-                    "0x1065d06f118df0b6ef154aafbaa867eea14abee3d8e90fbcd87cd55c27a6bf72",
-                    "0x101af41ac5a9481cf2516665f24670380ac029004eb826b6fa31fb5758a5a1fc",
-                    "0xd1e021f84e0b17a480578a7d306f6ad00bd0980d3305e79fb1c407b8dac3159",
-                    "0x49052cc493f78c02ac65edfbc5c10b5dc6fb67a17cfe7415c39d3e84871de9e",
-                    "0x258647ab2c8baa784d436cc26b6eebd7be7727e3c185e9e4814b477062f0752",
-                    "0xd9a78b0bb87d21346de8d201ca0c7e95457e0ed38b22204d7f46fe31015ff0f",
-                    "0x10c61a618d749dc3276529774cd7765813d0110ffe60836ac205a3482bcacf3b",
-                    "0xa77010f722de2ed4f23ad5889cc7f40f5f894194c3c3b245ea982df18eb9675",
-                    "0x122635dda752343a6d2a8f256eb96a1444422f55fae8d2d83adc6dcd54e900c7",
-                    "0x9f55be5438f3629f4b73ba4147b59e15fe28d1e679490f02c76bdda12bb94cd",
-                    "0xd2b5ef2f99466292c2e74813a77a03d87f8ebfac93ded092d93e7cb1a7a8a90",
-                    "0xfac99e0822153485a9f6338d8234876a545da6da560fa1e34b9f6f497023124",
-                    "0x33d41d7d08fb81b2002344c249558332e97d6c89744b8e4a6f84e67e1090c69",
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-                    "0x915b09bdd6a24c4929c4f496bbbe383b5564fb6b6a64a603ee17c00037a98b3",
-                    "0xa67a9fa170c829ba9468e880848ff87f12267394bfcd2ec6fdf199747dce13",
-                    "0xe4f643ed7c1053e685b028ea781f26ee535c8df164b6f5d397d07f6c8930a2b",
-                    "0xb67ae8e4ab67109af5ffdd886f27bd5ba885cbe465d62e6b8d2c0ab4af4751a",
-                    "0x1220faed980453b623d740a610d112307f19b979f692febb8ca9229dad8790ce",
-                    "0xe8d6ebdc0894ad83a113af7119a2037c6f580ee3348644bdef9cb29c959e2b2",
-                    "0xb46b820a5069c08ba3cf5ea5ae8dbe8f21138518fa8d2298586768e3c406f2a",
-                    "0xdfbd521d3658d4e131109edb746ea202b61aa2787932c445e7a5f35977ffba",
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-                    "0xff50197ecccdc177febe02d9880ec23d55df2ad57f42759d2ea0087cbb33f2f",
-                    "0x118e908dff6726767a4d1a32e5e014d12ef652c134aec832e6bef96e20769866",
-                    "0x80c3421f94680dacd88465ca29d1f3902d1b2344073a028adffc3c4a952333e",
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-                    "0xc03e29b3551b4cc8e4700d85bc6373cd7795f338f7e82370fa99b912abaddad",
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-                    "0xc2fcc67cbcef9b61ed27b7c17e9e27bc1b97a21b736ad126e824a61aaefff5a",
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-                    "0xa037b5fa6e61b2450156e80ce32d968efc17c2a49e787d18186e927405826ff",
-                    "0x1049bcc65f64d633e5498d24779816549a3614abf755b24eed5d2493712cc8f2",
-                    "0x1261f6b935ad8ce604df4ad7cbe3c0c20a626489209f089f6cc80dd1dc1731e1",
-                    "0xae5443382e20b33829f6a52eaacb580cf9203f9661df2e4b5f6434dab7b6db3",
-                    "0x19d6472bbe78521562a967d52b2ae15087b1f9c6e642c4691fa718d884c0274",
-                    "0x3ebd34fccd0a36afc38689bc7f686e538d61741ada2e3e4719197b76945da86",
-                    "0x560e9ea20238ee557c2dfd47f965efe52a44ed448c3e4360eef234a1b8928d9",
-                    "0xff44618ec57ef5b01307338abe2354e156c4dd45ee72c15b881cf343e3fdc35",
-                    "0x64d4aee9040d91545a189e7867dfc901b6bb4b2df45b1ecbc538f728c3804e9",
-                    "0x67a4801dc661c33317e6cea046d4f8f86fb56049262afe4b5bc8f627cf29172",
-                    "0x3f1bd955dc6dc2ef5a3a6346ac680cfaba073f942b81c33c4234dc504aa4147",
-                    "0x4e8cb6da282069fd79cb39c9adf1ec045e40452dbf0b3b249012a6359b2eedf",
-                    "0xa50104b4f8271b72dfa63e1463793bbbabec93176252f668b0b13cb8328ed49",
-                    "0x2d1ae801cc31a6695a3837a02602b8637d43749c0ef68f2c066195f68ee0e08",
-                    "0x4527008fee915ec483cd274232cdeb5ffd58c166f4b3ab6c1df059cfafe5395",
-                    "0xff07efd669fac3fa3b310302041610d5726c860d6c9c46bd38aaf08482216de",
-                    "0xcb82d0a0f89b7c5ca4cf7a9c8300bee62962f704b3e980c8cc5d247366d6b64",
-                    "0x10ebc71f3e7c00dd1dfebf895190ded2cbcba920bbfc7ffd492618bb1b774683",
-                    "0x33a6c7fac1cda0b394b770441d997a661fecee07da92090c0d6e1c748cb6e04",
-                    "0x8aec02852f5723215c32f52b8479740c4dbc5381797e28fe2d7ebd4d4c52706",
-                    "0x4abdbd95051bc158b8acf0a731685940e33cc52e3bcfee59406e54aa87eb8dd",
-                    "0xd0cd0dc006a0b69b2ba43977baa417cf83dfb5dffd7c9d7c529b9a666307878",
-                    "0xefc89fbfd7be8258cf086e066deb8d5c5e1b2e5e1f3bb4428161b7a7f13ddb1",
-                    "0x10b7984e110c11ef7efeaaa5b7696cfc5ed3e71a9e8c81c5b629a5696480ce97",
-                    "0x4bf4944627b7775f3615f140865b09bddfab4f5e1c6e977536726f402e4ad68",
-                    "0x7ba3291a4150991f148618b2b73f7880cd76eaceb3c6429974e232fe07bf37c",
-                    "0x9bc5514bbf9e6bbbbf27ce1c8d8b274b7e8f40c7629191215ab73765a9d5735",
-                    "0x22911af8b5c751c2382b71ac8068792a4774e8b231f5fb2e71ead4d9a5fe7ff",
-                    "0x2e498e0b6eceb39ed9f6be88d6ffb836837d202d73384fee32ac05c7e0dc30e",
-                    "0x1584b5d8456708b1077346119335baa80385a8488fea9ef7d8171967b93c",
-                    "0x331cad2cf9b6e4c774c6729a003d22d3fc3ddacfd15d30bde0afb8b5bc46fd4",
-                    "0x5c03191e5244e91ce779d5c8f926371e575eba5032e5f618acf27fbccb153ac",
-                    "0x62aa587e15d505ad67606d72c6f7e0d50abc494abb114fdb85eba148bcfac38",
-                    "0x5d195fcb380e4a11e4a17a814430f7164357d614457f61740778c3eddfab58e",
-                    "0xe73948c70a3ccda7190ae073a54d95de8211ac3ba8fc25c30e1c0a13c962793",
-                    "0x54822cdfbaf3af7e868df18628053103f67c8edb7fd69907fef6e6e1cd03a94"
-                ]
-            ]
+                "2878142440770287446237103243570433635916060847890000492456275976003550583942", 
+                "7581986747702364392257503612715167286857424030265102790915724415703872137486", 
+                "82640310927743198664550767151312393063879669961366890571375144793986128510", 
+                "1993344095428118188371379780027716529856355178339508848345834912187066201031"
+            ], 
+            "params": {
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 32
+            }
         }
     ]
 }
\ No newline at end of file
diff --git a/ecc/bn254/fr/sis/sis.go b/ecc/bn254/fr/sis/sis.go
index fb4582c676..5af87d5e1b 100644
--- a/ecc/bn254/fr/sis/sis.go
+++ b/ecc/bn254/fr/sis/sis.go
@@ -1,6 +1,8 @@
 // Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
 package sis
 
 import (
@@ -8,7 +10,6 @@ import (
 	"encoding/binary"
 	"errors"
 	"hash"
-	"math/big"
 	"math/bits"
 
 	"github.com/bits-and-blooms/bitset"
@@ -99,10 +100,10 @@ func NewRSis(seed int64, logTwoDegree, logTwoBound, maxNbElementsToHash int) (*R
 	}
 
 	// domains (shift is √{gen} )
-	var shift fr.Element
-	shift.SetString("19103219067921713944291392827692070036145651957329286315305642004821462161904") // -> 2²⁸-th root of unity of bn254
-	e := int64(1 << (28 - (logTwoDegree + 1)))
-	shift.Exp(shift, big.NewInt(e))
+	shift, err := fr.Generator(uint64(2 * degree))
+	if err != nil {
+		return nil, err
+	}
 
 	r := &RSis{
 		LogTwoBound:         logTwoBound,
@@ -168,9 +169,10 @@ func (r *RSis) Sum(b []byte) []byte {
 	m := r.bufM
 	mValues := r.bufMValues
 
-	if fastPath {
-		// fast path.
-		limbDecomposeBytes8_64(buf, m, mValues)
+	if r.LogTwoBound < 8 && (8%r.LogTwoBound == 0) {
+		limbDecomposeBytesSmallBound(buf, m, r.LogTwoBound, r.Degree, mValues)
+	} else if r.LogTwoBound >= 8 && (fr.Bytes*8)%r.LogTwoBound == 0 {
+		limbDecomposeBytesMiddleBound(buf, m, r.LogTwoBound, r.Degree, mValues)
 	} else {
 		limbDecomposeBytes(buf, m, r.LogTwoBound, r.Degree, mValues)
 	}
@@ -322,6 +324,71 @@ func LimbDecomposeBytes(buf []byte, m fr.Vector, logTwoBound int) {
 	limbDecomposeBytes(buf, m, logTwoBound, 0, nil)
 }
 
+// decomposes m as by taking chunks of logTwoBound bits at a time. The buffer is interpreted like this:
+// [0xa,        ..            , 0x1 | 0xa ... ]
+//
+//	<- #bytes in a field element ->
+//	<-0xa is the MSB, 0x1 the LSB->
+//	<-we read this chunk from right
+//	   			to left 	 	 ->
+//
+// This function is called when logTwoBound divides the number of bits used to represent a
+// fr element.
+// From a slice of field elements m:=[a_0, a_1, ...]
+// Doing h.Sum(h.Write([Marshal[a_i] for i in len(m)])) is the same than
+// writing the a_i in little endian, and then taking logTwoBound bits at a time.
+//
+// ex: m := [0x1, 0x3]
+// in the hash buffer, it is interpreted like that as a stream of bits:
+// [100...0 110...0] corresponding to [0x1, 0x3] in little endian, so first bit = LSbit
+// then the stream of bits is splitted in chunks of logTwoBound bits.
+//
+// This function is called when logTwoBound divides 8.
+func limbDecomposeBytesSmallBound(buf []byte, m fr.Vector, logTwoBound, degree int, mValues *bitset.BitSet) {
+	mask := byte((1 << logTwoBound) - 1)
+	nbChunksPerBytes := 8 / logTwoBound
+	nbFieldsElmts := len(buf) / fr.Bytes
+	for i := 0; i < nbFieldsElmts; i++ {
+		for j := fr.Bytes - 1; j >= 0; j-- {
+			curByte := buf[i*fr.Bytes+j]
+			curPos := i*fr.Bytes*nbChunksPerBytes + (fr.Bytes-1-j)*nbChunksPerBytes
+			for k := 0; k < nbChunksPerBytes; k++ {
+
+				m[curPos+k][0] = uint64((curByte >> (k * logTwoBound)) & mask)
+
+				// Check if mPos is zero and mark as non-zero in the bitset if not
+				if m[curPos+k][0] != 0 && mValues != nil {
+					mValues.Set(uint((curPos + k) / degree))
+				}
+			}
+		}
+	}
+}
+
+// limbDecomposeBytesMiddleBound same function than limbDecomposeBytesSmallBound, but logTwoBound is
+// a multiple of 8, and divides the number of bits of the fields.
+func limbDecomposeBytesMiddleBound(buf []byte, m fr.Vector, logTwoBound, degree int, mValues *bitset.BitSet) {
+	nbFieldsElmts := len(buf) / fr.Bytes
+	nbChunksPerElements := fr.Bytes * 8 / logTwoBound
+	nbBytesInChunk := logTwoBound / 8
+	curElmt := 0
+	for i := 0; i < nbFieldsElmts; i++ {
+		for j := nbChunksPerElements; j > 0; j-- {
+			curPos := i*fr.Bytes + j*nbBytesInChunk
+			for k := 1; k <= nbBytesInChunk; k++ {
+
+				m[curElmt][0] |= (uint64(buf[curPos-k]) << ((k - 1) * 8))
+
+			}
+			// Check if mPos is zero and mark as non-zero in the bitset if not
+			if m[curElmt][0] != 0 && mValues != nil {
+				mValues.Set(uint((curElmt) / degree))
+			}
+			curElmt += 1
+		}
+	}
+}
+
 // Split an slice of bytes representing an array of serialized field element in
 // big-endian form into an array of limbs representing the same field elements
 // in little-endian form. Namely, if our field is represented with 64 bits and we
@@ -339,9 +406,9 @@ func limbDecomposeBytes(buf []byte, m fr.Vector, logTwoBound, degree int, mValue
 	// bitwise decomposition of the buffer, in order to build m (the vector to hash)
 	// as a list of polynomials, whose coefficients are less than r.B bits long.
 	// Say buf=[0xbe,0x0f]. As a stream of bits it is interpreted like this:
-	// 10111110 00001111. BitAt(0)=1 (=leftmost bit), bitAt(1)=0 (=second leftmost bit), etc.
+	// 10111110 00001111. getIthBit(0)=1 (=leftmost bit), getIthBit(1)=0 (=second leftmost bit), etc.
 	nbBits := len(buf) * 8
-	bitAt := func(i int) uint8 {
+	getIthBit := func(i int) uint8 {
 		k := i / 8
 		if k >= len(buf) {
 			return 0
@@ -363,7 +430,8 @@ func limbDecomposeBytes(buf []byte, m fr.Vector, logTwoBound, degree int, mValue
 			// and set the bits from LSB to MSB.
 			at := fieldStart + fr.Bytes*8 - bitInField - 1
 
-			m[mPos][0] |= uint64(bitAt(at) << j)
+			m[mPos][0] |= uint64(getIthBit(at) << j)
+
 			bitInField++
 
 			// Check if mPos is zero and mark as non-zero in the bitset if not
@@ -388,7 +456,9 @@ func limbDecomposeBytes8_64(buf []byte, m fr.Vector, mValues *bitset.BitSet) {
 
 	for startPos := fr.Bytes - 1; startPos < len(buf); startPos += fr.Bytes {
 		for i := startPos; i >= startPos-fr.Bytes+1; i-- {
+
 			m[j][0] = uint64(buf[i])
+
 			if m[j][0] != 0 {
 				mValues.Set(uint(j / degree))
 			}
diff --git a/ecc/bn254/fr/sis/sis_test.go b/ecc/bn254/fr/sis/sis_test.go
index 8a2c55f892..08431ad778 100644
--- a/ecc/bn254/fr/sis/sis_test.go
+++ b/ecc/bn254/fr/sis/sis_test.go
@@ -1,6 +1,8 @@
 // Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
 package sis
 
 import (
@@ -37,7 +39,7 @@ var params128Bits []sisParams = []sisParams{
 }
 
 type TestCases struct {
-	Inputs  [][]fr.Element `json:"inputs"`
+	Inputs  []fr.Element `json:"inputs"`
 	Entries []struct {
 		Params struct {
 			Seed                int64 `json:"seed"`
@@ -45,7 +47,7 @@ type TestCases struct {
 			LogTwoBound         int   `json:"logTwoBound"`
 			MaxNbElementsToHash int   `json:"maxNbElementsToHash"`
 		} `json:"params"`
-		Expected [][]fr.Element `json:"expected"`
+		Expected []fr.Element `json:"expected"`
 	} `json:"entries"`
 }
 
@@ -62,7 +64,10 @@ func TestReference(t *testing.T) {
 	err = json.Unmarshal(data, &testCases)
 	assert.NoError(err, "reading test cases failed")
 
+	inputs := testCases.Inputs
+
 	for testCaseID, testCase := range testCases.Entries {
+
 		// create the SIS instance
 		sis, err := NewRSis(testCase.Params.Seed, testCase.Params.LogTwoDegree, testCase.Params.LogTwoBound, testCase.Params.MaxNbElementsToHash)
 		assert.NoError(err)
@@ -70,153 +75,167 @@ func TestReference(t *testing.T) {
 		// key generation same than in sage
 		makeKeyDeterministic(t, sis, testCase.Params.Seed)
 
-		for i, in := range testCases.Inputs {
-			sis.Reset()
-
-			// hash test case entry input and compare with expected (computed by sage)
-			got, err := sis.Hash(in)
-			assert.NoError(err)
-			if len(testCase.Expected[i]) == 0 {
-				for _, e := range got {
-					assert.True(e.IsZero(), "mismatch between reference test and computed value")
-				}
-			} else {
-				assert.EqualValues(
-					testCase.Expected[i], got,
-					"mismatch between reference test and computed value (testcase %v - input n° %v)",
-					testCaseID, i,
-				)
-			}
+		sis.Reset()
 
-			// ensure max nb elements to hash has no incidence on result.
-			if len(in) < testCase.Params.MaxNbElementsToHash {
-				sis2, err := NewRSis(testCase.Params.Seed, testCase.Params.LogTwoDegree, testCase.Params.LogTwoBound, len(in))
-				assert.NoError(err)
-				makeKeyDeterministic(t, sis2, testCase.Params.Seed)
-
-				got2, err := sis2.Hash(in)
-				assert.NoError(err)
-				if len(testCase.Expected[i]) == 0 {
-					for _, e := range got2 {
-						assert.True(e.IsZero(), "mismatch between reference test and computed value")
-					}
-				} else {
-					assert.EqualValues(got, got2, "max nb elements to hash change SIS result")
-				}
-			}
+		// hash test case entry input and compare with expected (computed by sage)
+		goHash, err := sis.Hash(inputs)
+		assert.NoError(err)
+
+		assert.EqualValues(
+			testCase.Expected, goHash,
+			"mismatch between reference test and computed value (testcase %v)",
+			testCaseID,
+		)
 
-		}
 	}
 
 }
 
-func TestMulMod(t *testing.T) {
+func TestLimbDecomposeBytesMiddleBound(t *testing.T) {
 
-	size := 4
+	var montConstant fr.Element
+	var bMontConstant big.Int
+	bMontConstant.SetUint64(1)
+	bMontConstant.Lsh(&bMontConstant, fr.Bytes*8)
+	montConstant.SetBigInt(&bMontConstant)
 
-	p := make([]fr.Element, size)
-	p[0].SetString("2389")
-	p[1].SetString("987192")
-	p[2].SetString("623")
-	p[3].SetString("91")
+	nbElmts := 10
+	a := make([]fr.Element, nbElmts)
+	for i := 0; i < nbElmts; i++ {
+		a[i].SetUint64(33)
+	}
+	var buf bytes.Buffer
+	for i := 0; i < nbElmts; i++ {
+		buf.Write(a[i].Marshal())
+	}
 
-	q := make([]fr.Element, size)
-	q[0].SetString("76755")
-	q[1].SetString("232893720")
-	q[2].SetString("989273")
-	q[3].SetString("675273")
+	logTwoBound := 8
 
-	// creation of the domain
-	var shift fr.Element
-	shift.SetString("19540430494807482326159819597004422086093766032135589407132600596362845576832")
-	domain := fft.NewDomain(uint64(size), fft.WithShift(shift))
+	for cc := 0; cc < 3; cc++ {
+		m := make(fr.Vector, nbElmts*fr.Bytes*8/logTwoBound)
+		limbDecomposeBytesMiddleBound(buf.Bytes(), m, logTwoBound, 4, nil)
 
-	// mul mod
-	domain.FFT(p, fft.DIF, fft.OnCoset())
-	domain.FFT(q, fft.DIF, fft.OnCoset())
-	r := mulMod(p, q)
-	domain.FFTInverse(r, fft.DIT, fft.OnCoset())
+		for i := 0; i < len(m); i++ {
+			m[i].Mul(&m[i], &montConstant)
+		}
 
-	// expected result
-	expectedr := make([]fr.Element, 4)
-	expectedr[0].SetString("21888242871839275222246405745257275088548364400416034343698204185887558114297")
-	expectedr[1].SetString("631644300118")
-	expectedr[2].SetString("229913166975959")
-	expectedr[3].SetString("1123315390878")
+		var x fr.Element
+		x.SetUint64(1 << logTwoBound)
 
-	for i := 0; i < 4; i++ {
-		if !expectedr[i].Equal(&r[i]) {
-			t.Fatal("product failed")
+		coeffsPerFieldsElmt := fr.Bytes * 8 / logTwoBound
+		for i := 0; i < nbElmts; i++ {
+			r := eval(m[i*coeffsPerFieldsElmt:(i+1)*coeffsPerFieldsElmt], x)
+			if !r.Equal(&a[i]) {
+				t.Fatal("limbDecomposeBytes failed")
+			}
 		}
+		logTwoBound *= 2
 	}
 
 }
 
-// Test the fact that the limb decomposition allows obtaining the original
-// field element by evaluating the polynomial whose the coeffiients are the
-// limbs.
-func TestLimbDecomposition(t *testing.T) {
+func TestLimbDecomposeBytesSmallBound(t *testing.T) {
 
-	// Skipping the test for 32 bits
-	if bits.UintSize == 32 {
-		t.Skip("skipping this test in 32bit.")
+	var montConstant fr.Element
+	var bMontConstant big.Int
+	bMontConstant.SetUint64(1)
+	bMontConstant.Lsh(&bMontConstant, fr.Bytes*8)
+	montConstant.SetBigInt(&bMontConstant)
+
+	nbElmts := 10
+	a := make([]fr.Element, nbElmts)
+	for i := 0; i < nbElmts; i++ {
+		a[i].SetRandom()
+	}
+	var buf bytes.Buffer
+	for i := 0; i < nbElmts; i++ {
+		buf.Write(a[i].Marshal())
 	}
 
-	sis, _ := NewRSis(0, 4, 4, 3)
+	logTwoBound := 2
 
-	testcases := []fr.Vector{
-		{fr.One()},
-		{fr.NewElement(2)},
-		{fr.NewElement(1 << 32), fr.NewElement(2), fr.NewElement(1)},
-	}
+	for cc := 0; cc < 3; cc++ {
 
-	for _, testcase := range testcases {
+		m := make(fr.Vector, nbElmts*fr.Bytes*8/logTwoBound)
+		m2 := make(fr.Vector, nbElmts*fr.Bytes*8/logTwoBound)
 
-		// clean the sis hasher
-		sis.bufMValues.ClearAll()
-		for i := 0; i < len(sis.bufM); i++ {
-			sis.bufM[i].SetZero()
-		}
-		for i := 0; i < len(sis.bufRes); i++ {
-			sis.bufRes[i].SetZero()
-		}
+		// the limbs are set as is, they are NOT converted in Montgomery form
+		limbDecomposeBytes(buf.Bytes(), m, logTwoBound, 4, nil)
+		limbDecomposeBytesSmallBound(buf.Bytes(), m2, logTwoBound, 4, nil)
 
-		buf := bytes.Buffer{}
-		for _, x := range testcase {
-			xBytes := x.Bytes()
-			buf.Write(xBytes[:])
+		for i := 0; i < len(m); i++ {
+			m[i].Mul(&m[i], &montConstant)
+			m2[i].Mul(&m2[i], &montConstant)
 		}
-		limbDecomposeBytes(buf.Bytes(), sis.bufM, sis.LogTwoBound, sis.Degree, sis.bufMValues)
-
-		// Just to test, this does not return panic
-		dummyBuffer := make(fr.Vector, 192)
-		LimbDecomposeBytes(buf.Bytes(), dummyBuffer, sis.LogTwoBound)
-
-		// b is a field element representing the max norm bound
-		// used for limb splitting the input field elements.
-		b := fr.NewElement(1 << sis.LogTwoBound)
-		numLimbsPerField := fr.Bytes * 8 / sis.LogTwoBound
-
-		// Compute r (corresponds to the Montgommery constant)
-		var r fr.Element
-		r.SetString("6350874878119819312338956282401532410528162663560392320966563075034087161851")
-
-		// Attempt to recompose the entry #i in the test-case
-		for i := range testcase {
-			// allegedly corresponds to the limbs of the entry i
-			subRes := sis.bufM[i*numLimbsPerField : (i+1)*numLimbsPerField]
-
-			// performs a Horner evaluation of subres by b
-			var y fr.Element
-			for j := numLimbsPerField - 1; j >= 0; j-- {
-				y.Mul(&y, &b)
-				y.Add(&y, &subRes[j])
+		var x fr.Element
+		x.SetUint64(1 << logTwoBound)
+
+		coeffsPerFieldsElmt := fr.Bytes * 8 / logTwoBound
+		for i := 0; i < nbElmts; i++ {
+			r := eval(m[i*coeffsPerFieldsElmt:(i+1)*coeffsPerFieldsElmt], x)
+			if !r.Equal(&a[i]) {
+				t.Fatal("limbDecomposeBytes failed")
+			}
+			r = eval(m2[i*coeffsPerFieldsElmt:(i+1)*coeffsPerFieldsElmt], x)
+			if !r.Equal(&a[i]) {
+				t.Fatal("limbDecomposeBytesSmallBound failed")
 			}
+		}
+		logTwoBound *= 2
+	}
+
+}
+
+func eval(p []fr.Element, x fr.Element) fr.Element {
+	var res fr.Element
+	for i := len(p) - 1; i >= 0; i-- {
+		res.Mul(&res, &x).Add(&res, &p[i])
+	}
+	return res
+}
+
+func TestMulMod(t *testing.T) {
+
+	size := 4
 
-			y.Mul(&y, &r)
-			require.Equal(t, testcase[i].String(), y.String(), "the subRes was %v", subRes)
+	p := make([]fr.Element, size)
+	q := make([]fr.Element, size)
+	pCopy := make([]fr.Element, size)
+	qCopy := make([]fr.Element, size)
+	for i := 0; i < size; i++ {
+		p[i].SetRandom()
+		pCopy[i].Set(&p[i])
+		q[i].SetRandom()
+		qCopy[i].Set(&q[i])
+	}
+
+	// creation of the domain
+	shift, err := fr.Generator(uint64(2 * size))
+	if err != nil {
+		t.Fatal(err)
+	}
+	var g fr.Element
+	g.Square(&shift)
+	domain := fft.NewDomain(uint64(size), fft.WithShift(shift))
+
+	// mul mod
+	domain.FFT(p, fft.DIF, fft.OnCoset())
+	domain.FFT(q, fft.DIF, fft.OnCoset())
+	r := mulMod(p, q)
+	domain.FFTInverse(r, fft.DIT, fft.OnCoset())
+
+	// manually check the product on the zeroes of X^4+1
+	for i := 0; i < 4; i++ {
+		u := eval(pCopy, shift)
+		v := eval(qCopy, shift)
+		w := eval(r, shift)
+		u.Mul(&u, &v)
+		if !w.Equal(&u) {
+			t.Fatal("mul mol failed")
 		}
+		shift.Mul(&shift, &g)
 	}
+
 }
 
 func makeKeyDeterministic(t *testing.T, sis *RSis, _seed int64) {
@@ -277,6 +296,51 @@ func estimateSisTheory(p sisParams) float64 {
 	return float64(r)
 }
 
+func BenchmarkDecomposition(b *testing.B) {
+
+	nbElmts := 1000
+	a := make([]fr.Element, nbElmts)
+	for i := 0; i < nbElmts; i++ {
+		a[i].SetRandom()
+	}
+	var buf bytes.Buffer
+	for i := 0; i < nbElmts; i++ {
+		buf.Write(a[i].Marshal())
+	}
+	logTwoBound := 4
+	m := make(fr.Vector, nbElmts*fr.Bytes*8/logTwoBound)
+
+	b.Run(fmt.Sprintf("limbDecomposeBytes logTwoBound=%d", logTwoBound), func(b *testing.B) {
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			limbDecomposeBytes(buf.Bytes(), m, logTwoBound, 4, nil)
+		}
+	})
+
+	b.Run(fmt.Sprintf("limbDecomposeByteSmallBound logTwoBound=%d", logTwoBound), func(b *testing.B) {
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			limbDecomposeBytesSmallBound(buf.Bytes(), m, logTwoBound, 4, nil)
+		}
+	})
+
+	logTwoBound = 16
+	b.Run(fmt.Sprintf("limbDecomposeBytes logTwoBound=%d", logTwoBound), func(b *testing.B) {
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			limbDecomposeBytes(buf.Bytes(), m, logTwoBound, 4, nil)
+		}
+	})
+
+	b.Run(fmt.Sprintf("limbDecomposeByteSmallBound logTwoBound=%d", logTwoBound), func(b *testing.B) {
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			limbDecomposeBytesMiddleBound(buf.Bytes(), m, logTwoBound, 4, nil)
+		}
+	})
+
+}
+
 func BenchmarkSIS(b *testing.B) {
 
 	// max nb field elements to hash
@@ -396,9 +460,7 @@ func TestLimbDecompositionFastPath(t *testing.T) {
 func TestUnrolledFFT(t *testing.T) {
 
 	var shift fr.Element
-	shift.SetString("19103219067921713944291392827692070036145651957329286315305642004821462161904") // -> 2²⁸-th root of unity of bn254
-	e := int64(1 << (28 - (6 + 1)))
-	shift.Exp(shift, big.NewInt(e))
+	shift.SetRandom()
 
 	const size = 64
 	assert := require.New(t)
diff --git a/ecc/bn254/fr/sis/test_cases.json b/ecc/bn254/fr/sis/test_cases.json
index 03b1d4e2bf..344e272497 100644
--- a/ecc/bn254/fr/sis/test_cases.json
+++ b/ecc/bn254/fr/sis/test_cases.json
@@ -1,117269 +1,86 @@
 {
     "inputs": [
-        [
-            "0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593effffffe"
-        ],
-        [
-            "0x1"
-        ],
-        [
-            "0x2a",
-            "0x1f40"
-        ],
-        [
-            "0x1",
-            "0x2",
-            "0x0",
-            "0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000000"
-        ],
-        [
-            "0x1",
-            "0x0"
-        ],
-        [
-            "0x0",
-            "0x1"
-        ],
-        [
-            "0x0"
-        ],
-        [
-            "0x0",
-            "0x0",
-            "0x0",
-            "0x0"
-        ],
-        [
-            "0x0",
-            "0x0",
-            "0x1f40",
-            "0x0"
-        ],
-        [],
-        [
-            "0x119f12976ca7475946d616a4374987cfbbf6636db762d93b494e2c9e0549c547"
-        ],
-        [
-            "0x155c5aaa579f7e914d8ab10ab4a96501930a5466199a33571b674e973692dcf0",
-            "0x155d29e2281124cbe693af253f11066900053e0b0490ea2d6a32582ddbefadb1"
-        ],
-        [
-            "0x210dab26ecb89460b987a848bd29979484a69ac578163caf939673c0ca0edea0",
-            "0xe8d74c41735e860265a6221fa63dfa9de8e45e424010053080325343cc00a82",
-            "0x2f24f9283253956512863da0151d5ad5a5bdb4ebe1565a75bd4e094b38829d34"
-        ],
-        [
-            "0x11344683663b7a41a0ae752ac2b16cba15c93b5929921b63ec917bd82ad44f6f",
-            "0x14bcad0d87017a68aba46b00ea3ed62fbc5c598273c5ded833e1eb7582fa9348",
-            "0x139db1bc30591e828ae2cfa61660c4f08d625e88221abb23c10948e77093130c",
-            "0x1e47555ecb8e2dc703524ddb979ee923d84988832ecdf3c1fc44efe933ea2616"
-        ],
-        [
-            "0x29e1498fa7cb4359a3104a64797724a111a2fb523ef9c6fc553d3b455d3dbc38",
-            "0x172374684f74f7ca0b8f24eb9d9defcc107b716b4a73945e21e63529b763b968",
-            "0x25cfb22a52b621990a222adafc99b5b60153ac87f9937352df03c3dc78a0c860",
-            "0x1635ee0aa211eb432594d671d482180332ec52f220f41e6bc3814578f067037a",
-            "0x17747148e6b8635b16634f4bfc2e1414829ec417bd4eb0cc823c6e56c2afe5cb"
-        ],
-        [
-            "0x2e04048554e8e5ab428552519db25acd7379c988094f1ed47f8aad986bf7645b",
-            "0x1fff018faaecc3227d4af3d3f2e8d30c223d542a0e09d192ffa5f487fd30bd3b",
-            "0xaa011b07a1f8cb4e9393f5e3638b836c0b35b292e02bdbd86d3eff048aa61f5",
-            "0x2bab73436f8e4cfd7818279699e5049b9bdad25e020750368793dc195126e1cb",
-            "0x1d9213a872f2046d00edbc295d16205b60a540ddef8c95139f104972ad38dc8c",
-            "0x119045ddbae518841b2253c92983bdcb590400146ea73156978c4558a22b53f2"
-        ],
-        [
-            "0x13e38e51cc1b85717cf16fbabad9a70e06648b4aaeb95730a45c6a01fb2320a1",
-            "0x1b3de55b832fa12b1dd4512955b9f3234c7bc268b5c2fd5ff288a4d28027a75b",
-            "0x1d0d1d50cbff436b459c913873f3788a4ac1b960a9a09c7c7eeb0c3b92bf5287",
-            "0x281c933f6ea0e2407ff1aeed044307196589255dddd46caac8738b8a27f8da0f",
-            "0x176a32143b233b837f49d4d74866d798ba7521d2c194d24b44a22c1bae0e9c91",
-            "0x2b4d9fbcfa0f07f0f1ee5b2f042d4e6bc7e1ead5311f031eb4d4cecca8e7c517",
-            "0x2d79e1fa08f5180dac8dc5eaa43c3572c5268b48898f28bf2121a1643ea7aca1"
-        ],
-        [
-            "0x2618d2164ff999b9094a7b02ba38d684040cddff0a1a52601d3f510e7b3a2683",
-            "0x24efd97f935a66d69fe03581dccc52c363a6e15760cdb5c50daf529b8af5944",
-            "0xf883b9f2bb5908a18bdee69df2663803183dd2bc499dc7f98b591c7b95b79b1",
-            "0x8fe6974c02840000db8bfc011b8a2a72810eb5a54b6c671cfcdc679eff20b44",
-            "0xff2c6ea8b2c48fb8708dc71e2eb26d468cd509d87ed003dbb17e4af914722dd",
-            "0x1eb849822ce82147c3d0ff3b4ea847de855ac20892cc0412b385349accc2d686",
-            "0x110123deddd5a1b8204d1c8cac762037f406823f55f3be14ba699714ae7fcd00",
-            "0xc3a6505705e1a7e991e2a031c0f114a4d8080cd2b198acb004699c5456ba61b"
-        ],
-        [
-            "0x1192e44cbf9df661961e365e42b70a6dcd28b54af69fc6c95d493d1c6277783a",
-            "0x2b4d55a62d21dc3c49c76847542d464006a4857923a0eb62924c9657fe0233a6",
-            "0x2e229139c4f8b0064eb4742a91e8ceecbf554f57cce4f867f4ebffa6d7015154",
-            "0x195b3c5c136db9e4969ec7320b0fc9cddec10d48332ea72b4b8e87a4996b2a10",
-            "0xf8b3cc0e1d28af99ffe6fc83035af095953228a0b41e0897ca85b612e9a82f2",
-            "0x2b1a4a411e102432e950e4641de6a4c72d9aa37d2d69c9b6f9afbb2cf0dfdb97",
-            "0x299428de0928d17b493a18b42585464de5496c9527a12c4a6cacbd572e93ca61",
-            "0x81440f5ea2a5f9ef67442d412e9f5300b8a8ede909e576c38b81b5abb084700",
-            "0xd706299351fd7eb91431b052c8813121e9b57b9790bdf2e511bfef71026d4c8"
-        ]
-    ],
+        "5", 
+        "25", 
+        "125", 
+        "625", 
+        "3125", 
+        "15625", 
+        "78125", 
+        "390625", 
+        "1953125", 
+        "9765625"
+    ], 
     "entries": [
         {
-            "params": {
-                "seed": 5,
-                "logTwoDegree": 2,
-                "logTwoBound": 3,
-                "maxNbElementsToHash": 10
-            },
             "expected": [
-                [
-                    "0x2266680c9e3e9a28773cba7ec9866f4ef64791ab9e17952669648bd202e43581",
-                    "0x278665ff30eefd90d5493f5c5a2ea98865fea676edf40cafebd56dfd64f2f1",
-                    "0x128a83ffd273771a4e9564ea4d255f166ec8c040c7ca197ef689fd4a30d42df5",
-                    "0x1d4f2b390d887293d8449b41ebd3a779fe127a347823a5049f8654e2e9871562"
-                ],
-                [
-                    "0xfbbfa0618236e04a0445c7d7f725215283b0279bfc843069a3d132c664b7893",
-                    "0x638f70151e8bd25e42ada8d661f4127ac23fb9fecc3071af0e732b67d5ec653",
-                    "0x11ba865299b3bc787389ca2dd9e274beb3a0bacafe312b60edd6114d14623053",
-                    "0x1ea05720c862342cec537f518d052bc7882d6dfef6a6040f0b5175600428b8f0"
-                ],
-                [
-                    "0x2dd4713360b194181af9605699e44442f8020d59f969f4accff022de1607a263",
-                    "0x300208d4fd79f59b7a86a61e187f54099a3cb543eb42d89e8a5a363b3a1532de",
-                    "0x2c772c5199b09806cbd047ebb28590ab9f65904ca22807714fc181181abf311a",
-                    "0x23b43702924632aa74d1d9409236b367c9fbaf4a4583e1ff7b4c799ca6195328"
-                ],
-                [
-                    "0x1f040e764712e847ce1617b259ffaf3edff798774addb1e6282a79ca99dbf928",
-                    "0x276f59df9af7b4890377199471fdde403187a928fa1a8a670db7c321f5ffbece",
-                    "0x123485bd7f1800b417bab2d410652fb7bf9cae068d40815cd5ca9284ea51560a",
-                    "0x213622fcede98a94f3078e08795b7dfaf5ddf37f69b9dc216006211421ca5597"
-                ],
-                [
-                    "0xfbbfa0618236e04a0445c7d7f725215283b0279bfc843069a3d132c664b7893",
-                    "0x638f70151e8bd25e42ada8d661f4127ac23fb9fecc3071af0e732b67d5ec653",
-                    "0x11ba865299b3bc787389ca2dd9e274beb3a0bacafe312b60edd6114d14623053",
-                    "0x1ea05720c862342cec537f518d052bc7882d6dfef6a6040f0b5175600428b8f0"
-                ],
-                [
-                    "0x1775cc1efbcf8db5874ea030d17fbb3ae342f627a4a403894b72a9666b743b2c",
-                    "0x12a21a823cea450c225996591ed876dca10665475891cdd6fec3fae5801868cf",
-                    "0xb3895ec23c34e2234895bb6923aea51dd750df4d3ac091ebddb0380c7a6d0c6",
-                    "0x244c158d357cb8e669cbb2e338c0e76849774e54c5477ca7f8a399e8f47f4a3c"
-                ],
-                [],
-                [],
-                [
-                    "0x23a32eb79d071592a95701193f4a585dd44494bbc1e5d0b11a30d7a339aa80f4",
-                    "0x2dc8a24b61a68c5e9c5e9102b6026130dfaeb5ca82df233a9b4531ae4843a6c",
-                    "0x1b3a080d11c1f4af701b28d569c9b263a97ba8c6a1da3445ea593c46e56135d9",
-                    "0x1a67fa02a2319d4395fca524c0083d9738e3bcc819a407a1b9cad0eff7a7baf2"
-                ],
-                [],
-                [
-                    "0x10fb34684603c92ef48974ab659d515319c508dd30d25eb07421d3a7a94b9d47",
-                    "0x146f29189aefd107dbcf6c3c1996a5ccd3ecb908c26324f8d28d299f688c0e27",
-                    "0x1f9f842a1cf304ded064062f528e54b6b0391876c83b543c8b81f84a8b20d34c",
-                    "0x1f7e0a40174c5cb48a5a1ae679839f58b316953c1904d9a4b58e077e00d0598b"
-                ],
-                [
-                    "0x77867159c74cef52c54d53f621b2a0f5163fe25832d9cc7c98a897316de0e75",
-                    "0x1a93aec3919123538cd6d804c61cfca25b9e6ab8af167a0235bc3e0d4a3a939f",
-                    "0x76657cf72d08107c947afd91b3888485b1313f7cc4c05e91193fc1ba30eae4b",
-                    "0x2811d2a94f1b59adc4302b09df81305ac20a5a0c26aaa7cc259f6ec4e66026fb"
-                ],
-                [
-                    "0x79c1b39d92f6fbe78f674b275e46a9ec6db7c502c068cd5609b447df17a936",
-                    "0x1f69cf5e7a80201a9aa107264d8fd2b57dd3a9ea004e74364008df8543b57e06",
-                    "0x2de660d11ea8fec316c945a6f4b84c479eabb4d261ac9e7ddd98db695c9ca55d",
-                    "0x1c96ff3f20ede0a9d524a262af20cb9383a6de8f76680aee485ec44a8eed6f49"
-                ],
-                [
-                    "0x11a6a1fe6f57518bbfab6e73d1c30c34e13f2c104b810a0965fdfcab9853cd64",
-                    "0x48e14b55a8926f9c5cd654671ba4baa499edbfa6452bcfb7225491afcdbd388",
-                    "0x14fa38b895638aae79f517d97e819b43a4478d85d86a77aaacd0cb98286094e2",
-                    "0x2338e6a8368ecad965f4640d0c87010333c751cb5ab5e2a002709cbf982fec95"
-                ],
-                [
-                    "0xa715c68b342af572f3e7acfd2734b719c8a516a53af6bd56098d6a70f951378",
-                    "0x1acd8007c5b29cc5642ee288fa83f10e4e078e837c54ad8e75279be4c4d51e86",
-                    "0x4210f83ee640a89355a118b8452f66b5665615fdcf350292d44f22dabd6b661",
-                    "0x25e324cc36ff5d0b321e62d66f6076dadd5cbd7408aefe63ae3bfddc29f154af"
-                ],
-                [
-                    "0x27c30958f83e5559b341ae1709756c1d75bfa85a400bb8e7bf39b7382b0ff0ea",
-                    "0xb68851d6931e3799524b6aeaba7c478e2a819c029a05fb44658b5392ece50c1",
-                    "0x2aa0c49e867c42eb24a9e82148efdeca08a89a959642d55175776faa357d7be1",
-                    "0x283c9ea70aa6a70041bdb75177af69195aed4b1ab5845a4972c41f4020f88d19"
-                ],
-                [
-                    "0x24800ffc9179c7569540f806044510facac7e8d435c9b866d2cb7c111d6af9a0",
-                    "0x1bad39bdaf8da34484c40845cf63752ffdab37eccc66cb91e117b4b3a4bac333",
-                    "0x8d62ea2f0319a0ea28117afd0f351302893434510ddf84dbc3621e2c6049e04",
-                    "0x12fadc4c7f94dc25a111a6ace57f82a4784ead1d202822613740138d0f129894"
-                ],
-                [
-                    "0x1add2ed7001734133719ad544a61d94071e0460c29957e014b555e22ac8c014f",
-                    "0xe4039e57734c4e813a0d4b3658f9a000cd304c70f6fe23e2f199bf04f200cdd",
-                    "0x25a9ae14ecbfd89d2d5be2e678d24e3290161f92064393661769a6b56b70d100",
-                    "0x4bb966ab8ae51e386f6c5be1b4c53e80b695e8fb80278a9d2bd659da10222c9"
-                ],
-                [
-                    "0x1db43d0ce999d854ce4b79a405bf05cd579fb8fbee0bf06cd51540ceb81d6332",
-                    "0x132ff2cbad0ed834d22bdc2cb8f0491b65e1af29d2371c85715ed6a7fb2c1cfc",
-                    "0x7cd589d008262a32121a8c4c0e76d53095f6c0ab4f0c56df27e9bf35a689f17",
-                    "0x1343fbbf2f0f7ef963113e1c82800f7f9a017d379e06bb16907fcf2ce03d7764"
-                ]
-            ]
-        },
-        {
+                "19052984516876627274640238270428312641066914502976343854130933042152395214437", 
+                "19579499093159636168223528817491239872946408580551360482200183465178423634745", 
+                "3708668380994841899936676613411331898010921342788081195849365322630935912434", 
+                "5433511930939366077412770734404741296375787859263964469718544218782774942954"
+            ], 
             "params": {
-                "seed": 5,
-                "logTwoDegree": 4,
-                "logTwoBound": 3,
-                "maxNbElementsToHash": 10
-            },
-            "expected": [
-                [
-                    "0x1aca8b5f9e595ac6855848c8bc935bf3a4161fc684eb1da710a9eb1ec9637afb",
-                    "0x2500ad3b9f47aa15fea2b4f4ba3b34db29555161f3c9787b31273f8578dc98ee",
-                    "0x128573d948aa1e5d7c8f04379bd043d114b09ab4a1d51b807a3b4be49661cac6",
-                    "0x295e7874cc5929896f892882548b9a9fc0ac1bb1fe5fe0e22d357c32e645018a",
-                    "0xcb1220cc9d918eef8c14e2f87516cbc4a6ee8ad240a38a5987654b37ce0f8b4",
-                    "0x572f2dcdf64334ee6ef1b169fbcc43c4804ca0b04145389ac578b1f616e85a7",
-                    "0x2f1bb861fda54f5f30852cf1b21ebb75255704ec7624db005862c9e2fd5a4e16",
-                    "0x1aee8bf9f2410de53580cce26720152663e95b7b96daca6fd0741ca33ac89759",
-                    "0x17d003ed086538642a4ab6302440b66e679bb2823ee14b44fc2d3e0d7dc0ca81",
-                    "0x282178ab02493623611cbb94f642d683761d64876ada460a2f492cafae0d25f",
-                    "0x19b212c31f850b5eaffdbcaf3a1d98db2788335cf37ce74af34df9a83783422c",
-                    "0x26cba2a55d6268c7bff2da5df9435d731ca85891dbb3924e74ec4b8986cbeb3d",
-                    "0x251053f8898df984aa0db4c872e4f9948949b04b9f3d953c009b4ffaa2be6760",
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-                    "0x189f5ddb0bd28df8ef4538ae4be73732facc7c13867f60d635d63319a0e31f8d",
-                    "0x2589bb7638d6f04eb6ccb289cb5b454d7b1c978fd4ae01470cea47892757a41",
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-                    "0x2a92337dc1e68ed4f668e6918375c4ed9eda9815313788aaa9f07046fea0d340",
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-                    "0x2a3666a4902357e64f009edf58b147184c1dfcee9c486b9e845e16caa469456",
-                    "0x1e8e6d40f7d7a738fa4e31c82675183efca6ef1dc2beb1dce05b70d2b6d26b2",
-                    "0xd5d0340812e07c997e068285009935fba6b20a2d41222224fc21c40180c739c",
-                    "0xbb01219b76861af5b03c722cb3e6b1fa78e4ce313b02b4173cfa12a20ff6d5c"
-                ]
-            ]
-        },
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 2
+            }
+        }, 
         {
-            "params": {
-                "seed": 5,
-                "logTwoDegree": 4,
-                "logTwoBound": 4,
-                "maxNbElementsToHash": 10
-            },
             "expected": [
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-                    "0x24ae56edbdba68b6a0988511596c6cbdead08fc23c428eea2da1629b63f10d4a",
-                    "0x7c1d0d670708293ac6900fcd496ea8ac6808b46e700963a459d75287a8147fe",
-                    "0x2ca4b5e4c6361f1dcb3ee664b26bed209bc701058038db31ca6ffb7fe7a98a13",
-                    "0xf5de0ef37cd728a5983512f55e6ab4d17b122714811286030475d8420548a5",
-                    "0x4deb0e9608187d3e5b468b11b9e72cba74680885091bf1b20bcf24e9febb307",
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-                    "0x16f2996aaa6e09660c5a32e76a3abeaf0634ba59baaee335894ddffc680af4ff",
-                    "0x5e19f52ab46a4f32f763749d85e85b0530ed78a894f754844ec3252c9986f97",
-                    "0x1e54c6640a4acbdf075a60526ab290b58c08b6a16fd969720e033c971a7e20d6",
-                    "0x2863d464b49b0cbe1304f53b3a9b2a47c2195e44c6def785315d1513e8d7fee0"
-                ],
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-                    "0x257cf81c5bac0f15893ca3a12ff4bbd1c9303c8d4c55829ec59dd4c140c1c949",
-                    "0x2fc5427247db5eb85e0680a46dd6751ac16aaf734668d10932d2e073d5650a14",
-                    "0x224498b9ba5a1d4d705359ee9919b3135732e3a4a53deedf7be1026398cd8809",
-                    "0x22075fd10f9b30db6ea4c935d7aa722da5e61290c260fda1fd4c14289378d518",
-                    "0x16df62e79bb3a835937183cd8642a532f5b6013e47632afed22d008c23bfab19",
-                    "0x58a6aa402f0dc61d495ec6c366df66f75e7445654d585e44c87ea13228dd5c4",
-                    "0x2fe3206c6317e4243ec12e40f140b22999340f9dc7936795175316fa50ebc620",
-                    "0x258010e38e82c6c7c9349d3ffb3d83a14bb7cde21a556111febfefc7fb7644be",
-                    "0xfb4d5724141609f7983fbd7d26c0d538c6dceb02b774f4e9899dba22567651d",
-                    "0x158c2e632a74b0e207c81a18416231d6d310be2cc8bc0d1c1fbec39400897704",
-                    "0x302c5bdd53d78ae99a2b17188c888910fca04abc71028b75410cd1e2fa86d591",
-                    "0x29b8c833d05aa6a1e1fdbcb08401d55aee8f443f66ef84a03758ce6fa8a821d9",
-                    "0x2657dfd8de69baca77bdc2022fdb7b7f20080ea4e28fb95b524153cdc6d5135f",
-                    "0x12949adf73fc24be508fec6872378c1dc31e1009ab85709b1c6a5fde76b73b44",
-                    "0x236c49ca786e49fbf17e033a2d0604d62b65af87d41e3e21527fb23bc799e528",
-                    "0x7367b16027cc90db4ba2e1951978bdb25d7f2b75769a72d61ded2a7633f6590"
-                ]
-            ]
-        },
-        {
+                "12217087487196706286935392960359417153662545188297682064251163865575683215147", 
+                "21548337336470889698231140636706520345756649225861573817734471546023502758709", 
+                "9320394412515272050870390009764753183869476247430369751056203305656629612983", 
+                "18570900243421525732330663177341878179250339015557480174214866645347627194504"
+            ], 
             "params": {
-                "seed": 5,
-                "logTwoDegree": 5,
-                "logTwoBound": 4,
-                "maxNbElementsToHash": 10
-            },
-            "expected": [
-                [
-                    "0xab048ca1f78a0f47f1ce9dfd599d29b6f802463ccc2bc790e567922fe883bc3",
-                    "0xab9ff696def32ef11fdd7b1074575607801610cf64f24a23d9c87578242631c",
-                    "0x1ed9e7f89449ce6c1f15707f1964df926b336ec9a514fbe68174943a89f48507",
-                    "0x19a44147b04c9f70e9ba98906ba6028b13caee59ab3ae5f8a9a905ac021504de",
-                    "0x45d361c358e3612dac386694b7853e22ff045aa10b75cdaaf046e9ed1f32e7e",
-                    "0x3c7e10643a8607d232928b9e692d5f4a42f93a197365089abcbc697bbf4b635",
-                    "0x2d85547048260c3f73ef8dd791e5c17313cb87d6684b0a6c6b8cfed6e7fe3cc5",
-                    "0x2bdff532534a2012091d072e79b3179686b2909d97c2020c5fb64b2b45a6a0f0",
-                    "0x226ba81edb399a357d11ba041fc640d3497d417de6d5b0a52f8cd7237c60d6b7",
-                    "0xdcdc8d363040d29e7c31e19fede76f7a1730181eb3a02b48b6beeef72f7953f",
-                    "0x100d639d1f6d63c5ebeb5dba8649c1622c54b6fc71e47fbe43196b7eff57d967",
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-                    "0x2a889d5d0e77dd13cfa879d126636b47cbc2172e2de4c7b19a28d58cae29b70d",
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-                    "0x17f8fddb31128c37d9d8c2006a1f7ea4121f3df79ecb785b0ef3b6846e703e5f",
-                    "0x16752d3c156dec176ff72661785008573066b32c0294713d51246cedbfb03069",
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-                    "0x1ebfe746acf8580635167a5b8259bed9a8ddecc6af63143959afcc05456fb3ed"
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-                    "0xe34b30662d1484d7684c9762568c3f9350f76e4a98e475d270406dcdd656343",
-                    "0x2c115c568f5602990bcb35fbd74b627ff0a99e4c6713926410119b0528d648d6",
-                    "0x1a752246bb01c7e0beb84495619128cba6c927fda444277f957621c1eaffb869",
-                    "0x11bc66c598608835ec867b66c8ed4da02d994bc450bc65420faddc79e08a17eb",
-                    "0x27cd76a79445f10394c38c65eaf0ad6ea8efc5d7caef00f788087bb13b82e330",
-                    "0xe2e08b1e927a11c43d13a1c76c14aa8aa974e4121cc2728dca55d874d199ad8",
-                    "0x7f8d9ab9427335ef7ed1cead2ba35bee6d5f3d18ff56a6a468819f35ea1d291",
-                    "0x3da26a8c7f98a12f5d7954536749d4a920c6db6b53b02666aeade34bd7130fc",
-                    "0x199b8a4039c2ecef990c9073f0c2df2e759cf5a6ccee547ccba50abecca344ec",
-                    "0x1da0aa4cf4a92b1c80e3b096ce88b88f4e79f049ecbac41f5b6710553415b67b",
-                    "0x175caf1277223bac98c9d0df4c702f38a7b0b5a8e1f993d6015a6003ce3c2463",
-                    "0x2f66d1b7a7bcc0fd09630e068e0cdca06a6f2d1234ecfd5dfb6f74d859825845",
-                    "0x2c9447465ab207a5d0ca0dc303d7a8d319eb5bf3cfef8b86f9ffb670a11084ba",
-                    "0x24c06ca6f1ae6def40f1eac818097e58a2e71f9690434695b91dc803ed6b1095",
-                    "0x1110cdcce422087281fdaa653fa7228eeb47b4fe5d4a39d5c27f0f4e8c118d3a",
-                    "0xeb01e7d4200abdfb284a6b291a705232e1a7f9aa31d0b847da4bd0052234f3c",
-                    "0x2ddd6c8c435cd1c7c045c010178503902b3063a32d4dcfe2cdad09e1c38c7d9f",
-                    "0x17804e6280f6192b56840805c506a503c90911c69ed267200e53aafac43ec8e5",
-                    "0x14beded6c0d19d66828888d7293abe24c08b7ac870c1f0fc0876ffee8e9689ed",
-                    "0x29c5907b1dc974ee7fddaa71c279570d93d66822eef924060902b838f4b0be3e",
-                    "0x17034fd15bf15659a1e3f10e301c9812b5b02bd459697492d77011331ba3896f",
-                    "0x259b00a2eb292e07dcb2a3008c6de66d3ede0561c62c6a80179b3182823b6da7",
-                    "0x20e23e9856b169ffbc0bfa8c89abdd98adc202910606c98e1f38059ad8766e0b",
-                    "0x202172d7a86f67fe2acff2e622075bdc17efc9ca8716c0a791ad21e30f06afa4",
-                    "0xe1e501feaf026787bdd9b43abade578c4af4c1a751eb59c024d64795fc7fe24",
-                    "0xcccf71649ebba0f23a2be779e6f2df8a036317642645b66d4378147c2541f36",
-                    "0x2f5bf1f5cb78f0b4496b268cee7c1b75404aeb32c39c1821e9085db30f9340c5",
-                    "0x11f22d6be5ccb9772855809abec97a4953f9ed7c92fc9bfeeae9f77b7f469891",
-                    "0x2e48f1c4ffbf21f29dda9305ab0226ddac92ccfcc87670ac2d39a7805fdb17ee",
-                    "0x2476b1def26b72dc4a91904f28bf690de9c0df413d9aff2b6356d11303105aa6",
-                    "0x197c70883e9d883200f9b8e9736151fef5cb34a790c786215dd6278ad3600ab3"
-                ]
-            ]
-        },
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 4
+            }
+        }, 
         {
-            "params": {
-                "seed": 5,
-                "logTwoDegree": 6,
-                "logTwoBound": 5,
-                "maxNbElementsToHash": 10
-            },
             "expected": [
-                [
-                    "0x2d86bf201d9cc51b130bfb75b7648d7bc93cb43195eb17908e9d2b67ac80a384",
-                    "0x23d9ed017e23a0b3ac57c2fd0c5f9e7ddfb99af53a615959ee8ebf9bf7aa0549",
-                    "0x25e74c50bf7513e56dc02d533a4aa07b78f4b9f65e48dc0b574217f0f06bfbcc",
-                    "0x2cbff030236dd7dd0a9ff8a168c60fdd37be517d737f8a8721a352de68ec3b65",
-                    "0x2bb55f01f16e62f6005ed1a9630352b6c36ba0ebaace8881ab52c60407531457",
-                    "0x16782cc75c504542f04d24dccdfdb391fcae812ca3d938ad267c8d29b216d0ba",
-                    "0xfec4e591be94cf57c5a4c822964a5b9146e92a9995da3f7db65bdebe2feeb6e",
-                    "0x28fff4a036ec795d1f77d414d23358905c9a8140da9df9000271f4a8c62b7832",
-                    "0xe2d6c0443fc8175c5484d15c333ad7c67f7e5834c651c7941b3ec77df21ad51",
-                    "0x2816cb6b530bf8e0dc296e6a33225d72ab742949ef73cb81913796c163abc9be",
-                    "0x1322f0b87e89a0f09ed58ad19b8b0a1a679bd7b30fbc6ea2d10f894ff0d57ba",
-                    "0x312ada8ce9c8f19c55ef2d25697102d0913e0c6ba91e750eef9390ac80e8202",
-                    "0x2d244ed84b0953cc0698832f0a6a0d77317fe481c7f55525468d0be7e5d90fde",
-                    "0x299569689209c384a7f35f9b4160ed1abeec8279a216c7eab537abdabe508f6",
-                    "0x5fa106cf2f8e785d53959776d627e0a39bb010e08eb751ca3b873709ec16cdb",
-                    "0x7d7594e02d6bf49019aae7313bf6166621de3bc7d0a1605327ada59fd29da0f",
-                    "0x24802df9d274b0cb25f4e941e1efaaf358338f920aac98437c3500241270ea64",
-                    "0x18dc8dca2418481dfb593a40f08c167ef71016330838c6624fc5762db962f3be",
-                    "0x16be19dad683828454821fd2cea02d8086134036dbb6c24ffe086395f9da504f",
-                    "0xf36770fdcbb03d68a044b28017b54d3c172789598977df9af144bf8ef37aff2",
-                    "0xf69a3f3a53432338c84c68c4bdb03316e041f070163bd746bc196aa16ebc37d",
-                    "0x1d32e7d160672289830405771de3c65436bc682360c1c6eb7bc33a3ad88123ee",
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-                    "0x5cd0c81f838998598c3b8d0bc37cc9ebb3c05b6792da0fe04ee687e722ed29d",
-                    "0x2363e7dfc0a92be4a26f7df35b39354b93d3c90ec3e9896692cb614ce43ed8dd",
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-                    "0xbc8134fd0fb5b015787b186adf0d91aff7da264ef5ea04d58865ee28833cf7b",
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-                    "0xc87047c4d5d0dca2075d4e341f05eeae0a178ee705a8cdbc5f22a9e9a88f24d",
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-                    "0x1b813f9f11a342bf7cd66935cbaf6544255061852f8af5849e25d101c51671b1",
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-                    "0x19d905b90de87f6a3e7988eb663c60ed04e7c80ec5688669b8e9fccf5d403a49",
-                    "0x1f18326e9d59bfb43c4dd86c80e649b5d3504f789602ec4a679111039a7bcd97",
-                    "0xb4c779be5649b65e32e72a3174478e956383bef6ee92da4db168e9dabf35bf3",
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-                    "0x47785d479fa98bb9f5769e6846e7ce87ad16b2bc46863aa157539fd3bcba2cb",
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-                    "0x10f6e5ee5349703e8bde55dc72949e6dcb253e5b2601b7d8d9d2533c64e1cc04",
-                    "0x243aa6a71efc4a127bab469bbccff868ba376f54b680d14ef32bdc59aa2f6791",
-                    "0x8ba2ec59e2a7d9e92001b69a44e252af391f84add665799fa71b0069ad1a43b",
-                    "0x14e0d4ba3c58d5d0002771c0e2115ecbedcffbf8a6783ab907bd447ae8e23c83",
-                    "0x4c7eb58fbe53188b5338b7bad6731fb5e97e160d097c4b59d50252527cebda5",
-                    "0x11150d32a1759473f3d8825a1635a3fcd729d75e24c588e40c12184e10144f0a",
-                    "0x27edbd1ed68e71bd72f5ea215c563969c6173893713c4e698ea9b8f379c4d666",
-                    "0x1bb1c5548a37caeae2fab791d58aa704a8e7dee297633346e26d0d59d3204f79",
-                    "0xe8fb09b35a6f1bed6f7c518b335897e365966931a070bc12b814f27a3daf4fd",
-                    "0x288272900c7ecd43d56df67f0c1fc72dbe93ee1c98d63066c0dfaf4de10ed7ed",
-                    "0x20932d1e0767967519fe8bafd74ab15795c73f1462d80bf198619071f72ab93d",
-                    "0xecd69850a4b3e2bbea08f756ba10f67b89cdc46d5d968095aa998a53728e49f",
-                    "0x29b0b0bb1c08409092da198bc6f11c070aabbb36da3b1daa3f3a24a8f8c13600",
-                    "0x2bb4ccccf336f63cb80fdf2ae62f55b19b2c097561e9421060c8031da443d825",
-                    "0x243da35d1b8c7ec585f195aa5b6539cf85478b959be0804cdd5d5b78f045ce9c",
-                    "0xf856626cd4fd6c2fbb1e178b934cf9637a30f79bfab1ba33d6a0994cee8dcef",
-                    "0x18152fffe4ae5cc21861c1b02a9ad8fca321708b902fcfe04211802930f172c",
-                    "0x23985ae127b15cfc9962fe41cf96fc53521ca9c5375c253aefff58aed226782b",
-                    "0x7e240fa29135925462195b2771c5da1ea8011a96f3e8ffc9a86aa1ba9e66d0f",
-                    "0x2c52f1ffa4a5760b8b17c33b90ffc69bed9753d3fb338b1d74be76c8f552c08b",
-                    "0x19e2637844a4f042c61446fafe3621ef7717dee450e0a9a3581a84f74f67150a",
-                    "0x2388b2287441166472c4ddc15075b0528d1c77cf8fc59a60ac94027d6ad55673",
-                    "0x8ced2afc2a08837475ae4f671022eaf28ff6eb7c0ef3a12595992495e5dae01",
-                    "0x5ee6b7d895a94124c0fa70ed52c11cf082703acd42ec5f9e5d5dee7b3368ff6",
-                    "0x11aeae23ba66f45802273fa2c37abc379b839a7ea56bcc13171faf3e2849a118",
-                    "0x1695214ba916108798ffa5930cb0b642a0a3b27896d9f580865da58cc37665e1",
-                    "0x26cdfdaca82bb5156f0406703833a570dd3a44c85c0a4fdfd4efa0d6a647637d",
-                    "0x11c627e84bea87799569233a04f1e921b365e70170f8c418927ded70c3aaed53",
-                    "0x2eb45ab3239e69233f579c361b65d732ae8211d9506416b963c7066172314047",
-                    "0x18bf7a9e2a580a394313ba733479646cbf1067279722a42455d0f3bac37fb26",
-                    "0x22089be60194c2cf03989e197aa2b25095541aeb8c61452d5c3caecfca6a49ea",
-                    "0x24c104b2cb8794fc89663e1ad52903e8a69e4ee185dfb581662adae6dce3e95",
-                    "0xa82ffc3f131658d6a80a3927e3c55d7749579b390425a767183998b82d3872f",
-                    "0x270c6dade2712d54e3e70237f6e831a398f4148b1970f6b5852a73f0bdfad613",
-                    "0x1fc1a39573f7c30fb6460946b000bebed85a1be795bed1ec7916dbe0e653dcf0",
-                    "0x1e7476ed643d1c0bd36c4a24714f3ab20fe1fd54dc3406a71102591eea9d002f",
-                    "0x2ec2a2aecffe4be869767b819cd09447f8b9e15152c48a3989704e9086ad0a57",
-                    "0x12abe16cf5ca85935e5c07e41ad1b140e466e7693ed2eb1b4f76d30c2c099b80",
-                    "0x1443ff5159da8d6f3b43c924c668b36062a4c7f490e6bb0de4223777201da25a",
-                    "0x297f5da0fee869b29380128d0aa9ddcf7823a3c43a8607b6a220a3c83bcb28a4",
-                    "0x2458aa2039fc4d407a93e765ce3540ee3b5819e123101d5797fa98745fc030c1",
-                    "0x6a0ea85545a58f6004ea98ae166f84ae01a0eab6577ed4c66066d08196e3c62",
-                    "0x2563c32f0e25208431dd5ca30a739da231ce557ca3e0e1c5f64c532ed51a8f5c",
-                    "0xf72601b45e0d8766591c706ac69bfa571ead4e667511df8b355f358aca704e6"
-                ]
-            ]
-        },
-        {
+                "16692170502388384390674572361848717230910923132874717358201841963873546552628", 
+                "10418559609645272031357396256918216874674189335083221341531922773216817537771", 
+                "906042409609440161513541043605057525610952609830270797384406918592312743401", 
+                "14580691556330400310069765056830001347584784126854837868214733018631095864290"
+            ], 
             "params": {
-                "seed": 5,
-                "logTwoDegree": 10,
-                "logTwoBound": 6,
-                "maxNbElementsToHash": 10
-            },
-            "expected": [
-                [
-                    "0x18f1f6b3b533a588dcb876427cd127b692619f105e64b19d47219dcba613521e",
-                    "0x178dc8c1b50973b20807ba8913037c731f3551e8357b234950084deea9a64572",
-                    "0x2c92be85ea5a0aabcf9d2beadb2635708bc5b20387809bc60b452d9f9021b2cd",
-                    "0x1e6d73cefcb6d59db1d19c06d20939104b78fb57971bdfe3d2ef6a039bde59de",
-                    "0x10d45bc1d8d91547e3c1ef9b433fa05df1757d5786f0508c854ddab87e8fa9ea",
-                    "0x21881d0705d5b39da64b3fdad887ed859e47854dc135cab25455c634c1f21ee9",
-                    "0x243c433cc3cfdafaca3629f16580573dacd7e8474969bf30537ea7dd692d0aed",
-                    "0x1fbe82113d04ba4025a049e058ce7163dcd5c49c1a1b9441f18d8f953b787dd1",
-                    "0xce9a760ad8ad29c254902841d835a666fd7d20a2563e69c0fb686989b31f63e",
-                    "0x6353f7552e5ce741629e75f5ba99476d83ab1503cced9932526da8a2b89aa1f",
-                    "0xf00f97107b5ca7d11a33af5cc5dc2a05cde65725a973b8cafe12bddc0651537",
-                    "0xd9222f0e990dbd206c2fe6e9a2fc38b8f07b881dfc02207ae4993aa14ebae50",
-                    "0x23999ad4b1b2b6f84e1f2e7afdd2a05d837d5f95012055763a99213ae764619d",
-                    "0x2bb9ef5602612317e1612c68cd2423837475e1a84c5234f263e819be6bf15145",
-                    "0xc8bb5e1d54d22434edbba1e6cc17dd68acf34e9a95c145ddc42b17526762897",
-                    "0x24c56031b54322a2d09f9e493546f86b1204c6ab50421d4c4a874819a7d09531",
-                    "0x5cd9ad0bb1e73567655e40515036329de359b95b1b75e2e4cc0990ad5501fd5",
-                    "0xd497d19e29dc7bf2adc939d0083a60f5ad009649d1783fdffc546ce33c87ad4",
-                    "0x76f1ec1334d4c6cca1495788b83d2c7933c3d0ef695c1538899a3295bbe83ff",
-                    "0x90e8b9c92415ad4f22bd3409fa51af42c686cd9b07032f5bf04972def839e51",
-                    "0x62799c6ef506725b4fdd1004291a1b9558c4c12ab2864229fa23d31a30d1227",
-                    "0x121da4dea394b559fb3dbee4dcdd6411b0b19a06b3984be0d8aa33664b268d1",
-                    "0x2f7949cb6e6029765e943ec16b24bd7179138dfa5dfa9da19bc9884c33fe7af2",
-                    "0x21e7f8bb75f3bd021d95174aed80462638f3f878ae6fa44a56c7880a5ec791e3",
-                    "0x1c30f1ad1cfc89a16844fa1525011b618a5a91c20370c65b753233538ff26849",
-                    "0xeeccd2be131d12bdae02f66c483a126467e5b9d145eb697b5d970f2705b61f8",
-                    "0xd122cfc62e305dae63924af79670bff26cd0cd301f01f778efc432bdcad8e59",
-                    "0x264f5c23cc5d8c43e3e0c3759b7de89c3fd9129a24f958b9ea401a5524229c46",
-                    "0x2dbe0ad1adf5414c14063be9b9f64faea0c62da471c83c17c1bfa78fbdc1e74c",
-                    "0x2e210a397140cbab67931a80de3a4081f0cd187b62b97fd42ae9815eaa61e37e",
-                    "0x1ae9decdd2986707d84b2675f886429709f0b78558755e272c878ccbf158ed75",
-                    "0xeb391098032d2c521a53f99a843f37b309941e6bd39bc371a6e7b2dbcd3a590",
-                    "0x1eb60d85329a11e0ddac0ca4976e2fd9fcf85b019ad06e871d0d774a4588168f",
-                    "0x13556bb2450b82ca8aac9d16fa12ba31c15f199c8841a1ab271991f78a883cd",
-                    "0x1e40b9a947c71a4af862518df8649c13166663f7cbb37365e3134f22ecd6d0be",
-                    "0x2f7179f9cac06fd0083b8db8d11860df576b634c6084cbdd5f1e8b93d5e6a342",
-                    "0x2a5305f18890e964cd58cc4d1e40fdd4c1fdb242a388897a47e37eb78f641c00",
-                    "0x2f91b303da4ed1470d839b7cf2f08a3fc3b79ec6f343efc7a8aa98143cce554d",
-                    "0x2a1dc62a05af1dec72145f76447b84d97fb3d584c85bf22a0cca579ea76034c8",
-                    "0xdb37ef5f670f786e03ec146686374e9c49b41a7bc33eb667658334d6eb3559a",
-                    "0x2aa7fa21c1368000651b6456cae1739be8eb9e7a08279730a32f37b9f5fa1758",
-                    "0x2c5b947f0459da5fa5998dcd5a9889a82fe7e537d04bd0d952224b14068ed31d",
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-                    "0xff0bdc801a52790f68d5f40ef18002c183feabd90e53de55c496e5310d825c4",
-                    "0x15a6a6be46fe16e0241dc0ff5bffe1aac40ade26a79ed789573df8b1614fb359",
-                    "0xdab322272af1026f27482d5a28167da5ef64f5fc32a2a2525fb080b45abd01a",
-                    "0x27727f6d59a1b76d80c77e91c74b4a8f10fcae8a28787408eb97ecf12a59686",
-                    "0x1b506fc73e32ab36796505ed0878f3a1b6fa1880e6f9ad93bf4db2f67a19e91b",
-                    "0x23312b82dd1619bb25f92438f716d2ad013880f4e6439b9883920f6eb028375c",
-                    "0x4d090ef70fc7fadcd2cec99d54d9837d9e4aab392cb9a619e82f8ff4eb3e425",
-                    "0x23b9b42ae73db33fd9a70e9d819dca613e7974b1a2316019054e6e5880a79c61",
-                    "0x6f7b13231fe7ddc211015ed4ddb573e36cb5778b67513d6a51d6bf82102c867",
-                    "0xf779d50f31ed5cc1720d19b093d9cb045e48c457b25c71040f1066a5182bd04",
-                    "0x11bcee4a2a90fc8dd096b9dd2d516a219acf4ed70acb6bd16272190d46ef2f99",
-                    "0x26a655de2d93ae21cbbae82d63f106a0f99004b9ee06539411d2e961168d791e",
-                    "0x45a3fc2c6df0460969da73356deee8d2837ec92642bf591edea167c701168fc",
-                    "0x168a4570db2aad29c72aef8828c0c1acb6e9f8a1e78544986da4cb69d27aab3e",
-                    "0xb6dc83c28c09bb649bf10a3133c5867a0e2e33d9818299eccb782e3386bb0ac"
-                ]
-            ]
-        },
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 8
+            }
+        }, 
         {
-            "params": {
-                "seed": 5,
-                "logTwoDegree": 11,
-                "logTwoBound": 7,
-                "maxNbElementsToHash": 10
-            },
             "expected": [
-                [
-                    "0x305890103a90a06f4bdf5d860c4eed863ff8cd0b65fed337281d2ddec80e0e4d",
-                    "0x1c6da82890c4cd3564c4f9844d6d46ccb91090122f7328491a60f79895119d33",
-                    "0x8d97c596607dfb45ed45d24fee686e43e74eee790031b69b51e92b7dc9d682b",
-                    "0x238db799e3110e08f75baaae69cc2758808c4cd18a153290b2f97c5ef1570c37",
-                    "0x2ae20d68b0f8cc9a2b1a23bd6d15841e02155871b0d24423671bcf3f7bbd7ca3",
-                    "0xc3c0b22a82a7b03d023151f67b27e33de54615e784bcc787e3323c363ea485d",
-                    "0x24616427e5c338a09271c49bf4406efd581ae3bdec490220ef995d3337712ab2",
-                    "0x11a35f1817af04135b5c64df486c0ab8c4c00ab11b2a48ad22fedab2a8df18a3",
-                    "0x3637eedbf71830e740d53a32d72c94052dd6986362d9be1055fba8ac4de52cd",
-                    "0x12285bdf02c084df13779da1804a1e661fd559a8a57d2d8655ee6b5215fc0eb3",
-                    "0x2e7cbabcc3ede62d261173a08693604b6de972d4c0bcb08363588d3d5990ddd2",
-                    "0x27c8ed86c1752df7fcb729c19d2d58c667e6ba414865cdc1b6460899404922e5",
-                    "0x294b1d128c6d18b15e0f66d14f9841a8a672c75c880a9c7f1bada23450d7a841",
-                    "0xd1c4c03e2f210effe747166ce8b75aad1334ca799014b6e06ec76a4a103d462",
-                    "0x8b0acc6eb9cb17b4a81943ed31a2b24c1dcbe99d09288ba3cbdf5602b7025af",
-                    "0x1824f827b15199ebad7890541a867b3ff21e4e85f8c896fc7995d0b9dd746ebc",
-                    "0x1afe5ea364f012c184966c237d704c10005e01d5ef74f5dd2a7b09307d9500ed",
-                    "0x1391480d6d461cdd3b02b5363d87c3e5606ae9b77acb1f1624ef0785175c3f70",
-                    "0x2ff8bbad8bc8801f89a064a292c6139efd2b9bc31dba4b797828b40e9293c84d",
-                    "0x1118ab5716db4916362d39e4a25b4e734d5f216e1487f7057f46e0cf25b3242c",
-                    "0x228cbe61413c079252d018510f9d4f955c4220423c595b4a7063c6bfe1e13975",
-                    "0x2777bfc2cb1b33acd4a9bc903568e61f6bf348df5ec4c9b6868ff7095d181b4",
-                    "0x13ab8dd8936c2f367012c979dee173e1ed2da49a755d1447abb05162ef802ee2",
-                    "0x9add79ba1815bb5ff48a51fea0e6133abf90863289066297900aa9d0c3451dd",
-                    "0xb3b242899356bf28cc8e950cb2049b7596ab17a6686e13c77350555428c55a5",
-                    "0x2ba354dfd90b3f0d397338811f51841fbeb8a76adf3cb899bfbd223edd5e2e82",
-                    "0x168ac6a20a67c7824cd0441ff40b78a3bd8edc99b7ee9fbf78bcdd74e443e3b7",
-                    "0x25a7bf241ee07f8ff8c60aedf71cc6da87f860345a599eae1942838357e6bc7c",
-                    "0x9221bf85ba92fab3293d092d7e0a815f8ead23666b9c7cc3ee4b3259cd98414",
-                    "0x910ae04ebcc3bb222a16cb6244254614994156a6cbe53c6d4aaaa1c5745fc49",
-                    "0x2bb23b325fb92f1a4aec80ce7a4f7c75cfa09076dafeb83ab6f25df6aca7270d",
-                    "0x814959e0982fa69e9e1e6686ccd49231cb0d9cd4620694f7aa88fe7c5f11c07",
-                    "0x2c742d2f1b998535b50f691b2ab8c1ae2603215f05f206e1c55e3dfaba834e38",
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-                    "0x16de63ea60d1f815e0cd5e37a68c18e6f7abe9a26f9f6d18961595e8a8394a13",
-                    "0x1089dd4a71f4d47a235017434ff630f9aee5595b02415e82c90417ef414773e6",
-                    "0x25b631522b500a3915c5fe0c64b0b1414adbed9d08e3ef623d41103973333946",
-                    "0xd31f0c0653aff3d093e84e2dd9868fe7b2daf2fa984a004c886a0434952ecc4",
-                    "0x299fa56afbf786a74835edf66a93ee1445c3089f0f04efacd6ae8afcffea7882",
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-                    "0xfc47aeb9adae8e27187d155de86b0a6fc3f7860b034f6d73151ca1d7d1332f0",
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-                    "0x2cea657e45a508cea377d026373773d2b9958af2fa7ab975df8a96d437026f38",
-                    "0x21169ccac8121f50910c11c168a6bef981f52cbb3af0b4f3475887e0cbcef719",
-                    "0xe5576b9d1fb76436a0d5add3ba7e8856e4d826e23422b074e3ae905e23b6d4b",
-                    "0x935771d7e9900a7fcb14a0134e49b36ad005fb27d9e415b398fa56c920a6d1a",
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-                    "0x107a8e2c06bdd4b23470b6384dd0620f089072a618d36e8aa8153a6ac39b442",
-                    "0xe24e8cae67d3e1e87abf34440fd89785ccbbe557c0621c88cf4c4eaabe1e3bd",
-                    "0x1e738c31e4b96a10855381c9ecace68ef45462750fa9ed1cc1bd1f25b1fadb49",
-                    "0x4f2a3a2ec4ea8b84c8c12917b94af0bd343f641abc4a7959a3a2d923a00670c",
-                    "0x13dd0b7601ab3de1e486a0709687ec0f8698336e06165bbcf379b8f5197040ba",
-                    "0x1b855a56daf63e225a8e0cc7b9ccb25afd13a35d3ca9159a11e7af6d5c1dbe29",
-                    "0xa7601298a22fbecf611deaebf2e86c85c26f0481a29e70982e5302989c3b9e9",
-                    "0x1803cc712a5063b5543e4a78b8de9987cc48696d4a3ddf96a4c6239e45bae685",
-                    "0x66d3c28fe0050856f504953c78898e31a0db92e586a2c2722e4aabb7408c0a",
-                    "0x2c324bff5b87c74848a9181c69294cb815185850df139c8b561408a43d1a131a",
-                    "0x6100290f8f62d4e8bbddea82b8b9519fbbf46671215aca3f8ab940da2491d96",
-                    "0xa599569bcb56ba8764e237f6f5a187e6cd50fe47f4d64acb829b1700a291a58",
-                    "0x1ab6e133e9edeb369f41d605bc1572b69b87f09fe19fa876f998ecc09eb02b3f",
-                    "0x204d7f7c504fb011e84995e6a6e70a8ea58ab263c14064f5a62f948817d12c1b",
-                    "0xfe9734a2e1f0d396277ab8017891b16f7821e99aac0fd7841c252a00699703f",
-                    "0x1fd9e2aa790a86e6a229484b0fa5023bdf7db98861c3ac6b5b5f662734321988",
-                    "0x8aecf98fe7e1c341e8aab0519be2a47a0f10d49ac4eb40969c3314791b28db9",
-                    "0x1c86e86b0268d4c072b59a1d89117085173b51af2f3eafb1b8fd783faaef6c51",
-                    "0x21d03116a39e716f4fac043ff4ba2b6ac41f998a55d8933f4108892769efc70b",
-                    "0xa0ff352a3a8b07914980a331fa2065a3624bade5302f836b4ec770da0209da",
-                    "0x2b694cded82f7ecb8352ee3b1ffdf0b41de22d6f085938b5a85ac5ea3ad0fa61",
-                    "0x240a34a028b55f0fdc3273a7b216a77c1d313cb0f5daf2b9df1fc471e7c98682",
-                    "0x202dc2a5fcb07d040ff1968b3ab64aaf13951702c601ed7a584d6d62c86a57f4",
-                    "0x1f08d22155e8820d7f5851a804a1e318693ee3906183508aa3a7ec2c9e883c04",
-                    "0x240158155c9cd36cddc204c69ab12feb9893e7627d86921038786d10fdd0c7e9",
-                    "0x568ca1e532d2adf3cd48eb2e10469fbab0565b4bac951186f2a1c33da8a4df8",
-                    "0x27d8a3d17ebe2e48266a53960d3bb957308367b4a6edbfc724214df33457c374",
-                    "0x252eed632200bb1c4a52ba96b59567539c7c7a1dbb5a611fcc74634c0005be1b",
-                    "0x99ea3ef1c245f33a737a751a0ce0abce9d24646a589a2acf32dc0ab410c6b13",
-                    "0x2b315ad4f3a6130cc24b12eff556c163763faf3906785d472f5e254c9c8419a8",
-                    "0x1e36cef6ede6420954c236eec0b4f15cf823450ef87696eb45d55728ebcde54f",
-                    "0x1e84bf83c538fd1e6714d18e92d94e9ae3377cf1d4c011d2c1f3031724fee4ed",
-                    "0x1174ddce24d06a11cee12969c99b09aa14ee68ad80eb6fc6f32e6a896dbc95bb"
-                ]
-            ]
-        },
-        {
+                "17810538377305826979727126885080619194828255122466505789376132059304678590982", 
+                "13274549151241879186367017598419480441052851608459995571043019156210835065884", 
+                "12217919828955713195296074461355704099077575572697456698819124326004773727872", 
+                "3325213248998312940839248497345183525722445334666772759713346022206056968778"
+            ], 
             "params": {
-                "seed": 5,
-                "logTwoDegree": 12,
-                "logTwoBound": 7,
-                "maxNbElementsToHash": 10
-            },
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 16
+            }
+        }, 
+        {
             "expected": [
-                [
-                    "0x262979080b1e153f76f52e84d7c99902b5030ce1f80d0d8ce5b24e81f83ee272",
-                    "0x1d0189f77dd34751b2a73ceab6356ebfb73fbd22893db53078ff8ab125fecb2f",
-                    "0x233768149d9b6030921485a6149c2b197368fee71be66d8514cc1e6ceaa21b6d",
-                    "0xa0bc65b2f258cb07773a356ee008dc3fa9d6984542b8cfdc66aa67e4c5d9d52",
-                    "0x1c55a49aed48797e6f1e8f2ad8a4a371838749d5cc9d615f9f613a1c91c33813",
-                    "0x1b037a57cf4dbcdabf291bd6d7772029c26f69f73e86d7d652d256062b8d1b08",
-                    "0x190ec066e990609f2e20ffcb0eb17e53e3441251bd209b21b51d08ca5e93847c",
-                    "0x2493f4ec82707e67e3ffe3b9c1f869f38a24fd835b7a4b8665f51fc1a32b6b92",
-                    "0x2462a1a73dc6bb711d37bb666405b841ba28f10c57d551a791199dcac51df4e1",
-                    "0x24917a24e50a0f05b0d1f20174214381880801297a6df6ad871c9d0f5d91b64e",
-                    "0x172e7c042c891c7081356314d3ba47118ae1452528b3536207cd098b2ddf10f7",
-                    "0xf76fab95cc6deb14632a0c5930c9d762dc16abd1e3f92af444b49263eb5893b",
-                    "0x1ac1969e1f4ca2843b2198cc5a38ab761ed084e8cba30b25e57c8b7fc4098231",
-                    "0x24a24b6ca97233afd2b1ac33cb8c762d0100ccac98f28c31e710f05f35979fd2",
-                    "0x2d1a14ae8beb38c0a9ef85170f932e539efbb3a84f31fbea8c1624ea94fdec73",
-                    "0x1a90a2aa1ffd28c461cdbd963f0f5edb842ca689ed0edc0ced50eb82c4606148",
-                    "0x12b49e794f83d909b0c858c5625499b7758b56edf524b3c600b4a8ae80c98508",
-                    "0xb2fe7d9d8480100ccf3e19c0e366e89bb5f06cac2dca7b24e5440c6b6d79ab3",
-                    "0x1c7b63a374c01d7f7c0bb844d36e757632a6bc883d43ee263307ce4e5c237450",
-                    "0x179da018c9328327376d5b634f08c409aa4349a89fc676a15c8251befbd724c6",
-                    "0x2f9439f4dc175ad24b590f52064fc38ed38f50f015be28b06d46c9dd88d26baa",
-                    "0x92aff8a1501c03738d260af8601e38058374a97fd6885efb2ed500824de601b",
-                    "0x91fef18e7f57cc26c33b840362b9f74ae8ea156ddba168b3b6d36fd11add3ee",
-                    "0x39a47cb9b51a891c925b3074128c6854a279ee489a604fc9a223a18b1197adf",
-                    "0x5c60bc146929ce870cb7ecd9ef82ca454509883316557dc1198e0559dc0a63a",
-                    "0x2778cbdd22b584e8067d55281952659b8a4996bc5294d917bcc7d37825a65859",
-                    "0xd2de0bcefeb8c92eb51edec5bd3047f5490ade666e57cd558bb0ed97e32768e",
-                    "0x127a7cdf5b41b0094f98a92a5fd1de2ffcf2e8e85a5b5d5d6993e18836882e1f",
-                    "0x4d7a9e75a04feed1d3671b5505bd9def9c064909f03f387af28986a0932c911",
-                    "0x29ca851569378a9d167a8a13bd7c7e85855801fe0e98160c7f524b515b7d6371",
-                    "0x25eb644318c31ca474b1eabc12fc3066c222747e80fe7479f15ac3a3ab3d5d8",
-                    "0x2ff53e09b754edc9023cdfe4001bab836358b1b15357ce08d70b63ddfbb5fbd9",
-                    "0xe5bd99f5e8b68bd7522062773aaa8acad2603c13a414c0e4f0e4315e34d51ae",
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-                    "0x43c7bc54b1aca471e6603f7ae8b21dad42cf8cc62c06ba66712e4e56b01256f",
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-                    "0x181fb45d91216b5b6fe088d70daea8700edb84d49d9a5f3a61c64803a6562a50",
-                    "0x4f49a7b994d507a66c5156b6df8e151527fbd2d37134896e932a26c81fa293c",
-                    "0x16de63ea60d1f815e0cd5e37a68c18e6f7abe9a26f9f6d18961595e8a8394a13",
-                    "0x1089dd4a71f4d47a235017434ff630f9aee5595b02415e82c90417ef414773e6",
-                    "0x25b631522b500a3915c5fe0c64b0b1414adbed9d08e3ef623d41103973333946",
-                    "0xd31f0c0653aff3d093e84e2dd9868fe7b2daf2fa984a004c886a0434952ecc4",
-                    "0x299fa56afbf786a74835edf66a93ee1445c3089f0f04efacd6ae8afcffea7882",
-                    "0x54f2ec8270fdd725deecd1d3dd8d7cd4c2ec962b55798ba1c264647470c613",
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-                    "0x2529f0875f716b4994488eddb2158db4b62d9ec07b323b8d13aae3788368fb36",
-                    "0x26bce93221dc34ef8c1e34389aac75bae165d3b3d9450471f2388ed0710cf296",
-                    "0xbe660cc8e9882517c8265434a407252a19f5cc75a7a6006c9f2f580812bbfc9",
-                    "0x2bc053a65060811bf41a0adf2150747a0561018572b20e7ce584625654c53d11",
-                    "0x29c184685342a254abf3c19f0d4393f678dec5a83b457e84bdb88cd90beaef0",
-                    "0x1a969e149366be4b1504af2fd73f115c2e38514b40a6a74f0a2af45a3d2a31d2",
-                    "0x297ba68c666666c41cd0b35b24a0bfd51fbd7cf6cca1ce8c9441716007dc4573",
-                    "0x2335f75d2541e3e05693788e98b9430311dd8609656b9a33b92e41dfd3a74a5b",
-                    "0x2a585a69b819d4d2e854c897f06ad1c1aa963255020b2e1f86897aaa389452bd",
-                    "0x80e6b553a8cc54350ae7bf347659a46ad8b024a2e20cfe12ad1d0cb111e13f3",
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-                    "0x2006a69043aeb20c0b2c6a14ef82ba2b446718146c9f166eea54aceac1c80a61",
-                    "0xfe6b3b631504d499ff8c0a65f6f0f4b60adc9e6d2a3bec817a568bc70034f76",
-                    "0x206d39010d8638d72cfdfacc1fc0ecac642f11a216fa2fb275b45719dacaa0e5",
-                    "0xfc13072046279055afbf0bcbe9d9a51136af8804498156374ddee804c69446b",
-                    "0x3ed9539c95a2a51e7ee8a1bc5ca3a75918aa627b097f75799a247ef0487c29",
-                    "0x226433b65e893e61350be45f09a2ecf2e8a01d6008a886c3720a73149cde62e7",
-                    "0x1f9317b18a9704f2967a5fa6a8b6a8edb32d70d71de854d6986ad7417d2ff148",
-                    "0x26c58bcd3a3bf66f8314ec20ca153409579b875a50a2bc9927627b3fe9d61e5c",
-                    "0x2287ce9722d7452762504084920dc50f7ae1cd3d59ceb6a500795d84f555b8cc",
-                    "0x722b4570bdf6d7cda3a6bbcf671ff5690349a759d34b1015c27017af7c75911",
-                    "0x227fadbbda031162b7895ef5c547b9a59295a62bdd8da142dae31971c4674eb7",
-                    "0xa157f6714ecaa0aab0684747a8e945c5a026c444a7125f0b02435020a82e941",
-                    "0xa3de3245cc5dbfa75f75be6ae48bd7743a5445ee6fca4312776bd06844f09e2",
-                    "0xcafffd2993f002ace0e317ee0b71862720f9ee6c9223d1223fcf14a55062c17",
-                    "0x2d5ef50efbdeed2caac2048182b1e395946bde04a14d53dc55e20906bc2e707",
-                    "0x24645aa194d73f4c3f3514cda39578384f0af135276dd41bd0da58883ff38448",
-                    "0x6fa1b2bc3d84788dc759d1d8e7e3f68d97bec693a4e957daf390a2ecc8ad65d",
-                    "0x14ddbd4bcc69e22f278b39921590acf7aa63096046305da59c100e2d8f0f81f1",
-                    "0x298bec257dfdc3088c6c1c67219ccf102ef7e7582e862b61860da70f2fa8bcc5",
-                    "0x1ad12f32a31cb9402b2b8e3a8cdb15f7caeb47ef32fa7fe118b10c273cafaa5a",
-                    "0x1372711df0fa23d11c026858de673a41e8064313a70dc38ff3cf21d6edd19a7a",
-                    "0x233c85c1e906e32585db46f0cc2cac093bceddd0e18f4ef88c178b1a93a16ca2",
-                    "0x114a1c14fdca275ac05b7078c64c6b21d7e9d40ca23dc879242aa9866f6e258e",
-                    "0x1f3e23de5d3867f921dbf5fc79ad5a6f7246e9144557ed33dbda81682de86ec1",
-                    "0x1c7bc05e7e139aa34fb73136b14b68d8047c4179889b690e507587baa54b7372",
-                    "0x294ea828a2b08d62addf7365fc9f2799c2179371c5b93ea4d7a0868bb118f2d2",
-                    "0x27b529cc802bc30ec9eca0b01450c12410e736176ed24f79f1cc7c9d9e368f6b",
-                    "0x171fbe82666a03591b5b92681694eb0d3c83dc41046d8f239108e6e9c69f2e02",
-                    "0x29f486642e634ec8772904b958544522fd04e73a34f73cdc2c6f9b8409423583",
-                    "0x2d09f23b520c1288b50f84c47989722a2373a5c09d36325a5d58870e94f0fa4d",
-                    "0x60d16c8e94aba799c58622ea44dfbcc6d86e1ad3184f3f1cbe3c32bef91f697",
-                    "0x1312cdcb8d43b3b1f72e49fbf404022860414486a971a1033ed70c11fc3d01dc",
-                    "0x20fda017dcef2f12899de93c6d5b7fb5f4e7efa4d4f57d353d6d6f251363cacd",
-                    "0x19764c41df3f7d8d406c3e5ace141968e6a79bee2284b67a1e43ba0bd0ee0872",
-                    "0x27a5be6daab0122b5b92ef71ab490fa67a5b63218da2636ad4ca6945dff6f2d0",
-                    "0x2b1a18c80b5ca3b69c896e9c774fdcd401bc97f85e7db170a9afd03df397ea01",
-                    "0x1d2cc4d028d9eebfe5b486475aaf9c1fd0f062775df1fb1e10322ac540e687e8",
-                    "0x7b72e196c45f05e3115254d6cce822a199fd4d4ace8b3375d9e81115dbefcb4",
-                    "0xeb3b2034d80401144d27deb46a9f3e3cabe6ceccb98791cd86ce7a61747f650",
-                    "0x11d730d7536fdcf4eed5e2d6a870b47b5cd3d689d9f79c7e183ab0924cb843d4",
-                    "0x282fdf358be46be570f6a7c5b289e5093fd3bf6513ec7764b7cd0c04c766a24",
-                    "0x1bdcc87eef24dc5d5a12b127a7a46dceebc696deb6d594a702f2a08fea1a4ae3",
-                    "0x160fba5c17e2a8f69cf650cb7a620097f3d7975a95d2d19bf82ee328b5c030ee",
-                    "0x2224b8885100d51cb140cd34d668d6bc2c0a16a7618be5896b3570a7fdd1f753",
-                    "0x250f20aa5b3ab9d1732573e8c4a70ff86bf9f6b152f4368fa4ead1e7aa281b21",
-                    "0x12c53cd472699707de64ebb99eaa213e03224f00e837e28e134b23df4ca78a99",
-                    "0x311905b8e21ca206876e7f06fe7c2558943201ba045341cad8daa71a7ef5f81",
-                    "0x1dcde6f1f9e13954433f28818a7ccb15df351373d0379bd8fb9c77810397864d",
-                    "0x23342a8c45e0de72d796704700340cc72bbb49d07dafb20558d265f679de4c3d",
-                    "0x206f0cbd5d5a470a3786072271d301d5c8a759996a23558fa259e14ff2204c5a",
-                    "0xd6b35ea9411e825c0099c23d3f0a01ff49580feb9986966cc420d1759ae95d1",
-                    "0x1e5068838ccded3148f1467a1f4ee1c8cb59f2126ce1ffce4f44df9e05f2e4e0",
-                    "0xc9e1f3870e8ce4d1bfd316a6cb9522a248b276ece290c145765e4c529a3e144",
-                    "0x1ec367ca9ad590fdfed26add23a7e4bdb4120fe6480bdfe82ac1c7f35d3ee837",
-                    "0x2dfa2df02263fa4fcfc24e2a7f6077b44cbfaea2e4f5e0ca3f58a1eea8057c6d",
-                    "0x135286ebae5bb95cc3c80b9db8e419edc55dd1f8ab37fdd6aaef497a4d4325e1",
-                    "0xccd65e42b0c64b3a93e570b90c503fefc40b452275d0eb03013c327a2c7f2ca",
-                    "0x2433b7a331c4709161288c2e9c9f094f258c1c6d5c6f4e11832e7279f120dae6",
-                    "0x631a7088adab00c78b941b23cda03c5495e1618e332389d776ce7b6a1fe4c80",
-                    "0x163689ce0500fbd4fc8c20adc11a533e477d2f46e62d75ec8c426dae9ffe09f1",
-                    "0x1d77a42b9af09b19ec6de246b2b87d2868bb40e442b889f102eb9f51ccdde295",
-                    "0x12b5d406fbf39ad5c69461c130ad9c197be6a72abe7d4c2c4915b4140b32cfea",
-                    "0x1b9ab60e6d41c848656549f836e9e0269afdc4987fb90151041284c7da25e45c",
-                    "0x21e85bf3f0485d3d73e16bc51620d3e442cf43bf77982b84c27fcf5294e2dbf0",
-                    "0xc2908810215a30b71f9fa52537919da6b27a6c6c521f1a4b02d93a5cdf799a2",
-                    "0x2c7e1485ef22414cd120dbe1c0762e22221200c398c69fef3f9214f1433b6aa1",
-                    "0x7a0000d064b6580854763cc3d7585b999a497abdd5a78c763debed9e6d30ea2",
-                    "0x4786e7c3f9d3b2b405018ef5b54609b91dc97052f8d85a6386df2b1c1b01e4e",
-                    "0x11bad795b57968df31e0f735f83a0f1036ff6cd00594cd4ed7f947ff1fe1ebc3",
-                    "0x210b97b69d5fd6e769f2dfe170166398ff3ee7aa3744e874da52d604dec5d492",
-                    "0x28599b7525713cfe32e8076e14c9b82fe63f7fd01a1b59cd368514ca0ec1bafc",
-                    "0x260dd6bd33d21eab955f96ff70e6e35d89e9740a0e4d79ce3756898f57ee8c",
-                    "0x1aac32441aa5050456a6a9df63cdd2d1dcfd42e675a60bd5f2a73140197425d1",
-                    "0x1e80984a5f6833f51e098fcb0555ee179e4e6cedba05dbded75a61fac0f06c8",
-                    "0x27a08f86680a25a97717d09762ca8e440e067dadbccb9b01b31ba6ec8141cf6a",
-                    "0x16f4e55e60461aa983e3a985476dbd5ff668c935c25bb223e54be64405a44018",
-                    "0x16bd86fb85c8d6634ab8c71803505b81a4f3b73431aef5a7fd64eecb0b1ff6a7",
-                    "0x19b2a66dce0794b563e8bb580b0424dc87ffd1196e5e18f7cf244e3f409f158e",
-                    "0x908edc714f37260bd6d242fd9ac2d695f394794b4e8cd006adef0735b65f64b",
-                    "0x1527934bd0d2d58bf648e898f270eec58f016d08bffb70ff66489a6dbbc79cb1",
-                    "0xb365af553e42142546e6f4c44badc902ecb969fefa892593617d445076cb8c2",
-                    "0x27a8dc8f443e58ede23d072f443f2b024b3cb33c56b58c6745a6daec52957ef5"
-                ]
-            ]
+                "1049896500426401685945922049369234922485914665192048996511968651754212430847", 
+                "18925053839250027789719219571375251204394727876911726560469458538529452247978", 
+                "9323628684818709197255012865135973461462156185665546071174101521851226715555", 
+                "16161396862971423997723820824078836309904422899378926199292781195549690434491"
+            ], 
+            "params": {
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 32
+            }
         }
     ]
 }
\ No newline at end of file
diff --git a/field/babybear/sis/sis.go b/field/babybear/sis/sis.go
new file mode 100644
index 0000000000..d1d2b92c64
--- /dev/null
+++ b/field/babybear/sis/sis.go
@@ -0,0 +1,468 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package sis
+
+import (
+	"bytes"
+	"encoding/binary"
+	"errors"
+	"hash"
+	"math/bits"
+
+	"github.com/bits-and-blooms/bitset"
+	"github.com/consensys/gnark-crypto/field/babybear"
+	"github.com/consensys/gnark-crypto/field/babybear/fft"
+	"github.com/consensys/gnark-crypto/internal/parallel"
+	"golang.org/x/crypto/blake2b"
+)
+
+var (
+	ErrNotAPowerOfTwo = errors.New("d must be a power of 2")
+)
+
+// Ring-SIS instance
+type RSis struct {
+
+	// buffer storing the data to hash
+	buffer bytes.Buffer
+
+	// Vectors in ℤ_{p}/Xⁿ+1
+	// A[i] is the i-th polynomial.
+	// Ag the evaluation form of the polynomials in A on the coset √(g) * <g>
+	A  [][]babybear.Element
+	Ag [][]babybear.Element
+
+	// LogTwoBound (Infinity norm) of the vector to hash. It means that each component in m
+	// is < 2^B, where m is the vector to hash (the hash being A*m).
+	// cf https://hackmd.io/7OODKWQZRRW9RxM5BaXtIw , B >= 3.
+	LogTwoBound int
+
+	// domain for the polynomial multiplication
+	Domain        *fft.Domain
+	twiddleCosets []babybear.Element // see FFT64 and precomputeTwiddlesCoset
+
+	// d, the degree of X^{d}+1
+	Degree int
+
+	// in bytes, represents the maximum number of bytes the .Write(...) will handle;
+	// ( maximum number of bytes to sum )
+	capacity            int
+	maxNbElementsToHash int
+
+	// allocate memory once per instance (used in Sum())
+	bufM, bufRes babybear.Vector
+	bufMValues   *bitset.BitSet
+}
+
+// NewRSis creates an instance of RSis.
+// seed: seed for the randomness for generating A.
+// logTwoDegree: if d := logTwoDegree, the ring will be ℤ_{p}[X]/Xᵈ-1, where X^{2ᵈ} is the 2ᵈ⁺¹-th cyclotomic polynomial
+// logTwoBound: the bound of the vector to hash (using the infinity norm).
+// maxNbElementsToHash: maximum number of field elements the instance handles
+// used to derived n, the number of polynomials in A, and max size of instance's internal buffer.
+func NewRSis(seed int64, logTwoDegree, logTwoBound, maxNbElementsToHash int) (*RSis, error) {
+
+	if logTwoBound > 64 {
+		return nil, errors.New("logTwoBound too large")
+	}
+	if bits.UintSize == 32 {
+		return nil, errors.New("unsupported architecture; need 64bit target")
+	}
+
+	degree := 1 << logTwoDegree
+	capacity := maxNbElementsToHash * babybear.Bytes
+
+	// n: number of polynomials in A
+	// len(m) == degree * n
+	// with each element in m being logTwoBounds bits from the instance buffer.
+	// that is, to fill m, we need [degree * n * logTwoBound] bits of data
+	// capacity == [degree * n * logTwoBound] / 8
+	// n == (capacity*8)/(degree*logTwoBound)
+
+	// First n <- #limbs to represent a single field element
+	n := (babybear.Bytes * 8) / logTwoBound
+	if n*logTwoBound < babybear.Bytes*8 {
+		n++
+	}
+
+	// Then multiply by the number of field elements
+	n *= maxNbElementsToHash
+
+	// And divide (+ ceil) to get the number of polynomials
+	if n%degree == 0 {
+		n /= degree
+	} else {
+		n /= degree // number of polynomials
+		n++
+	}
+
+	// domains (shift is √{gen} )
+	shift, err := babybear.Generator(uint64(2 * degree))
+	if err != nil {
+		return nil, err
+	}
+
+	r := &RSis{
+		LogTwoBound:         logTwoBound,
+		capacity:            capacity,
+		Degree:              degree,
+		Domain:              fft.NewDomain(uint64(degree), fft.WithShift(shift)),
+		A:                   make([][]babybear.Element, n),
+		Ag:                  make([][]babybear.Element, n),
+		bufM:                make(babybear.Vector, degree*n),
+		bufRes:              make(babybear.Vector, degree),
+		bufMValues:          bitset.New(uint(n)),
+		maxNbElementsToHash: maxNbElementsToHash,
+	}
+	if r.LogTwoBound == 8 && r.Degree == 64 {
+		// TODO @gbotrel fixme, that's dirty.
+		r.twiddleCosets = PrecomputeTwiddlesCoset(r.Domain.Generator, r.Domain.FrMultiplicativeGen)
+	}
+
+	// filling A
+	a := make([]babybear.Element, n*r.Degree)
+	ag := make([]babybear.Element, n*r.Degree)
+
+	parallel.Execute(n, func(start, end int) {
+		var buf bytes.Buffer
+		for i := start; i < end; i++ {
+			rstart, rend := i*r.Degree, (i+1)*r.Degree
+			r.A[i] = a[rstart:rend:rend]
+			r.Ag[i] = ag[rstart:rend:rend]
+			for j := 0; j < r.Degree; j++ {
+				r.A[i][j] = genRandom(seed, int64(i), int64(j), &buf)
+			}
+
+			// fill Ag the evaluation form of the polynomials in A on the coset √(g) * <g>
+			copy(r.Ag[i], r.A[i])
+			r.Domain.FFT(r.Ag[i], fft.DIF, fft.OnCoset())
+		}
+	})
+
+	return r, nil
+}
+
+func (r *RSis) Write(p []byte) (n int, err error) {
+	r.buffer.Write(p)
+	return len(p), nil
+}
+
+// Sum appends the current hash to b and returns the resulting slice.
+// It does not change the underlying hash state.
+// The instance buffer is interpreted as a sequence of coefficients of size r.Bound bits long.
+// The function returns the hash of the polynomial as a a sequence []babybear.Elements, interpreted as []bytes,
+// corresponding to sum_i A[i]*m Mod X^{d}+1
+func (r *RSis) Sum(b []byte) []byte {
+	buf := r.buffer.Bytes()
+	if len(buf) > r.capacity {
+		panic("buffer too large")
+	}
+
+	fastPath := r.LogTwoBound == 8 && r.Degree == 64
+
+	// clear the buffers of the instance.
+	defer r.cleanupBuffers()
+
+	m := r.bufM
+	mValues := r.bufMValues
+
+	if r.LogTwoBound < 8 && (8%r.LogTwoBound == 0) {
+		limbDecomposeBytesSmallBound(buf, m, r.LogTwoBound, r.Degree, mValues)
+	} else if r.LogTwoBound >= 8 && (babybear.Bytes*8)%r.LogTwoBound == 0 {
+		limbDecomposeBytesMiddleBound(buf, m, r.LogTwoBound, r.Degree, mValues)
+	} else {
+		limbDecomposeBytes(buf, m, r.LogTwoBound, r.Degree, mValues)
+	}
+
+	// we can hash now.
+	res := r.bufRes
+
+	// method 1: fft
+	for i := 0; i < len(r.Ag); i++ {
+		if !mValues.Test(uint(i)) {
+			// means m[i*r.Degree : (i+1)*r.Degree] == [0...0]
+			// we can skip this, FFT(0) = 0
+			continue
+		}
+		k := m[i*r.Degree : (i+1)*r.Degree]
+		if fastPath {
+			// fast path.
+			FFT64(k, r.twiddleCosets)
+		} else {
+			r.Domain.FFT(k, fft.DIF, fft.OnCoset(), fft.WithNbTasks(1))
+		}
+		mulModAcc(res, r.Ag[i], k)
+	}
+	r.Domain.FFTInverse(res, fft.DIT, fft.OnCoset(), fft.WithNbTasks(1)) // -> reduces mod Xᵈ+1
+
+	resBytes, err := res.MarshalBinary()
+	if err != nil {
+		panic(err)
+	}
+
+	return append(b, resBytes[4:]...) // first 4 bytes are uint32(len(res))
+}
+
+// Reset resets the Hash to its initial state.
+func (r *RSis) Reset() {
+	r.buffer.Reset()
+}
+
+// Size returns the number of bytes Sum will return.
+func (r *RSis) Size() int {
+
+	// The size in bits is the size in bits of a polynomial in A.
+	degree := len(r.A[0])
+	totalSize := degree * babybear.Modulus().BitLen() / 8
+
+	return totalSize
+}
+
+// BlockSize returns the hash's underlying block size.
+// The Write method must be able to accept any amount
+// of data, but it may operate more efficiently if all writes
+// are a multiple of the block size.
+func (r *RSis) BlockSize() int {
+	return 0
+}
+
+// Construct a hasher generator. It takes as input the same parameters
+// as `NewRingSIS` and outputs a function which returns fresh hasher
+// everytime it is called
+func NewRingSISMaker(seed int64, logTwoDegree, logTwoBound, maxNbElementsToHash int) (func() hash.Hash, error) {
+	return func() hash.Hash {
+		h, err := NewRSis(seed, logTwoDegree, logTwoBound, maxNbElementsToHash)
+		if err != nil {
+			panic(err)
+		}
+		return h
+	}, nil
+
+}
+
+func genRandom(seed, i, j int64, buf *bytes.Buffer) babybear.Element {
+
+	buf.Reset()
+	buf.WriteString("SIS")
+	binary.Write(buf, binary.BigEndian, seed)
+	binary.Write(buf, binary.BigEndian, i)
+	binary.Write(buf, binary.BigEndian, j)
+
+	digest := blake2b.Sum256(buf.Bytes())
+
+	var res babybear.Element
+	res.SetBytes(digest[:])
+
+	return res
+}
+
+// mulMod computes p * q in ℤ_{p}[X]/Xᵈ+1.
+// Is assumed that pLagrangeShifted and qLagrangeShifted are of the correct sizes
+// and that they are in evaluation form on √(g) * <g>
+// The result is not FFTinversed. The fft inverse is done once every
+// multiplications are done.
+func mulMod(pLagrangeCosetBitReversed, qLagrangeCosetBitReversed []babybear.Element) []babybear.Element {
+
+	res := make([]babybear.Element, len(pLagrangeCosetBitReversed))
+	for i := 0; i < len(pLagrangeCosetBitReversed); i++ {
+		res[i].Mul(&pLagrangeCosetBitReversed[i], &qLagrangeCosetBitReversed[i])
+	}
+
+	// NOT fft inv for now, wait until every part of the keys have been multiplied
+	// r.Domain.FFTInverse(res, fft.DIT, true)
+
+	return res
+
+}
+
+// mulMod + accumulate in res.
+func mulModAcc(res []babybear.Element, pLagrangeCosetBitReversed, qLagrangeCosetBitReversed []babybear.Element) {
+	var t babybear.Element
+	for i := 0; i < len(pLagrangeCosetBitReversed); i++ {
+		t.Mul(&pLagrangeCosetBitReversed[i], &qLagrangeCosetBitReversed[i])
+		res[i].Add(&res[i], &t)
+	}
+}
+
+// Returns a clone of the RSis parameters with a fresh and empty buffer. Does not
+// mutate the current instance. The keys and the public parameters of the SIS
+// instance are not deep-copied. It is useful when we want to hash in parallel.
+// Otherwise, we would have to generate an entire RSis for each thread.
+func (r *RSis) CopyWithFreshBuffer() RSis {
+	res := *r
+	res.buffer = bytes.Buffer{}
+	res.bufM = make(babybear.Vector, len(r.bufM))
+	res.bufMValues = bitset.New(r.bufMValues.Len())
+	res.bufRes = make(babybear.Vector, len(r.bufRes))
+	return res
+}
+
+// Cleanup the buffers of the RSis instance
+func (r *RSis) cleanupBuffers() {
+	r.bufMValues.ClearAll()
+	for i := 0; i < len(r.bufM); i++ {
+		r.bufM[i].SetZero()
+	}
+	for i := 0; i < len(r.bufRes); i++ {
+		r.bufRes[i].SetZero()
+	}
+}
+
+// Split an slice of bytes representing an array of serialized field element in
+// big-endian form into an array of limbs representing the same field elements
+// in little-endian form. Namely, if our field is represented with 64 bits and we
+// have the following field element 0x0123456789abcdef (0 being the most significant
+// character and and f being the least significant one) and our log norm bound is
+// 16 (so 1 hex character = 1 limb). The function assigns the values of m to [f, e,
+// d, c, b, a, ..., 3, 2, 1, 0]. m should be preallocated and zeroized. Additionally,
+// we have the guarantee that 2 bits contributing to different field elements cannot
+// be part of the same limb.
+func LimbDecomposeBytes(buf []byte, m babybear.Vector, logTwoBound int) {
+	limbDecomposeBytes(buf, m, logTwoBound, 0, nil)
+}
+
+// decomposes m as by taking chunks of logTwoBound bits at a time. The buffer is interpreted like this:
+// [0xa,        ..            , 0x1 | 0xa ... ]
+//
+//	<- #bytes in a field element ->
+//	<-0xa is the MSB, 0x1 the LSB->
+//	<-we read this chunk from right
+//	   			to left 	 	 ->
+//
+// This function is called when logTwoBound divides the number of bits used to represent a
+// babybear element.
+// From a slice of field elements m:=[a_0, a_1, ...]
+// Doing h.Sum(h.Write([Marshal[a_i] for i in len(m)])) is the same than
+// writing the a_i in little endian, and then taking logTwoBound bits at a time.
+//
+// ex: m := [0x1, 0x3]
+// in the hash buffer, it is interpreted like that as a stream of bits:
+// [100...0 110...0] corresponding to [0x1, 0x3] in little endian, so first bit = LSbit
+// then the stream of bits is splitted in chunks of logTwoBound bits.
+//
+// This function is called when logTwoBound divides 8.
+func limbDecomposeBytesSmallBound(buf []byte, m babybear.Vector, logTwoBound, degree int, mValues *bitset.BitSet) {
+	mask := byte((1 << logTwoBound) - 1)
+	nbChunksPerBytes := 8 / logTwoBound
+	nbFieldsElmts := len(buf) / babybear.Bytes
+	for i := 0; i < nbFieldsElmts; i++ {
+		for j := babybear.Bytes - 1; j >= 0; j-- {
+			curByte := buf[i*babybear.Bytes+j]
+			curPos := i*babybear.Bytes*nbChunksPerBytes + (babybear.Bytes-1-j)*nbChunksPerBytes
+			for k := 0; k < nbChunksPerBytes; k++ {
+
+				m[curPos+k][0] = uint32((curByte >> (k * logTwoBound)) & mask)
+
+				// Check if mPos is zero and mark as non-zero in the bitset if not
+				if m[curPos+k][0] != 0 && mValues != nil {
+					mValues.Set(uint((curPos + k) / degree))
+				}
+			}
+		}
+	}
+}
+
+// limbDecomposeBytesMiddleBound same function than limbDecomposeBytesSmallBound, but logTwoBound is
+// a multiple of 8, and divides the number of bits of the fields.
+func limbDecomposeBytesMiddleBound(buf []byte, m babybear.Vector, logTwoBound, degree int, mValues *bitset.BitSet) {
+	nbFieldsElmts := len(buf) / babybear.Bytes
+	nbChunksPerElements := babybear.Bytes * 8 / logTwoBound
+	nbBytesInChunk := logTwoBound / 8
+	curElmt := 0
+	for i := 0; i < nbFieldsElmts; i++ {
+		for j := nbChunksPerElements; j > 0; j-- {
+			curPos := i*babybear.Bytes + j*nbBytesInChunk
+			for k := 1; k <= nbBytesInChunk; k++ {
+
+				m[curElmt][0] |= (uint32(buf[curPos-k]) << ((k - 1) * 8))
+
+			}
+			// Check if mPos is zero and mark as non-zero in the bitset if not
+			if m[curElmt][0] != 0 && mValues != nil {
+				mValues.Set(uint((curElmt) / degree))
+			}
+			curElmt += 1
+		}
+	}
+}
+
+// Split an slice of bytes representing an array of serialized field element in
+// big-endian form into an array of limbs representing the same field elements
+// in little-endian form. Namely, if our field is represented with 64 bits and we
+// have the following field element 0x0123456789abcdef (0 being the most significant
+// character and and f being the least significant one) and our log norm bound is
+// 16 (so 1 hex character = 1 limb). The function assigns the values of m to [f, e,
+// d, c, b, a, ..., 3, 2, 1, 0]. m should be preallocated and zeroized. mValues is
+// an optional bitSet. If provided, it must be empty. The function will set bit "i"
+// to indicate the that i-th SIS input polynomial should be non-zero. Recall, that a
+// SIS polynomial corresponds to a chunk of limbs of size `degree`. Additionally,
+// we have the guarantee that 2 bits contributing to different field elements cannot
+// be part of the same limb.
+func limbDecomposeBytes(buf []byte, m babybear.Vector, logTwoBound, degree int, mValues *bitset.BitSet) {
+
+	// bitwise decomposition of the buffer, in order to build m (the vector to hash)
+	// as a list of polynomials, whose coefficients are less than r.B bits long.
+	// Say buf=[0xbe,0x0f]. As a stream of bits it is interpreted like this:
+	// 10111110 00001111. getIthBit(0)=1 (=leftmost bit), getIthBit(1)=0 (=second leftmost bit), etc.
+	nbBits := len(buf) * 8
+	getIthBit := func(i int) uint8 {
+		k := i / 8
+		if k >= len(buf) {
+			return 0
+		}
+		b := buf[k]
+		j := i % 8
+		return b >> (7 - j) & 1
+	}
+
+	// we process the input buffer by blocks of r.LogTwoBound bits
+	// each of these block (<< 64bits) are interpreted as a coefficient
+	mPos := 0
+	for fieldStart := 0; fieldStart < nbBits; {
+		for bitInField := 0; bitInField < babybear.Bytes*8; {
+
+			j := bitInField % logTwoBound
+
+			// r.LogTwoBound < 64; we just use the first word of our element here,
+			// and set the bits from LSB to MSB.
+			at := fieldStart + babybear.Bytes*8 - bitInField - 1
+
+			m[mPos][0] |= uint32(getIthBit(at) << j)
+
+			bitInField++
+
+			// Check if mPos is zero and mark as non-zero in the bitset if not
+			if m[mPos][0] != 0 && mValues != nil {
+				mValues.Set(uint(mPos / degree))
+			}
+
+			if j == logTwoBound-1 || bitInField == babybear.Bytes*8 {
+				mPos++
+			}
+		}
+		fieldStart += babybear.Bytes * 8
+	}
+}
+
+// see limbDecomposeBytes; this function is optimized for the case where
+// logTwoBound == 8 and degree == 64
+func limbDecomposeBytes8_64(buf []byte, m babybear.Vector, mValues *bitset.BitSet) {
+	// with logTwoBound == 8, we can actually advance byte per byte.
+	const degree = 64
+	j := 0
+
+	for startPos := babybear.Bytes - 1; startPos < len(buf); startPos += babybear.Bytes {
+		for i := startPos; i >= startPos-babybear.Bytes+1; i-- {
+
+			m[j][0] = uint32(buf[i])
+
+			if m[j][0] != 0 {
+				mValues.Set(uint(j / degree))
+			}
+			j++
+		}
+	}
+}
diff --git a/field/babybear/sis/sis.py b/field/babybear/sis/sis.py
new file mode 100644
index 0000000000..fd6cb6611f
--- /dev/null
+++ b/field/babybear/sis/sis.py
@@ -0,0 +1,254 @@
+## "sage sis.sage" will generate test_cases.json
+## tested with a fresh sage install on macOS (Feb 2023)
+
+import json
+
+# Babybear FR
+#2^31 - 2^27 + 1
+R = 2**31-2**27+1
+FR_BYTE_SIZE = 4
+FR_BIT_SIZE = FR_BYTE_SIZE*8
+GFR = GF(R)
+FR.<x> = GFR[]
+Z = IntegerRing()
+
+# Montgomery constant
+RR = GFR(2**(FR_BYTE_SIZE*8))
+
+# utils
+
+
+def build_poly(a):
+    """ Builds a poly from the array a
+
+    Args:
+        a an array
+
+    Returns:
+        a[0]+a[1]*X + .. + a[n]*X**n
+    """
+
+    res = GFR(0)
+    for i, v in enumerate(a):
+        res += GFR(v)*x**i
+    return res
+
+
+def get_ith_bit(i, b):
+    """
+    Args:
+        i: index of the bit to retrieve
+        b: array of bytes
+
+    Returns:
+        the i-th bit of b, when it is written b[0] || b[1] || ...
+    """
+    k = i//8
+    if k >= len(b):
+        return 0
+    j = i % 8
+    return (b[k] >> (7-j)) & 1
+
+
+def to_bytes(m, s):
+    """
+
+    Args:
+        m: an integer
+        s: the expected number of bytes of the result. If s is bigger than the
+        number of bytes in m, the remaining bytes are set to zero.
+
+    Returns:
+        the byte representation of m as a byte array, as
+        in gnark-crypto.
+    """
+    _m = Z(m)
+    res = s*[0]
+    mask = 255
+    for i in range(s):
+        res[s-1-i] = _m & 255
+        _m = _m >> 8
+    return res
+
+
+def split_coeffs(b, logTwoBound):
+    """
+    Args:
+        b: an array of bytes
+        logTwoBound: number of bits of the bound
+
+    Returns:
+        an array of coeffs, each coeff being the i-th chunk of logTwoBounds bits of b.
+        The coeffs are formed as follow. The input byte string is implicitly parsed as
+        a slice of field elements of FR_BYTE_SIZE bytes each in bigendian-natural form. the outputs
+        are in a little-endian form. That is, each chunk of size FR_BIT_SIZE / logTwoBounds of the
+        output can be seen as a polynomial, such that, when evaluated at 2 we get the original
+        field element.
+    """
+    nbBits = len(b)*8
+    res = [] 
+    i = 0
+
+    if len(b) % FR_BYTE_SIZE != 0:
+        exit("the length of b should divide the field size")
+
+    # The number of fields that we are parsing. In case we have that
+    # logTwoBound does not divide the number of bits to represent a
+    # field element, we do not merge them.
+    nbField = len(b) / FR_BYTE_SIZE
+    nbBitsInField = int(FR_BYTE_SIZE * 8)
+    
+    for fieldID in range(nbField):
+        fieldStart = fieldID * FR_BIT_SIZE
+        e = 0
+        for bitInField in range(nbBitsInField):
+            j = bitInField % logTwoBound
+            at = fieldStart + nbBitsInField - 1 - bitInField
+            e |= get_ith_bit(at, b) << j 
+            # Switch to a new limb
+            if j == logTwoBound - 1 or bitInField == FR_BYTE_SIZE * 8 - 1:
+                res.append(e)
+                e = 0
+
+    # careful Montgomery constant...
+    return [GFR(e)*RR**-1 for e in res]
+
+
+def poly_pseudo_rand(seed, n):
+    """ Generates a pseudo random polynomial of size n from seed.
+
+    Args:
+        seed: seed for the pseudo random gen
+        n: degree of the polynomial
+    """
+    seed = GFR(seed)
+    a = n*[0]
+    for i in range(n):
+        a[i] = seed**2
+        seed = a[i]
+    return build_poly(a)
+
+
+# SIS
+class SIS:
+    def __init__(self, seed, logTwoDegree, logTwoBound, maxNbElementsToHash):
+        """
+            Args:
+                seed
+                logTwoDegree: 
+                logTwoBound: bound of SIS
+                maxNbElementsToHash
+        """
+        capacity = maxNbElementsToHash * FR_BYTE_SIZE
+        degree = 1 << logTwoDegree
+
+        n = capacity * 8 / logTwoBound  # number of coefficients
+        if n % degree == 0:  # check how sage / python rounds the int div.
+            n = n / degree
+        else:
+            n = n / degree
+            n = n + 1
+
+        n = int(n)
+
+        self.logTwoBound = logTwoBound
+        self.degree = degree
+        self.size = n
+        self.key = n * [0]
+        for i in range(n):
+            self.key[i] = poly_pseudo_rand(seed, self.degree)
+            seed += 1
+
+    def hash(self, inputs):
+        """ 
+        Args:
+           inputs is a vector of FR elements
+
+        Returns:
+            the sis hash of m.
+        """
+        b = []
+        for i in inputs:
+            b.extend(to_bytes(i, FR_BYTE_SIZE))
+
+        return self.hash_bytes(b)
+
+    def hash_bytes(self, b):
+        """ 
+        Args:
+            b is a list of bytes to hash
+
+        Returns:
+            the sis hash of m.
+        """
+        # step 1: build the polynomials from m
+        c = split_coeffs(b, self.logTwoBound)
+        mp = [build_poly(c[self.degree*i:self.degree*(i+1)])
+              for i in range(self.size)]
+
+        # step 2: compute sum_i mp[i]*key[i] mod X^n+1
+        modulo = x**self.degree+1
+        res = 0
+        for i in range(self.size):
+            res += self.key[i]*mp[i]
+        res = res % modulo
+        return res
+
+
+def vectorToString(v):
+    # v is a vector of field elements
+    # we return a list of strings in base10
+    r = []
+    for e in v:
+        r.append("{}".format(Z(e)))
+        # r.append("0x" + Z(e).hex())
+    return r
+    
+
+def SISParams(seed, logTwoDegree, logTwoBound, maxNbElementsToHash):
+    p = {}
+    p['seed'] = int(seed)
+    p['logTwoDegree'] = int(logTwoDegree)
+    p['logTwoBound'] = int(logTwoBound)
+    p['maxNbElementsToHash'] = int(maxNbElementsToHash)
+    return p
+
+PARAMS = [
+
+    # call to limbDecomposeBytes
+    # SISParams(5, 2, 3, 10),
+    
+    # call to limbDecomposeBytesSmallBound
+    SISParams(5, 2, 2, 10),
+    SISParams(5, 2, 4, 10),
+
+    # call to limbDecomposeBytesSmallBound
+    SISParams(5, 2, 8, 10),
+    SISParams(5, 2, 16, 10),
+    SISParams(5, 2, 32, 10),
+]
+
+INPUTS = [GFR(5)**(i+1) for i in range(10)]
+
+TEST_CASES = {}
+
+TEST_CASES['inputs'] = vectorToString(INPUTS)
+TEST_CASES['entries'] = []
+
+for p in PARAMS:
+
+    entry = {}
+    entry['params'] = p 
+    # print("generating test cases with SIS params " + json.dumps(p))
+    instance = SIS(p['seed'], p['logTwoDegree'], p['logTwoBound'], p['maxNbElementsToHash'])
+
+    # hash the vector
+    hResult = instance.hash(INPUTS)
+    entry['expected'] = vectorToString(hResult)
+    
+    TEST_CASES['entries'].append(entry)
+
+
+TEST_CASES_json = json.dumps(TEST_CASES, indent=4)
+with open("test_cases.json", "w") as outfile:
+    outfile.write(TEST_CASES_json)
diff --git a/field/babybear/sis/sis_fft.go b/field/babybear/sis/sis_fft.go
new file mode 100644
index 0000000000..0b5cc37994
--- /dev/null
+++ b/field/babybear/sis/sis_fft.go
@@ -0,0 +1,556 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package sis
+
+import (
+	"github.com/consensys/gnark-crypto/field/babybear"
+	"math/big"
+)
+
+// FFT64 is generated by gnark-crypto and contains the unrolled code for FFT (DIF) on 64 elements
+// equivalent code: r.Domain.FFT(k, fft.DIF, fft.OnCoset(), fft.WithNbTasks(1))
+// twiddlesCoset must be pre-computed from twiddles and coset table, see PrecomputeTwiddlesCoset
+func FFT64(a []babybear.Element, twiddlesCoset []babybear.Element) {
+
+	a[32].Mul(&a[32], &twiddlesCoset[0])
+	a[33].Mul(&a[33], &twiddlesCoset[0])
+	a[34].Mul(&a[34], &twiddlesCoset[0])
+	a[35].Mul(&a[35], &twiddlesCoset[0])
+	a[36].Mul(&a[36], &twiddlesCoset[0])
+	a[37].Mul(&a[37], &twiddlesCoset[0])
+	a[38].Mul(&a[38], &twiddlesCoset[0])
+	a[39].Mul(&a[39], &twiddlesCoset[0])
+	a[40].Mul(&a[40], &twiddlesCoset[0])
+	a[41].Mul(&a[41], &twiddlesCoset[0])
+	a[42].Mul(&a[42], &twiddlesCoset[0])
+	a[43].Mul(&a[43], &twiddlesCoset[0])
+	a[44].Mul(&a[44], &twiddlesCoset[0])
+	a[45].Mul(&a[45], &twiddlesCoset[0])
+	a[46].Mul(&a[46], &twiddlesCoset[0])
+	a[47].Mul(&a[47], &twiddlesCoset[0])
+	a[48].Mul(&a[48], &twiddlesCoset[0])
+	a[49].Mul(&a[49], &twiddlesCoset[0])
+	a[50].Mul(&a[50], &twiddlesCoset[0])
+	a[51].Mul(&a[51], &twiddlesCoset[0])
+	a[52].Mul(&a[52], &twiddlesCoset[0])
+	a[53].Mul(&a[53], &twiddlesCoset[0])
+	a[54].Mul(&a[54], &twiddlesCoset[0])
+	a[55].Mul(&a[55], &twiddlesCoset[0])
+	a[56].Mul(&a[56], &twiddlesCoset[0])
+	a[57].Mul(&a[57], &twiddlesCoset[0])
+	a[58].Mul(&a[58], &twiddlesCoset[0])
+	a[59].Mul(&a[59], &twiddlesCoset[0])
+	a[60].Mul(&a[60], &twiddlesCoset[0])
+	a[61].Mul(&a[61], &twiddlesCoset[0])
+	a[62].Mul(&a[62], &twiddlesCoset[0])
+	a[63].Mul(&a[63], &twiddlesCoset[0])
+	babybear.Butterfly(&a[0], &a[32])
+	babybear.Butterfly(&a[1], &a[33])
+	babybear.Butterfly(&a[2], &a[34])
+	babybear.Butterfly(&a[3], &a[35])
+	babybear.Butterfly(&a[4], &a[36])
+	babybear.Butterfly(&a[5], &a[37])
+	babybear.Butterfly(&a[6], &a[38])
+	babybear.Butterfly(&a[7], &a[39])
+	babybear.Butterfly(&a[8], &a[40])
+	babybear.Butterfly(&a[9], &a[41])
+	babybear.Butterfly(&a[10], &a[42])
+	babybear.Butterfly(&a[11], &a[43])
+	babybear.Butterfly(&a[12], &a[44])
+	babybear.Butterfly(&a[13], &a[45])
+	babybear.Butterfly(&a[14], &a[46])
+	babybear.Butterfly(&a[15], &a[47])
+	babybear.Butterfly(&a[16], &a[48])
+	babybear.Butterfly(&a[17], &a[49])
+	babybear.Butterfly(&a[18], &a[50])
+	babybear.Butterfly(&a[19], &a[51])
+	babybear.Butterfly(&a[20], &a[52])
+	babybear.Butterfly(&a[21], &a[53])
+	babybear.Butterfly(&a[22], &a[54])
+	babybear.Butterfly(&a[23], &a[55])
+	babybear.Butterfly(&a[24], &a[56])
+	babybear.Butterfly(&a[25], &a[57])
+	babybear.Butterfly(&a[26], &a[58])
+	babybear.Butterfly(&a[27], &a[59])
+	babybear.Butterfly(&a[28], &a[60])
+	babybear.Butterfly(&a[29], &a[61])
+	babybear.Butterfly(&a[30], &a[62])
+	babybear.Butterfly(&a[31], &a[63])
+	a[16].Mul(&a[16], &twiddlesCoset[1])
+	a[17].Mul(&a[17], &twiddlesCoset[1])
+	a[18].Mul(&a[18], &twiddlesCoset[1])
+	a[19].Mul(&a[19], &twiddlesCoset[1])
+	a[20].Mul(&a[20], &twiddlesCoset[1])
+	a[21].Mul(&a[21], &twiddlesCoset[1])
+	a[22].Mul(&a[22], &twiddlesCoset[1])
+	a[23].Mul(&a[23], &twiddlesCoset[1])
+	a[24].Mul(&a[24], &twiddlesCoset[1])
+	a[25].Mul(&a[25], &twiddlesCoset[1])
+	a[26].Mul(&a[26], &twiddlesCoset[1])
+	a[27].Mul(&a[27], &twiddlesCoset[1])
+	a[28].Mul(&a[28], &twiddlesCoset[1])
+	a[29].Mul(&a[29], &twiddlesCoset[1])
+	a[30].Mul(&a[30], &twiddlesCoset[1])
+	a[31].Mul(&a[31], &twiddlesCoset[1])
+	a[48].Mul(&a[48], &twiddlesCoset[2])
+	a[49].Mul(&a[49], &twiddlesCoset[2])
+	a[50].Mul(&a[50], &twiddlesCoset[2])
+	a[51].Mul(&a[51], &twiddlesCoset[2])
+	a[52].Mul(&a[52], &twiddlesCoset[2])
+	a[53].Mul(&a[53], &twiddlesCoset[2])
+	a[54].Mul(&a[54], &twiddlesCoset[2])
+	a[55].Mul(&a[55], &twiddlesCoset[2])
+	a[56].Mul(&a[56], &twiddlesCoset[2])
+	a[57].Mul(&a[57], &twiddlesCoset[2])
+	a[58].Mul(&a[58], &twiddlesCoset[2])
+	a[59].Mul(&a[59], &twiddlesCoset[2])
+	a[60].Mul(&a[60], &twiddlesCoset[2])
+	a[61].Mul(&a[61], &twiddlesCoset[2])
+	a[62].Mul(&a[62], &twiddlesCoset[2])
+	a[63].Mul(&a[63], &twiddlesCoset[2])
+	babybear.Butterfly(&a[0], &a[16])
+	babybear.Butterfly(&a[1], &a[17])
+	babybear.Butterfly(&a[2], &a[18])
+	babybear.Butterfly(&a[3], &a[19])
+	babybear.Butterfly(&a[4], &a[20])
+	babybear.Butterfly(&a[5], &a[21])
+	babybear.Butterfly(&a[6], &a[22])
+	babybear.Butterfly(&a[7], &a[23])
+	babybear.Butterfly(&a[8], &a[24])
+	babybear.Butterfly(&a[9], &a[25])
+	babybear.Butterfly(&a[10], &a[26])
+	babybear.Butterfly(&a[11], &a[27])
+	babybear.Butterfly(&a[12], &a[28])
+	babybear.Butterfly(&a[13], &a[29])
+	babybear.Butterfly(&a[14], &a[30])
+	babybear.Butterfly(&a[15], &a[31])
+	babybear.Butterfly(&a[32], &a[48])
+	babybear.Butterfly(&a[33], &a[49])
+	babybear.Butterfly(&a[34], &a[50])
+	babybear.Butterfly(&a[35], &a[51])
+	babybear.Butterfly(&a[36], &a[52])
+	babybear.Butterfly(&a[37], &a[53])
+	babybear.Butterfly(&a[38], &a[54])
+	babybear.Butterfly(&a[39], &a[55])
+	babybear.Butterfly(&a[40], &a[56])
+	babybear.Butterfly(&a[41], &a[57])
+	babybear.Butterfly(&a[42], &a[58])
+	babybear.Butterfly(&a[43], &a[59])
+	babybear.Butterfly(&a[44], &a[60])
+	babybear.Butterfly(&a[45], &a[61])
+	babybear.Butterfly(&a[46], &a[62])
+	babybear.Butterfly(&a[47], &a[63])
+	a[8].Mul(&a[8], &twiddlesCoset[3])
+	a[9].Mul(&a[9], &twiddlesCoset[3])
+	a[10].Mul(&a[10], &twiddlesCoset[3])
+	a[11].Mul(&a[11], &twiddlesCoset[3])
+	a[12].Mul(&a[12], &twiddlesCoset[3])
+	a[13].Mul(&a[13], &twiddlesCoset[3])
+	a[14].Mul(&a[14], &twiddlesCoset[3])
+	a[15].Mul(&a[15], &twiddlesCoset[3])
+	a[24].Mul(&a[24], &twiddlesCoset[4])
+	a[25].Mul(&a[25], &twiddlesCoset[4])
+	a[26].Mul(&a[26], &twiddlesCoset[4])
+	a[27].Mul(&a[27], &twiddlesCoset[4])
+	a[28].Mul(&a[28], &twiddlesCoset[4])
+	a[29].Mul(&a[29], &twiddlesCoset[4])
+	a[30].Mul(&a[30], &twiddlesCoset[4])
+	a[31].Mul(&a[31], &twiddlesCoset[4])
+	a[40].Mul(&a[40], &twiddlesCoset[5])
+	a[41].Mul(&a[41], &twiddlesCoset[5])
+	a[42].Mul(&a[42], &twiddlesCoset[5])
+	a[43].Mul(&a[43], &twiddlesCoset[5])
+	a[44].Mul(&a[44], &twiddlesCoset[5])
+	a[45].Mul(&a[45], &twiddlesCoset[5])
+	a[46].Mul(&a[46], &twiddlesCoset[5])
+	a[47].Mul(&a[47], &twiddlesCoset[5])
+	a[56].Mul(&a[56], &twiddlesCoset[6])
+	a[57].Mul(&a[57], &twiddlesCoset[6])
+	a[58].Mul(&a[58], &twiddlesCoset[6])
+	a[59].Mul(&a[59], &twiddlesCoset[6])
+	a[60].Mul(&a[60], &twiddlesCoset[6])
+	a[61].Mul(&a[61], &twiddlesCoset[6])
+	a[62].Mul(&a[62], &twiddlesCoset[6])
+	a[63].Mul(&a[63], &twiddlesCoset[6])
+	babybear.Butterfly(&a[0], &a[8])
+	babybear.Butterfly(&a[1], &a[9])
+	babybear.Butterfly(&a[2], &a[10])
+	babybear.Butterfly(&a[3], &a[11])
+	babybear.Butterfly(&a[4], &a[12])
+	babybear.Butterfly(&a[5], &a[13])
+	babybear.Butterfly(&a[6], &a[14])
+	babybear.Butterfly(&a[7], &a[15])
+	babybear.Butterfly(&a[16], &a[24])
+	babybear.Butterfly(&a[17], &a[25])
+	babybear.Butterfly(&a[18], &a[26])
+	babybear.Butterfly(&a[19], &a[27])
+	babybear.Butterfly(&a[20], &a[28])
+	babybear.Butterfly(&a[21], &a[29])
+	babybear.Butterfly(&a[22], &a[30])
+	babybear.Butterfly(&a[23], &a[31])
+	babybear.Butterfly(&a[32], &a[40])
+	babybear.Butterfly(&a[33], &a[41])
+	babybear.Butterfly(&a[34], &a[42])
+	babybear.Butterfly(&a[35], &a[43])
+	babybear.Butterfly(&a[36], &a[44])
+	babybear.Butterfly(&a[37], &a[45])
+	babybear.Butterfly(&a[38], &a[46])
+	babybear.Butterfly(&a[39], &a[47])
+	babybear.Butterfly(&a[48], &a[56])
+	babybear.Butterfly(&a[49], &a[57])
+	babybear.Butterfly(&a[50], &a[58])
+	babybear.Butterfly(&a[51], &a[59])
+	babybear.Butterfly(&a[52], &a[60])
+	babybear.Butterfly(&a[53], &a[61])
+	babybear.Butterfly(&a[54], &a[62])
+	babybear.Butterfly(&a[55], &a[63])
+	a[4].Mul(&a[4], &twiddlesCoset[7])
+	a[5].Mul(&a[5], &twiddlesCoset[7])
+	a[6].Mul(&a[6], &twiddlesCoset[7])
+	a[7].Mul(&a[7], &twiddlesCoset[7])
+	a[12].Mul(&a[12], &twiddlesCoset[8])
+	a[13].Mul(&a[13], &twiddlesCoset[8])
+	a[14].Mul(&a[14], &twiddlesCoset[8])
+	a[15].Mul(&a[15], &twiddlesCoset[8])
+	a[20].Mul(&a[20], &twiddlesCoset[9])
+	a[21].Mul(&a[21], &twiddlesCoset[9])
+	a[22].Mul(&a[22], &twiddlesCoset[9])
+	a[23].Mul(&a[23], &twiddlesCoset[9])
+	a[28].Mul(&a[28], &twiddlesCoset[10])
+	a[29].Mul(&a[29], &twiddlesCoset[10])
+	a[30].Mul(&a[30], &twiddlesCoset[10])
+	a[31].Mul(&a[31], &twiddlesCoset[10])
+	a[36].Mul(&a[36], &twiddlesCoset[11])
+	a[37].Mul(&a[37], &twiddlesCoset[11])
+	a[38].Mul(&a[38], &twiddlesCoset[11])
+	a[39].Mul(&a[39], &twiddlesCoset[11])
+	a[44].Mul(&a[44], &twiddlesCoset[12])
+	a[45].Mul(&a[45], &twiddlesCoset[12])
+	a[46].Mul(&a[46], &twiddlesCoset[12])
+	a[47].Mul(&a[47], &twiddlesCoset[12])
+	a[52].Mul(&a[52], &twiddlesCoset[13])
+	a[53].Mul(&a[53], &twiddlesCoset[13])
+	a[54].Mul(&a[54], &twiddlesCoset[13])
+	a[55].Mul(&a[55], &twiddlesCoset[13])
+	a[60].Mul(&a[60], &twiddlesCoset[14])
+	a[61].Mul(&a[61], &twiddlesCoset[14])
+	a[62].Mul(&a[62], &twiddlesCoset[14])
+	a[63].Mul(&a[63], &twiddlesCoset[14])
+	babybear.Butterfly(&a[0], &a[4])
+	babybear.Butterfly(&a[1], &a[5])
+	babybear.Butterfly(&a[2], &a[6])
+	babybear.Butterfly(&a[3], &a[7])
+	babybear.Butterfly(&a[8], &a[12])
+	babybear.Butterfly(&a[9], &a[13])
+	babybear.Butterfly(&a[10], &a[14])
+	babybear.Butterfly(&a[11], &a[15])
+	babybear.Butterfly(&a[16], &a[20])
+	babybear.Butterfly(&a[17], &a[21])
+	babybear.Butterfly(&a[18], &a[22])
+	babybear.Butterfly(&a[19], &a[23])
+	babybear.Butterfly(&a[24], &a[28])
+	babybear.Butterfly(&a[25], &a[29])
+	babybear.Butterfly(&a[26], &a[30])
+	babybear.Butterfly(&a[27], &a[31])
+	babybear.Butterfly(&a[32], &a[36])
+	babybear.Butterfly(&a[33], &a[37])
+	babybear.Butterfly(&a[34], &a[38])
+	babybear.Butterfly(&a[35], &a[39])
+	babybear.Butterfly(&a[40], &a[44])
+	babybear.Butterfly(&a[41], &a[45])
+	babybear.Butterfly(&a[42], &a[46])
+	babybear.Butterfly(&a[43], &a[47])
+	babybear.Butterfly(&a[48], &a[52])
+	babybear.Butterfly(&a[49], &a[53])
+	babybear.Butterfly(&a[50], &a[54])
+	babybear.Butterfly(&a[51], &a[55])
+	babybear.Butterfly(&a[56], &a[60])
+	babybear.Butterfly(&a[57], &a[61])
+	babybear.Butterfly(&a[58], &a[62])
+	babybear.Butterfly(&a[59], &a[63])
+	a[2].Mul(&a[2], &twiddlesCoset[15])
+	a[3].Mul(&a[3], &twiddlesCoset[15])
+	a[6].Mul(&a[6], &twiddlesCoset[16])
+	a[7].Mul(&a[7], &twiddlesCoset[16])
+	a[10].Mul(&a[10], &twiddlesCoset[17])
+	a[11].Mul(&a[11], &twiddlesCoset[17])
+	a[14].Mul(&a[14], &twiddlesCoset[18])
+	a[15].Mul(&a[15], &twiddlesCoset[18])
+	a[18].Mul(&a[18], &twiddlesCoset[19])
+	a[19].Mul(&a[19], &twiddlesCoset[19])
+	a[22].Mul(&a[22], &twiddlesCoset[20])
+	a[23].Mul(&a[23], &twiddlesCoset[20])
+	a[26].Mul(&a[26], &twiddlesCoset[21])
+	a[27].Mul(&a[27], &twiddlesCoset[21])
+	a[30].Mul(&a[30], &twiddlesCoset[22])
+	a[31].Mul(&a[31], &twiddlesCoset[22])
+	a[34].Mul(&a[34], &twiddlesCoset[23])
+	a[35].Mul(&a[35], &twiddlesCoset[23])
+	a[38].Mul(&a[38], &twiddlesCoset[24])
+	a[39].Mul(&a[39], &twiddlesCoset[24])
+	a[42].Mul(&a[42], &twiddlesCoset[25])
+	a[43].Mul(&a[43], &twiddlesCoset[25])
+	a[46].Mul(&a[46], &twiddlesCoset[26])
+	a[47].Mul(&a[47], &twiddlesCoset[26])
+	a[50].Mul(&a[50], &twiddlesCoset[27])
+	a[51].Mul(&a[51], &twiddlesCoset[27])
+	a[54].Mul(&a[54], &twiddlesCoset[28])
+	a[55].Mul(&a[55], &twiddlesCoset[28])
+	a[58].Mul(&a[58], &twiddlesCoset[29])
+	a[59].Mul(&a[59], &twiddlesCoset[29])
+	a[62].Mul(&a[62], &twiddlesCoset[30])
+	a[63].Mul(&a[63], &twiddlesCoset[30])
+	babybear.Butterfly(&a[0], &a[2])
+	babybear.Butterfly(&a[1], &a[3])
+	babybear.Butterfly(&a[4], &a[6])
+	babybear.Butterfly(&a[5], &a[7])
+	babybear.Butterfly(&a[8], &a[10])
+	babybear.Butterfly(&a[9], &a[11])
+	babybear.Butterfly(&a[12], &a[14])
+	babybear.Butterfly(&a[13], &a[15])
+	babybear.Butterfly(&a[16], &a[18])
+	babybear.Butterfly(&a[17], &a[19])
+	babybear.Butterfly(&a[20], &a[22])
+	babybear.Butterfly(&a[21], &a[23])
+	babybear.Butterfly(&a[24], &a[26])
+	babybear.Butterfly(&a[25], &a[27])
+	babybear.Butterfly(&a[28], &a[30])
+	babybear.Butterfly(&a[29], &a[31])
+	babybear.Butterfly(&a[32], &a[34])
+	babybear.Butterfly(&a[33], &a[35])
+	babybear.Butterfly(&a[36], &a[38])
+	babybear.Butterfly(&a[37], &a[39])
+	babybear.Butterfly(&a[40], &a[42])
+	babybear.Butterfly(&a[41], &a[43])
+	babybear.Butterfly(&a[44], &a[46])
+	babybear.Butterfly(&a[45], &a[47])
+	babybear.Butterfly(&a[48], &a[50])
+	babybear.Butterfly(&a[49], &a[51])
+	babybear.Butterfly(&a[52], &a[54])
+	babybear.Butterfly(&a[53], &a[55])
+	babybear.Butterfly(&a[56], &a[58])
+	babybear.Butterfly(&a[57], &a[59])
+	babybear.Butterfly(&a[60], &a[62])
+	babybear.Butterfly(&a[61], &a[63])
+	a[1].Mul(&a[1], &twiddlesCoset[31])
+	a[3].Mul(&a[3], &twiddlesCoset[32])
+	a[5].Mul(&a[5], &twiddlesCoset[33])
+	a[7].Mul(&a[7], &twiddlesCoset[34])
+	a[9].Mul(&a[9], &twiddlesCoset[35])
+	a[11].Mul(&a[11], &twiddlesCoset[36])
+	a[13].Mul(&a[13], &twiddlesCoset[37])
+	a[15].Mul(&a[15], &twiddlesCoset[38])
+	a[17].Mul(&a[17], &twiddlesCoset[39])
+	a[19].Mul(&a[19], &twiddlesCoset[40])
+	a[21].Mul(&a[21], &twiddlesCoset[41])
+	a[23].Mul(&a[23], &twiddlesCoset[42])
+	a[25].Mul(&a[25], &twiddlesCoset[43])
+	a[27].Mul(&a[27], &twiddlesCoset[44])
+	a[29].Mul(&a[29], &twiddlesCoset[45])
+	a[31].Mul(&a[31], &twiddlesCoset[46])
+	a[33].Mul(&a[33], &twiddlesCoset[47])
+	a[35].Mul(&a[35], &twiddlesCoset[48])
+	a[37].Mul(&a[37], &twiddlesCoset[49])
+	a[39].Mul(&a[39], &twiddlesCoset[50])
+	a[41].Mul(&a[41], &twiddlesCoset[51])
+	a[43].Mul(&a[43], &twiddlesCoset[52])
+	a[45].Mul(&a[45], &twiddlesCoset[53])
+	a[47].Mul(&a[47], &twiddlesCoset[54])
+	a[49].Mul(&a[49], &twiddlesCoset[55])
+	a[51].Mul(&a[51], &twiddlesCoset[56])
+	a[53].Mul(&a[53], &twiddlesCoset[57])
+	a[55].Mul(&a[55], &twiddlesCoset[58])
+	a[57].Mul(&a[57], &twiddlesCoset[59])
+	a[59].Mul(&a[59], &twiddlesCoset[60])
+	a[61].Mul(&a[61], &twiddlesCoset[61])
+	a[63].Mul(&a[63], &twiddlesCoset[62])
+	babybear.Butterfly(&a[0], &a[1])
+	babybear.Butterfly(&a[2], &a[3])
+	babybear.Butterfly(&a[4], &a[5])
+	babybear.Butterfly(&a[6], &a[7])
+	babybear.Butterfly(&a[8], &a[9])
+	babybear.Butterfly(&a[10], &a[11])
+	babybear.Butterfly(&a[12], &a[13])
+	babybear.Butterfly(&a[14], &a[15])
+	babybear.Butterfly(&a[16], &a[17])
+	babybear.Butterfly(&a[18], &a[19])
+	babybear.Butterfly(&a[20], &a[21])
+	babybear.Butterfly(&a[22], &a[23])
+	babybear.Butterfly(&a[24], &a[25])
+	babybear.Butterfly(&a[26], &a[27])
+	babybear.Butterfly(&a[28], &a[29])
+	babybear.Butterfly(&a[30], &a[31])
+	babybear.Butterfly(&a[32], &a[33])
+	babybear.Butterfly(&a[34], &a[35])
+	babybear.Butterfly(&a[36], &a[37])
+	babybear.Butterfly(&a[38], &a[39])
+	babybear.Butterfly(&a[40], &a[41])
+	babybear.Butterfly(&a[42], &a[43])
+	babybear.Butterfly(&a[44], &a[45])
+	babybear.Butterfly(&a[46], &a[47])
+	babybear.Butterfly(&a[48], &a[49])
+	babybear.Butterfly(&a[50], &a[51])
+	babybear.Butterfly(&a[52], &a[53])
+	babybear.Butterfly(&a[54], &a[55])
+	babybear.Butterfly(&a[56], &a[57])
+	babybear.Butterfly(&a[58], &a[59])
+	babybear.Butterfly(&a[60], &a[61])
+	babybear.Butterfly(&a[62], &a[63])
+}
+
+// PrecomputeTwiddlesCoset precomputes twiddlesCoset from twiddles and coset table
+// it then return all elements in the correct order for the unrolled FFT.
+func PrecomputeTwiddlesCoset(generator, shifter babybear.Element) []babybear.Element {
+	toReturn := make([]babybear.Element, 63)
+	var r, s babybear.Element
+	e := new(big.Int)
+
+	s = shifter
+	for k := 0; k < 5; k++ {
+		s.Square(&s)
+	}
+	toReturn[0] = s
+	s = shifter
+	for k := 0; k < 4; k++ {
+		s.Square(&s)
+	}
+	toReturn[1] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<4*1)))
+	toReturn[2].Mul(&r, &s)
+	s = shifter
+	for k := 0; k < 3; k++ {
+		s.Square(&s)
+	}
+	toReturn[3] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<3*2)))
+	toReturn[4].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<3*1)))
+	toReturn[5].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<3*3)))
+	toReturn[6].Mul(&r, &s)
+	s = shifter
+	for k := 0; k < 2; k++ {
+		s.Square(&s)
+	}
+	toReturn[7] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<2*4)))
+	toReturn[8].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*2)))
+	toReturn[9].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*6)))
+	toReturn[10].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*1)))
+	toReturn[11].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*5)))
+	toReturn[12].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*3)))
+	toReturn[13].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*7)))
+	toReturn[14].Mul(&r, &s)
+	s = shifter
+	for k := 0; k < 1; k++ {
+		s.Square(&s)
+	}
+	toReturn[15] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<1*8)))
+	toReturn[16].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*4)))
+	toReturn[17].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*12)))
+	toReturn[18].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*2)))
+	toReturn[19].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*10)))
+	toReturn[20].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*6)))
+	toReturn[21].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*14)))
+	toReturn[22].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*1)))
+	toReturn[23].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*9)))
+	toReturn[24].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*5)))
+	toReturn[25].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*13)))
+	toReturn[26].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*3)))
+	toReturn[27].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*11)))
+	toReturn[28].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*7)))
+	toReturn[29].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*15)))
+	toReturn[30].Mul(&r, &s)
+	s = shifter
+	for k := 0; k < 0; k++ {
+		s.Square(&s)
+	}
+	toReturn[31] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<0*16)))
+	toReturn[32].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*8)))
+	toReturn[33].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*24)))
+	toReturn[34].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*4)))
+	toReturn[35].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*20)))
+	toReturn[36].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*12)))
+	toReturn[37].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*28)))
+	toReturn[38].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*2)))
+	toReturn[39].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*18)))
+	toReturn[40].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*10)))
+	toReturn[41].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*26)))
+	toReturn[42].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*6)))
+	toReturn[43].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*22)))
+	toReturn[44].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*14)))
+	toReturn[45].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*30)))
+	toReturn[46].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*1)))
+	toReturn[47].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*17)))
+	toReturn[48].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*9)))
+	toReturn[49].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*25)))
+	toReturn[50].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*5)))
+	toReturn[51].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*21)))
+	toReturn[52].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*13)))
+	toReturn[53].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*29)))
+	toReturn[54].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*3)))
+	toReturn[55].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*19)))
+	toReturn[56].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*11)))
+	toReturn[57].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*27)))
+	toReturn[58].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*7)))
+	toReturn[59].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*23)))
+	toReturn[60].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*15)))
+	toReturn[61].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*31)))
+	toReturn[62].Mul(&r, &s)
+	return toReturn
+}
diff --git a/field/babybear/sis/sis_test.go b/field/babybear/sis/sis_test.go
new file mode 100644
index 0000000000..5fb044de67
--- /dev/null
+++ b/field/babybear/sis/sis_test.go
@@ -0,0 +1,488 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package sis
+
+import (
+	"bytes"
+	"crypto/rand"
+	"encoding/binary"
+	"encoding/json"
+	"fmt"
+	"io"
+	"math/big"
+	"math/bits"
+	"os"
+	"testing"
+	"time"
+
+	"github.com/bits-and-blooms/bitset"
+	"github.com/consensys/gnark-crypto/field/babybear"
+	"github.com/consensys/gnark-crypto/field/babybear/fft"
+	"github.com/stretchr/testify/require"
+)
+
+type sisParams struct {
+	logTwoBound, logTwoDegree int
+}
+
+var params128Bits []sisParams = []sisParams{
+	{logTwoBound: 2, logTwoDegree: 3},
+	{logTwoBound: 4, logTwoDegree: 4},
+	{logTwoBound: 6, logTwoDegree: 5},
+	{logTwoBound: 8, logTwoDegree: 6},
+	{logTwoBound: 10, logTwoDegree: 6},
+	{logTwoBound: 16, logTwoDegree: 7},
+	{logTwoBound: 32, logTwoDegree: 8},
+}
+
+type TestCases struct {
+	Inputs  []babybear.Element `json:"inputs"`
+	Entries []struct {
+		Params struct {
+			Seed                int64 `json:"seed"`
+			LogTwoDegree        int   `json:"logTwoDegree"`
+			LogTwoBound         int   `json:"logTwoBound"`
+			MaxNbElementsToHash int   `json:"maxNbElementsToHash"`
+		} `json:"params"`
+		Expected []babybear.Element `json:"expected"`
+	} `json:"entries"`
+}
+
+func TestReference(t *testing.T) {
+	if bits.UintSize == 32 {
+		t.Skip("skipping this test in 32bit.")
+	}
+	assert := require.New(t)
+
+	// read the test case file
+	var testCases TestCases
+	data, err := os.ReadFile("test_cases.json")
+	assert.NoError(err, "reading test cases failed")
+	err = json.Unmarshal(data, &testCases)
+	assert.NoError(err, "reading test cases failed")
+
+	inputs := testCases.Inputs
+
+	for testCaseID, testCase := range testCases.Entries {
+
+		// create the SIS instance
+		sis, err := NewRSis(testCase.Params.Seed, testCase.Params.LogTwoDegree, testCase.Params.LogTwoBound, testCase.Params.MaxNbElementsToHash)
+		assert.NoError(err)
+
+		// key generation same than in sage
+		makeKeyDeterministic(t, sis, testCase.Params.Seed)
+
+		sis.Reset()
+
+		// hash test case entry input and compare with expected (computed by sage)
+		goHash, err := sis.Hash(inputs)
+		assert.NoError(err)
+
+		assert.EqualValues(
+			testCase.Expected, goHash,
+			"mismatch between reference test and computed value (testcase %v)",
+			testCaseID,
+		)
+
+	}
+
+}
+
+func TestLimbDecomposeBytesMiddleBound(t *testing.T) {
+
+	var montConstant babybear.Element
+	var bMontConstant big.Int
+	bMontConstant.SetUint64(1)
+	bMontConstant.Lsh(&bMontConstant, babybear.Bytes*8)
+	montConstant.SetBigInt(&bMontConstant)
+
+	nbElmts := 10
+	a := make([]babybear.Element, nbElmts)
+	for i := 0; i < nbElmts; i++ {
+		a[i].SetUint64(33)
+	}
+	var buf bytes.Buffer
+	for i := 0; i < nbElmts; i++ {
+		buf.Write(a[i].Marshal())
+	}
+
+	logTwoBound := 8
+
+	for cc := 0; cc < 3; cc++ {
+		m := make(babybear.Vector, nbElmts*babybear.Bytes*8/logTwoBound)
+		limbDecomposeBytesMiddleBound(buf.Bytes(), m, logTwoBound, 4, nil)
+
+		for i := 0; i < len(m); i++ {
+			m[i].Mul(&m[i], &montConstant)
+		}
+
+		var x babybear.Element
+		x.SetUint64(1 << logTwoBound)
+
+		coeffsPerFieldsElmt := babybear.Bytes * 8 / logTwoBound
+		for i := 0; i < nbElmts; i++ {
+			r := eval(m[i*coeffsPerFieldsElmt:(i+1)*coeffsPerFieldsElmt], x)
+			if !r.Equal(&a[i]) {
+				t.Fatal("limbDecomposeBytes failed")
+			}
+		}
+		logTwoBound *= 2
+	}
+
+}
+
+func TestLimbDecomposeBytesSmallBound(t *testing.T) {
+
+	var montConstant babybear.Element
+	var bMontConstant big.Int
+	bMontConstant.SetUint64(1)
+	bMontConstant.Lsh(&bMontConstant, babybear.Bytes*8)
+	montConstant.SetBigInt(&bMontConstant)
+
+	nbElmts := 10
+	a := make([]babybear.Element, nbElmts)
+	for i := 0; i < nbElmts; i++ {
+		a[i].SetRandom()
+	}
+	var buf bytes.Buffer
+	for i := 0; i < nbElmts; i++ {
+		buf.Write(a[i].Marshal())
+	}
+
+	logTwoBound := 2
+
+	for cc := 0; cc < 3; cc++ {
+
+		m := make(babybear.Vector, nbElmts*babybear.Bytes*8/logTwoBound)
+		m2 := make(babybear.Vector, nbElmts*babybear.Bytes*8/logTwoBound)
+
+		// the limbs are set as is, they are NOT converted in Montgomery form
+		limbDecomposeBytes(buf.Bytes(), m, logTwoBound, 4, nil)
+		limbDecomposeBytesSmallBound(buf.Bytes(), m2, logTwoBound, 4, nil)
+
+		for i := 0; i < len(m); i++ {
+			m[i].Mul(&m[i], &montConstant)
+			m2[i].Mul(&m2[i], &montConstant)
+		}
+		var x babybear.Element
+		x.SetUint64(1 << logTwoBound)
+
+		coeffsPerFieldsElmt := babybear.Bytes * 8 / logTwoBound
+		for i := 0; i < nbElmts; i++ {
+			r := eval(m[i*coeffsPerFieldsElmt:(i+1)*coeffsPerFieldsElmt], x)
+			if !r.Equal(&a[i]) {
+				t.Fatal("limbDecomposeBytes failed")
+			}
+			r = eval(m2[i*coeffsPerFieldsElmt:(i+1)*coeffsPerFieldsElmt], x)
+			if !r.Equal(&a[i]) {
+				t.Fatal("limbDecomposeBytesSmallBound failed")
+			}
+		}
+		logTwoBound *= 2
+	}
+
+}
+
+func eval(p []babybear.Element, x babybear.Element) babybear.Element {
+	var res babybear.Element
+	for i := len(p) - 1; i >= 0; i-- {
+		res.Mul(&res, &x).Add(&res, &p[i])
+	}
+	return res
+}
+
+func TestMulMod(t *testing.T) {
+
+	size := 4
+
+	p := make([]babybear.Element, size)
+	q := make([]babybear.Element, size)
+	pCopy := make([]babybear.Element, size)
+	qCopy := make([]babybear.Element, size)
+	for i := 0; i < size; i++ {
+		p[i].SetRandom()
+		pCopy[i].Set(&p[i])
+		q[i].SetRandom()
+		qCopy[i].Set(&q[i])
+	}
+
+	// creation of the domain
+	shift, err := babybear.Generator(uint64(2 * size))
+	if err != nil {
+		t.Fatal(err)
+	}
+	var g babybear.Element
+	g.Square(&shift)
+	domain := fft.NewDomain(uint64(size), fft.WithShift(shift))
+
+	// mul mod
+	domain.FFT(p, fft.DIF, fft.OnCoset())
+	domain.FFT(q, fft.DIF, fft.OnCoset())
+	r := mulMod(p, q)
+	domain.FFTInverse(r, fft.DIT, fft.OnCoset())
+
+	// manually check the product on the zeroes of X^4+1
+	for i := 0; i < 4; i++ {
+		u := eval(pCopy, shift)
+		v := eval(qCopy, shift)
+		w := eval(r, shift)
+		u.Mul(&u, &v)
+		if !w.Equal(&u) {
+			t.Fatal("mul mol failed")
+		}
+		shift.Mul(&shift, &g)
+	}
+
+}
+
+func makeKeyDeterministic(t *testing.T, sis *RSis, _seed int64) {
+	t.Helper()
+	// generate the key deterministically, the same way
+	// we do in sage to generate the test vectors.
+
+	polyRand := func(seed babybear.Element, deg int) []babybear.Element {
+		res := make([]babybear.Element, deg)
+		for i := 0; i < deg; i++ {
+			res[i].Square(&seed)
+			seed.Set(&res[i])
+		}
+		return res
+	}
+
+	var seed, one babybear.Element
+	one.SetOne()
+	seed.SetInt64(_seed)
+	for i := 0; i < len(sis.A); i++ {
+		sis.A[i] = polyRand(seed, sis.Degree)
+		copy(sis.Ag[i], sis.A[i])
+		sis.Domain.FFT(sis.Ag[i], fft.DIF, fft.OnCoset())
+		seed.Add(&seed, &one)
+	}
+}
+
+const (
+	LATENCY_MUL_FIELD_NS int = 18
+	LATENCY_ADD_FIELD_NS int = 4
+)
+
+// Estimate the theoretical performances that are achievable using ring-SIS
+// operations. The time is obtained by counting the number of additions and
+// multiplications occurring in the computation. This does not account for the
+// possibilities to use SIMD instructions or for cache-locality issues. Thus, it
+// does not represents a maximum even though it returns a good idea of what is
+// achievable . This returns performances in term of ns/field. This also does not
+// account for the time taken for "limb-splitting" the input.
+func estimateSisTheory(p sisParams) float64 {
+
+	// Since the FFT occurs over a coset, we need to multiply all the coefficients
+	// of the input by some coset factors (for an entire polynomial)
+	timeCosetShift := (1 << p.logTwoDegree) * LATENCY_MUL_FIELD_NS
+
+	// The two additions are from the butterfly, and the multiplication represents
+	// the one by the twiddle. (for an entire polynomial)
+	timeFFT := (1 << p.logTwoDegree) * p.logTwoDegree * (2*LATENCY_ADD_FIELD_NS + LATENCY_MUL_FIELD_NS)
+
+	// Time taken to multiply by the key and accumulate (for an entire polynomial)
+	timeMulAddKey := (1 << p.logTwoDegree) * (LATENCY_MUL_FIELD_NS + LATENCY_ADD_FIELD_NS)
+
+	// Total computation time for an entire polynomial
+	totalTimePoly := timeCosetShift + timeFFT + timeMulAddKey
+
+	// Convert this into a time per input field
+	r := totalTimePoly * babybear.Bits / p.logTwoBound / (1 << p.logTwoDegree)
+	return float64(r)
+}
+
+func BenchmarkDecomposition(b *testing.B) {
+
+	nbElmts := 1000
+	a := make([]babybear.Element, nbElmts)
+	for i := 0; i < nbElmts; i++ {
+		a[i].SetRandom()
+	}
+	var buf bytes.Buffer
+	for i := 0; i < nbElmts; i++ {
+		buf.Write(a[i].Marshal())
+	}
+	logTwoBound := 4
+	m := make(babybear.Vector, nbElmts*babybear.Bytes*8/logTwoBound)
+
+	b.Run(fmt.Sprintf("limbDecomposeBytes logTwoBound=%d", logTwoBound), func(b *testing.B) {
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			limbDecomposeBytes(buf.Bytes(), m, logTwoBound, 4, nil)
+		}
+	})
+
+	b.Run(fmt.Sprintf("limbDecomposeByteSmallBound logTwoBound=%d", logTwoBound), func(b *testing.B) {
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			limbDecomposeBytesSmallBound(buf.Bytes(), m, logTwoBound, 4, nil)
+		}
+	})
+
+	logTwoBound = 16
+	b.Run(fmt.Sprintf("limbDecomposeBytes logTwoBound=%d", logTwoBound), func(b *testing.B) {
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			limbDecomposeBytes(buf.Bytes(), m, logTwoBound, 4, nil)
+		}
+	})
+
+	b.Run(fmt.Sprintf("limbDecomposeByteSmallBound logTwoBound=%d", logTwoBound), func(b *testing.B) {
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			limbDecomposeBytesMiddleBound(buf.Bytes(), m, logTwoBound, 4, nil)
+		}
+	})
+
+}
+
+func BenchmarkSIS(b *testing.B) {
+
+	// max nb field elements to hash
+	const nbInputs = 1 << 16
+
+	// Assign the input with random bytes. In practice, theses bytes encodes
+	// a string of field element. It would be more meaningful to take a slice
+	// of field element directly because otherwise the conversion time is not
+	// accounted for in the benchmark.
+	inputs := make(babybear.Vector, nbInputs)
+	for i := 0; i < len(inputs); i++ {
+		inputs[i].SetRandom()
+	}
+
+	for _, param := range params128Bits {
+		for n := 1 << 10; n <= nbInputs; n <<= 1 {
+			in := inputs[:n]
+			benchmarkSIS(b, in, false, param.logTwoBound, param.logTwoDegree, estimateSisTheory(param))
+		}
+
+	}
+}
+
+func benchmarkSIS(b *testing.B, input []babybear.Element, sparse bool, logTwoBound, logTwoDegree int, theoretical float64) {
+	b.Helper()
+
+	n := len(input)
+
+	benchName := "ring-sis/"
+	if sparse {
+		benchName += "sparse/"
+	}
+	benchName += fmt.Sprintf("inputs=%v/log2-bound=%v/log2-degree=%v", n, logTwoBound, logTwoDegree)
+
+	b.Run(benchName, func(b *testing.B) {
+		instance, err := NewRSis(0, logTwoDegree, logTwoBound, n)
+		if err != nil {
+			b.Fatal(err)
+		}
+
+		// We introduce a custom metric which is the time per field element
+		// Since the benchmark object allows to report extra meta but does
+		// not allow accessing them. We measure the time ourself.
+
+		startTime := time.Now()
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			_, err = instance.Hash(input)
+			if err != nil {
+				b.Fatal(err)
+			}
+		}
+		b.StopTimer()
+
+		totalDuration := time.Since(startTime)
+		nsPerField := totalDuration.Nanoseconds() / int64(b.N) / int64(n)
+
+		b.ReportMetric(float64(nsPerField), "ns/field")
+
+		b.ReportMetric(theoretical, "ns/field(theory)")
+
+	})
+}
+
+// Hash interprets the input vector as a sequence of coefficients of size r.LogTwoBound bits long,
+// and return the hash of the polynomial corresponding to the sum sum_i A[i]*m Mod X^{d}+1
+//
+// It is equivalent to calling r.Write(element.Marshal()); outBytes = r.Sum(nil);
+// ! note @gbotrel: this is a place holder, may not make sense
+func (r *RSis) Hash(v []babybear.Element) ([]babybear.Element, error) {
+	if len(v) > r.maxNbElementsToHash {
+		return nil, fmt.Errorf("can't hash more than %d elements with params provided in constructor", r.maxNbElementsToHash)
+	}
+
+	r.Reset()
+	for _, e := range v {
+		r.Write(e.Marshal())
+	}
+	sum := r.Sum(nil)
+	var rlen [4]byte
+	binary.BigEndian.PutUint32(rlen[:], uint32(len(sum)/babybear.Bytes))
+	reader := io.MultiReader(bytes.NewReader(rlen[:]), bytes.NewReader(sum))
+	var result babybear.Vector
+	_, err := result.ReadFrom(reader)
+	if err != nil {
+		return nil, err
+	}
+	return result, nil
+}
+
+func TestLimbDecompositionFastPath(t *testing.T) {
+	assert := require.New(t)
+
+	for size := babybear.Bytes; size < 5*babybear.Bytes; size += babybear.Bytes {
+		// Test the fast path of limbDecomposeBytes8_64
+		buf := make([]byte, size)
+		m := make([]babybear.Element, size)
+		mValues := bitset.New(uint(size))
+		n := make([]babybear.Element, size)
+		nValues := bitset.New(uint(size))
+
+		// Generate a random buffer
+		_, err := rand.Read(buf)
+		assert.NoError(err)
+
+		limbDecomposeBytes8_64(buf, m, mValues)
+		limbDecomposeBytes(buf, n, 8, 64, nValues)
+
+		for i := 0; i < size; i++ {
+			assert.Equal(mValues.Test(uint(i)), nValues.Test(uint(i)))
+			assert.True(m[i].Equal(&n[i]))
+		}
+	}
+
+}
+
+func TestUnrolledFFT(t *testing.T) {
+
+	var shift babybear.Element
+	shift.SetRandom()
+
+	const size = 64
+	assert := require.New(t)
+	domain := fft.NewDomain(size, fft.WithShift(shift))
+
+	k1 := make([]babybear.Element, size)
+	for i := 0; i < size; i++ {
+		k1[i].SetRandom()
+	}
+	k2 := make([]babybear.Element, size)
+	copy(k2, k1)
+
+	// default FFT
+	domain.FFT(k1, fft.DIF, fft.OnCoset(), fft.WithNbTasks(1))
+
+	// unrolled FFT
+	twiddlesCoset := PrecomputeTwiddlesCoset(domain.Generator, domain.FrMultiplicativeGen)
+	FFT64(k2, twiddlesCoset)
+
+	// compare results
+	for i := 0; i < size; i++ {
+		// fmt.Printf("i = %d, k1 = %v, k2 = %v\n", i, k1[i].String(), k2[i].String())
+		assert.True(k1[i].Equal(&k2[i]), "i = %d", i)
+	}
+}
diff --git a/field/babybear/sis/test_cases.json b/field/babybear/sis/test_cases.json
new file mode 100644
index 0000000000..4038261424
--- /dev/null
+++ b/field/babybear/sis/test_cases.json
@@ -0,0 +1,86 @@
+{
+    "inputs": [
+        "5", 
+        "25", 
+        "125", 
+        "625", 
+        "3125", 
+        "15625", 
+        "78125", 
+        "390625", 
+        "1953125", 
+        "9765625"
+    ], 
+    "entries": [
+        {
+            "expected": [
+                "1581938715", 
+                "867003107", 
+                "1424242116", 
+                "1719513893"
+            ], 
+            "params": {
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 2
+            }
+        }, 
+        {
+            "expected": [
+                "116436545", 
+                "1673152565", 
+                "822138567", 
+                "831029584"
+            ], 
+            "params": {
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 4
+            }
+        }, 
+        {
+            "expected": [
+                "321194463", 
+                "1664226729", 
+                "942419694", 
+                "1859696009"
+            ], 
+            "params": {
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 8
+            }
+        }, 
+        {
+            "expected": [
+                "795703659", 
+                "510103776", 
+                "441667609", 
+                "1728365390"
+            ], 
+            "params": {
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 16
+            }
+        }, 
+        {
+            "expected": [
+                "1544968630", 
+                "1904160646", 
+                "1787655994", 
+                "1155357728"
+            ], 
+            "params": {
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 32
+            }
+        }
+    ]
+}
\ No newline at end of file
diff --git a/field/generator/generator.go b/field/generator/generator.go
index 29943ef6e4..d6a5cd277f 100644
--- a/field/generator/generator.go
+++ b/field/generator/generator.go
@@ -50,6 +50,13 @@ func GenerateFF(F *config.Field, outputDir string, options ...Option) error {
 		}
 	}
 
+	// generate SIS
+	if cfg.HasSIS() {
+		if err := generateSIS(F, outputDir); err != nil {
+			return err
+		}
+	}
+
 	return runFormatters(outputDir)
 }
 
diff --git a/field/generator/generator_fft.go b/field/generator/generator_fft.go
index 72ef9aa42d..4a6ffa26a7 100644
--- a/field/generator/generator_fft.go
+++ b/field/generator/generator_fft.go
@@ -49,20 +49,7 @@ func generateFFT(F *config.Field, fft *config.FFT, outputDir string) error {
 	}
 
 	funcs := make(map[string]interface{})
-	funcs["bitReverse"] = func(n, i int64) uint64 {
-		nn := uint64(64 - bits.TrailingZeros64(uint64(n)))
-		r := make([]uint64, n)
-		for i := 0; i < len(r); i++ {
-			r[i] = uint64(i)
-		}
-		for i := 0; i < len(r); i++ {
-			irev := bits.Reverse64(r[i]) >> nn
-			if irev > uint64(i) {
-				r[i], r[irev] = r[irev], r[i]
-			}
-		}
-		return r[i]
-	}
+	funcs["bitReverse"] = bitReverse
 	funcs["reverseBits"] = func(x, n any) uint64 {
 		return bits.Reverse64(anyToUint64(x)) >> anyToUint64(n)
 	}
@@ -229,3 +216,18 @@ func init() {
 	))
 
 }
+
+func bitReverse(n, i int64) uint64 {
+	nn := uint64(64 - bits.TrailingZeros64(uint64(n)))
+	r := make([]uint64, n)
+	for i := 0; i < len(r); i++ {
+		r[i] = uint64(i)
+	}
+	for i := 0; i < len(r); i++ {
+		irev := bits.Reverse64(r[i]) >> nn
+		if irev > uint64(i) {
+			r[i], r[irev] = r[irev], r[i]
+		}
+	}
+	return r[i]
+}
diff --git a/field/generator/generator_sis.go b/field/generator/generator_sis.go
new file mode 100644
index 0000000000..f8f456b29c
--- /dev/null
+++ b/field/generator/generator_sis.go
@@ -0,0 +1,53 @@
+package generator
+
+import (
+	"path/filepath"
+
+	"github.com/consensys/bavard"
+	"github.com/consensys/gnark-crypto/field/generator/config"
+)
+
+func generateSIS(F *config.Field, outputDir string) error {
+
+	fieldImportPath, err := getImportPath(outputDir)
+	if err != nil {
+		return err
+	}
+
+	outputDir = filepath.Join(outputDir, "sis")
+
+	entries := []bavard.Entry{
+		{File: filepath.Join(outputDir, "sis_fft.go"), Templates: []string{"fft.go.tmpl"}},
+		{File: filepath.Join(outputDir, "sis.go"), Templates: []string{"sis.go.tmpl"}},
+		{File: filepath.Join(outputDir, "sis_test.go"), Templates: []string{"sis.test.go.tmpl"}},
+	}
+
+	funcs := make(map[string]interface{})
+	funcs["bitReverse"] = bitReverse
+
+	bavardOpts := []func(*bavard.Bavard) error{bavard.Funcs(funcs)}
+
+	type sisTemplateData struct {
+		FF               string
+		FieldPackagePath string
+	}
+
+	data := &sisTemplateData{
+		FF:               F.PackageName,
+		FieldPackagePath: fieldImportPath,
+	}
+
+	bgen := bavard.NewBatchGenerator("Consensys Software Inc.", 2020, "consensys/gnark-crypto")
+
+	sisTemplatesRootDir, err := findTemplatesRootDir()
+	if err != nil {
+		return err
+	}
+	sisTemplatesRootDir = filepath.Join(sisTemplatesRootDir, "sis")
+
+	if err := bgen.GenerateWithOptions(data, "sis", sisTemplatesRootDir, bavardOpts, entries...); err != nil {
+		return err
+	}
+
+	return runFormatters(outputDir)
+}
diff --git a/field/generator/internal/templates/sis/fft.go.tmpl b/field/generator/internal/templates/sis/fft.go.tmpl
new file mode 100644
index 0000000000..777eb8610a
--- /dev/null
+++ b/field/generator/internal/templates/sis/fft.go.tmpl
@@ -0,0 +1,82 @@
+import (
+	"{{ .FieldPackagePath }}"
+	"math/big"
+)
+
+// FFT64 is generated by gnark-crypto and contains the unrolled code for FFT (DIF) on 64 elements
+// equivalent code: r.Domain.FFT(k, fft.DIF, fft.OnCoset(), fft.WithNbTasks(1))
+// twiddlesCoset must be pre-computed from twiddles and coset table, see PrecomputeTwiddlesCoset
+func FFT64(a []{{ .FF }}.Element,  twiddlesCoset []{{ .FF }}.Element) {
+
+	{{- /* notes: 
+		this function can be updated with larger n
+		nbSteps must be updated too such as 1 << nbSteps == n
+		butterflies and multiplication are separated for size n = 8, must check perf for larger n
+	 */}}
+	 {{$tIndex := 0}}
+	{{ $n := 64}}
+	{{ $m := div $n 2}}
+	{{ $split := 1}}
+	{{ $split = div $split 1}}
+	{{- range $step := reverse (iterate 0 6)}} 
+
+		{{- $offset := 0}}
+		{{- range $s := iterate 0 $split}}
+			{{- range $i := iterate 0 $m}}
+				{{- $j := add $i $offset}}
+				{{- $k := add $j $m}}
+				a[{{$k}}].Mul(&a[{{$k}}], &twiddlesCoset[{{$tIndex}}])
+			{{- end}}
+			{{- $offset = add $offset $n}}
+			{{- $tIndex = add $tIndex 1}}
+		{{- end}}
+
+		{{- $offset := 0}}
+		{{- range $s := iterate 0 $split}}
+			{{- range $i := iterate 0 $m}}
+				{{- $j := add $i $offset}}
+				{{- $k := add $j $m}}
+				{{ $.FF }}.Butterfly(&a[{{$j}}], &a[{{$k}}])
+			{{- end}}
+			{{- $offset = add $offset $n}}
+		{{- end}}
+		
+		{{- $n = div $n 2}}
+		{{- $m = div $n 2}}
+		{{- $split = mul $split 2}}
+	{{- end}}
+}
+
+// PrecomputeTwiddlesCoset precomputes twiddlesCoset from twiddles and coset table
+// it then return all elements in the correct order for the unrolled FFT.
+func PrecomputeTwiddlesCoset(generator, shifter {{ .FF }}.Element) []{{ .FF }}.Element {
+	toReturn := make([]{{ .FF }}.Element,  63)
+	var r, s {{ .FF }}.Element
+	e := new(big.Int)
+	{{ $n := 64}}
+	{{ $m := div $n 2}}
+	{{ $split := 1}}
+	{{ $split = div $split 1}}
+	{{ $j := 0}}
+	{{- range $step := reverse (iterate 0 6)}} 
+		s = shifter
+		for k:=0; k <{{$step}};k++ {
+			s.Square(&s)
+		}
+		
+		{{- $offset := 0}}
+		{{- range $s := iterate 0 $split}}
+			{{- $exp := bitReverse $split $s}}
+			{{- if eq $exp 0}}
+				toReturn[{{$j}}] = s
+			{{- else}}
+				r.Exp(generator, e.SetUint64(uint64(1<<{{$step}} * {{$exp}})))
+				toReturn[{{$j}}].Mul(&r, &s)
+			{{- end}}
+			{{- $j = add $j 1}}
+		{{- end}}
+
+		{{- $split = mul $split 2}}
+	{{- end}}
+	return toReturn
+}
\ No newline at end of file
diff --git a/field/generator/internal/templates/sis/sis.go.tmpl b/field/generator/internal/templates/sis/sis.go.tmpl
new file mode 100644
index 0000000000..8f40014ff6
--- /dev/null
+++ b/field/generator/internal/templates/sis/sis.go.tmpl
@@ -0,0 +1,472 @@
+import (
+	"bytes"
+	"encoding/binary"
+	"errors"
+	"hash"
+	"math/bits"
+
+	"github.com/bits-and-blooms/bitset"
+	"{{ .FieldPackagePath }}"
+	"{{ .FieldPackagePath }}/fft"
+	"github.com/consensys/gnark-crypto/internal/parallel"
+	"golang.org/x/crypto/blake2b"
+)
+
+var (
+	ErrNotAPowerOfTwo = errors.New("d must be a power of 2")
+)
+
+// Ring-SIS instance
+type RSis struct {
+
+	// buffer storing the data to hash
+	buffer bytes.Buffer
+
+	// Vectors in ℤ_{p}/Xⁿ+1
+	// A[i] is the i-th polynomial.
+	// Ag the evaluation form of the polynomials in A on the coset √(g) * <g>
+	A  [][]{{ .FF }}.Element
+	Ag [][]{{ .FF }}.Element
+
+	// LogTwoBound (Infinity norm) of the vector to hash. It means that each component in m
+	// is < 2^B, where m is the vector to hash (the hash being A*m).
+	// cf https://hackmd.io/7OODKWQZRRW9RxM5BaXtIw , B >= 3.
+	LogTwoBound int
+
+	// domain for the polynomial multiplication
+	Domain        *fft.Domain
+	twiddleCosets []{{ .FF }}.Element // see FFT64 and precomputeTwiddlesCoset
+
+	// d, the degree of X^{d}+1
+	Degree int
+
+	// in bytes, represents the maximum number of bytes the .Write(...) will handle;
+	// ( maximum number of bytes to sum )
+	capacity            int
+	maxNbElementsToHash int
+
+	// allocate memory once per instance (used in Sum())
+	bufM, bufRes {{ .FF }}.Vector
+	bufMValues   *bitset.BitSet
+}
+
+// NewRSis creates an instance of RSis.
+// seed: seed for the randomness for generating A.
+// logTwoDegree: if d := logTwoDegree, the ring will be ℤ_{p}[X]/Xᵈ-1, where X^{2ᵈ} is the 2ᵈ⁺¹-th cyclotomic polynomial
+// logTwoBound: the bound of the vector to hash (using the infinity norm).
+// maxNbElementsToHash: maximum number of field elements the instance handles
+// used to derived n, the number of polynomials in A, and max size of instance's internal buffer.
+func NewRSis(seed int64, logTwoDegree, logTwoBound, maxNbElementsToHash int) (*RSis, error) {
+
+	if logTwoBound > 64 {
+		return nil, errors.New("logTwoBound too large")
+	}
+	if bits.UintSize == 32 {
+		return nil, errors.New("unsupported architecture; need 64bit target")
+	}
+
+	degree := 1 << logTwoDegree
+	capacity := maxNbElementsToHash * {{ .FF }}.Bytes
+
+	// n: number of polynomials in A
+	// len(m) == degree * n
+	// with each element in m being logTwoBounds bits from the instance buffer.
+	// that is, to fill m, we need [degree * n * logTwoBound] bits of data
+	// capacity == [degree * n * logTwoBound] / 8
+	// n == (capacity*8)/(degree*logTwoBound)
+
+	// First n <- #limbs to represent a single field element
+	n := ({{ .FF }}.Bytes * 8) / logTwoBound
+	if n*logTwoBound < {{ .FF }}.Bytes*8 {
+		n++
+	}
+
+	// Then multiply by the number of field elements
+	n *= maxNbElementsToHash
+
+	// And divide (+ ceil) to get the number of polynomials
+	if n%degree == 0 {
+		n /= degree
+	} else {
+		n /= degree // number of polynomials
+		n++
+	}
+
+	// domains (shift is √{gen} )
+	shift, err := {{ .FF }}.Generator(uint64(2*degree))
+	if err!= nil {
+		return nil, err
+	}
+
+	r := &RSis{
+		LogTwoBound:         logTwoBound,
+		capacity:            capacity,
+		Degree:              degree,
+		Domain:              fft.NewDomain(uint64(degree), fft.WithShift(shift)),
+		A:                   make([][]{{ .FF }}.Element, n),
+		Ag:                  make([][]{{ .FF }}.Element, n),
+		bufM:                make({{ .FF }}.Vector, degree*n),
+		bufRes:              make({{ .FF }}.Vector, degree),
+		bufMValues:          bitset.New(uint(n)),
+		maxNbElementsToHash: maxNbElementsToHash,
+	}
+	if r.LogTwoBound == 8 && r.Degree == 64 {
+		// TODO @gbotrel fixme, that's dirty.
+		r.twiddleCosets = PrecomputeTwiddlesCoset(r.Domain.Generator, r.Domain.FrMultiplicativeGen)
+	}
+
+	// filling A
+	a := make([]{{ .FF }}.Element, n*r.Degree)
+	ag := make([]{{ .FF }}.Element, n*r.Degree)
+
+	parallel.Execute(n, func(start, end int) {
+		var buf bytes.Buffer
+		for i := start; i < end; i++ {
+			rstart, rend := i*r.Degree, (i+1)*r.Degree
+			r.A[i] = a[rstart:rend:rend]
+			r.Ag[i] = ag[rstart:rend:rend]
+			for j := 0; j < r.Degree; j++ {
+				r.A[i][j] = genRandom(seed, int64(i), int64(j), &buf)
+			}
+
+			// fill Ag the evaluation form of the polynomials in A on the coset √(g) * <g>
+			copy(r.Ag[i], r.A[i])
+			r.Domain.FFT(r.Ag[i], fft.DIF, fft.OnCoset())
+		}
+	})
+
+	return r, nil
+}
+
+func (r *RSis) Write(p []byte) (n int, err error) {
+	r.buffer.Write(p)
+	return len(p), nil
+}
+
+// Sum appends the current hash to b and returns the resulting slice.
+// It does not change the underlying hash state.
+// The instance buffer is interpreted as a sequence of coefficients of size r.Bound bits long.
+// The function returns the hash of the polynomial as a a sequence []{{ .FF }}.Elements, interpreted as []bytes,
+// corresponding to sum_i A[i]*m Mod X^{d}+1
+func (r *RSis) Sum(b []byte) []byte {
+	buf := r.buffer.Bytes()
+	if len(buf) > r.capacity {
+		panic("buffer too large")
+	}
+
+	fastPath := r.LogTwoBound == 8 && r.Degree == 64
+
+	// clear the buffers of the instance.
+	defer r.cleanupBuffers()
+
+	m := r.bufM
+	mValues := r.bufMValues
+
+	if r.LogTwoBound<8 && (8%r.LogTwoBound==0) {
+		limbDecomposeBytesSmallBound(buf, m, r.LogTwoBound, r.Degree, mValues)
+	} else if r.LogTwoBound>=8 && ({{ .FF }}.Bytes*8)%r.LogTwoBound == 0 {
+		limbDecomposeBytesMiddleBound(buf, m, r.LogTwoBound, r.Degree, mValues)
+	} else {
+		limbDecomposeBytes(buf, m, r.LogTwoBound, r.Degree, mValues)
+	}
+
+	// we can hash now.
+	res := r.bufRes
+
+	// method 1: fft
+	for i := 0; i < len(r.Ag); i++ {
+		if !mValues.Test(uint(i)) {
+			// means m[i*r.Degree : (i+1)*r.Degree] == [0...0]
+			// we can skip this, FFT(0) = 0
+			continue
+		}
+		k := m[i*r.Degree : (i+1)*r.Degree]
+		if fastPath {
+			// fast path.
+			FFT64(k, r.twiddleCosets)
+		} else {
+			r.Domain.FFT(k, fft.DIF, fft.OnCoset(), fft.WithNbTasks(1))
+		}
+		mulModAcc(res, r.Ag[i], k)
+	}
+	r.Domain.FFTInverse(res, fft.DIT, fft.OnCoset(), fft.WithNbTasks(1)) // -> reduces mod Xᵈ+1
+
+	resBytes, err := res.MarshalBinary()
+	if err != nil {
+		panic(err)
+	}
+
+	return append(b, resBytes[4:]...) // first 4 bytes are uint32(len(res))
+}
+
+// Reset resets the Hash to its initial state.
+func (r *RSis) Reset() {
+	r.buffer.Reset()
+}
+
+// Size returns the number of bytes Sum will return.
+func (r *RSis) Size() int {
+
+	// The size in bits is the size in bits of a polynomial in A.
+	degree := len(r.A[0])
+	totalSize := degree * {{ .FF }}.Modulus().BitLen() / 8
+
+	return totalSize
+}
+
+// BlockSize returns the hash's underlying block size.
+// The Write method must be able to accept any amount
+// of data, but it may operate more efficiently if all writes
+// are a multiple of the block size.
+func (r *RSis) BlockSize() int {
+	return 0
+}
+
+// Construct a hasher generator. It takes as input the same parameters
+// as `NewRingSIS` and outputs a function which returns fresh hasher
+// everytime it is called
+func NewRingSISMaker(seed int64, logTwoDegree, logTwoBound, maxNbElementsToHash int) (func() hash.Hash, error) {
+	return func() hash.Hash {
+		h, err := NewRSis(seed, logTwoDegree, logTwoBound, maxNbElementsToHash)
+		if err != nil {
+			panic(err)
+		}
+		return h
+	}, nil
+
+}
+
+func genRandom(seed, i, j int64, buf *bytes.Buffer) {{ .FF }}.Element {
+
+	buf.Reset()
+	buf.WriteString("SIS")
+	binary.Write(buf, binary.BigEndian, seed)
+	binary.Write(buf, binary.BigEndian, i)
+	binary.Write(buf, binary.BigEndian, j)
+
+	digest := blake2b.Sum256(buf.Bytes())
+
+	var res {{ .FF }}.Element
+	res.SetBytes(digest[:])
+
+	return res
+}
+
+// mulMod computes p * q in ℤ_{p}[X]/Xᵈ+1.
+// Is assumed that pLagrangeShifted and qLagrangeShifted are of the correct sizes
+// and that they are in evaluation form on √(g) * <g>
+// The result is not FFTinversed. The fft inverse is done once every
+// multiplications are done.
+func mulMod(pLagrangeCosetBitReversed, qLagrangeCosetBitReversed []{{ .FF }}.Element) []{{ .FF }}.Element {
+
+	res := make([]{{ .FF }}.Element, len(pLagrangeCosetBitReversed))
+	for i := 0; i < len(pLagrangeCosetBitReversed); i++ {
+		res[i].Mul(&pLagrangeCosetBitReversed[i], &qLagrangeCosetBitReversed[i])
+	}
+
+	// NOT fft inv for now, wait until every part of the keys have been multiplied
+	// r.Domain.FFTInverse(res, fft.DIT, true)
+
+	return res
+
+}
+
+// mulMod + accumulate in res.
+func mulModAcc(res []{{ .FF }}.Element, pLagrangeCosetBitReversed, qLagrangeCosetBitReversed []{{ .FF }}.Element) {
+	var t {{ .FF }}.Element
+	for i := 0; i < len(pLagrangeCosetBitReversed); i++ {
+		t.Mul(&pLagrangeCosetBitReversed[i], &qLagrangeCosetBitReversed[i])
+		res[i].Add(&res[i], &t)
+	}
+}
+
+// Returns a clone of the RSis parameters with a fresh and empty buffer. Does not
+// mutate the current instance. The keys and the public parameters of the SIS
+// instance are not deep-copied. It is useful when we want to hash in parallel.
+// Otherwise, we would have to generate an entire RSis for each thread.
+func (r *RSis) CopyWithFreshBuffer() RSis {
+	res := *r
+	res.buffer = bytes.Buffer{}
+	res.bufM = make({{ .FF }}.Vector, len(r.bufM))
+	res.bufMValues = bitset.New(r.bufMValues.Len())
+	res.bufRes = make({{ .FF }}.Vector, len(r.bufRes))
+	return res
+}
+
+// Cleanup the buffers of the RSis instance
+func (r *RSis) cleanupBuffers() {
+	r.bufMValues.ClearAll()
+	for i := 0; i < len(r.bufM); i++ {
+		r.bufM[i].SetZero()
+	}
+	for i := 0; i < len(r.bufRes); i++ {
+		r.bufRes[i].SetZero()
+	}
+}
+
+// Split an slice of bytes representing an array of serialized field element in
+// big-endian form into an array of limbs representing the same field elements
+// in little-endian form. Namely, if our field is represented with 64 bits and we
+// have the following field element 0x0123456789abcdef (0 being the most significant
+// character and and f being the least significant one) and our log norm bound is
+// 16 (so 1 hex character = 1 limb). The function assigns the values of m to [f, e,
+// d, c, b, a, ..., 3, 2, 1, 0]. m should be preallocated and zeroized. Additionally,
+// we have the guarantee that 2 bits contributing to different field elements cannot
+// be part of the same limb.
+func LimbDecomposeBytes(buf []byte, m {{ .FF }}.Vector, logTwoBound int) {
+	limbDecomposeBytes(buf, m, logTwoBound, 0, nil)
+}
+
+// decomposes m as by taking chunks of logTwoBound bits at a time. The buffer is interpreted like this:
+// [0xa,        ..            , 0x1 | 0xa ... ]
+//  <- #bytes in a field element ->
+//  <-0xa is the MSB, 0x1 the LSB->
+//  <-we read this chunk from right
+//     			to left 	 	 ->
+//
+//
+// This function is called when logTwoBound divides the number of bits used to represent a
+// {{ .FF }} element.
+// From a slice of field elements m:=[a_0, a_1, ...]
+// Doing h.Sum(h.Write([Marshal[a_i] for i in len(m)])) is the same than
+// writing the a_i in little endian, and then taking logTwoBound bits at a time.
+//
+// ex: m := [0x1, 0x3]
+// in the hash buffer, it is interpreted like that as a stream of bits:
+// [100...0 110...0] corresponding to [0x1, 0x3] in little endian, so first bit = LSbit
+// then the stream of bits is splitted in chunks of logTwoBound bits.
+//
+// This function is called when logTwoBound divides 8.
+func limbDecomposeBytesSmallBound(buf []byte, m {{ .FF }}.Vector, logTwoBound, degree int, mValues *bitset.BitSet) {
+	mask := byte((1 << logTwoBound) - 1)
+	nbChunksPerBytes := 8 / logTwoBound
+	nbFieldsElmts := len(buf) / {{ .FF }}.Bytes
+	for i := 0; i < nbFieldsElmts; i++ {
+		for j := {{ .FF }}.Bytes - 1; j >= 0; j-- {
+			curByte := buf[i*{{ .FF }}.Bytes+j]
+			curPos := i*{{ .FF }}.Bytes*nbChunksPerBytes + ({{ .FF }}.Bytes-1-j)*nbChunksPerBytes
+			for k := 0; k < nbChunksPerBytes; k++ {
+
+                {{ if (or (eq .FF "babybear") (eq .FF "koalabear" ) ) }}
+				m[curPos+k][0] = uint32((curByte >> (k * logTwoBound)) & mask)
+                {{ else }}
+                m[curPos+k][0] = uint64((curByte >> (k * logTwoBound)) & mask)
+                {{ end }}
+
+				// Check if mPos is zero and mark as non-zero in the bitset if not
+				if m[curPos+k][0] != 0 && mValues != nil {
+					mValues.Set(uint((curPos + k) / degree))
+				}
+			}
+		}
+	}
+}
+
+// limbDecomposeBytesMiddleBound same function than limbDecomposeBytesSmallBound, but logTwoBound is
+// a multiple of 8, and divides the number of bits of the fields.
+func limbDecomposeBytesMiddleBound(buf []byte, m {{ .FF }}.Vector, logTwoBound, degree int, mValues *bitset.BitSet) {
+	nbFieldsElmts := len(buf) / {{ .FF }}.Bytes
+	nbChunksPerElements := {{ .FF }}.Bytes * 8 / logTwoBound
+	nbBytesInChunk := logTwoBound / 8
+	curElmt := 0
+	for i := 0; i < nbFieldsElmts; i++ {
+		for j := nbChunksPerElements; j > 0; j-- {
+			curPos := i*{{ .FF }}.Bytes + j*nbBytesInChunk
+			for k := 1; k <= nbBytesInChunk; k++ {
+                {{ if (or (eq .FF "babybear") (eq .FF "koalabear" ) ) }}
+				m[curElmt][0] |= (uint32(buf[curPos-k]) << ((k - 1) * 8))
+                {{ else }}
+                m[curElmt][0] |= (uint64(buf[curPos-k]) << ((k - 1) * 8))
+                {{ end }}
+			}
+            // Check if mPos is zero and mark as non-zero in the bitset if not
+			if m[curElmt][0] != 0 && mValues != nil {
+				mValues.Set(uint((curElmt) / degree))
+			}
+			curElmt += 1
+		}
+	}
+}
+
+// Split an slice of bytes representing an array of serialized field element in
+// big-endian form into an array of limbs representing the same field elements
+// in little-endian form. Namely, if our field is represented with 64 bits and we
+// have the following field element 0x0123456789abcdef (0 being the most significant
+// character and and f being the least significant one) and our log norm bound is
+// 16 (so 1 hex character = 1 limb). The function assigns the values of m to [f, e,
+// d, c, b, a, ..., 3, 2, 1, 0]. m should be preallocated and zeroized. mValues is
+// an optional bitSet. If provided, it must be empty. The function will set bit "i"
+// to indicate the that i-th SIS input polynomial should be non-zero. Recall, that a
+// SIS polynomial corresponds to a chunk of limbs of size `degree`. Additionally,
+// we have the guarantee that 2 bits contributing to different field elements cannot
+// be part of the same limb.
+func limbDecomposeBytes(buf []byte, m {{ .FF }}.Vector, logTwoBound, degree int, mValues *bitset.BitSet) {
+
+	// bitwise decomposition of the buffer, in order to build m (the vector to hash)
+	// as a list of polynomials, whose coefficients are less than r.B bits long.
+	// Say buf=[0xbe,0x0f]. As a stream of bits it is interpreted like this:
+	// 10111110 00001111. getIthBit(0)=1 (=leftmost bit), getIthBit(1)=0 (=second leftmost bit), etc.
+	nbBits := len(buf) * 8
+	getIthBit := func(i int) uint8 {
+		k := i / 8
+		if k >= len(buf) {
+			return 0
+		}
+		b := buf[k]
+		j := i % 8
+		return b >> (7 - j) & 1
+	}
+
+	// we process the input buffer by blocks of r.LogTwoBound bits
+	// each of these block (<< 64bits) are interpreted as a coefficient
+	mPos := 0
+	for fieldStart := 0; fieldStart < nbBits; {
+		for bitInField := 0; bitInField < {{ .FF }}.Bytes*8; {
+
+			j := bitInField % logTwoBound
+
+			// r.LogTwoBound < 64; we just use the first word of our element here,
+			// and set the bits from LSB to MSB.
+			at := fieldStart + {{ .FF }}.Bytes*8 - bitInField - 1
+
+            {{ if (or (eq .FF "babybear") (eq .FF "koalabear" ) ) }}
+			m[mPos][0] |= uint32(getIthBit(at) << j)
+            {{ else  }}
+            m[mPos][0] |= uint64(getIthBit(at) << j)
+            {{ end }}
+			bitInField++
+
+			// Check if mPos is zero and mark as non-zero in the bitset if not
+			if m[mPos][0] != 0 && mValues != nil {
+				mValues.Set(uint(mPos / degree))
+			}
+
+			if j == logTwoBound-1 || bitInField == {{ .FF }}.Bytes*8 {
+				mPos++
+			}
+		}
+		fieldStart += {{ .FF }}.Bytes * 8
+	}
+}
+
+// see limbDecomposeBytes; this function is optimized for the case where
+// logTwoBound == 8 and degree == 64
+func limbDecomposeBytes8_64(buf []byte, m {{ .FF }}.Vector, mValues *bitset.BitSet) {
+	// with logTwoBound == 8, we can actually advance byte per byte.
+	const degree = 64
+	j := 0
+
+	for startPos := {{ .FF }}.Bytes - 1; startPos < len(buf); startPos += {{ .FF }}.Bytes {
+		for i := startPos; i >= startPos-{{ .FF }}.Bytes+1; i-- {
+			{{ if (or (eq .FF "babybear") (eq .FF "koalabear") ) }}
+            m[j][0] = uint32(buf[i])
+            {{ else }}
+            m[j][0] = uint64(buf[i])
+            {{ end }}
+			if m[j][0] != 0 {
+				mValues.Set(uint(j / degree))
+			}
+			j++
+		}
+	}
+}
diff --git a/field/generator/internal/templates/sis/sis.test.go.tmpl b/field/generator/internal/templates/sis/sis.test.go.tmpl
new file mode 100644
index 0000000000..3433c4b07c
--- /dev/null
+++ b/field/generator/internal/templates/sis/sis.test.go.tmpl
@@ -0,0 +1,481 @@
+import (
+	"bytes"
+	"crypto/rand"
+	"encoding/binary"
+	"encoding/json"
+	"fmt"
+	"io"
+	"math/bits"
+	"os"
+	"testing"
+	"time"
+    "math/big"
+
+	"github.com/bits-and-blooms/bitset"
+	"{{ .FieldPackagePath }}"
+	"{{ .FieldPackagePath }}/fft"
+	"github.com/stretchr/testify/require"
+)
+
+type sisParams struct {
+	logTwoBound, logTwoDegree int
+}
+
+var params128Bits []sisParams = []sisParams{
+	{logTwoBound: 2, logTwoDegree: 3},
+	{logTwoBound: 4, logTwoDegree: 4},
+	{logTwoBound: 6, logTwoDegree: 5},
+	{logTwoBound: 8, logTwoDegree: 6},
+	{logTwoBound: 10, logTwoDegree: 6},
+	{logTwoBound: 16, logTwoDegree: 7},
+	{logTwoBound: 32, logTwoDegree: 8},
+}
+
+type TestCases struct {
+	Inputs  []{{ .FF }}.Element `json:"inputs"`
+	Entries []struct {
+		Params struct {
+			Seed                int64 `json:"seed"`
+			LogTwoDegree        int   `json:"logTwoDegree"`
+			LogTwoBound         int   `json:"logTwoBound"`
+			MaxNbElementsToHash int   `json:"maxNbElementsToHash"`
+		} `json:"params"`
+		Expected []{{ .FF }}.Element `json:"expected"`
+	} `json:"entries"`
+}
+
+func TestReference(t *testing.T) {
+	if bits.UintSize == 32 {
+		t.Skip("skipping this test in 32bit.")
+	}
+	assert := require.New(t)
+
+	// read the test case file
+	var testCases TestCases
+	data, err := os.ReadFile("test_cases.json")
+	assert.NoError(err, "reading test cases failed")
+	err = json.Unmarshal(data, &testCases)
+	assert.NoError(err, "reading test cases failed")
+
+	inputs := testCases.Inputs
+
+	for testCaseID, testCase := range testCases.Entries {
+
+		// create the SIS instance
+		sis, err := NewRSis(testCase.Params.Seed, testCase.Params.LogTwoDegree, testCase.Params.LogTwoBound, testCase.Params.MaxNbElementsToHash)
+		assert.NoError(err)
+
+		// key generation same than in sage
+		makeKeyDeterministic(t, sis, testCase.Params.Seed)
+
+		sis.Reset()
+
+		// hash test case entry input and compare with expected (computed by sage)
+		goHash, err := sis.Hash(inputs)
+		assert.NoError(err)
+
+		assert.EqualValues(
+			testCase.Expected, goHash,
+			"mismatch between reference test and computed value (testcase %v)",
+			testCaseID,
+		)
+
+	}
+
+}
+
+func TestLimbDecomposeBytesMiddleBound(t *testing.T) {
+
+	var montConstant {{ .FF }}.Element
+	var bMontConstant big.Int
+	bMontConstant.SetUint64(1)
+	bMontConstant.Lsh(&bMontConstant, {{ .FF }}.Bytes*8)
+	montConstant.SetBigInt(&bMontConstant)
+
+	nbElmts := 10
+	a := make([]{{ .FF }}.Element, nbElmts)
+	for i := 0; i < nbElmts; i++ {
+		a[i].SetUint64(33)
+	}
+	var buf bytes.Buffer
+	for i := 0; i < nbElmts; i++ {
+		buf.Write(a[i].Marshal())
+	}
+
+	logTwoBound := 8
+
+    for cc:=0;cc<3; cc++ {
+        m := make({{ .FF }}.Vector, nbElmts*{{ .FF }}.Bytes*8/logTwoBound)
+        limbDecomposeBytesMiddleBound(buf.Bytes(), m, logTwoBound, 4, nil)
+
+        for i := 0; i < len(m); i++ {
+            m[i].Mul(&m[i], &montConstant)
+        }
+
+        var x {{ .FF }}.Element
+        x.SetUint64(1 << logTwoBound)
+
+        coeffsPerFieldsElmt := {{ .FF }}.Bytes * 8 / logTwoBound
+        for i := 0; i < nbElmts; i++ {
+            r := eval(m[i*coeffsPerFieldsElmt:(i+1)*coeffsPerFieldsElmt], x)
+            if !r.Equal(&a[i]) {
+                t.Fatal("limbDecomposeBytes failed")
+            }
+        }
+        logTwoBound*=2
+    }
+
+}
+
+func TestLimbDecomposeBytesSmallBound(t *testing.T) {
+
+	var montConstant {{ .FF }}.Element
+	var bMontConstant big.Int
+	bMontConstant.SetUint64(1)
+	bMontConstant.Lsh(&bMontConstant, {{ .FF }}.Bytes*8)
+	montConstant.SetBigInt(&bMontConstant)
+
+	nbElmts := 10	
+	a := make([]{{ .FF }}.Element, nbElmts)
+	for i := 0; i<nbElmts; i++ {
+		a[i].SetRandom()
+	}
+	var buf bytes.Buffer
+	for i := 0; i<nbElmts; i++ {
+		buf.Write(a[i].Marshal())
+	}
+
+	logTwoBound := 2
+
+	for cc := 0; cc < 3; cc++ {
+
+		m := make({{ .FF }}.Vector, nbElmts*{{ .FF }}.Bytes*8/logTwoBound)
+		m2 := make({{ .FF }}.Vector, nbElmts*{{ .FF }}.Bytes*8/logTwoBound)
+
+		// the limbs are set as is, they are NOT converted in Montgomery form
+		limbDecomposeBytes(buf.Bytes(), m, logTwoBound, 4, nil)
+		limbDecomposeBytesSmallBound(buf.Bytes(), m2, logTwoBound, 4, nil)
+
+		for i := 0; i < len(m); i++ {
+			m[i].Mul(&m[i], &montConstant)
+			m2[i].Mul(&m2[i], &montConstant)
+		}
+		var x {{ .FF }}.Element
+		x.SetUint64(1 << logTwoBound)
+
+		coeffsPerFieldsElmt := {{ .FF }}.Bytes * 8 / logTwoBound
+		for i := 0; i < nbElmts; i++ {
+			r := eval(m[i*coeffsPerFieldsElmt:(i+1)*coeffsPerFieldsElmt], x)
+			if !r.Equal(&a[i]) {
+				t.Fatal("limbDecomposeBytes failed")
+			}
+			r = eval(m2[i*coeffsPerFieldsElmt:(i+1)*coeffsPerFieldsElmt], x)
+			if !r.Equal(&a[i]) {
+				t.Fatal("limbDecomposeBytesSmallBound failed")
+			}
+		}
+		logTwoBound *= 2
+	}
+
+}
+
+func eval(p []{{ .FF }}.Element, x {{ .FF }}.Element) {{ .FF }}.Element {
+	var res {{ .FF }}.Element
+	for i := len(p) - 1; i >= 0; i-- {
+		res.Mul(&res, &x).Add(&res, &p[i])
+	}
+	return res
+}
+
+func TestMulMod(t *testing.T) {
+
+	size := 4
+
+	p := make([]{{ .FF }}.Element, size)
+	q := make([]{{ .FF }}.Element, size)
+	pCopy := make([]{{ .FF }}.Element, size)
+	qCopy := make([]{{ .FF }}.Element, size)
+	for i := 0; i < size; i++ {
+		p[i].SetRandom()
+		pCopy[i].Set(&p[i])
+		q[i].SetRandom()
+		qCopy[i].Set(&q[i])
+	}
+
+	// creation of the domain
+	shift, err := {{ .FF }}.Generator(uint64(2 * size))
+	if err != nil {
+		t.Fatal(err)
+	}
+	var g {{ .FF }}.Element
+	g.Square(&shift)
+	domain := fft.NewDomain(uint64(size), fft.WithShift(shift))
+
+	// mul mod
+	domain.FFT(p, fft.DIF, fft.OnCoset())
+	domain.FFT(q, fft.DIF, fft.OnCoset())
+	r := mulMod(p, q)
+	domain.FFTInverse(r, fft.DIT, fft.OnCoset())
+
+	// manually check the product on the zeroes of X^4+1
+	for i := 0; i < 4; i++ {
+		u := eval(pCopy, shift)
+		v := eval(qCopy, shift)
+		w := eval(r, shift)
+		u.Mul(&u, &v)
+		if !w.Equal(&u) {
+			t.Fatal("mul mol failed")
+		}
+		shift.Mul(&shift, &g)
+	}
+
+}
+
+func makeKeyDeterministic(t *testing.T, sis *RSis, _seed int64) {
+	t.Helper()
+	// generate the key deterministically, the same way
+	// we do in sage to generate the test vectors.
+
+	polyRand := func(seed {{ .FF }}.Element, deg int) []{{ .FF }}.Element {
+		res := make([]{{ .FF }}.Element, deg)
+		for i := 0; i < deg; i++ {
+			res[i].Square(&seed)
+			seed.Set(&res[i])
+		}
+		return res
+	}
+
+	var seed, one {{ .FF }}.Element
+	one.SetOne()
+	seed.SetInt64(_seed)
+	for i := 0; i < len(sis.A); i++ {
+		sis.A[i] = polyRand(seed, sis.Degree)
+		copy(sis.Ag[i], sis.A[i])
+		sis.Domain.FFT(sis.Ag[i], fft.DIF, fft.OnCoset())
+		seed.Add(&seed, &one)
+	}
+}
+
+const (
+	LATENCY_MUL_FIELD_NS int = 18
+	LATENCY_ADD_FIELD_NS int = 4
+)
+
+// Estimate the theoretical performances that are achievable using ring-SIS
+// operations. The time is obtained by counting the number of additions and
+// multiplications occurring in the computation. This does not account for the
+// possibilities to use SIMD instructions or for cache-locality issues. Thus, it
+// does not represents a maximum even though it returns a good idea of what is
+// achievable . This returns performances in term of ns/field. This also does not
+// account for the time taken for "limb-splitting" the input.
+func estimateSisTheory(p sisParams) float64 {
+
+	// Since the FFT occurs over a coset, we need to multiply all the coefficients
+	// of the input by some coset factors (for an entire polynomial)
+	timeCosetShift := (1 << p.logTwoDegree) * LATENCY_MUL_FIELD_NS
+
+	// The two additions are from the butterfly, and the multiplication represents
+	// the one by the twiddle. (for an entire polynomial)
+	timeFFT := (1 << p.logTwoDegree) * p.logTwoDegree * (2*LATENCY_ADD_FIELD_NS + LATENCY_MUL_FIELD_NS)
+
+	// Time taken to multiply by the key and accumulate (for an entire polynomial)
+	timeMulAddKey := (1 << p.logTwoDegree) * (LATENCY_MUL_FIELD_NS + LATENCY_ADD_FIELD_NS)
+
+	// Total computation time for an entire polynomial
+	totalTimePoly := timeCosetShift + timeFFT + timeMulAddKey
+
+	// Convert this into a time per input field
+	r := totalTimePoly * {{ .FF }}.Bits / p.logTwoBound / (1 << p.logTwoDegree)
+	return float64(r)
+}
+
+func BenchmarkDecomposition(b *testing.B) {
+
+	nbElmts := 1000
+	a := make([]{{ .FF }}.Element, nbElmts)
+	for i := 0; i < nbElmts; i++ {
+		a[i].SetRandom()
+	}
+	var buf bytes.Buffer
+	for i := 0; i < nbElmts; i++ {
+		buf.Write(a[i].Marshal())
+	}
+	logTwoBound := 4
+	m := make({{ .FF }}.Vector, nbElmts*{{ .FF }}.Bytes*8/logTwoBound)
+
+	b.Run(fmt.Sprintf("limbDecomposeBytes logTwoBound=%d", logTwoBound), func(b *testing.B) {
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			limbDecomposeBytes(buf.Bytes(), m, logTwoBound, 4, nil)
+		}
+	})
+
+	b.Run(fmt.Sprintf("limbDecomposeByteSmallBound logTwoBound=%d", logTwoBound), func(b *testing.B) {
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			limbDecomposeBytesSmallBound(buf.Bytes(), m, logTwoBound, 4, nil)
+		}
+	})
+
+	logTwoBound = 16
+	b.Run(fmt.Sprintf("limbDecomposeBytes logTwoBound=%d", logTwoBound), func(b *testing.B) {
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			limbDecomposeBytes(buf.Bytes(), m, logTwoBound, 4, nil)
+		}
+	})
+
+	b.Run(fmt.Sprintf("limbDecomposeByteSmallBound logTwoBound=%d", logTwoBound), func(b *testing.B) {
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			limbDecomposeBytesMiddleBound(buf.Bytes(), m, logTwoBound, 4, nil)
+		}
+	})
+
+}
+
+func BenchmarkSIS(b *testing.B) {
+
+	// max nb field elements to hash
+	const nbInputs = 1 << 16
+
+	// Assign the input with random bytes. In practice, theses bytes encodes
+	// a string of field element. It would be more meaningful to take a slice
+	// of field element directly because otherwise the conversion time is not
+	// accounted for in the benchmark.
+	inputs := make({{ .FF }}.Vector, nbInputs)
+	for i := 0; i < len(inputs); i++ {
+		inputs[i].SetRandom()
+	}
+
+	for _, param := range params128Bits {
+		for n := 1 << 10; n <= nbInputs; n <<= 1 {
+			in := inputs[:n]
+			benchmarkSIS(b, in, false, param.logTwoBound, param.logTwoDegree, estimateSisTheory(param))
+		}
+
+	}
+}
+
+func benchmarkSIS(b *testing.B, input []{{ .FF }}.Element, sparse bool, logTwoBound, logTwoDegree int, theoretical float64) {
+	b.Helper()
+
+	n := len(input)
+
+	benchName := "ring-sis/"
+	if sparse {
+		benchName += "sparse/"
+	}
+	benchName += fmt.Sprintf("inputs=%v/log2-bound=%v/log2-degree=%v", n, logTwoBound, logTwoDegree)
+
+	b.Run(benchName, func(b *testing.B) {
+		instance, err := NewRSis(0, logTwoDegree, logTwoBound, n)
+		if err != nil {
+			b.Fatal(err)
+		}
+
+		// We introduce a custom metric which is the time per field element
+		// Since the benchmark object allows to report extra meta but does
+		// not allow accessing them. We measure the time ourself.
+
+		startTime := time.Now()
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			_, err = instance.Hash(input)
+			if err != nil {
+				b.Fatal(err)
+			}
+		}
+		b.StopTimer()
+
+		totalDuration := time.Since(startTime)
+		nsPerField := totalDuration.Nanoseconds() / int64(b.N) / int64(n)
+
+		b.ReportMetric(float64(nsPerField), "ns/field")
+
+		b.ReportMetric(theoretical, "ns/field(theory)")
+
+	})
+}
+
+// Hash interprets the input vector as a sequence of coefficients of size r.LogTwoBound bits long,
+// and return the hash of the polynomial corresponding to the sum sum_i A[i]*m Mod X^{d}+1
+//
+// It is equivalent to calling r.Write(element.Marshal()); outBytes = r.Sum(nil);
+// ! note @gbotrel: this is a place holder, may not make sense
+func (r *RSis) Hash(v []{{ .FF }}.Element) ([]{{ .FF }}.Element, error) {
+	if len(v) > r.maxNbElementsToHash {
+		return nil, fmt.Errorf("can't hash more than %d elements with params provided in constructor", r.maxNbElementsToHash)
+	}
+
+	r.Reset()
+	for _, e := range v {
+		r.Write(e.Marshal())
+	}
+	sum := r.Sum(nil)
+	var rlen [4]byte
+	binary.BigEndian.PutUint32(rlen[:], uint32(len(sum)/{{ .FF }}.Bytes))
+	reader := io.MultiReader(bytes.NewReader(rlen[:]), bytes.NewReader(sum))
+	var result {{ .FF }}.Vector
+	_, err := result.ReadFrom(reader)
+	if err != nil {
+		return nil, err
+	}
+	return result, nil
+}
+
+func TestLimbDecompositionFastPath(t *testing.T) {
+	assert := require.New(t)
+
+	for size := {{ .FF }}.Bytes; size < 5*{{ .FF }}.Bytes; size += {{ .FF }}.Bytes {
+		// Test the fast path of limbDecomposeBytes8_64
+		buf := make([]byte, size)
+		m := make([]{{ .FF }}.Element, size)
+		mValues := bitset.New(uint(size))
+		n := make([]{{ .FF }}.Element, size)
+		nValues := bitset.New(uint(size))
+
+		// Generate a random buffer
+		_, err := rand.Read(buf)
+		assert.NoError(err)
+
+		limbDecomposeBytes8_64(buf, m, mValues)
+		limbDecomposeBytes(buf, n, 8, 64, nValues)
+
+		for i := 0; i < size; i++ {
+			assert.Equal(mValues.Test(uint(i)), nValues.Test(uint(i)))
+			assert.True(m[i].Equal(&n[i]))
+		}
+	}
+
+}   
+
+func TestUnrolledFFT(t *testing.T) {
+
+	var shift {{ .FF }}.Element
+	shift.SetRandom()
+
+	const size = 64
+	assert := require.New(t)
+	domain := fft.NewDomain(size, fft.WithShift(shift))
+
+	k1 := make([]{{ .FF }}.Element, size)
+	for i := 0; i < size; i++ {
+		k1[i].SetRandom()
+	}
+	k2 := make([]{{ .FF }}.Element, size)
+	copy(k2, k1)
+
+	// default FFT
+	domain.FFT(k1, fft.DIF, fft.OnCoset(), fft.WithNbTasks(1))
+
+	// unrolled FFT
+	twiddlesCoset := PrecomputeTwiddlesCoset(domain.Generator, domain.FrMultiplicativeGen)
+	FFT64(k2, twiddlesCoset)
+
+	// compare results
+	for i := 0; i < size; i++ {
+		// fmt.Printf("i = %d, k1 = %v, k2 = %v\n", i, k1[i].String(), k2[i].String())
+		assert.True(k1[i].Equal(&k2[i]), "i = %d", i)
+	}
+}
diff --git a/field/generator/options.go b/field/generator/options.go
index 71f7ee0212..5ef420f950 100644
--- a/field/generator/options.go
+++ b/field/generator/options.go
@@ -9,6 +9,11 @@ type Option func(*generatorConfig)
 type generatorConfig struct {
 	fftConfig *config.FFT
 	asmConfig *config.Assembly
+	withSIS   bool
+}
+
+func (cfg *generatorConfig) HasSIS() bool {
+	return cfg.withSIS
 }
 
 func (cfg *generatorConfig) HasFFT() bool {
@@ -23,6 +28,12 @@ func (cfg *generatorConfig) HasAMD64() bool {
 	return cfg.asmConfig != nil && cfg.asmConfig.BuildDir != ""
 }
 
+func WithSIS() Option {
+	return func(opt *generatorConfig) {
+		opt.withSIS = true
+	}
+}
+
 func WithFFT(cfg *config.FFT) Option {
 	return func(opt *generatorConfig) {
 		opt.fftConfig = cfg
diff --git a/field/goldilocks/sis/sis.go b/field/goldilocks/sis/sis.go
new file mode 100644
index 0000000000..7dafd5c715
--- /dev/null
+++ b/field/goldilocks/sis/sis.go
@@ -0,0 +1,468 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package sis
+
+import (
+	"bytes"
+	"encoding/binary"
+	"errors"
+	"hash"
+	"math/bits"
+
+	"github.com/bits-and-blooms/bitset"
+	"github.com/consensys/gnark-crypto/field/goldilocks"
+	"github.com/consensys/gnark-crypto/field/goldilocks/fft"
+	"github.com/consensys/gnark-crypto/internal/parallel"
+	"golang.org/x/crypto/blake2b"
+)
+
+var (
+	ErrNotAPowerOfTwo = errors.New("d must be a power of 2")
+)
+
+// Ring-SIS instance
+type RSis struct {
+
+	// buffer storing the data to hash
+	buffer bytes.Buffer
+
+	// Vectors in ℤ_{p}/Xⁿ+1
+	// A[i] is the i-th polynomial.
+	// Ag the evaluation form of the polynomials in A on the coset √(g) * <g>
+	A  [][]goldilocks.Element
+	Ag [][]goldilocks.Element
+
+	// LogTwoBound (Infinity norm) of the vector to hash. It means that each component in m
+	// is < 2^B, where m is the vector to hash (the hash being A*m).
+	// cf https://hackmd.io/7OODKWQZRRW9RxM5BaXtIw , B >= 3.
+	LogTwoBound int
+
+	// domain for the polynomial multiplication
+	Domain        *fft.Domain
+	twiddleCosets []goldilocks.Element // see FFT64 and precomputeTwiddlesCoset
+
+	// d, the degree of X^{d}+1
+	Degree int
+
+	// in bytes, represents the maximum number of bytes the .Write(...) will handle;
+	// ( maximum number of bytes to sum )
+	capacity            int
+	maxNbElementsToHash int
+
+	// allocate memory once per instance (used in Sum())
+	bufM, bufRes goldilocks.Vector
+	bufMValues   *bitset.BitSet
+}
+
+// NewRSis creates an instance of RSis.
+// seed: seed for the randomness for generating A.
+// logTwoDegree: if d := logTwoDegree, the ring will be ℤ_{p}[X]/Xᵈ-1, where X^{2ᵈ} is the 2ᵈ⁺¹-th cyclotomic polynomial
+// logTwoBound: the bound of the vector to hash (using the infinity norm).
+// maxNbElementsToHash: maximum number of field elements the instance handles
+// used to derived n, the number of polynomials in A, and max size of instance's internal buffer.
+func NewRSis(seed int64, logTwoDegree, logTwoBound, maxNbElementsToHash int) (*RSis, error) {
+
+	if logTwoBound > 64 {
+		return nil, errors.New("logTwoBound too large")
+	}
+	if bits.UintSize == 32 {
+		return nil, errors.New("unsupported architecture; need 64bit target")
+	}
+
+	degree := 1 << logTwoDegree
+	capacity := maxNbElementsToHash * goldilocks.Bytes
+
+	// n: number of polynomials in A
+	// len(m) == degree * n
+	// with each element in m being logTwoBounds bits from the instance buffer.
+	// that is, to fill m, we need [degree * n * logTwoBound] bits of data
+	// capacity == [degree * n * logTwoBound] / 8
+	// n == (capacity*8)/(degree*logTwoBound)
+
+	// First n <- #limbs to represent a single field element
+	n := (goldilocks.Bytes * 8) / logTwoBound
+	if n*logTwoBound < goldilocks.Bytes*8 {
+		n++
+	}
+
+	// Then multiply by the number of field elements
+	n *= maxNbElementsToHash
+
+	// And divide (+ ceil) to get the number of polynomials
+	if n%degree == 0 {
+		n /= degree
+	} else {
+		n /= degree // number of polynomials
+		n++
+	}
+
+	// domains (shift is √{gen} )
+	shift, err := goldilocks.Generator(uint64(2 * degree))
+	if err != nil {
+		return nil, err
+	}
+
+	r := &RSis{
+		LogTwoBound:         logTwoBound,
+		capacity:            capacity,
+		Degree:              degree,
+		Domain:              fft.NewDomain(uint64(degree), fft.WithShift(shift)),
+		A:                   make([][]goldilocks.Element, n),
+		Ag:                  make([][]goldilocks.Element, n),
+		bufM:                make(goldilocks.Vector, degree*n),
+		bufRes:              make(goldilocks.Vector, degree),
+		bufMValues:          bitset.New(uint(n)),
+		maxNbElementsToHash: maxNbElementsToHash,
+	}
+	if r.LogTwoBound == 8 && r.Degree == 64 {
+		// TODO @gbotrel fixme, that's dirty.
+		r.twiddleCosets = PrecomputeTwiddlesCoset(r.Domain.Generator, r.Domain.FrMultiplicativeGen)
+	}
+
+	// filling A
+	a := make([]goldilocks.Element, n*r.Degree)
+	ag := make([]goldilocks.Element, n*r.Degree)
+
+	parallel.Execute(n, func(start, end int) {
+		var buf bytes.Buffer
+		for i := start; i < end; i++ {
+			rstart, rend := i*r.Degree, (i+1)*r.Degree
+			r.A[i] = a[rstart:rend:rend]
+			r.Ag[i] = ag[rstart:rend:rend]
+			for j := 0; j < r.Degree; j++ {
+				r.A[i][j] = genRandom(seed, int64(i), int64(j), &buf)
+			}
+
+			// fill Ag the evaluation form of the polynomials in A on the coset √(g) * <g>
+			copy(r.Ag[i], r.A[i])
+			r.Domain.FFT(r.Ag[i], fft.DIF, fft.OnCoset())
+		}
+	})
+
+	return r, nil
+}
+
+func (r *RSis) Write(p []byte) (n int, err error) {
+	r.buffer.Write(p)
+	return len(p), nil
+}
+
+// Sum appends the current hash to b and returns the resulting slice.
+// It does not change the underlying hash state.
+// The instance buffer is interpreted as a sequence of coefficients of size r.Bound bits long.
+// The function returns the hash of the polynomial as a a sequence []goldilocks.Elements, interpreted as []bytes,
+// corresponding to sum_i A[i]*m Mod X^{d}+1
+func (r *RSis) Sum(b []byte) []byte {
+	buf := r.buffer.Bytes()
+	if len(buf) > r.capacity {
+		panic("buffer too large")
+	}
+
+	fastPath := r.LogTwoBound == 8 && r.Degree == 64
+
+	// clear the buffers of the instance.
+	defer r.cleanupBuffers()
+
+	m := r.bufM
+	mValues := r.bufMValues
+
+	if r.LogTwoBound < 8 && (8%r.LogTwoBound == 0) {
+		limbDecomposeBytesSmallBound(buf, m, r.LogTwoBound, r.Degree, mValues)
+	} else if r.LogTwoBound >= 8 && (goldilocks.Bytes*8)%r.LogTwoBound == 0 {
+		limbDecomposeBytesMiddleBound(buf, m, r.LogTwoBound, r.Degree, mValues)
+	} else {
+		limbDecomposeBytes(buf, m, r.LogTwoBound, r.Degree, mValues)
+	}
+
+	// we can hash now.
+	res := r.bufRes
+
+	// method 1: fft
+	for i := 0; i < len(r.Ag); i++ {
+		if !mValues.Test(uint(i)) {
+			// means m[i*r.Degree : (i+1)*r.Degree] == [0...0]
+			// we can skip this, FFT(0) = 0
+			continue
+		}
+		k := m[i*r.Degree : (i+1)*r.Degree]
+		if fastPath {
+			// fast path.
+			FFT64(k, r.twiddleCosets)
+		} else {
+			r.Domain.FFT(k, fft.DIF, fft.OnCoset(), fft.WithNbTasks(1))
+		}
+		mulModAcc(res, r.Ag[i], k)
+	}
+	r.Domain.FFTInverse(res, fft.DIT, fft.OnCoset(), fft.WithNbTasks(1)) // -> reduces mod Xᵈ+1
+
+	resBytes, err := res.MarshalBinary()
+	if err != nil {
+		panic(err)
+	}
+
+	return append(b, resBytes[4:]...) // first 4 bytes are uint32(len(res))
+}
+
+// Reset resets the Hash to its initial state.
+func (r *RSis) Reset() {
+	r.buffer.Reset()
+}
+
+// Size returns the number of bytes Sum will return.
+func (r *RSis) Size() int {
+
+	// The size in bits is the size in bits of a polynomial in A.
+	degree := len(r.A[0])
+	totalSize := degree * goldilocks.Modulus().BitLen() / 8
+
+	return totalSize
+}
+
+// BlockSize returns the hash's underlying block size.
+// The Write method must be able to accept any amount
+// of data, but it may operate more efficiently if all writes
+// are a multiple of the block size.
+func (r *RSis) BlockSize() int {
+	return 0
+}
+
+// Construct a hasher generator. It takes as input the same parameters
+// as `NewRingSIS` and outputs a function which returns fresh hasher
+// everytime it is called
+func NewRingSISMaker(seed int64, logTwoDegree, logTwoBound, maxNbElementsToHash int) (func() hash.Hash, error) {
+	return func() hash.Hash {
+		h, err := NewRSis(seed, logTwoDegree, logTwoBound, maxNbElementsToHash)
+		if err != nil {
+			panic(err)
+		}
+		return h
+	}, nil
+
+}
+
+func genRandom(seed, i, j int64, buf *bytes.Buffer) goldilocks.Element {
+
+	buf.Reset()
+	buf.WriteString("SIS")
+	binary.Write(buf, binary.BigEndian, seed)
+	binary.Write(buf, binary.BigEndian, i)
+	binary.Write(buf, binary.BigEndian, j)
+
+	digest := blake2b.Sum256(buf.Bytes())
+
+	var res goldilocks.Element
+	res.SetBytes(digest[:])
+
+	return res
+}
+
+// mulMod computes p * q in ℤ_{p}[X]/Xᵈ+1.
+// Is assumed that pLagrangeShifted and qLagrangeShifted are of the correct sizes
+// and that they are in evaluation form on √(g) * <g>
+// The result is not FFTinversed. The fft inverse is done once every
+// multiplications are done.
+func mulMod(pLagrangeCosetBitReversed, qLagrangeCosetBitReversed []goldilocks.Element) []goldilocks.Element {
+
+	res := make([]goldilocks.Element, len(pLagrangeCosetBitReversed))
+	for i := 0; i < len(pLagrangeCosetBitReversed); i++ {
+		res[i].Mul(&pLagrangeCosetBitReversed[i], &qLagrangeCosetBitReversed[i])
+	}
+
+	// NOT fft inv for now, wait until every part of the keys have been multiplied
+	// r.Domain.FFTInverse(res, fft.DIT, true)
+
+	return res
+
+}
+
+// mulMod + accumulate in res.
+func mulModAcc(res []goldilocks.Element, pLagrangeCosetBitReversed, qLagrangeCosetBitReversed []goldilocks.Element) {
+	var t goldilocks.Element
+	for i := 0; i < len(pLagrangeCosetBitReversed); i++ {
+		t.Mul(&pLagrangeCosetBitReversed[i], &qLagrangeCosetBitReversed[i])
+		res[i].Add(&res[i], &t)
+	}
+}
+
+// Returns a clone of the RSis parameters with a fresh and empty buffer. Does not
+// mutate the current instance. The keys and the public parameters of the SIS
+// instance are not deep-copied. It is useful when we want to hash in parallel.
+// Otherwise, we would have to generate an entire RSis for each thread.
+func (r *RSis) CopyWithFreshBuffer() RSis {
+	res := *r
+	res.buffer = bytes.Buffer{}
+	res.bufM = make(goldilocks.Vector, len(r.bufM))
+	res.bufMValues = bitset.New(r.bufMValues.Len())
+	res.bufRes = make(goldilocks.Vector, len(r.bufRes))
+	return res
+}
+
+// Cleanup the buffers of the RSis instance
+func (r *RSis) cleanupBuffers() {
+	r.bufMValues.ClearAll()
+	for i := 0; i < len(r.bufM); i++ {
+		r.bufM[i].SetZero()
+	}
+	for i := 0; i < len(r.bufRes); i++ {
+		r.bufRes[i].SetZero()
+	}
+}
+
+// Split an slice of bytes representing an array of serialized field element in
+// big-endian form into an array of limbs representing the same field elements
+// in little-endian form. Namely, if our field is represented with 64 bits and we
+// have the following field element 0x0123456789abcdef (0 being the most significant
+// character and and f being the least significant one) and our log norm bound is
+// 16 (so 1 hex character = 1 limb). The function assigns the values of m to [f, e,
+// d, c, b, a, ..., 3, 2, 1, 0]. m should be preallocated and zeroized. Additionally,
+// we have the guarantee that 2 bits contributing to different field elements cannot
+// be part of the same limb.
+func LimbDecomposeBytes(buf []byte, m goldilocks.Vector, logTwoBound int) {
+	limbDecomposeBytes(buf, m, logTwoBound, 0, nil)
+}
+
+// decomposes m as by taking chunks of logTwoBound bits at a time. The buffer is interpreted like this:
+// [0xa,        ..            , 0x1 | 0xa ... ]
+//
+//	<- #bytes in a field element ->
+//	<-0xa is the MSB, 0x1 the LSB->
+//	<-we read this chunk from right
+//	   			to left 	 	 ->
+//
+// This function is called when logTwoBound divides the number of bits used to represent a
+// goldilocks element.
+// From a slice of field elements m:=[a_0, a_1, ...]
+// Doing h.Sum(h.Write([Marshal[a_i] for i in len(m)])) is the same than
+// writing the a_i in little endian, and then taking logTwoBound bits at a time.
+//
+// ex: m := [0x1, 0x3]
+// in the hash buffer, it is interpreted like that as a stream of bits:
+// [100...0 110...0] corresponding to [0x1, 0x3] in little endian, so first bit = LSbit
+// then the stream of bits is splitted in chunks of logTwoBound bits.
+//
+// This function is called when logTwoBound divides 8.
+func limbDecomposeBytesSmallBound(buf []byte, m goldilocks.Vector, logTwoBound, degree int, mValues *bitset.BitSet) {
+	mask := byte((1 << logTwoBound) - 1)
+	nbChunksPerBytes := 8 / logTwoBound
+	nbFieldsElmts := len(buf) / goldilocks.Bytes
+	for i := 0; i < nbFieldsElmts; i++ {
+		for j := goldilocks.Bytes - 1; j >= 0; j-- {
+			curByte := buf[i*goldilocks.Bytes+j]
+			curPos := i*goldilocks.Bytes*nbChunksPerBytes + (goldilocks.Bytes-1-j)*nbChunksPerBytes
+			for k := 0; k < nbChunksPerBytes; k++ {
+
+				m[curPos+k][0] = uint64((curByte >> (k * logTwoBound)) & mask)
+
+				// Check if mPos is zero and mark as non-zero in the bitset if not
+				if m[curPos+k][0] != 0 && mValues != nil {
+					mValues.Set(uint((curPos + k) / degree))
+				}
+			}
+		}
+	}
+}
+
+// limbDecomposeBytesMiddleBound same function than limbDecomposeBytesSmallBound, but logTwoBound is
+// a multiple of 8, and divides the number of bits of the fields.
+func limbDecomposeBytesMiddleBound(buf []byte, m goldilocks.Vector, logTwoBound, degree int, mValues *bitset.BitSet) {
+	nbFieldsElmts := len(buf) / goldilocks.Bytes
+	nbChunksPerElements := goldilocks.Bytes * 8 / logTwoBound
+	nbBytesInChunk := logTwoBound / 8
+	curElmt := 0
+	for i := 0; i < nbFieldsElmts; i++ {
+		for j := nbChunksPerElements; j > 0; j-- {
+			curPos := i*goldilocks.Bytes + j*nbBytesInChunk
+			for k := 1; k <= nbBytesInChunk; k++ {
+
+				m[curElmt][0] |= (uint64(buf[curPos-k]) << ((k - 1) * 8))
+
+			}
+			// Check if mPos is zero and mark as non-zero in the bitset if not
+			if m[curElmt][0] != 0 && mValues != nil {
+				mValues.Set(uint((curElmt) / degree))
+			}
+			curElmt += 1
+		}
+	}
+}
+
+// Split an slice of bytes representing an array of serialized field element in
+// big-endian form into an array of limbs representing the same field elements
+// in little-endian form. Namely, if our field is represented with 64 bits and we
+// have the following field element 0x0123456789abcdef (0 being the most significant
+// character and and f being the least significant one) and our log norm bound is
+// 16 (so 1 hex character = 1 limb). The function assigns the values of m to [f, e,
+// d, c, b, a, ..., 3, 2, 1, 0]. m should be preallocated and zeroized. mValues is
+// an optional bitSet. If provided, it must be empty. The function will set bit "i"
+// to indicate the that i-th SIS input polynomial should be non-zero. Recall, that a
+// SIS polynomial corresponds to a chunk of limbs of size `degree`. Additionally,
+// we have the guarantee that 2 bits contributing to different field elements cannot
+// be part of the same limb.
+func limbDecomposeBytes(buf []byte, m goldilocks.Vector, logTwoBound, degree int, mValues *bitset.BitSet) {
+
+	// bitwise decomposition of the buffer, in order to build m (the vector to hash)
+	// as a list of polynomials, whose coefficients are less than r.B bits long.
+	// Say buf=[0xbe,0x0f]. As a stream of bits it is interpreted like this:
+	// 10111110 00001111. getIthBit(0)=1 (=leftmost bit), getIthBit(1)=0 (=second leftmost bit), etc.
+	nbBits := len(buf) * 8
+	getIthBit := func(i int) uint8 {
+		k := i / 8
+		if k >= len(buf) {
+			return 0
+		}
+		b := buf[k]
+		j := i % 8
+		return b >> (7 - j) & 1
+	}
+
+	// we process the input buffer by blocks of r.LogTwoBound bits
+	// each of these block (<< 64bits) are interpreted as a coefficient
+	mPos := 0
+	for fieldStart := 0; fieldStart < nbBits; {
+		for bitInField := 0; bitInField < goldilocks.Bytes*8; {
+
+			j := bitInField % logTwoBound
+
+			// r.LogTwoBound < 64; we just use the first word of our element here,
+			// and set the bits from LSB to MSB.
+			at := fieldStart + goldilocks.Bytes*8 - bitInField - 1
+
+			m[mPos][0] |= uint64(getIthBit(at) << j)
+
+			bitInField++
+
+			// Check if mPos is zero and mark as non-zero in the bitset if not
+			if m[mPos][0] != 0 && mValues != nil {
+				mValues.Set(uint(mPos / degree))
+			}
+
+			if j == logTwoBound-1 || bitInField == goldilocks.Bytes*8 {
+				mPos++
+			}
+		}
+		fieldStart += goldilocks.Bytes * 8
+	}
+}
+
+// see limbDecomposeBytes; this function is optimized for the case where
+// logTwoBound == 8 and degree == 64
+func limbDecomposeBytes8_64(buf []byte, m goldilocks.Vector, mValues *bitset.BitSet) {
+	// with logTwoBound == 8, we can actually advance byte per byte.
+	const degree = 64
+	j := 0
+
+	for startPos := goldilocks.Bytes - 1; startPos < len(buf); startPos += goldilocks.Bytes {
+		for i := startPos; i >= startPos-goldilocks.Bytes+1; i-- {
+
+			m[j][0] = uint64(buf[i])
+
+			if m[j][0] != 0 {
+				mValues.Set(uint(j / degree))
+			}
+			j++
+		}
+	}
+}
diff --git a/field/goldilocks/sis/sis.py b/field/goldilocks/sis/sis.py
new file mode 100644
index 0000000000..7ff252b52d
--- /dev/null
+++ b/field/goldilocks/sis/sis.py
@@ -0,0 +1,253 @@
+## "sage sis.sage" will generate test_cases.json
+## tested with a fresh sage install on macOS (Feb 2023)
+
+import json
+
+# Goldilocks FR
+R = 18446744069414584321
+FR_BYTE_SIZE = 8
+FR_BIT_SIZE = FR_BYTE_SIZE*8
+GFR = GF(R)
+FR.<x> = GFR[]
+Z = IntegerRing()
+
+# Montgomery constant
+RR = GFR(2**(FR_BYTE_SIZE*8))
+
+# utils
+
+
+def build_poly(a):
+    """ Builds a poly from the array a
+
+    Args:
+        a an array
+
+    Returns:
+        a[0]+a[1]*X + .. + a[n]*X**n
+    """
+
+    res = GFR(0)
+    for i, v in enumerate(a):
+        res += GFR(v)*x**i
+    return res
+
+
+def get_ith_bit(i, b):
+    """
+    Args:
+        i: index of the bit to retrieve
+        b: array of bytes
+
+    Returns:
+        the i-th bit of b, when it is written b[0] || b[1] || ...
+    """
+    k = i//8
+    if k >= len(b):
+        return 0
+    j = i % 8
+    return (b[k] >> (7-j)) & 1
+
+
+def to_bytes(m, s):
+    """
+
+    Args:
+        m: an integer
+        s: the expected number of bytes of the result. If s is bigger than the
+        number of bytes in m, the remaining bytes are set to zero.
+
+    Returns:
+        the byte representation of m as a byte array, as
+        in gnark-crypto.
+    """
+    _m = Z(m)
+    res = s*[0]
+    mask = 255
+    for i in range(s):
+        res[s-1-i] = _m & 255
+        _m = _m >> 8
+    return res
+
+
+def split_coeffs(b, logTwoBound):
+    """
+    Args:
+        b: an array of bytes
+        logTwoBound: number of bits of the bound
+
+    Returns:
+        an array of coeffs, each coeff being the i-th chunk of logTwoBounds bits of b.
+        The coeffs are formed as follow. The input byte string is implicitly parsed as
+        a slice of field elements of FR_BYTE_SIZE bytes each in bigendian-natural form. the outputs
+        are in a little-endian form. That is, each chunk of size FR_BIT_SIZE / logTwoBounds of the
+        output can be seen as a polynomial, such that, when evaluated at 2 we get the original
+        field element.
+    """
+    nbBits = len(b)*8
+    res = [] 
+    i = 0
+
+    if len(b) % FR_BYTE_SIZE != 0:
+        exit("the length of b should divide the field size")
+
+    # The number of fields that we are parsing. In case we have that
+    # logTwoBound does not divide the number of bits to represent a
+    # field element, we do not merge them.
+    nbField = len(b) / FR_BYTE_SIZE
+    nbBitsInField = int(FR_BYTE_SIZE * 8)
+    
+    for fieldID in range(nbField):
+        fieldStart = fieldID * FR_BIT_SIZE
+        e = 0
+        for bitInField in range(nbBitsInField):
+            j = bitInField % logTwoBound
+            at = fieldStart + nbBitsInField - 1 - bitInField
+            e |= get_ith_bit(at, b) << j 
+            # Switch to a new limb
+            if j == logTwoBound - 1 or bitInField == FR_BYTE_SIZE * 8 - 1:
+                res.append(e)
+                e = 0
+
+    # careful Montgomery constant...
+    return [GFR(e)*RR**-1 for e in res]
+
+
+def poly_pseudo_rand(seed, n):
+    """ Generates a pseudo random polynomial of size n from seed.
+
+    Args:
+        seed: seed for the pseudo random gen
+        n: degree of the polynomial
+    """
+    seed = GFR(seed)
+    a = n*[0]
+    for i in range(n):
+        a[i] = seed**2
+        seed = a[i]
+    return build_poly(a)
+
+
+# SIS
+class SIS:
+    def __init__(self, seed, logTwoDegree, logTwoBound, maxNbElementsToHash):
+        """
+            Args:
+                seed
+                logTwoDegree: 
+                logTwoBound: bound of SIS
+                maxNbElementsToHash
+        """
+        capacity = maxNbElementsToHash * FR_BYTE_SIZE
+        degree = 1 << logTwoDegree
+
+        n = capacity * 8 / logTwoBound  # number of coefficients
+        if n % degree == 0:  # check how sage / python rounds the int div.
+            n = n / degree
+        else:
+            n = n / degree
+            n = n + 1
+
+        n = int(n)
+
+        self.logTwoBound = logTwoBound
+        self.degree = degree
+        self.size = n
+        self.key = n * [0]
+        for i in range(n):
+            self.key[i] = poly_pseudo_rand(seed, self.degree)
+            seed += 1
+
+    def hash(self, inputs):
+        """ 
+        Args:
+           inputs is a vector of FR elements
+
+        Returns:
+            the sis hash of m.
+        """
+        b = []
+        for i in inputs:
+            b.extend(to_bytes(i, FR_BYTE_SIZE))
+
+        return self.hash_bytes(b)
+
+    def hash_bytes(self, b):
+        """ 
+        Args:
+            b is a list of bytes to hash
+
+        Returns:
+            the sis hash of m.
+        """
+        # step 1: build the polynomials from m
+        c = split_coeffs(b, self.logTwoBound)
+        mp = [build_poly(c[self.degree*i:self.degree*(i+1)])
+              for i in range(self.size)]
+
+        # step 2: compute sum_i mp[i]*key[i] mod X^n+1
+        modulo = x**self.degree+1
+        res = 0
+        for i in range(self.size):
+            res += self.key[i]*mp[i]
+        res = res % modulo
+        return res
+
+
+def vectorToString(v):
+    # v is a vector of field elements
+    # we return a list of strings in base10
+    r = []
+    for e in v:
+        r.append("{}".format(Z(e)))
+        # r.append("0x" + Z(e).hex())
+    return r
+    
+
+def SISParams(seed, logTwoDegree, logTwoBound, maxNbElementsToHash):
+    p = {}
+    p['seed'] = int(seed)
+    p['logTwoDegree'] = int(logTwoDegree)
+    p['logTwoBound'] = int(logTwoBound)
+    p['maxNbElementsToHash'] = int(maxNbElementsToHash)
+    return p
+
+PARAMS = [
+
+    # call to limbDecomposeBytes
+    # SISParams(5, 2, 3, 10),
+    
+    # call to limbDecomposeBytesSmallBound
+    SISParams(5, 2, 2, 10),
+    SISParams(5, 2, 4, 10),
+
+    # call to limbDecomposeBytesSmallBound
+    SISParams(5, 2, 8, 10),
+    SISParams(5, 2, 16, 10),
+    SISParams(5, 2, 32, 10),
+]
+
+INPUTS = [GFR(5)**(i+1) for i in range(10)]
+
+TEST_CASES = {}
+
+TEST_CASES['inputs'] = vectorToString(INPUTS)
+TEST_CASES['entries'] = []
+
+for p in PARAMS:
+
+    entry = {}
+    entry['params'] = p 
+    # print("generating test cases with SIS params " + json.dumps(p))
+    instance = SIS(p['seed'], p['logTwoDegree'], p['logTwoBound'], p['maxNbElementsToHash'])
+
+    # hash the vector
+    hResult = instance.hash(INPUTS)
+    entry['expected'] = vectorToString(hResult)
+    
+    TEST_CASES['entries'].append(entry)
+
+
+TEST_CASES_json = json.dumps(TEST_CASES, indent=4)
+with open("test_cases.json", "w") as outfile:
+    outfile.write(TEST_CASES_json)
diff --git a/field/goldilocks/sis/sis_fft.go b/field/goldilocks/sis/sis_fft.go
new file mode 100644
index 0000000000..06691b4c9d
--- /dev/null
+++ b/field/goldilocks/sis/sis_fft.go
@@ -0,0 +1,556 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package sis
+
+import (
+	"github.com/consensys/gnark-crypto/field/goldilocks"
+	"math/big"
+)
+
+// FFT64 is generated by gnark-crypto and contains the unrolled code for FFT (DIF) on 64 elements
+// equivalent code: r.Domain.FFT(k, fft.DIF, fft.OnCoset(), fft.WithNbTasks(1))
+// twiddlesCoset must be pre-computed from twiddles and coset table, see PrecomputeTwiddlesCoset
+func FFT64(a []goldilocks.Element, twiddlesCoset []goldilocks.Element) {
+
+	a[32].Mul(&a[32], &twiddlesCoset[0])
+	a[33].Mul(&a[33], &twiddlesCoset[0])
+	a[34].Mul(&a[34], &twiddlesCoset[0])
+	a[35].Mul(&a[35], &twiddlesCoset[0])
+	a[36].Mul(&a[36], &twiddlesCoset[0])
+	a[37].Mul(&a[37], &twiddlesCoset[0])
+	a[38].Mul(&a[38], &twiddlesCoset[0])
+	a[39].Mul(&a[39], &twiddlesCoset[0])
+	a[40].Mul(&a[40], &twiddlesCoset[0])
+	a[41].Mul(&a[41], &twiddlesCoset[0])
+	a[42].Mul(&a[42], &twiddlesCoset[0])
+	a[43].Mul(&a[43], &twiddlesCoset[0])
+	a[44].Mul(&a[44], &twiddlesCoset[0])
+	a[45].Mul(&a[45], &twiddlesCoset[0])
+	a[46].Mul(&a[46], &twiddlesCoset[0])
+	a[47].Mul(&a[47], &twiddlesCoset[0])
+	a[48].Mul(&a[48], &twiddlesCoset[0])
+	a[49].Mul(&a[49], &twiddlesCoset[0])
+	a[50].Mul(&a[50], &twiddlesCoset[0])
+	a[51].Mul(&a[51], &twiddlesCoset[0])
+	a[52].Mul(&a[52], &twiddlesCoset[0])
+	a[53].Mul(&a[53], &twiddlesCoset[0])
+	a[54].Mul(&a[54], &twiddlesCoset[0])
+	a[55].Mul(&a[55], &twiddlesCoset[0])
+	a[56].Mul(&a[56], &twiddlesCoset[0])
+	a[57].Mul(&a[57], &twiddlesCoset[0])
+	a[58].Mul(&a[58], &twiddlesCoset[0])
+	a[59].Mul(&a[59], &twiddlesCoset[0])
+	a[60].Mul(&a[60], &twiddlesCoset[0])
+	a[61].Mul(&a[61], &twiddlesCoset[0])
+	a[62].Mul(&a[62], &twiddlesCoset[0])
+	a[63].Mul(&a[63], &twiddlesCoset[0])
+	goldilocks.Butterfly(&a[0], &a[32])
+	goldilocks.Butterfly(&a[1], &a[33])
+	goldilocks.Butterfly(&a[2], &a[34])
+	goldilocks.Butterfly(&a[3], &a[35])
+	goldilocks.Butterfly(&a[4], &a[36])
+	goldilocks.Butterfly(&a[5], &a[37])
+	goldilocks.Butterfly(&a[6], &a[38])
+	goldilocks.Butterfly(&a[7], &a[39])
+	goldilocks.Butterfly(&a[8], &a[40])
+	goldilocks.Butterfly(&a[9], &a[41])
+	goldilocks.Butterfly(&a[10], &a[42])
+	goldilocks.Butterfly(&a[11], &a[43])
+	goldilocks.Butterfly(&a[12], &a[44])
+	goldilocks.Butterfly(&a[13], &a[45])
+	goldilocks.Butterfly(&a[14], &a[46])
+	goldilocks.Butterfly(&a[15], &a[47])
+	goldilocks.Butterfly(&a[16], &a[48])
+	goldilocks.Butterfly(&a[17], &a[49])
+	goldilocks.Butterfly(&a[18], &a[50])
+	goldilocks.Butterfly(&a[19], &a[51])
+	goldilocks.Butterfly(&a[20], &a[52])
+	goldilocks.Butterfly(&a[21], &a[53])
+	goldilocks.Butterfly(&a[22], &a[54])
+	goldilocks.Butterfly(&a[23], &a[55])
+	goldilocks.Butterfly(&a[24], &a[56])
+	goldilocks.Butterfly(&a[25], &a[57])
+	goldilocks.Butterfly(&a[26], &a[58])
+	goldilocks.Butterfly(&a[27], &a[59])
+	goldilocks.Butterfly(&a[28], &a[60])
+	goldilocks.Butterfly(&a[29], &a[61])
+	goldilocks.Butterfly(&a[30], &a[62])
+	goldilocks.Butterfly(&a[31], &a[63])
+	a[16].Mul(&a[16], &twiddlesCoset[1])
+	a[17].Mul(&a[17], &twiddlesCoset[1])
+	a[18].Mul(&a[18], &twiddlesCoset[1])
+	a[19].Mul(&a[19], &twiddlesCoset[1])
+	a[20].Mul(&a[20], &twiddlesCoset[1])
+	a[21].Mul(&a[21], &twiddlesCoset[1])
+	a[22].Mul(&a[22], &twiddlesCoset[1])
+	a[23].Mul(&a[23], &twiddlesCoset[1])
+	a[24].Mul(&a[24], &twiddlesCoset[1])
+	a[25].Mul(&a[25], &twiddlesCoset[1])
+	a[26].Mul(&a[26], &twiddlesCoset[1])
+	a[27].Mul(&a[27], &twiddlesCoset[1])
+	a[28].Mul(&a[28], &twiddlesCoset[1])
+	a[29].Mul(&a[29], &twiddlesCoset[1])
+	a[30].Mul(&a[30], &twiddlesCoset[1])
+	a[31].Mul(&a[31], &twiddlesCoset[1])
+	a[48].Mul(&a[48], &twiddlesCoset[2])
+	a[49].Mul(&a[49], &twiddlesCoset[2])
+	a[50].Mul(&a[50], &twiddlesCoset[2])
+	a[51].Mul(&a[51], &twiddlesCoset[2])
+	a[52].Mul(&a[52], &twiddlesCoset[2])
+	a[53].Mul(&a[53], &twiddlesCoset[2])
+	a[54].Mul(&a[54], &twiddlesCoset[2])
+	a[55].Mul(&a[55], &twiddlesCoset[2])
+	a[56].Mul(&a[56], &twiddlesCoset[2])
+	a[57].Mul(&a[57], &twiddlesCoset[2])
+	a[58].Mul(&a[58], &twiddlesCoset[2])
+	a[59].Mul(&a[59], &twiddlesCoset[2])
+	a[60].Mul(&a[60], &twiddlesCoset[2])
+	a[61].Mul(&a[61], &twiddlesCoset[2])
+	a[62].Mul(&a[62], &twiddlesCoset[2])
+	a[63].Mul(&a[63], &twiddlesCoset[2])
+	goldilocks.Butterfly(&a[0], &a[16])
+	goldilocks.Butterfly(&a[1], &a[17])
+	goldilocks.Butterfly(&a[2], &a[18])
+	goldilocks.Butterfly(&a[3], &a[19])
+	goldilocks.Butterfly(&a[4], &a[20])
+	goldilocks.Butterfly(&a[5], &a[21])
+	goldilocks.Butterfly(&a[6], &a[22])
+	goldilocks.Butterfly(&a[7], &a[23])
+	goldilocks.Butterfly(&a[8], &a[24])
+	goldilocks.Butterfly(&a[9], &a[25])
+	goldilocks.Butterfly(&a[10], &a[26])
+	goldilocks.Butterfly(&a[11], &a[27])
+	goldilocks.Butterfly(&a[12], &a[28])
+	goldilocks.Butterfly(&a[13], &a[29])
+	goldilocks.Butterfly(&a[14], &a[30])
+	goldilocks.Butterfly(&a[15], &a[31])
+	goldilocks.Butterfly(&a[32], &a[48])
+	goldilocks.Butterfly(&a[33], &a[49])
+	goldilocks.Butterfly(&a[34], &a[50])
+	goldilocks.Butterfly(&a[35], &a[51])
+	goldilocks.Butterfly(&a[36], &a[52])
+	goldilocks.Butterfly(&a[37], &a[53])
+	goldilocks.Butterfly(&a[38], &a[54])
+	goldilocks.Butterfly(&a[39], &a[55])
+	goldilocks.Butterfly(&a[40], &a[56])
+	goldilocks.Butterfly(&a[41], &a[57])
+	goldilocks.Butterfly(&a[42], &a[58])
+	goldilocks.Butterfly(&a[43], &a[59])
+	goldilocks.Butterfly(&a[44], &a[60])
+	goldilocks.Butterfly(&a[45], &a[61])
+	goldilocks.Butterfly(&a[46], &a[62])
+	goldilocks.Butterfly(&a[47], &a[63])
+	a[8].Mul(&a[8], &twiddlesCoset[3])
+	a[9].Mul(&a[9], &twiddlesCoset[3])
+	a[10].Mul(&a[10], &twiddlesCoset[3])
+	a[11].Mul(&a[11], &twiddlesCoset[3])
+	a[12].Mul(&a[12], &twiddlesCoset[3])
+	a[13].Mul(&a[13], &twiddlesCoset[3])
+	a[14].Mul(&a[14], &twiddlesCoset[3])
+	a[15].Mul(&a[15], &twiddlesCoset[3])
+	a[24].Mul(&a[24], &twiddlesCoset[4])
+	a[25].Mul(&a[25], &twiddlesCoset[4])
+	a[26].Mul(&a[26], &twiddlesCoset[4])
+	a[27].Mul(&a[27], &twiddlesCoset[4])
+	a[28].Mul(&a[28], &twiddlesCoset[4])
+	a[29].Mul(&a[29], &twiddlesCoset[4])
+	a[30].Mul(&a[30], &twiddlesCoset[4])
+	a[31].Mul(&a[31], &twiddlesCoset[4])
+	a[40].Mul(&a[40], &twiddlesCoset[5])
+	a[41].Mul(&a[41], &twiddlesCoset[5])
+	a[42].Mul(&a[42], &twiddlesCoset[5])
+	a[43].Mul(&a[43], &twiddlesCoset[5])
+	a[44].Mul(&a[44], &twiddlesCoset[5])
+	a[45].Mul(&a[45], &twiddlesCoset[5])
+	a[46].Mul(&a[46], &twiddlesCoset[5])
+	a[47].Mul(&a[47], &twiddlesCoset[5])
+	a[56].Mul(&a[56], &twiddlesCoset[6])
+	a[57].Mul(&a[57], &twiddlesCoset[6])
+	a[58].Mul(&a[58], &twiddlesCoset[6])
+	a[59].Mul(&a[59], &twiddlesCoset[6])
+	a[60].Mul(&a[60], &twiddlesCoset[6])
+	a[61].Mul(&a[61], &twiddlesCoset[6])
+	a[62].Mul(&a[62], &twiddlesCoset[6])
+	a[63].Mul(&a[63], &twiddlesCoset[6])
+	goldilocks.Butterfly(&a[0], &a[8])
+	goldilocks.Butterfly(&a[1], &a[9])
+	goldilocks.Butterfly(&a[2], &a[10])
+	goldilocks.Butterfly(&a[3], &a[11])
+	goldilocks.Butterfly(&a[4], &a[12])
+	goldilocks.Butterfly(&a[5], &a[13])
+	goldilocks.Butterfly(&a[6], &a[14])
+	goldilocks.Butterfly(&a[7], &a[15])
+	goldilocks.Butterfly(&a[16], &a[24])
+	goldilocks.Butterfly(&a[17], &a[25])
+	goldilocks.Butterfly(&a[18], &a[26])
+	goldilocks.Butterfly(&a[19], &a[27])
+	goldilocks.Butterfly(&a[20], &a[28])
+	goldilocks.Butterfly(&a[21], &a[29])
+	goldilocks.Butterfly(&a[22], &a[30])
+	goldilocks.Butterfly(&a[23], &a[31])
+	goldilocks.Butterfly(&a[32], &a[40])
+	goldilocks.Butterfly(&a[33], &a[41])
+	goldilocks.Butterfly(&a[34], &a[42])
+	goldilocks.Butterfly(&a[35], &a[43])
+	goldilocks.Butterfly(&a[36], &a[44])
+	goldilocks.Butterfly(&a[37], &a[45])
+	goldilocks.Butterfly(&a[38], &a[46])
+	goldilocks.Butterfly(&a[39], &a[47])
+	goldilocks.Butterfly(&a[48], &a[56])
+	goldilocks.Butterfly(&a[49], &a[57])
+	goldilocks.Butterfly(&a[50], &a[58])
+	goldilocks.Butterfly(&a[51], &a[59])
+	goldilocks.Butterfly(&a[52], &a[60])
+	goldilocks.Butterfly(&a[53], &a[61])
+	goldilocks.Butterfly(&a[54], &a[62])
+	goldilocks.Butterfly(&a[55], &a[63])
+	a[4].Mul(&a[4], &twiddlesCoset[7])
+	a[5].Mul(&a[5], &twiddlesCoset[7])
+	a[6].Mul(&a[6], &twiddlesCoset[7])
+	a[7].Mul(&a[7], &twiddlesCoset[7])
+	a[12].Mul(&a[12], &twiddlesCoset[8])
+	a[13].Mul(&a[13], &twiddlesCoset[8])
+	a[14].Mul(&a[14], &twiddlesCoset[8])
+	a[15].Mul(&a[15], &twiddlesCoset[8])
+	a[20].Mul(&a[20], &twiddlesCoset[9])
+	a[21].Mul(&a[21], &twiddlesCoset[9])
+	a[22].Mul(&a[22], &twiddlesCoset[9])
+	a[23].Mul(&a[23], &twiddlesCoset[9])
+	a[28].Mul(&a[28], &twiddlesCoset[10])
+	a[29].Mul(&a[29], &twiddlesCoset[10])
+	a[30].Mul(&a[30], &twiddlesCoset[10])
+	a[31].Mul(&a[31], &twiddlesCoset[10])
+	a[36].Mul(&a[36], &twiddlesCoset[11])
+	a[37].Mul(&a[37], &twiddlesCoset[11])
+	a[38].Mul(&a[38], &twiddlesCoset[11])
+	a[39].Mul(&a[39], &twiddlesCoset[11])
+	a[44].Mul(&a[44], &twiddlesCoset[12])
+	a[45].Mul(&a[45], &twiddlesCoset[12])
+	a[46].Mul(&a[46], &twiddlesCoset[12])
+	a[47].Mul(&a[47], &twiddlesCoset[12])
+	a[52].Mul(&a[52], &twiddlesCoset[13])
+	a[53].Mul(&a[53], &twiddlesCoset[13])
+	a[54].Mul(&a[54], &twiddlesCoset[13])
+	a[55].Mul(&a[55], &twiddlesCoset[13])
+	a[60].Mul(&a[60], &twiddlesCoset[14])
+	a[61].Mul(&a[61], &twiddlesCoset[14])
+	a[62].Mul(&a[62], &twiddlesCoset[14])
+	a[63].Mul(&a[63], &twiddlesCoset[14])
+	goldilocks.Butterfly(&a[0], &a[4])
+	goldilocks.Butterfly(&a[1], &a[5])
+	goldilocks.Butterfly(&a[2], &a[6])
+	goldilocks.Butterfly(&a[3], &a[7])
+	goldilocks.Butterfly(&a[8], &a[12])
+	goldilocks.Butterfly(&a[9], &a[13])
+	goldilocks.Butterfly(&a[10], &a[14])
+	goldilocks.Butterfly(&a[11], &a[15])
+	goldilocks.Butterfly(&a[16], &a[20])
+	goldilocks.Butterfly(&a[17], &a[21])
+	goldilocks.Butterfly(&a[18], &a[22])
+	goldilocks.Butterfly(&a[19], &a[23])
+	goldilocks.Butterfly(&a[24], &a[28])
+	goldilocks.Butterfly(&a[25], &a[29])
+	goldilocks.Butterfly(&a[26], &a[30])
+	goldilocks.Butterfly(&a[27], &a[31])
+	goldilocks.Butterfly(&a[32], &a[36])
+	goldilocks.Butterfly(&a[33], &a[37])
+	goldilocks.Butterfly(&a[34], &a[38])
+	goldilocks.Butterfly(&a[35], &a[39])
+	goldilocks.Butterfly(&a[40], &a[44])
+	goldilocks.Butterfly(&a[41], &a[45])
+	goldilocks.Butterfly(&a[42], &a[46])
+	goldilocks.Butterfly(&a[43], &a[47])
+	goldilocks.Butterfly(&a[48], &a[52])
+	goldilocks.Butterfly(&a[49], &a[53])
+	goldilocks.Butterfly(&a[50], &a[54])
+	goldilocks.Butterfly(&a[51], &a[55])
+	goldilocks.Butterfly(&a[56], &a[60])
+	goldilocks.Butterfly(&a[57], &a[61])
+	goldilocks.Butterfly(&a[58], &a[62])
+	goldilocks.Butterfly(&a[59], &a[63])
+	a[2].Mul(&a[2], &twiddlesCoset[15])
+	a[3].Mul(&a[3], &twiddlesCoset[15])
+	a[6].Mul(&a[6], &twiddlesCoset[16])
+	a[7].Mul(&a[7], &twiddlesCoset[16])
+	a[10].Mul(&a[10], &twiddlesCoset[17])
+	a[11].Mul(&a[11], &twiddlesCoset[17])
+	a[14].Mul(&a[14], &twiddlesCoset[18])
+	a[15].Mul(&a[15], &twiddlesCoset[18])
+	a[18].Mul(&a[18], &twiddlesCoset[19])
+	a[19].Mul(&a[19], &twiddlesCoset[19])
+	a[22].Mul(&a[22], &twiddlesCoset[20])
+	a[23].Mul(&a[23], &twiddlesCoset[20])
+	a[26].Mul(&a[26], &twiddlesCoset[21])
+	a[27].Mul(&a[27], &twiddlesCoset[21])
+	a[30].Mul(&a[30], &twiddlesCoset[22])
+	a[31].Mul(&a[31], &twiddlesCoset[22])
+	a[34].Mul(&a[34], &twiddlesCoset[23])
+	a[35].Mul(&a[35], &twiddlesCoset[23])
+	a[38].Mul(&a[38], &twiddlesCoset[24])
+	a[39].Mul(&a[39], &twiddlesCoset[24])
+	a[42].Mul(&a[42], &twiddlesCoset[25])
+	a[43].Mul(&a[43], &twiddlesCoset[25])
+	a[46].Mul(&a[46], &twiddlesCoset[26])
+	a[47].Mul(&a[47], &twiddlesCoset[26])
+	a[50].Mul(&a[50], &twiddlesCoset[27])
+	a[51].Mul(&a[51], &twiddlesCoset[27])
+	a[54].Mul(&a[54], &twiddlesCoset[28])
+	a[55].Mul(&a[55], &twiddlesCoset[28])
+	a[58].Mul(&a[58], &twiddlesCoset[29])
+	a[59].Mul(&a[59], &twiddlesCoset[29])
+	a[62].Mul(&a[62], &twiddlesCoset[30])
+	a[63].Mul(&a[63], &twiddlesCoset[30])
+	goldilocks.Butterfly(&a[0], &a[2])
+	goldilocks.Butterfly(&a[1], &a[3])
+	goldilocks.Butterfly(&a[4], &a[6])
+	goldilocks.Butterfly(&a[5], &a[7])
+	goldilocks.Butterfly(&a[8], &a[10])
+	goldilocks.Butterfly(&a[9], &a[11])
+	goldilocks.Butterfly(&a[12], &a[14])
+	goldilocks.Butterfly(&a[13], &a[15])
+	goldilocks.Butterfly(&a[16], &a[18])
+	goldilocks.Butterfly(&a[17], &a[19])
+	goldilocks.Butterfly(&a[20], &a[22])
+	goldilocks.Butterfly(&a[21], &a[23])
+	goldilocks.Butterfly(&a[24], &a[26])
+	goldilocks.Butterfly(&a[25], &a[27])
+	goldilocks.Butterfly(&a[28], &a[30])
+	goldilocks.Butterfly(&a[29], &a[31])
+	goldilocks.Butterfly(&a[32], &a[34])
+	goldilocks.Butterfly(&a[33], &a[35])
+	goldilocks.Butterfly(&a[36], &a[38])
+	goldilocks.Butterfly(&a[37], &a[39])
+	goldilocks.Butterfly(&a[40], &a[42])
+	goldilocks.Butterfly(&a[41], &a[43])
+	goldilocks.Butterfly(&a[44], &a[46])
+	goldilocks.Butterfly(&a[45], &a[47])
+	goldilocks.Butterfly(&a[48], &a[50])
+	goldilocks.Butterfly(&a[49], &a[51])
+	goldilocks.Butterfly(&a[52], &a[54])
+	goldilocks.Butterfly(&a[53], &a[55])
+	goldilocks.Butterfly(&a[56], &a[58])
+	goldilocks.Butterfly(&a[57], &a[59])
+	goldilocks.Butterfly(&a[60], &a[62])
+	goldilocks.Butterfly(&a[61], &a[63])
+	a[1].Mul(&a[1], &twiddlesCoset[31])
+	a[3].Mul(&a[3], &twiddlesCoset[32])
+	a[5].Mul(&a[5], &twiddlesCoset[33])
+	a[7].Mul(&a[7], &twiddlesCoset[34])
+	a[9].Mul(&a[9], &twiddlesCoset[35])
+	a[11].Mul(&a[11], &twiddlesCoset[36])
+	a[13].Mul(&a[13], &twiddlesCoset[37])
+	a[15].Mul(&a[15], &twiddlesCoset[38])
+	a[17].Mul(&a[17], &twiddlesCoset[39])
+	a[19].Mul(&a[19], &twiddlesCoset[40])
+	a[21].Mul(&a[21], &twiddlesCoset[41])
+	a[23].Mul(&a[23], &twiddlesCoset[42])
+	a[25].Mul(&a[25], &twiddlesCoset[43])
+	a[27].Mul(&a[27], &twiddlesCoset[44])
+	a[29].Mul(&a[29], &twiddlesCoset[45])
+	a[31].Mul(&a[31], &twiddlesCoset[46])
+	a[33].Mul(&a[33], &twiddlesCoset[47])
+	a[35].Mul(&a[35], &twiddlesCoset[48])
+	a[37].Mul(&a[37], &twiddlesCoset[49])
+	a[39].Mul(&a[39], &twiddlesCoset[50])
+	a[41].Mul(&a[41], &twiddlesCoset[51])
+	a[43].Mul(&a[43], &twiddlesCoset[52])
+	a[45].Mul(&a[45], &twiddlesCoset[53])
+	a[47].Mul(&a[47], &twiddlesCoset[54])
+	a[49].Mul(&a[49], &twiddlesCoset[55])
+	a[51].Mul(&a[51], &twiddlesCoset[56])
+	a[53].Mul(&a[53], &twiddlesCoset[57])
+	a[55].Mul(&a[55], &twiddlesCoset[58])
+	a[57].Mul(&a[57], &twiddlesCoset[59])
+	a[59].Mul(&a[59], &twiddlesCoset[60])
+	a[61].Mul(&a[61], &twiddlesCoset[61])
+	a[63].Mul(&a[63], &twiddlesCoset[62])
+	goldilocks.Butterfly(&a[0], &a[1])
+	goldilocks.Butterfly(&a[2], &a[3])
+	goldilocks.Butterfly(&a[4], &a[5])
+	goldilocks.Butterfly(&a[6], &a[7])
+	goldilocks.Butterfly(&a[8], &a[9])
+	goldilocks.Butterfly(&a[10], &a[11])
+	goldilocks.Butterfly(&a[12], &a[13])
+	goldilocks.Butterfly(&a[14], &a[15])
+	goldilocks.Butterfly(&a[16], &a[17])
+	goldilocks.Butterfly(&a[18], &a[19])
+	goldilocks.Butterfly(&a[20], &a[21])
+	goldilocks.Butterfly(&a[22], &a[23])
+	goldilocks.Butterfly(&a[24], &a[25])
+	goldilocks.Butterfly(&a[26], &a[27])
+	goldilocks.Butterfly(&a[28], &a[29])
+	goldilocks.Butterfly(&a[30], &a[31])
+	goldilocks.Butterfly(&a[32], &a[33])
+	goldilocks.Butterfly(&a[34], &a[35])
+	goldilocks.Butterfly(&a[36], &a[37])
+	goldilocks.Butterfly(&a[38], &a[39])
+	goldilocks.Butterfly(&a[40], &a[41])
+	goldilocks.Butterfly(&a[42], &a[43])
+	goldilocks.Butterfly(&a[44], &a[45])
+	goldilocks.Butterfly(&a[46], &a[47])
+	goldilocks.Butterfly(&a[48], &a[49])
+	goldilocks.Butterfly(&a[50], &a[51])
+	goldilocks.Butterfly(&a[52], &a[53])
+	goldilocks.Butterfly(&a[54], &a[55])
+	goldilocks.Butterfly(&a[56], &a[57])
+	goldilocks.Butterfly(&a[58], &a[59])
+	goldilocks.Butterfly(&a[60], &a[61])
+	goldilocks.Butterfly(&a[62], &a[63])
+}
+
+// PrecomputeTwiddlesCoset precomputes twiddlesCoset from twiddles and coset table
+// it then return all elements in the correct order for the unrolled FFT.
+func PrecomputeTwiddlesCoset(generator, shifter goldilocks.Element) []goldilocks.Element {
+	toReturn := make([]goldilocks.Element, 63)
+	var r, s goldilocks.Element
+	e := new(big.Int)
+
+	s = shifter
+	for k := 0; k < 5; k++ {
+		s.Square(&s)
+	}
+	toReturn[0] = s
+	s = shifter
+	for k := 0; k < 4; k++ {
+		s.Square(&s)
+	}
+	toReturn[1] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<4*1)))
+	toReturn[2].Mul(&r, &s)
+	s = shifter
+	for k := 0; k < 3; k++ {
+		s.Square(&s)
+	}
+	toReturn[3] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<3*2)))
+	toReturn[4].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<3*1)))
+	toReturn[5].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<3*3)))
+	toReturn[6].Mul(&r, &s)
+	s = shifter
+	for k := 0; k < 2; k++ {
+		s.Square(&s)
+	}
+	toReturn[7] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<2*4)))
+	toReturn[8].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*2)))
+	toReturn[9].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*6)))
+	toReturn[10].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*1)))
+	toReturn[11].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*5)))
+	toReturn[12].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*3)))
+	toReturn[13].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*7)))
+	toReturn[14].Mul(&r, &s)
+	s = shifter
+	for k := 0; k < 1; k++ {
+		s.Square(&s)
+	}
+	toReturn[15] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<1*8)))
+	toReturn[16].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*4)))
+	toReturn[17].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*12)))
+	toReturn[18].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*2)))
+	toReturn[19].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*10)))
+	toReturn[20].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*6)))
+	toReturn[21].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*14)))
+	toReturn[22].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*1)))
+	toReturn[23].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*9)))
+	toReturn[24].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*5)))
+	toReturn[25].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*13)))
+	toReturn[26].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*3)))
+	toReturn[27].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*11)))
+	toReturn[28].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*7)))
+	toReturn[29].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*15)))
+	toReturn[30].Mul(&r, &s)
+	s = shifter
+	for k := 0; k < 0; k++ {
+		s.Square(&s)
+	}
+	toReturn[31] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<0*16)))
+	toReturn[32].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*8)))
+	toReturn[33].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*24)))
+	toReturn[34].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*4)))
+	toReturn[35].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*20)))
+	toReturn[36].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*12)))
+	toReturn[37].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*28)))
+	toReturn[38].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*2)))
+	toReturn[39].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*18)))
+	toReturn[40].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*10)))
+	toReturn[41].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*26)))
+	toReturn[42].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*6)))
+	toReturn[43].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*22)))
+	toReturn[44].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*14)))
+	toReturn[45].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*30)))
+	toReturn[46].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*1)))
+	toReturn[47].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*17)))
+	toReturn[48].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*9)))
+	toReturn[49].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*25)))
+	toReturn[50].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*5)))
+	toReturn[51].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*21)))
+	toReturn[52].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*13)))
+	toReturn[53].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*29)))
+	toReturn[54].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*3)))
+	toReturn[55].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*19)))
+	toReturn[56].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*11)))
+	toReturn[57].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*27)))
+	toReturn[58].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*7)))
+	toReturn[59].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*23)))
+	toReturn[60].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*15)))
+	toReturn[61].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*31)))
+	toReturn[62].Mul(&r, &s)
+	return toReturn
+}
diff --git a/field/goldilocks/sis/sis_test.go b/field/goldilocks/sis/sis_test.go
new file mode 100644
index 0000000000..ad7c2dc7ac
--- /dev/null
+++ b/field/goldilocks/sis/sis_test.go
@@ -0,0 +1,488 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package sis
+
+import (
+	"bytes"
+	"crypto/rand"
+	"encoding/binary"
+	"encoding/json"
+	"fmt"
+	"io"
+	"math/big"
+	"math/bits"
+	"os"
+	"testing"
+	"time"
+
+	"github.com/bits-and-blooms/bitset"
+	"github.com/consensys/gnark-crypto/field/goldilocks"
+	"github.com/consensys/gnark-crypto/field/goldilocks/fft"
+	"github.com/stretchr/testify/require"
+)
+
+type sisParams struct {
+	logTwoBound, logTwoDegree int
+}
+
+var params128Bits []sisParams = []sisParams{
+	{logTwoBound: 2, logTwoDegree: 3},
+	{logTwoBound: 4, logTwoDegree: 4},
+	{logTwoBound: 6, logTwoDegree: 5},
+	{logTwoBound: 8, logTwoDegree: 6},
+	{logTwoBound: 10, logTwoDegree: 6},
+	{logTwoBound: 16, logTwoDegree: 7},
+	{logTwoBound: 32, logTwoDegree: 8},
+}
+
+type TestCases struct {
+	Inputs  []goldilocks.Element `json:"inputs"`
+	Entries []struct {
+		Params struct {
+			Seed                int64 `json:"seed"`
+			LogTwoDegree        int   `json:"logTwoDegree"`
+			LogTwoBound         int   `json:"logTwoBound"`
+			MaxNbElementsToHash int   `json:"maxNbElementsToHash"`
+		} `json:"params"`
+		Expected []goldilocks.Element `json:"expected"`
+	} `json:"entries"`
+}
+
+func TestReference(t *testing.T) {
+	if bits.UintSize == 32 {
+		t.Skip("skipping this test in 32bit.")
+	}
+	assert := require.New(t)
+
+	// read the test case file
+	var testCases TestCases
+	data, err := os.ReadFile("test_cases.json")
+	assert.NoError(err, "reading test cases failed")
+	err = json.Unmarshal(data, &testCases)
+	assert.NoError(err, "reading test cases failed")
+
+	inputs := testCases.Inputs
+
+	for testCaseID, testCase := range testCases.Entries {
+
+		// create the SIS instance
+		sis, err := NewRSis(testCase.Params.Seed, testCase.Params.LogTwoDegree, testCase.Params.LogTwoBound, testCase.Params.MaxNbElementsToHash)
+		assert.NoError(err)
+
+		// key generation same than in sage
+		makeKeyDeterministic(t, sis, testCase.Params.Seed)
+
+		sis.Reset()
+
+		// hash test case entry input and compare with expected (computed by sage)
+		goHash, err := sis.Hash(inputs)
+		assert.NoError(err)
+
+		assert.EqualValues(
+			testCase.Expected, goHash,
+			"mismatch between reference test and computed value (testcase %v)",
+			testCaseID,
+		)
+
+	}
+
+}
+
+func TestLimbDecomposeBytesMiddleBound(t *testing.T) {
+
+	var montConstant goldilocks.Element
+	var bMontConstant big.Int
+	bMontConstant.SetUint64(1)
+	bMontConstant.Lsh(&bMontConstant, goldilocks.Bytes*8)
+	montConstant.SetBigInt(&bMontConstant)
+
+	nbElmts := 10
+	a := make([]goldilocks.Element, nbElmts)
+	for i := 0; i < nbElmts; i++ {
+		a[i].SetUint64(33)
+	}
+	var buf bytes.Buffer
+	for i := 0; i < nbElmts; i++ {
+		buf.Write(a[i].Marshal())
+	}
+
+	logTwoBound := 8
+
+	for cc := 0; cc < 3; cc++ {
+		m := make(goldilocks.Vector, nbElmts*goldilocks.Bytes*8/logTwoBound)
+		limbDecomposeBytesMiddleBound(buf.Bytes(), m, logTwoBound, 4, nil)
+
+		for i := 0; i < len(m); i++ {
+			m[i].Mul(&m[i], &montConstant)
+		}
+
+		var x goldilocks.Element
+		x.SetUint64(1 << logTwoBound)
+
+		coeffsPerFieldsElmt := goldilocks.Bytes * 8 / logTwoBound
+		for i := 0; i < nbElmts; i++ {
+			r := eval(m[i*coeffsPerFieldsElmt:(i+1)*coeffsPerFieldsElmt], x)
+			if !r.Equal(&a[i]) {
+				t.Fatal("limbDecomposeBytes failed")
+			}
+		}
+		logTwoBound *= 2
+	}
+
+}
+
+func TestLimbDecomposeBytesSmallBound(t *testing.T) {
+
+	var montConstant goldilocks.Element
+	var bMontConstant big.Int
+	bMontConstant.SetUint64(1)
+	bMontConstant.Lsh(&bMontConstant, goldilocks.Bytes*8)
+	montConstant.SetBigInt(&bMontConstant)
+
+	nbElmts := 10
+	a := make([]goldilocks.Element, nbElmts)
+	for i := 0; i < nbElmts; i++ {
+		a[i].SetRandom()
+	}
+	var buf bytes.Buffer
+	for i := 0; i < nbElmts; i++ {
+		buf.Write(a[i].Marshal())
+	}
+
+	logTwoBound := 2
+
+	for cc := 0; cc < 3; cc++ {
+
+		m := make(goldilocks.Vector, nbElmts*goldilocks.Bytes*8/logTwoBound)
+		m2 := make(goldilocks.Vector, nbElmts*goldilocks.Bytes*8/logTwoBound)
+
+		// the limbs are set as is, they are NOT converted in Montgomery form
+		limbDecomposeBytes(buf.Bytes(), m, logTwoBound, 4, nil)
+		limbDecomposeBytesSmallBound(buf.Bytes(), m2, logTwoBound, 4, nil)
+
+		for i := 0; i < len(m); i++ {
+			m[i].Mul(&m[i], &montConstant)
+			m2[i].Mul(&m2[i], &montConstant)
+		}
+		var x goldilocks.Element
+		x.SetUint64(1 << logTwoBound)
+
+		coeffsPerFieldsElmt := goldilocks.Bytes * 8 / logTwoBound
+		for i := 0; i < nbElmts; i++ {
+			r := eval(m[i*coeffsPerFieldsElmt:(i+1)*coeffsPerFieldsElmt], x)
+			if !r.Equal(&a[i]) {
+				t.Fatal("limbDecomposeBytes failed")
+			}
+			r = eval(m2[i*coeffsPerFieldsElmt:(i+1)*coeffsPerFieldsElmt], x)
+			if !r.Equal(&a[i]) {
+				t.Fatal("limbDecomposeBytesSmallBound failed")
+			}
+		}
+		logTwoBound *= 2
+	}
+
+}
+
+func eval(p []goldilocks.Element, x goldilocks.Element) goldilocks.Element {
+	var res goldilocks.Element
+	for i := len(p) - 1; i >= 0; i-- {
+		res.Mul(&res, &x).Add(&res, &p[i])
+	}
+	return res
+}
+
+func TestMulMod(t *testing.T) {
+
+	size := 4
+
+	p := make([]goldilocks.Element, size)
+	q := make([]goldilocks.Element, size)
+	pCopy := make([]goldilocks.Element, size)
+	qCopy := make([]goldilocks.Element, size)
+	for i := 0; i < size; i++ {
+		p[i].SetRandom()
+		pCopy[i].Set(&p[i])
+		q[i].SetRandom()
+		qCopy[i].Set(&q[i])
+	}
+
+	// creation of the domain
+	shift, err := goldilocks.Generator(uint64(2 * size))
+	if err != nil {
+		t.Fatal(err)
+	}
+	var g goldilocks.Element
+	g.Square(&shift)
+	domain := fft.NewDomain(uint64(size), fft.WithShift(shift))
+
+	// mul mod
+	domain.FFT(p, fft.DIF, fft.OnCoset())
+	domain.FFT(q, fft.DIF, fft.OnCoset())
+	r := mulMod(p, q)
+	domain.FFTInverse(r, fft.DIT, fft.OnCoset())
+
+	// manually check the product on the zeroes of X^4+1
+	for i := 0; i < 4; i++ {
+		u := eval(pCopy, shift)
+		v := eval(qCopy, shift)
+		w := eval(r, shift)
+		u.Mul(&u, &v)
+		if !w.Equal(&u) {
+			t.Fatal("mul mol failed")
+		}
+		shift.Mul(&shift, &g)
+	}
+
+}
+
+func makeKeyDeterministic(t *testing.T, sis *RSis, _seed int64) {
+	t.Helper()
+	// generate the key deterministically, the same way
+	// we do in sage to generate the test vectors.
+
+	polyRand := func(seed goldilocks.Element, deg int) []goldilocks.Element {
+		res := make([]goldilocks.Element, deg)
+		for i := 0; i < deg; i++ {
+			res[i].Square(&seed)
+			seed.Set(&res[i])
+		}
+		return res
+	}
+
+	var seed, one goldilocks.Element
+	one.SetOne()
+	seed.SetInt64(_seed)
+	for i := 0; i < len(sis.A); i++ {
+		sis.A[i] = polyRand(seed, sis.Degree)
+		copy(sis.Ag[i], sis.A[i])
+		sis.Domain.FFT(sis.Ag[i], fft.DIF, fft.OnCoset())
+		seed.Add(&seed, &one)
+	}
+}
+
+const (
+	LATENCY_MUL_FIELD_NS int = 18
+	LATENCY_ADD_FIELD_NS int = 4
+)
+
+// Estimate the theoretical performances that are achievable using ring-SIS
+// operations. The time is obtained by counting the number of additions and
+// multiplications occurring in the computation. This does not account for the
+// possibilities to use SIMD instructions or for cache-locality issues. Thus, it
+// does not represents a maximum even though it returns a good idea of what is
+// achievable . This returns performances in term of ns/field. This also does not
+// account for the time taken for "limb-splitting" the input.
+func estimateSisTheory(p sisParams) float64 {
+
+	// Since the FFT occurs over a coset, we need to multiply all the coefficients
+	// of the input by some coset factors (for an entire polynomial)
+	timeCosetShift := (1 << p.logTwoDegree) * LATENCY_MUL_FIELD_NS
+
+	// The two additions are from the butterfly, and the multiplication represents
+	// the one by the twiddle. (for an entire polynomial)
+	timeFFT := (1 << p.logTwoDegree) * p.logTwoDegree * (2*LATENCY_ADD_FIELD_NS + LATENCY_MUL_FIELD_NS)
+
+	// Time taken to multiply by the key and accumulate (for an entire polynomial)
+	timeMulAddKey := (1 << p.logTwoDegree) * (LATENCY_MUL_FIELD_NS + LATENCY_ADD_FIELD_NS)
+
+	// Total computation time for an entire polynomial
+	totalTimePoly := timeCosetShift + timeFFT + timeMulAddKey
+
+	// Convert this into a time per input field
+	r := totalTimePoly * goldilocks.Bits / p.logTwoBound / (1 << p.logTwoDegree)
+	return float64(r)
+}
+
+func BenchmarkDecomposition(b *testing.B) {
+
+	nbElmts := 1000
+	a := make([]goldilocks.Element, nbElmts)
+	for i := 0; i < nbElmts; i++ {
+		a[i].SetRandom()
+	}
+	var buf bytes.Buffer
+	for i := 0; i < nbElmts; i++ {
+		buf.Write(a[i].Marshal())
+	}
+	logTwoBound := 4
+	m := make(goldilocks.Vector, nbElmts*goldilocks.Bytes*8/logTwoBound)
+
+	b.Run(fmt.Sprintf("limbDecomposeBytes logTwoBound=%d", logTwoBound), func(b *testing.B) {
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			limbDecomposeBytes(buf.Bytes(), m, logTwoBound, 4, nil)
+		}
+	})
+
+	b.Run(fmt.Sprintf("limbDecomposeByteSmallBound logTwoBound=%d", logTwoBound), func(b *testing.B) {
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			limbDecomposeBytesSmallBound(buf.Bytes(), m, logTwoBound, 4, nil)
+		}
+	})
+
+	logTwoBound = 16
+	b.Run(fmt.Sprintf("limbDecomposeBytes logTwoBound=%d", logTwoBound), func(b *testing.B) {
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			limbDecomposeBytes(buf.Bytes(), m, logTwoBound, 4, nil)
+		}
+	})
+
+	b.Run(fmt.Sprintf("limbDecomposeByteSmallBound logTwoBound=%d", logTwoBound), func(b *testing.B) {
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			limbDecomposeBytesMiddleBound(buf.Bytes(), m, logTwoBound, 4, nil)
+		}
+	})
+
+}
+
+func BenchmarkSIS(b *testing.B) {
+
+	// max nb field elements to hash
+	const nbInputs = 1 << 16
+
+	// Assign the input with random bytes. In practice, theses bytes encodes
+	// a string of field element. It would be more meaningful to take a slice
+	// of field element directly because otherwise the conversion time is not
+	// accounted for in the benchmark.
+	inputs := make(goldilocks.Vector, nbInputs)
+	for i := 0; i < len(inputs); i++ {
+		inputs[i].SetRandom()
+	}
+
+	for _, param := range params128Bits {
+		for n := 1 << 10; n <= nbInputs; n <<= 1 {
+			in := inputs[:n]
+			benchmarkSIS(b, in, false, param.logTwoBound, param.logTwoDegree, estimateSisTheory(param))
+		}
+
+	}
+}
+
+func benchmarkSIS(b *testing.B, input []goldilocks.Element, sparse bool, logTwoBound, logTwoDegree int, theoretical float64) {
+	b.Helper()
+
+	n := len(input)
+
+	benchName := "ring-sis/"
+	if sparse {
+		benchName += "sparse/"
+	}
+	benchName += fmt.Sprintf("inputs=%v/log2-bound=%v/log2-degree=%v", n, logTwoBound, logTwoDegree)
+
+	b.Run(benchName, func(b *testing.B) {
+		instance, err := NewRSis(0, logTwoDegree, logTwoBound, n)
+		if err != nil {
+			b.Fatal(err)
+		}
+
+		// We introduce a custom metric which is the time per field element
+		// Since the benchmark object allows to report extra meta but does
+		// not allow accessing them. We measure the time ourself.
+
+		startTime := time.Now()
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			_, err = instance.Hash(input)
+			if err != nil {
+				b.Fatal(err)
+			}
+		}
+		b.StopTimer()
+
+		totalDuration := time.Since(startTime)
+		nsPerField := totalDuration.Nanoseconds() / int64(b.N) / int64(n)
+
+		b.ReportMetric(float64(nsPerField), "ns/field")
+
+		b.ReportMetric(theoretical, "ns/field(theory)")
+
+	})
+}
+
+// Hash interprets the input vector as a sequence of coefficients of size r.LogTwoBound bits long,
+// and return the hash of the polynomial corresponding to the sum sum_i A[i]*m Mod X^{d}+1
+//
+// It is equivalent to calling r.Write(element.Marshal()); outBytes = r.Sum(nil);
+// ! note @gbotrel: this is a place holder, may not make sense
+func (r *RSis) Hash(v []goldilocks.Element) ([]goldilocks.Element, error) {
+	if len(v) > r.maxNbElementsToHash {
+		return nil, fmt.Errorf("can't hash more than %d elements with params provided in constructor", r.maxNbElementsToHash)
+	}
+
+	r.Reset()
+	for _, e := range v {
+		r.Write(e.Marshal())
+	}
+	sum := r.Sum(nil)
+	var rlen [4]byte
+	binary.BigEndian.PutUint32(rlen[:], uint32(len(sum)/goldilocks.Bytes))
+	reader := io.MultiReader(bytes.NewReader(rlen[:]), bytes.NewReader(sum))
+	var result goldilocks.Vector
+	_, err := result.ReadFrom(reader)
+	if err != nil {
+		return nil, err
+	}
+	return result, nil
+}
+
+func TestLimbDecompositionFastPath(t *testing.T) {
+	assert := require.New(t)
+
+	for size := goldilocks.Bytes; size < 5*goldilocks.Bytes; size += goldilocks.Bytes {
+		// Test the fast path of limbDecomposeBytes8_64
+		buf := make([]byte, size)
+		m := make([]goldilocks.Element, size)
+		mValues := bitset.New(uint(size))
+		n := make([]goldilocks.Element, size)
+		nValues := bitset.New(uint(size))
+
+		// Generate a random buffer
+		_, err := rand.Read(buf)
+		assert.NoError(err)
+
+		limbDecomposeBytes8_64(buf, m, mValues)
+		limbDecomposeBytes(buf, n, 8, 64, nValues)
+
+		for i := 0; i < size; i++ {
+			assert.Equal(mValues.Test(uint(i)), nValues.Test(uint(i)))
+			assert.True(m[i].Equal(&n[i]))
+		}
+	}
+
+}
+
+func TestUnrolledFFT(t *testing.T) {
+
+	var shift goldilocks.Element
+	shift.SetRandom()
+
+	const size = 64
+	assert := require.New(t)
+	domain := fft.NewDomain(size, fft.WithShift(shift))
+
+	k1 := make([]goldilocks.Element, size)
+	for i := 0; i < size; i++ {
+		k1[i].SetRandom()
+	}
+	k2 := make([]goldilocks.Element, size)
+	copy(k2, k1)
+
+	// default FFT
+	domain.FFT(k1, fft.DIF, fft.OnCoset(), fft.WithNbTasks(1))
+
+	// unrolled FFT
+	twiddlesCoset := PrecomputeTwiddlesCoset(domain.Generator, domain.FrMultiplicativeGen)
+	FFT64(k2, twiddlesCoset)
+
+	// compare results
+	for i := 0; i < size; i++ {
+		// fmt.Printf("i = %d, k1 = %v, k2 = %v\n", i, k1[i].String(), k2[i].String())
+		assert.True(k1[i].Equal(&k2[i]), "i = %d", i)
+	}
+}
diff --git a/field/goldilocks/sis/test_cases.json b/field/goldilocks/sis/test_cases.json
new file mode 100644
index 0000000000..604bf3b16d
--- /dev/null
+++ b/field/goldilocks/sis/test_cases.json
@@ -0,0 +1,86 @@
+{
+    "inputs": [
+        "5", 
+        "25", 
+        "125", 
+        "625", 
+        "3125", 
+        "15625", 
+        "78125", 
+        "390625", 
+        "1953125", 
+        "9765625"
+    ], 
+    "entries": [
+        {
+            "expected": [
+                "14292815897629737005", 
+                "14412331386882095654", 
+                "4765275140261239004", 
+                "18446467110636878855"
+            ], 
+            "params": {
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 2
+            }
+        }, 
+        {
+            "expected": [
+                "6136719466656174339", 
+                "10677685852493372570", 
+                "10609649644101265204", 
+                "13138416660811125021"
+            ], 
+            "params": {
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 4
+            }
+        }, 
+        {
+            "expected": [
+                "1469278791547763826", 
+                "13102782547626544571", 
+                "5716962054955342095", 
+                "13145028471706541345"
+            ], 
+            "params": {
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 8
+            }
+        }, 
+        {
+            "expected": [
+                "16998801099365187301", 
+                "4701872446083432449", 
+                "5552874848046302376", 
+                "17206722168184702101"
+            ], 
+            "params": {
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 16
+            }
+        }, 
+        {
+            "expected": [
+                "17921074088525069217", 
+                "4993238238686835368", 
+                "146008809091911085", 
+                "11703400074969462255"
+            ], 
+            "params": {
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 32
+            }
+        }
+    ]
+}
\ No newline at end of file
diff --git a/field/internal/main.go b/field/internal/main.go
index d2dcc7294f..46412585eb 100644
--- a/field/internal/main.go
+++ b/field/internal/main.go
@@ -34,6 +34,7 @@ func main() {
 		if err := generator.GenerateFF(fc, filepath.Join("..", f.name),
 			generator.WithASM(&config.Assembly{BuildDir: asmDirIncludePath, IncludeDir: asmDirIncludePath}),
 			generator.WithFFT(&config.FFT{}), // TODO @gbotrel
+			generator.WithSIS(),
 		); err != nil {
 			panic(err)
 		}
diff --git a/field/koalabear/sis/sis.go b/field/koalabear/sis/sis.go
new file mode 100644
index 0000000000..a58727b547
--- /dev/null
+++ b/field/koalabear/sis/sis.go
@@ -0,0 +1,468 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package sis
+
+import (
+	"bytes"
+	"encoding/binary"
+	"errors"
+	"hash"
+	"math/bits"
+
+	"github.com/bits-and-blooms/bitset"
+	"github.com/consensys/gnark-crypto/field/koalabear"
+	"github.com/consensys/gnark-crypto/field/koalabear/fft"
+	"github.com/consensys/gnark-crypto/internal/parallel"
+	"golang.org/x/crypto/blake2b"
+)
+
+var (
+	ErrNotAPowerOfTwo = errors.New("d must be a power of 2")
+)
+
+// Ring-SIS instance
+type RSis struct {
+
+	// buffer storing the data to hash
+	buffer bytes.Buffer
+
+	// Vectors in ℤ_{p}/Xⁿ+1
+	// A[i] is the i-th polynomial.
+	// Ag the evaluation form of the polynomials in A on the coset √(g) * <g>
+	A  [][]koalabear.Element
+	Ag [][]koalabear.Element
+
+	// LogTwoBound (Infinity norm) of the vector to hash. It means that each component in m
+	// is < 2^B, where m is the vector to hash (the hash being A*m).
+	// cf https://hackmd.io/7OODKWQZRRW9RxM5BaXtIw , B >= 3.
+	LogTwoBound int
+
+	// domain for the polynomial multiplication
+	Domain        *fft.Domain
+	twiddleCosets []koalabear.Element // see FFT64 and precomputeTwiddlesCoset
+
+	// d, the degree of X^{d}+1
+	Degree int
+
+	// in bytes, represents the maximum number of bytes the .Write(...) will handle;
+	// ( maximum number of bytes to sum )
+	capacity            int
+	maxNbElementsToHash int
+
+	// allocate memory once per instance (used in Sum())
+	bufM, bufRes koalabear.Vector
+	bufMValues   *bitset.BitSet
+}
+
+// NewRSis creates an instance of RSis.
+// seed: seed for the randomness for generating A.
+// logTwoDegree: if d := logTwoDegree, the ring will be ℤ_{p}[X]/Xᵈ-1, where X^{2ᵈ} is the 2ᵈ⁺¹-th cyclotomic polynomial
+// logTwoBound: the bound of the vector to hash (using the infinity norm).
+// maxNbElementsToHash: maximum number of field elements the instance handles
+// used to derived n, the number of polynomials in A, and max size of instance's internal buffer.
+func NewRSis(seed int64, logTwoDegree, logTwoBound, maxNbElementsToHash int) (*RSis, error) {
+
+	if logTwoBound > 64 {
+		return nil, errors.New("logTwoBound too large")
+	}
+	if bits.UintSize == 32 {
+		return nil, errors.New("unsupported architecture; need 64bit target")
+	}
+
+	degree := 1 << logTwoDegree
+	capacity := maxNbElementsToHash * koalabear.Bytes
+
+	// n: number of polynomials in A
+	// len(m) == degree * n
+	// with each element in m being logTwoBounds bits from the instance buffer.
+	// that is, to fill m, we need [degree * n * logTwoBound] bits of data
+	// capacity == [degree * n * logTwoBound] / 8
+	// n == (capacity*8)/(degree*logTwoBound)
+
+	// First n <- #limbs to represent a single field element
+	n := (koalabear.Bytes * 8) / logTwoBound
+	if n*logTwoBound < koalabear.Bytes*8 {
+		n++
+	}
+
+	// Then multiply by the number of field elements
+	n *= maxNbElementsToHash
+
+	// And divide (+ ceil) to get the number of polynomials
+	if n%degree == 0 {
+		n /= degree
+	} else {
+		n /= degree // number of polynomials
+		n++
+	}
+
+	// domains (shift is √{gen} )
+	shift, err := koalabear.Generator(uint64(2 * degree))
+	if err != nil {
+		return nil, err
+	}
+
+	r := &RSis{
+		LogTwoBound:         logTwoBound,
+		capacity:            capacity,
+		Degree:              degree,
+		Domain:              fft.NewDomain(uint64(degree), fft.WithShift(shift)),
+		A:                   make([][]koalabear.Element, n),
+		Ag:                  make([][]koalabear.Element, n),
+		bufM:                make(koalabear.Vector, degree*n),
+		bufRes:              make(koalabear.Vector, degree),
+		bufMValues:          bitset.New(uint(n)),
+		maxNbElementsToHash: maxNbElementsToHash,
+	}
+	if r.LogTwoBound == 8 && r.Degree == 64 {
+		// TODO @gbotrel fixme, that's dirty.
+		r.twiddleCosets = PrecomputeTwiddlesCoset(r.Domain.Generator, r.Domain.FrMultiplicativeGen)
+	}
+
+	// filling A
+	a := make([]koalabear.Element, n*r.Degree)
+	ag := make([]koalabear.Element, n*r.Degree)
+
+	parallel.Execute(n, func(start, end int) {
+		var buf bytes.Buffer
+		for i := start; i < end; i++ {
+			rstart, rend := i*r.Degree, (i+1)*r.Degree
+			r.A[i] = a[rstart:rend:rend]
+			r.Ag[i] = ag[rstart:rend:rend]
+			for j := 0; j < r.Degree; j++ {
+				r.A[i][j] = genRandom(seed, int64(i), int64(j), &buf)
+			}
+
+			// fill Ag the evaluation form of the polynomials in A on the coset √(g) * <g>
+			copy(r.Ag[i], r.A[i])
+			r.Domain.FFT(r.Ag[i], fft.DIF, fft.OnCoset())
+		}
+	})
+
+	return r, nil
+}
+
+func (r *RSis) Write(p []byte) (n int, err error) {
+	r.buffer.Write(p)
+	return len(p), nil
+}
+
+// Sum appends the current hash to b and returns the resulting slice.
+// It does not change the underlying hash state.
+// The instance buffer is interpreted as a sequence of coefficients of size r.Bound bits long.
+// The function returns the hash of the polynomial as a a sequence []koalabear.Elements, interpreted as []bytes,
+// corresponding to sum_i A[i]*m Mod X^{d}+1
+func (r *RSis) Sum(b []byte) []byte {
+	buf := r.buffer.Bytes()
+	if len(buf) > r.capacity {
+		panic("buffer too large")
+	}
+
+	fastPath := r.LogTwoBound == 8 && r.Degree == 64
+
+	// clear the buffers of the instance.
+	defer r.cleanupBuffers()
+
+	m := r.bufM
+	mValues := r.bufMValues
+
+	if r.LogTwoBound < 8 && (8%r.LogTwoBound == 0) {
+		limbDecomposeBytesSmallBound(buf, m, r.LogTwoBound, r.Degree, mValues)
+	} else if r.LogTwoBound >= 8 && (koalabear.Bytes*8)%r.LogTwoBound == 0 {
+		limbDecomposeBytesMiddleBound(buf, m, r.LogTwoBound, r.Degree, mValues)
+	} else {
+		limbDecomposeBytes(buf, m, r.LogTwoBound, r.Degree, mValues)
+	}
+
+	// we can hash now.
+	res := r.bufRes
+
+	// method 1: fft
+	for i := 0; i < len(r.Ag); i++ {
+		if !mValues.Test(uint(i)) {
+			// means m[i*r.Degree : (i+1)*r.Degree] == [0...0]
+			// we can skip this, FFT(0) = 0
+			continue
+		}
+		k := m[i*r.Degree : (i+1)*r.Degree]
+		if fastPath {
+			// fast path.
+			FFT64(k, r.twiddleCosets)
+		} else {
+			r.Domain.FFT(k, fft.DIF, fft.OnCoset(), fft.WithNbTasks(1))
+		}
+		mulModAcc(res, r.Ag[i], k)
+	}
+	r.Domain.FFTInverse(res, fft.DIT, fft.OnCoset(), fft.WithNbTasks(1)) // -> reduces mod Xᵈ+1
+
+	resBytes, err := res.MarshalBinary()
+	if err != nil {
+		panic(err)
+	}
+
+	return append(b, resBytes[4:]...) // first 4 bytes are uint32(len(res))
+}
+
+// Reset resets the Hash to its initial state.
+func (r *RSis) Reset() {
+	r.buffer.Reset()
+}
+
+// Size returns the number of bytes Sum will return.
+func (r *RSis) Size() int {
+
+	// The size in bits is the size in bits of a polynomial in A.
+	degree := len(r.A[0])
+	totalSize := degree * koalabear.Modulus().BitLen() / 8
+
+	return totalSize
+}
+
+// BlockSize returns the hash's underlying block size.
+// The Write method must be able to accept any amount
+// of data, but it may operate more efficiently if all writes
+// are a multiple of the block size.
+func (r *RSis) BlockSize() int {
+	return 0
+}
+
+// Construct a hasher generator. It takes as input the same parameters
+// as `NewRingSIS` and outputs a function which returns fresh hasher
+// everytime it is called
+func NewRingSISMaker(seed int64, logTwoDegree, logTwoBound, maxNbElementsToHash int) (func() hash.Hash, error) {
+	return func() hash.Hash {
+		h, err := NewRSis(seed, logTwoDegree, logTwoBound, maxNbElementsToHash)
+		if err != nil {
+			panic(err)
+		}
+		return h
+	}, nil
+
+}
+
+func genRandom(seed, i, j int64, buf *bytes.Buffer) koalabear.Element {
+
+	buf.Reset()
+	buf.WriteString("SIS")
+	binary.Write(buf, binary.BigEndian, seed)
+	binary.Write(buf, binary.BigEndian, i)
+	binary.Write(buf, binary.BigEndian, j)
+
+	digest := blake2b.Sum256(buf.Bytes())
+
+	var res koalabear.Element
+	res.SetBytes(digest[:])
+
+	return res
+}
+
+// mulMod computes p * q in ℤ_{p}[X]/Xᵈ+1.
+// Is assumed that pLagrangeShifted and qLagrangeShifted are of the correct sizes
+// and that they are in evaluation form on √(g) * <g>
+// The result is not FFTinversed. The fft inverse is done once every
+// multiplications are done.
+func mulMod(pLagrangeCosetBitReversed, qLagrangeCosetBitReversed []koalabear.Element) []koalabear.Element {
+
+	res := make([]koalabear.Element, len(pLagrangeCosetBitReversed))
+	for i := 0; i < len(pLagrangeCosetBitReversed); i++ {
+		res[i].Mul(&pLagrangeCosetBitReversed[i], &qLagrangeCosetBitReversed[i])
+	}
+
+	// NOT fft inv for now, wait until every part of the keys have been multiplied
+	// r.Domain.FFTInverse(res, fft.DIT, true)
+
+	return res
+
+}
+
+// mulMod + accumulate in res.
+func mulModAcc(res []koalabear.Element, pLagrangeCosetBitReversed, qLagrangeCosetBitReversed []koalabear.Element) {
+	var t koalabear.Element
+	for i := 0; i < len(pLagrangeCosetBitReversed); i++ {
+		t.Mul(&pLagrangeCosetBitReversed[i], &qLagrangeCosetBitReversed[i])
+		res[i].Add(&res[i], &t)
+	}
+}
+
+// Returns a clone of the RSis parameters with a fresh and empty buffer. Does not
+// mutate the current instance. The keys and the public parameters of the SIS
+// instance are not deep-copied. It is useful when we want to hash in parallel.
+// Otherwise, we would have to generate an entire RSis for each thread.
+func (r *RSis) CopyWithFreshBuffer() RSis {
+	res := *r
+	res.buffer = bytes.Buffer{}
+	res.bufM = make(koalabear.Vector, len(r.bufM))
+	res.bufMValues = bitset.New(r.bufMValues.Len())
+	res.bufRes = make(koalabear.Vector, len(r.bufRes))
+	return res
+}
+
+// Cleanup the buffers of the RSis instance
+func (r *RSis) cleanupBuffers() {
+	r.bufMValues.ClearAll()
+	for i := 0; i < len(r.bufM); i++ {
+		r.bufM[i].SetZero()
+	}
+	for i := 0; i < len(r.bufRes); i++ {
+		r.bufRes[i].SetZero()
+	}
+}
+
+// Split an slice of bytes representing an array of serialized field element in
+// big-endian form into an array of limbs representing the same field elements
+// in little-endian form. Namely, if our field is represented with 64 bits and we
+// have the following field element 0x0123456789abcdef (0 being the most significant
+// character and and f being the least significant one) and our log norm bound is
+// 16 (so 1 hex character = 1 limb). The function assigns the values of m to [f, e,
+// d, c, b, a, ..., 3, 2, 1, 0]. m should be preallocated and zeroized. Additionally,
+// we have the guarantee that 2 bits contributing to different field elements cannot
+// be part of the same limb.
+func LimbDecomposeBytes(buf []byte, m koalabear.Vector, logTwoBound int) {
+	limbDecomposeBytes(buf, m, logTwoBound, 0, nil)
+}
+
+// decomposes m as by taking chunks of logTwoBound bits at a time. The buffer is interpreted like this:
+// [0xa,        ..            , 0x1 | 0xa ... ]
+//
+//	<- #bytes in a field element ->
+//	<-0xa is the MSB, 0x1 the LSB->
+//	<-we read this chunk from right
+//	   			to left 	 	 ->
+//
+// This function is called when logTwoBound divides the number of bits used to represent a
+// koalabear element.
+// From a slice of field elements m:=[a_0, a_1, ...]
+// Doing h.Sum(h.Write([Marshal[a_i] for i in len(m)])) is the same than
+// writing the a_i in little endian, and then taking logTwoBound bits at a time.
+//
+// ex: m := [0x1, 0x3]
+// in the hash buffer, it is interpreted like that as a stream of bits:
+// [100...0 110...0] corresponding to [0x1, 0x3] in little endian, so first bit = LSbit
+// then the stream of bits is splitted in chunks of logTwoBound bits.
+//
+// This function is called when logTwoBound divides 8.
+func limbDecomposeBytesSmallBound(buf []byte, m koalabear.Vector, logTwoBound, degree int, mValues *bitset.BitSet) {
+	mask := byte((1 << logTwoBound) - 1)
+	nbChunksPerBytes := 8 / logTwoBound
+	nbFieldsElmts := len(buf) / koalabear.Bytes
+	for i := 0; i < nbFieldsElmts; i++ {
+		for j := koalabear.Bytes - 1; j >= 0; j-- {
+			curByte := buf[i*koalabear.Bytes+j]
+			curPos := i*koalabear.Bytes*nbChunksPerBytes + (koalabear.Bytes-1-j)*nbChunksPerBytes
+			for k := 0; k < nbChunksPerBytes; k++ {
+
+				m[curPos+k][0] = uint32((curByte >> (k * logTwoBound)) & mask)
+
+				// Check if mPos is zero and mark as non-zero in the bitset if not
+				if m[curPos+k][0] != 0 && mValues != nil {
+					mValues.Set(uint((curPos + k) / degree))
+				}
+			}
+		}
+	}
+}
+
+// limbDecomposeBytesMiddleBound same function than limbDecomposeBytesSmallBound, but logTwoBound is
+// a multiple of 8, and divides the number of bits of the fields.
+func limbDecomposeBytesMiddleBound(buf []byte, m koalabear.Vector, logTwoBound, degree int, mValues *bitset.BitSet) {
+	nbFieldsElmts := len(buf) / koalabear.Bytes
+	nbChunksPerElements := koalabear.Bytes * 8 / logTwoBound
+	nbBytesInChunk := logTwoBound / 8
+	curElmt := 0
+	for i := 0; i < nbFieldsElmts; i++ {
+		for j := nbChunksPerElements; j > 0; j-- {
+			curPos := i*koalabear.Bytes + j*nbBytesInChunk
+			for k := 1; k <= nbBytesInChunk; k++ {
+
+				m[curElmt][0] |= (uint32(buf[curPos-k]) << ((k - 1) * 8))
+
+			}
+			// Check if mPos is zero and mark as non-zero in the bitset if not
+			if m[curElmt][0] != 0 && mValues != nil {
+				mValues.Set(uint((curElmt) / degree))
+			}
+			curElmt += 1
+		}
+	}
+}
+
+// Split an slice of bytes representing an array of serialized field element in
+// big-endian form into an array of limbs representing the same field elements
+// in little-endian form. Namely, if our field is represented with 64 bits and we
+// have the following field element 0x0123456789abcdef (0 being the most significant
+// character and and f being the least significant one) and our log norm bound is
+// 16 (so 1 hex character = 1 limb). The function assigns the values of m to [f, e,
+// d, c, b, a, ..., 3, 2, 1, 0]. m should be preallocated and zeroized. mValues is
+// an optional bitSet. If provided, it must be empty. The function will set bit "i"
+// to indicate the that i-th SIS input polynomial should be non-zero. Recall, that a
+// SIS polynomial corresponds to a chunk of limbs of size `degree`. Additionally,
+// we have the guarantee that 2 bits contributing to different field elements cannot
+// be part of the same limb.
+func limbDecomposeBytes(buf []byte, m koalabear.Vector, logTwoBound, degree int, mValues *bitset.BitSet) {
+
+	// bitwise decomposition of the buffer, in order to build m (the vector to hash)
+	// as a list of polynomials, whose coefficients are less than r.B bits long.
+	// Say buf=[0xbe,0x0f]. As a stream of bits it is interpreted like this:
+	// 10111110 00001111. getIthBit(0)=1 (=leftmost bit), getIthBit(1)=0 (=second leftmost bit), etc.
+	nbBits := len(buf) * 8
+	getIthBit := func(i int) uint8 {
+		k := i / 8
+		if k >= len(buf) {
+			return 0
+		}
+		b := buf[k]
+		j := i % 8
+		return b >> (7 - j) & 1
+	}
+
+	// we process the input buffer by blocks of r.LogTwoBound bits
+	// each of these block (<< 64bits) are interpreted as a coefficient
+	mPos := 0
+	for fieldStart := 0; fieldStart < nbBits; {
+		for bitInField := 0; bitInField < koalabear.Bytes*8; {
+
+			j := bitInField % logTwoBound
+
+			// r.LogTwoBound < 64; we just use the first word of our element here,
+			// and set the bits from LSB to MSB.
+			at := fieldStart + koalabear.Bytes*8 - bitInField - 1
+
+			m[mPos][0] |= uint32(getIthBit(at) << j)
+
+			bitInField++
+
+			// Check if mPos is zero and mark as non-zero in the bitset if not
+			if m[mPos][0] != 0 && mValues != nil {
+				mValues.Set(uint(mPos / degree))
+			}
+
+			if j == logTwoBound-1 || bitInField == koalabear.Bytes*8 {
+				mPos++
+			}
+		}
+		fieldStart += koalabear.Bytes * 8
+	}
+}
+
+// see limbDecomposeBytes; this function is optimized for the case where
+// logTwoBound == 8 and degree == 64
+func limbDecomposeBytes8_64(buf []byte, m koalabear.Vector, mValues *bitset.BitSet) {
+	// with logTwoBound == 8, we can actually advance byte per byte.
+	const degree = 64
+	j := 0
+
+	for startPos := koalabear.Bytes - 1; startPos < len(buf); startPos += koalabear.Bytes {
+		for i := startPos; i >= startPos-koalabear.Bytes+1; i-- {
+
+			m[j][0] = uint32(buf[i])
+
+			if m[j][0] != 0 {
+				mValues.Set(uint(j / degree))
+			}
+			j++
+		}
+	}
+}
diff --git a/field/koalabear/sis/sis_fft.go b/field/koalabear/sis/sis_fft.go
new file mode 100644
index 0000000000..e0d544f9c8
--- /dev/null
+++ b/field/koalabear/sis/sis_fft.go
@@ -0,0 +1,556 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package sis
+
+import (
+	"github.com/consensys/gnark-crypto/field/koalabear"
+	"math/big"
+)
+
+// FFT64 is generated by gnark-crypto and contains the unrolled code for FFT (DIF) on 64 elements
+// equivalent code: r.Domain.FFT(k, fft.DIF, fft.OnCoset(), fft.WithNbTasks(1))
+// twiddlesCoset must be pre-computed from twiddles and coset table, see PrecomputeTwiddlesCoset
+func FFT64(a []koalabear.Element, twiddlesCoset []koalabear.Element) {
+
+	a[32].Mul(&a[32], &twiddlesCoset[0])
+	a[33].Mul(&a[33], &twiddlesCoset[0])
+	a[34].Mul(&a[34], &twiddlesCoset[0])
+	a[35].Mul(&a[35], &twiddlesCoset[0])
+	a[36].Mul(&a[36], &twiddlesCoset[0])
+	a[37].Mul(&a[37], &twiddlesCoset[0])
+	a[38].Mul(&a[38], &twiddlesCoset[0])
+	a[39].Mul(&a[39], &twiddlesCoset[0])
+	a[40].Mul(&a[40], &twiddlesCoset[0])
+	a[41].Mul(&a[41], &twiddlesCoset[0])
+	a[42].Mul(&a[42], &twiddlesCoset[0])
+	a[43].Mul(&a[43], &twiddlesCoset[0])
+	a[44].Mul(&a[44], &twiddlesCoset[0])
+	a[45].Mul(&a[45], &twiddlesCoset[0])
+	a[46].Mul(&a[46], &twiddlesCoset[0])
+	a[47].Mul(&a[47], &twiddlesCoset[0])
+	a[48].Mul(&a[48], &twiddlesCoset[0])
+	a[49].Mul(&a[49], &twiddlesCoset[0])
+	a[50].Mul(&a[50], &twiddlesCoset[0])
+	a[51].Mul(&a[51], &twiddlesCoset[0])
+	a[52].Mul(&a[52], &twiddlesCoset[0])
+	a[53].Mul(&a[53], &twiddlesCoset[0])
+	a[54].Mul(&a[54], &twiddlesCoset[0])
+	a[55].Mul(&a[55], &twiddlesCoset[0])
+	a[56].Mul(&a[56], &twiddlesCoset[0])
+	a[57].Mul(&a[57], &twiddlesCoset[0])
+	a[58].Mul(&a[58], &twiddlesCoset[0])
+	a[59].Mul(&a[59], &twiddlesCoset[0])
+	a[60].Mul(&a[60], &twiddlesCoset[0])
+	a[61].Mul(&a[61], &twiddlesCoset[0])
+	a[62].Mul(&a[62], &twiddlesCoset[0])
+	a[63].Mul(&a[63], &twiddlesCoset[0])
+	koalabear.Butterfly(&a[0], &a[32])
+	koalabear.Butterfly(&a[1], &a[33])
+	koalabear.Butterfly(&a[2], &a[34])
+	koalabear.Butterfly(&a[3], &a[35])
+	koalabear.Butterfly(&a[4], &a[36])
+	koalabear.Butterfly(&a[5], &a[37])
+	koalabear.Butterfly(&a[6], &a[38])
+	koalabear.Butterfly(&a[7], &a[39])
+	koalabear.Butterfly(&a[8], &a[40])
+	koalabear.Butterfly(&a[9], &a[41])
+	koalabear.Butterfly(&a[10], &a[42])
+	koalabear.Butterfly(&a[11], &a[43])
+	koalabear.Butterfly(&a[12], &a[44])
+	koalabear.Butterfly(&a[13], &a[45])
+	koalabear.Butterfly(&a[14], &a[46])
+	koalabear.Butterfly(&a[15], &a[47])
+	koalabear.Butterfly(&a[16], &a[48])
+	koalabear.Butterfly(&a[17], &a[49])
+	koalabear.Butterfly(&a[18], &a[50])
+	koalabear.Butterfly(&a[19], &a[51])
+	koalabear.Butterfly(&a[20], &a[52])
+	koalabear.Butterfly(&a[21], &a[53])
+	koalabear.Butterfly(&a[22], &a[54])
+	koalabear.Butterfly(&a[23], &a[55])
+	koalabear.Butterfly(&a[24], &a[56])
+	koalabear.Butterfly(&a[25], &a[57])
+	koalabear.Butterfly(&a[26], &a[58])
+	koalabear.Butterfly(&a[27], &a[59])
+	koalabear.Butterfly(&a[28], &a[60])
+	koalabear.Butterfly(&a[29], &a[61])
+	koalabear.Butterfly(&a[30], &a[62])
+	koalabear.Butterfly(&a[31], &a[63])
+	a[16].Mul(&a[16], &twiddlesCoset[1])
+	a[17].Mul(&a[17], &twiddlesCoset[1])
+	a[18].Mul(&a[18], &twiddlesCoset[1])
+	a[19].Mul(&a[19], &twiddlesCoset[1])
+	a[20].Mul(&a[20], &twiddlesCoset[1])
+	a[21].Mul(&a[21], &twiddlesCoset[1])
+	a[22].Mul(&a[22], &twiddlesCoset[1])
+	a[23].Mul(&a[23], &twiddlesCoset[1])
+	a[24].Mul(&a[24], &twiddlesCoset[1])
+	a[25].Mul(&a[25], &twiddlesCoset[1])
+	a[26].Mul(&a[26], &twiddlesCoset[1])
+	a[27].Mul(&a[27], &twiddlesCoset[1])
+	a[28].Mul(&a[28], &twiddlesCoset[1])
+	a[29].Mul(&a[29], &twiddlesCoset[1])
+	a[30].Mul(&a[30], &twiddlesCoset[1])
+	a[31].Mul(&a[31], &twiddlesCoset[1])
+	a[48].Mul(&a[48], &twiddlesCoset[2])
+	a[49].Mul(&a[49], &twiddlesCoset[2])
+	a[50].Mul(&a[50], &twiddlesCoset[2])
+	a[51].Mul(&a[51], &twiddlesCoset[2])
+	a[52].Mul(&a[52], &twiddlesCoset[2])
+	a[53].Mul(&a[53], &twiddlesCoset[2])
+	a[54].Mul(&a[54], &twiddlesCoset[2])
+	a[55].Mul(&a[55], &twiddlesCoset[2])
+	a[56].Mul(&a[56], &twiddlesCoset[2])
+	a[57].Mul(&a[57], &twiddlesCoset[2])
+	a[58].Mul(&a[58], &twiddlesCoset[2])
+	a[59].Mul(&a[59], &twiddlesCoset[2])
+	a[60].Mul(&a[60], &twiddlesCoset[2])
+	a[61].Mul(&a[61], &twiddlesCoset[2])
+	a[62].Mul(&a[62], &twiddlesCoset[2])
+	a[63].Mul(&a[63], &twiddlesCoset[2])
+	koalabear.Butterfly(&a[0], &a[16])
+	koalabear.Butterfly(&a[1], &a[17])
+	koalabear.Butterfly(&a[2], &a[18])
+	koalabear.Butterfly(&a[3], &a[19])
+	koalabear.Butterfly(&a[4], &a[20])
+	koalabear.Butterfly(&a[5], &a[21])
+	koalabear.Butterfly(&a[6], &a[22])
+	koalabear.Butterfly(&a[7], &a[23])
+	koalabear.Butterfly(&a[8], &a[24])
+	koalabear.Butterfly(&a[9], &a[25])
+	koalabear.Butterfly(&a[10], &a[26])
+	koalabear.Butterfly(&a[11], &a[27])
+	koalabear.Butterfly(&a[12], &a[28])
+	koalabear.Butterfly(&a[13], &a[29])
+	koalabear.Butterfly(&a[14], &a[30])
+	koalabear.Butterfly(&a[15], &a[31])
+	koalabear.Butterfly(&a[32], &a[48])
+	koalabear.Butterfly(&a[33], &a[49])
+	koalabear.Butterfly(&a[34], &a[50])
+	koalabear.Butterfly(&a[35], &a[51])
+	koalabear.Butterfly(&a[36], &a[52])
+	koalabear.Butterfly(&a[37], &a[53])
+	koalabear.Butterfly(&a[38], &a[54])
+	koalabear.Butterfly(&a[39], &a[55])
+	koalabear.Butterfly(&a[40], &a[56])
+	koalabear.Butterfly(&a[41], &a[57])
+	koalabear.Butterfly(&a[42], &a[58])
+	koalabear.Butterfly(&a[43], &a[59])
+	koalabear.Butterfly(&a[44], &a[60])
+	koalabear.Butterfly(&a[45], &a[61])
+	koalabear.Butterfly(&a[46], &a[62])
+	koalabear.Butterfly(&a[47], &a[63])
+	a[8].Mul(&a[8], &twiddlesCoset[3])
+	a[9].Mul(&a[9], &twiddlesCoset[3])
+	a[10].Mul(&a[10], &twiddlesCoset[3])
+	a[11].Mul(&a[11], &twiddlesCoset[3])
+	a[12].Mul(&a[12], &twiddlesCoset[3])
+	a[13].Mul(&a[13], &twiddlesCoset[3])
+	a[14].Mul(&a[14], &twiddlesCoset[3])
+	a[15].Mul(&a[15], &twiddlesCoset[3])
+	a[24].Mul(&a[24], &twiddlesCoset[4])
+	a[25].Mul(&a[25], &twiddlesCoset[4])
+	a[26].Mul(&a[26], &twiddlesCoset[4])
+	a[27].Mul(&a[27], &twiddlesCoset[4])
+	a[28].Mul(&a[28], &twiddlesCoset[4])
+	a[29].Mul(&a[29], &twiddlesCoset[4])
+	a[30].Mul(&a[30], &twiddlesCoset[4])
+	a[31].Mul(&a[31], &twiddlesCoset[4])
+	a[40].Mul(&a[40], &twiddlesCoset[5])
+	a[41].Mul(&a[41], &twiddlesCoset[5])
+	a[42].Mul(&a[42], &twiddlesCoset[5])
+	a[43].Mul(&a[43], &twiddlesCoset[5])
+	a[44].Mul(&a[44], &twiddlesCoset[5])
+	a[45].Mul(&a[45], &twiddlesCoset[5])
+	a[46].Mul(&a[46], &twiddlesCoset[5])
+	a[47].Mul(&a[47], &twiddlesCoset[5])
+	a[56].Mul(&a[56], &twiddlesCoset[6])
+	a[57].Mul(&a[57], &twiddlesCoset[6])
+	a[58].Mul(&a[58], &twiddlesCoset[6])
+	a[59].Mul(&a[59], &twiddlesCoset[6])
+	a[60].Mul(&a[60], &twiddlesCoset[6])
+	a[61].Mul(&a[61], &twiddlesCoset[6])
+	a[62].Mul(&a[62], &twiddlesCoset[6])
+	a[63].Mul(&a[63], &twiddlesCoset[6])
+	koalabear.Butterfly(&a[0], &a[8])
+	koalabear.Butterfly(&a[1], &a[9])
+	koalabear.Butterfly(&a[2], &a[10])
+	koalabear.Butterfly(&a[3], &a[11])
+	koalabear.Butterfly(&a[4], &a[12])
+	koalabear.Butterfly(&a[5], &a[13])
+	koalabear.Butterfly(&a[6], &a[14])
+	koalabear.Butterfly(&a[7], &a[15])
+	koalabear.Butterfly(&a[16], &a[24])
+	koalabear.Butterfly(&a[17], &a[25])
+	koalabear.Butterfly(&a[18], &a[26])
+	koalabear.Butterfly(&a[19], &a[27])
+	koalabear.Butterfly(&a[20], &a[28])
+	koalabear.Butterfly(&a[21], &a[29])
+	koalabear.Butterfly(&a[22], &a[30])
+	koalabear.Butterfly(&a[23], &a[31])
+	koalabear.Butterfly(&a[32], &a[40])
+	koalabear.Butterfly(&a[33], &a[41])
+	koalabear.Butterfly(&a[34], &a[42])
+	koalabear.Butterfly(&a[35], &a[43])
+	koalabear.Butterfly(&a[36], &a[44])
+	koalabear.Butterfly(&a[37], &a[45])
+	koalabear.Butterfly(&a[38], &a[46])
+	koalabear.Butterfly(&a[39], &a[47])
+	koalabear.Butterfly(&a[48], &a[56])
+	koalabear.Butterfly(&a[49], &a[57])
+	koalabear.Butterfly(&a[50], &a[58])
+	koalabear.Butterfly(&a[51], &a[59])
+	koalabear.Butterfly(&a[52], &a[60])
+	koalabear.Butterfly(&a[53], &a[61])
+	koalabear.Butterfly(&a[54], &a[62])
+	koalabear.Butterfly(&a[55], &a[63])
+	a[4].Mul(&a[4], &twiddlesCoset[7])
+	a[5].Mul(&a[5], &twiddlesCoset[7])
+	a[6].Mul(&a[6], &twiddlesCoset[7])
+	a[7].Mul(&a[7], &twiddlesCoset[7])
+	a[12].Mul(&a[12], &twiddlesCoset[8])
+	a[13].Mul(&a[13], &twiddlesCoset[8])
+	a[14].Mul(&a[14], &twiddlesCoset[8])
+	a[15].Mul(&a[15], &twiddlesCoset[8])
+	a[20].Mul(&a[20], &twiddlesCoset[9])
+	a[21].Mul(&a[21], &twiddlesCoset[9])
+	a[22].Mul(&a[22], &twiddlesCoset[9])
+	a[23].Mul(&a[23], &twiddlesCoset[9])
+	a[28].Mul(&a[28], &twiddlesCoset[10])
+	a[29].Mul(&a[29], &twiddlesCoset[10])
+	a[30].Mul(&a[30], &twiddlesCoset[10])
+	a[31].Mul(&a[31], &twiddlesCoset[10])
+	a[36].Mul(&a[36], &twiddlesCoset[11])
+	a[37].Mul(&a[37], &twiddlesCoset[11])
+	a[38].Mul(&a[38], &twiddlesCoset[11])
+	a[39].Mul(&a[39], &twiddlesCoset[11])
+	a[44].Mul(&a[44], &twiddlesCoset[12])
+	a[45].Mul(&a[45], &twiddlesCoset[12])
+	a[46].Mul(&a[46], &twiddlesCoset[12])
+	a[47].Mul(&a[47], &twiddlesCoset[12])
+	a[52].Mul(&a[52], &twiddlesCoset[13])
+	a[53].Mul(&a[53], &twiddlesCoset[13])
+	a[54].Mul(&a[54], &twiddlesCoset[13])
+	a[55].Mul(&a[55], &twiddlesCoset[13])
+	a[60].Mul(&a[60], &twiddlesCoset[14])
+	a[61].Mul(&a[61], &twiddlesCoset[14])
+	a[62].Mul(&a[62], &twiddlesCoset[14])
+	a[63].Mul(&a[63], &twiddlesCoset[14])
+	koalabear.Butterfly(&a[0], &a[4])
+	koalabear.Butterfly(&a[1], &a[5])
+	koalabear.Butterfly(&a[2], &a[6])
+	koalabear.Butterfly(&a[3], &a[7])
+	koalabear.Butterfly(&a[8], &a[12])
+	koalabear.Butterfly(&a[9], &a[13])
+	koalabear.Butterfly(&a[10], &a[14])
+	koalabear.Butterfly(&a[11], &a[15])
+	koalabear.Butterfly(&a[16], &a[20])
+	koalabear.Butterfly(&a[17], &a[21])
+	koalabear.Butterfly(&a[18], &a[22])
+	koalabear.Butterfly(&a[19], &a[23])
+	koalabear.Butterfly(&a[24], &a[28])
+	koalabear.Butterfly(&a[25], &a[29])
+	koalabear.Butterfly(&a[26], &a[30])
+	koalabear.Butterfly(&a[27], &a[31])
+	koalabear.Butterfly(&a[32], &a[36])
+	koalabear.Butterfly(&a[33], &a[37])
+	koalabear.Butterfly(&a[34], &a[38])
+	koalabear.Butterfly(&a[35], &a[39])
+	koalabear.Butterfly(&a[40], &a[44])
+	koalabear.Butterfly(&a[41], &a[45])
+	koalabear.Butterfly(&a[42], &a[46])
+	koalabear.Butterfly(&a[43], &a[47])
+	koalabear.Butterfly(&a[48], &a[52])
+	koalabear.Butterfly(&a[49], &a[53])
+	koalabear.Butterfly(&a[50], &a[54])
+	koalabear.Butterfly(&a[51], &a[55])
+	koalabear.Butterfly(&a[56], &a[60])
+	koalabear.Butterfly(&a[57], &a[61])
+	koalabear.Butterfly(&a[58], &a[62])
+	koalabear.Butterfly(&a[59], &a[63])
+	a[2].Mul(&a[2], &twiddlesCoset[15])
+	a[3].Mul(&a[3], &twiddlesCoset[15])
+	a[6].Mul(&a[6], &twiddlesCoset[16])
+	a[7].Mul(&a[7], &twiddlesCoset[16])
+	a[10].Mul(&a[10], &twiddlesCoset[17])
+	a[11].Mul(&a[11], &twiddlesCoset[17])
+	a[14].Mul(&a[14], &twiddlesCoset[18])
+	a[15].Mul(&a[15], &twiddlesCoset[18])
+	a[18].Mul(&a[18], &twiddlesCoset[19])
+	a[19].Mul(&a[19], &twiddlesCoset[19])
+	a[22].Mul(&a[22], &twiddlesCoset[20])
+	a[23].Mul(&a[23], &twiddlesCoset[20])
+	a[26].Mul(&a[26], &twiddlesCoset[21])
+	a[27].Mul(&a[27], &twiddlesCoset[21])
+	a[30].Mul(&a[30], &twiddlesCoset[22])
+	a[31].Mul(&a[31], &twiddlesCoset[22])
+	a[34].Mul(&a[34], &twiddlesCoset[23])
+	a[35].Mul(&a[35], &twiddlesCoset[23])
+	a[38].Mul(&a[38], &twiddlesCoset[24])
+	a[39].Mul(&a[39], &twiddlesCoset[24])
+	a[42].Mul(&a[42], &twiddlesCoset[25])
+	a[43].Mul(&a[43], &twiddlesCoset[25])
+	a[46].Mul(&a[46], &twiddlesCoset[26])
+	a[47].Mul(&a[47], &twiddlesCoset[26])
+	a[50].Mul(&a[50], &twiddlesCoset[27])
+	a[51].Mul(&a[51], &twiddlesCoset[27])
+	a[54].Mul(&a[54], &twiddlesCoset[28])
+	a[55].Mul(&a[55], &twiddlesCoset[28])
+	a[58].Mul(&a[58], &twiddlesCoset[29])
+	a[59].Mul(&a[59], &twiddlesCoset[29])
+	a[62].Mul(&a[62], &twiddlesCoset[30])
+	a[63].Mul(&a[63], &twiddlesCoset[30])
+	koalabear.Butterfly(&a[0], &a[2])
+	koalabear.Butterfly(&a[1], &a[3])
+	koalabear.Butterfly(&a[4], &a[6])
+	koalabear.Butterfly(&a[5], &a[7])
+	koalabear.Butterfly(&a[8], &a[10])
+	koalabear.Butterfly(&a[9], &a[11])
+	koalabear.Butterfly(&a[12], &a[14])
+	koalabear.Butterfly(&a[13], &a[15])
+	koalabear.Butterfly(&a[16], &a[18])
+	koalabear.Butterfly(&a[17], &a[19])
+	koalabear.Butterfly(&a[20], &a[22])
+	koalabear.Butterfly(&a[21], &a[23])
+	koalabear.Butterfly(&a[24], &a[26])
+	koalabear.Butterfly(&a[25], &a[27])
+	koalabear.Butterfly(&a[28], &a[30])
+	koalabear.Butterfly(&a[29], &a[31])
+	koalabear.Butterfly(&a[32], &a[34])
+	koalabear.Butterfly(&a[33], &a[35])
+	koalabear.Butterfly(&a[36], &a[38])
+	koalabear.Butterfly(&a[37], &a[39])
+	koalabear.Butterfly(&a[40], &a[42])
+	koalabear.Butterfly(&a[41], &a[43])
+	koalabear.Butterfly(&a[44], &a[46])
+	koalabear.Butterfly(&a[45], &a[47])
+	koalabear.Butterfly(&a[48], &a[50])
+	koalabear.Butterfly(&a[49], &a[51])
+	koalabear.Butterfly(&a[52], &a[54])
+	koalabear.Butterfly(&a[53], &a[55])
+	koalabear.Butterfly(&a[56], &a[58])
+	koalabear.Butterfly(&a[57], &a[59])
+	koalabear.Butterfly(&a[60], &a[62])
+	koalabear.Butterfly(&a[61], &a[63])
+	a[1].Mul(&a[1], &twiddlesCoset[31])
+	a[3].Mul(&a[3], &twiddlesCoset[32])
+	a[5].Mul(&a[5], &twiddlesCoset[33])
+	a[7].Mul(&a[7], &twiddlesCoset[34])
+	a[9].Mul(&a[9], &twiddlesCoset[35])
+	a[11].Mul(&a[11], &twiddlesCoset[36])
+	a[13].Mul(&a[13], &twiddlesCoset[37])
+	a[15].Mul(&a[15], &twiddlesCoset[38])
+	a[17].Mul(&a[17], &twiddlesCoset[39])
+	a[19].Mul(&a[19], &twiddlesCoset[40])
+	a[21].Mul(&a[21], &twiddlesCoset[41])
+	a[23].Mul(&a[23], &twiddlesCoset[42])
+	a[25].Mul(&a[25], &twiddlesCoset[43])
+	a[27].Mul(&a[27], &twiddlesCoset[44])
+	a[29].Mul(&a[29], &twiddlesCoset[45])
+	a[31].Mul(&a[31], &twiddlesCoset[46])
+	a[33].Mul(&a[33], &twiddlesCoset[47])
+	a[35].Mul(&a[35], &twiddlesCoset[48])
+	a[37].Mul(&a[37], &twiddlesCoset[49])
+	a[39].Mul(&a[39], &twiddlesCoset[50])
+	a[41].Mul(&a[41], &twiddlesCoset[51])
+	a[43].Mul(&a[43], &twiddlesCoset[52])
+	a[45].Mul(&a[45], &twiddlesCoset[53])
+	a[47].Mul(&a[47], &twiddlesCoset[54])
+	a[49].Mul(&a[49], &twiddlesCoset[55])
+	a[51].Mul(&a[51], &twiddlesCoset[56])
+	a[53].Mul(&a[53], &twiddlesCoset[57])
+	a[55].Mul(&a[55], &twiddlesCoset[58])
+	a[57].Mul(&a[57], &twiddlesCoset[59])
+	a[59].Mul(&a[59], &twiddlesCoset[60])
+	a[61].Mul(&a[61], &twiddlesCoset[61])
+	a[63].Mul(&a[63], &twiddlesCoset[62])
+	koalabear.Butterfly(&a[0], &a[1])
+	koalabear.Butterfly(&a[2], &a[3])
+	koalabear.Butterfly(&a[4], &a[5])
+	koalabear.Butterfly(&a[6], &a[7])
+	koalabear.Butterfly(&a[8], &a[9])
+	koalabear.Butterfly(&a[10], &a[11])
+	koalabear.Butterfly(&a[12], &a[13])
+	koalabear.Butterfly(&a[14], &a[15])
+	koalabear.Butterfly(&a[16], &a[17])
+	koalabear.Butterfly(&a[18], &a[19])
+	koalabear.Butterfly(&a[20], &a[21])
+	koalabear.Butterfly(&a[22], &a[23])
+	koalabear.Butterfly(&a[24], &a[25])
+	koalabear.Butterfly(&a[26], &a[27])
+	koalabear.Butterfly(&a[28], &a[29])
+	koalabear.Butterfly(&a[30], &a[31])
+	koalabear.Butterfly(&a[32], &a[33])
+	koalabear.Butterfly(&a[34], &a[35])
+	koalabear.Butterfly(&a[36], &a[37])
+	koalabear.Butterfly(&a[38], &a[39])
+	koalabear.Butterfly(&a[40], &a[41])
+	koalabear.Butterfly(&a[42], &a[43])
+	koalabear.Butterfly(&a[44], &a[45])
+	koalabear.Butterfly(&a[46], &a[47])
+	koalabear.Butterfly(&a[48], &a[49])
+	koalabear.Butterfly(&a[50], &a[51])
+	koalabear.Butterfly(&a[52], &a[53])
+	koalabear.Butterfly(&a[54], &a[55])
+	koalabear.Butterfly(&a[56], &a[57])
+	koalabear.Butterfly(&a[58], &a[59])
+	koalabear.Butterfly(&a[60], &a[61])
+	koalabear.Butterfly(&a[62], &a[63])
+}
+
+// PrecomputeTwiddlesCoset precomputes twiddlesCoset from twiddles and coset table
+// it then return all elements in the correct order for the unrolled FFT.
+func PrecomputeTwiddlesCoset(generator, shifter koalabear.Element) []koalabear.Element {
+	toReturn := make([]koalabear.Element, 63)
+	var r, s koalabear.Element
+	e := new(big.Int)
+
+	s = shifter
+	for k := 0; k < 5; k++ {
+		s.Square(&s)
+	}
+	toReturn[0] = s
+	s = shifter
+	for k := 0; k < 4; k++ {
+		s.Square(&s)
+	}
+	toReturn[1] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<4*1)))
+	toReturn[2].Mul(&r, &s)
+	s = shifter
+	for k := 0; k < 3; k++ {
+		s.Square(&s)
+	}
+	toReturn[3] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<3*2)))
+	toReturn[4].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<3*1)))
+	toReturn[5].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<3*3)))
+	toReturn[6].Mul(&r, &s)
+	s = shifter
+	for k := 0; k < 2; k++ {
+		s.Square(&s)
+	}
+	toReturn[7] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<2*4)))
+	toReturn[8].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*2)))
+	toReturn[9].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*6)))
+	toReturn[10].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*1)))
+	toReturn[11].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*5)))
+	toReturn[12].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*3)))
+	toReturn[13].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*7)))
+	toReturn[14].Mul(&r, &s)
+	s = shifter
+	for k := 0; k < 1; k++ {
+		s.Square(&s)
+	}
+	toReturn[15] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<1*8)))
+	toReturn[16].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*4)))
+	toReturn[17].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*12)))
+	toReturn[18].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*2)))
+	toReturn[19].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*10)))
+	toReturn[20].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*6)))
+	toReturn[21].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*14)))
+	toReturn[22].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*1)))
+	toReturn[23].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*9)))
+	toReturn[24].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*5)))
+	toReturn[25].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*13)))
+	toReturn[26].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*3)))
+	toReturn[27].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*11)))
+	toReturn[28].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*7)))
+	toReturn[29].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*15)))
+	toReturn[30].Mul(&r, &s)
+	s = shifter
+	for k := 0; k < 0; k++ {
+		s.Square(&s)
+	}
+	toReturn[31] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<0*16)))
+	toReturn[32].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*8)))
+	toReturn[33].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*24)))
+	toReturn[34].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*4)))
+	toReturn[35].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*20)))
+	toReturn[36].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*12)))
+	toReturn[37].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*28)))
+	toReturn[38].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*2)))
+	toReturn[39].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*18)))
+	toReturn[40].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*10)))
+	toReturn[41].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*26)))
+	toReturn[42].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*6)))
+	toReturn[43].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*22)))
+	toReturn[44].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*14)))
+	toReturn[45].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*30)))
+	toReturn[46].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*1)))
+	toReturn[47].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*17)))
+	toReturn[48].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*9)))
+	toReturn[49].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*25)))
+	toReturn[50].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*5)))
+	toReturn[51].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*21)))
+	toReturn[52].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*13)))
+	toReturn[53].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*29)))
+	toReturn[54].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*3)))
+	toReturn[55].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*19)))
+	toReturn[56].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*11)))
+	toReturn[57].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*27)))
+	toReturn[58].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*7)))
+	toReturn[59].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*23)))
+	toReturn[60].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*15)))
+	toReturn[61].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*31)))
+	toReturn[62].Mul(&r, &s)
+	return toReturn
+}
diff --git a/field/koalabear/sis/sis_test.go b/field/koalabear/sis/sis_test.go
new file mode 100644
index 0000000000..ca0fb3da68
--- /dev/null
+++ b/field/koalabear/sis/sis_test.go
@@ -0,0 +1,488 @@
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package sis
+
+import (
+	"bytes"
+	"crypto/rand"
+	"encoding/binary"
+	"encoding/json"
+	"fmt"
+	"io"
+	"math/big"
+	"math/bits"
+	"os"
+	"testing"
+	"time"
+
+	"github.com/bits-and-blooms/bitset"
+	"github.com/consensys/gnark-crypto/field/koalabear"
+	"github.com/consensys/gnark-crypto/field/koalabear/fft"
+	"github.com/stretchr/testify/require"
+)
+
+type sisParams struct {
+	logTwoBound, logTwoDegree int
+}
+
+var params128Bits []sisParams = []sisParams{
+	{logTwoBound: 2, logTwoDegree: 3},
+	{logTwoBound: 4, logTwoDegree: 4},
+	{logTwoBound: 6, logTwoDegree: 5},
+	{logTwoBound: 8, logTwoDegree: 6},
+	{logTwoBound: 10, logTwoDegree: 6},
+	{logTwoBound: 16, logTwoDegree: 7},
+	{logTwoBound: 32, logTwoDegree: 8},
+}
+
+type TestCases struct {
+	Inputs  []koalabear.Element `json:"inputs"`
+	Entries []struct {
+		Params struct {
+			Seed                int64 `json:"seed"`
+			LogTwoDegree        int   `json:"logTwoDegree"`
+			LogTwoBound         int   `json:"logTwoBound"`
+			MaxNbElementsToHash int   `json:"maxNbElementsToHash"`
+		} `json:"params"`
+		Expected []koalabear.Element `json:"expected"`
+	} `json:"entries"`
+}
+
+func TestReference(t *testing.T) {
+	if bits.UintSize == 32 {
+		t.Skip("skipping this test in 32bit.")
+	}
+	assert := require.New(t)
+
+	// read the test case file
+	var testCases TestCases
+	data, err := os.ReadFile("test_cases.json")
+	assert.NoError(err, "reading test cases failed")
+	err = json.Unmarshal(data, &testCases)
+	assert.NoError(err, "reading test cases failed")
+
+	inputs := testCases.Inputs
+
+	for testCaseID, testCase := range testCases.Entries {
+
+		// create the SIS instance
+		sis, err := NewRSis(testCase.Params.Seed, testCase.Params.LogTwoDegree, testCase.Params.LogTwoBound, testCase.Params.MaxNbElementsToHash)
+		assert.NoError(err)
+
+		// key generation same than in sage
+		makeKeyDeterministic(t, sis, testCase.Params.Seed)
+
+		sis.Reset()
+
+		// hash test case entry input and compare with expected (computed by sage)
+		goHash, err := sis.Hash(inputs)
+		assert.NoError(err)
+
+		assert.EqualValues(
+			testCase.Expected, goHash,
+			"mismatch between reference test and computed value (testcase %v)",
+			testCaseID,
+		)
+
+	}
+
+}
+
+func TestLimbDecomposeBytesMiddleBound(t *testing.T) {
+
+	var montConstant koalabear.Element
+	var bMontConstant big.Int
+	bMontConstant.SetUint64(1)
+	bMontConstant.Lsh(&bMontConstant, koalabear.Bytes*8)
+	montConstant.SetBigInt(&bMontConstant)
+
+	nbElmts := 10
+	a := make([]koalabear.Element, nbElmts)
+	for i := 0; i < nbElmts; i++ {
+		a[i].SetUint64(33)
+	}
+	var buf bytes.Buffer
+	for i := 0; i < nbElmts; i++ {
+		buf.Write(a[i].Marshal())
+	}
+
+	logTwoBound := 8
+
+	for cc := 0; cc < 3; cc++ {
+		m := make(koalabear.Vector, nbElmts*koalabear.Bytes*8/logTwoBound)
+		limbDecomposeBytesMiddleBound(buf.Bytes(), m, logTwoBound, 4, nil)
+
+		for i := 0; i < len(m); i++ {
+			m[i].Mul(&m[i], &montConstant)
+		}
+
+		var x koalabear.Element
+		x.SetUint64(1 << logTwoBound)
+
+		coeffsPerFieldsElmt := koalabear.Bytes * 8 / logTwoBound
+		for i := 0; i < nbElmts; i++ {
+			r := eval(m[i*coeffsPerFieldsElmt:(i+1)*coeffsPerFieldsElmt], x)
+			if !r.Equal(&a[i]) {
+				t.Fatal("limbDecomposeBytes failed")
+			}
+		}
+		logTwoBound *= 2
+	}
+
+}
+
+func TestLimbDecomposeBytesSmallBound(t *testing.T) {
+
+	var montConstant koalabear.Element
+	var bMontConstant big.Int
+	bMontConstant.SetUint64(1)
+	bMontConstant.Lsh(&bMontConstant, koalabear.Bytes*8)
+	montConstant.SetBigInt(&bMontConstant)
+
+	nbElmts := 10
+	a := make([]koalabear.Element, nbElmts)
+	for i := 0; i < nbElmts; i++ {
+		a[i].SetRandom()
+	}
+	var buf bytes.Buffer
+	for i := 0; i < nbElmts; i++ {
+		buf.Write(a[i].Marshal())
+	}
+
+	logTwoBound := 2
+
+	for cc := 0; cc < 3; cc++ {
+
+		m := make(koalabear.Vector, nbElmts*koalabear.Bytes*8/logTwoBound)
+		m2 := make(koalabear.Vector, nbElmts*koalabear.Bytes*8/logTwoBound)
+
+		// the limbs are set as is, they are NOT converted in Montgomery form
+		limbDecomposeBytes(buf.Bytes(), m, logTwoBound, 4, nil)
+		limbDecomposeBytesSmallBound(buf.Bytes(), m2, logTwoBound, 4, nil)
+
+		for i := 0; i < len(m); i++ {
+			m[i].Mul(&m[i], &montConstant)
+			m2[i].Mul(&m2[i], &montConstant)
+		}
+		var x koalabear.Element
+		x.SetUint64(1 << logTwoBound)
+
+		coeffsPerFieldsElmt := koalabear.Bytes * 8 / logTwoBound
+		for i := 0; i < nbElmts; i++ {
+			r := eval(m[i*coeffsPerFieldsElmt:(i+1)*coeffsPerFieldsElmt], x)
+			if !r.Equal(&a[i]) {
+				t.Fatal("limbDecomposeBytes failed")
+			}
+			r = eval(m2[i*coeffsPerFieldsElmt:(i+1)*coeffsPerFieldsElmt], x)
+			if !r.Equal(&a[i]) {
+				t.Fatal("limbDecomposeBytesSmallBound failed")
+			}
+		}
+		logTwoBound *= 2
+	}
+
+}
+
+func eval(p []koalabear.Element, x koalabear.Element) koalabear.Element {
+	var res koalabear.Element
+	for i := len(p) - 1; i >= 0; i-- {
+		res.Mul(&res, &x).Add(&res, &p[i])
+	}
+	return res
+}
+
+func TestMulMod(t *testing.T) {
+
+	size := 4
+
+	p := make([]koalabear.Element, size)
+	q := make([]koalabear.Element, size)
+	pCopy := make([]koalabear.Element, size)
+	qCopy := make([]koalabear.Element, size)
+	for i := 0; i < size; i++ {
+		p[i].SetRandom()
+		pCopy[i].Set(&p[i])
+		q[i].SetRandom()
+		qCopy[i].Set(&q[i])
+	}
+
+	// creation of the domain
+	shift, err := koalabear.Generator(uint64(2 * size))
+	if err != nil {
+		t.Fatal(err)
+	}
+	var g koalabear.Element
+	g.Square(&shift)
+	domain := fft.NewDomain(uint64(size), fft.WithShift(shift))
+
+	// mul mod
+	domain.FFT(p, fft.DIF, fft.OnCoset())
+	domain.FFT(q, fft.DIF, fft.OnCoset())
+	r := mulMod(p, q)
+	domain.FFTInverse(r, fft.DIT, fft.OnCoset())
+
+	// manually check the product on the zeroes of X^4+1
+	for i := 0; i < 4; i++ {
+		u := eval(pCopy, shift)
+		v := eval(qCopy, shift)
+		w := eval(r, shift)
+		u.Mul(&u, &v)
+		if !w.Equal(&u) {
+			t.Fatal("mul mol failed")
+		}
+		shift.Mul(&shift, &g)
+	}
+
+}
+
+func makeKeyDeterministic(t *testing.T, sis *RSis, _seed int64) {
+	t.Helper()
+	// generate the key deterministically, the same way
+	// we do in sage to generate the test vectors.
+
+	polyRand := func(seed koalabear.Element, deg int) []koalabear.Element {
+		res := make([]koalabear.Element, deg)
+		for i := 0; i < deg; i++ {
+			res[i].Square(&seed)
+			seed.Set(&res[i])
+		}
+		return res
+	}
+
+	var seed, one koalabear.Element
+	one.SetOne()
+	seed.SetInt64(_seed)
+	for i := 0; i < len(sis.A); i++ {
+		sis.A[i] = polyRand(seed, sis.Degree)
+		copy(sis.Ag[i], sis.A[i])
+		sis.Domain.FFT(sis.Ag[i], fft.DIF, fft.OnCoset())
+		seed.Add(&seed, &one)
+	}
+}
+
+const (
+	LATENCY_MUL_FIELD_NS int = 18
+	LATENCY_ADD_FIELD_NS int = 4
+)
+
+// Estimate the theoretical performances that are achievable using ring-SIS
+// operations. The time is obtained by counting the number of additions and
+// multiplications occurring in the computation. This does not account for the
+// possibilities to use SIMD instructions or for cache-locality issues. Thus, it
+// does not represents a maximum even though it returns a good idea of what is
+// achievable . This returns performances in term of ns/field. This also does not
+// account for the time taken for "limb-splitting" the input.
+func estimateSisTheory(p sisParams) float64 {
+
+	// Since the FFT occurs over a coset, we need to multiply all the coefficients
+	// of the input by some coset factors (for an entire polynomial)
+	timeCosetShift := (1 << p.logTwoDegree) * LATENCY_MUL_FIELD_NS
+
+	// The two additions are from the butterfly, and the multiplication represents
+	// the one by the twiddle. (for an entire polynomial)
+	timeFFT := (1 << p.logTwoDegree) * p.logTwoDegree * (2*LATENCY_ADD_FIELD_NS + LATENCY_MUL_FIELD_NS)
+
+	// Time taken to multiply by the key and accumulate (for an entire polynomial)
+	timeMulAddKey := (1 << p.logTwoDegree) * (LATENCY_MUL_FIELD_NS + LATENCY_ADD_FIELD_NS)
+
+	// Total computation time for an entire polynomial
+	totalTimePoly := timeCosetShift + timeFFT + timeMulAddKey
+
+	// Convert this into a time per input field
+	r := totalTimePoly * koalabear.Bits / p.logTwoBound / (1 << p.logTwoDegree)
+	return float64(r)
+}
+
+func BenchmarkDecomposition(b *testing.B) {
+
+	nbElmts := 1000
+	a := make([]koalabear.Element, nbElmts)
+	for i := 0; i < nbElmts; i++ {
+		a[i].SetRandom()
+	}
+	var buf bytes.Buffer
+	for i := 0; i < nbElmts; i++ {
+		buf.Write(a[i].Marshal())
+	}
+	logTwoBound := 4
+	m := make(koalabear.Vector, nbElmts*koalabear.Bytes*8/logTwoBound)
+
+	b.Run(fmt.Sprintf("limbDecomposeBytes logTwoBound=%d", logTwoBound), func(b *testing.B) {
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			limbDecomposeBytes(buf.Bytes(), m, logTwoBound, 4, nil)
+		}
+	})
+
+	b.Run(fmt.Sprintf("limbDecomposeByteSmallBound logTwoBound=%d", logTwoBound), func(b *testing.B) {
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			limbDecomposeBytesSmallBound(buf.Bytes(), m, logTwoBound, 4, nil)
+		}
+	})
+
+	logTwoBound = 16
+	b.Run(fmt.Sprintf("limbDecomposeBytes logTwoBound=%d", logTwoBound), func(b *testing.B) {
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			limbDecomposeBytes(buf.Bytes(), m, logTwoBound, 4, nil)
+		}
+	})
+
+	b.Run(fmt.Sprintf("limbDecomposeByteSmallBound logTwoBound=%d", logTwoBound), func(b *testing.B) {
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			limbDecomposeBytesMiddleBound(buf.Bytes(), m, logTwoBound, 4, nil)
+		}
+	})
+
+}
+
+func BenchmarkSIS(b *testing.B) {
+
+	// max nb field elements to hash
+	const nbInputs = 1 << 16
+
+	// Assign the input with random bytes. In practice, theses bytes encodes
+	// a string of field element. It would be more meaningful to take a slice
+	// of field element directly because otherwise the conversion time is not
+	// accounted for in the benchmark.
+	inputs := make(koalabear.Vector, nbInputs)
+	for i := 0; i < len(inputs); i++ {
+		inputs[i].SetRandom()
+	}
+
+	for _, param := range params128Bits {
+		for n := 1 << 10; n <= nbInputs; n <<= 1 {
+			in := inputs[:n]
+			benchmarkSIS(b, in, false, param.logTwoBound, param.logTwoDegree, estimateSisTheory(param))
+		}
+
+	}
+}
+
+func benchmarkSIS(b *testing.B, input []koalabear.Element, sparse bool, logTwoBound, logTwoDegree int, theoretical float64) {
+	b.Helper()
+
+	n := len(input)
+
+	benchName := "ring-sis/"
+	if sparse {
+		benchName += "sparse/"
+	}
+	benchName += fmt.Sprintf("inputs=%v/log2-bound=%v/log2-degree=%v", n, logTwoBound, logTwoDegree)
+
+	b.Run(benchName, func(b *testing.B) {
+		instance, err := NewRSis(0, logTwoDegree, logTwoBound, n)
+		if err != nil {
+			b.Fatal(err)
+		}
+
+		// We introduce a custom metric which is the time per field element
+		// Since the benchmark object allows to report extra meta but does
+		// not allow accessing them. We measure the time ourself.
+
+		startTime := time.Now()
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			_, err = instance.Hash(input)
+			if err != nil {
+				b.Fatal(err)
+			}
+		}
+		b.StopTimer()
+
+		totalDuration := time.Since(startTime)
+		nsPerField := totalDuration.Nanoseconds() / int64(b.N) / int64(n)
+
+		b.ReportMetric(float64(nsPerField), "ns/field")
+
+		b.ReportMetric(theoretical, "ns/field(theory)")
+
+	})
+}
+
+// Hash interprets the input vector as a sequence of coefficients of size r.LogTwoBound bits long,
+// and return the hash of the polynomial corresponding to the sum sum_i A[i]*m Mod X^{d}+1
+//
+// It is equivalent to calling r.Write(element.Marshal()); outBytes = r.Sum(nil);
+// ! note @gbotrel: this is a place holder, may not make sense
+func (r *RSis) Hash(v []koalabear.Element) ([]koalabear.Element, error) {
+	if len(v) > r.maxNbElementsToHash {
+		return nil, fmt.Errorf("can't hash more than %d elements with params provided in constructor", r.maxNbElementsToHash)
+	}
+
+	r.Reset()
+	for _, e := range v {
+		r.Write(e.Marshal())
+	}
+	sum := r.Sum(nil)
+	var rlen [4]byte
+	binary.BigEndian.PutUint32(rlen[:], uint32(len(sum)/koalabear.Bytes))
+	reader := io.MultiReader(bytes.NewReader(rlen[:]), bytes.NewReader(sum))
+	var result koalabear.Vector
+	_, err := result.ReadFrom(reader)
+	if err != nil {
+		return nil, err
+	}
+	return result, nil
+}
+
+func TestLimbDecompositionFastPath(t *testing.T) {
+	assert := require.New(t)
+
+	for size := koalabear.Bytes; size < 5*koalabear.Bytes; size += koalabear.Bytes {
+		// Test the fast path of limbDecomposeBytes8_64
+		buf := make([]byte, size)
+		m := make([]koalabear.Element, size)
+		mValues := bitset.New(uint(size))
+		n := make([]koalabear.Element, size)
+		nValues := bitset.New(uint(size))
+
+		// Generate a random buffer
+		_, err := rand.Read(buf)
+		assert.NoError(err)
+
+		limbDecomposeBytes8_64(buf, m, mValues)
+		limbDecomposeBytes(buf, n, 8, 64, nValues)
+
+		for i := 0; i < size; i++ {
+			assert.Equal(mValues.Test(uint(i)), nValues.Test(uint(i)))
+			assert.True(m[i].Equal(&n[i]))
+		}
+	}
+
+}
+
+func TestUnrolledFFT(t *testing.T) {
+
+	var shift koalabear.Element
+	shift.SetRandom()
+
+	const size = 64
+	assert := require.New(t)
+	domain := fft.NewDomain(size, fft.WithShift(shift))
+
+	k1 := make([]koalabear.Element, size)
+	for i := 0; i < size; i++ {
+		k1[i].SetRandom()
+	}
+	k2 := make([]koalabear.Element, size)
+	copy(k2, k1)
+
+	// default FFT
+	domain.FFT(k1, fft.DIF, fft.OnCoset(), fft.WithNbTasks(1))
+
+	// unrolled FFT
+	twiddlesCoset := PrecomputeTwiddlesCoset(domain.Generator, domain.FrMultiplicativeGen)
+	FFT64(k2, twiddlesCoset)
+
+	// compare results
+	for i := 0; i < size; i++ {
+		// fmt.Printf("i = %d, k1 = %v, k2 = %v\n", i, k1[i].String(), k2[i].String())
+		assert.True(k1[i].Equal(&k2[i]), "i = %d", i)
+	}
+}
diff --git a/field/koalabear/sis/test_cases.json b/field/koalabear/sis/test_cases.json
new file mode 100644
index 0000000000..9f6643e024
--- /dev/null
+++ b/field/koalabear/sis/test_cases.json
@@ -0,0 +1,86 @@
+{
+    "inputs": [
+        "5", 
+        "25", 
+        "125", 
+        "625", 
+        "3125", 
+        "15625", 
+        "78125", 
+        "390625", 
+        "1953125", 
+        "9765625"
+    ], 
+    "entries": [
+        {
+            "expected": [
+                "745870982", 
+                "1291673658", 
+                "1214702901", 
+                "833819120"
+            ], 
+            "params": {
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 2
+            }
+        }, 
+        {
+            "expected": [
+                "39890339", 
+                "1535248400", 
+                "902492181", 
+                "1900916241"
+            ], 
+            "params": {
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 4
+            }
+        }, 
+        {
+            "expected": [
+                "1199943011", 
+                "1708241314", 
+                "2087716601", 
+                "1674811485"
+            ], 
+            "params": {
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 8
+            }
+        }, 
+        {
+            "expected": [
+                "459992085", 
+                "1905368748", 
+                "1952707382", 
+                "1821305102"
+            ], 
+            "params": {
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 16
+            }
+        }, 
+        {
+            "expected": [
+                "1865346304", 
+                "336969822", 
+                "1474104401", 
+                "690634525"
+            ], 
+            "params": {
+                "maxNbElementsToHash": 10, 
+                "seed": 5, 
+                "logTwoDegree": 2, 
+                "logTwoBound": 32
+            }
+        }
+    ]
+}
\ No newline at end of file
diff --git a/internal/generator/main.go b/internal/generator/main.go
index 619314f630..d6b45d629a 100644
--- a/internal/generator/main.go
+++ b/internal/generator/main.go
@@ -75,11 +75,14 @@ func main() {
 
 			conf.FpUnusedBits = 64 - (conf.Fp.NbBits % 64)
 
+			frOpts := []generator.Option{generator.WithASM(asmConfig)}
 			if !(conf.Equal(config.STARK_CURVE) || conf.Equal(config.SECP256K1)) {
-				assertNoError(generator.GenerateFF(conf.Fr, filepath.Join(curveDir, "fr"), generator.WithASM(asmConfig), generator.WithFFT(fftConfig)))
-			} else {
-				assertNoError(generator.GenerateFF(conf.Fr, filepath.Join(curveDir, "fr"), generator.WithASM(asmConfig)))
+				frOpts = append(frOpts, generator.WithFFT(fftConfig))
 			}
+			if conf.Equal(config.BLS12_377) {
+				frOpts = append(frOpts, generator.WithSIS())
+			}
+			assertNoError(generator.GenerateFF(conf.Fr, filepath.Join(curveDir, "fr"), frOpts...))
 			assertNoError(generator.GenerateFF(conf.Fp, filepath.Join(curveDir, "fp"), generator.WithASM(asmConfig)))
 
 			// generate ecdsa

From f08f759bd65b08153d5da4c4ad935f73f230cbc9 Mon Sep 17 00:00:00 2001
From: Arya Tabaie <arya.pourtabatabaie@gmail.com>
Date: Sat, 21 Dec 2024 08:49:50 -0600
Subject: [PATCH 101/114] Feat/write point slice ptr (#585)

Co-authored-by: Arya Tabaie <15056835+Tabaie@users.noreply.github.com>
---
 ecc/bls12-377/marshal.go                        | 10 +++++++++-
 ecc/bls12-381/marshal.go                        | 10 +++++++++-
 ecc/bls24-315/marshal.go                        | 10 +++++++++-
 ecc/bls24-317/marshal.go                        | 10 +++++++++-
 ecc/bn254/marshal.go                            | 10 +++++++++-
 ecc/bw6-633/marshal.go                          | 10 +++++++++-
 ecc/bw6-761/marshal.go                          | 10 +++++++++-
 ecc/utils.go                                    |  3 ++-
 internal/generator/ecc/template/marshal.go.tmpl |  6 +++++-
 9 files changed, 70 insertions(+), 9 deletions(-)

diff --git a/ecc/bls12-377/marshal.go b/ecc/bls12-377/marshal.go
index 560b22a37e..e6be30a2ee 100644
--- a/ecc/bls12-377/marshal.go
+++ b/ecc/bls12-377/marshal.go
@@ -435,7 +435,7 @@ func NewEncoder(w io.Writer, options ...func(*Encoder)) *Encoder {
 }
 
 // Encode writes the binary encoding of v to the stream
-// type must be uint64, *fr.Element, *fp.Element, *G1Affine, *G2Affine, []G1Affine or []G2Affine
+// type must be uint64, *fr.Element, *fp.Element, *G1Affine, *G2Affine, []G1Affine, []G2Affine, *[]G1Affine or *[]G2Affine
 func (enc *Encoder) Encode(v interface{}) (err error) {
 	if enc.raw {
 		return enc.encodeRaw(v)
@@ -565,6 +565,8 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 			}
 		}
 		return
+	case *[]G1Affine:
+		return enc.encode(*t)
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -584,6 +586,8 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 			}
 		}
 		return nil
+	case *[]G2Affine:
+		return enc.encode(*t)
 	case []G2Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -702,6 +706,8 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 			}
 		}
 		return
+	case *[]G1Affine:
+		return enc.encodeRaw(*t)
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -721,6 +727,8 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 			}
 		}
 		return nil
+	case *[]G2Affine:
+		return enc.encodeRaw(*t)
 	case []G2Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
diff --git a/ecc/bls12-381/marshal.go b/ecc/bls12-381/marshal.go
index f647957143..3abb837ba6 100644
--- a/ecc/bls12-381/marshal.go
+++ b/ecc/bls12-381/marshal.go
@@ -435,7 +435,7 @@ func NewEncoder(w io.Writer, options ...func(*Encoder)) *Encoder {
 }
 
 // Encode writes the binary encoding of v to the stream
-// type must be uint64, *fr.Element, *fp.Element, *G1Affine, *G2Affine, []G1Affine or []G2Affine
+// type must be uint64, *fr.Element, *fp.Element, *G1Affine, *G2Affine, []G1Affine, []G2Affine, *[]G1Affine or *[]G2Affine
 func (enc *Encoder) Encode(v interface{}) (err error) {
 	if enc.raw {
 		return enc.encodeRaw(v)
@@ -565,6 +565,8 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 			}
 		}
 		return
+	case *[]G1Affine:
+		return enc.encode(*t)
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -584,6 +586,8 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 			}
 		}
 		return nil
+	case *[]G2Affine:
+		return enc.encode(*t)
 	case []G2Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -702,6 +706,8 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 			}
 		}
 		return
+	case *[]G1Affine:
+		return enc.encodeRaw(*t)
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -721,6 +727,8 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 			}
 		}
 		return nil
+	case *[]G2Affine:
+		return enc.encodeRaw(*t)
 	case []G2Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
diff --git a/ecc/bls24-315/marshal.go b/ecc/bls24-315/marshal.go
index 3b6c69362f..45ed61b8aa 100644
--- a/ecc/bls24-315/marshal.go
+++ b/ecc/bls24-315/marshal.go
@@ -435,7 +435,7 @@ func NewEncoder(w io.Writer, options ...func(*Encoder)) *Encoder {
 }
 
 // Encode writes the binary encoding of v to the stream
-// type must be uint64, *fr.Element, *fp.Element, *G1Affine, *G2Affine, []G1Affine or []G2Affine
+// type must be uint64, *fr.Element, *fp.Element, *G1Affine, *G2Affine, []G1Affine, []G2Affine, *[]G1Affine or *[]G2Affine
 func (enc *Encoder) Encode(v interface{}) (err error) {
 	if enc.raw {
 		return enc.encodeRaw(v)
@@ -565,6 +565,8 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 			}
 		}
 		return
+	case *[]G1Affine:
+		return enc.encode(*t)
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -584,6 +586,8 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 			}
 		}
 		return nil
+	case *[]G2Affine:
+		return enc.encode(*t)
 	case []G2Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -702,6 +706,8 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 			}
 		}
 		return
+	case *[]G1Affine:
+		return enc.encodeRaw(*t)
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -721,6 +727,8 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 			}
 		}
 		return nil
+	case *[]G2Affine:
+		return enc.encodeRaw(*t)
 	case []G2Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
diff --git a/ecc/bls24-317/marshal.go b/ecc/bls24-317/marshal.go
index cc267843bc..763eb62c94 100644
--- a/ecc/bls24-317/marshal.go
+++ b/ecc/bls24-317/marshal.go
@@ -435,7 +435,7 @@ func NewEncoder(w io.Writer, options ...func(*Encoder)) *Encoder {
 }
 
 // Encode writes the binary encoding of v to the stream
-// type must be uint64, *fr.Element, *fp.Element, *G1Affine, *G2Affine, []G1Affine or []G2Affine
+// type must be uint64, *fr.Element, *fp.Element, *G1Affine, *G2Affine, []G1Affine, []G2Affine, *[]G1Affine or *[]G2Affine
 func (enc *Encoder) Encode(v interface{}) (err error) {
 	if enc.raw {
 		return enc.encodeRaw(v)
@@ -565,6 +565,8 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 			}
 		}
 		return
+	case *[]G1Affine:
+		return enc.encode(*t)
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -584,6 +586,8 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 			}
 		}
 		return nil
+	case *[]G2Affine:
+		return enc.encode(*t)
 	case []G2Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -702,6 +706,8 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 			}
 		}
 		return
+	case *[]G1Affine:
+		return enc.encodeRaw(*t)
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -721,6 +727,8 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 			}
 		}
 		return nil
+	case *[]G2Affine:
+		return enc.encodeRaw(*t)
 	case []G2Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
diff --git a/ecc/bn254/marshal.go b/ecc/bn254/marshal.go
index 4db3316aa7..ea09bfbef0 100644
--- a/ecc/bn254/marshal.go
+++ b/ecc/bn254/marshal.go
@@ -400,7 +400,7 @@ func NewEncoder(w io.Writer, options ...func(*Encoder)) *Encoder {
 }
 
 // Encode writes the binary encoding of v to the stream
-// type must be uint64, *fr.Element, *fp.Element, *G1Affine, *G2Affine, []G1Affine or []G2Affine
+// type must be uint64, *fr.Element, *fp.Element, *G1Affine, *G2Affine, []G1Affine, []G2Affine, *[]G1Affine or *[]G2Affine
 func (enc *Encoder) Encode(v interface{}) (err error) {
 	if enc.raw {
 		return enc.encodeRaw(v)
@@ -530,6 +530,8 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 			}
 		}
 		return
+	case *[]G1Affine:
+		return enc.encode(*t)
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -549,6 +551,8 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 			}
 		}
 		return nil
+	case *[]G2Affine:
+		return enc.encode(*t)
 	case []G2Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -667,6 +671,8 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 			}
 		}
 		return
+	case *[]G1Affine:
+		return enc.encodeRaw(*t)
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -686,6 +692,8 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 			}
 		}
 		return nil
+	case *[]G2Affine:
+		return enc.encodeRaw(*t)
 	case []G2Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
diff --git a/ecc/bw6-633/marshal.go b/ecc/bw6-633/marshal.go
index edc60f546a..2463435468 100644
--- a/ecc/bw6-633/marshal.go
+++ b/ecc/bw6-633/marshal.go
@@ -435,7 +435,7 @@ func NewEncoder(w io.Writer, options ...func(*Encoder)) *Encoder {
 }
 
 // Encode writes the binary encoding of v to the stream
-// type must be uint64, *fr.Element, *fp.Element, *G1Affine, *G2Affine, []G1Affine or []G2Affine
+// type must be uint64, *fr.Element, *fp.Element, *G1Affine, *G2Affine, []G1Affine, []G2Affine, *[]G1Affine or *[]G2Affine
 func (enc *Encoder) Encode(v interface{}) (err error) {
 	if enc.raw {
 		return enc.encodeRaw(v)
@@ -565,6 +565,8 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 			}
 		}
 		return
+	case *[]G1Affine:
+		return enc.encode(*t)
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -584,6 +586,8 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 			}
 		}
 		return nil
+	case *[]G2Affine:
+		return enc.encode(*t)
 	case []G2Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -702,6 +706,8 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 			}
 		}
 		return
+	case *[]G1Affine:
+		return enc.encodeRaw(*t)
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -721,6 +727,8 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 			}
 		}
 		return nil
+	case *[]G2Affine:
+		return enc.encodeRaw(*t)
 	case []G2Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
diff --git a/ecc/bw6-761/marshal.go b/ecc/bw6-761/marshal.go
index ee4d185e2b..a173dd35e2 100644
--- a/ecc/bw6-761/marshal.go
+++ b/ecc/bw6-761/marshal.go
@@ -435,7 +435,7 @@ func NewEncoder(w io.Writer, options ...func(*Encoder)) *Encoder {
 }
 
 // Encode writes the binary encoding of v to the stream
-// type must be uint64, *fr.Element, *fp.Element, *G1Affine, *G2Affine, []G1Affine or []G2Affine
+// type must be uint64, *fr.Element, *fp.Element, *G1Affine, *G2Affine, []G1Affine, []G2Affine, *[]G1Affine or *[]G2Affine
 func (enc *Encoder) Encode(v interface{}) (err error) {
 	if enc.raw {
 		return enc.encodeRaw(v)
@@ -565,6 +565,8 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 			}
 		}
 		return
+	case *[]G1Affine:
+		return enc.encode(*t)
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -584,6 +586,8 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 			}
 		}
 		return nil
+	case *[]G2Affine:
+		return enc.encode(*t)
 	case []G2Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -702,6 +706,8 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 			}
 		}
 		return
+	case *[]G1Affine:
+		return enc.encodeRaw(*t)
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -721,6 +727,8 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 			}
 		}
 		return nil
+	case *[]G2Affine:
+		return enc.encodeRaw(*t)
 	case []G2Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
diff --git a/ecc/utils.go b/ecc/utils.go
index 78126fc1cc..c86c6295eb 100644
--- a/ecc/utils.go
+++ b/ecc/utils.go
@@ -178,7 +178,8 @@ func getVector(l *Lattice, a, b *big.Int) [2]big.Int {
 	return res
 }
 
-// NextPowerOfTwo returns the next power of 2 of n
+// NextPowerOfTwo(n) = 2^⌈log₂(n)⌉
+// or 2ᵏ where 2ᵏ⁻¹ < n ≤ 2ᵏ
 func NextPowerOfTwo(n uint64) uint64 {
 	c := bits.OnesCount64(n)
 	if c == 0 {
diff --git a/internal/generator/ecc/template/marshal.go.tmpl b/internal/generator/ecc/template/marshal.go.tmpl
index d26de5fa79..2f1bd7b914 100644
--- a/internal/generator/ecc/template/marshal.go.tmpl
+++ b/internal/generator/ecc/template/marshal.go.tmpl
@@ -464,7 +464,7 @@ func NewEncoder(w io.Writer, options ...func(*Encoder)) *Encoder {
 
 
 // Encode writes the binary encoding of v to the stream
-// type must be uint64, *fr.Element, *fp.Element, *G1Affine, *G2Affine, []G1Affine or []G2Affine
+// type must be uint64, *fr.Element, *fp.Element, *G1Affine, *G2Affine, []G1Affine, []G2Affine, *[]G1Affine or *[]G2Affine
 func (enc *Encoder) Encode(v interface{}) (err error) {
 	if enc.raw {
 		return enc.encodeRaw(v)
@@ -645,6 +645,8 @@ func (enc *Encoder) encode{{- $.Raw}}(v interface{}) (err error) {
 			}
 		}
 		return
+	case *[]G1Affine:
+		return enc.encode{{- $.Raw}}(*t)
 	case []G1Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))
@@ -664,6 +666,8 @@ func (enc *Encoder) encode{{- $.Raw}}(v interface{}) (err error) {
 			}
 		}
 		return nil
+	case *[]G2Affine:
+		return enc.encode{{- $.Raw}}(*t)
 	case []G2Affine:
 		// write slice length
 		err = binary.Write(enc.w, binary.BigEndian, uint32(len(t)))

From 41949a66ca879b61c367cf9652462e3cc400598b Mon Sep 17 00:00:00 2001
From: ThomasPiellard <thomas.piellard@consensys.net>
Date: Sat, 21 Dec 2024 16:17:52 +0100
Subject: [PATCH 102/114] feat: cleaned iop (#587)

---
 ecc/bls12-377/fr/iop/expressions.go           |   1 -
 ecc/bls12-377/fr/iop/polynomial.go            | 165 ++++++++++--------
 ecc/bls12-377/fr/iop/polynomial_test.go       | 123 +++++++------
 ecc/bls12-377/fr/iop/quotient.go              |   1 -
 ecc/bls12-381/fr/iop/expressions.go           |   1 -
 ecc/bls12-381/fr/iop/polynomial.go            | 165 ++++++++++--------
 ecc/bls12-381/fr/iop/polynomial_test.go       | 123 +++++++------
 ecc/bls12-381/fr/iop/quotient.go              |   1 -
 ecc/bls24-315/fr/iop/expressions.go           |   1 -
 ecc/bls24-315/fr/iop/polynomial.go            | 165 ++++++++++--------
 ecc/bls24-315/fr/iop/polynomial_test.go       | 123 +++++++------
 ecc/bls24-315/fr/iop/quotient.go              |   1 -
 ecc/bls24-317/fr/iop/expressions.go           |   1 -
 ecc/bls24-317/fr/iop/polynomial.go            | 165 ++++++++++--------
 ecc/bls24-317/fr/iop/polynomial_test.go       | 123 +++++++------
 ecc/bls24-317/fr/iop/quotient.go              |   1 -
 ecc/bn254/fr/iop/expressions.go               |   1 -
 ecc/bn254/fr/iop/polynomial.go                | 165 ++++++++++--------
 ecc/bn254/fr/iop/polynomial_test.go           | 123 +++++++------
 ecc/bn254/fr/iop/quotient.go                  |   1 -
 ecc/bw6-633/fr/iop/expressions.go             |   1 -
 ecc/bw6-633/fr/iop/polynomial.go              | 165 ++++++++++--------
 ecc/bw6-633/fr/iop/polynomial_test.go         | 123 +++++++------
 ecc/bw6-633/fr/iop/quotient.go                |   1 -
 ecc/bw6-761/fr/iop/expressions.go             |   1 -
 ecc/bw6-761/fr/iop/polynomial.go              | 165 ++++++++++--------
 ecc/bw6-761/fr/iop/polynomial_test.go         | 123 +++++++------
 ecc/bw6-761/fr/iop/quotient.go                |   1 -
 .../iop/template/expressions.go.tmpl          |   3 +-
 .../generator/iop/template/polynomial.go.tmpl | 165 ++++++++++--------
 .../iop/template/polynomial.test.go.tmpl      | 132 +++++++-------
 .../generator/iop/template/quotient.go.tmpl   |   6 +-
 32 files changed, 1279 insertions(+), 1057 deletions(-)

diff --git a/ecc/bls12-377/fr/iop/expressions.go b/ecc/bls12-377/fr/iop/expressions.go
index db75f5d8fc..b9195244b0 100644
--- a/ecc/bls12-377/fr/iop/expressions.go
+++ b/ecc/bls12-377/fr/iop/expressions.go
@@ -67,7 +67,6 @@ func Evaluate(f Expression, r []fr.Element, form Form, x ...*Polynomial) (*Polyn
 
 	res := NewPolynomial(&r, form)
 	res.size = x[0].size
-	res.blindedSize = x[0].size
 	res.shift = 0
 
 	return res, nil
diff --git a/ecc/bls12-377/fr/iop/polynomial.go b/ecc/bls12-377/fr/iop/polynomial.go
index 83ba068533..c793a71407 100644
--- a/ecc/bls12-377/fr/iop/polynomial.go
+++ b/ecc/bls12-377/fr/iop/polynomial.go
@@ -61,9 +61,9 @@ var (
 // default blindedSize=Size, until the polynomial is blinded.
 type Polynomial struct {
 	*polynomial
-	shift       int
-	size        int
-	blindedSize int
+	shift int
+	size  int
+	coset fr.Element // needed for evaluating the polynomial when it is expressed in Lagrange shifted basis
 }
 
 // NewPolynomial returned a Polynomial from the provided coefficients in the given form.
@@ -72,9 +72,8 @@ type Polynomial struct {
 // shouldn't be mutated.
 func NewPolynomial(coeffs *[]fr.Element, form Form) *Polynomial {
 	return &Polynomial{
-		polynomial:  newPolynomial(coeffs, form),
-		size:        len(*coeffs),
-		blindedSize: len(*coeffs),
+		polynomial: newPolynomial(coeffs, form),
+		size:       len(*coeffs),
 	}
 }
 
@@ -85,12 +84,6 @@ func (p *Polynomial) Shift(shift int) *Polynomial {
 	return p
 }
 
-// BlindedSize returns the the size of the polynomial when it is blinded. By
-// default blindedSize=Size, until the polynomial is blinded.
-func (p *Polynomial) BlindedSize() int {
-	return p.blindedSize
-}
-
 // Size returns the real size of the polynomial (seen as a vector).
 // For instance if len(P)=32 but P.Size=8, it means that P has been
 // extended (e.g. it is evaluated on a larger set) but P is a polynomial
@@ -108,69 +101,31 @@ func (p *Polynomial) SetSize(size int) {
 	p.size = size
 }
 
-// SetBlindedSize sets the blinded size of the polynomial.
-func (p *Polynomial) SetBlindedSize(size int) {
-	p.blindedSize = size
-}
-
-// Blind blinds a polynomial q by adding Q(X)*(X^{n}-1),
-// where deg Q = blindingOrder and Q is random, and n is the
-// size of q. Sets the result to p and returns it.
-//
-// blindingOrder is the degree of Q, where the blinding is Q(X)*(X^{n}-1)
-// where n is the size of p. The size of p is modified since the underlying
-// polynomial is of bigger degree now. The new size is p.Size+1+blindingOrder.
-//
-// /!\ The code panics if wq is not in canonical, regular layout
-func (p *Polynomial) Blind(blindingOrder int) *Polynomial {
-	// check that p is in canonical basis
-	if p.Form != canonicalRegular {
-		panic("the input must be in canonical basis, regular layout")
-	}
-
-	// we add Q*(x^{n}-1) so the new size is deg(Q)+n+1
-	// where n is the size of wq.
-	newSize := p.size + blindingOrder + 1
-
-	// Resize p. The size of wq might has already been increased
-	// (e.g. when the polynomial is evaluated on a larger domain),
-	// if that's the case we don't resize the polynomial.
-	p.grow(newSize)
-
-	// blinding: we add Q(X)(X^{n}-1) to P, where deg(Q)=blindingOrder
-	var r fr.Element
-
-	for i := 0; i <= blindingOrder; i++ {
-		r.SetRandom()
-		(*p.coefficients)[i].Sub(&(*p.coefficients)[i], &r)
-		(*p.coefficients)[i+p.size].Add(&(*p.coefficients)[i+p.size], &r)
-	}
-	p.blindedSize = newSize
-
-	return p
-}
-
 // Evaluate evaluates p at x.
 // The code panics if the function is not in canonical form.
 func (p *Polynomial) Evaluate(x fr.Element) fr.Element {
 
+	if p.Basis == LagrangeCoset {
+		x.Div(&x, &p.coset)
+	}
+
 	if p.shift == 0 {
 		return p.polynomial.evaluate(x)
 	}
 
 	var g fr.Element
-	gen, err := fft.Generator(uint64(p.size))
-	if err != nil {
-		panic(err)
-	}
 	if p.shift <= 5 {
+		gen, err := fft.Generator(uint64(p.size))
+		if err != nil {
+			panic(err)
+		}
 		g = smallExp(gen, p.shift)
 		x.Mul(&x, &g)
 		return p.polynomial.evaluate(x)
 	}
 
 	bs := big.NewInt(int64(p.shift))
-	g = *g.Exp(gen, bs)
+	g = *g.Exp(g, bs)
 	x.Mul(&x, &g)
 
 	return p.polynomial.evaluate(x)
@@ -245,20 +200,60 @@ func (p *polynomial) clone(capacity ...int) *polynomial {
 func (p *polynomial) evaluate(x fr.Element) fr.Element {
 
 	var r fr.Element
-	if p.Basis != Canonical {
-		panic("p must be in canonical basis")
+
+	evalLagrange := func() {
+		sizeP := p.coefficients.Len()
+		w, err := fft.Generator(uint64(sizeP))
+		if err != nil {
+			panic(err)
+		}
+		var accw fr.Element
+		accw.SetOne()
+		dens := make([]fr.Element, sizeP) // [x-1, x-ω, x-ω², ...]
+		for i := 0; i < sizeP; i++ {
+			dens[i].Sub(&x, &accw)
+			accw.Mul(&accw, &w)
+		}
+		invdens := fr.BatchInvert(dens) // [1/(x-1), 1/(x-ω), 1/(x-ω²), ...]
+		var tmp fr.Element
+		var one fr.Element
+		one.SetOne()
+		tmp.Exp(x, big.NewInt(int64(sizeP))).Sub(&tmp, &one) // xⁿ-1
+		var li fr.Element
+		li.SetUint64(uint64(sizeP)).Inverse(&li).Mul(&li, &tmp) // 1/n * (xⁿ-1)
+		if p.Layout == Regular {
+			for i := 0; i < sizeP; i++ {
+				li.Mul(&li, &invdens[i]) // li <- li*ω/(x-ωⁱ)
+				tmp.Mul(&li, &(*p.coefficients)[i])
+				r.Add(&r, &tmp)
+				li.Mul(&li, &dens[i]).Mul(&li, &w) // li <- li*ω*(x-ωⁱ)
+			}
+		} else {
+			nn := uint64(64 - bits.TrailingZeros(uint(p.coefficients.Len())))
+			for i := 0; i < sizeP; i++ {
+				iRev := bits.Reverse64(uint64(i)) >> nn
+				li.Mul(&li, &invdens[i]) // li <- li*ω/(x-ωⁱ)
+				tmp.Mul(&li, &(*p.coefficients)[iRev])
+				r.Add(&r, &tmp)
+				li.Mul(&li, &dens[i]).Mul(&li, &w) // li <- li*ω*(x-ωⁱ)
+			}
+		}
 	}
 
-	if p.Layout == Regular {
-		for i := p.coefficients.Len() - 1; i >= 0; i-- {
-			r.Mul(&r, &x).Add(&r, &(*p.coefficients)[i])
+	if p.Basis == Canonical {
+		if p.Layout == Regular {
+			for i := p.coefficients.Len() - 1; i >= 0; i-- {
+				r.Mul(&r, &x).Add(&r, &(*p.coefficients)[i])
+			}
+		} else {
+			nn := uint64(64 - bits.TrailingZeros(uint(p.coefficients.Len())))
+			for i := p.coefficients.Len() - 1; i >= 0; i-- {
+				iRev := bits.Reverse64(uint64(i)) >> nn
+				r.Mul(&r, &x).Add(&r, &(*p.coefficients)[iRev])
+			}
 		}
 	} else {
-		nn := uint64(64 - bits.TrailingZeros(uint(p.coefficients.Len())))
-		for i := p.coefficients.Len() - 1; i >= 0; i-- {
-			iRev := bits.Reverse64(uint64(i)) >> nn
-			r.Mul(&r, &x).Add(&r, &(*p.coefficients)[iRev])
-		}
+		evalLagrange()
 	}
 
 	return r
@@ -362,6 +357,11 @@ func (p *polynomial) grow(newSize int) {
 
 // ToLagrangeCoset Sets p to q, in LagrangeCoset form and returns it.
 func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial {
+	cosetTable, err := d.CosetTable()
+	if err != nil {
+		panic(err)
+	}
+	p.coset.Set(&cosetTable[1])
 	id := p.Form
 	p.grow(int(d.Cardinality))
 	switch id {
@@ -391,6 +391,7 @@ func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial {
 
 // WriteTo implements io.WriterTo
 func (p *Polynomial) WriteTo(w io.Writer) (int64, error) {
+
 	// encode coefficients
 	n, err := p.polynomial.coefficients.WriteTo(w)
 	if err != nil {
@@ -403,7 +404,6 @@ func (p *Polynomial) WriteTo(w io.Writer) (int64, error) {
 		uint32(p.Layout),
 		uint32(p.shift),
 		uint32(p.size),
-		uint32(p.blindedSize),
 	}
 	for _, v := range data {
 		err = binary.Write(w, binary.BigEndian, v)
@@ -412,6 +412,15 @@ func (p *Polynomial) WriteTo(w io.Writer) (int64, error) {
 		}
 		n += 4
 	}
+
+	var buf [fr.Bytes]byte
+	fr.BigEndian.PutElement(&buf, p.coset)
+	m, err := w.Write(buf[:])
+	n += int64(m)
+	if err != nil {
+		return n, err
+	}
+
 	return n, nil
 }
 
@@ -430,8 +439,8 @@ func (p *Polynomial) ReadFrom(r io.Reader) (int64, error) {
 		return n, err
 	}
 
-	// decode Form.Basis, Form.Layout, shift, size & blindedSize as uint32
-	var data [5]uint32
+	// decode Form.Basis, Form.Layout, shift as uint32
+	var data [4]uint32
 	var buf [4]byte
 	for i := range data {
 		read, err := io.ReadFull(r, buf[:4])
@@ -446,7 +455,17 @@ func (p *Polynomial) ReadFrom(r io.Reader) (int64, error) {
 	p.Layout = Layout(data[1])
 	p.shift = int(data[2])
 	p.size = int(data[3])
-	p.blindedSize = int(data[4])
+
+	var bufFr [fr.Bytes]byte
+	read, err := io.ReadFull(r, bufFr[:])
+	n += int64(read)
+	if err != nil {
+		return n, err
+	}
+	p.coset, err = fr.BigEndian.Element(&bufFr)
+	if err != nil {
+		return n, err
+	}
 
 	return n, nil
 }
diff --git a/ecc/bls12-377/fr/iop/polynomial_test.go b/ecc/bls12-377/fr/iop/polynomial_test.go
index b0decababf..a7b0ec595a 100644
--- a/ecc/bls12-377/fr/iop/polynomial_test.go
+++ b/ecc/bls12-377/fr/iop/polynomial_test.go
@@ -23,14 +23,14 @@ func TestEvaluation(t *testing.T) {
 	shift := 2
 	d := fft.NewDomain(uint64(size))
 	c := randomVector(size)
-	wp := NewPolynomial(c, Form{Basis: Canonical, Layout: Regular})
-	wps := wp.ShallowClone().Shift(shift)
-	ref := wp.Clone()
+	p := NewPolynomial(c, Form{Basis: Canonical, Layout: Regular})
+	ps := p.ShallowClone().Shift(shift)
+	ref := p.Clone()
 	ref.ToLagrange(d).ToRegular()
 
-	// regular layout
-	a := wp.Evaluate(d.Generator)
-	b := wps.Evaluate(d.Generator)
+	// canonical regular
+	a := p.Evaluate(d.Generator)
+	b := ps.Evaluate(d.Generator)
 	if !a.Equal(&ref.Coefficients()[1]) {
 		t.Fatal("error evaluation")
 	}
@@ -38,11 +38,11 @@ func TestEvaluation(t *testing.T) {
 		t.Fatal("error evaluation shifted")
 	}
 
-	// bit reversed layout
-	wp.ToBitReverse()
-	wps.ToBitReverse()
-	a = wp.Evaluate(d.Generator)
-	b = wps.Evaluate(d.Generator)
+	// canonical bit reversed
+	p.ToBitReverse()
+	ps.ToBitReverse()
+	a = p.Evaluate(d.Generator)
+	b = ps.Evaluate(d.Generator)
 	if !a.Equal(&ref.Coefficients()[1]) {
 		t.Fatal("error evaluation")
 	}
@@ -50,6 +50,60 @@ func TestEvaluation(t *testing.T) {
 		t.Fatal("error evaluation shifted")
 	}
 
+	// get reference values
+	var x fr.Element
+	x.SetRandom()
+	expectedEval := p.ToRegular().Evaluate(x)
+	expectedEvalShifted := ps.ToRegular().Evaluate(x)
+
+	// lagrange regular
+	p.ToLagrange(d).ToRegular()
+	ps.ToLagrange(d).ToRegular()
+	plx := p.Evaluate(x)
+	pslx := ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange shifted")
+	}
+
+	// lagrange bit reverse
+	p.ToBitReverse()
+	ps.ToBitReverse()
+	plx = p.Evaluate(x)
+	pslx = ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange shifted")
+	}
+
+	// lagrange coset regular
+	p.ToLagrangeCoset(d).ToRegular()
+	ps.ToLagrangeCoset(d).ToRegular()
+	plx = p.Evaluate(x)
+	pslx = ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange coset")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange coset shifted")
+	}
+
+	// lagrange coset bit reverse
+	p.ToRegular().ToBitReverse()
+	ps.ToRegular().ToBitReverse()
+	plx = p.Evaluate(x)
+	pslx = ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange coset")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange coset shifted")
+	}
+
 }
 
 func randomVector(size int) *[]fr.Element {
@@ -113,10 +167,9 @@ func TestRoundTrip(t *testing.T) {
 
 	size := 8
 	d := fft.NewDomain(uint64(8))
-	blindingOrder := 2
 
-	p := NewPolynomial(randomVector(size), Form{Basis: Lagrange, Layout: Regular}).ToCanonical(d).ToRegular()
-	p.Blind(blindingOrder)
+	p := NewPolynomial(randomVector(size), Form{Basis: Canonical, Layout: Regular})
+	p.ToLagrangeCoset(d)
 
 	// serialize
 	written, err := p.WriteTo(&buf)
@@ -134,52 +187,10 @@ func TestRoundTrip(t *testing.T) {
 	assert.Equal(p.Layout, reconstructed.Layout)
 	assert.Equal(p.shift, reconstructed.shift)
 	assert.Equal(p.size, reconstructed.size)
-	assert.Equal(p.blindedSize, reconstructed.blindedSize)
 	c1, c2 := p.Coefficients(), reconstructed.Coefficients()
 	assert.True(reflect.DeepEqual(c1, c2))
 }
 
-func TestBlinding(t *testing.T) {
-
-	size := 8
-	d := fft.NewDomain(uint64(8))
-	blindingOrder := 2
-
-	// generate a random polynomial in Lagrange form for the moment
-	// to check that an error is raised when the polynomial is not
-	// in canonical form.
-	wp := NewPolynomial(randomVector(size), Form{Basis: Lagrange, Layout: Regular})
-
-	// checks the blinding is correct: the evaluation of the blinded polynomial
-	// should be the same as the original on d's domain
-	wp.Basis = Canonical
-	wt := wp.Clone()
-	wt.Blind(blindingOrder)
-	if wt.coefficients.Len() != blindingOrder+size+1 {
-		t.Fatal("size of blinded polynomial is incorrect")
-	}
-	if wt.blindedSize != size+blindingOrder+1 {
-		t.Fatal("Size field of blinded polynomial is incorrect")
-	}
-	if wt.size != size {
-		t.Fatal("the size should not have been modified")
-	}
-	x := make([]fr.Element, size)
-	x[0].SetOne()
-	for i := 1; i < size; i++ {
-		x[i].Mul(&x[i-1], &d.Generator)
-	}
-	var a, b fr.Element
-	for i := 0; i < size; i++ {
-		a = wt.Evaluate(x[i])
-		b = wp.Evaluate(x[i])
-		if a != b {
-			t.Fatal("polynomial and its blinded version should be equal on V(X^{n}-1)")
-		}
-	}
-
-}
-
 // list of functions to turn a polynomial in Lagrange-regular form
 // to all different forms in ordered using this encoding:
 // int(p.Basis)*4 + int(p.Layout)*2 + int(p.Status)
diff --git a/ecc/bls12-377/fr/iop/quotient.go b/ecc/bls12-377/fr/iop/quotient.go
index 698ff0bb37..44ad792b5d 100644
--- a/ecc/bls12-377/fr/iop/quotient.go
+++ b/ecc/bls12-377/fr/iop/quotient.go
@@ -35,7 +35,6 @@ func DivideByXMinusOne(a *Polynomial, domains [2]*fft.Domain) (*Polynomial, erro
 	coeffs := make([]fr.Element, a.coefficients.Len())
 	res := NewPolynomial(&coeffs, Form{Layout: BitReverse, Basis: LagrangeCoset})
 	res.size = a.size
-	res.blindedSize = a.blindedSize
 
 	nn := uint64(64 - bits.TrailingZeros(uint(nbElmts)))
 	parallel.Execute(a.coefficients.Len(), func(start, end int) {
diff --git a/ecc/bls12-381/fr/iop/expressions.go b/ecc/bls12-381/fr/iop/expressions.go
index 2926911d05..57822fd3cc 100644
--- a/ecc/bls12-381/fr/iop/expressions.go
+++ b/ecc/bls12-381/fr/iop/expressions.go
@@ -67,7 +67,6 @@ func Evaluate(f Expression, r []fr.Element, form Form, x ...*Polynomial) (*Polyn
 
 	res := NewPolynomial(&r, form)
 	res.size = x[0].size
-	res.blindedSize = x[0].size
 	res.shift = 0
 
 	return res, nil
diff --git a/ecc/bls12-381/fr/iop/polynomial.go b/ecc/bls12-381/fr/iop/polynomial.go
index ed805584c0..9d20272e31 100644
--- a/ecc/bls12-381/fr/iop/polynomial.go
+++ b/ecc/bls12-381/fr/iop/polynomial.go
@@ -61,9 +61,9 @@ var (
 // default blindedSize=Size, until the polynomial is blinded.
 type Polynomial struct {
 	*polynomial
-	shift       int
-	size        int
-	blindedSize int
+	shift int
+	size  int
+	coset fr.Element // needed for evaluating the polynomial when it is expressed in Lagrange shifted basis
 }
 
 // NewPolynomial returned a Polynomial from the provided coefficients in the given form.
@@ -72,9 +72,8 @@ type Polynomial struct {
 // shouldn't be mutated.
 func NewPolynomial(coeffs *[]fr.Element, form Form) *Polynomial {
 	return &Polynomial{
-		polynomial:  newPolynomial(coeffs, form),
-		size:        len(*coeffs),
-		blindedSize: len(*coeffs),
+		polynomial: newPolynomial(coeffs, form),
+		size:       len(*coeffs),
 	}
 }
 
@@ -85,12 +84,6 @@ func (p *Polynomial) Shift(shift int) *Polynomial {
 	return p
 }
 
-// BlindedSize returns the the size of the polynomial when it is blinded. By
-// default blindedSize=Size, until the polynomial is blinded.
-func (p *Polynomial) BlindedSize() int {
-	return p.blindedSize
-}
-
 // Size returns the real size of the polynomial (seen as a vector).
 // For instance if len(P)=32 but P.Size=8, it means that P has been
 // extended (e.g. it is evaluated on a larger set) but P is a polynomial
@@ -108,69 +101,31 @@ func (p *Polynomial) SetSize(size int) {
 	p.size = size
 }
 
-// SetBlindedSize sets the blinded size of the polynomial.
-func (p *Polynomial) SetBlindedSize(size int) {
-	p.blindedSize = size
-}
-
-// Blind blinds a polynomial q by adding Q(X)*(X^{n}-1),
-// where deg Q = blindingOrder and Q is random, and n is the
-// size of q. Sets the result to p and returns it.
-//
-// blindingOrder is the degree of Q, where the blinding is Q(X)*(X^{n}-1)
-// where n is the size of p. The size of p is modified since the underlying
-// polynomial is of bigger degree now. The new size is p.Size+1+blindingOrder.
-//
-// /!\ The code panics if wq is not in canonical, regular layout
-func (p *Polynomial) Blind(blindingOrder int) *Polynomial {
-	// check that p is in canonical basis
-	if p.Form != canonicalRegular {
-		panic("the input must be in canonical basis, regular layout")
-	}
-
-	// we add Q*(x^{n}-1) so the new size is deg(Q)+n+1
-	// where n is the size of wq.
-	newSize := p.size + blindingOrder + 1
-
-	// Resize p. The size of wq might has already been increased
-	// (e.g. when the polynomial is evaluated on a larger domain),
-	// if that's the case we don't resize the polynomial.
-	p.grow(newSize)
-
-	// blinding: we add Q(X)(X^{n}-1) to P, where deg(Q)=blindingOrder
-	var r fr.Element
-
-	for i := 0; i <= blindingOrder; i++ {
-		r.SetRandom()
-		(*p.coefficients)[i].Sub(&(*p.coefficients)[i], &r)
-		(*p.coefficients)[i+p.size].Add(&(*p.coefficients)[i+p.size], &r)
-	}
-	p.blindedSize = newSize
-
-	return p
-}
-
 // Evaluate evaluates p at x.
 // The code panics if the function is not in canonical form.
 func (p *Polynomial) Evaluate(x fr.Element) fr.Element {
 
+	if p.Basis == LagrangeCoset {
+		x.Div(&x, &p.coset)
+	}
+
 	if p.shift == 0 {
 		return p.polynomial.evaluate(x)
 	}
 
 	var g fr.Element
-	gen, err := fft.Generator(uint64(p.size))
-	if err != nil {
-		panic(err)
-	}
 	if p.shift <= 5 {
+		gen, err := fft.Generator(uint64(p.size))
+		if err != nil {
+			panic(err)
+		}
 		g = smallExp(gen, p.shift)
 		x.Mul(&x, &g)
 		return p.polynomial.evaluate(x)
 	}
 
 	bs := big.NewInt(int64(p.shift))
-	g = *g.Exp(gen, bs)
+	g = *g.Exp(g, bs)
 	x.Mul(&x, &g)
 
 	return p.polynomial.evaluate(x)
@@ -245,20 +200,60 @@ func (p *polynomial) clone(capacity ...int) *polynomial {
 func (p *polynomial) evaluate(x fr.Element) fr.Element {
 
 	var r fr.Element
-	if p.Basis != Canonical {
-		panic("p must be in canonical basis")
+
+	evalLagrange := func() {
+		sizeP := p.coefficients.Len()
+		w, err := fft.Generator(uint64(sizeP))
+		if err != nil {
+			panic(err)
+		}
+		var accw fr.Element
+		accw.SetOne()
+		dens := make([]fr.Element, sizeP) // [x-1, x-ω, x-ω², ...]
+		for i := 0; i < sizeP; i++ {
+			dens[i].Sub(&x, &accw)
+			accw.Mul(&accw, &w)
+		}
+		invdens := fr.BatchInvert(dens) // [1/(x-1), 1/(x-ω), 1/(x-ω²), ...]
+		var tmp fr.Element
+		var one fr.Element
+		one.SetOne()
+		tmp.Exp(x, big.NewInt(int64(sizeP))).Sub(&tmp, &one) // xⁿ-1
+		var li fr.Element
+		li.SetUint64(uint64(sizeP)).Inverse(&li).Mul(&li, &tmp) // 1/n * (xⁿ-1)
+		if p.Layout == Regular {
+			for i := 0; i < sizeP; i++ {
+				li.Mul(&li, &invdens[i]) // li <- li*ω/(x-ωⁱ)
+				tmp.Mul(&li, &(*p.coefficients)[i])
+				r.Add(&r, &tmp)
+				li.Mul(&li, &dens[i]).Mul(&li, &w) // li <- li*ω*(x-ωⁱ)
+			}
+		} else {
+			nn := uint64(64 - bits.TrailingZeros(uint(p.coefficients.Len())))
+			for i := 0; i < sizeP; i++ {
+				iRev := bits.Reverse64(uint64(i)) >> nn
+				li.Mul(&li, &invdens[i]) // li <- li*ω/(x-ωⁱ)
+				tmp.Mul(&li, &(*p.coefficients)[iRev])
+				r.Add(&r, &tmp)
+				li.Mul(&li, &dens[i]).Mul(&li, &w) // li <- li*ω*(x-ωⁱ)
+			}
+		}
 	}
 
-	if p.Layout == Regular {
-		for i := p.coefficients.Len() - 1; i >= 0; i-- {
-			r.Mul(&r, &x).Add(&r, &(*p.coefficients)[i])
+	if p.Basis == Canonical {
+		if p.Layout == Regular {
+			for i := p.coefficients.Len() - 1; i >= 0; i-- {
+				r.Mul(&r, &x).Add(&r, &(*p.coefficients)[i])
+			}
+		} else {
+			nn := uint64(64 - bits.TrailingZeros(uint(p.coefficients.Len())))
+			for i := p.coefficients.Len() - 1; i >= 0; i-- {
+				iRev := bits.Reverse64(uint64(i)) >> nn
+				r.Mul(&r, &x).Add(&r, &(*p.coefficients)[iRev])
+			}
 		}
 	} else {
-		nn := uint64(64 - bits.TrailingZeros(uint(p.coefficients.Len())))
-		for i := p.coefficients.Len() - 1; i >= 0; i-- {
-			iRev := bits.Reverse64(uint64(i)) >> nn
-			r.Mul(&r, &x).Add(&r, &(*p.coefficients)[iRev])
-		}
+		evalLagrange()
 	}
 
 	return r
@@ -362,6 +357,11 @@ func (p *polynomial) grow(newSize int) {
 
 // ToLagrangeCoset Sets p to q, in LagrangeCoset form and returns it.
 func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial {
+	cosetTable, err := d.CosetTable()
+	if err != nil {
+		panic(err)
+	}
+	p.coset.Set(&cosetTable[1])
 	id := p.Form
 	p.grow(int(d.Cardinality))
 	switch id {
@@ -391,6 +391,7 @@ func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial {
 
 // WriteTo implements io.WriterTo
 func (p *Polynomial) WriteTo(w io.Writer) (int64, error) {
+
 	// encode coefficients
 	n, err := p.polynomial.coefficients.WriteTo(w)
 	if err != nil {
@@ -403,7 +404,6 @@ func (p *Polynomial) WriteTo(w io.Writer) (int64, error) {
 		uint32(p.Layout),
 		uint32(p.shift),
 		uint32(p.size),
-		uint32(p.blindedSize),
 	}
 	for _, v := range data {
 		err = binary.Write(w, binary.BigEndian, v)
@@ -412,6 +412,15 @@ func (p *Polynomial) WriteTo(w io.Writer) (int64, error) {
 		}
 		n += 4
 	}
+
+	var buf [fr.Bytes]byte
+	fr.BigEndian.PutElement(&buf, p.coset)
+	m, err := w.Write(buf[:])
+	n += int64(m)
+	if err != nil {
+		return n, err
+	}
+
 	return n, nil
 }
 
@@ -430,8 +439,8 @@ func (p *Polynomial) ReadFrom(r io.Reader) (int64, error) {
 		return n, err
 	}
 
-	// decode Form.Basis, Form.Layout, shift, size & blindedSize as uint32
-	var data [5]uint32
+	// decode Form.Basis, Form.Layout, shift as uint32
+	var data [4]uint32
 	var buf [4]byte
 	for i := range data {
 		read, err := io.ReadFull(r, buf[:4])
@@ -446,7 +455,17 @@ func (p *Polynomial) ReadFrom(r io.Reader) (int64, error) {
 	p.Layout = Layout(data[1])
 	p.shift = int(data[2])
 	p.size = int(data[3])
-	p.blindedSize = int(data[4])
+
+	var bufFr [fr.Bytes]byte
+	read, err := io.ReadFull(r, bufFr[:])
+	n += int64(read)
+	if err != nil {
+		return n, err
+	}
+	p.coset, err = fr.BigEndian.Element(&bufFr)
+	if err != nil {
+		return n, err
+	}
 
 	return n, nil
 }
diff --git a/ecc/bls12-381/fr/iop/polynomial_test.go b/ecc/bls12-381/fr/iop/polynomial_test.go
index cba62562d3..96f67f8f82 100644
--- a/ecc/bls12-381/fr/iop/polynomial_test.go
+++ b/ecc/bls12-381/fr/iop/polynomial_test.go
@@ -23,14 +23,14 @@ func TestEvaluation(t *testing.T) {
 	shift := 2
 	d := fft.NewDomain(uint64(size))
 	c := randomVector(size)
-	wp := NewPolynomial(c, Form{Basis: Canonical, Layout: Regular})
-	wps := wp.ShallowClone().Shift(shift)
-	ref := wp.Clone()
+	p := NewPolynomial(c, Form{Basis: Canonical, Layout: Regular})
+	ps := p.ShallowClone().Shift(shift)
+	ref := p.Clone()
 	ref.ToLagrange(d).ToRegular()
 
-	// regular layout
-	a := wp.Evaluate(d.Generator)
-	b := wps.Evaluate(d.Generator)
+	// canonical regular
+	a := p.Evaluate(d.Generator)
+	b := ps.Evaluate(d.Generator)
 	if !a.Equal(&ref.Coefficients()[1]) {
 		t.Fatal("error evaluation")
 	}
@@ -38,11 +38,11 @@ func TestEvaluation(t *testing.T) {
 		t.Fatal("error evaluation shifted")
 	}
 
-	// bit reversed layout
-	wp.ToBitReverse()
-	wps.ToBitReverse()
-	a = wp.Evaluate(d.Generator)
-	b = wps.Evaluate(d.Generator)
+	// canonical bit reversed
+	p.ToBitReverse()
+	ps.ToBitReverse()
+	a = p.Evaluate(d.Generator)
+	b = ps.Evaluate(d.Generator)
 	if !a.Equal(&ref.Coefficients()[1]) {
 		t.Fatal("error evaluation")
 	}
@@ -50,6 +50,60 @@ func TestEvaluation(t *testing.T) {
 		t.Fatal("error evaluation shifted")
 	}
 
+	// get reference values
+	var x fr.Element
+	x.SetRandom()
+	expectedEval := p.ToRegular().Evaluate(x)
+	expectedEvalShifted := ps.ToRegular().Evaluate(x)
+
+	// lagrange regular
+	p.ToLagrange(d).ToRegular()
+	ps.ToLagrange(d).ToRegular()
+	plx := p.Evaluate(x)
+	pslx := ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange shifted")
+	}
+
+	// lagrange bit reverse
+	p.ToBitReverse()
+	ps.ToBitReverse()
+	plx = p.Evaluate(x)
+	pslx = ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange shifted")
+	}
+
+	// lagrange coset regular
+	p.ToLagrangeCoset(d).ToRegular()
+	ps.ToLagrangeCoset(d).ToRegular()
+	plx = p.Evaluate(x)
+	pslx = ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange coset")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange coset shifted")
+	}
+
+	// lagrange coset bit reverse
+	p.ToRegular().ToBitReverse()
+	ps.ToRegular().ToBitReverse()
+	plx = p.Evaluate(x)
+	pslx = ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange coset")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange coset shifted")
+	}
+
 }
 
 func randomVector(size int) *[]fr.Element {
@@ -113,10 +167,9 @@ func TestRoundTrip(t *testing.T) {
 
 	size := 8
 	d := fft.NewDomain(uint64(8))
-	blindingOrder := 2
 
-	p := NewPolynomial(randomVector(size), Form{Basis: Lagrange, Layout: Regular}).ToCanonical(d).ToRegular()
-	p.Blind(blindingOrder)
+	p := NewPolynomial(randomVector(size), Form{Basis: Canonical, Layout: Regular})
+	p.ToLagrangeCoset(d)
 
 	// serialize
 	written, err := p.WriteTo(&buf)
@@ -134,52 +187,10 @@ func TestRoundTrip(t *testing.T) {
 	assert.Equal(p.Layout, reconstructed.Layout)
 	assert.Equal(p.shift, reconstructed.shift)
 	assert.Equal(p.size, reconstructed.size)
-	assert.Equal(p.blindedSize, reconstructed.blindedSize)
 	c1, c2 := p.Coefficients(), reconstructed.Coefficients()
 	assert.True(reflect.DeepEqual(c1, c2))
 }
 
-func TestBlinding(t *testing.T) {
-
-	size := 8
-	d := fft.NewDomain(uint64(8))
-	blindingOrder := 2
-
-	// generate a random polynomial in Lagrange form for the moment
-	// to check that an error is raised when the polynomial is not
-	// in canonical form.
-	wp := NewPolynomial(randomVector(size), Form{Basis: Lagrange, Layout: Regular})
-
-	// checks the blinding is correct: the evaluation of the blinded polynomial
-	// should be the same as the original on d's domain
-	wp.Basis = Canonical
-	wt := wp.Clone()
-	wt.Blind(blindingOrder)
-	if wt.coefficients.Len() != blindingOrder+size+1 {
-		t.Fatal("size of blinded polynomial is incorrect")
-	}
-	if wt.blindedSize != size+blindingOrder+1 {
-		t.Fatal("Size field of blinded polynomial is incorrect")
-	}
-	if wt.size != size {
-		t.Fatal("the size should not have been modified")
-	}
-	x := make([]fr.Element, size)
-	x[0].SetOne()
-	for i := 1; i < size; i++ {
-		x[i].Mul(&x[i-1], &d.Generator)
-	}
-	var a, b fr.Element
-	for i := 0; i < size; i++ {
-		a = wt.Evaluate(x[i])
-		b = wp.Evaluate(x[i])
-		if a != b {
-			t.Fatal("polynomial and its blinded version should be equal on V(X^{n}-1)")
-		}
-	}
-
-}
-
 // list of functions to turn a polynomial in Lagrange-regular form
 // to all different forms in ordered using this encoding:
 // int(p.Basis)*4 + int(p.Layout)*2 + int(p.Status)
diff --git a/ecc/bls12-381/fr/iop/quotient.go b/ecc/bls12-381/fr/iop/quotient.go
index 5c4b2a9eb8..9d75028f1b 100644
--- a/ecc/bls12-381/fr/iop/quotient.go
+++ b/ecc/bls12-381/fr/iop/quotient.go
@@ -35,7 +35,6 @@ func DivideByXMinusOne(a *Polynomial, domains [2]*fft.Domain) (*Polynomial, erro
 	coeffs := make([]fr.Element, a.coefficients.Len())
 	res := NewPolynomial(&coeffs, Form{Layout: BitReverse, Basis: LagrangeCoset})
 	res.size = a.size
-	res.blindedSize = a.blindedSize
 
 	nn := uint64(64 - bits.TrailingZeros(uint(nbElmts)))
 	parallel.Execute(a.coefficients.Len(), func(start, end int) {
diff --git a/ecc/bls24-315/fr/iop/expressions.go b/ecc/bls24-315/fr/iop/expressions.go
index b4706d77d6..be044147f9 100644
--- a/ecc/bls24-315/fr/iop/expressions.go
+++ b/ecc/bls24-315/fr/iop/expressions.go
@@ -67,7 +67,6 @@ func Evaluate(f Expression, r []fr.Element, form Form, x ...*Polynomial) (*Polyn
 
 	res := NewPolynomial(&r, form)
 	res.size = x[0].size
-	res.blindedSize = x[0].size
 	res.shift = 0
 
 	return res, nil
diff --git a/ecc/bls24-315/fr/iop/polynomial.go b/ecc/bls24-315/fr/iop/polynomial.go
index 33a5265ee4..91ee36796a 100644
--- a/ecc/bls24-315/fr/iop/polynomial.go
+++ b/ecc/bls24-315/fr/iop/polynomial.go
@@ -61,9 +61,9 @@ var (
 // default blindedSize=Size, until the polynomial is blinded.
 type Polynomial struct {
 	*polynomial
-	shift       int
-	size        int
-	blindedSize int
+	shift int
+	size  int
+	coset fr.Element // needed for evaluating the polynomial when it is expressed in Lagrange shifted basis
 }
 
 // NewPolynomial returned a Polynomial from the provided coefficients in the given form.
@@ -72,9 +72,8 @@ type Polynomial struct {
 // shouldn't be mutated.
 func NewPolynomial(coeffs *[]fr.Element, form Form) *Polynomial {
 	return &Polynomial{
-		polynomial:  newPolynomial(coeffs, form),
-		size:        len(*coeffs),
-		blindedSize: len(*coeffs),
+		polynomial: newPolynomial(coeffs, form),
+		size:       len(*coeffs),
 	}
 }
 
@@ -85,12 +84,6 @@ func (p *Polynomial) Shift(shift int) *Polynomial {
 	return p
 }
 
-// BlindedSize returns the the size of the polynomial when it is blinded. By
-// default blindedSize=Size, until the polynomial is blinded.
-func (p *Polynomial) BlindedSize() int {
-	return p.blindedSize
-}
-
 // Size returns the real size of the polynomial (seen as a vector).
 // For instance if len(P)=32 but P.Size=8, it means that P has been
 // extended (e.g. it is evaluated on a larger set) but P is a polynomial
@@ -108,69 +101,31 @@ func (p *Polynomial) SetSize(size int) {
 	p.size = size
 }
 
-// SetBlindedSize sets the blinded size of the polynomial.
-func (p *Polynomial) SetBlindedSize(size int) {
-	p.blindedSize = size
-}
-
-// Blind blinds a polynomial q by adding Q(X)*(X^{n}-1),
-// where deg Q = blindingOrder and Q is random, and n is the
-// size of q. Sets the result to p and returns it.
-//
-// blindingOrder is the degree of Q, where the blinding is Q(X)*(X^{n}-1)
-// where n is the size of p. The size of p is modified since the underlying
-// polynomial is of bigger degree now. The new size is p.Size+1+blindingOrder.
-//
-// /!\ The code panics if wq is not in canonical, regular layout
-func (p *Polynomial) Blind(blindingOrder int) *Polynomial {
-	// check that p is in canonical basis
-	if p.Form != canonicalRegular {
-		panic("the input must be in canonical basis, regular layout")
-	}
-
-	// we add Q*(x^{n}-1) so the new size is deg(Q)+n+1
-	// where n is the size of wq.
-	newSize := p.size + blindingOrder + 1
-
-	// Resize p. The size of wq might has already been increased
-	// (e.g. when the polynomial is evaluated on a larger domain),
-	// if that's the case we don't resize the polynomial.
-	p.grow(newSize)
-
-	// blinding: we add Q(X)(X^{n}-1) to P, where deg(Q)=blindingOrder
-	var r fr.Element
-
-	for i := 0; i <= blindingOrder; i++ {
-		r.SetRandom()
-		(*p.coefficients)[i].Sub(&(*p.coefficients)[i], &r)
-		(*p.coefficients)[i+p.size].Add(&(*p.coefficients)[i+p.size], &r)
-	}
-	p.blindedSize = newSize
-
-	return p
-}
-
 // Evaluate evaluates p at x.
 // The code panics if the function is not in canonical form.
 func (p *Polynomial) Evaluate(x fr.Element) fr.Element {
 
+	if p.Basis == LagrangeCoset {
+		x.Div(&x, &p.coset)
+	}
+
 	if p.shift == 0 {
 		return p.polynomial.evaluate(x)
 	}
 
 	var g fr.Element
-	gen, err := fft.Generator(uint64(p.size))
-	if err != nil {
-		panic(err)
-	}
 	if p.shift <= 5 {
+		gen, err := fft.Generator(uint64(p.size))
+		if err != nil {
+			panic(err)
+		}
 		g = smallExp(gen, p.shift)
 		x.Mul(&x, &g)
 		return p.polynomial.evaluate(x)
 	}
 
 	bs := big.NewInt(int64(p.shift))
-	g = *g.Exp(gen, bs)
+	g = *g.Exp(g, bs)
 	x.Mul(&x, &g)
 
 	return p.polynomial.evaluate(x)
@@ -245,20 +200,60 @@ func (p *polynomial) clone(capacity ...int) *polynomial {
 func (p *polynomial) evaluate(x fr.Element) fr.Element {
 
 	var r fr.Element
-	if p.Basis != Canonical {
-		panic("p must be in canonical basis")
+
+	evalLagrange := func() {
+		sizeP := p.coefficients.Len()
+		w, err := fft.Generator(uint64(sizeP))
+		if err != nil {
+			panic(err)
+		}
+		var accw fr.Element
+		accw.SetOne()
+		dens := make([]fr.Element, sizeP) // [x-1, x-ω, x-ω², ...]
+		for i := 0; i < sizeP; i++ {
+			dens[i].Sub(&x, &accw)
+			accw.Mul(&accw, &w)
+		}
+		invdens := fr.BatchInvert(dens) // [1/(x-1), 1/(x-ω), 1/(x-ω²), ...]
+		var tmp fr.Element
+		var one fr.Element
+		one.SetOne()
+		tmp.Exp(x, big.NewInt(int64(sizeP))).Sub(&tmp, &one) // xⁿ-1
+		var li fr.Element
+		li.SetUint64(uint64(sizeP)).Inverse(&li).Mul(&li, &tmp) // 1/n * (xⁿ-1)
+		if p.Layout == Regular {
+			for i := 0; i < sizeP; i++ {
+				li.Mul(&li, &invdens[i]) // li <- li*ω/(x-ωⁱ)
+				tmp.Mul(&li, &(*p.coefficients)[i])
+				r.Add(&r, &tmp)
+				li.Mul(&li, &dens[i]).Mul(&li, &w) // li <- li*ω*(x-ωⁱ)
+			}
+		} else {
+			nn := uint64(64 - bits.TrailingZeros(uint(p.coefficients.Len())))
+			for i := 0; i < sizeP; i++ {
+				iRev := bits.Reverse64(uint64(i)) >> nn
+				li.Mul(&li, &invdens[i]) // li <- li*ω/(x-ωⁱ)
+				tmp.Mul(&li, &(*p.coefficients)[iRev])
+				r.Add(&r, &tmp)
+				li.Mul(&li, &dens[i]).Mul(&li, &w) // li <- li*ω*(x-ωⁱ)
+			}
+		}
 	}
 
-	if p.Layout == Regular {
-		for i := p.coefficients.Len() - 1; i >= 0; i-- {
-			r.Mul(&r, &x).Add(&r, &(*p.coefficients)[i])
+	if p.Basis == Canonical {
+		if p.Layout == Regular {
+			for i := p.coefficients.Len() - 1; i >= 0; i-- {
+				r.Mul(&r, &x).Add(&r, &(*p.coefficients)[i])
+			}
+		} else {
+			nn := uint64(64 - bits.TrailingZeros(uint(p.coefficients.Len())))
+			for i := p.coefficients.Len() - 1; i >= 0; i-- {
+				iRev := bits.Reverse64(uint64(i)) >> nn
+				r.Mul(&r, &x).Add(&r, &(*p.coefficients)[iRev])
+			}
 		}
 	} else {
-		nn := uint64(64 - bits.TrailingZeros(uint(p.coefficients.Len())))
-		for i := p.coefficients.Len() - 1; i >= 0; i-- {
-			iRev := bits.Reverse64(uint64(i)) >> nn
-			r.Mul(&r, &x).Add(&r, &(*p.coefficients)[iRev])
-		}
+		evalLagrange()
 	}
 
 	return r
@@ -362,6 +357,11 @@ func (p *polynomial) grow(newSize int) {
 
 // ToLagrangeCoset Sets p to q, in LagrangeCoset form and returns it.
 func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial {
+	cosetTable, err := d.CosetTable()
+	if err != nil {
+		panic(err)
+	}
+	p.coset.Set(&cosetTable[1])
 	id := p.Form
 	p.grow(int(d.Cardinality))
 	switch id {
@@ -391,6 +391,7 @@ func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial {
 
 // WriteTo implements io.WriterTo
 func (p *Polynomial) WriteTo(w io.Writer) (int64, error) {
+
 	// encode coefficients
 	n, err := p.polynomial.coefficients.WriteTo(w)
 	if err != nil {
@@ -403,7 +404,6 @@ func (p *Polynomial) WriteTo(w io.Writer) (int64, error) {
 		uint32(p.Layout),
 		uint32(p.shift),
 		uint32(p.size),
-		uint32(p.blindedSize),
 	}
 	for _, v := range data {
 		err = binary.Write(w, binary.BigEndian, v)
@@ -412,6 +412,15 @@ func (p *Polynomial) WriteTo(w io.Writer) (int64, error) {
 		}
 		n += 4
 	}
+
+	var buf [fr.Bytes]byte
+	fr.BigEndian.PutElement(&buf, p.coset)
+	m, err := w.Write(buf[:])
+	n += int64(m)
+	if err != nil {
+		return n, err
+	}
+
 	return n, nil
 }
 
@@ -430,8 +439,8 @@ func (p *Polynomial) ReadFrom(r io.Reader) (int64, error) {
 		return n, err
 	}
 
-	// decode Form.Basis, Form.Layout, shift, size & blindedSize as uint32
-	var data [5]uint32
+	// decode Form.Basis, Form.Layout, shift as uint32
+	var data [4]uint32
 	var buf [4]byte
 	for i := range data {
 		read, err := io.ReadFull(r, buf[:4])
@@ -446,7 +455,17 @@ func (p *Polynomial) ReadFrom(r io.Reader) (int64, error) {
 	p.Layout = Layout(data[1])
 	p.shift = int(data[2])
 	p.size = int(data[3])
-	p.blindedSize = int(data[4])
+
+	var bufFr [fr.Bytes]byte
+	read, err := io.ReadFull(r, bufFr[:])
+	n += int64(read)
+	if err != nil {
+		return n, err
+	}
+	p.coset, err = fr.BigEndian.Element(&bufFr)
+	if err != nil {
+		return n, err
+	}
 
 	return n, nil
 }
diff --git a/ecc/bls24-315/fr/iop/polynomial_test.go b/ecc/bls24-315/fr/iop/polynomial_test.go
index 89d65b2fd6..a8e86b350f 100644
--- a/ecc/bls24-315/fr/iop/polynomial_test.go
+++ b/ecc/bls24-315/fr/iop/polynomial_test.go
@@ -23,14 +23,14 @@ func TestEvaluation(t *testing.T) {
 	shift := 2
 	d := fft.NewDomain(uint64(size))
 	c := randomVector(size)
-	wp := NewPolynomial(c, Form{Basis: Canonical, Layout: Regular})
-	wps := wp.ShallowClone().Shift(shift)
-	ref := wp.Clone()
+	p := NewPolynomial(c, Form{Basis: Canonical, Layout: Regular})
+	ps := p.ShallowClone().Shift(shift)
+	ref := p.Clone()
 	ref.ToLagrange(d).ToRegular()
 
-	// regular layout
-	a := wp.Evaluate(d.Generator)
-	b := wps.Evaluate(d.Generator)
+	// canonical regular
+	a := p.Evaluate(d.Generator)
+	b := ps.Evaluate(d.Generator)
 	if !a.Equal(&ref.Coefficients()[1]) {
 		t.Fatal("error evaluation")
 	}
@@ -38,11 +38,11 @@ func TestEvaluation(t *testing.T) {
 		t.Fatal("error evaluation shifted")
 	}
 
-	// bit reversed layout
-	wp.ToBitReverse()
-	wps.ToBitReverse()
-	a = wp.Evaluate(d.Generator)
-	b = wps.Evaluate(d.Generator)
+	// canonical bit reversed
+	p.ToBitReverse()
+	ps.ToBitReverse()
+	a = p.Evaluate(d.Generator)
+	b = ps.Evaluate(d.Generator)
 	if !a.Equal(&ref.Coefficients()[1]) {
 		t.Fatal("error evaluation")
 	}
@@ -50,6 +50,60 @@ func TestEvaluation(t *testing.T) {
 		t.Fatal("error evaluation shifted")
 	}
 
+	// get reference values
+	var x fr.Element
+	x.SetRandom()
+	expectedEval := p.ToRegular().Evaluate(x)
+	expectedEvalShifted := ps.ToRegular().Evaluate(x)
+
+	// lagrange regular
+	p.ToLagrange(d).ToRegular()
+	ps.ToLagrange(d).ToRegular()
+	plx := p.Evaluate(x)
+	pslx := ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange shifted")
+	}
+
+	// lagrange bit reverse
+	p.ToBitReverse()
+	ps.ToBitReverse()
+	plx = p.Evaluate(x)
+	pslx = ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange shifted")
+	}
+
+	// lagrange coset regular
+	p.ToLagrangeCoset(d).ToRegular()
+	ps.ToLagrangeCoset(d).ToRegular()
+	plx = p.Evaluate(x)
+	pslx = ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange coset")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange coset shifted")
+	}
+
+	// lagrange coset bit reverse
+	p.ToRegular().ToBitReverse()
+	ps.ToRegular().ToBitReverse()
+	plx = p.Evaluate(x)
+	pslx = ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange coset")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange coset shifted")
+	}
+
 }
 
 func randomVector(size int) *[]fr.Element {
@@ -113,10 +167,9 @@ func TestRoundTrip(t *testing.T) {
 
 	size := 8
 	d := fft.NewDomain(uint64(8))
-	blindingOrder := 2
 
-	p := NewPolynomial(randomVector(size), Form{Basis: Lagrange, Layout: Regular}).ToCanonical(d).ToRegular()
-	p.Blind(blindingOrder)
+	p := NewPolynomial(randomVector(size), Form{Basis: Canonical, Layout: Regular})
+	p.ToLagrangeCoset(d)
 
 	// serialize
 	written, err := p.WriteTo(&buf)
@@ -134,52 +187,10 @@ func TestRoundTrip(t *testing.T) {
 	assert.Equal(p.Layout, reconstructed.Layout)
 	assert.Equal(p.shift, reconstructed.shift)
 	assert.Equal(p.size, reconstructed.size)
-	assert.Equal(p.blindedSize, reconstructed.blindedSize)
 	c1, c2 := p.Coefficients(), reconstructed.Coefficients()
 	assert.True(reflect.DeepEqual(c1, c2))
 }
 
-func TestBlinding(t *testing.T) {
-
-	size := 8
-	d := fft.NewDomain(uint64(8))
-	blindingOrder := 2
-
-	// generate a random polynomial in Lagrange form for the moment
-	// to check that an error is raised when the polynomial is not
-	// in canonical form.
-	wp := NewPolynomial(randomVector(size), Form{Basis: Lagrange, Layout: Regular})
-
-	// checks the blinding is correct: the evaluation of the blinded polynomial
-	// should be the same as the original on d's domain
-	wp.Basis = Canonical
-	wt := wp.Clone()
-	wt.Blind(blindingOrder)
-	if wt.coefficients.Len() != blindingOrder+size+1 {
-		t.Fatal("size of blinded polynomial is incorrect")
-	}
-	if wt.blindedSize != size+blindingOrder+1 {
-		t.Fatal("Size field of blinded polynomial is incorrect")
-	}
-	if wt.size != size {
-		t.Fatal("the size should not have been modified")
-	}
-	x := make([]fr.Element, size)
-	x[0].SetOne()
-	for i := 1; i < size; i++ {
-		x[i].Mul(&x[i-1], &d.Generator)
-	}
-	var a, b fr.Element
-	for i := 0; i < size; i++ {
-		a = wt.Evaluate(x[i])
-		b = wp.Evaluate(x[i])
-		if a != b {
-			t.Fatal("polynomial and its blinded version should be equal on V(X^{n}-1)")
-		}
-	}
-
-}
-
 // list of functions to turn a polynomial in Lagrange-regular form
 // to all different forms in ordered using this encoding:
 // int(p.Basis)*4 + int(p.Layout)*2 + int(p.Status)
diff --git a/ecc/bls24-315/fr/iop/quotient.go b/ecc/bls24-315/fr/iop/quotient.go
index b023028856..be2c4dc48f 100644
--- a/ecc/bls24-315/fr/iop/quotient.go
+++ b/ecc/bls24-315/fr/iop/quotient.go
@@ -35,7 +35,6 @@ func DivideByXMinusOne(a *Polynomial, domains [2]*fft.Domain) (*Polynomial, erro
 	coeffs := make([]fr.Element, a.coefficients.Len())
 	res := NewPolynomial(&coeffs, Form{Layout: BitReverse, Basis: LagrangeCoset})
 	res.size = a.size
-	res.blindedSize = a.blindedSize
 
 	nn := uint64(64 - bits.TrailingZeros(uint(nbElmts)))
 	parallel.Execute(a.coefficients.Len(), func(start, end int) {
diff --git a/ecc/bls24-317/fr/iop/expressions.go b/ecc/bls24-317/fr/iop/expressions.go
index 5c4d901223..8aa5681e32 100644
--- a/ecc/bls24-317/fr/iop/expressions.go
+++ b/ecc/bls24-317/fr/iop/expressions.go
@@ -67,7 +67,6 @@ func Evaluate(f Expression, r []fr.Element, form Form, x ...*Polynomial) (*Polyn
 
 	res := NewPolynomial(&r, form)
 	res.size = x[0].size
-	res.blindedSize = x[0].size
 	res.shift = 0
 
 	return res, nil
diff --git a/ecc/bls24-317/fr/iop/polynomial.go b/ecc/bls24-317/fr/iop/polynomial.go
index 701a833862..ef62148eac 100644
--- a/ecc/bls24-317/fr/iop/polynomial.go
+++ b/ecc/bls24-317/fr/iop/polynomial.go
@@ -61,9 +61,9 @@ var (
 // default blindedSize=Size, until the polynomial is blinded.
 type Polynomial struct {
 	*polynomial
-	shift       int
-	size        int
-	blindedSize int
+	shift int
+	size  int
+	coset fr.Element // needed for evaluating the polynomial when it is expressed in Lagrange shifted basis
 }
 
 // NewPolynomial returned a Polynomial from the provided coefficients in the given form.
@@ -72,9 +72,8 @@ type Polynomial struct {
 // shouldn't be mutated.
 func NewPolynomial(coeffs *[]fr.Element, form Form) *Polynomial {
 	return &Polynomial{
-		polynomial:  newPolynomial(coeffs, form),
-		size:        len(*coeffs),
-		blindedSize: len(*coeffs),
+		polynomial: newPolynomial(coeffs, form),
+		size:       len(*coeffs),
 	}
 }
 
@@ -85,12 +84,6 @@ func (p *Polynomial) Shift(shift int) *Polynomial {
 	return p
 }
 
-// BlindedSize returns the the size of the polynomial when it is blinded. By
-// default blindedSize=Size, until the polynomial is blinded.
-func (p *Polynomial) BlindedSize() int {
-	return p.blindedSize
-}
-
 // Size returns the real size of the polynomial (seen as a vector).
 // For instance if len(P)=32 but P.Size=8, it means that P has been
 // extended (e.g. it is evaluated on a larger set) but P is a polynomial
@@ -108,69 +101,31 @@ func (p *Polynomial) SetSize(size int) {
 	p.size = size
 }
 
-// SetBlindedSize sets the blinded size of the polynomial.
-func (p *Polynomial) SetBlindedSize(size int) {
-	p.blindedSize = size
-}
-
-// Blind blinds a polynomial q by adding Q(X)*(X^{n}-1),
-// where deg Q = blindingOrder and Q is random, and n is the
-// size of q. Sets the result to p and returns it.
-//
-// blindingOrder is the degree of Q, where the blinding is Q(X)*(X^{n}-1)
-// where n is the size of p. The size of p is modified since the underlying
-// polynomial is of bigger degree now. The new size is p.Size+1+blindingOrder.
-//
-// /!\ The code panics if wq is not in canonical, regular layout
-func (p *Polynomial) Blind(blindingOrder int) *Polynomial {
-	// check that p is in canonical basis
-	if p.Form != canonicalRegular {
-		panic("the input must be in canonical basis, regular layout")
-	}
-
-	// we add Q*(x^{n}-1) so the new size is deg(Q)+n+1
-	// where n is the size of wq.
-	newSize := p.size + blindingOrder + 1
-
-	// Resize p. The size of wq might has already been increased
-	// (e.g. when the polynomial is evaluated on a larger domain),
-	// if that's the case we don't resize the polynomial.
-	p.grow(newSize)
-
-	// blinding: we add Q(X)(X^{n}-1) to P, where deg(Q)=blindingOrder
-	var r fr.Element
-
-	for i := 0; i <= blindingOrder; i++ {
-		r.SetRandom()
-		(*p.coefficients)[i].Sub(&(*p.coefficients)[i], &r)
-		(*p.coefficients)[i+p.size].Add(&(*p.coefficients)[i+p.size], &r)
-	}
-	p.blindedSize = newSize
-
-	return p
-}
-
 // Evaluate evaluates p at x.
 // The code panics if the function is not in canonical form.
 func (p *Polynomial) Evaluate(x fr.Element) fr.Element {
 
+	if p.Basis == LagrangeCoset {
+		x.Div(&x, &p.coset)
+	}
+
 	if p.shift == 0 {
 		return p.polynomial.evaluate(x)
 	}
 
 	var g fr.Element
-	gen, err := fft.Generator(uint64(p.size))
-	if err != nil {
-		panic(err)
-	}
 	if p.shift <= 5 {
+		gen, err := fft.Generator(uint64(p.size))
+		if err != nil {
+			panic(err)
+		}
 		g = smallExp(gen, p.shift)
 		x.Mul(&x, &g)
 		return p.polynomial.evaluate(x)
 	}
 
 	bs := big.NewInt(int64(p.shift))
-	g = *g.Exp(gen, bs)
+	g = *g.Exp(g, bs)
 	x.Mul(&x, &g)
 
 	return p.polynomial.evaluate(x)
@@ -245,20 +200,60 @@ func (p *polynomial) clone(capacity ...int) *polynomial {
 func (p *polynomial) evaluate(x fr.Element) fr.Element {
 
 	var r fr.Element
-	if p.Basis != Canonical {
-		panic("p must be in canonical basis")
+
+	evalLagrange := func() {
+		sizeP := p.coefficients.Len()
+		w, err := fft.Generator(uint64(sizeP))
+		if err != nil {
+			panic(err)
+		}
+		var accw fr.Element
+		accw.SetOne()
+		dens := make([]fr.Element, sizeP) // [x-1, x-ω, x-ω², ...]
+		for i := 0; i < sizeP; i++ {
+			dens[i].Sub(&x, &accw)
+			accw.Mul(&accw, &w)
+		}
+		invdens := fr.BatchInvert(dens) // [1/(x-1), 1/(x-ω), 1/(x-ω²), ...]
+		var tmp fr.Element
+		var one fr.Element
+		one.SetOne()
+		tmp.Exp(x, big.NewInt(int64(sizeP))).Sub(&tmp, &one) // xⁿ-1
+		var li fr.Element
+		li.SetUint64(uint64(sizeP)).Inverse(&li).Mul(&li, &tmp) // 1/n * (xⁿ-1)
+		if p.Layout == Regular {
+			for i := 0; i < sizeP; i++ {
+				li.Mul(&li, &invdens[i]) // li <- li*ω/(x-ωⁱ)
+				tmp.Mul(&li, &(*p.coefficients)[i])
+				r.Add(&r, &tmp)
+				li.Mul(&li, &dens[i]).Mul(&li, &w) // li <- li*ω*(x-ωⁱ)
+			}
+		} else {
+			nn := uint64(64 - bits.TrailingZeros(uint(p.coefficients.Len())))
+			for i := 0; i < sizeP; i++ {
+				iRev := bits.Reverse64(uint64(i)) >> nn
+				li.Mul(&li, &invdens[i]) // li <- li*ω/(x-ωⁱ)
+				tmp.Mul(&li, &(*p.coefficients)[iRev])
+				r.Add(&r, &tmp)
+				li.Mul(&li, &dens[i]).Mul(&li, &w) // li <- li*ω*(x-ωⁱ)
+			}
+		}
 	}
 
-	if p.Layout == Regular {
-		for i := p.coefficients.Len() - 1; i >= 0; i-- {
-			r.Mul(&r, &x).Add(&r, &(*p.coefficients)[i])
+	if p.Basis == Canonical {
+		if p.Layout == Regular {
+			for i := p.coefficients.Len() - 1; i >= 0; i-- {
+				r.Mul(&r, &x).Add(&r, &(*p.coefficients)[i])
+			}
+		} else {
+			nn := uint64(64 - bits.TrailingZeros(uint(p.coefficients.Len())))
+			for i := p.coefficients.Len() - 1; i >= 0; i-- {
+				iRev := bits.Reverse64(uint64(i)) >> nn
+				r.Mul(&r, &x).Add(&r, &(*p.coefficients)[iRev])
+			}
 		}
 	} else {
-		nn := uint64(64 - bits.TrailingZeros(uint(p.coefficients.Len())))
-		for i := p.coefficients.Len() - 1; i >= 0; i-- {
-			iRev := bits.Reverse64(uint64(i)) >> nn
-			r.Mul(&r, &x).Add(&r, &(*p.coefficients)[iRev])
-		}
+		evalLagrange()
 	}
 
 	return r
@@ -362,6 +357,11 @@ func (p *polynomial) grow(newSize int) {
 
 // ToLagrangeCoset Sets p to q, in LagrangeCoset form and returns it.
 func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial {
+	cosetTable, err := d.CosetTable()
+	if err != nil {
+		panic(err)
+	}
+	p.coset.Set(&cosetTable[1])
 	id := p.Form
 	p.grow(int(d.Cardinality))
 	switch id {
@@ -391,6 +391,7 @@ func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial {
 
 // WriteTo implements io.WriterTo
 func (p *Polynomial) WriteTo(w io.Writer) (int64, error) {
+
 	// encode coefficients
 	n, err := p.polynomial.coefficients.WriteTo(w)
 	if err != nil {
@@ -403,7 +404,6 @@ func (p *Polynomial) WriteTo(w io.Writer) (int64, error) {
 		uint32(p.Layout),
 		uint32(p.shift),
 		uint32(p.size),
-		uint32(p.blindedSize),
 	}
 	for _, v := range data {
 		err = binary.Write(w, binary.BigEndian, v)
@@ -412,6 +412,15 @@ func (p *Polynomial) WriteTo(w io.Writer) (int64, error) {
 		}
 		n += 4
 	}
+
+	var buf [fr.Bytes]byte
+	fr.BigEndian.PutElement(&buf, p.coset)
+	m, err := w.Write(buf[:])
+	n += int64(m)
+	if err != nil {
+		return n, err
+	}
+
 	return n, nil
 }
 
@@ -430,8 +439,8 @@ func (p *Polynomial) ReadFrom(r io.Reader) (int64, error) {
 		return n, err
 	}
 
-	// decode Form.Basis, Form.Layout, shift, size & blindedSize as uint32
-	var data [5]uint32
+	// decode Form.Basis, Form.Layout, shift as uint32
+	var data [4]uint32
 	var buf [4]byte
 	for i := range data {
 		read, err := io.ReadFull(r, buf[:4])
@@ -446,7 +455,17 @@ func (p *Polynomial) ReadFrom(r io.Reader) (int64, error) {
 	p.Layout = Layout(data[1])
 	p.shift = int(data[2])
 	p.size = int(data[3])
-	p.blindedSize = int(data[4])
+
+	var bufFr [fr.Bytes]byte
+	read, err := io.ReadFull(r, bufFr[:])
+	n += int64(read)
+	if err != nil {
+		return n, err
+	}
+	p.coset, err = fr.BigEndian.Element(&bufFr)
+	if err != nil {
+		return n, err
+	}
 
 	return n, nil
 }
diff --git a/ecc/bls24-317/fr/iop/polynomial_test.go b/ecc/bls24-317/fr/iop/polynomial_test.go
index 3066d383ca..3153fd5963 100644
--- a/ecc/bls24-317/fr/iop/polynomial_test.go
+++ b/ecc/bls24-317/fr/iop/polynomial_test.go
@@ -23,14 +23,14 @@ func TestEvaluation(t *testing.T) {
 	shift := 2
 	d := fft.NewDomain(uint64(size))
 	c := randomVector(size)
-	wp := NewPolynomial(c, Form{Basis: Canonical, Layout: Regular})
-	wps := wp.ShallowClone().Shift(shift)
-	ref := wp.Clone()
+	p := NewPolynomial(c, Form{Basis: Canonical, Layout: Regular})
+	ps := p.ShallowClone().Shift(shift)
+	ref := p.Clone()
 	ref.ToLagrange(d).ToRegular()
 
-	// regular layout
-	a := wp.Evaluate(d.Generator)
-	b := wps.Evaluate(d.Generator)
+	// canonical regular
+	a := p.Evaluate(d.Generator)
+	b := ps.Evaluate(d.Generator)
 	if !a.Equal(&ref.Coefficients()[1]) {
 		t.Fatal("error evaluation")
 	}
@@ -38,11 +38,11 @@ func TestEvaluation(t *testing.T) {
 		t.Fatal("error evaluation shifted")
 	}
 
-	// bit reversed layout
-	wp.ToBitReverse()
-	wps.ToBitReverse()
-	a = wp.Evaluate(d.Generator)
-	b = wps.Evaluate(d.Generator)
+	// canonical bit reversed
+	p.ToBitReverse()
+	ps.ToBitReverse()
+	a = p.Evaluate(d.Generator)
+	b = ps.Evaluate(d.Generator)
 	if !a.Equal(&ref.Coefficients()[1]) {
 		t.Fatal("error evaluation")
 	}
@@ -50,6 +50,60 @@ func TestEvaluation(t *testing.T) {
 		t.Fatal("error evaluation shifted")
 	}
 
+	// get reference values
+	var x fr.Element
+	x.SetRandom()
+	expectedEval := p.ToRegular().Evaluate(x)
+	expectedEvalShifted := ps.ToRegular().Evaluate(x)
+
+	// lagrange regular
+	p.ToLagrange(d).ToRegular()
+	ps.ToLagrange(d).ToRegular()
+	plx := p.Evaluate(x)
+	pslx := ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange shifted")
+	}
+
+	// lagrange bit reverse
+	p.ToBitReverse()
+	ps.ToBitReverse()
+	plx = p.Evaluate(x)
+	pslx = ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange shifted")
+	}
+
+	// lagrange coset regular
+	p.ToLagrangeCoset(d).ToRegular()
+	ps.ToLagrangeCoset(d).ToRegular()
+	plx = p.Evaluate(x)
+	pslx = ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange coset")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange coset shifted")
+	}
+
+	// lagrange coset bit reverse
+	p.ToRegular().ToBitReverse()
+	ps.ToRegular().ToBitReverse()
+	plx = p.Evaluate(x)
+	pslx = ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange coset")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange coset shifted")
+	}
+
 }
 
 func randomVector(size int) *[]fr.Element {
@@ -113,10 +167,9 @@ func TestRoundTrip(t *testing.T) {
 
 	size := 8
 	d := fft.NewDomain(uint64(8))
-	blindingOrder := 2
 
-	p := NewPolynomial(randomVector(size), Form{Basis: Lagrange, Layout: Regular}).ToCanonical(d).ToRegular()
-	p.Blind(blindingOrder)
+	p := NewPolynomial(randomVector(size), Form{Basis: Canonical, Layout: Regular})
+	p.ToLagrangeCoset(d)
 
 	// serialize
 	written, err := p.WriteTo(&buf)
@@ -134,52 +187,10 @@ func TestRoundTrip(t *testing.T) {
 	assert.Equal(p.Layout, reconstructed.Layout)
 	assert.Equal(p.shift, reconstructed.shift)
 	assert.Equal(p.size, reconstructed.size)
-	assert.Equal(p.blindedSize, reconstructed.blindedSize)
 	c1, c2 := p.Coefficients(), reconstructed.Coefficients()
 	assert.True(reflect.DeepEqual(c1, c2))
 }
 
-func TestBlinding(t *testing.T) {
-
-	size := 8
-	d := fft.NewDomain(uint64(8))
-	blindingOrder := 2
-
-	// generate a random polynomial in Lagrange form for the moment
-	// to check that an error is raised when the polynomial is not
-	// in canonical form.
-	wp := NewPolynomial(randomVector(size), Form{Basis: Lagrange, Layout: Regular})
-
-	// checks the blinding is correct: the evaluation of the blinded polynomial
-	// should be the same as the original on d's domain
-	wp.Basis = Canonical
-	wt := wp.Clone()
-	wt.Blind(blindingOrder)
-	if wt.coefficients.Len() != blindingOrder+size+1 {
-		t.Fatal("size of blinded polynomial is incorrect")
-	}
-	if wt.blindedSize != size+blindingOrder+1 {
-		t.Fatal("Size field of blinded polynomial is incorrect")
-	}
-	if wt.size != size {
-		t.Fatal("the size should not have been modified")
-	}
-	x := make([]fr.Element, size)
-	x[0].SetOne()
-	for i := 1; i < size; i++ {
-		x[i].Mul(&x[i-1], &d.Generator)
-	}
-	var a, b fr.Element
-	for i := 0; i < size; i++ {
-		a = wt.Evaluate(x[i])
-		b = wp.Evaluate(x[i])
-		if a != b {
-			t.Fatal("polynomial and its blinded version should be equal on V(X^{n}-1)")
-		}
-	}
-
-}
-
 // list of functions to turn a polynomial in Lagrange-regular form
 // to all different forms in ordered using this encoding:
 // int(p.Basis)*4 + int(p.Layout)*2 + int(p.Status)
diff --git a/ecc/bls24-317/fr/iop/quotient.go b/ecc/bls24-317/fr/iop/quotient.go
index 22561fbdc1..9697b89361 100644
--- a/ecc/bls24-317/fr/iop/quotient.go
+++ b/ecc/bls24-317/fr/iop/quotient.go
@@ -35,7 +35,6 @@ func DivideByXMinusOne(a *Polynomial, domains [2]*fft.Domain) (*Polynomial, erro
 	coeffs := make([]fr.Element, a.coefficients.Len())
 	res := NewPolynomial(&coeffs, Form{Layout: BitReverse, Basis: LagrangeCoset})
 	res.size = a.size
-	res.blindedSize = a.blindedSize
 
 	nn := uint64(64 - bits.TrailingZeros(uint(nbElmts)))
 	parallel.Execute(a.coefficients.Len(), func(start, end int) {
diff --git a/ecc/bn254/fr/iop/expressions.go b/ecc/bn254/fr/iop/expressions.go
index 396a25bc0f..57b95b2d6d 100644
--- a/ecc/bn254/fr/iop/expressions.go
+++ b/ecc/bn254/fr/iop/expressions.go
@@ -67,7 +67,6 @@ func Evaluate(f Expression, r []fr.Element, form Form, x ...*Polynomial) (*Polyn
 
 	res := NewPolynomial(&r, form)
 	res.size = x[0].size
-	res.blindedSize = x[0].size
 	res.shift = 0
 
 	return res, nil
diff --git a/ecc/bn254/fr/iop/polynomial.go b/ecc/bn254/fr/iop/polynomial.go
index 4eb7e6bb8c..d5e1e0ad4f 100644
--- a/ecc/bn254/fr/iop/polynomial.go
+++ b/ecc/bn254/fr/iop/polynomial.go
@@ -61,9 +61,9 @@ var (
 // default blindedSize=Size, until the polynomial is blinded.
 type Polynomial struct {
 	*polynomial
-	shift       int
-	size        int
-	blindedSize int
+	shift int
+	size  int
+	coset fr.Element // needed for evaluating the polynomial when it is expressed in Lagrange shifted basis
 }
 
 // NewPolynomial returned a Polynomial from the provided coefficients in the given form.
@@ -72,9 +72,8 @@ type Polynomial struct {
 // shouldn't be mutated.
 func NewPolynomial(coeffs *[]fr.Element, form Form) *Polynomial {
 	return &Polynomial{
-		polynomial:  newPolynomial(coeffs, form),
-		size:        len(*coeffs),
-		blindedSize: len(*coeffs),
+		polynomial: newPolynomial(coeffs, form),
+		size:       len(*coeffs),
 	}
 }
 
@@ -85,12 +84,6 @@ func (p *Polynomial) Shift(shift int) *Polynomial {
 	return p
 }
 
-// BlindedSize returns the the size of the polynomial when it is blinded. By
-// default blindedSize=Size, until the polynomial is blinded.
-func (p *Polynomial) BlindedSize() int {
-	return p.blindedSize
-}
-
 // Size returns the real size of the polynomial (seen as a vector).
 // For instance if len(P)=32 but P.Size=8, it means that P has been
 // extended (e.g. it is evaluated on a larger set) but P is a polynomial
@@ -108,69 +101,31 @@ func (p *Polynomial) SetSize(size int) {
 	p.size = size
 }
 
-// SetBlindedSize sets the blinded size of the polynomial.
-func (p *Polynomial) SetBlindedSize(size int) {
-	p.blindedSize = size
-}
-
-// Blind blinds a polynomial q by adding Q(X)*(X^{n}-1),
-// where deg Q = blindingOrder and Q is random, and n is the
-// size of q. Sets the result to p and returns it.
-//
-// blindingOrder is the degree of Q, where the blinding is Q(X)*(X^{n}-1)
-// where n is the size of p. The size of p is modified since the underlying
-// polynomial is of bigger degree now. The new size is p.Size+1+blindingOrder.
-//
-// /!\ The code panics if wq is not in canonical, regular layout
-func (p *Polynomial) Blind(blindingOrder int) *Polynomial {
-	// check that p is in canonical basis
-	if p.Form != canonicalRegular {
-		panic("the input must be in canonical basis, regular layout")
-	}
-
-	// we add Q*(x^{n}-1) so the new size is deg(Q)+n+1
-	// where n is the size of wq.
-	newSize := p.size + blindingOrder + 1
-
-	// Resize p. The size of wq might has already been increased
-	// (e.g. when the polynomial is evaluated on a larger domain),
-	// if that's the case we don't resize the polynomial.
-	p.grow(newSize)
-
-	// blinding: we add Q(X)(X^{n}-1) to P, where deg(Q)=blindingOrder
-	var r fr.Element
-
-	for i := 0; i <= blindingOrder; i++ {
-		r.SetRandom()
-		(*p.coefficients)[i].Sub(&(*p.coefficients)[i], &r)
-		(*p.coefficients)[i+p.size].Add(&(*p.coefficients)[i+p.size], &r)
-	}
-	p.blindedSize = newSize
-
-	return p
-}
-
 // Evaluate evaluates p at x.
 // The code panics if the function is not in canonical form.
 func (p *Polynomial) Evaluate(x fr.Element) fr.Element {
 
+	if p.Basis == LagrangeCoset {
+		x.Div(&x, &p.coset)
+	}
+
 	if p.shift == 0 {
 		return p.polynomial.evaluate(x)
 	}
 
 	var g fr.Element
-	gen, err := fft.Generator(uint64(p.size))
-	if err != nil {
-		panic(err)
-	}
 	if p.shift <= 5 {
+		gen, err := fft.Generator(uint64(p.size))
+		if err != nil {
+			panic(err)
+		}
 		g = smallExp(gen, p.shift)
 		x.Mul(&x, &g)
 		return p.polynomial.evaluate(x)
 	}
 
 	bs := big.NewInt(int64(p.shift))
-	g = *g.Exp(gen, bs)
+	g = *g.Exp(g, bs)
 	x.Mul(&x, &g)
 
 	return p.polynomial.evaluate(x)
@@ -245,20 +200,60 @@ func (p *polynomial) clone(capacity ...int) *polynomial {
 func (p *polynomial) evaluate(x fr.Element) fr.Element {
 
 	var r fr.Element
-	if p.Basis != Canonical {
-		panic("p must be in canonical basis")
+
+	evalLagrange := func() {
+		sizeP := p.coefficients.Len()
+		w, err := fft.Generator(uint64(sizeP))
+		if err != nil {
+			panic(err)
+		}
+		var accw fr.Element
+		accw.SetOne()
+		dens := make([]fr.Element, sizeP) // [x-1, x-ω, x-ω², ...]
+		for i := 0; i < sizeP; i++ {
+			dens[i].Sub(&x, &accw)
+			accw.Mul(&accw, &w)
+		}
+		invdens := fr.BatchInvert(dens) // [1/(x-1), 1/(x-ω), 1/(x-ω²), ...]
+		var tmp fr.Element
+		var one fr.Element
+		one.SetOne()
+		tmp.Exp(x, big.NewInt(int64(sizeP))).Sub(&tmp, &one) // xⁿ-1
+		var li fr.Element
+		li.SetUint64(uint64(sizeP)).Inverse(&li).Mul(&li, &tmp) // 1/n * (xⁿ-1)
+		if p.Layout == Regular {
+			for i := 0; i < sizeP; i++ {
+				li.Mul(&li, &invdens[i]) // li <- li*ω/(x-ωⁱ)
+				tmp.Mul(&li, &(*p.coefficients)[i])
+				r.Add(&r, &tmp)
+				li.Mul(&li, &dens[i]).Mul(&li, &w) // li <- li*ω*(x-ωⁱ)
+			}
+		} else {
+			nn := uint64(64 - bits.TrailingZeros(uint(p.coefficients.Len())))
+			for i := 0; i < sizeP; i++ {
+				iRev := bits.Reverse64(uint64(i)) >> nn
+				li.Mul(&li, &invdens[i]) // li <- li*ω/(x-ωⁱ)
+				tmp.Mul(&li, &(*p.coefficients)[iRev])
+				r.Add(&r, &tmp)
+				li.Mul(&li, &dens[i]).Mul(&li, &w) // li <- li*ω*(x-ωⁱ)
+			}
+		}
 	}
 
-	if p.Layout == Regular {
-		for i := p.coefficients.Len() - 1; i >= 0; i-- {
-			r.Mul(&r, &x).Add(&r, &(*p.coefficients)[i])
+	if p.Basis == Canonical {
+		if p.Layout == Regular {
+			for i := p.coefficients.Len() - 1; i >= 0; i-- {
+				r.Mul(&r, &x).Add(&r, &(*p.coefficients)[i])
+			}
+		} else {
+			nn := uint64(64 - bits.TrailingZeros(uint(p.coefficients.Len())))
+			for i := p.coefficients.Len() - 1; i >= 0; i-- {
+				iRev := bits.Reverse64(uint64(i)) >> nn
+				r.Mul(&r, &x).Add(&r, &(*p.coefficients)[iRev])
+			}
 		}
 	} else {
-		nn := uint64(64 - bits.TrailingZeros(uint(p.coefficients.Len())))
-		for i := p.coefficients.Len() - 1; i >= 0; i-- {
-			iRev := bits.Reverse64(uint64(i)) >> nn
-			r.Mul(&r, &x).Add(&r, &(*p.coefficients)[iRev])
-		}
+		evalLagrange()
 	}
 
 	return r
@@ -362,6 +357,11 @@ func (p *polynomial) grow(newSize int) {
 
 // ToLagrangeCoset Sets p to q, in LagrangeCoset form and returns it.
 func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial {
+	cosetTable, err := d.CosetTable()
+	if err != nil {
+		panic(err)
+	}
+	p.coset.Set(&cosetTable[1])
 	id := p.Form
 	p.grow(int(d.Cardinality))
 	switch id {
@@ -391,6 +391,7 @@ func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial {
 
 // WriteTo implements io.WriterTo
 func (p *Polynomial) WriteTo(w io.Writer) (int64, error) {
+
 	// encode coefficients
 	n, err := p.polynomial.coefficients.WriteTo(w)
 	if err != nil {
@@ -403,7 +404,6 @@ func (p *Polynomial) WriteTo(w io.Writer) (int64, error) {
 		uint32(p.Layout),
 		uint32(p.shift),
 		uint32(p.size),
-		uint32(p.blindedSize),
 	}
 	for _, v := range data {
 		err = binary.Write(w, binary.BigEndian, v)
@@ -412,6 +412,15 @@ func (p *Polynomial) WriteTo(w io.Writer) (int64, error) {
 		}
 		n += 4
 	}
+
+	var buf [fr.Bytes]byte
+	fr.BigEndian.PutElement(&buf, p.coset)
+	m, err := w.Write(buf[:])
+	n += int64(m)
+	if err != nil {
+		return n, err
+	}
+
 	return n, nil
 }
 
@@ -430,8 +439,8 @@ func (p *Polynomial) ReadFrom(r io.Reader) (int64, error) {
 		return n, err
 	}
 
-	// decode Form.Basis, Form.Layout, shift, size & blindedSize as uint32
-	var data [5]uint32
+	// decode Form.Basis, Form.Layout, shift as uint32
+	var data [4]uint32
 	var buf [4]byte
 	for i := range data {
 		read, err := io.ReadFull(r, buf[:4])
@@ -446,7 +455,17 @@ func (p *Polynomial) ReadFrom(r io.Reader) (int64, error) {
 	p.Layout = Layout(data[1])
 	p.shift = int(data[2])
 	p.size = int(data[3])
-	p.blindedSize = int(data[4])
+
+	var bufFr [fr.Bytes]byte
+	read, err := io.ReadFull(r, bufFr[:])
+	n += int64(read)
+	if err != nil {
+		return n, err
+	}
+	p.coset, err = fr.BigEndian.Element(&bufFr)
+	if err != nil {
+		return n, err
+	}
 
 	return n, nil
 }
diff --git a/ecc/bn254/fr/iop/polynomial_test.go b/ecc/bn254/fr/iop/polynomial_test.go
index 8bce78d41b..b716b83912 100644
--- a/ecc/bn254/fr/iop/polynomial_test.go
+++ b/ecc/bn254/fr/iop/polynomial_test.go
@@ -23,14 +23,14 @@ func TestEvaluation(t *testing.T) {
 	shift := 2
 	d := fft.NewDomain(uint64(size))
 	c := randomVector(size)
-	wp := NewPolynomial(c, Form{Basis: Canonical, Layout: Regular})
-	wps := wp.ShallowClone().Shift(shift)
-	ref := wp.Clone()
+	p := NewPolynomial(c, Form{Basis: Canonical, Layout: Regular})
+	ps := p.ShallowClone().Shift(shift)
+	ref := p.Clone()
 	ref.ToLagrange(d).ToRegular()
 
-	// regular layout
-	a := wp.Evaluate(d.Generator)
-	b := wps.Evaluate(d.Generator)
+	// canonical regular
+	a := p.Evaluate(d.Generator)
+	b := ps.Evaluate(d.Generator)
 	if !a.Equal(&ref.Coefficients()[1]) {
 		t.Fatal("error evaluation")
 	}
@@ -38,11 +38,11 @@ func TestEvaluation(t *testing.T) {
 		t.Fatal("error evaluation shifted")
 	}
 
-	// bit reversed layout
-	wp.ToBitReverse()
-	wps.ToBitReverse()
-	a = wp.Evaluate(d.Generator)
-	b = wps.Evaluate(d.Generator)
+	// canonical bit reversed
+	p.ToBitReverse()
+	ps.ToBitReverse()
+	a = p.Evaluate(d.Generator)
+	b = ps.Evaluate(d.Generator)
 	if !a.Equal(&ref.Coefficients()[1]) {
 		t.Fatal("error evaluation")
 	}
@@ -50,6 +50,60 @@ func TestEvaluation(t *testing.T) {
 		t.Fatal("error evaluation shifted")
 	}
 
+	// get reference values
+	var x fr.Element
+	x.SetRandom()
+	expectedEval := p.ToRegular().Evaluate(x)
+	expectedEvalShifted := ps.ToRegular().Evaluate(x)
+
+	// lagrange regular
+	p.ToLagrange(d).ToRegular()
+	ps.ToLagrange(d).ToRegular()
+	plx := p.Evaluate(x)
+	pslx := ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange shifted")
+	}
+
+	// lagrange bit reverse
+	p.ToBitReverse()
+	ps.ToBitReverse()
+	plx = p.Evaluate(x)
+	pslx = ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange shifted")
+	}
+
+	// lagrange coset regular
+	p.ToLagrangeCoset(d).ToRegular()
+	ps.ToLagrangeCoset(d).ToRegular()
+	plx = p.Evaluate(x)
+	pslx = ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange coset")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange coset shifted")
+	}
+
+	// lagrange coset bit reverse
+	p.ToRegular().ToBitReverse()
+	ps.ToRegular().ToBitReverse()
+	plx = p.Evaluate(x)
+	pslx = ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange coset")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange coset shifted")
+	}
+
 }
 
 func randomVector(size int) *[]fr.Element {
@@ -113,10 +167,9 @@ func TestRoundTrip(t *testing.T) {
 
 	size := 8
 	d := fft.NewDomain(uint64(8))
-	blindingOrder := 2
 
-	p := NewPolynomial(randomVector(size), Form{Basis: Lagrange, Layout: Regular}).ToCanonical(d).ToRegular()
-	p.Blind(blindingOrder)
+	p := NewPolynomial(randomVector(size), Form{Basis: Canonical, Layout: Regular})
+	p.ToLagrangeCoset(d)
 
 	// serialize
 	written, err := p.WriteTo(&buf)
@@ -134,52 +187,10 @@ func TestRoundTrip(t *testing.T) {
 	assert.Equal(p.Layout, reconstructed.Layout)
 	assert.Equal(p.shift, reconstructed.shift)
 	assert.Equal(p.size, reconstructed.size)
-	assert.Equal(p.blindedSize, reconstructed.blindedSize)
 	c1, c2 := p.Coefficients(), reconstructed.Coefficients()
 	assert.True(reflect.DeepEqual(c1, c2))
 }
 
-func TestBlinding(t *testing.T) {
-
-	size := 8
-	d := fft.NewDomain(uint64(8))
-	blindingOrder := 2
-
-	// generate a random polynomial in Lagrange form for the moment
-	// to check that an error is raised when the polynomial is not
-	// in canonical form.
-	wp := NewPolynomial(randomVector(size), Form{Basis: Lagrange, Layout: Regular})
-
-	// checks the blinding is correct: the evaluation of the blinded polynomial
-	// should be the same as the original on d's domain
-	wp.Basis = Canonical
-	wt := wp.Clone()
-	wt.Blind(blindingOrder)
-	if wt.coefficients.Len() != blindingOrder+size+1 {
-		t.Fatal("size of blinded polynomial is incorrect")
-	}
-	if wt.blindedSize != size+blindingOrder+1 {
-		t.Fatal("Size field of blinded polynomial is incorrect")
-	}
-	if wt.size != size {
-		t.Fatal("the size should not have been modified")
-	}
-	x := make([]fr.Element, size)
-	x[0].SetOne()
-	for i := 1; i < size; i++ {
-		x[i].Mul(&x[i-1], &d.Generator)
-	}
-	var a, b fr.Element
-	for i := 0; i < size; i++ {
-		a = wt.Evaluate(x[i])
-		b = wp.Evaluate(x[i])
-		if a != b {
-			t.Fatal("polynomial and its blinded version should be equal on V(X^{n}-1)")
-		}
-	}
-
-}
-
 // list of functions to turn a polynomial in Lagrange-regular form
 // to all different forms in ordered using this encoding:
 // int(p.Basis)*4 + int(p.Layout)*2 + int(p.Status)
diff --git a/ecc/bn254/fr/iop/quotient.go b/ecc/bn254/fr/iop/quotient.go
index 09c3d6681f..89056e1d12 100644
--- a/ecc/bn254/fr/iop/quotient.go
+++ b/ecc/bn254/fr/iop/quotient.go
@@ -35,7 +35,6 @@ func DivideByXMinusOne(a *Polynomial, domains [2]*fft.Domain) (*Polynomial, erro
 	coeffs := make([]fr.Element, a.coefficients.Len())
 	res := NewPolynomial(&coeffs, Form{Layout: BitReverse, Basis: LagrangeCoset})
 	res.size = a.size
-	res.blindedSize = a.blindedSize
 
 	nn := uint64(64 - bits.TrailingZeros(uint(nbElmts)))
 	parallel.Execute(a.coefficients.Len(), func(start, end int) {
diff --git a/ecc/bw6-633/fr/iop/expressions.go b/ecc/bw6-633/fr/iop/expressions.go
index ea9678075b..08c735962f 100644
--- a/ecc/bw6-633/fr/iop/expressions.go
+++ b/ecc/bw6-633/fr/iop/expressions.go
@@ -67,7 +67,6 @@ func Evaluate(f Expression, r []fr.Element, form Form, x ...*Polynomial) (*Polyn
 
 	res := NewPolynomial(&r, form)
 	res.size = x[0].size
-	res.blindedSize = x[0].size
 	res.shift = 0
 
 	return res, nil
diff --git a/ecc/bw6-633/fr/iop/polynomial.go b/ecc/bw6-633/fr/iop/polynomial.go
index 0d5c2cf8a2..354007c795 100644
--- a/ecc/bw6-633/fr/iop/polynomial.go
+++ b/ecc/bw6-633/fr/iop/polynomial.go
@@ -61,9 +61,9 @@ var (
 // default blindedSize=Size, until the polynomial is blinded.
 type Polynomial struct {
 	*polynomial
-	shift       int
-	size        int
-	blindedSize int
+	shift int
+	size  int
+	coset fr.Element // needed for evaluating the polynomial when it is expressed in Lagrange shifted basis
 }
 
 // NewPolynomial returned a Polynomial from the provided coefficients in the given form.
@@ -72,9 +72,8 @@ type Polynomial struct {
 // shouldn't be mutated.
 func NewPolynomial(coeffs *[]fr.Element, form Form) *Polynomial {
 	return &Polynomial{
-		polynomial:  newPolynomial(coeffs, form),
-		size:        len(*coeffs),
-		blindedSize: len(*coeffs),
+		polynomial: newPolynomial(coeffs, form),
+		size:       len(*coeffs),
 	}
 }
 
@@ -85,12 +84,6 @@ func (p *Polynomial) Shift(shift int) *Polynomial {
 	return p
 }
 
-// BlindedSize returns the the size of the polynomial when it is blinded. By
-// default blindedSize=Size, until the polynomial is blinded.
-func (p *Polynomial) BlindedSize() int {
-	return p.blindedSize
-}
-
 // Size returns the real size of the polynomial (seen as a vector).
 // For instance if len(P)=32 but P.Size=8, it means that P has been
 // extended (e.g. it is evaluated on a larger set) but P is a polynomial
@@ -108,69 +101,31 @@ func (p *Polynomial) SetSize(size int) {
 	p.size = size
 }
 
-// SetBlindedSize sets the blinded size of the polynomial.
-func (p *Polynomial) SetBlindedSize(size int) {
-	p.blindedSize = size
-}
-
-// Blind blinds a polynomial q by adding Q(X)*(X^{n}-1),
-// where deg Q = blindingOrder and Q is random, and n is the
-// size of q. Sets the result to p and returns it.
-//
-// blindingOrder is the degree of Q, where the blinding is Q(X)*(X^{n}-1)
-// where n is the size of p. The size of p is modified since the underlying
-// polynomial is of bigger degree now. The new size is p.Size+1+blindingOrder.
-//
-// /!\ The code panics if wq is not in canonical, regular layout
-func (p *Polynomial) Blind(blindingOrder int) *Polynomial {
-	// check that p is in canonical basis
-	if p.Form != canonicalRegular {
-		panic("the input must be in canonical basis, regular layout")
-	}
-
-	// we add Q*(x^{n}-1) so the new size is deg(Q)+n+1
-	// where n is the size of wq.
-	newSize := p.size + blindingOrder + 1
-
-	// Resize p. The size of wq might has already been increased
-	// (e.g. when the polynomial is evaluated on a larger domain),
-	// if that's the case we don't resize the polynomial.
-	p.grow(newSize)
-
-	// blinding: we add Q(X)(X^{n}-1) to P, where deg(Q)=blindingOrder
-	var r fr.Element
-
-	for i := 0; i <= blindingOrder; i++ {
-		r.SetRandom()
-		(*p.coefficients)[i].Sub(&(*p.coefficients)[i], &r)
-		(*p.coefficients)[i+p.size].Add(&(*p.coefficients)[i+p.size], &r)
-	}
-	p.blindedSize = newSize
-
-	return p
-}
-
 // Evaluate evaluates p at x.
 // The code panics if the function is not in canonical form.
 func (p *Polynomial) Evaluate(x fr.Element) fr.Element {
 
+	if p.Basis == LagrangeCoset {
+		x.Div(&x, &p.coset)
+	}
+
 	if p.shift == 0 {
 		return p.polynomial.evaluate(x)
 	}
 
 	var g fr.Element
-	gen, err := fft.Generator(uint64(p.size))
-	if err != nil {
-		panic(err)
-	}
 	if p.shift <= 5 {
+		gen, err := fft.Generator(uint64(p.size))
+		if err != nil {
+			panic(err)
+		}
 		g = smallExp(gen, p.shift)
 		x.Mul(&x, &g)
 		return p.polynomial.evaluate(x)
 	}
 
 	bs := big.NewInt(int64(p.shift))
-	g = *g.Exp(gen, bs)
+	g = *g.Exp(g, bs)
 	x.Mul(&x, &g)
 
 	return p.polynomial.evaluate(x)
@@ -245,20 +200,60 @@ func (p *polynomial) clone(capacity ...int) *polynomial {
 func (p *polynomial) evaluate(x fr.Element) fr.Element {
 
 	var r fr.Element
-	if p.Basis != Canonical {
-		panic("p must be in canonical basis")
+
+	evalLagrange := func() {
+		sizeP := p.coefficients.Len()
+		w, err := fft.Generator(uint64(sizeP))
+		if err != nil {
+			panic(err)
+		}
+		var accw fr.Element
+		accw.SetOne()
+		dens := make([]fr.Element, sizeP) // [x-1, x-ω, x-ω², ...]
+		for i := 0; i < sizeP; i++ {
+			dens[i].Sub(&x, &accw)
+			accw.Mul(&accw, &w)
+		}
+		invdens := fr.BatchInvert(dens) // [1/(x-1), 1/(x-ω), 1/(x-ω²), ...]
+		var tmp fr.Element
+		var one fr.Element
+		one.SetOne()
+		tmp.Exp(x, big.NewInt(int64(sizeP))).Sub(&tmp, &one) // xⁿ-1
+		var li fr.Element
+		li.SetUint64(uint64(sizeP)).Inverse(&li).Mul(&li, &tmp) // 1/n * (xⁿ-1)
+		if p.Layout == Regular {
+			for i := 0; i < sizeP; i++ {
+				li.Mul(&li, &invdens[i]) // li <- li*ω/(x-ωⁱ)
+				tmp.Mul(&li, &(*p.coefficients)[i])
+				r.Add(&r, &tmp)
+				li.Mul(&li, &dens[i]).Mul(&li, &w) // li <- li*ω*(x-ωⁱ)
+			}
+		} else {
+			nn := uint64(64 - bits.TrailingZeros(uint(p.coefficients.Len())))
+			for i := 0; i < sizeP; i++ {
+				iRev := bits.Reverse64(uint64(i)) >> nn
+				li.Mul(&li, &invdens[i]) // li <- li*ω/(x-ωⁱ)
+				tmp.Mul(&li, &(*p.coefficients)[iRev])
+				r.Add(&r, &tmp)
+				li.Mul(&li, &dens[i]).Mul(&li, &w) // li <- li*ω*(x-ωⁱ)
+			}
+		}
 	}
 
-	if p.Layout == Regular {
-		for i := p.coefficients.Len() - 1; i >= 0; i-- {
-			r.Mul(&r, &x).Add(&r, &(*p.coefficients)[i])
+	if p.Basis == Canonical {
+		if p.Layout == Regular {
+			for i := p.coefficients.Len() - 1; i >= 0; i-- {
+				r.Mul(&r, &x).Add(&r, &(*p.coefficients)[i])
+			}
+		} else {
+			nn := uint64(64 - bits.TrailingZeros(uint(p.coefficients.Len())))
+			for i := p.coefficients.Len() - 1; i >= 0; i-- {
+				iRev := bits.Reverse64(uint64(i)) >> nn
+				r.Mul(&r, &x).Add(&r, &(*p.coefficients)[iRev])
+			}
 		}
 	} else {
-		nn := uint64(64 - bits.TrailingZeros(uint(p.coefficients.Len())))
-		for i := p.coefficients.Len() - 1; i >= 0; i-- {
-			iRev := bits.Reverse64(uint64(i)) >> nn
-			r.Mul(&r, &x).Add(&r, &(*p.coefficients)[iRev])
-		}
+		evalLagrange()
 	}
 
 	return r
@@ -362,6 +357,11 @@ func (p *polynomial) grow(newSize int) {
 
 // ToLagrangeCoset Sets p to q, in LagrangeCoset form and returns it.
 func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial {
+	cosetTable, err := d.CosetTable()
+	if err != nil {
+		panic(err)
+	}
+	p.coset.Set(&cosetTable[1])
 	id := p.Form
 	p.grow(int(d.Cardinality))
 	switch id {
@@ -391,6 +391,7 @@ func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial {
 
 // WriteTo implements io.WriterTo
 func (p *Polynomial) WriteTo(w io.Writer) (int64, error) {
+
 	// encode coefficients
 	n, err := p.polynomial.coefficients.WriteTo(w)
 	if err != nil {
@@ -403,7 +404,6 @@ func (p *Polynomial) WriteTo(w io.Writer) (int64, error) {
 		uint32(p.Layout),
 		uint32(p.shift),
 		uint32(p.size),
-		uint32(p.blindedSize),
 	}
 	for _, v := range data {
 		err = binary.Write(w, binary.BigEndian, v)
@@ -412,6 +412,15 @@ func (p *Polynomial) WriteTo(w io.Writer) (int64, error) {
 		}
 		n += 4
 	}
+
+	var buf [fr.Bytes]byte
+	fr.BigEndian.PutElement(&buf, p.coset)
+	m, err := w.Write(buf[:])
+	n += int64(m)
+	if err != nil {
+		return n, err
+	}
+
 	return n, nil
 }
 
@@ -430,8 +439,8 @@ func (p *Polynomial) ReadFrom(r io.Reader) (int64, error) {
 		return n, err
 	}
 
-	// decode Form.Basis, Form.Layout, shift, size & blindedSize as uint32
-	var data [5]uint32
+	// decode Form.Basis, Form.Layout, shift as uint32
+	var data [4]uint32
 	var buf [4]byte
 	for i := range data {
 		read, err := io.ReadFull(r, buf[:4])
@@ -446,7 +455,17 @@ func (p *Polynomial) ReadFrom(r io.Reader) (int64, error) {
 	p.Layout = Layout(data[1])
 	p.shift = int(data[2])
 	p.size = int(data[3])
-	p.blindedSize = int(data[4])
+
+	var bufFr [fr.Bytes]byte
+	read, err := io.ReadFull(r, bufFr[:])
+	n += int64(read)
+	if err != nil {
+		return n, err
+	}
+	p.coset, err = fr.BigEndian.Element(&bufFr)
+	if err != nil {
+		return n, err
+	}
 
 	return n, nil
 }
diff --git a/ecc/bw6-633/fr/iop/polynomial_test.go b/ecc/bw6-633/fr/iop/polynomial_test.go
index 9ac04bf6f9..584ec9c043 100644
--- a/ecc/bw6-633/fr/iop/polynomial_test.go
+++ b/ecc/bw6-633/fr/iop/polynomial_test.go
@@ -23,14 +23,14 @@ func TestEvaluation(t *testing.T) {
 	shift := 2
 	d := fft.NewDomain(uint64(size))
 	c := randomVector(size)
-	wp := NewPolynomial(c, Form{Basis: Canonical, Layout: Regular})
-	wps := wp.ShallowClone().Shift(shift)
-	ref := wp.Clone()
+	p := NewPolynomial(c, Form{Basis: Canonical, Layout: Regular})
+	ps := p.ShallowClone().Shift(shift)
+	ref := p.Clone()
 	ref.ToLagrange(d).ToRegular()
 
-	// regular layout
-	a := wp.Evaluate(d.Generator)
-	b := wps.Evaluate(d.Generator)
+	// canonical regular
+	a := p.Evaluate(d.Generator)
+	b := ps.Evaluate(d.Generator)
 	if !a.Equal(&ref.Coefficients()[1]) {
 		t.Fatal("error evaluation")
 	}
@@ -38,11 +38,11 @@ func TestEvaluation(t *testing.T) {
 		t.Fatal("error evaluation shifted")
 	}
 
-	// bit reversed layout
-	wp.ToBitReverse()
-	wps.ToBitReverse()
-	a = wp.Evaluate(d.Generator)
-	b = wps.Evaluate(d.Generator)
+	// canonical bit reversed
+	p.ToBitReverse()
+	ps.ToBitReverse()
+	a = p.Evaluate(d.Generator)
+	b = ps.Evaluate(d.Generator)
 	if !a.Equal(&ref.Coefficients()[1]) {
 		t.Fatal("error evaluation")
 	}
@@ -50,6 +50,60 @@ func TestEvaluation(t *testing.T) {
 		t.Fatal("error evaluation shifted")
 	}
 
+	// get reference values
+	var x fr.Element
+	x.SetRandom()
+	expectedEval := p.ToRegular().Evaluate(x)
+	expectedEvalShifted := ps.ToRegular().Evaluate(x)
+
+	// lagrange regular
+	p.ToLagrange(d).ToRegular()
+	ps.ToLagrange(d).ToRegular()
+	plx := p.Evaluate(x)
+	pslx := ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange shifted")
+	}
+
+	// lagrange bit reverse
+	p.ToBitReverse()
+	ps.ToBitReverse()
+	plx = p.Evaluate(x)
+	pslx = ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange shifted")
+	}
+
+	// lagrange coset regular
+	p.ToLagrangeCoset(d).ToRegular()
+	ps.ToLagrangeCoset(d).ToRegular()
+	plx = p.Evaluate(x)
+	pslx = ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange coset")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange coset shifted")
+	}
+
+	// lagrange coset bit reverse
+	p.ToRegular().ToBitReverse()
+	ps.ToRegular().ToBitReverse()
+	plx = p.Evaluate(x)
+	pslx = ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange coset")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange coset shifted")
+	}
+
 }
 
 func randomVector(size int) *[]fr.Element {
@@ -113,10 +167,9 @@ func TestRoundTrip(t *testing.T) {
 
 	size := 8
 	d := fft.NewDomain(uint64(8))
-	blindingOrder := 2
 
-	p := NewPolynomial(randomVector(size), Form{Basis: Lagrange, Layout: Regular}).ToCanonical(d).ToRegular()
-	p.Blind(blindingOrder)
+	p := NewPolynomial(randomVector(size), Form{Basis: Canonical, Layout: Regular})
+	p.ToLagrangeCoset(d)
 
 	// serialize
 	written, err := p.WriteTo(&buf)
@@ -134,52 +187,10 @@ func TestRoundTrip(t *testing.T) {
 	assert.Equal(p.Layout, reconstructed.Layout)
 	assert.Equal(p.shift, reconstructed.shift)
 	assert.Equal(p.size, reconstructed.size)
-	assert.Equal(p.blindedSize, reconstructed.blindedSize)
 	c1, c2 := p.Coefficients(), reconstructed.Coefficients()
 	assert.True(reflect.DeepEqual(c1, c2))
 }
 
-func TestBlinding(t *testing.T) {
-
-	size := 8
-	d := fft.NewDomain(uint64(8))
-	blindingOrder := 2
-
-	// generate a random polynomial in Lagrange form for the moment
-	// to check that an error is raised when the polynomial is not
-	// in canonical form.
-	wp := NewPolynomial(randomVector(size), Form{Basis: Lagrange, Layout: Regular})
-
-	// checks the blinding is correct: the evaluation of the blinded polynomial
-	// should be the same as the original on d's domain
-	wp.Basis = Canonical
-	wt := wp.Clone()
-	wt.Blind(blindingOrder)
-	if wt.coefficients.Len() != blindingOrder+size+1 {
-		t.Fatal("size of blinded polynomial is incorrect")
-	}
-	if wt.blindedSize != size+blindingOrder+1 {
-		t.Fatal("Size field of blinded polynomial is incorrect")
-	}
-	if wt.size != size {
-		t.Fatal("the size should not have been modified")
-	}
-	x := make([]fr.Element, size)
-	x[0].SetOne()
-	for i := 1; i < size; i++ {
-		x[i].Mul(&x[i-1], &d.Generator)
-	}
-	var a, b fr.Element
-	for i := 0; i < size; i++ {
-		a = wt.Evaluate(x[i])
-		b = wp.Evaluate(x[i])
-		if a != b {
-			t.Fatal("polynomial and its blinded version should be equal on V(X^{n}-1)")
-		}
-	}
-
-}
-
 // list of functions to turn a polynomial in Lagrange-regular form
 // to all different forms in ordered using this encoding:
 // int(p.Basis)*4 + int(p.Layout)*2 + int(p.Status)
diff --git a/ecc/bw6-633/fr/iop/quotient.go b/ecc/bw6-633/fr/iop/quotient.go
index 4420c026b2..7344abd32b 100644
--- a/ecc/bw6-633/fr/iop/quotient.go
+++ b/ecc/bw6-633/fr/iop/quotient.go
@@ -35,7 +35,6 @@ func DivideByXMinusOne(a *Polynomial, domains [2]*fft.Domain) (*Polynomial, erro
 	coeffs := make([]fr.Element, a.coefficients.Len())
 	res := NewPolynomial(&coeffs, Form{Layout: BitReverse, Basis: LagrangeCoset})
 	res.size = a.size
-	res.blindedSize = a.blindedSize
 
 	nn := uint64(64 - bits.TrailingZeros(uint(nbElmts)))
 	parallel.Execute(a.coefficients.Len(), func(start, end int) {
diff --git a/ecc/bw6-761/fr/iop/expressions.go b/ecc/bw6-761/fr/iop/expressions.go
index ac0bd11bc8..3941e95266 100644
--- a/ecc/bw6-761/fr/iop/expressions.go
+++ b/ecc/bw6-761/fr/iop/expressions.go
@@ -67,7 +67,6 @@ func Evaluate(f Expression, r []fr.Element, form Form, x ...*Polynomial) (*Polyn
 
 	res := NewPolynomial(&r, form)
 	res.size = x[0].size
-	res.blindedSize = x[0].size
 	res.shift = 0
 
 	return res, nil
diff --git a/ecc/bw6-761/fr/iop/polynomial.go b/ecc/bw6-761/fr/iop/polynomial.go
index 210e7a6b10..94fbb2d751 100644
--- a/ecc/bw6-761/fr/iop/polynomial.go
+++ b/ecc/bw6-761/fr/iop/polynomial.go
@@ -61,9 +61,9 @@ var (
 // default blindedSize=Size, until the polynomial is blinded.
 type Polynomial struct {
 	*polynomial
-	shift       int
-	size        int
-	blindedSize int
+	shift int
+	size  int
+	coset fr.Element // needed for evaluating the polynomial when it is expressed in Lagrange shifted basis
 }
 
 // NewPolynomial returned a Polynomial from the provided coefficients in the given form.
@@ -72,9 +72,8 @@ type Polynomial struct {
 // shouldn't be mutated.
 func NewPolynomial(coeffs *[]fr.Element, form Form) *Polynomial {
 	return &Polynomial{
-		polynomial:  newPolynomial(coeffs, form),
-		size:        len(*coeffs),
-		blindedSize: len(*coeffs),
+		polynomial: newPolynomial(coeffs, form),
+		size:       len(*coeffs),
 	}
 }
 
@@ -85,12 +84,6 @@ func (p *Polynomial) Shift(shift int) *Polynomial {
 	return p
 }
 
-// BlindedSize returns the the size of the polynomial when it is blinded. By
-// default blindedSize=Size, until the polynomial is blinded.
-func (p *Polynomial) BlindedSize() int {
-	return p.blindedSize
-}
-
 // Size returns the real size of the polynomial (seen as a vector).
 // For instance if len(P)=32 but P.Size=8, it means that P has been
 // extended (e.g. it is evaluated on a larger set) but P is a polynomial
@@ -108,69 +101,31 @@ func (p *Polynomial) SetSize(size int) {
 	p.size = size
 }
 
-// SetBlindedSize sets the blinded size of the polynomial.
-func (p *Polynomial) SetBlindedSize(size int) {
-	p.blindedSize = size
-}
-
-// Blind blinds a polynomial q by adding Q(X)*(X^{n}-1),
-// where deg Q = blindingOrder and Q is random, and n is the
-// size of q. Sets the result to p and returns it.
-//
-// blindingOrder is the degree of Q, where the blinding is Q(X)*(X^{n}-1)
-// where n is the size of p. The size of p is modified since the underlying
-// polynomial is of bigger degree now. The new size is p.Size+1+blindingOrder.
-//
-// /!\ The code panics if wq is not in canonical, regular layout
-func (p *Polynomial) Blind(blindingOrder int) *Polynomial {
-	// check that p is in canonical basis
-	if p.Form != canonicalRegular {
-		panic("the input must be in canonical basis, regular layout")
-	}
-
-	// we add Q*(x^{n}-1) so the new size is deg(Q)+n+1
-	// where n is the size of wq.
-	newSize := p.size + blindingOrder + 1
-
-	// Resize p. The size of wq might has already been increased
-	// (e.g. when the polynomial is evaluated on a larger domain),
-	// if that's the case we don't resize the polynomial.
-	p.grow(newSize)
-
-	// blinding: we add Q(X)(X^{n}-1) to P, where deg(Q)=blindingOrder
-	var r fr.Element
-
-	for i := 0; i <= blindingOrder; i++ {
-		r.SetRandom()
-		(*p.coefficients)[i].Sub(&(*p.coefficients)[i], &r)
-		(*p.coefficients)[i+p.size].Add(&(*p.coefficients)[i+p.size], &r)
-	}
-	p.blindedSize = newSize
-
-	return p
-}
-
 // Evaluate evaluates p at x.
 // The code panics if the function is not in canonical form.
 func (p *Polynomial) Evaluate(x fr.Element) fr.Element {
 
+	if p.Basis == LagrangeCoset {
+		x.Div(&x, &p.coset)
+	}
+
 	if p.shift == 0 {
 		return p.polynomial.evaluate(x)
 	}
 
 	var g fr.Element
-	gen, err := fft.Generator(uint64(p.size))
-	if err != nil {
-		panic(err)
-	}
 	if p.shift <= 5 {
+		gen, err := fft.Generator(uint64(p.size))
+		if err != nil {
+			panic(err)
+		}
 		g = smallExp(gen, p.shift)
 		x.Mul(&x, &g)
 		return p.polynomial.evaluate(x)
 	}
 
 	bs := big.NewInt(int64(p.shift))
-	g = *g.Exp(gen, bs)
+	g = *g.Exp(g, bs)
 	x.Mul(&x, &g)
 
 	return p.polynomial.evaluate(x)
@@ -245,20 +200,60 @@ func (p *polynomial) clone(capacity ...int) *polynomial {
 func (p *polynomial) evaluate(x fr.Element) fr.Element {
 
 	var r fr.Element
-	if p.Basis != Canonical {
-		panic("p must be in canonical basis")
+
+	evalLagrange := func() {
+		sizeP := p.coefficients.Len()
+		w, err := fft.Generator(uint64(sizeP))
+		if err != nil {
+			panic(err)
+		}
+		var accw fr.Element
+		accw.SetOne()
+		dens := make([]fr.Element, sizeP) // [x-1, x-ω, x-ω², ...]
+		for i := 0; i < sizeP; i++ {
+			dens[i].Sub(&x, &accw)
+			accw.Mul(&accw, &w)
+		}
+		invdens := fr.BatchInvert(dens) // [1/(x-1), 1/(x-ω), 1/(x-ω²), ...]
+		var tmp fr.Element
+		var one fr.Element
+		one.SetOne()
+		tmp.Exp(x, big.NewInt(int64(sizeP))).Sub(&tmp, &one) // xⁿ-1
+		var li fr.Element
+		li.SetUint64(uint64(sizeP)).Inverse(&li).Mul(&li, &tmp) // 1/n * (xⁿ-1)
+		if p.Layout == Regular {
+			for i := 0; i < sizeP; i++ {
+				li.Mul(&li, &invdens[i]) // li <- li*ω/(x-ωⁱ)
+				tmp.Mul(&li, &(*p.coefficients)[i])
+				r.Add(&r, &tmp)
+				li.Mul(&li, &dens[i]).Mul(&li, &w) // li <- li*ω*(x-ωⁱ)
+			}
+		} else {
+			nn := uint64(64 - bits.TrailingZeros(uint(p.coefficients.Len())))
+			for i := 0; i < sizeP; i++ {
+				iRev := bits.Reverse64(uint64(i)) >> nn
+				li.Mul(&li, &invdens[i]) // li <- li*ω/(x-ωⁱ)
+				tmp.Mul(&li, &(*p.coefficients)[iRev])
+				r.Add(&r, &tmp)
+				li.Mul(&li, &dens[i]).Mul(&li, &w) // li <- li*ω*(x-ωⁱ)
+			}
+		}
 	}
 
-	if p.Layout == Regular {
-		for i := p.coefficients.Len() - 1; i >= 0; i-- {
-			r.Mul(&r, &x).Add(&r, &(*p.coefficients)[i])
+	if p.Basis == Canonical {
+		if p.Layout == Regular {
+			for i := p.coefficients.Len() - 1; i >= 0; i-- {
+				r.Mul(&r, &x).Add(&r, &(*p.coefficients)[i])
+			}
+		} else {
+			nn := uint64(64 - bits.TrailingZeros(uint(p.coefficients.Len())))
+			for i := p.coefficients.Len() - 1; i >= 0; i-- {
+				iRev := bits.Reverse64(uint64(i)) >> nn
+				r.Mul(&r, &x).Add(&r, &(*p.coefficients)[iRev])
+			}
 		}
 	} else {
-		nn := uint64(64 - bits.TrailingZeros(uint(p.coefficients.Len())))
-		for i := p.coefficients.Len() - 1; i >= 0; i-- {
-			iRev := bits.Reverse64(uint64(i)) >> nn
-			r.Mul(&r, &x).Add(&r, &(*p.coefficients)[iRev])
-		}
+		evalLagrange()
 	}
 
 	return r
@@ -362,6 +357,11 @@ func (p *polynomial) grow(newSize int) {
 
 // ToLagrangeCoset Sets p to q, in LagrangeCoset form and returns it.
 func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial {
+	cosetTable, err := d.CosetTable()
+	if err != nil {
+		panic(err)
+	}
+	p.coset.Set(&cosetTable[1])
 	id := p.Form
 	p.grow(int(d.Cardinality))
 	switch id {
@@ -391,6 +391,7 @@ func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial {
 
 // WriteTo implements io.WriterTo
 func (p *Polynomial) WriteTo(w io.Writer) (int64, error) {
+
 	// encode coefficients
 	n, err := p.polynomial.coefficients.WriteTo(w)
 	if err != nil {
@@ -403,7 +404,6 @@ func (p *Polynomial) WriteTo(w io.Writer) (int64, error) {
 		uint32(p.Layout),
 		uint32(p.shift),
 		uint32(p.size),
-		uint32(p.blindedSize),
 	}
 	for _, v := range data {
 		err = binary.Write(w, binary.BigEndian, v)
@@ -412,6 +412,15 @@ func (p *Polynomial) WriteTo(w io.Writer) (int64, error) {
 		}
 		n += 4
 	}
+
+	var buf [fr.Bytes]byte
+	fr.BigEndian.PutElement(&buf, p.coset)
+	m, err := w.Write(buf[:])
+	n += int64(m)
+	if err != nil {
+		return n, err
+	}
+
 	return n, nil
 }
 
@@ -430,8 +439,8 @@ func (p *Polynomial) ReadFrom(r io.Reader) (int64, error) {
 		return n, err
 	}
 
-	// decode Form.Basis, Form.Layout, shift, size & blindedSize as uint32
-	var data [5]uint32
+	// decode Form.Basis, Form.Layout, shift as uint32
+	var data [4]uint32
 	var buf [4]byte
 	for i := range data {
 		read, err := io.ReadFull(r, buf[:4])
@@ -446,7 +455,17 @@ func (p *Polynomial) ReadFrom(r io.Reader) (int64, error) {
 	p.Layout = Layout(data[1])
 	p.shift = int(data[2])
 	p.size = int(data[3])
-	p.blindedSize = int(data[4])
+
+	var bufFr [fr.Bytes]byte
+	read, err := io.ReadFull(r, bufFr[:])
+	n += int64(read)
+	if err != nil {
+		return n, err
+	}
+	p.coset, err = fr.BigEndian.Element(&bufFr)
+	if err != nil {
+		return n, err
+	}
 
 	return n, nil
 }
diff --git a/ecc/bw6-761/fr/iop/polynomial_test.go b/ecc/bw6-761/fr/iop/polynomial_test.go
index cee823decb..b04551d9a6 100644
--- a/ecc/bw6-761/fr/iop/polynomial_test.go
+++ b/ecc/bw6-761/fr/iop/polynomial_test.go
@@ -23,14 +23,14 @@ func TestEvaluation(t *testing.T) {
 	shift := 2
 	d := fft.NewDomain(uint64(size))
 	c := randomVector(size)
-	wp := NewPolynomial(c, Form{Basis: Canonical, Layout: Regular})
-	wps := wp.ShallowClone().Shift(shift)
-	ref := wp.Clone()
+	p := NewPolynomial(c, Form{Basis: Canonical, Layout: Regular})
+	ps := p.ShallowClone().Shift(shift)
+	ref := p.Clone()
 	ref.ToLagrange(d).ToRegular()
 
-	// regular layout
-	a := wp.Evaluate(d.Generator)
-	b := wps.Evaluate(d.Generator)
+	// canonical regular
+	a := p.Evaluate(d.Generator)
+	b := ps.Evaluate(d.Generator)
 	if !a.Equal(&ref.Coefficients()[1]) {
 		t.Fatal("error evaluation")
 	}
@@ -38,11 +38,11 @@ func TestEvaluation(t *testing.T) {
 		t.Fatal("error evaluation shifted")
 	}
 
-	// bit reversed layout
-	wp.ToBitReverse()
-	wps.ToBitReverse()
-	a = wp.Evaluate(d.Generator)
-	b = wps.Evaluate(d.Generator)
+	// canonical bit reversed
+	p.ToBitReverse()
+	ps.ToBitReverse()
+	a = p.Evaluate(d.Generator)
+	b = ps.Evaluate(d.Generator)
 	if !a.Equal(&ref.Coefficients()[1]) {
 		t.Fatal("error evaluation")
 	}
@@ -50,6 +50,60 @@ func TestEvaluation(t *testing.T) {
 		t.Fatal("error evaluation shifted")
 	}
 
+	// get reference values
+	var x fr.Element
+	x.SetRandom()
+	expectedEval := p.ToRegular().Evaluate(x)
+	expectedEvalShifted := ps.ToRegular().Evaluate(x)
+
+	// lagrange regular
+	p.ToLagrange(d).ToRegular()
+	ps.ToLagrange(d).ToRegular()
+	plx := p.Evaluate(x)
+	pslx := ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange shifted")
+	}
+
+	// lagrange bit reverse
+	p.ToBitReverse()
+	ps.ToBitReverse()
+	plx = p.Evaluate(x)
+	pslx = ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange shifted")
+	}
+
+	// lagrange coset regular
+	p.ToLagrangeCoset(d).ToRegular()
+	ps.ToLagrangeCoset(d).ToRegular()
+	plx = p.Evaluate(x)
+	pslx = ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange coset")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange coset shifted")
+	}
+
+	// lagrange coset bit reverse
+	p.ToRegular().ToBitReverse()
+	ps.ToRegular().ToBitReverse()
+	plx = p.Evaluate(x)
+	pslx = ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange coset")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange coset shifted")
+	}
+
 }
 
 func randomVector(size int) *[]fr.Element {
@@ -113,10 +167,9 @@ func TestRoundTrip(t *testing.T) {
 
 	size := 8
 	d := fft.NewDomain(uint64(8))
-	blindingOrder := 2
 
-	p := NewPolynomial(randomVector(size), Form{Basis: Lagrange, Layout: Regular}).ToCanonical(d).ToRegular()
-	p.Blind(blindingOrder)
+	p := NewPolynomial(randomVector(size), Form{Basis: Canonical, Layout: Regular})
+	p.ToLagrangeCoset(d)
 
 	// serialize
 	written, err := p.WriteTo(&buf)
@@ -134,52 +187,10 @@ func TestRoundTrip(t *testing.T) {
 	assert.Equal(p.Layout, reconstructed.Layout)
 	assert.Equal(p.shift, reconstructed.shift)
 	assert.Equal(p.size, reconstructed.size)
-	assert.Equal(p.blindedSize, reconstructed.blindedSize)
 	c1, c2 := p.Coefficients(), reconstructed.Coefficients()
 	assert.True(reflect.DeepEqual(c1, c2))
 }
 
-func TestBlinding(t *testing.T) {
-
-	size := 8
-	d := fft.NewDomain(uint64(8))
-	blindingOrder := 2
-
-	// generate a random polynomial in Lagrange form for the moment
-	// to check that an error is raised when the polynomial is not
-	// in canonical form.
-	wp := NewPolynomial(randomVector(size), Form{Basis: Lagrange, Layout: Regular})
-
-	// checks the blinding is correct: the evaluation of the blinded polynomial
-	// should be the same as the original on d's domain
-	wp.Basis = Canonical
-	wt := wp.Clone()
-	wt.Blind(blindingOrder)
-	if wt.coefficients.Len() != blindingOrder+size+1 {
-		t.Fatal("size of blinded polynomial is incorrect")
-	}
-	if wt.blindedSize != size+blindingOrder+1 {
-		t.Fatal("Size field of blinded polynomial is incorrect")
-	}
-	if wt.size != size {
-		t.Fatal("the size should not have been modified")
-	}
-	x := make([]fr.Element, size)
-	x[0].SetOne()
-	for i := 1; i < size; i++ {
-		x[i].Mul(&x[i-1], &d.Generator)
-	}
-	var a, b fr.Element
-	for i := 0; i < size; i++ {
-		a = wt.Evaluate(x[i])
-		b = wp.Evaluate(x[i])
-		if a != b {
-			t.Fatal("polynomial and its blinded version should be equal on V(X^{n}-1)")
-		}
-	}
-
-}
-
 // list of functions to turn a polynomial in Lagrange-regular form
 // to all different forms in ordered using this encoding:
 // int(p.Basis)*4 + int(p.Layout)*2 + int(p.Status)
diff --git a/ecc/bw6-761/fr/iop/quotient.go b/ecc/bw6-761/fr/iop/quotient.go
index 2c3f93e5e1..6329b85400 100644
--- a/ecc/bw6-761/fr/iop/quotient.go
+++ b/ecc/bw6-761/fr/iop/quotient.go
@@ -35,7 +35,6 @@ func DivideByXMinusOne(a *Polynomial, domains [2]*fft.Domain) (*Polynomial, erro
 	coeffs := make([]fr.Element, a.coefficients.Len())
 	res := NewPolynomial(&coeffs, Form{Layout: BitReverse, Basis: LagrangeCoset})
 	res.size = a.size
-	res.blindedSize = a.blindedSize
 
 	nn := uint64(64 - bits.TrailingZeros(uint(nbElmts)))
 	parallel.Execute(a.coefficients.Len(), func(start, end int) {
diff --git a/internal/generator/iop/template/expressions.go.tmpl b/internal/generator/iop/template/expressions.go.tmpl
index ddf2330242..2692768753 100644
--- a/internal/generator/iop/template/expressions.go.tmpl
+++ b/internal/generator/iop/template/expressions.go.tmpl
@@ -60,8 +60,7 @@ func Evaluate(f Expression, r []fr.Element, form Form, x ...*Polynomial) (*Polyn
 
 	res := NewPolynomial(&r, form)
 	res.size = x[0].size
-	res.blindedSize = x[0].size
 	res.shift = 0
 
 	return res, nil
-}
+}
\ No newline at end of file
diff --git a/internal/generator/iop/template/polynomial.go.tmpl b/internal/generator/iop/template/polynomial.go.tmpl
index 9f5cb333e6..50a446e092 100644
--- a/internal/generator/iop/template/polynomial.go.tmpl
+++ b/internal/generator/iop/template/polynomial.go.tmpl
@@ -54,9 +54,9 @@ var (
 // default blindedSize=Size, until the polynomial is blinded.
 type Polynomial struct {
 	*polynomial
-	shift       int
-	size        int
-	blindedSize int
+	shift int
+	size  int
+	coset fr.Element // needed for evaluating the polynomial when it is expressed in Lagrange shifted basis
 }
 
 // NewPolynomial returned a Polynomial from the provided coefficients in the given form.
@@ -65,9 +65,8 @@ type Polynomial struct {
 // shouldn't be mutated.
 func NewPolynomial(coeffs *[]fr.Element, form Form) *Polynomial {
 	return &Polynomial{
-		polynomial:  newPolynomial(coeffs, form),
-		size:        len(*coeffs),
-		blindedSize: len(*coeffs),
+		polynomial: newPolynomial(coeffs, form),
+		size:       len(*coeffs),
 	}
 }
 
@@ -78,12 +77,6 @@ func (p *Polynomial) Shift(shift int) *Polynomial {
 	return p
 }
 
-// BlindedSize returns the the size of the polynomial when it is blinded. By
-// default blindedSize=Size, until the polynomial is blinded.
-func (p *Polynomial) BlindedSize() int {
-	return p.blindedSize
-}
-
 // Size returns the real size of the polynomial (seen as a vector).
 // For instance if len(P)=32 but P.Size=8, it means that P has been
 // extended (e.g. it is evaluated on a larger set) but P is a polynomial
@@ -101,69 +94,31 @@ func (p *Polynomial) SetSize(size int) {
 	p.size = size
 }
 
-// SetBlindedSize sets the blinded size of the polynomial.
-func (p *Polynomial) SetBlindedSize(size int) {
-	p.blindedSize = size
-}
-
-// Blind blinds a polynomial q by adding Q(X)*(X^{n}-1),
-// where deg Q = blindingOrder and Q is random, and n is the
-// size of q. Sets the result to p and returns it.
-//
-// blindingOrder is the degree of Q, where the blinding is Q(X)*(X^{n}-1)
-// where n is the size of p. The size of p is modified since the underlying
-// polynomial is of bigger degree now. The new size is p.Size+1+blindingOrder.
-//
-// /!\ The code panics if wq is not in canonical, regular layout
-func (p *Polynomial) Blind(blindingOrder int) *Polynomial {
-	// check that p is in canonical basis
-	if p.Form != canonicalRegular {
-		panic("the input must be in canonical basis, regular layout")
-	}
-
-	// we add Q*(x^{n}-1) so the new size is deg(Q)+n+1
-	// where n is the size of wq.
-	newSize := p.size + blindingOrder + 1
-
-	// Resize p. The size of wq might has already been increased
-	// (e.g. when the polynomial is evaluated on a larger domain),
-	// if that's the case we don't resize the polynomial.
-	p.grow(newSize)
-
-	// blinding: we add Q(X)(X^{n}-1) to P, where deg(Q)=blindingOrder
-	var r fr.Element
-
-	for i := 0; i <= blindingOrder; i++ {
-		r.SetRandom()
-		(*p.coefficients)[i].Sub(&(*p.coefficients)[i], &r)
-		(*p.coefficients)[i+p.size].Add(&(*p.coefficients)[i+p.size], &r)
-	}
-	p.blindedSize = newSize
-
-	return p
-}
-
 // Evaluate evaluates p at x.
 // The code panics if the function is not in canonical form.
 func (p *Polynomial) Evaluate(x fr.Element) fr.Element {
 
+	if p.Basis == LagrangeCoset {
+		x.Div(&x, &p.coset)
+	}
+
 	if p.shift == 0 {
 		return p.polynomial.evaluate(x)
 	}
 
 	var g fr.Element
-	gen, err := fft.Generator(uint64(p.size))
-	if err != nil {
-		panic(err)
-	}
 	if p.shift <= 5 {
+		gen, err := fft.Generator(uint64(p.size))
+		if err != nil {
+			panic(err)
+		}
 		g = smallExp(gen, p.shift)
 		x.Mul(&x, &g)
 		return p.polynomial.evaluate(x)
 	}
 
 	bs := big.NewInt(int64(p.shift))
-	g = *g.Exp(gen, bs)
+	g = *g.Exp(g, bs)
 	x.Mul(&x, &g)
 
 	return p.polynomial.evaluate(x)
@@ -238,20 +193,60 @@ func (p *polynomial) clone(capacity ...int) *polynomial {
 func (p *polynomial) evaluate(x fr.Element) fr.Element {
 
 	var r fr.Element
-	if p.Basis != Canonical {
-		panic("p must be in canonical basis")
+
+	evalLagrange := func() {
+		sizeP := p.coefficients.Len()
+		w, err := fft.Generator(uint64(sizeP))
+		if err != nil {
+			panic(err)
+		}
+		var accw fr.Element
+		accw.SetOne()
+		dens := make([]fr.Element, sizeP) // [x-1, x-ω, x-ω², ...]
+		for i := 0; i < sizeP; i++ {
+			dens[i].Sub(&x, &accw)
+			accw.Mul(&accw, &w)
+		}
+		invdens := fr.BatchInvert(dens) // [1/(x-1), 1/(x-ω), 1/(x-ω²), ...]
+		var tmp fr.Element
+		var one fr.Element
+		one.SetOne()
+		tmp.Exp(x, big.NewInt(int64(sizeP))).Sub(&tmp, &one) // xⁿ-1
+		var li fr.Element
+		li.SetUint64(uint64(sizeP)).Inverse(&li).Mul(&li, &tmp) // 1/n * (xⁿ-1)
+		if p.Layout == Regular {
+			for i := 0; i < sizeP; i++ {
+				li.Mul(&li, &invdens[i]) // li <- li*ω/(x-ωⁱ)
+				tmp.Mul(&li, &(*p.coefficients)[i])
+				r.Add(&r, &tmp)
+				li.Mul(&li, &dens[i]).Mul(&li, &w) // li <- li*ω*(x-ωⁱ)
+			}
+		} else {
+			nn := uint64(64 - bits.TrailingZeros(uint(p.coefficients.Len())))
+			for i := 0; i < sizeP; i++ {
+				iRev := bits.Reverse64(uint64(i)) >> nn
+				li.Mul(&li, &invdens[i]) // li <- li*ω/(x-ωⁱ)
+				tmp.Mul(&li, &(*p.coefficients)[iRev])
+				r.Add(&r, &tmp)
+				li.Mul(&li, &dens[i]).Mul(&li, &w) // li <- li*ω*(x-ωⁱ)
+			}
+		}
 	}
 
-	if p.Layout == Regular {
-		for i := p.coefficients.Len() - 1; i >= 0; i-- {
-			r.Mul(&r, &x).Add(&r, &(*p.coefficients)[i])
+	if p.Basis == Canonical {
+		if p.Layout == Regular {
+			for i := p.coefficients.Len() - 1; i >= 0; i-- {
+				r.Mul(&r, &x).Add(&r, &(*p.coefficients)[i])
+			}
+		} else {
+			nn := uint64(64 - bits.TrailingZeros(uint(p.coefficients.Len())))
+			for i := p.coefficients.Len() - 1; i >= 0; i-- {
+				iRev := bits.Reverse64(uint64(i)) >> nn
+				r.Mul(&r, &x).Add(&r, &(*p.coefficients)[iRev])
+			}
 		}
 	} else {
-		nn := uint64(64 - bits.TrailingZeros(uint(p.coefficients.Len())))
-		for i := p.coefficients.Len() - 1; i >= 0; i-- {
-			iRev := bits.Reverse64(uint64(i)) >> nn
-			r.Mul(&r, &x).Add(&r, &(*p.coefficients)[iRev])
-		}
+		evalLagrange()
 	}
 
 	return r
@@ -355,6 +350,11 @@ func (p *polynomial) grow(newSize int) {
 
 // ToLagrangeCoset Sets p to q, in LagrangeCoset form and returns it.
 func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial {
+	cosetTable, err := d.CosetTable()
+	if err != nil {
+		panic(err)
+	}
+	p.coset.Set(&cosetTable[1])
 	id := p.Form
 	p.grow(int(d.Cardinality))
 	switch id {
@@ -384,6 +384,7 @@ func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial {
 
 // WriteTo implements io.WriterTo
 func (p *Polynomial) WriteTo(w io.Writer) (int64, error) {
+
 	// encode coefficients
 	n, err := p.polynomial.coefficients.WriteTo(w)
 	if err != nil {
@@ -396,7 +397,6 @@ func (p *Polynomial) WriteTo(w io.Writer) (int64, error) {
 		uint32(p.Layout),
 		uint32(p.shift),
 		uint32(p.size),
-		uint32(p.blindedSize),
 	}
 	for _, v := range data {
 		err = binary.Write(w, binary.BigEndian, v)
@@ -405,6 +405,15 @@ func (p *Polynomial) WriteTo(w io.Writer) (int64, error) {
 		}
 		n += 4
 	}
+
+	var buf [fr.Bytes]byte
+	fr.BigEndian.PutElement(&buf, p.coset)
+	m, err := w.Write(buf[:])
+	n += int64(m)
+	if err != nil {
+		return n, err
+	}
+
 	return n, nil
 }
 
@@ -423,8 +432,8 @@ func (p *Polynomial) ReadFrom(r io.Reader) (int64, error) {
 		return n, err
 	}
 
-	// decode Form.Basis, Form.Layout, shift, size & blindedSize as uint32
-	var data [5]uint32
+	// decode Form.Basis, Form.Layout, shift as uint32
+	var data [4]uint32
 	var buf [4]byte
 	for i := range data {
 		read, err := io.ReadFull(r, buf[:4])
@@ -439,7 +448,17 @@ func (p *Polynomial) ReadFrom(r io.Reader) (int64, error) {
 	p.Layout = Layout(data[1])
 	p.shift = int(data[2])
 	p.size = int(data[3])
-	p.blindedSize = int(data[4])
+
+	var bufFr [fr.Bytes]byte
+	read, err := io.ReadFull(r, bufFr[:])
+	n += int64(read)
+	if err != nil {
+		return n, err
+	}
+	p.coset, err = fr.BigEndian.Element(&bufFr)
+	if err != nil {
+		return n, err
+	}
 
 	return n, nil
 }
\ No newline at end of file
diff --git a/internal/generator/iop/template/polynomial.test.go.tmpl b/internal/generator/iop/template/polynomial.test.go.tmpl
index 0bf76239be..11cf1cf1e1 100644
--- a/internal/generator/iop/template/polynomial.test.go.tmpl
+++ b/internal/generator/iop/template/polynomial.test.go.tmpl
@@ -16,14 +16,14 @@ func TestEvaluation(t *testing.T) {
 	shift := 2
 	d := fft.NewDomain(uint64(size))
 	c := randomVector(size)
-	wp := NewPolynomial(c, Form{Basis: Canonical, Layout: Regular})
-	wps := wp.ShallowClone().Shift(shift)
-	ref := wp.Clone()
+	p := NewPolynomial(c, Form{Basis: Canonical, Layout: Regular})
+	ps := p.ShallowClone().Shift(shift)
+	ref := p.Clone()
 	ref.ToLagrange(d).ToRegular()
 
-	// regular layout
-	a := wp.Evaluate(d.Generator)
-	b := wps.Evaluate(d.Generator)
+	// canonical regular
+	a := p.Evaluate(d.Generator)
+	b := ps.Evaluate(d.Generator)
 	if !a.Equal(&ref.Coefficients()[1]) {
 		t.Fatal("error evaluation")
 	}
@@ -31,11 +31,11 @@ func TestEvaluation(t *testing.T) {
 		t.Fatal("error evaluation shifted")
 	}
 
-	// bit reversed layout
-	wp.ToBitReverse()
-	wps.ToBitReverse()
-	a = wp.Evaluate(d.Generator)
-	b = wps.Evaluate(d.Generator)
+	// canonical bit reversed
+	p.ToBitReverse()
+	ps.ToBitReverse()
+	a = p.Evaluate(d.Generator)
+	b = ps.Evaluate(d.Generator)
 	if !a.Equal(&ref.Coefficients()[1]) {
 		t.Fatal("error evaluation")
 	}
@@ -43,6 +43,60 @@ func TestEvaluation(t *testing.T) {
 		t.Fatal("error evaluation shifted")
 	}
 
+	// get reference values
+	var x fr.Element
+	x.SetRandom()
+	expectedEval := p.ToRegular().Evaluate(x)
+	expectedEvalShifted := ps.ToRegular().Evaluate(x)
+
+	// lagrange regular
+	p.ToLagrange(d).ToRegular()
+	ps.ToLagrange(d).ToRegular()
+	plx := p.Evaluate(x)
+	pslx := ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange shifted")
+	}
+
+	// lagrange bit reverse
+	p.ToBitReverse()
+	ps.ToBitReverse()
+	plx = p.Evaluate(x)
+	pslx = ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange shifted")
+	}
+
+	// lagrange coset regular
+	p.ToLagrangeCoset(d).ToRegular()
+	ps.ToLagrangeCoset(d).ToRegular()
+	plx = p.Evaluate(x)
+	pslx = ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange coset")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange coset shifted")
+	}
+
+	// lagrange coset bit reverse
+	p.ToRegular().ToBitReverse()
+	ps.ToRegular().ToBitReverse()
+	plx = p.Evaluate(x)
+	pslx = ps.Evaluate(x)
+	if !plx.Equal(&expectedEval) {
+		t.Fatal("error evaluation lagrange coset")
+	}
+	if !pslx.Equal(&expectedEvalShifted) {
+		t.Fatal("error evaluation lagrange coset shifted")
+	}
+
 }
 
 func randomVector(size int) *[]fr.Element {
@@ -100,17 +154,15 @@ func TestGetCoeff(t *testing.T) {
 
 }
 
-
 func TestRoundTrip(t *testing.T) {
 	assert := require.New(t)
 	var buf bytes.Buffer
 
 	size := 8
 	d := fft.NewDomain(uint64(8))
-	blindingOrder := 2
 
-	p := NewPolynomial(randomVector(size), Form{Basis:Lagrange, Layout: Regular}).ToCanonical(d).ToRegular()
-	p.Blind(blindingOrder)
+	p := NewPolynomial(randomVector(size), Form{Basis: Canonical, Layout: Regular})
+	p.ToLagrangeCoset(d)
 
 	// serialize
 	written, err := p.WriteTo(&buf)
@@ -123,57 +175,15 @@ func TestRoundTrip(t *testing.T) {
 
 	assert.Equal(read, written, "number of bytes written != number of bytes read")
 
-	// compare 
+	// compare
 	assert.Equal(p.Basis, reconstructed.Basis)
 	assert.Equal(p.Layout, reconstructed.Layout)
 	assert.Equal(p.shift, reconstructed.shift)
 	assert.Equal(p.size, reconstructed.size)
-	assert.Equal(p.blindedSize, reconstructed.blindedSize)
 	c1, c2 := p.Coefficients(), reconstructed.Coefficients()
 	assert.True(reflect.DeepEqual(c1, c2))
 }
 
-func TestBlinding(t *testing.T) {
-
-	size := 8
-	d := fft.NewDomain(uint64(8))
-	blindingOrder := 2
-
-	// generate a random polynomial in Lagrange form for the moment
-	// to check that an error is raised when the polynomial is not
-	// in canonical form.
-	wp := NewPolynomial(randomVector(size), Form{Basis:Lagrange, Layout: Regular})
-
-	// checks the blinding is correct: the evaluation of the blinded polynomial
-	// should be the same as the original on d's domain
-	wp.Basis = Canonical
-	wt := wp.Clone()
-	wt.Blind(blindingOrder)
-	if wt.coefficients.Len() != blindingOrder+size+1 {
-		t.Fatal("size of blinded polynomial is incorrect")
-	}
-	if wt.blindedSize != size+blindingOrder+1 {
-		t.Fatal("Size field of blinded polynomial is incorrect")
-	}
-	if wt.size != size {
-		t.Fatal("the size should not have been modified")
-	}
-	x := make([]fr.Element, size)
-	x[0].SetOne()
-	for i := 1; i < size; i++ {
-		x[i].Mul(&x[i-1], &d.Generator)
-	}
-	var a, b fr.Element
-	for i := 0; i < size; i++ {
-		a = wt.Evaluate(x[i])
-		b = wp.Evaluate(x[i])
-		if a != b {
-			t.Fatal("polynomial and its blinded version should be equal on V(X^{n}-1)")
-		}
-	}
-
-}
-
 // list of functions to turn a polynomial in Lagrange-regular form
 // to all different forms in ordered using this encoding:
 // int(p.Basis)*4 + int(p.Layout)*2 + int(p.Status)
@@ -263,8 +273,8 @@ func cmpCoefficents(p, q *fr.Vector) bool {
 		return false
 	}
 	for i := 0; i < p.Len(); i++ {
-		if !((*p)[i].Equal(&(*q)[i])){
-			return false 
+		if !((*p)[i].Equal(&(*q)[i])) {
+			return false
 		}
 	}
 	return true
@@ -709,4 +719,4 @@ func TestPutInLagrangeCosetForm(t *testing.T) {
 		}
 	}
 
-}
+}
\ No newline at end of file
diff --git a/internal/generator/iop/template/quotient.go.tmpl b/internal/generator/iop/template/quotient.go.tmpl
index aacb3283e8..5943283f22 100644
--- a/internal/generator/iop/template/quotient.go.tmpl
+++ b/internal/generator/iop/template/quotient.go.tmpl
@@ -28,10 +28,9 @@ func DivideByXMinusOne(a *Polynomial, domains [2]*fft.Domain) (*Polynomial, erro
 	coeffs := make([]fr.Element, a.coefficients.Len())
 	res := NewPolynomial(&coeffs, Form{Layout: BitReverse, Basis: LagrangeCoset})
 	res.size = a.size
-	res.blindedSize = a.blindedSize
 
 	nn := uint64(64 - bits.TrailingZeros(uint(nbElmts)))
-	parallel.Execute(a.coefficients.Len(), func(start, end int){
+	parallel.Execute(a.coefficients.Len(), func(start, end int) {
 		for i := start; i < end; i++ {
 			iRev := bits.Reverse64(uint64(i)) >> nn
 			c := a.GetCoeff(i)
@@ -39,7 +38,6 @@ func DivideByXMinusOne(a *Polynomial, domains [2]*fft.Domain) (*Polynomial, erro
 				Mul(&c, &xnMinusOneInverseLagrangeCoset[i%rho])
 		}
 	})
-	
 
 	res.ToCanonical(domains[1])
 
@@ -71,4 +69,4 @@ func evaluateXnMinusOneDomainBigCoset(domains [2]*fft.Domain) []fr.Element {
 	res = fr.BatchInvert(res)
 
 	return res
-}
+}
\ No newline at end of file

From 12f9a755962717f56e548c13066903297d318a02 Mon Sep 17 00:00:00 2001
From: cuibuwei <166905851+cuibuwei@users.noreply.github.com>
Date: Wed, 4 Dec 2024 07:49:02 +0800
Subject: [PATCH 103/114] chore: fix some function names in comment (#559)

Signed-off-by: cuibuwei <cuibuwei@gmail.com>
---
 ecc/bls12-377/fr/fri/fri_test.go                 | 2 +-
 ecc/bls12-381/fr/fri/fri_test.go                 | 2 +-
 ecc/bls24-315/fr/fri/fri_test.go                 | 2 +-
 ecc/bls24-317/fr/fri/fri_test.go                 | 2 +-
 ecc/bn254/fr/fri/fri_test.go                     | 2 +-
 ecc/bw6-633/fr/fri/fri_test.go                   | 2 +-
 ecc/bw6-761/fr/fri/fri_test.go                   | 2 +-
 internal/generator/fri/template/fri.test.go.tmpl | 2 +-
 8 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/ecc/bls12-377/fr/fri/fri_test.go b/ecc/bls12-377/fr/fri/fri_test.go
index 6d8b082ace..8c637fa732 100644
--- a/ecc/bls12-377/fr/fri/fri_test.go
+++ b/ecc/bls12-377/fr/fri/fri_test.go
@@ -39,7 +39,7 @@ func randomPolynomial(size uint64, seed int32) []fr.Element {
 	return p
 }
 
-// convertOrderCanonical convert the index i, an entry in a
+// convertSortedCanonical convert the index i, an entry in a
 // sorted polynomial, to the corresponding entry in canonical
 // representation. n is the size of the polynomial.
 func convertSortedCanonical(i, n int) int {
diff --git a/ecc/bls12-381/fr/fri/fri_test.go b/ecc/bls12-381/fr/fri/fri_test.go
index 6f479e148e..53e29eb47c 100644
--- a/ecc/bls12-381/fr/fri/fri_test.go
+++ b/ecc/bls12-381/fr/fri/fri_test.go
@@ -39,7 +39,7 @@ func randomPolynomial(size uint64, seed int32) []fr.Element {
 	return p
 }
 
-// convertOrderCanonical convert the index i, an entry in a
+// convertSortedCanonical convert the index i, an entry in a
 // sorted polynomial, to the corresponding entry in canonical
 // representation. n is the size of the polynomial.
 func convertSortedCanonical(i, n int) int {
diff --git a/ecc/bls24-315/fr/fri/fri_test.go b/ecc/bls24-315/fr/fri/fri_test.go
index d6731670d6..8779681e93 100644
--- a/ecc/bls24-315/fr/fri/fri_test.go
+++ b/ecc/bls24-315/fr/fri/fri_test.go
@@ -39,7 +39,7 @@ func randomPolynomial(size uint64, seed int32) []fr.Element {
 	return p
 }
 
-// convertOrderCanonical convert the index i, an entry in a
+// convertSortedCanonical convert the index i, an entry in a
 // sorted polynomial, to the corresponding entry in canonical
 // representation. n is the size of the polynomial.
 func convertSortedCanonical(i, n int) int {
diff --git a/ecc/bls24-317/fr/fri/fri_test.go b/ecc/bls24-317/fr/fri/fri_test.go
index 90fda8fc02..78d2ba03be 100644
--- a/ecc/bls24-317/fr/fri/fri_test.go
+++ b/ecc/bls24-317/fr/fri/fri_test.go
@@ -39,7 +39,7 @@ func randomPolynomial(size uint64, seed int32) []fr.Element {
 	return p
 }
 
-// convertOrderCanonical convert the index i, an entry in a
+// convertSortedCanonical convert the index i, an entry in a
 // sorted polynomial, to the corresponding entry in canonical
 // representation. n is the size of the polynomial.
 func convertSortedCanonical(i, n int) int {
diff --git a/ecc/bn254/fr/fri/fri_test.go b/ecc/bn254/fr/fri/fri_test.go
index 3e7f236f7c..9092076f81 100644
--- a/ecc/bn254/fr/fri/fri_test.go
+++ b/ecc/bn254/fr/fri/fri_test.go
@@ -39,7 +39,7 @@ func randomPolynomial(size uint64, seed int32) []fr.Element {
 	return p
 }
 
-// convertOrderCanonical convert the index i, an entry in a
+// convertSortedCanonical convert the index i, an entry in a
 // sorted polynomial, to the corresponding entry in canonical
 // representation. n is the size of the polynomial.
 func convertSortedCanonical(i, n int) int {
diff --git a/ecc/bw6-633/fr/fri/fri_test.go b/ecc/bw6-633/fr/fri/fri_test.go
index 336ee07c0b..27719d6a22 100644
--- a/ecc/bw6-633/fr/fri/fri_test.go
+++ b/ecc/bw6-633/fr/fri/fri_test.go
@@ -39,7 +39,7 @@ func randomPolynomial(size uint64, seed int32) []fr.Element {
 	return p
 }
 
-// convertOrderCanonical convert the index i, an entry in a
+// convertSortedCanonical convert the index i, an entry in a
 // sorted polynomial, to the corresponding entry in canonical
 // representation. n is the size of the polynomial.
 func convertSortedCanonical(i, n int) int {
diff --git a/ecc/bw6-761/fr/fri/fri_test.go b/ecc/bw6-761/fr/fri/fri_test.go
index 95efe748ff..d3907b4fc7 100644
--- a/ecc/bw6-761/fr/fri/fri_test.go
+++ b/ecc/bw6-761/fr/fri/fri_test.go
@@ -39,7 +39,7 @@ func randomPolynomial(size uint64, seed int32) []fr.Element {
 	return p
 }
 
-// convertOrderCanonical convert the index i, an entry in a
+// convertSortedCanonical convert the index i, an entry in a
 // sorted polynomial, to the corresponding entry in canonical
 // representation. n is the size of the polynomial.
 func convertSortedCanonical(i, n int) int {
diff --git a/internal/generator/fri/template/fri.test.go.tmpl b/internal/generator/fri/template/fri.test.go.tmpl
index 0c6b357194..9c3bdeb8dc 100644
--- a/internal/generator/fri/template/fri.test.go.tmpl
+++ b/internal/generator/fri/template/fri.test.go.tmpl
@@ -32,7 +32,7 @@ func randomPolynomial(size uint64, seed int32) []fr.Element {
 	return p
 }
 
-// convertOrderCanonical convert the index i, an entry in a
+// convertSortedCanonical convert the index i, an entry in a
 // sorted polynomial, to the corresponding entry in canonical
 // representation. n is the size of the polynomial.
 func convertSortedCanonical(i, n int) int {

From b163543535816186004ff3785d5b837ebe07ae36 Mon Sep 17 00:00:00 2001
From: zhiqiangxu <652732310@qq.com>
Date: Wed, 4 Dec 2024 08:00:26 +0800
Subject: [PATCH 104/114] fix comment of v for `SetBigInt` (#541)

Co-authored-by: Ivo Kubjas <ivo.kubjas@consensys.net>
---
 ecc/bls12-377/fp/element.go                        | 2 +-
 ecc/bls12-377/fr/element.go                        | 2 +-
 ecc/bls12-381/fp/element.go                        | 2 +-
 ecc/bls12-381/fr/element.go                        | 2 +-
 ecc/bls24-315/fp/element.go                        | 2 +-
 ecc/bls24-315/fr/element.go                        | 2 +-
 ecc/bls24-317/fp/element.go                        | 2 +-
 ecc/bls24-317/fr/element.go                        | 2 +-
 ecc/bn254/fp/element.go                            | 2 +-
 ecc/bn254/fr/element.go                            | 2 +-
 ecc/bw6-633/fp/element.go                          | 2 +-
 ecc/bw6-633/fr/element.go                          | 2 +-
 ecc/bw6-761/fp/element.go                          | 2 +-
 ecc/bw6-761/fr/element.go                          | 2 +-
 ecc/secp256k1/fp/element.go                        | 2 +-
 ecc/secp256k1/fr/element.go                        | 2 +-
 ecc/stark-curve/fp/element.go                      | 2 +-
 ecc/stark-curve/fr/element.go                      | 2 +-
 field/babybear/element.go                          | 2 +-
 field/generator/internal/templates/element/conv.go | 2 +-
 field/goldilocks/element.go                        | 2 +-
 field/koalabear/element.go                         | 2 +-
 22 files changed, 22 insertions(+), 22 deletions(-)

diff --git a/ecc/bls12-377/fp/element.go b/ecc/bls12-377/fp/element.go
index 9358a37a88..9d985aecc3 100644
--- a/ecc/bls12-377/fp/element.go
+++ b/ecc/bls12-377/fp/element.go
@@ -1087,7 +1087,7 @@ func (z *Element) SetBigInt(v *big.Int) *Element {
 		// v == 0
 		return z
 	} else if c != 1 && v.Cmp(&zero) != -1 {
-		// 0 < v < q
+		// 0 <= v < q
 		return z.setBigInt(v)
 	}
 
diff --git a/ecc/bls12-377/fr/element.go b/ecc/bls12-377/fr/element.go
index 108ec017e7..890c54488a 100644
--- a/ecc/bls12-377/fr/element.go
+++ b/ecc/bls12-377/fr/element.go
@@ -928,7 +928,7 @@ func (z *Element) SetBigInt(v *big.Int) *Element {
 		// v == 0
 		return z
 	} else if c != 1 && v.Cmp(&zero) != -1 {
-		// 0 < v < q
+		// 0 <= v < q
 		return z.setBigInt(v)
 	}
 
diff --git a/ecc/bls12-381/fp/element.go b/ecc/bls12-381/fp/element.go
index 0daf55c732..d9e9bc8abd 100644
--- a/ecc/bls12-381/fp/element.go
+++ b/ecc/bls12-381/fp/element.go
@@ -1087,7 +1087,7 @@ func (z *Element) SetBigInt(v *big.Int) *Element {
 		// v == 0
 		return z
 	} else if c != 1 && v.Cmp(&zero) != -1 {
-		// 0 < v < q
+		// 0 <= v < q
 		return z.setBigInt(v)
 	}
 
diff --git a/ecc/bls12-381/fr/element.go b/ecc/bls12-381/fr/element.go
index da8a896aa8..cceff96d20 100644
--- a/ecc/bls12-381/fr/element.go
+++ b/ecc/bls12-381/fr/element.go
@@ -928,7 +928,7 @@ func (z *Element) SetBigInt(v *big.Int) *Element {
 		// v == 0
 		return z
 	} else if c != 1 && v.Cmp(&zero) != -1 {
-		// 0 < v < q
+		// 0 <= v < q
 		return z.setBigInt(v)
 	}
 
diff --git a/ecc/bls24-315/fp/element.go b/ecc/bls24-315/fp/element.go
index 6e044eb0a9..a6856c7eff 100644
--- a/ecc/bls24-315/fp/element.go
+++ b/ecc/bls24-315/fp/element.go
@@ -1003,7 +1003,7 @@ func (z *Element) SetBigInt(v *big.Int) *Element {
 		// v == 0
 		return z
 	} else if c != 1 && v.Cmp(&zero) != -1 {
-		// 0 < v < q
+		// 0 <= v < q
 		return z.setBigInt(v)
 	}
 
diff --git a/ecc/bls24-315/fr/element.go b/ecc/bls24-315/fr/element.go
index 26f9cdafd1..e00694d13c 100644
--- a/ecc/bls24-315/fr/element.go
+++ b/ecc/bls24-315/fr/element.go
@@ -928,7 +928,7 @@ func (z *Element) SetBigInt(v *big.Int) *Element {
 		// v == 0
 		return z
 	} else if c != 1 && v.Cmp(&zero) != -1 {
-		// 0 < v < q
+		// 0 <= v < q
 		return z.setBigInt(v)
 	}
 
diff --git a/ecc/bls24-317/fp/element.go b/ecc/bls24-317/fp/element.go
index 45b1fdb2a6..b84042c3bd 100644
--- a/ecc/bls24-317/fp/element.go
+++ b/ecc/bls24-317/fp/element.go
@@ -1003,7 +1003,7 @@ func (z *Element) SetBigInt(v *big.Int) *Element {
 		// v == 0
 		return z
 	} else if c != 1 && v.Cmp(&zero) != -1 {
-		// 0 < v < q
+		// 0 <= v < q
 		return z.setBigInt(v)
 	}
 
diff --git a/ecc/bls24-317/fr/element.go b/ecc/bls24-317/fr/element.go
index 129e9307ac..762012336c 100644
--- a/ecc/bls24-317/fr/element.go
+++ b/ecc/bls24-317/fr/element.go
@@ -928,7 +928,7 @@ func (z *Element) SetBigInt(v *big.Int) *Element {
 		// v == 0
 		return z
 	} else if c != 1 && v.Cmp(&zero) != -1 {
-		// 0 < v < q
+		// 0 <= v < q
 		return z.setBigInt(v)
 	}
 
diff --git a/ecc/bn254/fp/element.go b/ecc/bn254/fp/element.go
index 9b37dc541c..ed963e2d50 100644
--- a/ecc/bn254/fp/element.go
+++ b/ecc/bn254/fp/element.go
@@ -928,7 +928,7 @@ func (z *Element) SetBigInt(v *big.Int) *Element {
 		// v == 0
 		return z
 	} else if c != 1 && v.Cmp(&zero) != -1 {
-		// 0 < v < q
+		// 0 <= v < q
 		return z.setBigInt(v)
 	}
 
diff --git a/ecc/bn254/fr/element.go b/ecc/bn254/fr/element.go
index 8e59ea748f..b34c9b59ba 100644
--- a/ecc/bn254/fr/element.go
+++ b/ecc/bn254/fr/element.go
@@ -928,7 +928,7 @@ func (z *Element) SetBigInt(v *big.Int) *Element {
 		// v == 0
 		return z
 	} else if c != 1 && v.Cmp(&zero) != -1 {
-		// 0 < v < q
+		// 0 <= v < q
 		return z.setBigInt(v)
 	}
 
diff --git a/ecc/bw6-633/fp/element.go b/ecc/bw6-633/fp/element.go
index b976ed3eb0..f096126d09 100644
--- a/ecc/bw6-633/fp/element.go
+++ b/ecc/bw6-633/fp/element.go
@@ -1483,7 +1483,7 @@ func (z *Element) SetBigInt(v *big.Int) *Element {
 		// v == 0
 		return z
 	} else if c != 1 && v.Cmp(&zero) != -1 {
-		// 0 < v < q
+		// 0 <= v < q
 		return z.setBigInt(v)
 	}
 
diff --git a/ecc/bw6-633/fr/element.go b/ecc/bw6-633/fr/element.go
index 7e16486ca6..7dfdf5e88e 100644
--- a/ecc/bw6-633/fr/element.go
+++ b/ecc/bw6-633/fr/element.go
@@ -1003,7 +1003,7 @@ func (z *Element) SetBigInt(v *big.Int) *Element {
 		// v == 0
 		return z
 	} else if c != 1 && v.Cmp(&zero) != -1 {
-		// 0 < v < q
+		// 0 <= v < q
 		return z.setBigInt(v)
 	}
 
diff --git a/ecc/bw6-761/fp/element.go b/ecc/bw6-761/fp/element.go
index 82a4a111d7..4083df4699 100644
--- a/ecc/bw6-761/fp/element.go
+++ b/ecc/bw6-761/fp/element.go
@@ -1717,7 +1717,7 @@ func (z *Element) SetBigInt(v *big.Int) *Element {
 		// v == 0
 		return z
 	} else if c != 1 && v.Cmp(&zero) != -1 {
-		// 0 < v < q
+		// 0 <= v < q
 		return z.setBigInt(v)
 	}
 
diff --git a/ecc/bw6-761/fr/element.go b/ecc/bw6-761/fr/element.go
index 98de557872..4775e29561 100644
--- a/ecc/bw6-761/fr/element.go
+++ b/ecc/bw6-761/fr/element.go
@@ -1087,7 +1087,7 @@ func (z *Element) SetBigInt(v *big.Int) *Element {
 		// v == 0
 		return z
 	} else if c != 1 && v.Cmp(&zero) != -1 {
-		// 0 < v < q
+		// 0 <= v < q
 		return z.setBigInt(v)
 	}
 
diff --git a/ecc/secp256k1/fp/element.go b/ecc/secp256k1/fp/element.go
index e7bb41de63..1fe3541a37 100644
--- a/ecc/secp256k1/fp/element.go
+++ b/ecc/secp256k1/fp/element.go
@@ -956,7 +956,7 @@ func (z *Element) SetBigInt(v *big.Int) *Element {
 		// v == 0
 		return z
 	} else if c != 1 && v.Cmp(&zero) != -1 {
-		// 0 < v < q
+		// 0 <= v < q
 		return z.setBigInt(v)
 	}
 
diff --git a/ecc/secp256k1/fr/element.go b/ecc/secp256k1/fr/element.go
index 7041cca6cd..1bf4a7c491 100644
--- a/ecc/secp256k1/fr/element.go
+++ b/ecc/secp256k1/fr/element.go
@@ -956,7 +956,7 @@ func (z *Element) SetBigInt(v *big.Int) *Element {
 		// v == 0
 		return z
 	} else if c != 1 && v.Cmp(&zero) != -1 {
-		// 0 < v < q
+		// 0 <= v < q
 		return z.setBigInt(v)
 	}
 
diff --git a/ecc/stark-curve/fp/element.go b/ecc/stark-curve/fp/element.go
index a0f588bc39..2e0a60ca6f 100644
--- a/ecc/stark-curve/fp/element.go
+++ b/ecc/stark-curve/fp/element.go
@@ -928,7 +928,7 @@ func (z *Element) SetBigInt(v *big.Int) *Element {
 		// v == 0
 		return z
 	} else if c != 1 && v.Cmp(&zero) != -1 {
-		// 0 < v < q
+		// 0 <= v < q
 		return z.setBigInt(v)
 	}
 
diff --git a/ecc/stark-curve/fr/element.go b/ecc/stark-curve/fr/element.go
index 7fa697492a..4e9fec24b4 100644
--- a/ecc/stark-curve/fr/element.go
+++ b/ecc/stark-curve/fr/element.go
@@ -928,7 +928,7 @@ func (z *Element) SetBigInt(v *big.Int) *Element {
 		// v == 0
 		return z
 	} else if c != 1 && v.Cmp(&zero) != -1 {
-		// 0 < v < q
+		// 0 <= v < q
 		return z.setBigInt(v)
 	}
 
diff --git a/field/babybear/element.go b/field/babybear/element.go
index c0a64a1a10..7ec0950bab 100644
--- a/field/babybear/element.go
+++ b/field/babybear/element.go
@@ -651,7 +651,7 @@ func (z *Element) SetBigInt(v *big.Int) *Element {
 		// v == 0
 		return z
 	} else if c != 1 && v.Cmp(&zero) != -1 {
-		// 0 < v < q
+		// 0 <= v < q
 		return z.setBigInt(v)
 	}
 
diff --git a/field/generator/internal/templates/element/conv.go b/field/generator/internal/templates/element/conv.go
index 1587bdb7fb..70bffcf631 100644
--- a/field/generator/internal/templates/element/conv.go
+++ b/field/generator/internal/templates/element/conv.go
@@ -189,7 +189,7 @@ func (z *{{.ElementName}}) SetBigInt(v *big.Int) *{{.ElementName}} {
 		// v == 0
 		return z
 	} else if c != 1 && v.Cmp(&zero) != -1 {
-		// 0 < v < q
+		// 0 <= v < q
 		return z.setBigInt(v)
 	}
 
diff --git a/field/goldilocks/element.go b/field/goldilocks/element.go
index 5f5319330e..885ac83488 100644
--- a/field/goldilocks/element.go
+++ b/field/goldilocks/element.go
@@ -674,7 +674,7 @@ func (z *Element) SetBigInt(v *big.Int) *Element {
 		// v == 0
 		return z
 	} else if c != 1 && v.Cmp(&zero) != -1 {
-		// 0 < v < q
+		// 0 <= v < q
 		return z.setBigInt(v)
 	}
 
diff --git a/field/koalabear/element.go b/field/koalabear/element.go
index 42ed0ebe00..214d9f5ab1 100644
--- a/field/koalabear/element.go
+++ b/field/koalabear/element.go
@@ -651,7 +651,7 @@ func (z *Element) SetBigInt(v *big.Int) *Element {
 		// v == 0
 		return z
 	} else if c != 1 && v.Cmp(&zero) != -1 {
-		// 0 < v < q
+		// 0 <= v < q
 		return z.setBigInt(v)
 	}
 

From 3d67d6ffcf9b1948202ef38500a0475d34ac9b77 Mon Sep 17 00:00:00 2001
From: leopardracer <136604165+leopardracer@users.noreply.github.com>
Date: Wed, 4 Dec 2024 14:00:54 +0200
Subject: [PATCH 105/114] Update ecc.md (#563)

---
 ecc/ecc.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/ecc/ecc.md b/ecc/ecc.md
index a0048b7fd0..ef795dd006 100644
--- a/ecc/ecc.md
+++ b/ecc/ecc.md
@@ -11,6 +11,6 @@
 
 ### Twisted edwards curves
 
-Each of these curve has a `twistededwards` sub-package with its companion curve. In particular, BLS12-381 comapnion curve is known as [Jubjub](https://z.cash/technology/jubjub/) and BN254's [Baby-Jubjub](https://iden3-docs.readthedocs.io/en/latest/_downloads/33717d75ab84e11313cc0d8a090b636f/Baby-Jubjub.pdf).
+Each of these curve has a `twistededwards` sub-package with its companion curve. In particular, BLS12-381 companion curve is known as [Jubjub](https://z.cash/technology/jubjub/) and BN254's [Baby-Jubjub](https://iden3-docs.readthedocs.io/en/latest/_downloads/33717d75ab84e11313cc0d8a090b636f/Baby-Jubjub.pdf).
 
 They are of particular interest as they allow efficient elliptic curve cryptography inside zkSNARK circuits.

From 0ee0e30f04685579f551a46bad4a9e8021c9cbeb Mon Sep 17 00:00:00 2001
From: ZhengXingRu <zhengxingru@yeah.net>
Date: Wed, 11 Dec 2024 17:01:55 +0800
Subject: [PATCH 106/114] chore: fix some function names in comment (#569)

Signed-off-by: standstaff <zhengxingru@yeah.net>
---
 field/generator/internal/addchain/addchain.go | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/field/generator/internal/addchain/addchain.go b/field/generator/internal/addchain/addchain.go
index 7dd42b1837..8667ba30ac 100644
--- a/field/generator/internal/addchain/addchain.go
+++ b/field/generator/internal/addchain/addchain.go
@@ -158,7 +158,7 @@ type AddChainData struct {
 	N string // base 16 value of the value
 }
 
-// PrepareData builds input template data for the given addition chain script.
+// prepareAddChainData builds input template data for the given addition chain script.
 func prepareAddChainData(s *ast.Chain, n string) (*AddChainData, error) {
 	// Prepare template data.
 	allocator := pass.Allocator{

From e3f887d805de7842b25cb11defc9faa6b29fe41a Mon Sep 17 00:00:00 2001
From: Devkuni <155117116+detrina@users.noreply.github.com>
Date: Thu, 19 Dec 2024 14:24:11 +0100
Subject: [PATCH 107/114] Corrected spelling and grammar mistakes (#581)

Co-authored-by: Ivo Kubjas <ivo.kubjas@consensys.net>
---
 ecc/bls12-377/fr/mimc/doc.go                             | 2 +-
 ecc/bls12-381/fr/mimc/doc.go                             | 2 +-
 ecc/bls24-315/fr/mimc/doc.go                             | 2 +-
 ecc/bls24-317/fr/mimc/doc.go                             | 2 +-
 ecc/bn254/fr/mimc/doc.go                                 | 2 +-
 ecc/bw6-633/fr/mimc/doc.go                               | 2 +-
 ecc/bw6-761/fr/mimc/doc.go                               | 2 +-
 internal/generator/crypto/hash/mimc/template/doc.go.tmpl | 2 +-
 8 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/ecc/bls12-377/fr/mimc/doc.go b/ecc/bls12-377/fr/mimc/doc.go
index 98aa3f8d81..900b977185 100644
--- a/ecc/bls12-377/fr/mimc/doc.go
+++ b/ecc/bls12-377/fr/mimc/doc.go
@@ -44,6 +44,6 @@
 // The MiMC hash function is defined over a field. The input to the hash
 // function is a byte slice. The byte slice is interpreted as a sequence of
 // field elements. Due to this interpretation, the input byte slice length must
-// be multiple of the field modulus size. And every secuence of byte slice for a
+// be multiple of the field modulus size. And every sequence of byte slice for a
 // single field element must be strictly less than the field modulus.
 package mimc
diff --git a/ecc/bls12-381/fr/mimc/doc.go b/ecc/bls12-381/fr/mimc/doc.go
index 98aa3f8d81..900b977185 100644
--- a/ecc/bls12-381/fr/mimc/doc.go
+++ b/ecc/bls12-381/fr/mimc/doc.go
@@ -44,6 +44,6 @@
 // The MiMC hash function is defined over a field. The input to the hash
 // function is a byte slice. The byte slice is interpreted as a sequence of
 // field elements. Due to this interpretation, the input byte slice length must
-// be multiple of the field modulus size. And every secuence of byte slice for a
+// be multiple of the field modulus size. And every sequence of byte slice for a
 // single field element must be strictly less than the field modulus.
 package mimc
diff --git a/ecc/bls24-315/fr/mimc/doc.go b/ecc/bls24-315/fr/mimc/doc.go
index 98aa3f8d81..900b977185 100644
--- a/ecc/bls24-315/fr/mimc/doc.go
+++ b/ecc/bls24-315/fr/mimc/doc.go
@@ -44,6 +44,6 @@
 // The MiMC hash function is defined over a field. The input to the hash
 // function is a byte slice. The byte slice is interpreted as a sequence of
 // field elements. Due to this interpretation, the input byte slice length must
-// be multiple of the field modulus size. And every secuence of byte slice for a
+// be multiple of the field modulus size. And every sequence of byte slice for a
 // single field element must be strictly less than the field modulus.
 package mimc
diff --git a/ecc/bls24-317/fr/mimc/doc.go b/ecc/bls24-317/fr/mimc/doc.go
index 98aa3f8d81..900b977185 100644
--- a/ecc/bls24-317/fr/mimc/doc.go
+++ b/ecc/bls24-317/fr/mimc/doc.go
@@ -44,6 +44,6 @@
 // The MiMC hash function is defined over a field. The input to the hash
 // function is a byte slice. The byte slice is interpreted as a sequence of
 // field elements. Due to this interpretation, the input byte slice length must
-// be multiple of the field modulus size. And every secuence of byte slice for a
+// be multiple of the field modulus size. And every sequence of byte slice for a
 // single field element must be strictly less than the field modulus.
 package mimc
diff --git a/ecc/bn254/fr/mimc/doc.go b/ecc/bn254/fr/mimc/doc.go
index 98aa3f8d81..900b977185 100644
--- a/ecc/bn254/fr/mimc/doc.go
+++ b/ecc/bn254/fr/mimc/doc.go
@@ -44,6 +44,6 @@
 // The MiMC hash function is defined over a field. The input to the hash
 // function is a byte slice. The byte slice is interpreted as a sequence of
 // field elements. Due to this interpretation, the input byte slice length must
-// be multiple of the field modulus size. And every secuence of byte slice for a
+// be multiple of the field modulus size. And every sequence of byte slice for a
 // single field element must be strictly less than the field modulus.
 package mimc
diff --git a/ecc/bw6-633/fr/mimc/doc.go b/ecc/bw6-633/fr/mimc/doc.go
index 98aa3f8d81..900b977185 100644
--- a/ecc/bw6-633/fr/mimc/doc.go
+++ b/ecc/bw6-633/fr/mimc/doc.go
@@ -44,6 +44,6 @@
 // The MiMC hash function is defined over a field. The input to the hash
 // function is a byte slice. The byte slice is interpreted as a sequence of
 // field elements. Due to this interpretation, the input byte slice length must
-// be multiple of the field modulus size. And every secuence of byte slice for a
+// be multiple of the field modulus size. And every sequence of byte slice for a
 // single field element must be strictly less than the field modulus.
 package mimc
diff --git a/ecc/bw6-761/fr/mimc/doc.go b/ecc/bw6-761/fr/mimc/doc.go
index 98aa3f8d81..900b977185 100644
--- a/ecc/bw6-761/fr/mimc/doc.go
+++ b/ecc/bw6-761/fr/mimc/doc.go
@@ -44,6 +44,6 @@
 // The MiMC hash function is defined over a field. The input to the hash
 // function is a byte slice. The byte slice is interpreted as a sequence of
 // field elements. Due to this interpretation, the input byte slice length must
-// be multiple of the field modulus size. And every secuence of byte slice for a
+// be multiple of the field modulus size. And every sequence of byte slice for a
 // single field element must be strictly less than the field modulus.
 package mimc
diff --git a/internal/generator/crypto/hash/mimc/template/doc.go.tmpl b/internal/generator/crypto/hash/mimc/template/doc.go.tmpl
index 38175ffd94..df5f1c5d22 100644
--- a/internal/generator/crypto/hash/mimc/template/doc.go.tmpl
+++ b/internal/generator/crypto/hash/mimc/template/doc.go.tmpl
@@ -39,6 +39,6 @@
 // The MiMC hash function is defined over a field. The input to the hash
 // function is a byte slice. The byte slice is interpreted as a sequence of
 // field elements. Due to this interpretation, the input byte slice length must
-// be multiple of the field modulus size. And every secuence of byte slice for a
+// be multiple of the field modulus size. And every sequence of byte slice for a
 // single field element must be strictly less than the field modulus.
 package {{.Package}}
\ No newline at end of file

From 93038f748a36696e9e07fe74e2f0ea180521c535 Mon Sep 17 00:00:00 2001
From: Romashka <chernozub777@gmail.com>
Date: Thu, 19 Dec 2024 15:27:38 +0200
Subject: [PATCH 108/114] typo-Update fflonk.go (#584)

Co-authored-by: Ivo Kubjas <ivo.kubjas@consensys.net>
---
 ecc/bls12-377/fflonk/fflonk.go                    | 2 +-
 ecc/bls12-381/fflonk/fflonk.go                    | 2 +-
 ecc/bls24-315/fflonk/fflonk.go                    | 2 +-
 ecc/bls24-317/fflonk/fflonk.go                    | 2 +-
 ecc/bn254/fflonk/fflonk.go                        | 2 +-
 ecc/bw6-633/fflonk/fflonk.go                      | 2 +-
 ecc/bw6-761/fflonk/fflonk.go                      | 2 +-
 internal/generator/fflonk/template/fflonk.go.tmpl | 2 +-
 8 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/ecc/bls12-377/fflonk/fflonk.go b/ecc/bls12-377/fflonk/fflonk.go
index 03f84b69bf..f0a72f53a7 100644
--- a/ecc/bls12-377/fflonk/fflonk.go
+++ b/ecc/bls12-377/fflonk/fflonk.go
@@ -153,7 +153,7 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 	for i := 0; i < len(proof.ClaimedValues); i++ {
 		sizeSi := len(proof.ClaimedValues[i][0])
 		for j := 1; j < len(proof.ClaimedValues[i]); j++ {
-			// each set of opening must be of the same size (opeings on powers of Si)
+			// each set of opening must be of the same size (openings on powers of Si)
 			if sizeSi != len(proof.ClaimedValues[i][j]) {
 				return ErrNbPolynomialsNbPoints
 			}
diff --git a/ecc/bls12-381/fflonk/fflonk.go b/ecc/bls12-381/fflonk/fflonk.go
index ef9af5489b..5636150d29 100644
--- a/ecc/bls12-381/fflonk/fflonk.go
+++ b/ecc/bls12-381/fflonk/fflonk.go
@@ -153,7 +153,7 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 	for i := 0; i < len(proof.ClaimedValues); i++ {
 		sizeSi := len(proof.ClaimedValues[i][0])
 		for j := 1; j < len(proof.ClaimedValues[i]); j++ {
-			// each set of opening must be of the same size (opeings on powers of Si)
+			// each set of opening must be of the same size (openings on powers of Si)
 			if sizeSi != len(proof.ClaimedValues[i][j]) {
 				return ErrNbPolynomialsNbPoints
 			}
diff --git a/ecc/bls24-315/fflonk/fflonk.go b/ecc/bls24-315/fflonk/fflonk.go
index 460b5e4ffc..2bdde82014 100644
--- a/ecc/bls24-315/fflonk/fflonk.go
+++ b/ecc/bls24-315/fflonk/fflonk.go
@@ -153,7 +153,7 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 	for i := 0; i < len(proof.ClaimedValues); i++ {
 		sizeSi := len(proof.ClaimedValues[i][0])
 		for j := 1; j < len(proof.ClaimedValues[i]); j++ {
-			// each set of opening must be of the same size (opeings on powers of Si)
+			// each set of opening must be of the same size (openings on powers of Si)
 			if sizeSi != len(proof.ClaimedValues[i][j]) {
 				return ErrNbPolynomialsNbPoints
 			}
diff --git a/ecc/bls24-317/fflonk/fflonk.go b/ecc/bls24-317/fflonk/fflonk.go
index 461c379e11..ceafbcfd71 100644
--- a/ecc/bls24-317/fflonk/fflonk.go
+++ b/ecc/bls24-317/fflonk/fflonk.go
@@ -153,7 +153,7 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 	for i := 0; i < len(proof.ClaimedValues); i++ {
 		sizeSi := len(proof.ClaimedValues[i][0])
 		for j := 1; j < len(proof.ClaimedValues[i]); j++ {
-			// each set of opening must be of the same size (opeings on powers of Si)
+			// each set of opening must be of the same size (openings on powers of Si)
 			if sizeSi != len(proof.ClaimedValues[i][j]) {
 				return ErrNbPolynomialsNbPoints
 			}
diff --git a/ecc/bn254/fflonk/fflonk.go b/ecc/bn254/fflonk/fflonk.go
index 72f8efead6..2e0498b0f3 100644
--- a/ecc/bn254/fflonk/fflonk.go
+++ b/ecc/bn254/fflonk/fflonk.go
@@ -153,7 +153,7 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 	for i := 0; i < len(proof.ClaimedValues); i++ {
 		sizeSi := len(proof.ClaimedValues[i][0])
 		for j := 1; j < len(proof.ClaimedValues[i]); j++ {
-			// each set of opening must be of the same size (opeings on powers of Si)
+			// each set of opening must be of the same size (openings on powers of Si)
 			if sizeSi != len(proof.ClaimedValues[i][j]) {
 				return ErrNbPolynomialsNbPoints
 			}
diff --git a/ecc/bw6-633/fflonk/fflonk.go b/ecc/bw6-633/fflonk/fflonk.go
index dcc9c98c78..eee6f4e6df 100644
--- a/ecc/bw6-633/fflonk/fflonk.go
+++ b/ecc/bw6-633/fflonk/fflonk.go
@@ -153,7 +153,7 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 	for i := 0; i < len(proof.ClaimedValues); i++ {
 		sizeSi := len(proof.ClaimedValues[i][0])
 		for j := 1; j < len(proof.ClaimedValues[i]); j++ {
-			// each set of opening must be of the same size (opeings on powers of Si)
+			// each set of opening must be of the same size (openings on powers of Si)
 			if sizeSi != len(proof.ClaimedValues[i][j]) {
 				return ErrNbPolynomialsNbPoints
 			}
diff --git a/ecc/bw6-761/fflonk/fflonk.go b/ecc/bw6-761/fflonk/fflonk.go
index e833ce793a..1339da3844 100644
--- a/ecc/bw6-761/fflonk/fflonk.go
+++ b/ecc/bw6-761/fflonk/fflonk.go
@@ -153,7 +153,7 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 	for i := 0; i < len(proof.ClaimedValues); i++ {
 		sizeSi := len(proof.ClaimedValues[i][0])
 		for j := 1; j < len(proof.ClaimedValues[i]); j++ {
-			// each set of opening must be of the same size (opeings on powers of Si)
+			// each set of opening must be of the same size (openings on powers of Si)
 			if sizeSi != len(proof.ClaimedValues[i][j]) {
 				return ErrNbPolynomialsNbPoints
 			}
diff --git a/internal/generator/fflonk/template/fflonk.go.tmpl b/internal/generator/fflonk/template/fflonk.go.tmpl
index f3baa753f3..08eb3ea0d9 100644
--- a/internal/generator/fflonk/template/fflonk.go.tmpl
+++ b/internal/generator/fflonk/template/fflonk.go.tmpl
@@ -146,7 +146,7 @@ func BatchVerify(proof OpeningProof, digests []kzg.Digest, points [][]fr.Element
 	for i := 0; i < len(proof.ClaimedValues); i++ {
 		sizeSi := len(proof.ClaimedValues[i][0])
 		for j := 1; j < len(proof.ClaimedValues[i]); j++ {
-			// each set of opening must be of the same size (opeings on powers of Si)
+			// each set of opening must be of the same size (openings on powers of Si)
 			if sizeSi != len(proof.ClaimedValues[i][j]) {
 				return ErrNbPolynomialsNbPoints
 			}

From 7d2dc77020fc6ce645599fc123f5497b7ba6f815 Mon Sep 17 00:00:00 2001
From: leo <lc582041246@gmail.com>
Date: Thu, 19 Dec 2024 21:39:19 +0800
Subject: [PATCH 109/114] chore: use errors.New to replace fmt.Errorf with no
 parameters (#575)

Signed-off-by: RiceChuan <lc582041246@gmail.com>
Co-authored-by: Ivo Kubjas <ivo.kubjas@consensys.net>
---
 ecc/bls12-377/fr/gkr/gkr.go                              | 9 +++++----
 ecc/bls12-377/fr/sumcheck/sumcheck.go                    | 4 ++--
 ecc/bls12-381/fr/gkr/gkr.go                              | 9 +++++----
 ecc/bls12-381/fr/sumcheck/sumcheck.go                    | 4 ++--
 ecc/bls24-315/fr/gkr/gkr.go                              | 9 +++++----
 ecc/bls24-315/fr/sumcheck/sumcheck.go                    | 4 ++--
 ecc/bls24-317/fr/gkr/gkr.go                              | 9 +++++----
 ecc/bls24-317/fr/sumcheck/sumcheck.go                    | 4 ++--
 ecc/bn254/fr/gkr/gkr.go                                  | 9 +++++----
 ecc/bn254/fr/sumcheck/sumcheck.go                        | 4 ++--
 ecc/bw6-633/fr/gkr/gkr.go                                | 9 +++++----
 ecc/bw6-633/fr/sumcheck/sumcheck.go                      | 4 ++--
 ecc/bw6-761/fr/gkr/gkr.go                                | 9 +++++----
 ecc/bw6-761/fr/sumcheck/sumcheck.go                      | 4 ++--
 internal/generator/gkr/template/gkr.go.tmpl              | 9 +++++----
 internal/generator/sumcheck/template/sumcheck.go.tmpl    | 4 ++--
 .../test_vector_utils/small_rational/gkr/gkr.go          | 9 +++++----
 .../small_rational/sumcheck/sumcheck.go                  | 4 ++--
 18 files changed, 63 insertions(+), 54 deletions(-)

diff --git a/ecc/bls12-377/fr/gkr/gkr.go b/ecc/bls12-377/fr/gkr/gkr.go
index fb3629fc0a..c55db62a4e 100644
--- a/ecc/bls12-377/fr/gkr/gkr.go
+++ b/ecc/bls12-377/fr/gkr/gkr.go
@@ -6,6 +6,7 @@
 package gkr
 
 import (
+	"errors"
 	"fmt"
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr/polynomial"
@@ -136,7 +137,7 @@ func (e *eqTimesGateEvalSumcheckLazyClaims) VerifyFinalEval(r []fr.Element, comb
 	if evaluation.Equal(&purportedValue) {
 		return nil
 	}
-	return fmt.Errorf("incompatible evaluations")
+	return errors.New("incompatible evaluations")
 }
 
 type eqTimesGateEvalSumcheckClaims struct {
@@ -461,7 +462,7 @@ func setup(c Circuit, assignment WireAssignment, transcriptSettings fiatshamir.S
 	o.nbVars = assignment.NumVars()
 	nbInstances := assignment.NumInstances()
 	if 1<<o.nbVars != nbInstances {
-		return o, fmt.Errorf("number of instances must be power of 2")
+		return o, errors.New("number of instances must be power of 2")
 	}
 
 	if o.pool == nil {
@@ -661,14 +662,14 @@ func Verify(c Circuit, assignment WireAssignment, proof Proof, transcriptSetting
 		if wire.noProof() { // input wires with one claim only
 			// make sure the proof is empty
 			if len(finalEvalProof) != 0 || len(proofW.PartialSumPolys) != 0 {
-				return fmt.Errorf("no proof allowed for input wire with a single claim")
+				return errors.New("no proof allowed for input wire with a single claim")
 			}
 
 			if wire.NbClaims() == 1 { // input wire
 				// simply evaluate and see if it matches
 				evaluation := assignment[wire].Evaluate(claim.evaluationPoints[0], claims.memPool)
 				if !claim.claimedEvaluations[0].Equal(&evaluation) {
-					return fmt.Errorf("incorrect input wire claim")
+					return errors.New("incorrect input wire claim")
 				}
 			}
 		} else if err = sumcheck.Verify(
diff --git a/ecc/bls12-377/fr/sumcheck/sumcheck.go b/ecc/bls12-377/fr/sumcheck/sumcheck.go
index 71033d0dfe..f475849557 100644
--- a/ecc/bls12-377/fr/sumcheck/sumcheck.go
+++ b/ecc/bls12-377/fr/sumcheck/sumcheck.go
@@ -6,7 +6,7 @@
 package sumcheck
 
 import (
-	"fmt"
+	"errors"
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr/polynomial"
 	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
@@ -151,7 +151,7 @@ func Verify(claims LazyClaims, proof Proof, transcriptSettings fiatshamir.Settin
 
 	for j := 0; j < claims.VarsNum(); j++ {
 		if len(proof.PartialSumPolys[j]) != claims.Degree(j) {
-			return fmt.Errorf("malformed proof")
+			return errors.New("malformed proof")
 		}
 		copy(gJ[1:], proof.PartialSumPolys[j])
 		gJ[0].Sub(&gJR, &proof.PartialSumPolys[j][0]) // Requirement that gⱼ(0) + gⱼ(1) = gⱼ₋₁(r)
diff --git a/ecc/bls12-381/fr/gkr/gkr.go b/ecc/bls12-381/fr/gkr/gkr.go
index 64398b3e2a..bdae61d49f 100644
--- a/ecc/bls12-381/fr/gkr/gkr.go
+++ b/ecc/bls12-381/fr/gkr/gkr.go
@@ -6,6 +6,7 @@
 package gkr
 
 import (
+	"errors"
 	"fmt"
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr/polynomial"
@@ -136,7 +137,7 @@ func (e *eqTimesGateEvalSumcheckLazyClaims) VerifyFinalEval(r []fr.Element, comb
 	if evaluation.Equal(&purportedValue) {
 		return nil
 	}
-	return fmt.Errorf("incompatible evaluations")
+	return errors.New("incompatible evaluations")
 }
 
 type eqTimesGateEvalSumcheckClaims struct {
@@ -461,7 +462,7 @@ func setup(c Circuit, assignment WireAssignment, transcriptSettings fiatshamir.S
 	o.nbVars = assignment.NumVars()
 	nbInstances := assignment.NumInstances()
 	if 1<<o.nbVars != nbInstances {
-		return o, fmt.Errorf("number of instances must be power of 2")
+		return o, errors.New("number of instances must be power of 2")
 	}
 
 	if o.pool == nil {
@@ -661,14 +662,14 @@ func Verify(c Circuit, assignment WireAssignment, proof Proof, transcriptSetting
 		if wire.noProof() { // input wires with one claim only
 			// make sure the proof is empty
 			if len(finalEvalProof) != 0 || len(proofW.PartialSumPolys) != 0 {
-				return fmt.Errorf("no proof allowed for input wire with a single claim")
+				return errors.New("no proof allowed for input wire with a single claim")
 			}
 
 			if wire.NbClaims() == 1 { // input wire
 				// simply evaluate and see if it matches
 				evaluation := assignment[wire].Evaluate(claim.evaluationPoints[0], claims.memPool)
 				if !claim.claimedEvaluations[0].Equal(&evaluation) {
-					return fmt.Errorf("incorrect input wire claim")
+					return errors.New("incorrect input wire claim")
 				}
 			}
 		} else if err = sumcheck.Verify(
diff --git a/ecc/bls12-381/fr/sumcheck/sumcheck.go b/ecc/bls12-381/fr/sumcheck/sumcheck.go
index ee6e6d80d8..269f2fa8be 100644
--- a/ecc/bls12-381/fr/sumcheck/sumcheck.go
+++ b/ecc/bls12-381/fr/sumcheck/sumcheck.go
@@ -6,7 +6,7 @@
 package sumcheck
 
 import (
-	"fmt"
+	"errors"
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr/polynomial"
 	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
@@ -151,7 +151,7 @@ func Verify(claims LazyClaims, proof Proof, transcriptSettings fiatshamir.Settin
 
 	for j := 0; j < claims.VarsNum(); j++ {
 		if len(proof.PartialSumPolys[j]) != claims.Degree(j) {
-			return fmt.Errorf("malformed proof")
+			return errors.New("malformed proof")
 		}
 		copy(gJ[1:], proof.PartialSumPolys[j])
 		gJ[0].Sub(&gJR, &proof.PartialSumPolys[j][0]) // Requirement that gⱼ(0) + gⱼ(1) = gⱼ₋₁(r)
diff --git a/ecc/bls24-315/fr/gkr/gkr.go b/ecc/bls24-315/fr/gkr/gkr.go
index abeeb3c24a..c88da7da8a 100644
--- a/ecc/bls24-315/fr/gkr/gkr.go
+++ b/ecc/bls24-315/fr/gkr/gkr.go
@@ -6,6 +6,7 @@
 package gkr
 
 import (
+	"errors"
 	"fmt"
 	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr/polynomial"
@@ -136,7 +137,7 @@ func (e *eqTimesGateEvalSumcheckLazyClaims) VerifyFinalEval(r []fr.Element, comb
 	if evaluation.Equal(&purportedValue) {
 		return nil
 	}
-	return fmt.Errorf("incompatible evaluations")
+	return errors.New("incompatible evaluations")
 }
 
 type eqTimesGateEvalSumcheckClaims struct {
@@ -461,7 +462,7 @@ func setup(c Circuit, assignment WireAssignment, transcriptSettings fiatshamir.S
 	o.nbVars = assignment.NumVars()
 	nbInstances := assignment.NumInstances()
 	if 1<<o.nbVars != nbInstances {
-		return o, fmt.Errorf("number of instances must be power of 2")
+		return o, errors.New("number of instances must be power of 2")
 	}
 
 	if o.pool == nil {
@@ -661,14 +662,14 @@ func Verify(c Circuit, assignment WireAssignment, proof Proof, transcriptSetting
 		if wire.noProof() { // input wires with one claim only
 			// make sure the proof is empty
 			if len(finalEvalProof) != 0 || len(proofW.PartialSumPolys) != 0 {
-				return fmt.Errorf("no proof allowed for input wire with a single claim")
+				return errors.New("no proof allowed for input wire with a single claim")
 			}
 
 			if wire.NbClaims() == 1 { // input wire
 				// simply evaluate and see if it matches
 				evaluation := assignment[wire].Evaluate(claim.evaluationPoints[0], claims.memPool)
 				if !claim.claimedEvaluations[0].Equal(&evaluation) {
-					return fmt.Errorf("incorrect input wire claim")
+					return errors.New("incorrect input wire claim")
 				}
 			}
 		} else if err = sumcheck.Verify(
diff --git a/ecc/bls24-315/fr/sumcheck/sumcheck.go b/ecc/bls24-315/fr/sumcheck/sumcheck.go
index 6cf52ba6cb..63523203a0 100644
--- a/ecc/bls24-315/fr/sumcheck/sumcheck.go
+++ b/ecc/bls24-315/fr/sumcheck/sumcheck.go
@@ -6,7 +6,7 @@
 package sumcheck
 
 import (
-	"fmt"
+	"errors"
 	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr/polynomial"
 	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
@@ -151,7 +151,7 @@ func Verify(claims LazyClaims, proof Proof, transcriptSettings fiatshamir.Settin
 
 	for j := 0; j < claims.VarsNum(); j++ {
 		if len(proof.PartialSumPolys[j]) != claims.Degree(j) {
-			return fmt.Errorf("malformed proof")
+			return errors.New("malformed proof")
 		}
 		copy(gJ[1:], proof.PartialSumPolys[j])
 		gJ[0].Sub(&gJR, &proof.PartialSumPolys[j][0]) // Requirement that gⱼ(0) + gⱼ(1) = gⱼ₋₁(r)
diff --git a/ecc/bls24-317/fr/gkr/gkr.go b/ecc/bls24-317/fr/gkr/gkr.go
index f0e865f872..c0b0bd4726 100644
--- a/ecc/bls24-317/fr/gkr/gkr.go
+++ b/ecc/bls24-317/fr/gkr/gkr.go
@@ -6,6 +6,7 @@
 package gkr
 
 import (
+	"errors"
 	"fmt"
 	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr/polynomial"
@@ -136,7 +137,7 @@ func (e *eqTimesGateEvalSumcheckLazyClaims) VerifyFinalEval(r []fr.Element, comb
 	if evaluation.Equal(&purportedValue) {
 		return nil
 	}
-	return fmt.Errorf("incompatible evaluations")
+	return errors.New("incompatible evaluations")
 }
 
 type eqTimesGateEvalSumcheckClaims struct {
@@ -461,7 +462,7 @@ func setup(c Circuit, assignment WireAssignment, transcriptSettings fiatshamir.S
 	o.nbVars = assignment.NumVars()
 	nbInstances := assignment.NumInstances()
 	if 1<<o.nbVars != nbInstances {
-		return o, fmt.Errorf("number of instances must be power of 2")
+		return o, errors.New("number of instances must be power of 2")
 	}
 
 	if o.pool == nil {
@@ -661,14 +662,14 @@ func Verify(c Circuit, assignment WireAssignment, proof Proof, transcriptSetting
 		if wire.noProof() { // input wires with one claim only
 			// make sure the proof is empty
 			if len(finalEvalProof) != 0 || len(proofW.PartialSumPolys) != 0 {
-				return fmt.Errorf("no proof allowed for input wire with a single claim")
+				return errors.New("no proof allowed for input wire with a single claim")
 			}
 
 			if wire.NbClaims() == 1 { // input wire
 				// simply evaluate and see if it matches
 				evaluation := assignment[wire].Evaluate(claim.evaluationPoints[0], claims.memPool)
 				if !claim.claimedEvaluations[0].Equal(&evaluation) {
-					return fmt.Errorf("incorrect input wire claim")
+					return errors.New("incorrect input wire claim")
 				}
 			}
 		} else if err = sumcheck.Verify(
diff --git a/ecc/bls24-317/fr/sumcheck/sumcheck.go b/ecc/bls24-317/fr/sumcheck/sumcheck.go
index 0ba7de052b..d6c8c5fd16 100644
--- a/ecc/bls24-317/fr/sumcheck/sumcheck.go
+++ b/ecc/bls24-317/fr/sumcheck/sumcheck.go
@@ -6,7 +6,7 @@
 package sumcheck
 
 import (
-	"fmt"
+	"errors"
 	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr/polynomial"
 	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
@@ -151,7 +151,7 @@ func Verify(claims LazyClaims, proof Proof, transcriptSettings fiatshamir.Settin
 
 	for j := 0; j < claims.VarsNum(); j++ {
 		if len(proof.PartialSumPolys[j]) != claims.Degree(j) {
-			return fmt.Errorf("malformed proof")
+			return errors.New("malformed proof")
 		}
 		copy(gJ[1:], proof.PartialSumPolys[j])
 		gJ[0].Sub(&gJR, &proof.PartialSumPolys[j][0]) // Requirement that gⱼ(0) + gⱼ(1) = gⱼ₋₁(r)
diff --git a/ecc/bn254/fr/gkr/gkr.go b/ecc/bn254/fr/gkr/gkr.go
index e52de1fc30..696f2e095e 100644
--- a/ecc/bn254/fr/gkr/gkr.go
+++ b/ecc/bn254/fr/gkr/gkr.go
@@ -6,6 +6,7 @@
 package gkr
 
 import (
+	"errors"
 	"fmt"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr/polynomial"
@@ -136,7 +137,7 @@ func (e *eqTimesGateEvalSumcheckLazyClaims) VerifyFinalEval(r []fr.Element, comb
 	if evaluation.Equal(&purportedValue) {
 		return nil
 	}
-	return fmt.Errorf("incompatible evaluations")
+	return errors.New("incompatible evaluations")
 }
 
 type eqTimesGateEvalSumcheckClaims struct {
@@ -461,7 +462,7 @@ func setup(c Circuit, assignment WireAssignment, transcriptSettings fiatshamir.S
 	o.nbVars = assignment.NumVars()
 	nbInstances := assignment.NumInstances()
 	if 1<<o.nbVars != nbInstances {
-		return o, fmt.Errorf("number of instances must be power of 2")
+		return o, errors.New("number of instances must be power of 2")
 	}
 
 	if o.pool == nil {
@@ -661,14 +662,14 @@ func Verify(c Circuit, assignment WireAssignment, proof Proof, transcriptSetting
 		if wire.noProof() { // input wires with one claim only
 			// make sure the proof is empty
 			if len(finalEvalProof) != 0 || len(proofW.PartialSumPolys) != 0 {
-				return fmt.Errorf("no proof allowed for input wire with a single claim")
+				return errors.New("no proof allowed for input wire with a single claim")
 			}
 
 			if wire.NbClaims() == 1 { // input wire
 				// simply evaluate and see if it matches
 				evaluation := assignment[wire].Evaluate(claim.evaluationPoints[0], claims.memPool)
 				if !claim.claimedEvaluations[0].Equal(&evaluation) {
-					return fmt.Errorf("incorrect input wire claim")
+					return errors.New("incorrect input wire claim")
 				}
 			}
 		} else if err = sumcheck.Verify(
diff --git a/ecc/bn254/fr/sumcheck/sumcheck.go b/ecc/bn254/fr/sumcheck/sumcheck.go
index 633d7c01c3..a44078c499 100644
--- a/ecc/bn254/fr/sumcheck/sumcheck.go
+++ b/ecc/bn254/fr/sumcheck/sumcheck.go
@@ -6,7 +6,7 @@
 package sumcheck
 
 import (
-	"fmt"
+	"errors"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr/polynomial"
 	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
@@ -151,7 +151,7 @@ func Verify(claims LazyClaims, proof Proof, transcriptSettings fiatshamir.Settin
 
 	for j := 0; j < claims.VarsNum(); j++ {
 		if len(proof.PartialSumPolys[j]) != claims.Degree(j) {
-			return fmt.Errorf("malformed proof")
+			return errors.New("malformed proof")
 		}
 		copy(gJ[1:], proof.PartialSumPolys[j])
 		gJ[0].Sub(&gJR, &proof.PartialSumPolys[j][0]) // Requirement that gⱼ(0) + gⱼ(1) = gⱼ₋₁(r)
diff --git a/ecc/bw6-633/fr/gkr/gkr.go b/ecc/bw6-633/fr/gkr/gkr.go
index 2f2b91b5ef..7229501364 100644
--- a/ecc/bw6-633/fr/gkr/gkr.go
+++ b/ecc/bw6-633/fr/gkr/gkr.go
@@ -6,6 +6,7 @@
 package gkr
 
 import (
+	"errors"
 	"fmt"
 	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
 	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr/polynomial"
@@ -136,7 +137,7 @@ func (e *eqTimesGateEvalSumcheckLazyClaims) VerifyFinalEval(r []fr.Element, comb
 	if evaluation.Equal(&purportedValue) {
 		return nil
 	}
-	return fmt.Errorf("incompatible evaluations")
+	return errors.New("incompatible evaluations")
 }
 
 type eqTimesGateEvalSumcheckClaims struct {
@@ -461,7 +462,7 @@ func setup(c Circuit, assignment WireAssignment, transcriptSettings fiatshamir.S
 	o.nbVars = assignment.NumVars()
 	nbInstances := assignment.NumInstances()
 	if 1<<o.nbVars != nbInstances {
-		return o, fmt.Errorf("number of instances must be power of 2")
+		return o, errors.New("number of instances must be power of 2")
 	}
 
 	if o.pool == nil {
@@ -661,14 +662,14 @@ func Verify(c Circuit, assignment WireAssignment, proof Proof, transcriptSetting
 		if wire.noProof() { // input wires with one claim only
 			// make sure the proof is empty
 			if len(finalEvalProof) != 0 || len(proofW.PartialSumPolys) != 0 {
-				return fmt.Errorf("no proof allowed for input wire with a single claim")
+				return errors.New("no proof allowed for input wire with a single claim")
 			}
 
 			if wire.NbClaims() == 1 { // input wire
 				// simply evaluate and see if it matches
 				evaluation := assignment[wire].Evaluate(claim.evaluationPoints[0], claims.memPool)
 				if !claim.claimedEvaluations[0].Equal(&evaluation) {
-					return fmt.Errorf("incorrect input wire claim")
+					return errors.New("incorrect input wire claim")
 				}
 			}
 		} else if err = sumcheck.Verify(
diff --git a/ecc/bw6-633/fr/sumcheck/sumcheck.go b/ecc/bw6-633/fr/sumcheck/sumcheck.go
index 902757717f..4c063b2476 100644
--- a/ecc/bw6-633/fr/sumcheck/sumcheck.go
+++ b/ecc/bw6-633/fr/sumcheck/sumcheck.go
@@ -6,7 +6,7 @@
 package sumcheck
 
 import (
-	"fmt"
+	"errors"
 	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
 	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr/polynomial"
 	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
@@ -151,7 +151,7 @@ func Verify(claims LazyClaims, proof Proof, transcriptSettings fiatshamir.Settin
 
 	for j := 0; j < claims.VarsNum(); j++ {
 		if len(proof.PartialSumPolys[j]) != claims.Degree(j) {
-			return fmt.Errorf("malformed proof")
+			return errors.New("malformed proof")
 		}
 		copy(gJ[1:], proof.PartialSumPolys[j])
 		gJ[0].Sub(&gJR, &proof.PartialSumPolys[j][0]) // Requirement that gⱼ(0) + gⱼ(1) = gⱼ₋₁(r)
diff --git a/ecc/bw6-761/fr/gkr/gkr.go b/ecc/bw6-761/fr/gkr/gkr.go
index eddfb771d5..3c58a7ae97 100644
--- a/ecc/bw6-761/fr/gkr/gkr.go
+++ b/ecc/bw6-761/fr/gkr/gkr.go
@@ -6,6 +6,7 @@
 package gkr
 
 import (
+	"errors"
 	"fmt"
 	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
 	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr/polynomial"
@@ -136,7 +137,7 @@ func (e *eqTimesGateEvalSumcheckLazyClaims) VerifyFinalEval(r []fr.Element, comb
 	if evaluation.Equal(&purportedValue) {
 		return nil
 	}
-	return fmt.Errorf("incompatible evaluations")
+	return errors.New("incompatible evaluations")
 }
 
 type eqTimesGateEvalSumcheckClaims struct {
@@ -461,7 +462,7 @@ func setup(c Circuit, assignment WireAssignment, transcriptSettings fiatshamir.S
 	o.nbVars = assignment.NumVars()
 	nbInstances := assignment.NumInstances()
 	if 1<<o.nbVars != nbInstances {
-		return o, fmt.Errorf("number of instances must be power of 2")
+		return o, errors.New("number of instances must be power of 2")
 	}
 
 	if o.pool == nil {
@@ -661,14 +662,14 @@ func Verify(c Circuit, assignment WireAssignment, proof Proof, transcriptSetting
 		if wire.noProof() { // input wires with one claim only
 			// make sure the proof is empty
 			if len(finalEvalProof) != 0 || len(proofW.PartialSumPolys) != 0 {
-				return fmt.Errorf("no proof allowed for input wire with a single claim")
+				return errors.New("no proof allowed for input wire with a single claim")
 			}
 
 			if wire.NbClaims() == 1 { // input wire
 				// simply evaluate and see if it matches
 				evaluation := assignment[wire].Evaluate(claim.evaluationPoints[0], claims.memPool)
 				if !claim.claimedEvaluations[0].Equal(&evaluation) {
-					return fmt.Errorf("incorrect input wire claim")
+					return errors.New("incorrect input wire claim")
 				}
 			}
 		} else if err = sumcheck.Verify(
diff --git a/ecc/bw6-761/fr/sumcheck/sumcheck.go b/ecc/bw6-761/fr/sumcheck/sumcheck.go
index ad97e14250..511c685a4d 100644
--- a/ecc/bw6-761/fr/sumcheck/sumcheck.go
+++ b/ecc/bw6-761/fr/sumcheck/sumcheck.go
@@ -6,7 +6,7 @@
 package sumcheck
 
 import (
-	"fmt"
+	"errors"
 	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
 	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr/polynomial"
 	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
@@ -151,7 +151,7 @@ func Verify(claims LazyClaims, proof Proof, transcriptSettings fiatshamir.Settin
 
 	for j := 0; j < claims.VarsNum(); j++ {
 		if len(proof.PartialSumPolys[j]) != claims.Degree(j) {
-			return fmt.Errorf("malformed proof")
+			return errors.New("malformed proof")
 		}
 		copy(gJ[1:], proof.PartialSumPolys[j])
 		gJ[0].Sub(&gJR, &proof.PartialSumPolys[j][0]) // Requirement that gⱼ(0) + gⱼ(1) = gⱼ₋₁(r)
diff --git a/internal/generator/gkr/template/gkr.go.tmpl b/internal/generator/gkr/template/gkr.go.tmpl
index e346ae9320..76ddf3bb2d 100644
--- a/internal/generator/gkr/template/gkr.go.tmpl
+++ b/internal/generator/gkr/template/gkr.go.tmpl
@@ -1,4 +1,5 @@
 import (
+	"errors"
 	"fmt"
 	"{{.FieldPackagePath}}"
 	"{{.FieldPackagePath}}/polynomial"
@@ -131,7 +132,7 @@ func (e *eqTimesGateEvalSumcheckLazyClaims) VerifyFinalEval(r []{{.ElementType}}
 	if evaluation.Equal(&purportedValue) {
 		return nil
 	}
-	return fmt.Errorf("incompatible evaluations")
+	return errors.New("incompatible evaluations")
 }
 
 type eqTimesGateEvalSumcheckClaims struct {
@@ -457,7 +458,7 @@ func setup(c Circuit, assignment WireAssignment, transcriptSettings fiatshamir.S
 	o.nbVars = assignment.NumVars()
 	nbInstances := assignment.NumInstances()
 	if 1<<o.nbVars != nbInstances {
-		return o, fmt.Errorf("number of instances must be power of 2")
+		return o, errors.New("number of instances must be power of 2")
 	}
 
 	if o.pool == nil {
@@ -657,14 +658,14 @@ func Verify(c Circuit, assignment WireAssignment, proof Proof, transcriptSetting
 		if wire.noProof() { // input wires with one claim only
 			// make sure the proof is empty
 			if len(finalEvalProof) != 0 || len(proofW.PartialSumPolys) != 0 {
-				return fmt.Errorf("no proof allowed for input wire with a single claim")
+				return errors.New("no proof allowed for input wire with a single claim")
 			}
 
 			if wire.NbClaims() == 1 { // input wire
 				// simply evaluate and see if it matches
 				evaluation := assignment[wire].Evaluate(claim.evaluationPoints[0], claims.memPool)
 				if !claim.claimedEvaluations[0].Equal(&evaluation) {
-					return fmt.Errorf("incorrect input wire claim")
+					return errors.New("incorrect input wire claim")
 				}
 			}
 		} else if err = sumcheck.Verify(
diff --git a/internal/generator/sumcheck/template/sumcheck.go.tmpl b/internal/generator/sumcheck/template/sumcheck.go.tmpl
index a4e17da827..2ca7ec4975 100644
--- a/internal/generator/sumcheck/template/sumcheck.go.tmpl
+++ b/internal/generator/sumcheck/template/sumcheck.go.tmpl
@@ -1,5 +1,5 @@
 import (
-	"fmt"
+	"errors"
 	"{{.FieldPackagePath}}"
 	"{{.FieldPackagePath}}/polynomial"
 	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
@@ -144,7 +144,7 @@ func Verify(claims LazyClaims, proof Proof, transcriptSettings fiatshamir.Settin
 
 	for j := 0; j < claims.VarsNum(); j++ {
 		if len(proof.PartialSumPolys[j]) != claims.Degree(j) {
-			return fmt.Errorf("malformed proof")
+			return errors.New("malformed proof")
 		}
 		copy(gJ[1:], proof.PartialSumPolys[j])
 		gJ[0].Sub(&gJR, &proof.PartialSumPolys[j][0]) // Requirement that gⱼ(0) + gⱼ(1) = gⱼ₋₁(r)
diff --git a/internal/generator/test_vector_utils/small_rational/gkr/gkr.go b/internal/generator/test_vector_utils/small_rational/gkr/gkr.go
index 52e301df67..73bb280a5a 100644
--- a/internal/generator/test_vector_utils/small_rational/gkr/gkr.go
+++ b/internal/generator/test_vector_utils/small_rational/gkr/gkr.go
@@ -6,6 +6,7 @@
 package gkr
 
 import (
+	"errors"
 	"fmt"
 	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
 	"github.com/consensys/gnark-crypto/internal/generator/test_vector_utils/small_rational"
@@ -136,7 +137,7 @@ func (e *eqTimesGateEvalSumcheckLazyClaims) VerifyFinalEval(r []small_rational.S
 	if evaluation.Equal(&purportedValue) {
 		return nil
 	}
-	return fmt.Errorf("incompatible evaluations")
+	return errors.New("incompatible evaluations")
 }
 
 type eqTimesGateEvalSumcheckClaims struct {
@@ -461,7 +462,7 @@ func setup(c Circuit, assignment WireAssignment, transcriptSettings fiatshamir.S
 	o.nbVars = assignment.NumVars()
 	nbInstances := assignment.NumInstances()
 	if 1<<o.nbVars != nbInstances {
-		return o, fmt.Errorf("number of instances must be power of 2")
+		return o, errors.New("number of instances must be power of 2")
 	}
 
 	if o.pool == nil {
@@ -661,14 +662,14 @@ func Verify(c Circuit, assignment WireAssignment, proof Proof, transcriptSetting
 		if wire.noProof() { // input wires with one claim only
 			// make sure the proof is empty
 			if len(finalEvalProof) != 0 || len(proofW.PartialSumPolys) != 0 {
-				return fmt.Errorf("no proof allowed for input wire with a single claim")
+				return errors.New("no proof allowed for input wire with a single claim")
 			}
 
 			if wire.NbClaims() == 1 { // input wire
 				// simply evaluate and see if it matches
 				evaluation := assignment[wire].Evaluate(claim.evaluationPoints[0], claims.memPool)
 				if !claim.claimedEvaluations[0].Equal(&evaluation) {
-					return fmt.Errorf("incorrect input wire claim")
+					return errors.New("incorrect input wire claim")
 				}
 			}
 		} else if err = sumcheck.Verify(
diff --git a/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck.go b/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck.go
index d5cd387d85..e711cbcf2c 100644
--- a/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck.go
+++ b/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck.go
@@ -6,7 +6,7 @@
 package sumcheck
 
 import (
-	"fmt"
+	"errors"
 	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
 	"github.com/consensys/gnark-crypto/internal/generator/test_vector_utils/small_rational"
 	"github.com/consensys/gnark-crypto/internal/generator/test_vector_utils/small_rational/polynomial"
@@ -151,7 +151,7 @@ func Verify(claims LazyClaims, proof Proof, transcriptSettings fiatshamir.Settin
 
 	for j := 0; j < claims.VarsNum(); j++ {
 		if len(proof.PartialSumPolys[j]) != claims.Degree(j) {
-			return fmt.Errorf("malformed proof")
+			return errors.New("malformed proof")
 		}
 		copy(gJ[1:], proof.PartialSumPolys[j])
 		gJ[0].Sub(&gJR, &proof.PartialSumPolys[j][0]) // Requirement that gⱼ(0) + gⱼ(1) = gⱼ₋₁(r)

From fd88e8b05c4ad4464bd87d8e963fb1f90dc3a514 Mon Sep 17 00:00:00 2001
From: Ocenka <testoviydiman1@gmail.com>
Date: Wed, 25 Dec 2024 23:27:30 +0000
Subject: [PATCH 110/114] Update broken links (#590)

---
 ecc/bw6-633/pairing.go                              | 2 +-
 ecc/stark-curve/pedersen-hash/pedersen_hash_test.go | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/ecc/bw6-633/pairing.go b/ecc/bw6-633/pairing.go
index a898b72528..130aec2b80 100644
--- a/ecc/bw6-633/pairing.go
+++ b/ecc/bw6-633/pairing.go
@@ -120,7 +120,7 @@ func FinalExponentiation(z *GT, _z ...*GT) GT {
 
 // MillerLoop computes the multi-Miller loop
 // computes the multi-Miller loop ∏ᵢ MillerLoop(Pᵢ, Qᵢ)
-// Alg.2 in https://eprint.iacr.org/2021/1359.qdf
+// Alg.2 in https://eprint.iacr.org/2021/1359.pdf
 func MillerLoop(P []G1Affine, Q []G2Affine) (GT, error) {
 	// check input size match
 	n := len(P)
diff --git a/ecc/stark-curve/pedersen-hash/pedersen_hash_test.go b/ecc/stark-curve/pedersen-hash/pedersen_hash_test.go
index fbd562c13f..76fed337b5 100644
--- a/ecc/stark-curve/pedersen-hash/pedersen_hash_test.go
+++ b/ecc/stark-curve/pedersen-hash/pedersen_hash_test.go
@@ -55,7 +55,7 @@ func TestPedersenArray(t *testing.T) {
 		// Contract address calculation. See the following links for how the
 		// calculation is carried out and the result referenced.
 		//
-		// https://docs.starknet.io/documentation/develop/Contracts/contract-address/
+		// https://docs.starknet.io/docs/Contracts/contract-address
 		// https://alpha4.starknet.io/feeder_gateway/get_transaction?transactionHash=0x1b50380d45ebd70876518203f131a12428b2ac1a3a75f1a74241a4abdd614e8
 		{
 			input: []string{

From 5f396f2f4ebae1fbe8ffb6f0e00ff4002f4d0cc6 Mon Sep 17 00:00:00 2001
From: Gautam Botrel <gautam.botrel@gmail.com>
Date: Mon, 6 Jan 2025 16:09:11 -0600
Subject: [PATCH 111/114] perf: adds (some) arm NEON assembly for koalabear and
 babybear (#588)

---
 field/asm/element_31b_arm64.s                 |  90 ++++++++
 field/babybear/doc.go                         |   2 +-
 field/babybear/element_arm64.s                |  10 +
 field/babybear/vector_amd64.go                |   6 +-
 field/babybear/vector_arm64.go                | 104 ++++++++++
 field/babybear/vector_purego.go               |   2 +-
 field/generator/asm/amd64/build.go            |   2 -
 field/generator/asm/arm64/build.go            |  20 ++
 field/generator/asm/arm64/element_vec_F31.go  | 196 ++++++++++++++++++
 field/generator/config/field_config.go        |   4 +-
 field/generator/generator_field.go            |  17 +-
 .../templates/element/vector_ops_asm.go       | 105 +++++++++-
 field/koalabear/doc.go                        |   2 +-
 field/koalabear/element_arm64.s               |  10 +
 field/koalabear/vector_amd64.go               |   6 +-
 field/koalabear/vector_arm64.go               | 104 ++++++++++
 field/koalabear/vector_purego.go              |   2 +-
 go.mod                                        |   2 +-
 go.sum                                        |   4 +-
 19 files changed, 656 insertions(+), 32 deletions(-)
 create mode 100644 field/asm/element_31b_arm64.s
 create mode 100644 field/babybear/element_arm64.s
 create mode 100644 field/babybear/vector_arm64.go
 create mode 100644 field/generator/asm/arm64/element_vec_F31.go
 create mode 100644 field/koalabear/element_arm64.s
 create mode 100644 field/koalabear/vector_arm64.go

diff --git a/field/asm/element_31b_arm64.s b/field/asm/element_31b_arm64.s
new file mode 100644
index 0000000000..6581ba0409
--- /dev/null
+++ b/field/asm/element_31b_arm64.s
@@ -0,0 +1,90 @@
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+#include "textflag.h"
+#include "funcdata.h"
+#include "go_asm.h"
+
+// addVec(res, a, b *Element, n uint64)
+// n is the number of blocks of 4 uint32 to process
+TEXT ·addVec(SB), NOFRAME|NOSPLIT, $0-32
+	LDP   res+0(FP), (R0, R1)
+	LDP   b+16(FP), (R2, R3)
+	VMOVS $const_q, V3
+	VDUP  V3.S[0], V3.S4      // broadcast q into V3
+
+loop1:
+	CBZ    R3, done2
+	VLD1.P 16(R1), [V0.S4]
+	VLD1.P 16(R2), [V1.S4]
+	VADD   V0.S4, V1.S4, V1.S4 // b = a + b
+	VSUB   V3.S4, V1.S4, V2.S4 // t = b - q
+	VUMIN  V2.S4, V1.S4, V1.S4 // b = min(t, b)
+	VST1.P [V1.S4], 16(R0)     // res = b
+	SUB    $1, R3, R3
+	JMP    loop1
+
+done2:
+	RET
+
+// subVec(res, a, b *Element, n uint64)
+// n is the number of blocks of 4 uint32 to process
+TEXT ·subVec(SB), NOFRAME|NOSPLIT, $0-32
+	LDP   res+0(FP), (R0, R1)
+	LDP   b+16(FP), (R2, R3)
+	VMOVS $const_q, V3
+	VDUP  V3.S[0], V3.S4      // broadcast q into V3
+
+loop3:
+	CBZ    R3, done4
+	VLD1.P 16(R1), [V0.S4]
+	VLD1.P 16(R2), [V1.S4]
+	VSUB   V1.S4, V0.S4, V1.S4 // b = a - b
+	VADD   V1.S4, V3.S4, V2.S4 // t = b + q
+	VUMIN  V2.S4, V1.S4, V1.S4 // b = min(t, b)
+	VST1.P [V1.S4], 16(R0)     // res = b
+	SUB    $1, R3, R3
+	JMP    loop3
+
+done4:
+	RET
+
+// sumVec(t *uint64, a *[]uint32, n uint64) res = sum(a[0...n])
+// n is the number of blocks of 16 uint32 to process
+TEXT ·sumVec(SB), NOFRAME|NOSPLIT, $0-24
+	// zeroing accumulators
+	VMOVQ $0, $0, V4
+	VMOVQ $0, $0, V5
+	VMOVQ $0, $0, V6
+	VMOVQ $0, $0, V7
+	LDP   t+0(FP), (R1, R0)
+	MOVD  n+16(FP), R2
+
+loop5:
+	CBZ R2, done6
+
+	// blockSize is 16 uint32; we load 4 vectors of 4 uint32 at a time
+	// (4*4)*4 = 64 bytes ~= 1 cache line
+	// since our values are 31 bits, we can add 2 by 2 these vectors
+	// we are left with 2 vectors of 4x32 bits values
+	// that we accumulate in 4*2*64bits accumulators
+	// the caller will reduce mod q the accumulators.
+
+	VLD2.P  32(R0), [V0.S4, V1.S4]
+	VADD    V0.S4, V1.S4, V0.S4    // a1 += a2
+	VLD2.P  32(R0), [V2.S4, V3.S4]
+	VADD    V2.S4, V3.S4, V2.S4    // a3 += a4
+	VUSHLL  $0, V0.S2, V1.D2       // convert low words to 64 bits
+	VADD    V1.D2, V5.D2, V5.D2    // acc2 += a2
+	VUSHLL2 $0, V0.S4, V0.D2       // convert high words to 64 bits
+	VADD    V0.D2, V4.D2, V4.D2    // acc1 += a1
+	VUSHLL  $0, V2.S2, V3.D2       // convert low words to 64 bits
+	VADD    V3.D2, V7.D2, V7.D2    // acc4 += a4
+	VUSHLL2 $0, V2.S4, V2.D2       // convert high words to 64 bits
+	VADD    V2.D2, V6.D2, V6.D2    // acc3 += a3
+	SUB     $1, R2, R2
+	JMP     loop5
+
+done6:
+	VADD   V4.D2, V6.D2, V4.D2   // acc1 += acc3
+	VADD   V5.D2, V7.D2, V5.D2   // acc2 += acc4
+	VST2.P [V4.D2, V5.D2], 0(R1) // store acc1 and acc2
+	RET
diff --git a/field/babybear/doc.go b/field/babybear/doc.go
index e134942b43..fc116bd84f 100644
--- a/field/babybear/doc.go
+++ b/field/babybear/doc.go
@@ -7,7 +7,7 @@
 //
 // The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
 //
-// Additionally babybear.Vector offers an API to manipulate []Element using AVX512 instructions if available.
+// Additionally babybear.Vector offers an API to manipulate []Element using AVX512/NEON instructions if available.
 //
 // The modulus is hardcoded in all the operations.
 //
diff --git a/field/babybear/element_arm64.s b/field/babybear/element_arm64.s
new file mode 100644
index 0000000000..f3ddfa315e
--- /dev/null
+++ b/field/babybear/element_arm64.s
@@ -0,0 +1,10 @@
+//go:build  !purego
+
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 8620676634583589757
+#include "../asm/element_31b_arm64.s"
+
diff --git a/field/babybear/vector_amd64.go b/field/babybear/vector_amd64.go
index 2ace506476..742b60ce2e 100644
--- a/field/babybear/vector_amd64.go
+++ b/field/babybear/vector_amd64.go
@@ -118,8 +118,7 @@ func (vector *Vector) Sum() (res Element) {
 	// we reduce the accumulators mod q and add to res
 	var v Element
 	for i := 0; i < 8; i++ {
-		t[i] %= q
-		v[0] = uint32(t[i])
+		v[0] = uint32(t[i] % q)
 		res.Add(&res, &v)
 	}
 	if n%blockSize != 0 {
@@ -153,8 +152,7 @@ func (vector *Vector) InnerProduct(other Vector) (res Element) {
 	// we reduce the accumulators mod q and add to res
 	var v Element
 	for i := 0; i < 8; i++ {
-		t[i] %= q
-		v[0] = uint32(t[i])
+		v[0] = uint32(t[i] % q)
 		res.Add(&res, &v)
 	}
 	if n%blockSize != 0 {
diff --git a/field/babybear/vector_arm64.go b/field/babybear/vector_arm64.go
new file mode 100644
index 0000000000..3ab1b562ff
--- /dev/null
+++ b/field/babybear/vector_arm64.go
@@ -0,0 +1,104 @@
+//go:build !purego
+
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package babybear
+
+//go:noescape
+func addVec(res, a, b *Element, n uint64)
+
+//go:noescape
+func subVec(res, a, b *Element, n uint64)
+
+//go:noescape
+func sumVec(t *uint64, a *Element, n uint64)
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Add: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+
+	const blockSize = 4
+	addVec(&(*vector)[0], &a[0], &b[0], n/blockSize)
+	if n%blockSize != 0 {
+		// call addVecGeneric on the rest
+		start := n - n%blockSize
+		addVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Sub: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+
+	const blockSize = 4
+	subVec(&(*vector)[0], &a[0], &b[0], n/blockSize)
+	if n%blockSize != 0 {
+		// call subVecGeneric on the rest
+		start := n - n%blockSize
+		subVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+
+	const blockSize = 16
+	var t [4]uint64 // stores the accumulators (not reduced mod q)
+	sumVec(&t[0], &(*vector)[0], n/blockSize)
+	// we reduce the accumulators mod q and add to res
+	var v Element
+	for i := 0; i < 4; i++ {
+		v[0] = uint32(t[i] % q)
+		res.Add(&res, &v)
+	}
+	if n%blockSize != 0 {
+		// call sumVecGeneric on the rest
+		start := n - n%blockSize
+		sumVecGeneric(&res, (*vector)[start:])
+	}
+
+	return
+}
+
+// note: unfortunately, as of Dec. 2024, Golang doesn't support enough NEON instructions
+// for these to be worth it in assembly. Will hopefully revisit in future versions.
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
diff --git a/field/babybear/vector_purego.go b/field/babybear/vector_purego.go
index 3d9177a0ef..8164830b26 100644
--- a/field/babybear/vector_purego.go
+++ b/field/babybear/vector_purego.go
@@ -1,4 +1,4 @@
-//go:build purego || !amd64
+//go:build purego || (!amd64 && !arm64)
 
 // Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
diff --git a/field/generator/asm/amd64/build.go b/field/generator/asm/amd64/build.go
index 3cce93670d..a5407b9d14 100644
--- a/field/generator/asm/amd64/build.go
+++ b/field/generator/asm/amd64/build.go
@@ -221,10 +221,8 @@ func GenerateCommonASM(w io.Writer, nbWords, nbBits int, hasVector bool) error {
 		if nbBits == 31 {
 			return GenerateF31ASM(f, hasVector)
 		} else {
-			fmt.Printf("nbWords: %d, nbBits: %d\n", nbWords, nbBits)
 			panic("not implemented")
 		}
-
 	}
 
 	f.GenerateReduceDefine()
diff --git a/field/generator/asm/arm64/build.go b/field/generator/asm/arm64/build.go
index c0d617410a..5b8d1893a0 100644
--- a/field/generator/asm/arm64/build.go
+++ b/field/generator/asm/arm64/build.go
@@ -55,6 +55,14 @@ func GenerateCommonASM(w io.Writer, nbWords, nbBits int, hasVector bool) error {
 	f.WriteLn("#include \"go_asm.h\"")
 	f.WriteLn("")
 
+	if nbWords == 1 {
+		if nbBits == 31 {
+			return GenerateF31ASM(f, hasVector)
+		} else {
+			panic("not implemented")
+		}
+	}
+
 	if f.NbWords%2 != 0 {
 		panic("NbWords must be even")
 	}
@@ -216,3 +224,15 @@ func ElementASMFileName(nbWords, nbBits int) string {
 	}
 	return fmt.Sprintf(nameWN, nbWords)
 }
+
+func GenerateF31ASM(f *FFArm64, hasVector bool) error {
+	if !hasVector {
+		return nil // nothing for now.
+	}
+
+	f.generateAddVecF31()
+	f.generateSubVecF31()
+	f.generateSumVecF31()
+
+	return nil
+}
diff --git a/field/generator/asm/arm64/element_vec_F31.go b/field/generator/asm/arm64/element_vec_F31.go
new file mode 100644
index 0000000000..6e6a818c53
--- /dev/null
+++ b/field/generator/asm/arm64/element_vec_F31.go
@@ -0,0 +1,196 @@
+package arm64
+
+import "github.com/consensys/bavard/arm64"
+
+func (f *FFArm64) generateAddVecF31() {
+	f.Comment("addVec(res, a, b *Element, n uint64)")
+	f.Comment("n is the number of blocks of 4 uint32 to process")
+	registers := f.FnHeader("addVec", 0, 32)
+	defer f.AssertCleanStack(0, 0)
+
+	// registers
+	resPtr := registers.Pop()
+	aPtr := registers.Pop()
+	bPtr := registers.Pop()
+	n := registers.Pop()
+
+	// labels
+	loop := f.NewLabel("loop")
+	done := f.NewLabel("done")
+
+	// load arguments
+	f.LDP("res+0(FP)", resPtr, aPtr)
+	f.LDP("b+16(FP)", bPtr, n)
+
+	a := registers.PopV()
+	b := registers.PopV()
+	t := registers.PopV()
+	q := registers.PopV()
+
+	f.VMOVS("$const_q", q)
+	f.VDUP(q.SAt(0), q.S4(), "broadcast q into "+string(q))
+
+	f.LABEL(loop)
+
+	f.CBZ(n, done)
+
+	const offset = 4 * 4 // we process 4 uint32 at a time
+
+	f.VLD1_P(offset, aPtr, a.S4())
+	f.VLD1_P(offset, bPtr, b.S4())
+
+	f.VADD(a.S4(), b.S4(), b.S4(), "b = a + b")
+	f.VSUB(q.S4(), b.S4(), t.S4(), "t = b - q")
+	f.VUMIN(t.S4(), b.S4(), b.S4(), "b = min(t, b)")
+	f.VST1_P(b.S4(), resPtr, offset, "res = b")
+
+	// decrement n
+	f.SUB(1, n, n)
+	f.JMP(loop)
+
+	f.LABEL(done)
+
+	registers.Push(resPtr, aPtr, bPtr, n)
+	registers.PushV(a, b, t, q)
+
+	f.RET()
+
+}
+
+func (f *FFArm64) generateSubVecF31() {
+	f.Comment("subVec(res, a, b *Element, n uint64)")
+	f.Comment("n is the number of blocks of 4 uint32 to process")
+	registers := f.FnHeader("subVec", 0, 32)
+	defer f.AssertCleanStack(0, 0)
+
+	// registers
+	resPtr := registers.Pop()
+	aPtr := registers.Pop()
+	bPtr := registers.Pop()
+	n := registers.Pop()
+
+	// labels
+	loop := f.NewLabel("loop")
+	done := f.NewLabel("done")
+
+	// load arguments
+	f.LDP("res+0(FP)", resPtr, aPtr)
+	f.LDP("b+16(FP)", bPtr, n)
+
+	a := registers.PopV()
+	b := registers.PopV()
+	t := registers.PopV()
+	q := registers.PopV()
+
+	f.VMOVS("$const_q", q)
+	f.VDUP(q.SAt(0), q.S4(), "broadcast q into "+string(q))
+
+	f.LABEL(loop)
+
+	f.CBZ(n, done)
+
+	const offset = 4 * 4 // we process 4 uint32 at a time
+
+	f.VLD1_P(offset, aPtr, a.S4())
+	f.VLD1_P(offset, bPtr, b.S4())
+
+	f.VSUB(b.S4(), a.S4(), b.S4(), "b = a - b")
+	f.VADD(b.S4(), q.S4(), t.S4(), "t = b + q")
+	f.VUMIN(t.S4(), b.S4(), b.S4(), "b = min(t, b)")
+	f.VST1_P(b.S4(), resPtr, offset, "res = b")
+
+	// decrement n
+	f.SUB(1, n, n)
+	f.JMP(loop)
+
+	f.LABEL(done)
+
+	registers.Push(resPtr, aPtr, bPtr, n)
+	registers.PushV(a, b, q, t)
+
+	f.RET()
+
+}
+
+func (f *FFArm64) generateSumVecF31() {
+	f.Comment("sumVec(t *uint64, a *[]uint32, n uint64) res = sum(a[0...n])")
+	f.Comment("n is the number of blocks of 16 uint32 to process")
+	registers := f.FnHeader("sumVec", 0, 3*8)
+	defer f.AssertCleanStack(0, 0)
+
+	// registers
+	aPtr := registers.Pop()
+	tPtr := registers.Pop()
+	n := registers.Pop()
+
+	a1 := registers.PopV()
+	a2 := registers.PopV()
+	a3 := registers.PopV()
+	a4 := registers.PopV()
+	acc1 := registers.PopV()
+	acc2 := registers.PopV()
+	acc3 := registers.PopV()
+	acc4 := registers.PopV()
+
+	f.Comment("zeroing accumulators")
+	f.VMOVQ_cst(0, 0, acc1)
+	f.VMOVQ_cst(0, 0, acc2)
+	f.VMOVQ_cst(0, 0, acc3)
+	f.VMOVQ_cst(0, 0, acc4)
+
+	acc1 = arm64.V4.D2()
+	acc2 = arm64.V5.D2()
+	acc3 = arm64.V6.D2()
+	acc4 = arm64.V7.D2()
+
+	// labels
+	loop := f.NewLabel("loop")
+	done := f.NewLabel("done")
+
+	// load arguments
+	f.LDP("t+0(FP)", tPtr, aPtr)
+	f.MOVD("n+16(FP)", n)
+
+	f.LABEL(loop)
+	f.CBZ(n, done)
+
+	f.WriteLn(`
+	// blockSize is 16 uint32; we load 4 vectors of 4 uint32 at a time
+	// (4*4)*4 = 64 bytes ~= 1 cache line
+	// since our values are 31 bits, we can add 2 by 2 these vectors
+	// we are left with 2 vectors of 4x32 bits values
+	// that we accumulate in 4*2*64bits accumulators
+	// the caller will reduce mod q the accumulators.
+	`)
+
+	const offset = 8 * 4
+	f.VLD2_P(offset, aPtr, a1.S4(), a2.S4())
+	f.VADD(a1.S4(), a2.S4(), a1.S4(), "a1 += a2")
+
+	f.VLD2_P(offset, aPtr, a3.S4(), a4.S4())
+	f.VADD(a3.S4(), a4.S4(), a3.S4(), "a3 += a4")
+
+	f.VUSHLL(0, a1.S2(), a2.D2(), "convert low words to 64 bits")
+	f.VADD(a2.D2(), acc2, acc2, "acc2 += a2")
+	f.VUSHLL2(0, a1.S4(), a1.D2(), "convert high words to 64 bits")
+	f.VADD(a1.D2(), acc1, acc1, "acc1 += a1")
+
+	f.VUSHLL(0, a3.S2(), a4.D2(), "convert low words to 64 bits")
+	f.VADD(a4.D2(), acc4, acc4, "acc4 += a4")
+	f.VUSHLL2(0, a3.S4(), a3.D2(), "convert high words to 64 bits")
+	f.VADD(a3.D2(), acc3, acc3, "acc3 += a3")
+
+	// decrement n
+	f.SUB(1, n, n)
+	f.JMP(loop)
+
+	f.LABEL(done)
+
+	f.VADD(acc1, acc3, acc1, "acc1 += acc3")
+	f.VADD(acc2, acc4, acc2, "acc2 += acc4")
+
+	f.VST2_P(acc1, acc2, tPtr, 0, "store acc1 and acc2")
+
+	f.RET()
+
+}
diff --git a/field/generator/config/field_config.go b/field/generator/config/field_config.go
index aa96da2fbe..173b678b34 100644
--- a/field/generator/config/field_config.go
+++ b/field/generator/config/field_config.go
@@ -299,8 +299,8 @@ func NewFieldConfig(packageName, elementName, modulus string, useAddChain bool)
 		F.GenerateOpsAMD64 = false
 	}
 	F.GenerateVectorOpsAMD64 = F.F31 || (F.GenerateOpsAMD64 && F.NbWords == 4 && F.NbBits > 225)
-	F.GenerateOpsARM64 = F.GenerateOpsAMD64 && (F.NbWords%2 == 0)
-	F.GenerateVectorOpsARM64 = false
+	F.GenerateOpsARM64 = F.F31 || (F.GenerateOpsAMD64 && (F.NbWords%2 == 0))
+	F.GenerateVectorOpsARM64 = F.F31
 
 	// setting Mu 2^288 / q
 	if F.NbWords == 4 {
diff --git a/field/generator/generator_field.go b/field/generator/generator_field.go
index 7e8b27cc10..203a56c93a 100644
--- a/field/generator/generator_field.go
+++ b/field/generator/generator_field.go
@@ -136,7 +136,6 @@ func generateField(F *config.Field, outputDir, asmDirIncludePath, hashArm64, has
 
 	if F.F31 {
 		pureGoBuildTag = "" // always generate pure go for F31
-		pureGoVectorBuildTag = "purego || (!amd64)"
 	}
 
 	var g errgroup.Group
@@ -151,20 +150,20 @@ func generateField(F *config.Field, outputDir, asmDirIncludePath, hashArm64, has
 	g.Go(generate("element_amd64.s", []string{element.IncludeASM}, only(F.GenerateOpsAMD64), withBuildTag("!purego"), withData(amd64d)))
 	g.Go(generate("element_arm64.s", []string{element.IncludeASM}, only(F.GenerateOpsARM64), withBuildTag("!purego"), withData(arm64d)))
 
-	g.Go(generate("element_amd64.go", []string{element.OpsAMD64, element.MulDoc}, only(!F.F31 && F.GenerateOpsAMD64), withBuildTag("!purego")))
-	g.Go(generate("element_arm64.go", []string{element.OpsARM64, element.MulNoCarry, element.Reduce}, only(!F.F31 && F.GenerateOpsARM64), withBuildTag("!purego")))
+	g.Go(generate("element_amd64.go", []string{element.OpsAMD64, element.MulDoc}, only(F.GenerateOpsAMD64 && !F.F31), withBuildTag("!purego")))
+	g.Go(generate("element_arm64.go", []string{element.OpsARM64, element.MulNoCarry, element.Reduce}, only(F.GenerateOpsARM64 && !F.F31), withBuildTag("!purego")))
 
 	g.Go(generate("element_purego.go", []string{element.OpsNoAsm, element.MulCIOS, element.MulNoCarry, element.Reduce, element.MulDoc}, withBuildTag(pureGoBuildTag)))
 
-	g.Go(generate("vector_amd64.go", []string{element.VectorOpsAmd64}, only(!F.F31 && F.GenerateVectorOpsAMD64), withBuildTag("!purego")))
-	g.Go(generate("vector_arm64.go", []string{element.VectorOpsArm64}, only(!F.F31 && F.GenerateVectorOpsARM64), withBuildTag("!purego")))
-
-	g.Go(generate("vector_amd64.go", []string{element.VectorOpsAmd64F31}, only(F.F31 && F.GenerateVectorOpsAMD64), withBuildTag("!purego")))
+	g.Go(generate("vector_amd64.go", []string{element.VectorOpsAmd64}, only(F.GenerateVectorOpsAMD64 && !F.F31), withBuildTag("!purego")))
+	g.Go(generate("vector_amd64.go", []string{element.VectorOpsAmd64F31}, only(F.GenerateVectorOpsAMD64 && F.F31), withBuildTag("!purego")))
+	g.Go(generate("vector_arm64.go", []string{element.VectorOpsArm64}, only(F.GenerateVectorOpsARM64 && !F.F31), withBuildTag("!purego")))
+	g.Go(generate("vector_arm64.go", []string{element.VectorOpsArm64F31}, only(F.GenerateVectorOpsARM64 && F.F31), withBuildTag("!purego")))
 
 	g.Go(generate("vector_purego.go", []string{element.VectorOpsPureGo}, withBuildTag(pureGoVectorBuildTag)))
 
-	g.Go(generate("asm_adx.go", []string{element.Asm}, only(!F.F31 && F.GenerateOpsAMD64), withBuildTag("!noadx")))
-	g.Go(generate("asm_noadx.go", []string{element.AsmNoAdx}, only(!F.F31 && F.GenerateOpsAMD64), withBuildTag("noadx")))
+	g.Go(generate("asm_adx.go", []string{element.Asm}, only(F.GenerateOpsAMD64 && !F.F31), withBuildTag("!noadx")))
+	g.Go(generate("asm_noadx.go", []string{element.AsmNoAdx}, only(F.GenerateOpsAMD64 && !F.F31), withBuildTag("noadx")))
 	g.Go(generate("asm_avx.go", []string{element.Avx}, only(F.GenerateVectorOpsAMD64), withBuildTag("!noavx")))
 	g.Go(generate("asm_noavx.go", []string{element.NoAvx}, only(F.GenerateVectorOpsAMD64), withBuildTag("noavx")))
 
diff --git a/field/generator/internal/templates/element/vector_ops_asm.go b/field/generator/internal/templates/element/vector_ops_asm.go
index aa00830dfd..2a1d0bf8e6 100644
--- a/field/generator/internal/templates/element/vector_ops_asm.go
+++ b/field/generator/internal/templates/element/vector_ops_asm.go
@@ -146,6 +146,105 @@ func mulVec(res, a, b *{{.ElementName}}, n uint64, qInvNeg uint64)
 
 const VectorOpsArm64 = VectorOpsPureGo
 
+const VectorOpsArm64F31 = `
+
+//go:noescape
+func addVec(res, a, b *{{.ElementName}}, n uint64)
+
+//go:noescape
+func subVec(res, a, b *{{.ElementName}}, n uint64)
+
+//go:noescape
+func sumVec(t *uint64, a *{{.ElementName}}, n uint64)
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Add: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+
+	const blockSize = 4
+	addVec(&(*vector)[0], &a[0], &b[0], n/blockSize)
+	if n % blockSize != 0 {
+		// call addVecGeneric on the rest
+		start := n - n % blockSize
+		addVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Sub: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+
+	const blockSize = 4
+	subVec(&(*vector)[0], &a[0], &b[0], n/blockSize)
+	if n % blockSize != 0 {
+		// call subVecGeneric on the rest
+		start := n - n % blockSize
+		subVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res {{.ElementName}}) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+
+	const blockSize = 16
+	var t [4]uint64 // stores the accumulators (not reduced mod q)
+	sumVec(&t[0], &(*vector)[0], n/blockSize)
+	// we reduce the accumulators mod q and add to res
+	var v {{.ElementName}}
+	for i := 0; i < 4; i++ {
+		v[0] = uint32(t[i] % q)
+		res.Add(&res, &v)
+	}
+	if n % blockSize != 0 {
+		// call sumVecGeneric on the rest
+		start := n - n % blockSize
+		sumVecGeneric(&res, (*vector)[start:])
+	}
+
+	return
+}
+
+// note: unfortunately, as of Dec. 2024, Golang doesn't support enough NEON instructions
+// for these to be worth it in assembly. Will hopefully revisit in future versions.
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *{{.ElementName}}) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res {{.ElementName}}) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
+`
+
 const VectorOpsAmd64F31 = `
 
 //go:noescape
@@ -259,8 +358,7 @@ func (vector *Vector) Sum() (res {{.ElementName}}) {
 	// we reduce the accumulators mod q and add to res
 	var v {{.ElementName}}
 	for i := 0; i < 8; i++ {
-		t[i] %= q
-		v[0] = uint32(t[i])
+		v[0] = uint32(t[i] % q)
 		res.Add(&res, &v)
 	}
 	if n % blockSize != 0 {
@@ -294,8 +392,7 @@ func (vector *Vector) InnerProduct(other Vector) (res {{.ElementName}}) {
 	// we reduce the accumulators mod q and add to res
 	var v {{.ElementName}}
 	for i := 0; i < 8; i++ {
-		t[i] %= q
-		v[0] = uint32(t[i])
+		v[0] = uint32(t[i] % q)
 		res.Add(&res, &v)
 	}
 	if n % blockSize != 0 {
diff --git a/field/koalabear/doc.go b/field/koalabear/doc.go
index 60c2390f6a..c102c15c78 100644
--- a/field/koalabear/doc.go
+++ b/field/koalabear/doc.go
@@ -7,7 +7,7 @@
 //
 // The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x).
 //
-// Additionally koalabear.Vector offers an API to manipulate []Element using AVX512 instructions if available.
+// Additionally koalabear.Vector offers an API to manipulate []Element using AVX512/NEON instructions if available.
 //
 // The modulus is hardcoded in all the operations.
 //
diff --git a/field/koalabear/element_arm64.s b/field/koalabear/element_arm64.s
new file mode 100644
index 0000000000..f3ddfa315e
--- /dev/null
+++ b/field/koalabear/element_arm64.s
@@ -0,0 +1,10 @@
+//go:build  !purego
+
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+// We include the hash to force the Go compiler to recompile: 8620676634583589757
+#include "../asm/element_31b_arm64.s"
+
diff --git a/field/koalabear/vector_amd64.go b/field/koalabear/vector_amd64.go
index cc80c68d04..ede9d1afa9 100644
--- a/field/koalabear/vector_amd64.go
+++ b/field/koalabear/vector_amd64.go
@@ -118,8 +118,7 @@ func (vector *Vector) Sum() (res Element) {
 	// we reduce the accumulators mod q and add to res
 	var v Element
 	for i := 0; i < 8; i++ {
-		t[i] %= q
-		v[0] = uint32(t[i])
+		v[0] = uint32(t[i] % q)
 		res.Add(&res, &v)
 	}
 	if n%blockSize != 0 {
@@ -153,8 +152,7 @@ func (vector *Vector) InnerProduct(other Vector) (res Element) {
 	// we reduce the accumulators mod q and add to res
 	var v Element
 	for i := 0; i < 8; i++ {
-		t[i] %= q
-		v[0] = uint32(t[i])
+		v[0] = uint32(t[i] % q)
 		res.Add(&res, &v)
 	}
 	if n%blockSize != 0 {
diff --git a/field/koalabear/vector_arm64.go b/field/koalabear/vector_arm64.go
new file mode 100644
index 0000000000..dd410b2058
--- /dev/null
+++ b/field/koalabear/vector_arm64.go
@@ -0,0 +1,104 @@
+//go:build !purego
+
+// Copyright 2020-2024 Consensys Software Inc.
+// Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
+
+// Code generated by consensys/gnark-crypto DO NOT EDIT
+
+package koalabear
+
+//go:noescape
+func addVec(res, a, b *Element, n uint64)
+
+//go:noescape
+func subVec(res, a, b *Element, n uint64)
+
+//go:noescape
+func sumVec(t *uint64, a *Element, n uint64)
+
+// Add adds two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Add(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Add: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+
+	const blockSize = 4
+	addVec(&(*vector)[0], &a[0], &b[0], n/blockSize)
+	if n%blockSize != 0 {
+		// call addVecGeneric on the rest
+		start := n - n%blockSize
+		addVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+}
+
+// Sub subtracts two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Sub(a, b Vector) {
+	if len(a) != len(b) || len(a) != len(*vector) {
+		panic("vector.Sub: vectors don't have the same length")
+	}
+	n := uint64(len(a))
+	if n == 0 {
+		return
+	}
+
+	const blockSize = 4
+	subVec(&(*vector)[0], &a[0], &b[0], n/blockSize)
+	if n%blockSize != 0 {
+		// call subVecGeneric on the rest
+		start := n - n%blockSize
+		subVecGeneric((*vector)[start:], a[start:], b[start:])
+	}
+}
+
+// Sum computes the sum of all elements in the vector.
+func (vector *Vector) Sum() (res Element) {
+	n := uint64(len(*vector))
+	if n == 0 {
+		return
+	}
+
+	const blockSize = 16
+	var t [4]uint64 // stores the accumulators (not reduced mod q)
+	sumVec(&t[0], &(*vector)[0], n/blockSize)
+	// we reduce the accumulators mod q and add to res
+	var v Element
+	for i := 0; i < 4; i++ {
+		v[0] = uint32(t[i] % q)
+		res.Add(&res, &v)
+	}
+	if n%blockSize != 0 {
+		// call sumVecGeneric on the rest
+		start := n - n%blockSize
+		sumVecGeneric(&res, (*vector)[start:])
+	}
+
+	return
+}
+
+// note: unfortunately, as of Dec. 2024, Golang doesn't support enough NEON instructions
+// for these to be worth it in assembly. Will hopefully revisit in future versions.
+
+// ScalarMul multiplies a vector by a scalar element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) ScalarMul(a Vector, b *Element) {
+	scalarMulVecGeneric(*vector, a, b)
+}
+
+// InnerProduct computes the inner product of two vectors.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) InnerProduct(other Vector) (res Element) {
+	innerProductVecGeneric(&res, *vector, other)
+	return
+}
+
+// Mul multiplies two vectors element-wise and stores the result in self.
+// It panics if the vectors don't have the same length.
+func (vector *Vector) Mul(a, b Vector) {
+	mulVecGeneric(*vector, a, b)
+}
diff --git a/field/koalabear/vector_purego.go b/field/koalabear/vector_purego.go
index c96e144f86..fa9715eaf5 100644
--- a/field/koalabear/vector_purego.go
+++ b/field/koalabear/vector_purego.go
@@ -1,4 +1,4 @@
-//go:build purego || !amd64
+//go:build purego || (!amd64 && !arm64)
 
 // Copyright 2020-2024 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
diff --git a/go.mod b/go.mod
index 226897a8a9..925b44c359 100644
--- a/go.mod
+++ b/go.mod
@@ -4,7 +4,7 @@ go 1.22
 
 require (
 	github.com/bits-and-blooms/bitset v1.14.2
-	github.com/consensys/bavard v0.1.24
+	github.com/consensys/bavard v0.1.25
 	github.com/leanovate/gopter v0.2.11
 	github.com/mmcloughlin/addchain v0.4.0
 	github.com/spf13/cobra v1.8.1
diff --git a/go.sum b/go.sum
index 5ff805b862..798885eed6 100644
--- a/go.sum
+++ b/go.sum
@@ -55,8 +55,8 @@ github.com/client9/misspell v0.3.4/go.mod h1:qj6jICC3Q7zFZvVWo7KLAzC3yx5G7kyvSDk
 github.com/cncf/udpa/go v0.0.0-20191209042840-269d4d468f6f/go.mod h1:M8M6+tZqaGXZJjfX53e64911xZQV5JYwmTeXPW+k8Sc=
 github.com/cncf/udpa/go v0.0.0-20200629203442-efcf912fb354/go.mod h1:WmhPx2Nbnhtbo57+VJT5O0JRkEi1Wbu0z5j0R8u5Hbk=
 github.com/cncf/udpa/go v0.0.0-20201120205902-5459f2c99403/go.mod h1:WmhPx2Nbnhtbo57+VJT5O0JRkEi1Wbu0z5j0R8u5Hbk=
-github.com/consensys/bavard v0.1.24 h1:Lfe+bjYbpaoT7K5JTFoMi5wo9V4REGLvQQbHmatoN2I=
-github.com/consensys/bavard v0.1.24/go.mod h1:k/zVjHHC4B+PQy1Pg7fgvG3ALicQw540Crag8qx+dZs=
+github.com/consensys/bavard v0.1.25 h1:5YcSBnp03/HvfpKaIQLr/ecspTp2k8YNR5rQLOWvUyc=
+github.com/consensys/bavard v0.1.25/go.mod h1:k/zVjHHC4B+PQy1Pg7fgvG3ALicQw540Crag8qx+dZs=
 github.com/coreos/go-semver v0.3.0/go.mod h1:nnelYz7RCh+5ahJtPPxZlU+153eP4D4r3EedlOD2RNk=
 github.com/coreos/go-systemd/v22 v22.3.2/go.mod h1:Y58oyj3AT4RCenI/lSvhwexgC+NSVTIJ3seZv2GcEnc=
 github.com/cpuguy83/go-md2man/v2 v2.0.0/go.mod h1:maD7wRr/U5Z6m/iR4s+kqSMx2CaBsrgA7czyZG/E6dU=

From 8a4cdf125924fdb80ddf1748dbac6242efbee611 Mon Sep 17 00:00:00 2001
From: Arya Tabaie <arya.pourtabatabaie@gmail.com>
Date: Tue, 7 Jan 2025 09:53:42 -0600
Subject: [PATCH 112/114] Change copyright year to 2025 (#595)

Co-authored-by: Arya Tabaie <15056835+Tabaie@users.noreply.github.com>
---
 ecc/bls12-377/ecdsa/doc.go                                      | 2 +-
 ecc/bls12-377/ecdsa/ecdsa.go                                    | 2 +-
 ecc/bls12-377/ecdsa/ecdsa_test.go                               | 2 +-
 ecc/bls12-377/ecdsa/marshal.go                                  | 2 +-
 ecc/bls12-377/ecdsa/marshal_test.go                             | 2 +-
 ecc/bls12-377/fflonk/doc.go                                     | 2 +-
 ecc/bls12-377/fflonk/example_test.go                            | 2 +-
 ecc/bls12-377/fflonk/fflonk.go                                  | 2 +-
 ecc/bls12-377/fflonk/fflonk_test.go                             | 2 +-
 ecc/bls12-377/fflonk/marshal.go                                 | 2 +-
 ecc/bls12-377/fp/arith.go                                       | 2 +-
 ecc/bls12-377/fp/asm_adx.go                                     | 2 +-
 ecc/bls12-377/fp/asm_noadx.go                                   | 2 +-
 ecc/bls12-377/fp/doc.go                                         | 2 +-
 ecc/bls12-377/fp/element.go                                     | 2 +-
 ecc/bls12-377/fp/element_amd64.go                               | 2 +-
 ecc/bls12-377/fp/element_amd64.s                                | 2 +-
 ecc/bls12-377/fp/element_arm64.go                               | 2 +-
 ecc/bls12-377/fp/element_arm64.s                                | 2 +-
 ecc/bls12-377/fp/element_exp.go                                 | 2 +-
 ecc/bls12-377/fp/element_purego.go                              | 2 +-
 ecc/bls12-377/fp/element_test.go                                | 2 +-
 ecc/bls12-377/fp/hash_to_field/doc.go                           | 2 +-
 ecc/bls12-377/fp/hash_to_field/hash_to_field.go                 | 2 +-
 ecc/bls12-377/fp/hash_to_field/hash_to_field_test.go            | 2 +-
 ecc/bls12-377/fp/vector.go                                      | 2 +-
 ecc/bls12-377/fp/vector_purego.go                               | 2 +-
 ecc/bls12-377/fp/vector_test.go                                 | 2 +-
 ecc/bls12-377/fr/arith.go                                       | 2 +-
 ecc/bls12-377/fr/asm_adx.go                                     | 2 +-
 ecc/bls12-377/fr/asm_avx.go                                     | 2 +-
 ecc/bls12-377/fr/asm_noadx.go                                   | 2 +-
 ecc/bls12-377/fr/asm_noavx.go                                   | 2 +-
 ecc/bls12-377/fr/doc.go                                         | 2 +-
 ecc/bls12-377/fr/element.go                                     | 2 +-
 ecc/bls12-377/fr/element_amd64.go                               | 2 +-
 ecc/bls12-377/fr/element_amd64.s                                | 2 +-
 ecc/bls12-377/fr/element_arm64.go                               | 2 +-
 ecc/bls12-377/fr/element_arm64.s                                | 2 +-
 ecc/bls12-377/fr/element_exp.go                                 | 2 +-
 ecc/bls12-377/fr/element_purego.go                              | 2 +-
 ecc/bls12-377/fr/element_test.go                                | 2 +-
 ecc/bls12-377/fr/fft/bitreverse.go                              | 2 +-
 ecc/bls12-377/fr/fft/bitreverse_test.go                         | 2 +-
 ecc/bls12-377/fr/fft/doc.go                                     | 2 +-
 ecc/bls12-377/fr/fft/domain.go                                  | 2 +-
 ecc/bls12-377/fr/fft/domain_test.go                             | 2 +-
 ecc/bls12-377/fr/fft/fft.go                                     | 2 +-
 ecc/bls12-377/fr/fft/fft_test.go                                | 2 +-
 ecc/bls12-377/fr/fft/options.go                                 | 2 +-
 ecc/bls12-377/fr/fri/doc.go                                     | 2 +-
 ecc/bls12-377/fr/fri/fri.go                                     | 2 +-
 ecc/bls12-377/fr/fri/fri_test.go                                | 2 +-
 ecc/bls12-377/fr/generator.go                                   | 2 +-
 ecc/bls12-377/fr/gkr/gkr.go                                     | 2 +-
 ecc/bls12-377/fr/gkr/gkr_test.go                                | 2 +-
 ecc/bls12-377/fr/hash_to_field/doc.go                           | 2 +-
 ecc/bls12-377/fr/hash_to_field/hash_to_field.go                 | 2 +-
 ecc/bls12-377/fr/hash_to_field/hash_to_field_test.go            | 2 +-
 ecc/bls12-377/fr/iop/doc.go                                     | 2 +-
 ecc/bls12-377/fr/iop/expressions.go                             | 2 +-
 ecc/bls12-377/fr/iop/expressions_test.go                        | 2 +-
 ecc/bls12-377/fr/iop/polynomial.go                              | 2 +-
 ecc/bls12-377/fr/iop/polynomial_test.go                         | 2 +-
 ecc/bls12-377/fr/iop/quotient.go                                | 2 +-
 ecc/bls12-377/fr/iop/quotient_test.go                           | 2 +-
 ecc/bls12-377/fr/iop/ratios.go                                  | 2 +-
 ecc/bls12-377/fr/iop/ratios_test.go                             | 2 +-
 ecc/bls12-377/fr/iop/utils.go                                   | 2 +-
 ecc/bls12-377/fr/mimc/doc.go                                    | 2 +-
 ecc/bls12-377/fr/mimc/mimc.go                                   | 2 +-
 ecc/bls12-377/fr/mimc/mimc_test.go                              | 2 +-
 ecc/bls12-377/fr/mimc/options.go                                | 2 +-
 ecc/bls12-377/fr/pedersen/doc.go                                | 2 +-
 ecc/bls12-377/fr/pedersen/example_test.go                       | 2 +-
 ecc/bls12-377/fr/pedersen/pedersen.go                           | 2 +-
 ecc/bls12-377/fr/pedersen/pedersen_test.go                      | 2 +-
 ecc/bls12-377/fr/permutation/doc.go                             | 2 +-
 ecc/bls12-377/fr/permutation/permutation.go                     | 2 +-
 ecc/bls12-377/fr/permutation/permutation_test.go                | 2 +-
 ecc/bls12-377/fr/plookup/doc.go                                 | 2 +-
 ecc/bls12-377/fr/plookup/plookup_test.go                        | 2 +-
 ecc/bls12-377/fr/plookup/table.go                               | 2 +-
 ecc/bls12-377/fr/plookup/vector.go                              | 2 +-
 ecc/bls12-377/fr/polynomial/doc.go                              | 2 +-
 ecc/bls12-377/fr/polynomial/multilin.go                         | 2 +-
 ecc/bls12-377/fr/polynomial/multilin_test.go                    | 2 +-
 ecc/bls12-377/fr/polynomial/polynomial.go                       | 2 +-
 ecc/bls12-377/fr/polynomial/polynomial_test.go                  | 2 +-
 ecc/bls12-377/fr/polynomial/pool.go                             | 2 +-
 ecc/bls12-377/fr/poseidon2/poseidon2.go                         | 2 +-
 ecc/bls12-377/fr/poseidon2/poseidon2_test.go                    | 2 +-
 ecc/bls12-377/fr/sis/sis.go                                     | 2 +-
 ecc/bls12-377/fr/sis/sis_fft.go                                 | 2 +-
 ecc/bls12-377/fr/sis/sis_test.go                                | 2 +-
 ecc/bls12-377/fr/sumcheck/sumcheck.go                           | 2 +-
 ecc/bls12-377/fr/sumcheck/sumcheck_test.go                      | 2 +-
 ecc/bls12-377/fr/test_vector_utils/test_vector_utils.go         | 2 +-
 ecc/bls12-377/fr/vector.go                                      | 2 +-
 ecc/bls12-377/fr/vector_amd64.go                                | 2 +-
 ecc/bls12-377/fr/vector_purego.go                               | 2 +-
 ecc/bls12-377/fr/vector_test.go                                 | 2 +-
 ecc/bls12-377/g1.go                                             | 2 +-
 ecc/bls12-377/g1_test.go                                        | 2 +-
 ecc/bls12-377/g2.go                                             | 2 +-
 ecc/bls12-377/g2_test.go                                        | 2 +-
 ecc/bls12-377/hash_to_g1.go                                     | 2 +-
 ecc/bls12-377/hash_to_g1_test.go                                | 2 +-
 ecc/bls12-377/hash_to_g2.go                                     | 2 +-
 ecc/bls12-377/hash_to_g2_test.go                                | 2 +-
 ecc/bls12-377/internal/fptower/asm.go                           | 2 +-
 ecc/bls12-377/internal/fptower/asm_noadx.go                     | 2 +-
 ecc/bls12-377/internal/fptower/e12.go                           | 2 +-
 ecc/bls12-377/internal/fptower/e12_test.go                      | 2 +-
 ecc/bls12-377/internal/fptower/e2.go                            | 2 +-
 ecc/bls12-377/internal/fptower/e2_amd64.go                      | 2 +-
 ecc/bls12-377/internal/fptower/e2_amd64.s                       | 2 +-
 ecc/bls12-377/internal/fptower/e2_fallback.go                   | 2 +-
 ecc/bls12-377/internal/fptower/e2_test.go                       | 2 +-
 ecc/bls12-377/internal/fptower/e6.go                            | 2 +-
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 ecc/bw6-633/fr/vector_test.go                                   | 2 +-
 ecc/bw6-633/g1.go                                               | 2 +-
 ecc/bw6-633/g1_test.go                                          | 2 +-
 ecc/bw6-633/g2.go                                               | 2 +-
 ecc/bw6-633/g2_test.go                                          | 2 +-
 ecc/bw6-633/hash_to_g1.go                                       | 2 +-
 ecc/bw6-633/hash_to_g1_test.go                                  | 2 +-
 ecc/bw6-633/hash_to_g2.go                                       | 2 +-
 ecc/bw6-633/hash_to_g2_test.go                                  | 2 +-
 ecc/bw6-633/kzg/doc.go                                          | 2 +-
 ecc/bw6-633/kzg/kzg.go                                          | 2 +-
 ecc/bw6-633/kzg/kzg_test.go                                     | 2 +-
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 ecc/bw6-633/multiexp_jacobian.go                                | 2 +-
 ecc/bw6-633/multiexp_test.go                                    | 2 +-
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 ecc/bw6-633/shplonk/doc.go                                      | 2 +-
 ecc/bw6-633/shplonk/example_test.go                             | 2 +-
 ecc/bw6-633/shplonk/marshal.go                                  | 2 +-
 ecc/bw6-633/shplonk/shplonk.go                                  | 2 +-
 ecc/bw6-633/shplonk/shplonk_test.go                             | 2 +-
 ecc/bw6-633/twistededwards/curve.go                             | 2 +-
 ecc/bw6-633/twistededwards/doc.go                               | 2 +-
 ecc/bw6-633/twistededwards/eddsa/doc.go                         | 2 +-
 ecc/bw6-633/twistededwards/eddsa/eddsa.go                       | 2 +-
 ecc/bw6-633/twistededwards/eddsa/eddsa_test.go                  | 2 +-
 ecc/bw6-633/twistededwards/eddsa/marshal.go                     | 2 +-
 ecc/bw6-633/twistededwards/point.go                             | 2 +-
 ecc/bw6-633/twistededwards/point_test.go                        | 2 +-
 ecc/bw6-761/ecdsa/doc.go                                        | 2 +-
 ecc/bw6-761/ecdsa/ecdsa.go                                      | 2 +-
 ecc/bw6-761/ecdsa/ecdsa_test.go                                 | 2 +-
 ecc/bw6-761/ecdsa/marshal.go                                    | 2 +-
 ecc/bw6-761/ecdsa/marshal_test.go                               | 2 +-
 ecc/bw6-761/fflonk/doc.go                                       | 2 +-
 ecc/bw6-761/fflonk/example_test.go                              | 2 +-
 ecc/bw6-761/fflonk/fflonk.go                                    | 2 +-
 ecc/bw6-761/fflonk/fflonk_test.go                               | 2 +-
 ecc/bw6-761/fflonk/marshal.go                                   | 2 +-
 ecc/bw6-761/fp/arith.go                                         | 2 +-
 ecc/bw6-761/fp/asm_adx.go                                       | 2 +-
 ecc/bw6-761/fp/asm_noadx.go                                     | 2 +-
 ecc/bw6-761/fp/doc.go                                           | 2 +-
 ecc/bw6-761/fp/element.go                                       | 2 +-
 ecc/bw6-761/fp/element_amd64.go                                 | 2 +-
 ecc/bw6-761/fp/element_amd64.s                                  | 2 +-
 ecc/bw6-761/fp/element_arm64.go                                 | 2 +-
 ecc/bw6-761/fp/element_arm64.s                                  | 2 +-
 ecc/bw6-761/fp/element_exp.go                                   | 2 +-
 ecc/bw6-761/fp/element_purego.go                                | 2 +-
 ecc/bw6-761/fp/element_test.go                                  | 2 +-
 ecc/bw6-761/fp/hash_to_field/doc.go                             | 2 +-
 ecc/bw6-761/fp/hash_to_field/hash_to_field.go                   | 2 +-
 ecc/bw6-761/fp/hash_to_field/hash_to_field_test.go              | 2 +-
 ecc/bw6-761/fp/vector.go                                        | 2 +-
 ecc/bw6-761/fp/vector_purego.go                                 | 2 +-
 ecc/bw6-761/fp/vector_test.go                                   | 2 +-
 ecc/bw6-761/fr/arith.go                                         | 2 +-
 ecc/bw6-761/fr/asm_adx.go                                       | 2 +-
 ecc/bw6-761/fr/asm_noadx.go                                     | 2 +-
 ecc/bw6-761/fr/doc.go                                           | 2 +-
 ecc/bw6-761/fr/element.go                                       | 2 +-
 ecc/bw6-761/fr/element_amd64.go                                 | 2 +-
 ecc/bw6-761/fr/element_amd64.s                                  | 2 +-
 ecc/bw6-761/fr/element_arm64.go                                 | 2 +-
 ecc/bw6-761/fr/element_arm64.s                                  | 2 +-
 ecc/bw6-761/fr/element_exp.go                                   | 2 +-
 ecc/bw6-761/fr/element_purego.go                                | 2 +-
 ecc/bw6-761/fr/element_test.go                                  | 2 +-
 ecc/bw6-761/fr/fft/bitreverse.go                                | 2 +-
 ecc/bw6-761/fr/fft/bitreverse_test.go                           | 2 +-
 ecc/bw6-761/fr/fft/doc.go                                       | 2 +-
 ecc/bw6-761/fr/fft/domain.go                                    | 2 +-
 ecc/bw6-761/fr/fft/domain_test.go                               | 2 +-
 ecc/bw6-761/fr/fft/fft.go                                       | 2 +-
 ecc/bw6-761/fr/fft/fft_test.go                                  | 2 +-
 ecc/bw6-761/fr/fft/options.go                                   | 2 +-
 ecc/bw6-761/fr/fri/doc.go                                       | 2 +-
 ecc/bw6-761/fr/fri/fri.go                                       | 2 +-
 ecc/bw6-761/fr/fri/fri_test.go                                  | 2 +-
 ecc/bw6-761/fr/generator.go                                     | 2 +-
 ecc/bw6-761/fr/gkr/gkr.go                                       | 2 +-
 ecc/bw6-761/fr/gkr/gkr_test.go                                  | 2 +-
 ecc/bw6-761/fr/hash_to_field/doc.go                             | 2 +-
 ecc/bw6-761/fr/hash_to_field/hash_to_field.go                   | 2 +-
 ecc/bw6-761/fr/hash_to_field/hash_to_field_test.go              | 2 +-
 ecc/bw6-761/fr/iop/doc.go                                       | 2 +-
 ecc/bw6-761/fr/iop/expressions.go                               | 2 +-
 ecc/bw6-761/fr/iop/expressions_test.go                          | 2 +-
 ecc/bw6-761/fr/iop/polynomial.go                                | 2 +-
 ecc/bw6-761/fr/iop/polynomial_test.go                           | 2 +-
 ecc/bw6-761/fr/iop/quotient.go                                  | 2 +-
 ecc/bw6-761/fr/iop/quotient_test.go                             | 2 +-
 ecc/bw6-761/fr/iop/ratios.go                                    | 2 +-
 ecc/bw6-761/fr/iop/ratios_test.go                               | 2 +-
 ecc/bw6-761/fr/iop/utils.go                                     | 2 +-
 ecc/bw6-761/fr/mimc/doc.go                                      | 2 +-
 ecc/bw6-761/fr/mimc/mimc.go                                     | 2 +-
 ecc/bw6-761/fr/mimc/mimc_test.go                                | 2 +-
 ecc/bw6-761/fr/mimc/options.go                                  | 2 +-
 ecc/bw6-761/fr/pedersen/doc.go                                  | 2 +-
 ecc/bw6-761/fr/pedersen/example_test.go                         | 2 +-
 ecc/bw6-761/fr/pedersen/pedersen.go                             | 2 +-
 ecc/bw6-761/fr/pedersen/pedersen_test.go                        | 2 +-
 ecc/bw6-761/fr/permutation/doc.go                               | 2 +-
 ecc/bw6-761/fr/permutation/permutation.go                       | 2 +-
 ecc/bw6-761/fr/permutation/permutation_test.go                  | 2 +-
 ecc/bw6-761/fr/plookup/doc.go                                   | 2 +-
 ecc/bw6-761/fr/plookup/plookup_test.go                          | 2 +-
 ecc/bw6-761/fr/plookup/table.go                                 | 2 +-
 ecc/bw6-761/fr/plookup/vector.go                                | 2 +-
 ecc/bw6-761/fr/polynomial/doc.go                                | 2 +-
 ecc/bw6-761/fr/polynomial/multilin.go                           | 2 +-
 ecc/bw6-761/fr/polynomial/multilin_test.go                      | 2 +-
 ecc/bw6-761/fr/polynomial/polynomial.go                         | 2 +-
 ecc/bw6-761/fr/polynomial/polynomial_test.go                    | 2 +-
 ecc/bw6-761/fr/polynomial/pool.go                               | 2 +-
 ecc/bw6-761/fr/poseidon2/poseidon2.go                           | 2 +-
 ecc/bw6-761/fr/poseidon2/poseidon2_test.go                      | 2 +-
 ecc/bw6-761/fr/sumcheck/sumcheck.go                             | 2 +-
 ecc/bw6-761/fr/sumcheck/sumcheck_test.go                        | 2 +-
 ecc/bw6-761/fr/test_vector_utils/test_vector_utils.go           | 2 +-
 ecc/bw6-761/fr/vector.go                                        | 2 +-
 ecc/bw6-761/fr/vector_purego.go                                 | 2 +-
 ecc/bw6-761/fr/vector_test.go                                   | 2 +-
 ecc/bw6-761/g1.go                                               | 2 +-
 ecc/bw6-761/g1_test.go                                          | 2 +-
 ecc/bw6-761/g2.go                                               | 2 +-
 ecc/bw6-761/g2_test.go                                          | 2 +-
 ecc/bw6-761/hash_to_g1.go                                       | 2 +-
 ecc/bw6-761/hash_to_g1_test.go                                  | 2 +-
 ecc/bw6-761/hash_to_g2.go                                       | 2 +-
 ecc/bw6-761/hash_to_g2_test.go                                  | 2 +-
 ecc/bw6-761/kzg/doc.go                                          | 2 +-
 ecc/bw6-761/kzg/kzg.go                                          | 2 +-
 ecc/bw6-761/kzg/kzg_test.go                                     | 2 +-
 ecc/bw6-761/kzg/marshal.go                                      | 2 +-
 ecc/bw6-761/kzg/utils.go                                        | 2 +-
 ecc/bw6-761/marshal.go                                          | 2 +-
 ecc/bw6-761/marshal_test.go                                     | 2 +-
 ecc/bw6-761/multiexp.go                                         | 2 +-
 ecc/bw6-761/multiexp_affine.go                                  | 2 +-
 ecc/bw6-761/multiexp_jacobian.go                                | 2 +-
 ecc/bw6-761/multiexp_test.go                                    | 2 +-
 ecc/bw6-761/pairing_test.go                                     | 2 +-
 ecc/bw6-761/shplonk/doc.go                                      | 2 +-
 ecc/bw6-761/shplonk/example_test.go                             | 2 +-
 ecc/bw6-761/shplonk/marshal.go                                  | 2 +-
 ecc/bw6-761/shplonk/shplonk.go                                  | 2 +-
 ecc/bw6-761/shplonk/shplonk_test.go                             | 2 +-
 ecc/bw6-761/twistededwards/curve.go                             | 2 +-
 ecc/bw6-761/twistededwards/doc.go                               | 2 +-
 ecc/bw6-761/twistededwards/eddsa/doc.go                         | 2 +-
 ecc/bw6-761/twistededwards/eddsa/eddsa.go                       | 2 +-
 ecc/bw6-761/twistededwards/eddsa/eddsa_test.go                  | 2 +-
 ecc/bw6-761/twistededwards/eddsa/marshal.go                     | 2 +-
 ecc/bw6-761/twistededwards/point.go                             | 2 +-
 ecc/bw6-761/twistededwards/point_test.go                        | 2 +-
 ecc/secp256k1/ecdsa/doc.go                                      | 2 +-
 ecc/secp256k1/ecdsa/ecdsa.go                                    | 2 +-
 ecc/secp256k1/ecdsa/ecdsa_test.go                               | 2 +-
 ecc/secp256k1/ecdsa/marshal.go                                  | 2 +-
 ecc/secp256k1/ecdsa/marshal_test.go                             | 2 +-
 ecc/secp256k1/fp/arith.go                                       | 2 +-
 ecc/secp256k1/fp/doc.go                                         | 2 +-
 ecc/secp256k1/fp/element.go                                     | 2 +-
 ecc/secp256k1/fp/element_exp.go                                 | 2 +-
 ecc/secp256k1/fp/element_purego.go                              | 2 +-
 ecc/secp256k1/fp/element_test.go                                | 2 +-
 ecc/secp256k1/fp/vector.go                                      | 2 +-
 ecc/secp256k1/fp/vector_purego.go                               | 2 +-
 ecc/secp256k1/fp/vector_test.go                                 | 2 +-
 ecc/secp256k1/fr/arith.go                                       | 2 +-
 ecc/secp256k1/fr/doc.go                                         | 2 +-
 ecc/secp256k1/fr/element.go                                     | 2 +-
 ecc/secp256k1/fr/element_exp.go                                 | 2 +-
 ecc/secp256k1/fr/element_purego.go                              | 2 +-
 ecc/secp256k1/fr/element_test.go                                | 2 +-
 ecc/secp256k1/fr/vector.go                                      | 2 +-
 ecc/secp256k1/fr/vector_purego.go                               | 2 +-
 ecc/secp256k1/fr/vector_test.go                                 | 2 +-
 ecc/secp256k1/g1.go                                             | 2 +-
 ecc/secp256k1/g1_test.go                                        | 2 +-
 ecc/secp256k1/hash_to_g1.go                                     | 2 +-
 ecc/secp256k1/hash_to_g1_test.go                                | 2 +-
 ecc/secp256k1/multiexp.go                                       | 2 +-
 ecc/secp256k1/multiexp_affine.go                                | 2 +-
 ecc/secp256k1/multiexp_jacobian.go                              | 2 +-
 ecc/secp256k1/multiexp_test.go                                  | 2 +-
 ecc/stark-curve/ecdsa/doc.go                                    | 2 +-
 ecc/stark-curve/ecdsa/ecdsa.go                                  | 2 +-
 ecc/stark-curve/ecdsa/ecdsa_test.go                             | 2 +-
 ecc/stark-curve/ecdsa/marshal.go                                | 2 +-
 ecc/stark-curve/ecdsa/marshal_test.go                           | 2 +-
 ecc/stark-curve/fp/arith.go                                     | 2 +-
 ecc/stark-curve/fp/asm_adx.go                                   | 2 +-
 ecc/stark-curve/fp/asm_avx.go                                   | 2 +-
 ecc/stark-curve/fp/asm_noadx.go                                 | 2 +-
 ecc/stark-curve/fp/asm_noavx.go                                 | 2 +-
 ecc/stark-curve/fp/doc.go                                       | 2 +-
 ecc/stark-curve/fp/element.go                                   | 2 +-
 ecc/stark-curve/fp/element_amd64.go                             | 2 +-
 ecc/stark-curve/fp/element_amd64.s                              | 2 +-
 ecc/stark-curve/fp/element_arm64.go                             | 2 +-
 ecc/stark-curve/fp/element_arm64.s                              | 2 +-
 ecc/stark-curve/fp/element_exp.go                               | 2 +-
 ecc/stark-curve/fp/element_purego.go                            | 2 +-
 ecc/stark-curve/fp/element_test.go                              | 2 +-
 ecc/stark-curve/fp/vector.go                                    | 2 +-
 ecc/stark-curve/fp/vector_amd64.go                              | 2 +-
 ecc/stark-curve/fp/vector_purego.go                             | 2 +-
 ecc/stark-curve/fp/vector_test.go                               | 2 +-
 ecc/stark-curve/fr/arith.go                                     | 2 +-
 ecc/stark-curve/fr/asm_adx.go                                   | 2 +-
 ecc/stark-curve/fr/asm_avx.go                                   | 2 +-
 ecc/stark-curve/fr/asm_noadx.go                                 | 2 +-
 ecc/stark-curve/fr/asm_noavx.go                                 | 2 +-
 ecc/stark-curve/fr/doc.go                                       | 2 +-
 ecc/stark-curve/fr/element.go                                   | 2 +-
 ecc/stark-curve/fr/element_amd64.go                             | 2 +-
 ecc/stark-curve/fr/element_amd64.s                              | 2 +-
 ecc/stark-curve/fr/element_arm64.go                             | 2 +-
 ecc/stark-curve/fr/element_arm64.s                              | 2 +-
 ecc/stark-curve/fr/element_purego.go                            | 2 +-
 ecc/stark-curve/fr/element_test.go                              | 2 +-
 ecc/stark-curve/fr/vector.go                                    | 2 +-
 ecc/stark-curve/fr/vector_amd64.go                              | 2 +-
 ecc/stark-curve/fr/vector_purego.go                             | 2 +-
 ecc/stark-curve/fr/vector_test.go                               | 2 +-
 fiat-shamir/transcript.go                                       | 2 +-
 fiat-shamir/transcript_test.go                                  | 2 +-
 field/babybear/asm_avx.go                                       | 2 +-
 field/babybear/asm_noavx.go                                     | 2 +-
 field/babybear/doc.go                                           | 2 +-
 field/babybear/element.go                                       | 2 +-
 field/babybear/element_amd64.s                                  | 2 +-
 field/babybear/element_exp.go                                   | 2 +-
 field/babybear/element_purego.go                                | 2 +-
 field/babybear/element_test.go                                  | 2 +-
 field/babybear/fft/bitreverse.go                                | 2 +-
 field/babybear/fft/bitreverse_test.go                           | 2 +-
 field/babybear/fft/doc.go                                       | 2 +-
 field/babybear/fft/domain.go                                    | 2 +-
 field/babybear/fft/domain_test.go                               | 2 +-
 field/babybear/fft/fft.go                                       | 2 +-
 field/babybear/fft/fft_test.go                                  | 2 +-
 field/babybear/fft/options.go                                   | 2 +-
 field/babybear/generator.go                                     | 2 +-
 field/babybear/sis/sis.go                                       | 2 +-
 field/babybear/sis/sis_fft.go                                   | 2 +-
 field/babybear/sis/sis_test.go                                  | 2 +-
 field/babybear/vector.go                                        | 2 +-
 field/babybear/vector_amd64.go                                  | 2 +-
 field/babybear/vector_purego.go                                 | 2 +-
 field/babybear/vector_test.go                                   | 2 +-
 field/generator/asm/amd64/asm_macros.go                         | 2 +-
 field/generator/asm/amd64/build.go                              | 2 +-
 field/generator/asm/amd64/element_butterfly.go                  | 2 +-
 field/generator/asm/amd64/element_frommont.go                   | 2 +-
 field/generator/asm/amd64/element_mul.go                        | 2 +-
 field/generator/asm/amd64/element_mul_constants.go              | 2 +-
 field/generator/asm/amd64/element_reduce.go                     | 2 +-
 field/generator/asm/amd64/element_vec_4words.go                 | 2 +-
 field/generator/asm/arm64/element_mul.go                        | 2 +-
 field/generator/config/field_config.go                          | 2 +-
 field/generator/generator_test.go                               | 2 +-
 field/goff/cmd/errors.go                                        | 2 +-
 field/goff/cmd/root.go                                          | 2 +-
 field/goff/cmd/version.go                                       | 2 +-
 field/goff/main.go                                              | 2 +-
 field/goldilocks/arith.go                                       | 2 +-
 field/goldilocks/doc.go                                         | 2 +-
 field/goldilocks/element.go                                     | 2 +-
 field/goldilocks/element_exp.go                                 | 2 +-
 field/goldilocks/element_purego.go                              | 2 +-
 field/goldilocks/element_test.go                                | 2 +-
 field/goldilocks/fft/bitreverse.go                              | 2 +-
 field/goldilocks/fft/bitreverse_test.go                         | 2 +-
 field/goldilocks/fft/doc.go                                     | 2 +-
 field/goldilocks/fft/domain.go                                  | 2 +-
 field/goldilocks/fft/domain_test.go                             | 2 +-
 field/goldilocks/fft/fft.go                                     | 2 +-
 field/goldilocks/fft/fft_test.go                                | 2 +-
 field/goldilocks/fft/options.go                                 | 2 +-
 field/goldilocks/generator.go                                   | 2 +-
 field/goldilocks/sis/sis.go                                     | 2 +-
 field/goldilocks/sis/sis_fft.go                                 | 2 +-
 field/goldilocks/sis/sis_test.go                                | 2 +-
 field/goldilocks/vector.go                                      | 2 +-
 field/goldilocks/vector_purego.go                               | 2 +-
 field/goldilocks/vector_test.go                                 | 2 +-
 field/koalabear/asm_avx.go                                      | 2 +-
 field/koalabear/asm_noavx.go                                    | 2 +-
 field/koalabear/doc.go                                          | 2 +-
 field/koalabear/element.go                                      | 2 +-
 field/koalabear/element_amd64.s                                 | 2 +-
 field/koalabear/element_exp.go                                  | 2 +-
 field/koalabear/element_purego.go                               | 2 +-
 field/koalabear/element_test.go                                 | 2 +-
 field/koalabear/fft/bitreverse.go                               | 2 +-
 field/koalabear/fft/bitreverse_test.go                          | 2 +-
 field/koalabear/fft/doc.go                                      | 2 +-
 field/koalabear/fft/domain.go                                   | 2 +-
 field/koalabear/fft/domain_test.go                              | 2 +-
 field/koalabear/fft/fft.go                                      | 2 +-
 field/koalabear/fft/fft_test.go                                 | 2 +-
 field/koalabear/fft/options.go                                  | 2 +-
 field/koalabear/generator.go                                    | 2 +-
 field/koalabear/sis/sis.go                                      | 2 +-
 field/koalabear/sis/sis_fft.go                                  | 2 +-
 field/koalabear/sis/sis_test.go                                 | 2 +-
 field/koalabear/vector.go                                       | 2 +-
 field/koalabear/vector_amd64.go                                 | 2 +-
 field/koalabear/vector_purego.go                                | 2 +-
 field/koalabear/vector_test.go                                  | 2 +-
 hash/hashes.go                                                  | 2 +-
 internal/generator/gkr/test_vectors/main.go                     | 2 +-
 internal/generator/test_vector_utils/small_rational/gkr/gkr.go  | 2 +-
 .../test_vector_utils/small_rational/polynomial/doc.go          | 2 +-
 .../test_vector_utils/small_rational/polynomial/multilin.go     | 2 +-
 .../test_vector_utils/small_rational/polynomial/polynomial.go   | 2 +-
 .../test_vector_utils/small_rational/polynomial/pool.go         | 2 +-
 .../test_vector_utils/small_rational/sumcheck/sumcheck.go       | 2 +-
 .../test_vector_utils/small_rational/sumcheck/sumcheck_test.go  | 2 +-
 .../small_rational/test_vector_utils/test_vector_utils.go       | 2 +-
 internal/generator/tower/asm/amd64/e2.go                        | 2 +-
 internal/generator/tower/asm/amd64/e2_bls381.go                 | 2 +-
 internal/generator/tower/asm/amd64/e2_bn254.go                  | 2 +-
 signature/ecdsa/ecdsa.go                                        | 2 +-
 signature/eddsa/eddsa.go                                        | 2 +-
 signature/signature.go                                          | 2 +-
 1129 files changed, 1129 insertions(+), 1129 deletions(-)

diff --git a/ecc/bls12-377/ecdsa/doc.go b/ecc/bls12-377/ecdsa/doc.go
index 90a024703d..43ec2e3578 100644
--- a/ecc/bls12-377/ecdsa/doc.go
+++ b/ecc/bls12-377/ecdsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/ecdsa/ecdsa.go b/ecc/bls12-377/ecdsa/ecdsa.go
index f14ab0d480..cf6510d50f 100644
--- a/ecc/bls12-377/ecdsa/ecdsa.go
+++ b/ecc/bls12-377/ecdsa/ecdsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/ecdsa/ecdsa_test.go b/ecc/bls12-377/ecdsa/ecdsa_test.go
index ccc12b07df..630c0fa001 100644
--- a/ecc/bls12-377/ecdsa/ecdsa_test.go
+++ b/ecc/bls12-377/ecdsa/ecdsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/ecdsa/marshal.go b/ecc/bls12-377/ecdsa/marshal.go
index 8f1caa7d3b..a7ab2f4905 100644
--- a/ecc/bls12-377/ecdsa/marshal.go
+++ b/ecc/bls12-377/ecdsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/ecdsa/marshal_test.go b/ecc/bls12-377/ecdsa/marshal_test.go
index 68096e88c3..7a375c09e9 100644
--- a/ecc/bls12-377/ecdsa/marshal_test.go
+++ b/ecc/bls12-377/ecdsa/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fflonk/doc.go b/ecc/bls12-377/fflonk/doc.go
index 67a8094e35..a2506720a8 100644
--- a/ecc/bls12-377/fflonk/doc.go
+++ b/ecc/bls12-377/fflonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fflonk/example_test.go b/ecc/bls12-377/fflonk/example_test.go
index 18961c170f..85f41a09fd 100644
--- a/ecc/bls12-377/fflonk/example_test.go
+++ b/ecc/bls12-377/fflonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fflonk/fflonk.go b/ecc/bls12-377/fflonk/fflonk.go
index f0a72f53a7..dda82a3dd2 100644
--- a/ecc/bls12-377/fflonk/fflonk.go
+++ b/ecc/bls12-377/fflonk/fflonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fflonk/fflonk_test.go b/ecc/bls12-377/fflonk/fflonk_test.go
index 3585194eca..e83131d8e4 100644
--- a/ecc/bls12-377/fflonk/fflonk_test.go
+++ b/ecc/bls12-377/fflonk/fflonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fflonk/marshal.go b/ecc/bls12-377/fflonk/marshal.go
index 0a379f4681..4ce930609d 100644
--- a/ecc/bls12-377/fflonk/marshal.go
+++ b/ecc/bls12-377/fflonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/arith.go b/ecc/bls12-377/fp/arith.go
index bb63552f5a..5c9905de80 100644
--- a/ecc/bls12-377/fp/arith.go
+++ b/ecc/bls12-377/fp/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/asm_adx.go b/ecc/bls12-377/fp/asm_adx.go
index 75e92992fe..8d85a11345 100644
--- a/ecc/bls12-377/fp/asm_adx.go
+++ b/ecc/bls12-377/fp/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/asm_noadx.go b/ecc/bls12-377/fp/asm_noadx.go
index 304dfb7209..75ca96d775 100644
--- a/ecc/bls12-377/fp/asm_noadx.go
+++ b/ecc/bls12-377/fp/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/doc.go b/ecc/bls12-377/fp/doc.go
index 9b31780d36..94fc02f30e 100644
--- a/ecc/bls12-377/fp/doc.go
+++ b/ecc/bls12-377/fp/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/element.go b/ecc/bls12-377/fp/element.go
index 9d985aecc3..163bfa737b 100644
--- a/ecc/bls12-377/fp/element.go
+++ b/ecc/bls12-377/fp/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/element_amd64.go b/ecc/bls12-377/fp/element_amd64.go
index 9cee062e5b..1a6e1cf5eb 100644
--- a/ecc/bls12-377/fp/element_amd64.go
+++ b/ecc/bls12-377/fp/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/element_amd64.s b/ecc/bls12-377/fp/element_amd64.s
index 719aecfbe9..db64f3a580 100644
--- a/ecc/bls12-377/fp/element_amd64.s
+++ b/ecc/bls12-377/fp/element_amd64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/element_arm64.go b/ecc/bls12-377/fp/element_arm64.go
index 4f2adff0c6..9126fb56b6 100644
--- a/ecc/bls12-377/fp/element_arm64.go
+++ b/ecc/bls12-377/fp/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/element_arm64.s b/ecc/bls12-377/fp/element_arm64.s
index b4dfd1612c..b656459e76 100644
--- a/ecc/bls12-377/fp/element_arm64.s
+++ b/ecc/bls12-377/fp/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/element_exp.go b/ecc/bls12-377/fp/element_exp.go
index 004fc14c8e..34f76d1aa7 100644
--- a/ecc/bls12-377/fp/element_exp.go
+++ b/ecc/bls12-377/fp/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/element_purego.go b/ecc/bls12-377/fp/element_purego.go
index 5d4a91ae59..8a2e93e999 100644
--- a/ecc/bls12-377/fp/element_purego.go
+++ b/ecc/bls12-377/fp/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/element_test.go b/ecc/bls12-377/fp/element_test.go
index 0538bba1d7..5e185773b5 100644
--- a/ecc/bls12-377/fp/element_test.go
+++ b/ecc/bls12-377/fp/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/hash_to_field/doc.go b/ecc/bls12-377/fp/hash_to_field/doc.go
index 08de8cbe24..965b38c7d6 100644
--- a/ecc/bls12-377/fp/hash_to_field/doc.go
+++ b/ecc/bls12-377/fp/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/hash_to_field/hash_to_field.go b/ecc/bls12-377/fp/hash_to_field/hash_to_field.go
index 2ac45dc6ea..2797a9aa87 100644
--- a/ecc/bls12-377/fp/hash_to_field/hash_to_field.go
+++ b/ecc/bls12-377/fp/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/hash_to_field/hash_to_field_test.go b/ecc/bls12-377/fp/hash_to_field/hash_to_field_test.go
index 320d2b607b..453d6658ad 100644
--- a/ecc/bls12-377/fp/hash_to_field/hash_to_field_test.go
+++ b/ecc/bls12-377/fp/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/vector.go b/ecc/bls12-377/fp/vector.go
index 93189079db..3ef556345e 100644
--- a/ecc/bls12-377/fp/vector.go
+++ b/ecc/bls12-377/fp/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/vector_purego.go b/ecc/bls12-377/fp/vector_purego.go
index 0cda361871..85670501df 100644
--- a/ecc/bls12-377/fp/vector_purego.go
+++ b/ecc/bls12-377/fp/vector_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fp/vector_test.go b/ecc/bls12-377/fp/vector_test.go
index 7075283b49..42b800c19d 100644
--- a/ecc/bls12-377/fp/vector_test.go
+++ b/ecc/bls12-377/fp/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/arith.go b/ecc/bls12-377/fr/arith.go
index dbba8a9ae4..8dbae56e32 100644
--- a/ecc/bls12-377/fr/arith.go
+++ b/ecc/bls12-377/fr/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/asm_adx.go b/ecc/bls12-377/fr/asm_adx.go
index 9b970335f1..52421cc159 100644
--- a/ecc/bls12-377/fr/asm_adx.go
+++ b/ecc/bls12-377/fr/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/asm_avx.go b/ecc/bls12-377/fr/asm_avx.go
index 2a0a166ed4..f89a44926d 100644
--- a/ecc/bls12-377/fr/asm_avx.go
+++ b/ecc/bls12-377/fr/asm_avx.go
@@ -1,6 +1,6 @@
 //go:build !noavx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/asm_noadx.go b/ecc/bls12-377/fr/asm_noadx.go
index 96741014f2..9c9c9dab5d 100644
--- a/ecc/bls12-377/fr/asm_noadx.go
+++ b/ecc/bls12-377/fr/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/asm_noavx.go b/ecc/bls12-377/fr/asm_noavx.go
index 3cb6968fb8..ae86f75e7f 100644
--- a/ecc/bls12-377/fr/asm_noavx.go
+++ b/ecc/bls12-377/fr/asm_noavx.go
@@ -1,6 +1,6 @@
 //go:build noavx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/doc.go b/ecc/bls12-377/fr/doc.go
index 45501aa438..50e4ef6350 100644
--- a/ecc/bls12-377/fr/doc.go
+++ b/ecc/bls12-377/fr/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/element.go b/ecc/bls12-377/fr/element.go
index 890c54488a..85bd40bb35 100644
--- a/ecc/bls12-377/fr/element.go
+++ b/ecc/bls12-377/fr/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/element_amd64.go b/ecc/bls12-377/fr/element_amd64.go
index 4c3f2a8567..7e76a943a1 100644
--- a/ecc/bls12-377/fr/element_amd64.go
+++ b/ecc/bls12-377/fr/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/element_amd64.s b/ecc/bls12-377/fr/element_amd64.s
index a7c6ffae66..41c54b1aa6 100644
--- a/ecc/bls12-377/fr/element_amd64.s
+++ b/ecc/bls12-377/fr/element_amd64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/element_arm64.go b/ecc/bls12-377/fr/element_arm64.go
index 932dc0a9ec..905e9e735b 100644
--- a/ecc/bls12-377/fr/element_arm64.go
+++ b/ecc/bls12-377/fr/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/element_arm64.s b/ecc/bls12-377/fr/element_arm64.s
index ef16eaba35..0668975118 100644
--- a/ecc/bls12-377/fr/element_arm64.s
+++ b/ecc/bls12-377/fr/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/element_exp.go b/ecc/bls12-377/fr/element_exp.go
index b007249841..9a42661630 100644
--- a/ecc/bls12-377/fr/element_exp.go
+++ b/ecc/bls12-377/fr/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/element_purego.go b/ecc/bls12-377/fr/element_purego.go
index de0345c006..537648f3d1 100644
--- a/ecc/bls12-377/fr/element_purego.go
+++ b/ecc/bls12-377/fr/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/element_test.go b/ecc/bls12-377/fr/element_test.go
index 9321545c8f..4f35f53f88 100644
--- a/ecc/bls12-377/fr/element_test.go
+++ b/ecc/bls12-377/fr/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/fft/bitreverse.go b/ecc/bls12-377/fr/fft/bitreverse.go
index c7c5bf6c29..e68fdb1736 100644
--- a/ecc/bls12-377/fr/fft/bitreverse.go
+++ b/ecc/bls12-377/fr/fft/bitreverse.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/fft/bitreverse_test.go b/ecc/bls12-377/fr/fft/bitreverse_test.go
index 26ed691e24..70abd18684 100644
--- a/ecc/bls12-377/fr/fft/bitreverse_test.go
+++ b/ecc/bls12-377/fr/fft/bitreverse_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/fft/doc.go b/ecc/bls12-377/fr/fft/doc.go
index 4cce0f9779..8176d8e77a 100644
--- a/ecc/bls12-377/fr/fft/doc.go
+++ b/ecc/bls12-377/fr/fft/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/fft/domain.go b/ecc/bls12-377/fr/fft/domain.go
index 2ed09b4050..84be489163 100644
--- a/ecc/bls12-377/fr/fft/domain.go
+++ b/ecc/bls12-377/fr/fft/domain.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/fft/domain_test.go b/ecc/bls12-377/fr/fft/domain_test.go
index e445d3cc12..7049120e6a 100644
--- a/ecc/bls12-377/fr/fft/domain_test.go
+++ b/ecc/bls12-377/fr/fft/domain_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/fft/fft.go b/ecc/bls12-377/fr/fft/fft.go
index 1877098040..e6d228ded7 100644
--- a/ecc/bls12-377/fr/fft/fft.go
+++ b/ecc/bls12-377/fr/fft/fft.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/fft/fft_test.go b/ecc/bls12-377/fr/fft/fft_test.go
index d20a8306b4..cf3b2711a8 100644
--- a/ecc/bls12-377/fr/fft/fft_test.go
+++ b/ecc/bls12-377/fr/fft/fft_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/fft/options.go b/ecc/bls12-377/fr/fft/options.go
index 853704d864..b4b1c04b6d 100644
--- a/ecc/bls12-377/fr/fft/options.go
+++ b/ecc/bls12-377/fr/fft/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/fri/doc.go b/ecc/bls12-377/fr/fri/doc.go
index cea69fc79a..164ee83268 100644
--- a/ecc/bls12-377/fr/fri/doc.go
+++ b/ecc/bls12-377/fr/fri/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/fri/fri.go b/ecc/bls12-377/fr/fri/fri.go
index 118feef439..1b2965c4d7 100644
--- a/ecc/bls12-377/fr/fri/fri.go
+++ b/ecc/bls12-377/fr/fri/fri.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/fri/fri_test.go b/ecc/bls12-377/fr/fri/fri_test.go
index 8c637fa732..8dd67628d6 100644
--- a/ecc/bls12-377/fr/fri/fri_test.go
+++ b/ecc/bls12-377/fr/fri/fri_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/generator.go b/ecc/bls12-377/fr/generator.go
index 56a2ff142f..7ca9c27bb9 100644
--- a/ecc/bls12-377/fr/generator.go
+++ b/ecc/bls12-377/fr/generator.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/gkr/gkr.go b/ecc/bls12-377/fr/gkr/gkr.go
index c55db62a4e..00eacd7837 100644
--- a/ecc/bls12-377/fr/gkr/gkr.go
+++ b/ecc/bls12-377/fr/gkr/gkr.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/gkr/gkr_test.go b/ecc/bls12-377/fr/gkr/gkr_test.go
index b85efd5dab..290ea4680b 100644
--- a/ecc/bls12-377/fr/gkr/gkr_test.go
+++ b/ecc/bls12-377/fr/gkr/gkr_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/hash_to_field/doc.go b/ecc/bls12-377/fr/hash_to_field/doc.go
index 589b45369b..1918c68a3b 100644
--- a/ecc/bls12-377/fr/hash_to_field/doc.go
+++ b/ecc/bls12-377/fr/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/hash_to_field/hash_to_field.go b/ecc/bls12-377/fr/hash_to_field/hash_to_field.go
index 19832eace7..57d2bf2539 100644
--- a/ecc/bls12-377/fr/hash_to_field/hash_to_field.go
+++ b/ecc/bls12-377/fr/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/hash_to_field/hash_to_field_test.go b/ecc/bls12-377/fr/hash_to_field/hash_to_field_test.go
index 2db6460369..76d0d7dbeb 100644
--- a/ecc/bls12-377/fr/hash_to_field/hash_to_field_test.go
+++ b/ecc/bls12-377/fr/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/iop/doc.go b/ecc/bls12-377/fr/iop/doc.go
index 2ef06dfe1a..6c9a441cc1 100644
--- a/ecc/bls12-377/fr/iop/doc.go
+++ b/ecc/bls12-377/fr/iop/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/iop/expressions.go b/ecc/bls12-377/fr/iop/expressions.go
index b9195244b0..3dc9d8b21e 100644
--- a/ecc/bls12-377/fr/iop/expressions.go
+++ b/ecc/bls12-377/fr/iop/expressions.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/iop/expressions_test.go b/ecc/bls12-377/fr/iop/expressions_test.go
index a116047266..e9d1270b80 100644
--- a/ecc/bls12-377/fr/iop/expressions_test.go
+++ b/ecc/bls12-377/fr/iop/expressions_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/iop/polynomial.go b/ecc/bls12-377/fr/iop/polynomial.go
index c793a71407..f120c5d575 100644
--- a/ecc/bls12-377/fr/iop/polynomial.go
+++ b/ecc/bls12-377/fr/iop/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/iop/polynomial_test.go b/ecc/bls12-377/fr/iop/polynomial_test.go
index a7b0ec595a..dc7644d8b2 100644
--- a/ecc/bls12-377/fr/iop/polynomial_test.go
+++ b/ecc/bls12-377/fr/iop/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/iop/quotient.go b/ecc/bls12-377/fr/iop/quotient.go
index 44ad792b5d..15e45d68d5 100644
--- a/ecc/bls12-377/fr/iop/quotient.go
+++ b/ecc/bls12-377/fr/iop/quotient.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/iop/quotient_test.go b/ecc/bls12-377/fr/iop/quotient_test.go
index 2050b7086f..5fe4378235 100644
--- a/ecc/bls12-377/fr/iop/quotient_test.go
+++ b/ecc/bls12-377/fr/iop/quotient_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/iop/ratios.go b/ecc/bls12-377/fr/iop/ratios.go
index 511a9a8b92..6cb3443296 100644
--- a/ecc/bls12-377/fr/iop/ratios.go
+++ b/ecc/bls12-377/fr/iop/ratios.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/iop/ratios_test.go b/ecc/bls12-377/fr/iop/ratios_test.go
index 02c4080532..6a993563e0 100644
--- a/ecc/bls12-377/fr/iop/ratios_test.go
+++ b/ecc/bls12-377/fr/iop/ratios_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/iop/utils.go b/ecc/bls12-377/fr/iop/utils.go
index e98ccac1be..ab09e07dc9 100644
--- a/ecc/bls12-377/fr/iop/utils.go
+++ b/ecc/bls12-377/fr/iop/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/mimc/doc.go b/ecc/bls12-377/fr/mimc/doc.go
index 900b977185..946e0dafaa 100644
--- a/ecc/bls12-377/fr/mimc/doc.go
+++ b/ecc/bls12-377/fr/mimc/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/mimc/mimc.go b/ecc/bls12-377/fr/mimc/mimc.go
index 43728abd36..4c4aec6c6c 100644
--- a/ecc/bls12-377/fr/mimc/mimc.go
+++ b/ecc/bls12-377/fr/mimc/mimc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/mimc/mimc_test.go b/ecc/bls12-377/fr/mimc/mimc_test.go
index b018112257..c89db0263f 100644
--- a/ecc/bls12-377/fr/mimc/mimc_test.go
+++ b/ecc/bls12-377/fr/mimc/mimc_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/mimc/options.go b/ecc/bls12-377/fr/mimc/options.go
index a83f77c05d..6130b098ce 100644
--- a/ecc/bls12-377/fr/mimc/options.go
+++ b/ecc/bls12-377/fr/mimc/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/pedersen/doc.go b/ecc/bls12-377/fr/pedersen/doc.go
index 2e24034936..dff1285d0e 100644
--- a/ecc/bls12-377/fr/pedersen/doc.go
+++ b/ecc/bls12-377/fr/pedersen/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/pedersen/example_test.go b/ecc/bls12-377/fr/pedersen/example_test.go
index cd7f417b6c..1d14b787de 100644
--- a/ecc/bls12-377/fr/pedersen/example_test.go
+++ b/ecc/bls12-377/fr/pedersen/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/pedersen/pedersen.go b/ecc/bls12-377/fr/pedersen/pedersen.go
index 59a189ad4e..fb1b41b90b 100644
--- a/ecc/bls12-377/fr/pedersen/pedersen.go
+++ b/ecc/bls12-377/fr/pedersen/pedersen.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/pedersen/pedersen_test.go b/ecc/bls12-377/fr/pedersen/pedersen_test.go
index 6178150443..fd3bee6fdc 100644
--- a/ecc/bls12-377/fr/pedersen/pedersen_test.go
+++ b/ecc/bls12-377/fr/pedersen/pedersen_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/permutation/doc.go b/ecc/bls12-377/fr/permutation/doc.go
index e24cd82923..4f2ea7b2e4 100644
--- a/ecc/bls12-377/fr/permutation/doc.go
+++ b/ecc/bls12-377/fr/permutation/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/permutation/permutation.go b/ecc/bls12-377/fr/permutation/permutation.go
index 81e3841775..46cc3d9f51 100644
--- a/ecc/bls12-377/fr/permutation/permutation.go
+++ b/ecc/bls12-377/fr/permutation/permutation.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/permutation/permutation_test.go b/ecc/bls12-377/fr/permutation/permutation_test.go
index 3f781c324a..8b61c3adca 100644
--- a/ecc/bls12-377/fr/permutation/permutation_test.go
+++ b/ecc/bls12-377/fr/permutation/permutation_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/plookup/doc.go b/ecc/bls12-377/fr/plookup/doc.go
index 7a02c59719..5507122fab 100644
--- a/ecc/bls12-377/fr/plookup/doc.go
+++ b/ecc/bls12-377/fr/plookup/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/plookup/plookup_test.go b/ecc/bls12-377/fr/plookup/plookup_test.go
index 317b54d27f..896fcbd342 100644
--- a/ecc/bls12-377/fr/plookup/plookup_test.go
+++ b/ecc/bls12-377/fr/plookup/plookup_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/plookup/table.go b/ecc/bls12-377/fr/plookup/table.go
index e23e0c54ff..9a63dfcd77 100644
--- a/ecc/bls12-377/fr/plookup/table.go
+++ b/ecc/bls12-377/fr/plookup/table.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/plookup/vector.go b/ecc/bls12-377/fr/plookup/vector.go
index 3b074b2bed..0027866651 100644
--- a/ecc/bls12-377/fr/plookup/vector.go
+++ b/ecc/bls12-377/fr/plookup/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/polynomial/doc.go b/ecc/bls12-377/fr/polynomial/doc.go
index fd96328e8f..ead3b5cba5 100644
--- a/ecc/bls12-377/fr/polynomial/doc.go
+++ b/ecc/bls12-377/fr/polynomial/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/polynomial/multilin.go b/ecc/bls12-377/fr/polynomial/multilin.go
index d7050da2a0..3bdd125bfa 100644
--- a/ecc/bls12-377/fr/polynomial/multilin.go
+++ b/ecc/bls12-377/fr/polynomial/multilin.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/polynomial/multilin_test.go b/ecc/bls12-377/fr/polynomial/multilin_test.go
index ec48360ad2..2cd7193542 100644
--- a/ecc/bls12-377/fr/polynomial/multilin_test.go
+++ b/ecc/bls12-377/fr/polynomial/multilin_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/polynomial/polynomial.go b/ecc/bls12-377/fr/polynomial/polynomial.go
index c108cbf852..c0cdd27a1f 100644
--- a/ecc/bls12-377/fr/polynomial/polynomial.go
+++ b/ecc/bls12-377/fr/polynomial/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/polynomial/polynomial_test.go b/ecc/bls12-377/fr/polynomial/polynomial_test.go
index 9d79bac673..7d12bccb7c 100644
--- a/ecc/bls12-377/fr/polynomial/polynomial_test.go
+++ b/ecc/bls12-377/fr/polynomial/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/polynomial/pool.go b/ecc/bls12-377/fr/polynomial/pool.go
index 939ed4d05e..37c598ee69 100644
--- a/ecc/bls12-377/fr/polynomial/pool.go
+++ b/ecc/bls12-377/fr/polynomial/pool.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/poseidon2/poseidon2.go b/ecc/bls12-377/fr/poseidon2/poseidon2.go
index 25b0cca670..a180904e0e 100644
--- a/ecc/bls12-377/fr/poseidon2/poseidon2.go
+++ b/ecc/bls12-377/fr/poseidon2/poseidon2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/poseidon2/poseidon2_test.go b/ecc/bls12-377/fr/poseidon2/poseidon2_test.go
index 220cc78db1..c123dee64d 100644
--- a/ecc/bls12-377/fr/poseidon2/poseidon2_test.go
+++ b/ecc/bls12-377/fr/poseidon2/poseidon2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/sis/sis.go b/ecc/bls12-377/fr/sis/sis.go
index f05720aa86..9d4e82fe45 100644
--- a/ecc/bls12-377/fr/sis/sis.go
+++ b/ecc/bls12-377/fr/sis/sis.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/sis/sis_fft.go b/ecc/bls12-377/fr/sis/sis_fft.go
index 79a4686489..f4f4db3abb 100644
--- a/ecc/bls12-377/fr/sis/sis_fft.go
+++ b/ecc/bls12-377/fr/sis/sis_fft.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/sis/sis_test.go b/ecc/bls12-377/fr/sis/sis_test.go
index 92834d50c4..f4292af51f 100644
--- a/ecc/bls12-377/fr/sis/sis_test.go
+++ b/ecc/bls12-377/fr/sis/sis_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/sumcheck/sumcheck.go b/ecc/bls12-377/fr/sumcheck/sumcheck.go
index f475849557..b3258bfaaa 100644
--- a/ecc/bls12-377/fr/sumcheck/sumcheck.go
+++ b/ecc/bls12-377/fr/sumcheck/sumcheck.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/sumcheck/sumcheck_test.go b/ecc/bls12-377/fr/sumcheck/sumcheck_test.go
index bccfcf0c85..6634b5b724 100644
--- a/ecc/bls12-377/fr/sumcheck/sumcheck_test.go
+++ b/ecc/bls12-377/fr/sumcheck/sumcheck_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/test_vector_utils/test_vector_utils.go b/ecc/bls12-377/fr/test_vector_utils/test_vector_utils.go
index b5a617a620..f6cbca6f6e 100644
--- a/ecc/bls12-377/fr/test_vector_utils/test_vector_utils.go
+++ b/ecc/bls12-377/fr/test_vector_utils/test_vector_utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/vector.go b/ecc/bls12-377/fr/vector.go
index 4654b1b2d3..7792a6f73b 100644
--- a/ecc/bls12-377/fr/vector.go
+++ b/ecc/bls12-377/fr/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/vector_amd64.go b/ecc/bls12-377/fr/vector_amd64.go
index a7dcec3b25..e3565da46a 100644
--- a/ecc/bls12-377/fr/vector_amd64.go
+++ b/ecc/bls12-377/fr/vector_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/vector_purego.go b/ecc/bls12-377/fr/vector_purego.go
index db43e73504..6608e394c7 100644
--- a/ecc/bls12-377/fr/vector_purego.go
+++ b/ecc/bls12-377/fr/vector_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || !amd64
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/fr/vector_test.go b/ecc/bls12-377/fr/vector_test.go
index f6179e7824..88c4ef318f 100644
--- a/ecc/bls12-377/fr/vector_test.go
+++ b/ecc/bls12-377/fr/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/g1.go b/ecc/bls12-377/g1.go
index ade683e458..9eb0e4c388 100644
--- a/ecc/bls12-377/g1.go
+++ b/ecc/bls12-377/g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/g1_test.go b/ecc/bls12-377/g1_test.go
index 97108da122..f32180292a 100644
--- a/ecc/bls12-377/g1_test.go
+++ b/ecc/bls12-377/g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/g2.go b/ecc/bls12-377/g2.go
index 8c4a0b487d..fa86a3b44b 100644
--- a/ecc/bls12-377/g2.go
+++ b/ecc/bls12-377/g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/g2_test.go b/ecc/bls12-377/g2_test.go
index 748685af26..eba5190a5c 100644
--- a/ecc/bls12-377/g2_test.go
+++ b/ecc/bls12-377/g2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/hash_to_g1.go b/ecc/bls12-377/hash_to_g1.go
index 5359d355a8..e3206b4193 100644
--- a/ecc/bls12-377/hash_to_g1.go
+++ b/ecc/bls12-377/hash_to_g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/hash_to_g1_test.go b/ecc/bls12-377/hash_to_g1_test.go
index 75f2c223cf..bf7a0cfa68 100644
--- a/ecc/bls12-377/hash_to_g1_test.go
+++ b/ecc/bls12-377/hash_to_g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/hash_to_g2.go b/ecc/bls12-377/hash_to_g2.go
index 9a8780de73..264c47c2d3 100644
--- a/ecc/bls12-377/hash_to_g2.go
+++ b/ecc/bls12-377/hash_to_g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/hash_to_g2_test.go b/ecc/bls12-377/hash_to_g2_test.go
index d1a47194a0..f48d73e442 100644
--- a/ecc/bls12-377/hash_to_g2_test.go
+++ b/ecc/bls12-377/hash_to_g2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/internal/fptower/asm.go b/ecc/bls12-377/internal/fptower/asm.go
index 7d64458b6c..c08e8f1574 100644
--- a/ecc/bls12-377/internal/fptower/asm.go
+++ b/ecc/bls12-377/internal/fptower/asm.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/internal/fptower/asm_noadx.go b/ecc/bls12-377/internal/fptower/asm_noadx.go
index 28588f65a0..1dc20b4991 100644
--- a/ecc/bls12-377/internal/fptower/asm_noadx.go
+++ b/ecc/bls12-377/internal/fptower/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/internal/fptower/e12.go b/ecc/bls12-377/internal/fptower/e12.go
index 1422adecd1..b27438a45d 100644
--- a/ecc/bls12-377/internal/fptower/e12.go
+++ b/ecc/bls12-377/internal/fptower/e12.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/internal/fptower/e12_test.go b/ecc/bls12-377/internal/fptower/e12_test.go
index 6cca730b47..5454fd7c79 100644
--- a/ecc/bls12-377/internal/fptower/e12_test.go
+++ b/ecc/bls12-377/internal/fptower/e12_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/internal/fptower/e2.go b/ecc/bls12-377/internal/fptower/e2.go
index 9fbdbd3d7c..37150e0dfe 100644
--- a/ecc/bls12-377/internal/fptower/e2.go
+++ b/ecc/bls12-377/internal/fptower/e2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/internal/fptower/e2_amd64.go b/ecc/bls12-377/internal/fptower/e2_amd64.go
index 6074023131..0089530007 100644
--- a/ecc/bls12-377/internal/fptower/e2_amd64.go
+++ b/ecc/bls12-377/internal/fptower/e2_amd64.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/internal/fptower/e2_amd64.s b/ecc/bls12-377/internal/fptower/e2_amd64.s
index 32e77dd787..e40a4d91e0 100644
--- a/ecc/bls12-377/internal/fptower/e2_amd64.s
+++ b/ecc/bls12-377/internal/fptower/e2_amd64.s
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 #include "textflag.h"
diff --git a/ecc/bls12-377/internal/fptower/e2_fallback.go b/ecc/bls12-377/internal/fptower/e2_fallback.go
index 3dff96dcea..7a2461ec53 100644
--- a/ecc/bls12-377/internal/fptower/e2_fallback.go
+++ b/ecc/bls12-377/internal/fptower/e2_fallback.go
@@ -1,6 +1,6 @@
 //go:build !amd64
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/internal/fptower/e2_test.go b/ecc/bls12-377/internal/fptower/e2_test.go
index d9653036c5..0506b172df 100644
--- a/ecc/bls12-377/internal/fptower/e2_test.go
+++ b/ecc/bls12-377/internal/fptower/e2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/internal/fptower/e6.go b/ecc/bls12-377/internal/fptower/e6.go
index a3bd71a6cc..13fdfdd297 100644
--- a/ecc/bls12-377/internal/fptower/e6.go
+++ b/ecc/bls12-377/internal/fptower/e6.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/internal/fptower/e6_test.go b/ecc/bls12-377/internal/fptower/e6_test.go
index d53b72ec93..e6367f2b65 100644
--- a/ecc/bls12-377/internal/fptower/e6_test.go
+++ b/ecc/bls12-377/internal/fptower/e6_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/kzg/doc.go b/ecc/bls12-377/kzg/doc.go
index 226614bbdf..3a86419c48 100644
--- a/ecc/bls12-377/kzg/doc.go
+++ b/ecc/bls12-377/kzg/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/kzg/kzg.go b/ecc/bls12-377/kzg/kzg.go
index a9a5d0fd98..8cdc8b8333 100644
--- a/ecc/bls12-377/kzg/kzg.go
+++ b/ecc/bls12-377/kzg/kzg.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/kzg/kzg_test.go b/ecc/bls12-377/kzg/kzg_test.go
index a357b996d0..50227679ff 100644
--- a/ecc/bls12-377/kzg/kzg_test.go
+++ b/ecc/bls12-377/kzg/kzg_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/kzg/marshal.go b/ecc/bls12-377/kzg/marshal.go
index 5561cb3786..e9315a3cff 100644
--- a/ecc/bls12-377/kzg/marshal.go
+++ b/ecc/bls12-377/kzg/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/kzg/utils.go b/ecc/bls12-377/kzg/utils.go
index 10248b3ae3..42f38d01d7 100644
--- a/ecc/bls12-377/kzg/utils.go
+++ b/ecc/bls12-377/kzg/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/marshal.go b/ecc/bls12-377/marshal.go
index e6be30a2ee..770f18c7e1 100644
--- a/ecc/bls12-377/marshal.go
+++ b/ecc/bls12-377/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/marshal_test.go b/ecc/bls12-377/marshal_test.go
index 705a756a02..73d236a615 100644
--- a/ecc/bls12-377/marshal_test.go
+++ b/ecc/bls12-377/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/multiexp.go b/ecc/bls12-377/multiexp.go
index 5aa960be69..93bbfa633d 100644
--- a/ecc/bls12-377/multiexp.go
+++ b/ecc/bls12-377/multiexp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/multiexp_affine.go b/ecc/bls12-377/multiexp_affine.go
index ff392b910d..d82f02e47b 100644
--- a/ecc/bls12-377/multiexp_affine.go
+++ b/ecc/bls12-377/multiexp_affine.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/multiexp_jacobian.go b/ecc/bls12-377/multiexp_jacobian.go
index 9e4f26ab79..5bc761f304 100644
--- a/ecc/bls12-377/multiexp_jacobian.go
+++ b/ecc/bls12-377/multiexp_jacobian.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/multiexp_test.go b/ecc/bls12-377/multiexp_test.go
index 2dc1ccd9a4..d979957a5d 100644
--- a/ecc/bls12-377/multiexp_test.go
+++ b/ecc/bls12-377/multiexp_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/pairing_test.go b/ecc/bls12-377/pairing_test.go
index d5a277eabf..b749d09bda 100644
--- a/ecc/bls12-377/pairing_test.go
+++ b/ecc/bls12-377/pairing_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/shplonk/doc.go b/ecc/bls12-377/shplonk/doc.go
index 0367893999..d63c7a3ddf 100644
--- a/ecc/bls12-377/shplonk/doc.go
+++ b/ecc/bls12-377/shplonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/shplonk/example_test.go b/ecc/bls12-377/shplonk/example_test.go
index e08750a9e7..796f452dc4 100644
--- a/ecc/bls12-377/shplonk/example_test.go
+++ b/ecc/bls12-377/shplonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/shplonk/marshal.go b/ecc/bls12-377/shplonk/marshal.go
index a2cb0ae8ba..a1c5b31ff0 100644
--- a/ecc/bls12-377/shplonk/marshal.go
+++ b/ecc/bls12-377/shplonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/shplonk/shplonk.go b/ecc/bls12-377/shplonk/shplonk.go
index b9d66a4cc4..f4da6dfd9e 100644
--- a/ecc/bls12-377/shplonk/shplonk.go
+++ b/ecc/bls12-377/shplonk/shplonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/shplonk/shplonk_test.go b/ecc/bls12-377/shplonk/shplonk_test.go
index a43a0677d2..376814e0b3 100644
--- a/ecc/bls12-377/shplonk/shplonk_test.go
+++ b/ecc/bls12-377/shplonk/shplonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/twistededwards/curve.go b/ecc/bls12-377/twistededwards/curve.go
index 5db85c848a..631b4891ec 100644
--- a/ecc/bls12-377/twistededwards/curve.go
+++ b/ecc/bls12-377/twistededwards/curve.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/twistededwards/doc.go b/ecc/bls12-377/twistededwards/doc.go
index 919017a004..d61b244a9a 100644
--- a/ecc/bls12-377/twistededwards/doc.go
+++ b/ecc/bls12-377/twistededwards/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/twistededwards/eddsa/doc.go b/ecc/bls12-377/twistededwards/eddsa/doc.go
index c6e33c0bd7..13f86b768c 100644
--- a/ecc/bls12-377/twistededwards/eddsa/doc.go
+++ b/ecc/bls12-377/twistededwards/eddsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/twistededwards/eddsa/eddsa.go b/ecc/bls12-377/twistededwards/eddsa/eddsa.go
index ba9553e54c..497216dfec 100644
--- a/ecc/bls12-377/twistededwards/eddsa/eddsa.go
+++ b/ecc/bls12-377/twistededwards/eddsa/eddsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/twistededwards/eddsa/eddsa_test.go b/ecc/bls12-377/twistededwards/eddsa/eddsa_test.go
index 4f79ebdf65..c1a5b130ce 100644
--- a/ecc/bls12-377/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bls12-377/twistededwards/eddsa/eddsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/twistededwards/eddsa/marshal.go b/ecc/bls12-377/twistededwards/eddsa/marshal.go
index d50f80abdc..afa43e5d9c 100644
--- a/ecc/bls12-377/twistededwards/eddsa/marshal.go
+++ b/ecc/bls12-377/twistededwards/eddsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/twistededwards/point.go b/ecc/bls12-377/twistededwards/point.go
index aa9333823f..bae514e98c 100644
--- a/ecc/bls12-377/twistededwards/point.go
+++ b/ecc/bls12-377/twistededwards/point.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-377/twistededwards/point_test.go b/ecc/bls12-377/twistededwards/point_test.go
index 0b293e1870..80dab85866 100644
--- a/ecc/bls12-377/twistededwards/point_test.go
+++ b/ecc/bls12-377/twistededwards/point_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/bandersnatch/curve.go b/ecc/bls12-381/bandersnatch/curve.go
index a0223d5646..0662033140 100644
--- a/ecc/bls12-381/bandersnatch/curve.go
+++ b/ecc/bls12-381/bandersnatch/curve.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/bandersnatch/doc.go b/ecc/bls12-381/bandersnatch/doc.go
index 04d84007a8..fa7b431d90 100644
--- a/ecc/bls12-381/bandersnatch/doc.go
+++ b/ecc/bls12-381/bandersnatch/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/bandersnatch/eddsa/doc.go b/ecc/bls12-381/bandersnatch/eddsa/doc.go
index 5581f06406..2426b1d017 100644
--- a/ecc/bls12-381/bandersnatch/eddsa/doc.go
+++ b/ecc/bls12-381/bandersnatch/eddsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/bandersnatch/eddsa/eddsa.go b/ecc/bls12-381/bandersnatch/eddsa/eddsa.go
index c10e701839..5569060705 100644
--- a/ecc/bls12-381/bandersnatch/eddsa/eddsa.go
+++ b/ecc/bls12-381/bandersnatch/eddsa/eddsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/bandersnatch/eddsa/eddsa_test.go b/ecc/bls12-381/bandersnatch/eddsa/eddsa_test.go
index c53bfc6cc8..9d73e340c3 100644
--- a/ecc/bls12-381/bandersnatch/eddsa/eddsa_test.go
+++ b/ecc/bls12-381/bandersnatch/eddsa/eddsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/bandersnatch/eddsa/marshal.go b/ecc/bls12-381/bandersnatch/eddsa/marshal.go
index 39dabf92f7..ecc5b5084f 100644
--- a/ecc/bls12-381/bandersnatch/eddsa/marshal.go
+++ b/ecc/bls12-381/bandersnatch/eddsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/bandersnatch/point.go b/ecc/bls12-381/bandersnatch/point.go
index abe0bc2a92..745154b3ef 100644
--- a/ecc/bls12-381/bandersnatch/point.go
+++ b/ecc/bls12-381/bandersnatch/point.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/bandersnatch/point_test.go b/ecc/bls12-381/bandersnatch/point_test.go
index 09b26f5e34..be843dd4c7 100644
--- a/ecc/bls12-381/bandersnatch/point_test.go
+++ b/ecc/bls12-381/bandersnatch/point_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/ecdsa/doc.go b/ecc/bls12-381/ecdsa/doc.go
index 3f362de501..a38206edf7 100644
--- a/ecc/bls12-381/ecdsa/doc.go
+++ b/ecc/bls12-381/ecdsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/ecdsa/ecdsa.go b/ecc/bls12-381/ecdsa/ecdsa.go
index 514c3c8cfc..fc7c8f4f28 100644
--- a/ecc/bls12-381/ecdsa/ecdsa.go
+++ b/ecc/bls12-381/ecdsa/ecdsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/ecdsa/ecdsa_test.go b/ecc/bls12-381/ecdsa/ecdsa_test.go
index 06e237766f..16dd1fad9d 100644
--- a/ecc/bls12-381/ecdsa/ecdsa_test.go
+++ b/ecc/bls12-381/ecdsa/ecdsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/ecdsa/marshal.go b/ecc/bls12-381/ecdsa/marshal.go
index 943016297d..c25eefd7c4 100644
--- a/ecc/bls12-381/ecdsa/marshal.go
+++ b/ecc/bls12-381/ecdsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/ecdsa/marshal_test.go b/ecc/bls12-381/ecdsa/marshal_test.go
index 7fe8623740..f1c0a8090c 100644
--- a/ecc/bls12-381/ecdsa/marshal_test.go
+++ b/ecc/bls12-381/ecdsa/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fflonk/doc.go b/ecc/bls12-381/fflonk/doc.go
index 67a8094e35..a2506720a8 100644
--- a/ecc/bls12-381/fflonk/doc.go
+++ b/ecc/bls12-381/fflonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fflonk/example_test.go b/ecc/bls12-381/fflonk/example_test.go
index ef4af9cc37..5fc4037015 100644
--- a/ecc/bls12-381/fflonk/example_test.go
+++ b/ecc/bls12-381/fflonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fflonk/fflonk.go b/ecc/bls12-381/fflonk/fflonk.go
index 5636150d29..e2f7fd7a32 100644
--- a/ecc/bls12-381/fflonk/fflonk.go
+++ b/ecc/bls12-381/fflonk/fflonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fflonk/fflonk_test.go b/ecc/bls12-381/fflonk/fflonk_test.go
index 38be0889d1..4eadcfc226 100644
--- a/ecc/bls12-381/fflonk/fflonk_test.go
+++ b/ecc/bls12-381/fflonk/fflonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fflonk/marshal.go b/ecc/bls12-381/fflonk/marshal.go
index f8a6ff57fb..91a45ae3be 100644
--- a/ecc/bls12-381/fflonk/marshal.go
+++ b/ecc/bls12-381/fflonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/arith.go b/ecc/bls12-381/fp/arith.go
index bb63552f5a..5c9905de80 100644
--- a/ecc/bls12-381/fp/arith.go
+++ b/ecc/bls12-381/fp/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/asm_adx.go b/ecc/bls12-381/fp/asm_adx.go
index 75e92992fe..8d85a11345 100644
--- a/ecc/bls12-381/fp/asm_adx.go
+++ b/ecc/bls12-381/fp/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/asm_noadx.go b/ecc/bls12-381/fp/asm_noadx.go
index 304dfb7209..75ca96d775 100644
--- a/ecc/bls12-381/fp/asm_noadx.go
+++ b/ecc/bls12-381/fp/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/doc.go b/ecc/bls12-381/fp/doc.go
index 1c2dab5466..5d70da537c 100644
--- a/ecc/bls12-381/fp/doc.go
+++ b/ecc/bls12-381/fp/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/element.go b/ecc/bls12-381/fp/element.go
index d9e9bc8abd..0a6ab8e21f 100644
--- a/ecc/bls12-381/fp/element.go
+++ b/ecc/bls12-381/fp/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/element_amd64.go b/ecc/bls12-381/fp/element_amd64.go
index 9cee062e5b..1a6e1cf5eb 100644
--- a/ecc/bls12-381/fp/element_amd64.go
+++ b/ecc/bls12-381/fp/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/element_amd64.s b/ecc/bls12-381/fp/element_amd64.s
index 719aecfbe9..db64f3a580 100644
--- a/ecc/bls12-381/fp/element_amd64.s
+++ b/ecc/bls12-381/fp/element_amd64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/element_arm64.go b/ecc/bls12-381/fp/element_arm64.go
index 59f2277cd2..2777b63249 100644
--- a/ecc/bls12-381/fp/element_arm64.go
+++ b/ecc/bls12-381/fp/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/element_arm64.s b/ecc/bls12-381/fp/element_arm64.s
index b4dfd1612c..b656459e76 100644
--- a/ecc/bls12-381/fp/element_arm64.s
+++ b/ecc/bls12-381/fp/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/element_exp.go b/ecc/bls12-381/fp/element_exp.go
index 4c05637d56..b21cc6041e 100644
--- a/ecc/bls12-381/fp/element_exp.go
+++ b/ecc/bls12-381/fp/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/element_purego.go b/ecc/bls12-381/fp/element_purego.go
index 911496ec20..f3170f77e0 100644
--- a/ecc/bls12-381/fp/element_purego.go
+++ b/ecc/bls12-381/fp/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/element_test.go b/ecc/bls12-381/fp/element_test.go
index 5a172e4fa7..1218924c46 100644
--- a/ecc/bls12-381/fp/element_test.go
+++ b/ecc/bls12-381/fp/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/hash_to_field/doc.go b/ecc/bls12-381/fp/hash_to_field/doc.go
index 317d96a2fa..ee3058a18b 100644
--- a/ecc/bls12-381/fp/hash_to_field/doc.go
+++ b/ecc/bls12-381/fp/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/hash_to_field/hash_to_field.go b/ecc/bls12-381/fp/hash_to_field/hash_to_field.go
index d54a80c18b..1869f49cc1 100644
--- a/ecc/bls12-381/fp/hash_to_field/hash_to_field.go
+++ b/ecc/bls12-381/fp/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/hash_to_field/hash_to_field_test.go b/ecc/bls12-381/fp/hash_to_field/hash_to_field_test.go
index 2fa293df7c..a34397a2b8 100644
--- a/ecc/bls12-381/fp/hash_to_field/hash_to_field_test.go
+++ b/ecc/bls12-381/fp/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/vector.go b/ecc/bls12-381/fp/vector.go
index 93189079db..3ef556345e 100644
--- a/ecc/bls12-381/fp/vector.go
+++ b/ecc/bls12-381/fp/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/vector_purego.go b/ecc/bls12-381/fp/vector_purego.go
index 0cda361871..85670501df 100644
--- a/ecc/bls12-381/fp/vector_purego.go
+++ b/ecc/bls12-381/fp/vector_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fp/vector_test.go b/ecc/bls12-381/fp/vector_test.go
index 7075283b49..42b800c19d 100644
--- a/ecc/bls12-381/fp/vector_test.go
+++ b/ecc/bls12-381/fp/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/arith.go b/ecc/bls12-381/fr/arith.go
index dbba8a9ae4..8dbae56e32 100644
--- a/ecc/bls12-381/fr/arith.go
+++ b/ecc/bls12-381/fr/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/asm_adx.go b/ecc/bls12-381/fr/asm_adx.go
index 9b970335f1..52421cc159 100644
--- a/ecc/bls12-381/fr/asm_adx.go
+++ b/ecc/bls12-381/fr/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/asm_avx.go b/ecc/bls12-381/fr/asm_avx.go
index 2a0a166ed4..f89a44926d 100644
--- a/ecc/bls12-381/fr/asm_avx.go
+++ b/ecc/bls12-381/fr/asm_avx.go
@@ -1,6 +1,6 @@
 //go:build !noavx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/asm_noadx.go b/ecc/bls12-381/fr/asm_noadx.go
index 96741014f2..9c9c9dab5d 100644
--- a/ecc/bls12-381/fr/asm_noadx.go
+++ b/ecc/bls12-381/fr/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/asm_noavx.go b/ecc/bls12-381/fr/asm_noavx.go
index 3cb6968fb8..ae86f75e7f 100644
--- a/ecc/bls12-381/fr/asm_noavx.go
+++ b/ecc/bls12-381/fr/asm_noavx.go
@@ -1,6 +1,6 @@
 //go:build noavx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/doc.go b/ecc/bls12-381/fr/doc.go
index f7880aa698..89c78bd60d 100644
--- a/ecc/bls12-381/fr/doc.go
+++ b/ecc/bls12-381/fr/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/element.go b/ecc/bls12-381/fr/element.go
index cceff96d20..7fe789341e 100644
--- a/ecc/bls12-381/fr/element.go
+++ b/ecc/bls12-381/fr/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/element_amd64.go b/ecc/bls12-381/fr/element_amd64.go
index 4c3f2a8567..7e76a943a1 100644
--- a/ecc/bls12-381/fr/element_amd64.go
+++ b/ecc/bls12-381/fr/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/element_amd64.s b/ecc/bls12-381/fr/element_amd64.s
index a7c6ffae66..41c54b1aa6 100644
--- a/ecc/bls12-381/fr/element_amd64.s
+++ b/ecc/bls12-381/fr/element_amd64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/element_arm64.go b/ecc/bls12-381/fr/element_arm64.go
index 6f8a9cb915..a15a7d206e 100644
--- a/ecc/bls12-381/fr/element_arm64.go
+++ b/ecc/bls12-381/fr/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/element_arm64.s b/ecc/bls12-381/fr/element_arm64.s
index ef16eaba35..0668975118 100644
--- a/ecc/bls12-381/fr/element_arm64.s
+++ b/ecc/bls12-381/fr/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/element_exp.go b/ecc/bls12-381/fr/element_exp.go
index b57921366d..9c01c57f9c 100644
--- a/ecc/bls12-381/fr/element_exp.go
+++ b/ecc/bls12-381/fr/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/element_purego.go b/ecc/bls12-381/fr/element_purego.go
index 68bd074b07..42ba2b9bbc 100644
--- a/ecc/bls12-381/fr/element_purego.go
+++ b/ecc/bls12-381/fr/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/element_test.go b/ecc/bls12-381/fr/element_test.go
index b86236997c..3da09ba85c 100644
--- a/ecc/bls12-381/fr/element_test.go
+++ b/ecc/bls12-381/fr/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/fft/bitreverse.go b/ecc/bls12-381/fr/fft/bitreverse.go
index 4fb86452ec..0ecd51d6c5 100644
--- a/ecc/bls12-381/fr/fft/bitreverse.go
+++ b/ecc/bls12-381/fr/fft/bitreverse.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/fft/bitreverse_test.go b/ecc/bls12-381/fr/fft/bitreverse_test.go
index 849a16bb26..70a9b34e71 100644
--- a/ecc/bls12-381/fr/fft/bitreverse_test.go
+++ b/ecc/bls12-381/fr/fft/bitreverse_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/fft/doc.go b/ecc/bls12-381/fr/fft/doc.go
index 4cce0f9779..8176d8e77a 100644
--- a/ecc/bls12-381/fr/fft/doc.go
+++ b/ecc/bls12-381/fr/fft/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/fft/domain.go b/ecc/bls12-381/fr/fft/domain.go
index db35cea919..c0f17725c6 100644
--- a/ecc/bls12-381/fr/fft/domain.go
+++ b/ecc/bls12-381/fr/fft/domain.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/fft/domain_test.go b/ecc/bls12-381/fr/fft/domain_test.go
index e445d3cc12..7049120e6a 100644
--- a/ecc/bls12-381/fr/fft/domain_test.go
+++ b/ecc/bls12-381/fr/fft/domain_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/fft/fft.go b/ecc/bls12-381/fr/fft/fft.go
index 4279e93d18..0627d85ce4 100644
--- a/ecc/bls12-381/fr/fft/fft.go
+++ b/ecc/bls12-381/fr/fft/fft.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/fft/fft_test.go b/ecc/bls12-381/fr/fft/fft_test.go
index 9858710ec2..a2de1acce0 100644
--- a/ecc/bls12-381/fr/fft/fft_test.go
+++ b/ecc/bls12-381/fr/fft/fft_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/fft/options.go b/ecc/bls12-381/fr/fft/options.go
index c1afb7b406..72b1911fae 100644
--- a/ecc/bls12-381/fr/fft/options.go
+++ b/ecc/bls12-381/fr/fft/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/fri/doc.go b/ecc/bls12-381/fr/fri/doc.go
index cea69fc79a..164ee83268 100644
--- a/ecc/bls12-381/fr/fri/doc.go
+++ b/ecc/bls12-381/fr/fri/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/fri/fri.go b/ecc/bls12-381/fr/fri/fri.go
index c09db4bd72..367e15a403 100644
--- a/ecc/bls12-381/fr/fri/fri.go
+++ b/ecc/bls12-381/fr/fri/fri.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/fri/fri_test.go b/ecc/bls12-381/fr/fri/fri_test.go
index 53e29eb47c..52367f9522 100644
--- a/ecc/bls12-381/fr/fri/fri_test.go
+++ b/ecc/bls12-381/fr/fri/fri_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/generator.go b/ecc/bls12-381/fr/generator.go
index fc5403501e..a0d24d2b34 100644
--- a/ecc/bls12-381/fr/generator.go
+++ b/ecc/bls12-381/fr/generator.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/gkr/gkr.go b/ecc/bls12-381/fr/gkr/gkr.go
index bdae61d49f..6f804fa1cd 100644
--- a/ecc/bls12-381/fr/gkr/gkr.go
+++ b/ecc/bls12-381/fr/gkr/gkr.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/gkr/gkr_test.go b/ecc/bls12-381/fr/gkr/gkr_test.go
index b3e91cab0f..f9e1c7eb01 100644
--- a/ecc/bls12-381/fr/gkr/gkr_test.go
+++ b/ecc/bls12-381/fr/gkr/gkr_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/hash_to_field/doc.go b/ecc/bls12-381/fr/hash_to_field/doc.go
index e50410d80a..0a09c4a2a0 100644
--- a/ecc/bls12-381/fr/hash_to_field/doc.go
+++ b/ecc/bls12-381/fr/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/hash_to_field/hash_to_field.go b/ecc/bls12-381/fr/hash_to_field/hash_to_field.go
index ef5ac1e400..a31829a7dc 100644
--- a/ecc/bls12-381/fr/hash_to_field/hash_to_field.go
+++ b/ecc/bls12-381/fr/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/hash_to_field/hash_to_field_test.go b/ecc/bls12-381/fr/hash_to_field/hash_to_field_test.go
index 6965382276..8f764905e6 100644
--- a/ecc/bls12-381/fr/hash_to_field/hash_to_field_test.go
+++ b/ecc/bls12-381/fr/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/iop/doc.go b/ecc/bls12-381/fr/iop/doc.go
index 2ef06dfe1a..6c9a441cc1 100644
--- a/ecc/bls12-381/fr/iop/doc.go
+++ b/ecc/bls12-381/fr/iop/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/iop/expressions.go b/ecc/bls12-381/fr/iop/expressions.go
index 57822fd3cc..c2300c0dfe 100644
--- a/ecc/bls12-381/fr/iop/expressions.go
+++ b/ecc/bls12-381/fr/iop/expressions.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/iop/expressions_test.go b/ecc/bls12-381/fr/iop/expressions_test.go
index c4d4e16273..3e25c5a269 100644
--- a/ecc/bls12-381/fr/iop/expressions_test.go
+++ b/ecc/bls12-381/fr/iop/expressions_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/iop/polynomial.go b/ecc/bls12-381/fr/iop/polynomial.go
index 9d20272e31..840160e8be 100644
--- a/ecc/bls12-381/fr/iop/polynomial.go
+++ b/ecc/bls12-381/fr/iop/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/iop/polynomial_test.go b/ecc/bls12-381/fr/iop/polynomial_test.go
index 96f67f8f82..0c96cbbccd 100644
--- a/ecc/bls12-381/fr/iop/polynomial_test.go
+++ b/ecc/bls12-381/fr/iop/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/iop/quotient.go b/ecc/bls12-381/fr/iop/quotient.go
index 9d75028f1b..1e19d0f1f4 100644
--- a/ecc/bls12-381/fr/iop/quotient.go
+++ b/ecc/bls12-381/fr/iop/quotient.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/iop/quotient_test.go b/ecc/bls12-381/fr/iop/quotient_test.go
index 78035417c0..63f94842c6 100644
--- a/ecc/bls12-381/fr/iop/quotient_test.go
+++ b/ecc/bls12-381/fr/iop/quotient_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/iop/ratios.go b/ecc/bls12-381/fr/iop/ratios.go
index 91946e3bbd..0e15103c88 100644
--- a/ecc/bls12-381/fr/iop/ratios.go
+++ b/ecc/bls12-381/fr/iop/ratios.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/iop/ratios_test.go b/ecc/bls12-381/fr/iop/ratios_test.go
index 0bb1c9b036..a06b933f4c 100644
--- a/ecc/bls12-381/fr/iop/ratios_test.go
+++ b/ecc/bls12-381/fr/iop/ratios_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/iop/utils.go b/ecc/bls12-381/fr/iop/utils.go
index 7f91ba67ee..8492cfd698 100644
--- a/ecc/bls12-381/fr/iop/utils.go
+++ b/ecc/bls12-381/fr/iop/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/mimc/doc.go b/ecc/bls12-381/fr/mimc/doc.go
index 900b977185..946e0dafaa 100644
--- a/ecc/bls12-381/fr/mimc/doc.go
+++ b/ecc/bls12-381/fr/mimc/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/mimc/mimc.go b/ecc/bls12-381/fr/mimc/mimc.go
index 6db9581b75..bedaf2d9e9 100644
--- a/ecc/bls12-381/fr/mimc/mimc.go
+++ b/ecc/bls12-381/fr/mimc/mimc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/mimc/mimc_test.go b/ecc/bls12-381/fr/mimc/mimc_test.go
index b8b94cc1ea..39821d582d 100644
--- a/ecc/bls12-381/fr/mimc/mimc_test.go
+++ b/ecc/bls12-381/fr/mimc/mimc_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/mimc/options.go b/ecc/bls12-381/fr/mimc/options.go
index a9d4a57beb..4d0a163455 100644
--- a/ecc/bls12-381/fr/mimc/options.go
+++ b/ecc/bls12-381/fr/mimc/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/pedersen/doc.go b/ecc/bls12-381/fr/pedersen/doc.go
index 2e24034936..dff1285d0e 100644
--- a/ecc/bls12-381/fr/pedersen/doc.go
+++ b/ecc/bls12-381/fr/pedersen/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/pedersen/example_test.go b/ecc/bls12-381/fr/pedersen/example_test.go
index 2e61788603..a315e6770a 100644
--- a/ecc/bls12-381/fr/pedersen/example_test.go
+++ b/ecc/bls12-381/fr/pedersen/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/pedersen/pedersen.go b/ecc/bls12-381/fr/pedersen/pedersen.go
index 1f9e904bff..e894a675ed 100644
--- a/ecc/bls12-381/fr/pedersen/pedersen.go
+++ b/ecc/bls12-381/fr/pedersen/pedersen.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/pedersen/pedersen_test.go b/ecc/bls12-381/fr/pedersen/pedersen_test.go
index db38149ebd..ead8e8adb8 100644
--- a/ecc/bls12-381/fr/pedersen/pedersen_test.go
+++ b/ecc/bls12-381/fr/pedersen/pedersen_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/permutation/doc.go b/ecc/bls12-381/fr/permutation/doc.go
index e24cd82923..4f2ea7b2e4 100644
--- a/ecc/bls12-381/fr/permutation/doc.go
+++ b/ecc/bls12-381/fr/permutation/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/permutation/permutation.go b/ecc/bls12-381/fr/permutation/permutation.go
index 598db32e18..eb6935d705 100644
--- a/ecc/bls12-381/fr/permutation/permutation.go
+++ b/ecc/bls12-381/fr/permutation/permutation.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/permutation/permutation_test.go b/ecc/bls12-381/fr/permutation/permutation_test.go
index 4777690a36..5b150c4fde 100644
--- a/ecc/bls12-381/fr/permutation/permutation_test.go
+++ b/ecc/bls12-381/fr/permutation/permutation_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/plookup/doc.go b/ecc/bls12-381/fr/plookup/doc.go
index 7a02c59719..5507122fab 100644
--- a/ecc/bls12-381/fr/plookup/doc.go
+++ b/ecc/bls12-381/fr/plookup/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/plookup/plookup_test.go b/ecc/bls12-381/fr/plookup/plookup_test.go
index adaa0f4e0b..b81ed0eee3 100644
--- a/ecc/bls12-381/fr/plookup/plookup_test.go
+++ b/ecc/bls12-381/fr/plookup/plookup_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/plookup/table.go b/ecc/bls12-381/fr/plookup/table.go
index 2a87f1016c..40c9d21218 100644
--- a/ecc/bls12-381/fr/plookup/table.go
+++ b/ecc/bls12-381/fr/plookup/table.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/plookup/vector.go b/ecc/bls12-381/fr/plookup/vector.go
index 81099f9253..12562d7b6a 100644
--- a/ecc/bls12-381/fr/plookup/vector.go
+++ b/ecc/bls12-381/fr/plookup/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/polynomial/doc.go b/ecc/bls12-381/fr/polynomial/doc.go
index fd96328e8f..ead3b5cba5 100644
--- a/ecc/bls12-381/fr/polynomial/doc.go
+++ b/ecc/bls12-381/fr/polynomial/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/polynomial/multilin.go b/ecc/bls12-381/fr/polynomial/multilin.go
index 6880aa976c..164a39c765 100644
--- a/ecc/bls12-381/fr/polynomial/multilin.go
+++ b/ecc/bls12-381/fr/polynomial/multilin.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/polynomial/multilin_test.go b/ecc/bls12-381/fr/polynomial/multilin_test.go
index a10ce6fada..dd3735fa72 100644
--- a/ecc/bls12-381/fr/polynomial/multilin_test.go
+++ b/ecc/bls12-381/fr/polynomial/multilin_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/polynomial/polynomial.go b/ecc/bls12-381/fr/polynomial/polynomial.go
index 97821d7281..032932d488 100644
--- a/ecc/bls12-381/fr/polynomial/polynomial.go
+++ b/ecc/bls12-381/fr/polynomial/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/polynomial/polynomial_test.go b/ecc/bls12-381/fr/polynomial/polynomial_test.go
index 33b8bc86e8..145775477c 100644
--- a/ecc/bls12-381/fr/polynomial/polynomial_test.go
+++ b/ecc/bls12-381/fr/polynomial/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/polynomial/pool.go b/ecc/bls12-381/fr/polynomial/pool.go
index d8703606f0..a899a74931 100644
--- a/ecc/bls12-381/fr/polynomial/pool.go
+++ b/ecc/bls12-381/fr/polynomial/pool.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/poseidon2/poseidon2.go b/ecc/bls12-381/fr/poseidon2/poseidon2.go
index 2933570497..481c81ba72 100644
--- a/ecc/bls12-381/fr/poseidon2/poseidon2.go
+++ b/ecc/bls12-381/fr/poseidon2/poseidon2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/poseidon2/poseidon2_test.go b/ecc/bls12-381/fr/poseidon2/poseidon2_test.go
index 21ad142725..4851c090ee 100644
--- a/ecc/bls12-381/fr/poseidon2/poseidon2_test.go
+++ b/ecc/bls12-381/fr/poseidon2/poseidon2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/sumcheck/sumcheck.go b/ecc/bls12-381/fr/sumcheck/sumcheck.go
index 269f2fa8be..234d182ab0 100644
--- a/ecc/bls12-381/fr/sumcheck/sumcheck.go
+++ b/ecc/bls12-381/fr/sumcheck/sumcheck.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/sumcheck/sumcheck_test.go b/ecc/bls12-381/fr/sumcheck/sumcheck_test.go
index e8c3134886..2ec7d9c166 100644
--- a/ecc/bls12-381/fr/sumcheck/sumcheck_test.go
+++ b/ecc/bls12-381/fr/sumcheck/sumcheck_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/test_vector_utils/test_vector_utils.go b/ecc/bls12-381/fr/test_vector_utils/test_vector_utils.go
index 802a39e536..7a1414595e 100644
--- a/ecc/bls12-381/fr/test_vector_utils/test_vector_utils.go
+++ b/ecc/bls12-381/fr/test_vector_utils/test_vector_utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/vector.go b/ecc/bls12-381/fr/vector.go
index 4654b1b2d3..7792a6f73b 100644
--- a/ecc/bls12-381/fr/vector.go
+++ b/ecc/bls12-381/fr/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/vector_amd64.go b/ecc/bls12-381/fr/vector_amd64.go
index a7dcec3b25..e3565da46a 100644
--- a/ecc/bls12-381/fr/vector_amd64.go
+++ b/ecc/bls12-381/fr/vector_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/vector_purego.go b/ecc/bls12-381/fr/vector_purego.go
index db43e73504..6608e394c7 100644
--- a/ecc/bls12-381/fr/vector_purego.go
+++ b/ecc/bls12-381/fr/vector_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || !amd64
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/fr/vector_test.go b/ecc/bls12-381/fr/vector_test.go
index f6179e7824..88c4ef318f 100644
--- a/ecc/bls12-381/fr/vector_test.go
+++ b/ecc/bls12-381/fr/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/g1.go b/ecc/bls12-381/g1.go
index 6ab856ca90..2d41c10c92 100644
--- a/ecc/bls12-381/g1.go
+++ b/ecc/bls12-381/g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/g1_test.go b/ecc/bls12-381/g1_test.go
index db2782524e..c705b7a678 100644
--- a/ecc/bls12-381/g1_test.go
+++ b/ecc/bls12-381/g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/g2.go b/ecc/bls12-381/g2.go
index a631408695..01a32a6abb 100644
--- a/ecc/bls12-381/g2.go
+++ b/ecc/bls12-381/g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/g2_test.go b/ecc/bls12-381/g2_test.go
index f2ff12473e..45753354c3 100644
--- a/ecc/bls12-381/g2_test.go
+++ b/ecc/bls12-381/g2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/hash_to_g1.go b/ecc/bls12-381/hash_to_g1.go
index a4b9f3d4c5..2c2c666fb5 100644
--- a/ecc/bls12-381/hash_to_g1.go
+++ b/ecc/bls12-381/hash_to_g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/hash_to_g1_test.go b/ecc/bls12-381/hash_to_g1_test.go
index 47e20b0549..8ef508675e 100644
--- a/ecc/bls12-381/hash_to_g1_test.go
+++ b/ecc/bls12-381/hash_to_g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/hash_to_g2.go b/ecc/bls12-381/hash_to_g2.go
index 27e970b6db..f8bef569c2 100644
--- a/ecc/bls12-381/hash_to_g2.go
+++ b/ecc/bls12-381/hash_to_g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/hash_to_g2_test.go b/ecc/bls12-381/hash_to_g2_test.go
index b714de662c..3800384df4 100644
--- a/ecc/bls12-381/hash_to_g2_test.go
+++ b/ecc/bls12-381/hash_to_g2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/internal/fptower/asm.go b/ecc/bls12-381/internal/fptower/asm.go
index 7d64458b6c..c08e8f1574 100644
--- a/ecc/bls12-381/internal/fptower/asm.go
+++ b/ecc/bls12-381/internal/fptower/asm.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/internal/fptower/asm_noadx.go b/ecc/bls12-381/internal/fptower/asm_noadx.go
index 28588f65a0..1dc20b4991 100644
--- a/ecc/bls12-381/internal/fptower/asm_noadx.go
+++ b/ecc/bls12-381/internal/fptower/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/internal/fptower/e12.go b/ecc/bls12-381/internal/fptower/e12.go
index 03f0568455..6a8838c7b4 100644
--- a/ecc/bls12-381/internal/fptower/e12.go
+++ b/ecc/bls12-381/internal/fptower/e12.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/internal/fptower/e12_test.go b/ecc/bls12-381/internal/fptower/e12_test.go
index aac39f80f1..18813442e0 100644
--- a/ecc/bls12-381/internal/fptower/e12_test.go
+++ b/ecc/bls12-381/internal/fptower/e12_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/internal/fptower/e2.go b/ecc/bls12-381/internal/fptower/e2.go
index 11f9d4c3c0..f86cefddca 100644
--- a/ecc/bls12-381/internal/fptower/e2.go
+++ b/ecc/bls12-381/internal/fptower/e2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/internal/fptower/e2_amd64.go b/ecc/bls12-381/internal/fptower/e2_amd64.go
index a73ff678a9..f0acaeab06 100644
--- a/ecc/bls12-381/internal/fptower/e2_amd64.go
+++ b/ecc/bls12-381/internal/fptower/e2_amd64.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/internal/fptower/e2_amd64.s b/ecc/bls12-381/internal/fptower/e2_amd64.s
index 8448eef7ca..882347950d 100644
--- a/ecc/bls12-381/internal/fptower/e2_amd64.s
+++ b/ecc/bls12-381/internal/fptower/e2_amd64.s
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 #include "textflag.h"
diff --git a/ecc/bls12-381/internal/fptower/e2_fallback.go b/ecc/bls12-381/internal/fptower/e2_fallback.go
index 3dff96dcea..7a2461ec53 100644
--- a/ecc/bls12-381/internal/fptower/e2_fallback.go
+++ b/ecc/bls12-381/internal/fptower/e2_fallback.go
@@ -1,6 +1,6 @@
 //go:build !amd64
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/internal/fptower/e2_test.go b/ecc/bls12-381/internal/fptower/e2_test.go
index 0f8a8ed5bc..8458b8040a 100644
--- a/ecc/bls12-381/internal/fptower/e2_test.go
+++ b/ecc/bls12-381/internal/fptower/e2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/internal/fptower/e6.go b/ecc/bls12-381/internal/fptower/e6.go
index a3bd71a6cc..13fdfdd297 100644
--- a/ecc/bls12-381/internal/fptower/e6.go
+++ b/ecc/bls12-381/internal/fptower/e6.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/internal/fptower/e6_test.go b/ecc/bls12-381/internal/fptower/e6_test.go
index 776ace70ae..9ccc2be85c 100644
--- a/ecc/bls12-381/internal/fptower/e6_test.go
+++ b/ecc/bls12-381/internal/fptower/e6_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/kzg/doc.go b/ecc/bls12-381/kzg/doc.go
index 226614bbdf..3a86419c48 100644
--- a/ecc/bls12-381/kzg/doc.go
+++ b/ecc/bls12-381/kzg/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/kzg/kzg.go b/ecc/bls12-381/kzg/kzg.go
index 14dfcef106..915d627ef1 100644
--- a/ecc/bls12-381/kzg/kzg.go
+++ b/ecc/bls12-381/kzg/kzg.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/kzg/kzg_test.go b/ecc/bls12-381/kzg/kzg_test.go
index 0883287cf7..cc167c9598 100644
--- a/ecc/bls12-381/kzg/kzg_test.go
+++ b/ecc/bls12-381/kzg/kzg_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/kzg/marshal.go b/ecc/bls12-381/kzg/marshal.go
index 11b9d5e09b..dfd546ee46 100644
--- a/ecc/bls12-381/kzg/marshal.go
+++ b/ecc/bls12-381/kzg/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/kzg/utils.go b/ecc/bls12-381/kzg/utils.go
index f796b1171b..f843fded85 100644
--- a/ecc/bls12-381/kzg/utils.go
+++ b/ecc/bls12-381/kzg/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/marshal.go b/ecc/bls12-381/marshal.go
index 3abb837ba6..dd36f429b1 100644
--- a/ecc/bls12-381/marshal.go
+++ b/ecc/bls12-381/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/marshal_test.go b/ecc/bls12-381/marshal_test.go
index b7d0f1916b..2b4f94f4bc 100644
--- a/ecc/bls12-381/marshal_test.go
+++ b/ecc/bls12-381/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/multiexp.go b/ecc/bls12-381/multiexp.go
index 319440b5d4..bd0427c04a 100644
--- a/ecc/bls12-381/multiexp.go
+++ b/ecc/bls12-381/multiexp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/multiexp_affine.go b/ecc/bls12-381/multiexp_affine.go
index 1df94806f3..a7005c76b5 100644
--- a/ecc/bls12-381/multiexp_affine.go
+++ b/ecc/bls12-381/multiexp_affine.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/multiexp_jacobian.go b/ecc/bls12-381/multiexp_jacobian.go
index 3d8a187f4f..b2a94f7937 100644
--- a/ecc/bls12-381/multiexp_jacobian.go
+++ b/ecc/bls12-381/multiexp_jacobian.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/multiexp_test.go b/ecc/bls12-381/multiexp_test.go
index 9336fb1058..b8a0eea2a9 100644
--- a/ecc/bls12-381/multiexp_test.go
+++ b/ecc/bls12-381/multiexp_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/pairing_test.go b/ecc/bls12-381/pairing_test.go
index 813c8c530d..a1c445fed4 100644
--- a/ecc/bls12-381/pairing_test.go
+++ b/ecc/bls12-381/pairing_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/shplonk/doc.go b/ecc/bls12-381/shplonk/doc.go
index 0367893999..d63c7a3ddf 100644
--- a/ecc/bls12-381/shplonk/doc.go
+++ b/ecc/bls12-381/shplonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/shplonk/example_test.go b/ecc/bls12-381/shplonk/example_test.go
index a350302627..eacb143710 100644
--- a/ecc/bls12-381/shplonk/example_test.go
+++ b/ecc/bls12-381/shplonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/shplonk/marshal.go b/ecc/bls12-381/shplonk/marshal.go
index f477d4e248..04e4c4496f 100644
--- a/ecc/bls12-381/shplonk/marshal.go
+++ b/ecc/bls12-381/shplonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/shplonk/shplonk.go b/ecc/bls12-381/shplonk/shplonk.go
index 44a6ad5f23..b8bf72ddb7 100644
--- a/ecc/bls12-381/shplonk/shplonk.go
+++ b/ecc/bls12-381/shplonk/shplonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/shplonk/shplonk_test.go b/ecc/bls12-381/shplonk/shplonk_test.go
index 240092d53a..4245d7cd1a 100644
--- a/ecc/bls12-381/shplonk/shplonk_test.go
+++ b/ecc/bls12-381/shplonk/shplonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/twistededwards/curve.go b/ecc/bls12-381/twistededwards/curve.go
index 43b1da7ef3..446aee203d 100644
--- a/ecc/bls12-381/twistededwards/curve.go
+++ b/ecc/bls12-381/twistededwards/curve.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/twistededwards/doc.go b/ecc/bls12-381/twistededwards/doc.go
index 53880a954b..656eea4604 100644
--- a/ecc/bls12-381/twistededwards/doc.go
+++ b/ecc/bls12-381/twistededwards/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/twistededwards/eddsa/doc.go b/ecc/bls12-381/twistededwards/eddsa/doc.go
index 5581f06406..2426b1d017 100644
--- a/ecc/bls12-381/twistededwards/eddsa/doc.go
+++ b/ecc/bls12-381/twistededwards/eddsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/twistededwards/eddsa/eddsa.go b/ecc/bls12-381/twistededwards/eddsa/eddsa.go
index c10e701839..5569060705 100644
--- a/ecc/bls12-381/twistededwards/eddsa/eddsa.go
+++ b/ecc/bls12-381/twistededwards/eddsa/eddsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/twistededwards/eddsa/eddsa_test.go b/ecc/bls12-381/twistededwards/eddsa/eddsa_test.go
index c53bfc6cc8..9d73e340c3 100644
--- a/ecc/bls12-381/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bls12-381/twistededwards/eddsa/eddsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/twistededwards/eddsa/marshal.go b/ecc/bls12-381/twistededwards/eddsa/marshal.go
index 39dabf92f7..ecc5b5084f 100644
--- a/ecc/bls12-381/twistededwards/eddsa/marshal.go
+++ b/ecc/bls12-381/twistededwards/eddsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/twistededwards/point.go b/ecc/bls12-381/twistededwards/point.go
index 7f759b673f..e7e6606e7e 100644
--- a/ecc/bls12-381/twistededwards/point.go
+++ b/ecc/bls12-381/twistededwards/point.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls12-381/twistededwards/point_test.go b/ecc/bls12-381/twistededwards/point_test.go
index e6918921a1..ef44e93fe7 100644
--- a/ecc/bls12-381/twistededwards/point_test.go
+++ b/ecc/bls12-381/twistededwards/point_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/ecdsa/doc.go b/ecc/bls24-315/ecdsa/doc.go
index f7d5d79b76..57f45e7d23 100644
--- a/ecc/bls24-315/ecdsa/doc.go
+++ b/ecc/bls24-315/ecdsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/ecdsa/ecdsa.go b/ecc/bls24-315/ecdsa/ecdsa.go
index 386e61e249..71e42a9ce4 100644
--- a/ecc/bls24-315/ecdsa/ecdsa.go
+++ b/ecc/bls24-315/ecdsa/ecdsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/ecdsa/ecdsa_test.go b/ecc/bls24-315/ecdsa/ecdsa_test.go
index a264c28340..2363cb0b41 100644
--- a/ecc/bls24-315/ecdsa/ecdsa_test.go
+++ b/ecc/bls24-315/ecdsa/ecdsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/ecdsa/marshal.go b/ecc/bls24-315/ecdsa/marshal.go
index 754a709fa5..b354f186ec 100644
--- a/ecc/bls24-315/ecdsa/marshal.go
+++ b/ecc/bls24-315/ecdsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/ecdsa/marshal_test.go b/ecc/bls24-315/ecdsa/marshal_test.go
index f82b378d8b..80554eea09 100644
--- a/ecc/bls24-315/ecdsa/marshal_test.go
+++ b/ecc/bls24-315/ecdsa/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fflonk/doc.go b/ecc/bls24-315/fflonk/doc.go
index 67a8094e35..a2506720a8 100644
--- a/ecc/bls24-315/fflonk/doc.go
+++ b/ecc/bls24-315/fflonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fflonk/example_test.go b/ecc/bls24-315/fflonk/example_test.go
index 64a58839b7..7b9d72520e 100644
--- a/ecc/bls24-315/fflonk/example_test.go
+++ b/ecc/bls24-315/fflonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fflonk/fflonk.go b/ecc/bls24-315/fflonk/fflonk.go
index 2bdde82014..d1a6a15a0d 100644
--- a/ecc/bls24-315/fflonk/fflonk.go
+++ b/ecc/bls24-315/fflonk/fflonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fflonk/fflonk_test.go b/ecc/bls24-315/fflonk/fflonk_test.go
index 11d09c1e20..05ff021c8c 100644
--- a/ecc/bls24-315/fflonk/fflonk_test.go
+++ b/ecc/bls24-315/fflonk/fflonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fflonk/marshal.go b/ecc/bls24-315/fflonk/marshal.go
index e73cc1c98f..a174b9fcf0 100644
--- a/ecc/bls24-315/fflonk/marshal.go
+++ b/ecc/bls24-315/fflonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/arith.go b/ecc/bls24-315/fp/arith.go
index bb63552f5a..5c9905de80 100644
--- a/ecc/bls24-315/fp/arith.go
+++ b/ecc/bls24-315/fp/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/asm_adx.go b/ecc/bls24-315/fp/asm_adx.go
index 75e92992fe..8d85a11345 100644
--- a/ecc/bls24-315/fp/asm_adx.go
+++ b/ecc/bls24-315/fp/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/asm_noadx.go b/ecc/bls24-315/fp/asm_noadx.go
index 304dfb7209..75ca96d775 100644
--- a/ecc/bls24-315/fp/asm_noadx.go
+++ b/ecc/bls24-315/fp/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/doc.go b/ecc/bls24-315/fp/doc.go
index bb419e36d3..637eda94c5 100644
--- a/ecc/bls24-315/fp/doc.go
+++ b/ecc/bls24-315/fp/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/element.go b/ecc/bls24-315/fp/element.go
index a6856c7eff..5c9d2ad40c 100644
--- a/ecc/bls24-315/fp/element.go
+++ b/ecc/bls24-315/fp/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/element_amd64.go b/ecc/bls24-315/fp/element_amd64.go
index 9cee062e5b..1a6e1cf5eb 100644
--- a/ecc/bls24-315/fp/element_amd64.go
+++ b/ecc/bls24-315/fp/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/element_amd64.s b/ecc/bls24-315/fp/element_amd64.s
index 0f7e0b89ff..be272d59ae 100644
--- a/ecc/bls24-315/fp/element_amd64.s
+++ b/ecc/bls24-315/fp/element_amd64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/element_exp.go b/ecc/bls24-315/fp/element_exp.go
index f85a7b3c70..c83eef8cac 100644
--- a/ecc/bls24-315/fp/element_exp.go
+++ b/ecc/bls24-315/fp/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/element_purego.go b/ecc/bls24-315/fp/element_purego.go
index a954563d21..ce12129cb7 100644
--- a/ecc/bls24-315/fp/element_purego.go
+++ b/ecc/bls24-315/fp/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || !amd64
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/element_test.go b/ecc/bls24-315/fp/element_test.go
index ada5a127d6..83ac219232 100644
--- a/ecc/bls24-315/fp/element_test.go
+++ b/ecc/bls24-315/fp/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/hash_to_field/doc.go b/ecc/bls24-315/fp/hash_to_field/doc.go
index 8ca5ee83c1..6397130531 100644
--- a/ecc/bls24-315/fp/hash_to_field/doc.go
+++ b/ecc/bls24-315/fp/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/hash_to_field/hash_to_field.go b/ecc/bls24-315/fp/hash_to_field/hash_to_field.go
index 5a5764ed80..a4e4cff53b 100644
--- a/ecc/bls24-315/fp/hash_to_field/hash_to_field.go
+++ b/ecc/bls24-315/fp/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/hash_to_field/hash_to_field_test.go b/ecc/bls24-315/fp/hash_to_field/hash_to_field_test.go
index 114009b320..6b3edb9bb9 100644
--- a/ecc/bls24-315/fp/hash_to_field/hash_to_field_test.go
+++ b/ecc/bls24-315/fp/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/vector.go b/ecc/bls24-315/fp/vector.go
index 6734ac80a3..130b16bc68 100644
--- a/ecc/bls24-315/fp/vector.go
+++ b/ecc/bls24-315/fp/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/vector_purego.go b/ecc/bls24-315/fp/vector_purego.go
index 0cda361871..85670501df 100644
--- a/ecc/bls24-315/fp/vector_purego.go
+++ b/ecc/bls24-315/fp/vector_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fp/vector_test.go b/ecc/bls24-315/fp/vector_test.go
index 46cad267bc..e3d9bd7c23 100644
--- a/ecc/bls24-315/fp/vector_test.go
+++ b/ecc/bls24-315/fp/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/arith.go b/ecc/bls24-315/fr/arith.go
index dbba8a9ae4..8dbae56e32 100644
--- a/ecc/bls24-315/fr/arith.go
+++ b/ecc/bls24-315/fr/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/asm_adx.go b/ecc/bls24-315/fr/asm_adx.go
index 9b970335f1..52421cc159 100644
--- a/ecc/bls24-315/fr/asm_adx.go
+++ b/ecc/bls24-315/fr/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/asm_avx.go b/ecc/bls24-315/fr/asm_avx.go
index 2a0a166ed4..f89a44926d 100644
--- a/ecc/bls24-315/fr/asm_avx.go
+++ b/ecc/bls24-315/fr/asm_avx.go
@@ -1,6 +1,6 @@
 //go:build !noavx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/asm_noadx.go b/ecc/bls24-315/fr/asm_noadx.go
index 96741014f2..9c9c9dab5d 100644
--- a/ecc/bls24-315/fr/asm_noadx.go
+++ b/ecc/bls24-315/fr/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/asm_noavx.go b/ecc/bls24-315/fr/asm_noavx.go
index 3cb6968fb8..ae86f75e7f 100644
--- a/ecc/bls24-315/fr/asm_noavx.go
+++ b/ecc/bls24-315/fr/asm_noavx.go
@@ -1,6 +1,6 @@
 //go:build noavx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/doc.go b/ecc/bls24-315/fr/doc.go
index ff95985edf..de2cfca9d4 100644
--- a/ecc/bls24-315/fr/doc.go
+++ b/ecc/bls24-315/fr/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/element.go b/ecc/bls24-315/fr/element.go
index e00694d13c..518f6908f4 100644
--- a/ecc/bls24-315/fr/element.go
+++ b/ecc/bls24-315/fr/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/element_amd64.go b/ecc/bls24-315/fr/element_amd64.go
index 4c3f2a8567..7e76a943a1 100644
--- a/ecc/bls24-315/fr/element_amd64.go
+++ b/ecc/bls24-315/fr/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/element_amd64.s b/ecc/bls24-315/fr/element_amd64.s
index a7c6ffae66..41c54b1aa6 100644
--- a/ecc/bls24-315/fr/element_amd64.s
+++ b/ecc/bls24-315/fr/element_amd64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/element_arm64.go b/ecc/bls24-315/fr/element_arm64.go
index 824692948c..3e0414a9c8 100644
--- a/ecc/bls24-315/fr/element_arm64.go
+++ b/ecc/bls24-315/fr/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/element_arm64.s b/ecc/bls24-315/fr/element_arm64.s
index ef16eaba35..0668975118 100644
--- a/ecc/bls24-315/fr/element_arm64.s
+++ b/ecc/bls24-315/fr/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/element_exp.go b/ecc/bls24-315/fr/element_exp.go
index 34f838ed2c..baf1fa314a 100644
--- a/ecc/bls24-315/fr/element_exp.go
+++ b/ecc/bls24-315/fr/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/element_purego.go b/ecc/bls24-315/fr/element_purego.go
index e490d3d702..6bf56f886f 100644
--- a/ecc/bls24-315/fr/element_purego.go
+++ b/ecc/bls24-315/fr/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/element_test.go b/ecc/bls24-315/fr/element_test.go
index 4f9bba391c..541f5a0614 100644
--- a/ecc/bls24-315/fr/element_test.go
+++ b/ecc/bls24-315/fr/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/fft/bitreverse.go b/ecc/bls24-315/fr/fft/bitreverse.go
index f8d74370ac..fee0b2860c 100644
--- a/ecc/bls24-315/fr/fft/bitreverse.go
+++ b/ecc/bls24-315/fr/fft/bitreverse.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/fft/bitreverse_test.go b/ecc/bls24-315/fr/fft/bitreverse_test.go
index b3bf26d767..c31f91f563 100644
--- a/ecc/bls24-315/fr/fft/bitreverse_test.go
+++ b/ecc/bls24-315/fr/fft/bitreverse_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/fft/doc.go b/ecc/bls24-315/fr/fft/doc.go
index 4cce0f9779..8176d8e77a 100644
--- a/ecc/bls24-315/fr/fft/doc.go
+++ b/ecc/bls24-315/fr/fft/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/fft/domain.go b/ecc/bls24-315/fr/fft/domain.go
index e624004bb8..04094d7c75 100644
--- a/ecc/bls24-315/fr/fft/domain.go
+++ b/ecc/bls24-315/fr/fft/domain.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/fft/domain_test.go b/ecc/bls24-315/fr/fft/domain_test.go
index e445d3cc12..7049120e6a 100644
--- a/ecc/bls24-315/fr/fft/domain_test.go
+++ b/ecc/bls24-315/fr/fft/domain_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/fft/fft.go b/ecc/bls24-315/fr/fft/fft.go
index aa3a9107b7..c88c924889 100644
--- a/ecc/bls24-315/fr/fft/fft.go
+++ b/ecc/bls24-315/fr/fft/fft.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/fft/fft_test.go b/ecc/bls24-315/fr/fft/fft_test.go
index 39fab1295d..73000af837 100644
--- a/ecc/bls24-315/fr/fft/fft_test.go
+++ b/ecc/bls24-315/fr/fft/fft_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/fft/options.go b/ecc/bls24-315/fr/fft/options.go
index 83d439844a..86b79fa17f 100644
--- a/ecc/bls24-315/fr/fft/options.go
+++ b/ecc/bls24-315/fr/fft/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/fri/doc.go b/ecc/bls24-315/fr/fri/doc.go
index cea69fc79a..164ee83268 100644
--- a/ecc/bls24-315/fr/fri/doc.go
+++ b/ecc/bls24-315/fr/fri/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/fri/fri.go b/ecc/bls24-315/fr/fri/fri.go
index de0669a0f2..d02603e12b 100644
--- a/ecc/bls24-315/fr/fri/fri.go
+++ b/ecc/bls24-315/fr/fri/fri.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/fri/fri_test.go b/ecc/bls24-315/fr/fri/fri_test.go
index 8779681e93..a26077e7cc 100644
--- a/ecc/bls24-315/fr/fri/fri_test.go
+++ b/ecc/bls24-315/fr/fri/fri_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/generator.go b/ecc/bls24-315/fr/generator.go
index 8e93206d41..8c37f4dcc1 100644
--- a/ecc/bls24-315/fr/generator.go
+++ b/ecc/bls24-315/fr/generator.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/gkr/gkr.go b/ecc/bls24-315/fr/gkr/gkr.go
index c88da7da8a..3511fecfa3 100644
--- a/ecc/bls24-315/fr/gkr/gkr.go
+++ b/ecc/bls24-315/fr/gkr/gkr.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/gkr/gkr_test.go b/ecc/bls24-315/fr/gkr/gkr_test.go
index e4aecce756..5205353670 100644
--- a/ecc/bls24-315/fr/gkr/gkr_test.go
+++ b/ecc/bls24-315/fr/gkr/gkr_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/hash_to_field/doc.go b/ecc/bls24-315/fr/hash_to_field/doc.go
index c912145689..368ec913ed 100644
--- a/ecc/bls24-315/fr/hash_to_field/doc.go
+++ b/ecc/bls24-315/fr/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/hash_to_field/hash_to_field.go b/ecc/bls24-315/fr/hash_to_field/hash_to_field.go
index 077fd835f5..6fef163048 100644
--- a/ecc/bls24-315/fr/hash_to_field/hash_to_field.go
+++ b/ecc/bls24-315/fr/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/hash_to_field/hash_to_field_test.go b/ecc/bls24-315/fr/hash_to_field/hash_to_field_test.go
index 2d144d57f6..428e774a81 100644
--- a/ecc/bls24-315/fr/hash_to_field/hash_to_field_test.go
+++ b/ecc/bls24-315/fr/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/iop/doc.go b/ecc/bls24-315/fr/iop/doc.go
index 2ef06dfe1a..6c9a441cc1 100644
--- a/ecc/bls24-315/fr/iop/doc.go
+++ b/ecc/bls24-315/fr/iop/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/iop/expressions.go b/ecc/bls24-315/fr/iop/expressions.go
index be044147f9..df6e899c17 100644
--- a/ecc/bls24-315/fr/iop/expressions.go
+++ b/ecc/bls24-315/fr/iop/expressions.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/iop/expressions_test.go b/ecc/bls24-315/fr/iop/expressions_test.go
index 9f151110f1..da465c1355 100644
--- a/ecc/bls24-315/fr/iop/expressions_test.go
+++ b/ecc/bls24-315/fr/iop/expressions_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/iop/polynomial.go b/ecc/bls24-315/fr/iop/polynomial.go
index 91ee36796a..b9f9eaf39c 100644
--- a/ecc/bls24-315/fr/iop/polynomial.go
+++ b/ecc/bls24-315/fr/iop/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/iop/polynomial_test.go b/ecc/bls24-315/fr/iop/polynomial_test.go
index a8e86b350f..2453676bb5 100644
--- a/ecc/bls24-315/fr/iop/polynomial_test.go
+++ b/ecc/bls24-315/fr/iop/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/iop/quotient.go b/ecc/bls24-315/fr/iop/quotient.go
index be2c4dc48f..99465ce40a 100644
--- a/ecc/bls24-315/fr/iop/quotient.go
+++ b/ecc/bls24-315/fr/iop/quotient.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/iop/quotient_test.go b/ecc/bls24-315/fr/iop/quotient_test.go
index acba6e7537..35b8e440fc 100644
--- a/ecc/bls24-315/fr/iop/quotient_test.go
+++ b/ecc/bls24-315/fr/iop/quotient_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/iop/ratios.go b/ecc/bls24-315/fr/iop/ratios.go
index c770531d85..dad1dd9da2 100644
--- a/ecc/bls24-315/fr/iop/ratios.go
+++ b/ecc/bls24-315/fr/iop/ratios.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/iop/ratios_test.go b/ecc/bls24-315/fr/iop/ratios_test.go
index 1a951f2769..b917b91253 100644
--- a/ecc/bls24-315/fr/iop/ratios_test.go
+++ b/ecc/bls24-315/fr/iop/ratios_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/iop/utils.go b/ecc/bls24-315/fr/iop/utils.go
index 7b70f0ad9c..1574835f79 100644
--- a/ecc/bls24-315/fr/iop/utils.go
+++ b/ecc/bls24-315/fr/iop/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/mimc/doc.go b/ecc/bls24-315/fr/mimc/doc.go
index 900b977185..946e0dafaa 100644
--- a/ecc/bls24-315/fr/mimc/doc.go
+++ b/ecc/bls24-315/fr/mimc/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/mimc/mimc.go b/ecc/bls24-315/fr/mimc/mimc.go
index 7f1ab7c7e8..35b38a584b 100644
--- a/ecc/bls24-315/fr/mimc/mimc.go
+++ b/ecc/bls24-315/fr/mimc/mimc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/mimc/mimc_test.go b/ecc/bls24-315/fr/mimc/mimc_test.go
index 58aa9449fe..6ae2375c35 100644
--- a/ecc/bls24-315/fr/mimc/mimc_test.go
+++ b/ecc/bls24-315/fr/mimc/mimc_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/mimc/options.go b/ecc/bls24-315/fr/mimc/options.go
index b850cc2ce3..26f8a54cb4 100644
--- a/ecc/bls24-315/fr/mimc/options.go
+++ b/ecc/bls24-315/fr/mimc/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/pedersen/doc.go b/ecc/bls24-315/fr/pedersen/doc.go
index 2e24034936..dff1285d0e 100644
--- a/ecc/bls24-315/fr/pedersen/doc.go
+++ b/ecc/bls24-315/fr/pedersen/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/pedersen/example_test.go b/ecc/bls24-315/fr/pedersen/example_test.go
index dd071f1143..7f70574d32 100644
--- a/ecc/bls24-315/fr/pedersen/example_test.go
+++ b/ecc/bls24-315/fr/pedersen/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/pedersen/pedersen.go b/ecc/bls24-315/fr/pedersen/pedersen.go
index fec061e224..d7c0b129c7 100644
--- a/ecc/bls24-315/fr/pedersen/pedersen.go
+++ b/ecc/bls24-315/fr/pedersen/pedersen.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/pedersen/pedersen_test.go b/ecc/bls24-315/fr/pedersen/pedersen_test.go
index 3fdc0ea160..4fce2e9b38 100644
--- a/ecc/bls24-315/fr/pedersen/pedersen_test.go
+++ b/ecc/bls24-315/fr/pedersen/pedersen_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/permutation/doc.go b/ecc/bls24-315/fr/permutation/doc.go
index e24cd82923..4f2ea7b2e4 100644
--- a/ecc/bls24-315/fr/permutation/doc.go
+++ b/ecc/bls24-315/fr/permutation/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/permutation/permutation.go b/ecc/bls24-315/fr/permutation/permutation.go
index fb99644a3a..0531c415d0 100644
--- a/ecc/bls24-315/fr/permutation/permutation.go
+++ b/ecc/bls24-315/fr/permutation/permutation.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/permutation/permutation_test.go b/ecc/bls24-315/fr/permutation/permutation_test.go
index 10e81920eb..9a5cdc70c7 100644
--- a/ecc/bls24-315/fr/permutation/permutation_test.go
+++ b/ecc/bls24-315/fr/permutation/permutation_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/plookup/doc.go b/ecc/bls24-315/fr/plookup/doc.go
index 7a02c59719..5507122fab 100644
--- a/ecc/bls24-315/fr/plookup/doc.go
+++ b/ecc/bls24-315/fr/plookup/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/plookup/plookup_test.go b/ecc/bls24-315/fr/plookup/plookup_test.go
index 2ea5988772..967dbe950c 100644
--- a/ecc/bls24-315/fr/plookup/plookup_test.go
+++ b/ecc/bls24-315/fr/plookup/plookup_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/plookup/table.go b/ecc/bls24-315/fr/plookup/table.go
index bf25270da3..d3e3d81656 100644
--- a/ecc/bls24-315/fr/plookup/table.go
+++ b/ecc/bls24-315/fr/plookup/table.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/plookup/vector.go b/ecc/bls24-315/fr/plookup/vector.go
index c271a720c7..2b02312adf 100644
--- a/ecc/bls24-315/fr/plookup/vector.go
+++ b/ecc/bls24-315/fr/plookup/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/polynomial/doc.go b/ecc/bls24-315/fr/polynomial/doc.go
index fd96328e8f..ead3b5cba5 100644
--- a/ecc/bls24-315/fr/polynomial/doc.go
+++ b/ecc/bls24-315/fr/polynomial/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/polynomial/multilin.go b/ecc/bls24-315/fr/polynomial/multilin.go
index 3e338d8bf3..4b73ed7be6 100644
--- a/ecc/bls24-315/fr/polynomial/multilin.go
+++ b/ecc/bls24-315/fr/polynomial/multilin.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/polynomial/multilin_test.go b/ecc/bls24-315/fr/polynomial/multilin_test.go
index 2d71dd8e7e..72a99c053f 100644
--- a/ecc/bls24-315/fr/polynomial/multilin_test.go
+++ b/ecc/bls24-315/fr/polynomial/multilin_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/polynomial/polynomial.go b/ecc/bls24-315/fr/polynomial/polynomial.go
index 98aad0c7ff..9a3911becc 100644
--- a/ecc/bls24-315/fr/polynomial/polynomial.go
+++ b/ecc/bls24-315/fr/polynomial/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/polynomial/polynomial_test.go b/ecc/bls24-315/fr/polynomial/polynomial_test.go
index 1ff8b39cf4..4a85b7a51b 100644
--- a/ecc/bls24-315/fr/polynomial/polynomial_test.go
+++ b/ecc/bls24-315/fr/polynomial/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/polynomial/pool.go b/ecc/bls24-315/fr/polynomial/pool.go
index 0e2fda71d6..77390a9a54 100644
--- a/ecc/bls24-315/fr/polynomial/pool.go
+++ b/ecc/bls24-315/fr/polynomial/pool.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/poseidon2/poseidon2.go b/ecc/bls24-315/fr/poseidon2/poseidon2.go
index c32028d7b0..824dcead74 100644
--- a/ecc/bls24-315/fr/poseidon2/poseidon2.go
+++ b/ecc/bls24-315/fr/poseidon2/poseidon2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/poseidon2/poseidon2_test.go b/ecc/bls24-315/fr/poseidon2/poseidon2_test.go
index 3fb0bc5d6e..41da3d5728 100644
--- a/ecc/bls24-315/fr/poseidon2/poseidon2_test.go
+++ b/ecc/bls24-315/fr/poseidon2/poseidon2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/sumcheck/sumcheck.go b/ecc/bls24-315/fr/sumcheck/sumcheck.go
index 63523203a0..8a256bc385 100644
--- a/ecc/bls24-315/fr/sumcheck/sumcheck.go
+++ b/ecc/bls24-315/fr/sumcheck/sumcheck.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/sumcheck/sumcheck_test.go b/ecc/bls24-315/fr/sumcheck/sumcheck_test.go
index 55e0ad74a5..cc64cb58f4 100644
--- a/ecc/bls24-315/fr/sumcheck/sumcheck_test.go
+++ b/ecc/bls24-315/fr/sumcheck/sumcheck_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/test_vector_utils/test_vector_utils.go b/ecc/bls24-315/fr/test_vector_utils/test_vector_utils.go
index 57942f2951..de3318ae96 100644
--- a/ecc/bls24-315/fr/test_vector_utils/test_vector_utils.go
+++ b/ecc/bls24-315/fr/test_vector_utils/test_vector_utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/vector.go b/ecc/bls24-315/fr/vector.go
index 4654b1b2d3..7792a6f73b 100644
--- a/ecc/bls24-315/fr/vector.go
+++ b/ecc/bls24-315/fr/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/vector_amd64.go b/ecc/bls24-315/fr/vector_amd64.go
index a7dcec3b25..e3565da46a 100644
--- a/ecc/bls24-315/fr/vector_amd64.go
+++ b/ecc/bls24-315/fr/vector_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/vector_purego.go b/ecc/bls24-315/fr/vector_purego.go
index db43e73504..6608e394c7 100644
--- a/ecc/bls24-315/fr/vector_purego.go
+++ b/ecc/bls24-315/fr/vector_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || !amd64
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/fr/vector_test.go b/ecc/bls24-315/fr/vector_test.go
index f6179e7824..88c4ef318f 100644
--- a/ecc/bls24-315/fr/vector_test.go
+++ b/ecc/bls24-315/fr/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/g1.go b/ecc/bls24-315/g1.go
index 78d959ae2a..4ced2cd0eb 100644
--- a/ecc/bls24-315/g1.go
+++ b/ecc/bls24-315/g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/g1_test.go b/ecc/bls24-315/g1_test.go
index 22597de99a..8cfd54e140 100644
--- a/ecc/bls24-315/g1_test.go
+++ b/ecc/bls24-315/g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/g2.go b/ecc/bls24-315/g2.go
index 5b96e16e1a..e97a4933ab 100644
--- a/ecc/bls24-315/g2.go
+++ b/ecc/bls24-315/g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/g2_test.go b/ecc/bls24-315/g2_test.go
index 8d630fabed..b748c00f66 100644
--- a/ecc/bls24-315/g2_test.go
+++ b/ecc/bls24-315/g2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/hash_to_g1.go b/ecc/bls24-315/hash_to_g1.go
index 45e5381028..d18357c844 100644
--- a/ecc/bls24-315/hash_to_g1.go
+++ b/ecc/bls24-315/hash_to_g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/hash_to_g1_test.go b/ecc/bls24-315/hash_to_g1_test.go
index 25f4f9aca4..0e856e5bf6 100644
--- a/ecc/bls24-315/hash_to_g1_test.go
+++ b/ecc/bls24-315/hash_to_g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/kzg/doc.go b/ecc/bls24-315/kzg/doc.go
index 226614bbdf..3a86419c48 100644
--- a/ecc/bls24-315/kzg/doc.go
+++ b/ecc/bls24-315/kzg/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/kzg/kzg.go b/ecc/bls24-315/kzg/kzg.go
index 1bad3cc88b..5b85c0c113 100644
--- a/ecc/bls24-315/kzg/kzg.go
+++ b/ecc/bls24-315/kzg/kzg.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/kzg/kzg_test.go b/ecc/bls24-315/kzg/kzg_test.go
index 5c8a7fd91c..19a4392fb3 100644
--- a/ecc/bls24-315/kzg/kzg_test.go
+++ b/ecc/bls24-315/kzg/kzg_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/kzg/marshal.go b/ecc/bls24-315/kzg/marshal.go
index a98fe4c32b..1d725192a5 100644
--- a/ecc/bls24-315/kzg/marshal.go
+++ b/ecc/bls24-315/kzg/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/kzg/utils.go b/ecc/bls24-315/kzg/utils.go
index d6a22906f3..f80a03bec9 100644
--- a/ecc/bls24-315/kzg/utils.go
+++ b/ecc/bls24-315/kzg/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/marshal.go b/ecc/bls24-315/marshal.go
index 45ed61b8aa..100e37ff68 100644
--- a/ecc/bls24-315/marshal.go
+++ b/ecc/bls24-315/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/marshal_test.go b/ecc/bls24-315/marshal_test.go
index 71be7ba234..3b0bf4e0f7 100644
--- a/ecc/bls24-315/marshal_test.go
+++ b/ecc/bls24-315/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/multiexp.go b/ecc/bls24-315/multiexp.go
index e704b09943..9c6bbc8e31 100644
--- a/ecc/bls24-315/multiexp.go
+++ b/ecc/bls24-315/multiexp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/multiexp_affine.go b/ecc/bls24-315/multiexp_affine.go
index 154405428b..d91ef2e163 100644
--- a/ecc/bls24-315/multiexp_affine.go
+++ b/ecc/bls24-315/multiexp_affine.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/multiexp_jacobian.go b/ecc/bls24-315/multiexp_jacobian.go
index 1c72b1e0e6..72fb12eafb 100644
--- a/ecc/bls24-315/multiexp_jacobian.go
+++ b/ecc/bls24-315/multiexp_jacobian.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/multiexp_test.go b/ecc/bls24-315/multiexp_test.go
index 25eeb0e8e1..077c24e57e 100644
--- a/ecc/bls24-315/multiexp_test.go
+++ b/ecc/bls24-315/multiexp_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/pairing_test.go b/ecc/bls24-315/pairing_test.go
index ed2f9bc485..fb863fd6a0 100644
--- a/ecc/bls24-315/pairing_test.go
+++ b/ecc/bls24-315/pairing_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/shplonk/doc.go b/ecc/bls24-315/shplonk/doc.go
index 0367893999..d63c7a3ddf 100644
--- a/ecc/bls24-315/shplonk/doc.go
+++ b/ecc/bls24-315/shplonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/shplonk/example_test.go b/ecc/bls24-315/shplonk/example_test.go
index 317f412b39..d34133d868 100644
--- a/ecc/bls24-315/shplonk/example_test.go
+++ b/ecc/bls24-315/shplonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/shplonk/marshal.go b/ecc/bls24-315/shplonk/marshal.go
index 52940254e6..c1bef1dfa6 100644
--- a/ecc/bls24-315/shplonk/marshal.go
+++ b/ecc/bls24-315/shplonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/shplonk/shplonk.go b/ecc/bls24-315/shplonk/shplonk.go
index 19b6b53340..a65189013e 100644
--- a/ecc/bls24-315/shplonk/shplonk.go
+++ b/ecc/bls24-315/shplonk/shplonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/shplonk/shplonk_test.go b/ecc/bls24-315/shplonk/shplonk_test.go
index 8ed6d65c5f..fd748cd67d 100644
--- a/ecc/bls24-315/shplonk/shplonk_test.go
+++ b/ecc/bls24-315/shplonk/shplonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/twistededwards/curve.go b/ecc/bls24-315/twistededwards/curve.go
index 0a84cf5207..d02efaba16 100644
--- a/ecc/bls24-315/twistededwards/curve.go
+++ b/ecc/bls24-315/twistededwards/curve.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/twistededwards/doc.go b/ecc/bls24-315/twistededwards/doc.go
index c513532070..8980250634 100644
--- a/ecc/bls24-315/twistededwards/doc.go
+++ b/ecc/bls24-315/twistededwards/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/twistededwards/eddsa/doc.go b/ecc/bls24-315/twistededwards/eddsa/doc.go
index 827da24f9f..e183ebefba 100644
--- a/ecc/bls24-315/twistededwards/eddsa/doc.go
+++ b/ecc/bls24-315/twistededwards/eddsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/twistededwards/eddsa/eddsa.go b/ecc/bls24-315/twistededwards/eddsa/eddsa.go
index 1b65d64116..a6991081e7 100644
--- a/ecc/bls24-315/twistededwards/eddsa/eddsa.go
+++ b/ecc/bls24-315/twistededwards/eddsa/eddsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/twistededwards/eddsa/eddsa_test.go b/ecc/bls24-315/twistededwards/eddsa/eddsa_test.go
index 3954c0a991..41bea003dc 100644
--- a/ecc/bls24-315/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bls24-315/twistededwards/eddsa/eddsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/twistededwards/eddsa/marshal.go b/ecc/bls24-315/twistededwards/eddsa/marshal.go
index 0972cd871a..fc29eaf598 100644
--- a/ecc/bls24-315/twistededwards/eddsa/marshal.go
+++ b/ecc/bls24-315/twistededwards/eddsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/twistededwards/point.go b/ecc/bls24-315/twistededwards/point.go
index eaa9e57382..b5fd09ab9b 100644
--- a/ecc/bls24-315/twistededwards/point.go
+++ b/ecc/bls24-315/twistededwards/point.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-315/twistededwards/point_test.go b/ecc/bls24-315/twistededwards/point_test.go
index e9ee8dafe8..411eba975a 100644
--- a/ecc/bls24-315/twistededwards/point_test.go
+++ b/ecc/bls24-315/twistededwards/point_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/ecdsa/doc.go b/ecc/bls24-317/ecdsa/doc.go
index 0ca93ecba4..625b215074 100644
--- a/ecc/bls24-317/ecdsa/doc.go
+++ b/ecc/bls24-317/ecdsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/ecdsa/ecdsa.go b/ecc/bls24-317/ecdsa/ecdsa.go
index 62f23ce1d6..848f88fccd 100644
--- a/ecc/bls24-317/ecdsa/ecdsa.go
+++ b/ecc/bls24-317/ecdsa/ecdsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/ecdsa/ecdsa_test.go b/ecc/bls24-317/ecdsa/ecdsa_test.go
index 0fe31803be..e5f28417ca 100644
--- a/ecc/bls24-317/ecdsa/ecdsa_test.go
+++ b/ecc/bls24-317/ecdsa/ecdsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/ecdsa/marshal.go b/ecc/bls24-317/ecdsa/marshal.go
index cab0aa0486..5f6d4bf4d5 100644
--- a/ecc/bls24-317/ecdsa/marshal.go
+++ b/ecc/bls24-317/ecdsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/ecdsa/marshal_test.go b/ecc/bls24-317/ecdsa/marshal_test.go
index 955f27d3ff..7fa0247904 100644
--- a/ecc/bls24-317/ecdsa/marshal_test.go
+++ b/ecc/bls24-317/ecdsa/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fflonk/doc.go b/ecc/bls24-317/fflonk/doc.go
index 67a8094e35..a2506720a8 100644
--- a/ecc/bls24-317/fflonk/doc.go
+++ b/ecc/bls24-317/fflonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fflonk/example_test.go b/ecc/bls24-317/fflonk/example_test.go
index 5515d272db..1a68eddd83 100644
--- a/ecc/bls24-317/fflonk/example_test.go
+++ b/ecc/bls24-317/fflonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fflonk/fflonk.go b/ecc/bls24-317/fflonk/fflonk.go
index ceafbcfd71..fa2a2fa394 100644
--- a/ecc/bls24-317/fflonk/fflonk.go
+++ b/ecc/bls24-317/fflonk/fflonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fflonk/fflonk_test.go b/ecc/bls24-317/fflonk/fflonk_test.go
index feeb7d0f94..8cc239b629 100644
--- a/ecc/bls24-317/fflonk/fflonk_test.go
+++ b/ecc/bls24-317/fflonk/fflonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fflonk/marshal.go b/ecc/bls24-317/fflonk/marshal.go
index ecc8c9c308..ccbb0fcbd2 100644
--- a/ecc/bls24-317/fflonk/marshal.go
+++ b/ecc/bls24-317/fflonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/arith.go b/ecc/bls24-317/fp/arith.go
index bb63552f5a..5c9905de80 100644
--- a/ecc/bls24-317/fp/arith.go
+++ b/ecc/bls24-317/fp/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/asm_adx.go b/ecc/bls24-317/fp/asm_adx.go
index 75e92992fe..8d85a11345 100644
--- a/ecc/bls24-317/fp/asm_adx.go
+++ b/ecc/bls24-317/fp/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/asm_noadx.go b/ecc/bls24-317/fp/asm_noadx.go
index 304dfb7209..75ca96d775 100644
--- a/ecc/bls24-317/fp/asm_noadx.go
+++ b/ecc/bls24-317/fp/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/doc.go b/ecc/bls24-317/fp/doc.go
index 4fa34b745f..a37f520e31 100644
--- a/ecc/bls24-317/fp/doc.go
+++ b/ecc/bls24-317/fp/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/element.go b/ecc/bls24-317/fp/element.go
index b84042c3bd..e061a5240c 100644
--- a/ecc/bls24-317/fp/element.go
+++ b/ecc/bls24-317/fp/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/element_amd64.go b/ecc/bls24-317/fp/element_amd64.go
index 9cee062e5b..1a6e1cf5eb 100644
--- a/ecc/bls24-317/fp/element_amd64.go
+++ b/ecc/bls24-317/fp/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/element_amd64.s b/ecc/bls24-317/fp/element_amd64.s
index 0f7e0b89ff..be272d59ae 100644
--- a/ecc/bls24-317/fp/element_amd64.s
+++ b/ecc/bls24-317/fp/element_amd64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/element_exp.go b/ecc/bls24-317/fp/element_exp.go
index 894c2b2c86..07d04349f1 100644
--- a/ecc/bls24-317/fp/element_exp.go
+++ b/ecc/bls24-317/fp/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/element_purego.go b/ecc/bls24-317/fp/element_purego.go
index 4dfa399e1d..b5c1224c69 100644
--- a/ecc/bls24-317/fp/element_purego.go
+++ b/ecc/bls24-317/fp/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || !amd64
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/element_test.go b/ecc/bls24-317/fp/element_test.go
index 2c6ee96935..6a627dfef5 100644
--- a/ecc/bls24-317/fp/element_test.go
+++ b/ecc/bls24-317/fp/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/hash_to_field/doc.go b/ecc/bls24-317/fp/hash_to_field/doc.go
index d867383832..c6d6bfb86a 100644
--- a/ecc/bls24-317/fp/hash_to_field/doc.go
+++ b/ecc/bls24-317/fp/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/hash_to_field/hash_to_field.go b/ecc/bls24-317/fp/hash_to_field/hash_to_field.go
index 2790fa6e29..c75268ce7b 100644
--- a/ecc/bls24-317/fp/hash_to_field/hash_to_field.go
+++ b/ecc/bls24-317/fp/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/hash_to_field/hash_to_field_test.go b/ecc/bls24-317/fp/hash_to_field/hash_to_field_test.go
index 388120a90b..aad2bc357f 100644
--- a/ecc/bls24-317/fp/hash_to_field/hash_to_field_test.go
+++ b/ecc/bls24-317/fp/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/vector.go b/ecc/bls24-317/fp/vector.go
index 6734ac80a3..130b16bc68 100644
--- a/ecc/bls24-317/fp/vector.go
+++ b/ecc/bls24-317/fp/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/vector_purego.go b/ecc/bls24-317/fp/vector_purego.go
index 0cda361871..85670501df 100644
--- a/ecc/bls24-317/fp/vector_purego.go
+++ b/ecc/bls24-317/fp/vector_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fp/vector_test.go b/ecc/bls24-317/fp/vector_test.go
index 46cad267bc..e3d9bd7c23 100644
--- a/ecc/bls24-317/fp/vector_test.go
+++ b/ecc/bls24-317/fp/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/arith.go b/ecc/bls24-317/fr/arith.go
index dbba8a9ae4..8dbae56e32 100644
--- a/ecc/bls24-317/fr/arith.go
+++ b/ecc/bls24-317/fr/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/asm_adx.go b/ecc/bls24-317/fr/asm_adx.go
index 9b970335f1..52421cc159 100644
--- a/ecc/bls24-317/fr/asm_adx.go
+++ b/ecc/bls24-317/fr/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/asm_avx.go b/ecc/bls24-317/fr/asm_avx.go
index 2a0a166ed4..f89a44926d 100644
--- a/ecc/bls24-317/fr/asm_avx.go
+++ b/ecc/bls24-317/fr/asm_avx.go
@@ -1,6 +1,6 @@
 //go:build !noavx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/asm_noadx.go b/ecc/bls24-317/fr/asm_noadx.go
index 96741014f2..9c9c9dab5d 100644
--- a/ecc/bls24-317/fr/asm_noadx.go
+++ b/ecc/bls24-317/fr/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/asm_noavx.go b/ecc/bls24-317/fr/asm_noavx.go
index 3cb6968fb8..ae86f75e7f 100644
--- a/ecc/bls24-317/fr/asm_noavx.go
+++ b/ecc/bls24-317/fr/asm_noavx.go
@@ -1,6 +1,6 @@
 //go:build noavx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/doc.go b/ecc/bls24-317/fr/doc.go
index 16e760a47c..d61eabbb67 100644
--- a/ecc/bls24-317/fr/doc.go
+++ b/ecc/bls24-317/fr/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/element.go b/ecc/bls24-317/fr/element.go
index 762012336c..01cbdc854f 100644
--- a/ecc/bls24-317/fr/element.go
+++ b/ecc/bls24-317/fr/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/element_amd64.go b/ecc/bls24-317/fr/element_amd64.go
index 4c3f2a8567..7e76a943a1 100644
--- a/ecc/bls24-317/fr/element_amd64.go
+++ b/ecc/bls24-317/fr/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/element_amd64.s b/ecc/bls24-317/fr/element_amd64.s
index a7c6ffae66..41c54b1aa6 100644
--- a/ecc/bls24-317/fr/element_amd64.s
+++ b/ecc/bls24-317/fr/element_amd64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/element_arm64.go b/ecc/bls24-317/fr/element_arm64.go
index 0811487b48..9ecf82faae 100644
--- a/ecc/bls24-317/fr/element_arm64.go
+++ b/ecc/bls24-317/fr/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/element_arm64.s b/ecc/bls24-317/fr/element_arm64.s
index ef16eaba35..0668975118 100644
--- a/ecc/bls24-317/fr/element_arm64.s
+++ b/ecc/bls24-317/fr/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/element_exp.go b/ecc/bls24-317/fr/element_exp.go
index 283689c158..ca192b6b2f 100644
--- a/ecc/bls24-317/fr/element_exp.go
+++ b/ecc/bls24-317/fr/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/element_purego.go b/ecc/bls24-317/fr/element_purego.go
index 41350c288f..7c6745f270 100644
--- a/ecc/bls24-317/fr/element_purego.go
+++ b/ecc/bls24-317/fr/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/element_test.go b/ecc/bls24-317/fr/element_test.go
index 01e1bd2b41..f4db326131 100644
--- a/ecc/bls24-317/fr/element_test.go
+++ b/ecc/bls24-317/fr/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/fft/bitreverse.go b/ecc/bls24-317/fr/fft/bitreverse.go
index 7f98fed65b..33a0421f41 100644
--- a/ecc/bls24-317/fr/fft/bitreverse.go
+++ b/ecc/bls24-317/fr/fft/bitreverse.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/fft/bitreverse_test.go b/ecc/bls24-317/fr/fft/bitreverse_test.go
index 1660d1a6a8..229334cc0e 100644
--- a/ecc/bls24-317/fr/fft/bitreverse_test.go
+++ b/ecc/bls24-317/fr/fft/bitreverse_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/fft/doc.go b/ecc/bls24-317/fr/fft/doc.go
index 4cce0f9779..8176d8e77a 100644
--- a/ecc/bls24-317/fr/fft/doc.go
+++ b/ecc/bls24-317/fr/fft/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/fft/domain.go b/ecc/bls24-317/fr/fft/domain.go
index 3ad6285647..82ec005569 100644
--- a/ecc/bls24-317/fr/fft/domain.go
+++ b/ecc/bls24-317/fr/fft/domain.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/fft/domain_test.go b/ecc/bls24-317/fr/fft/domain_test.go
index e445d3cc12..7049120e6a 100644
--- a/ecc/bls24-317/fr/fft/domain_test.go
+++ b/ecc/bls24-317/fr/fft/domain_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/fft/fft.go b/ecc/bls24-317/fr/fft/fft.go
index 2938090085..1479c3a078 100644
--- a/ecc/bls24-317/fr/fft/fft.go
+++ b/ecc/bls24-317/fr/fft/fft.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/fft/fft_test.go b/ecc/bls24-317/fr/fft/fft_test.go
index f09a213089..0cbc6ccca2 100644
--- a/ecc/bls24-317/fr/fft/fft_test.go
+++ b/ecc/bls24-317/fr/fft/fft_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/fft/options.go b/ecc/bls24-317/fr/fft/options.go
index b0c2cf89dc..7f213a41fa 100644
--- a/ecc/bls24-317/fr/fft/options.go
+++ b/ecc/bls24-317/fr/fft/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/fri/doc.go b/ecc/bls24-317/fr/fri/doc.go
index cea69fc79a..164ee83268 100644
--- a/ecc/bls24-317/fr/fri/doc.go
+++ b/ecc/bls24-317/fr/fri/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/fri/fri.go b/ecc/bls24-317/fr/fri/fri.go
index 5edecb72d7..28a497de7b 100644
--- a/ecc/bls24-317/fr/fri/fri.go
+++ b/ecc/bls24-317/fr/fri/fri.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/fri/fri_test.go b/ecc/bls24-317/fr/fri/fri_test.go
index 78d2ba03be..de10405284 100644
--- a/ecc/bls24-317/fr/fri/fri_test.go
+++ b/ecc/bls24-317/fr/fri/fri_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/generator.go b/ecc/bls24-317/fr/generator.go
index 4c3e708ba0..fafd41e0da 100644
--- a/ecc/bls24-317/fr/generator.go
+++ b/ecc/bls24-317/fr/generator.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/gkr/gkr.go b/ecc/bls24-317/fr/gkr/gkr.go
index c0b0bd4726..21d8a8cc0f 100644
--- a/ecc/bls24-317/fr/gkr/gkr.go
+++ b/ecc/bls24-317/fr/gkr/gkr.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/gkr/gkr_test.go b/ecc/bls24-317/fr/gkr/gkr_test.go
index fd90fec0cd..7fc09698c3 100644
--- a/ecc/bls24-317/fr/gkr/gkr_test.go
+++ b/ecc/bls24-317/fr/gkr/gkr_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/hash_to_field/doc.go b/ecc/bls24-317/fr/hash_to_field/doc.go
index e9ae11fec2..3ec207adae 100644
--- a/ecc/bls24-317/fr/hash_to_field/doc.go
+++ b/ecc/bls24-317/fr/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/hash_to_field/hash_to_field.go b/ecc/bls24-317/fr/hash_to_field/hash_to_field.go
index c48bb88330..572e9c3ecd 100644
--- a/ecc/bls24-317/fr/hash_to_field/hash_to_field.go
+++ b/ecc/bls24-317/fr/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/hash_to_field/hash_to_field_test.go b/ecc/bls24-317/fr/hash_to_field/hash_to_field_test.go
index 567bd8d19a..44b1074f2a 100644
--- a/ecc/bls24-317/fr/hash_to_field/hash_to_field_test.go
+++ b/ecc/bls24-317/fr/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/iop/doc.go b/ecc/bls24-317/fr/iop/doc.go
index 2ef06dfe1a..6c9a441cc1 100644
--- a/ecc/bls24-317/fr/iop/doc.go
+++ b/ecc/bls24-317/fr/iop/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/iop/expressions.go b/ecc/bls24-317/fr/iop/expressions.go
index 8aa5681e32..4648a888e1 100644
--- a/ecc/bls24-317/fr/iop/expressions.go
+++ b/ecc/bls24-317/fr/iop/expressions.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/iop/expressions_test.go b/ecc/bls24-317/fr/iop/expressions_test.go
index d662b45c6e..6093c937b2 100644
--- a/ecc/bls24-317/fr/iop/expressions_test.go
+++ b/ecc/bls24-317/fr/iop/expressions_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/iop/polynomial.go b/ecc/bls24-317/fr/iop/polynomial.go
index ef62148eac..765fd1451c 100644
--- a/ecc/bls24-317/fr/iop/polynomial.go
+++ b/ecc/bls24-317/fr/iop/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/iop/polynomial_test.go b/ecc/bls24-317/fr/iop/polynomial_test.go
index 3153fd5963..a9cecc3e22 100644
--- a/ecc/bls24-317/fr/iop/polynomial_test.go
+++ b/ecc/bls24-317/fr/iop/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/iop/quotient.go b/ecc/bls24-317/fr/iop/quotient.go
index 9697b89361..0105f299e6 100644
--- a/ecc/bls24-317/fr/iop/quotient.go
+++ b/ecc/bls24-317/fr/iop/quotient.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/iop/quotient_test.go b/ecc/bls24-317/fr/iop/quotient_test.go
index b932d330b2..91b9c42ba5 100644
--- a/ecc/bls24-317/fr/iop/quotient_test.go
+++ b/ecc/bls24-317/fr/iop/quotient_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/iop/ratios.go b/ecc/bls24-317/fr/iop/ratios.go
index ce121e0dfe..0cd03ddc50 100644
--- a/ecc/bls24-317/fr/iop/ratios.go
+++ b/ecc/bls24-317/fr/iop/ratios.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/iop/ratios_test.go b/ecc/bls24-317/fr/iop/ratios_test.go
index 6cea40ffd2..4b8e2a2638 100644
--- a/ecc/bls24-317/fr/iop/ratios_test.go
+++ b/ecc/bls24-317/fr/iop/ratios_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/iop/utils.go b/ecc/bls24-317/fr/iop/utils.go
index f0bf5c89b5..138d31d4cf 100644
--- a/ecc/bls24-317/fr/iop/utils.go
+++ b/ecc/bls24-317/fr/iop/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/mimc/doc.go b/ecc/bls24-317/fr/mimc/doc.go
index 900b977185..946e0dafaa 100644
--- a/ecc/bls24-317/fr/mimc/doc.go
+++ b/ecc/bls24-317/fr/mimc/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/mimc/mimc.go b/ecc/bls24-317/fr/mimc/mimc.go
index c4ca3df7c1..1807b6726b 100644
--- a/ecc/bls24-317/fr/mimc/mimc.go
+++ b/ecc/bls24-317/fr/mimc/mimc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/mimc/mimc_test.go b/ecc/bls24-317/fr/mimc/mimc_test.go
index 54f4ce08aa..2b26296eb3 100644
--- a/ecc/bls24-317/fr/mimc/mimc_test.go
+++ b/ecc/bls24-317/fr/mimc/mimc_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/mimc/options.go b/ecc/bls24-317/fr/mimc/options.go
index a212de8177..0d6ed65394 100644
--- a/ecc/bls24-317/fr/mimc/options.go
+++ b/ecc/bls24-317/fr/mimc/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/pedersen/doc.go b/ecc/bls24-317/fr/pedersen/doc.go
index 2e24034936..dff1285d0e 100644
--- a/ecc/bls24-317/fr/pedersen/doc.go
+++ b/ecc/bls24-317/fr/pedersen/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/pedersen/example_test.go b/ecc/bls24-317/fr/pedersen/example_test.go
index 55c9ce1004..88b2a336fc 100644
--- a/ecc/bls24-317/fr/pedersen/example_test.go
+++ b/ecc/bls24-317/fr/pedersen/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/pedersen/pedersen.go b/ecc/bls24-317/fr/pedersen/pedersen.go
index 17df43c6de..2ff5965a6c 100644
--- a/ecc/bls24-317/fr/pedersen/pedersen.go
+++ b/ecc/bls24-317/fr/pedersen/pedersen.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/pedersen/pedersen_test.go b/ecc/bls24-317/fr/pedersen/pedersen_test.go
index 98c3c808d2..d9831aab0b 100644
--- a/ecc/bls24-317/fr/pedersen/pedersen_test.go
+++ b/ecc/bls24-317/fr/pedersen/pedersen_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/permutation/doc.go b/ecc/bls24-317/fr/permutation/doc.go
index e24cd82923..4f2ea7b2e4 100644
--- a/ecc/bls24-317/fr/permutation/doc.go
+++ b/ecc/bls24-317/fr/permutation/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/permutation/permutation.go b/ecc/bls24-317/fr/permutation/permutation.go
index 98e2033333..b9e7f3d74e 100644
--- a/ecc/bls24-317/fr/permutation/permutation.go
+++ b/ecc/bls24-317/fr/permutation/permutation.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/permutation/permutation_test.go b/ecc/bls24-317/fr/permutation/permutation_test.go
index 88ab4f62fb..eeebcdaa2c 100644
--- a/ecc/bls24-317/fr/permutation/permutation_test.go
+++ b/ecc/bls24-317/fr/permutation/permutation_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/plookup/doc.go b/ecc/bls24-317/fr/plookup/doc.go
index 7a02c59719..5507122fab 100644
--- a/ecc/bls24-317/fr/plookup/doc.go
+++ b/ecc/bls24-317/fr/plookup/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/plookup/plookup_test.go b/ecc/bls24-317/fr/plookup/plookup_test.go
index 27b71155d3..36e08fddc7 100644
--- a/ecc/bls24-317/fr/plookup/plookup_test.go
+++ b/ecc/bls24-317/fr/plookup/plookup_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/plookup/table.go b/ecc/bls24-317/fr/plookup/table.go
index 3b11b74f7e..f820e9d32b 100644
--- a/ecc/bls24-317/fr/plookup/table.go
+++ b/ecc/bls24-317/fr/plookup/table.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/plookup/vector.go b/ecc/bls24-317/fr/plookup/vector.go
index 7b1abb02a2..fbcdb3e68b 100644
--- a/ecc/bls24-317/fr/plookup/vector.go
+++ b/ecc/bls24-317/fr/plookup/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/polynomial/doc.go b/ecc/bls24-317/fr/polynomial/doc.go
index fd96328e8f..ead3b5cba5 100644
--- a/ecc/bls24-317/fr/polynomial/doc.go
+++ b/ecc/bls24-317/fr/polynomial/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/polynomial/multilin.go b/ecc/bls24-317/fr/polynomial/multilin.go
index dd87335979..50968eccf0 100644
--- a/ecc/bls24-317/fr/polynomial/multilin.go
+++ b/ecc/bls24-317/fr/polynomial/multilin.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/polynomial/multilin_test.go b/ecc/bls24-317/fr/polynomial/multilin_test.go
index cd7a79aef4..2246666c5a 100644
--- a/ecc/bls24-317/fr/polynomial/multilin_test.go
+++ b/ecc/bls24-317/fr/polynomial/multilin_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/polynomial/polynomial.go b/ecc/bls24-317/fr/polynomial/polynomial.go
index 9a5e88d50a..994b7c4bd5 100644
--- a/ecc/bls24-317/fr/polynomial/polynomial.go
+++ b/ecc/bls24-317/fr/polynomial/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/polynomial/polynomial_test.go b/ecc/bls24-317/fr/polynomial/polynomial_test.go
index 405cee1554..3059949480 100644
--- a/ecc/bls24-317/fr/polynomial/polynomial_test.go
+++ b/ecc/bls24-317/fr/polynomial/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/polynomial/pool.go b/ecc/bls24-317/fr/polynomial/pool.go
index 1d22d71c4a..2955c19699 100644
--- a/ecc/bls24-317/fr/polynomial/pool.go
+++ b/ecc/bls24-317/fr/polynomial/pool.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/poseidon2/poseidon2.go b/ecc/bls24-317/fr/poseidon2/poseidon2.go
index d117b4cf24..74bec677a8 100644
--- a/ecc/bls24-317/fr/poseidon2/poseidon2.go
+++ b/ecc/bls24-317/fr/poseidon2/poseidon2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/poseidon2/poseidon2_test.go b/ecc/bls24-317/fr/poseidon2/poseidon2_test.go
index 3819256f1d..eb107b7a64 100644
--- a/ecc/bls24-317/fr/poseidon2/poseidon2_test.go
+++ b/ecc/bls24-317/fr/poseidon2/poseidon2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/sumcheck/sumcheck.go b/ecc/bls24-317/fr/sumcheck/sumcheck.go
index d6c8c5fd16..16e185683a 100644
--- a/ecc/bls24-317/fr/sumcheck/sumcheck.go
+++ b/ecc/bls24-317/fr/sumcheck/sumcheck.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/sumcheck/sumcheck_test.go b/ecc/bls24-317/fr/sumcheck/sumcheck_test.go
index 23e578f997..a950b2b525 100644
--- a/ecc/bls24-317/fr/sumcheck/sumcheck_test.go
+++ b/ecc/bls24-317/fr/sumcheck/sumcheck_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/test_vector_utils/test_vector_utils.go b/ecc/bls24-317/fr/test_vector_utils/test_vector_utils.go
index 457cd4f90a..1f91003ca1 100644
--- a/ecc/bls24-317/fr/test_vector_utils/test_vector_utils.go
+++ b/ecc/bls24-317/fr/test_vector_utils/test_vector_utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/vector.go b/ecc/bls24-317/fr/vector.go
index 4654b1b2d3..7792a6f73b 100644
--- a/ecc/bls24-317/fr/vector.go
+++ b/ecc/bls24-317/fr/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/vector_amd64.go b/ecc/bls24-317/fr/vector_amd64.go
index a7dcec3b25..e3565da46a 100644
--- a/ecc/bls24-317/fr/vector_amd64.go
+++ b/ecc/bls24-317/fr/vector_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/vector_purego.go b/ecc/bls24-317/fr/vector_purego.go
index db43e73504..6608e394c7 100644
--- a/ecc/bls24-317/fr/vector_purego.go
+++ b/ecc/bls24-317/fr/vector_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || !amd64
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/fr/vector_test.go b/ecc/bls24-317/fr/vector_test.go
index f6179e7824..88c4ef318f 100644
--- a/ecc/bls24-317/fr/vector_test.go
+++ b/ecc/bls24-317/fr/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/g1.go b/ecc/bls24-317/g1.go
index 5ef6d07fd5..1d6cb221b5 100644
--- a/ecc/bls24-317/g1.go
+++ b/ecc/bls24-317/g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/g1_test.go b/ecc/bls24-317/g1_test.go
index d1bd90ba35..647f6a6c4c 100644
--- a/ecc/bls24-317/g1_test.go
+++ b/ecc/bls24-317/g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/g2.go b/ecc/bls24-317/g2.go
index a5bfac4672..9dd813ade8 100644
--- a/ecc/bls24-317/g2.go
+++ b/ecc/bls24-317/g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/g2_test.go b/ecc/bls24-317/g2_test.go
index df7af3eec8..8d4e7aca31 100644
--- a/ecc/bls24-317/g2_test.go
+++ b/ecc/bls24-317/g2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/hash_to_g1.go b/ecc/bls24-317/hash_to_g1.go
index 38211f5c36..7a0115df75 100644
--- a/ecc/bls24-317/hash_to_g1.go
+++ b/ecc/bls24-317/hash_to_g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/hash_to_g1_test.go b/ecc/bls24-317/hash_to_g1_test.go
index 5c72f5ad0d..e3647fdea4 100644
--- a/ecc/bls24-317/hash_to_g1_test.go
+++ b/ecc/bls24-317/hash_to_g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/kzg/doc.go b/ecc/bls24-317/kzg/doc.go
index 226614bbdf..3a86419c48 100644
--- a/ecc/bls24-317/kzg/doc.go
+++ b/ecc/bls24-317/kzg/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/kzg/kzg.go b/ecc/bls24-317/kzg/kzg.go
index 16008e9885..245d2643dc 100644
--- a/ecc/bls24-317/kzg/kzg.go
+++ b/ecc/bls24-317/kzg/kzg.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/kzg/kzg_test.go b/ecc/bls24-317/kzg/kzg_test.go
index 10c75771a4..5180d5dc95 100644
--- a/ecc/bls24-317/kzg/kzg_test.go
+++ b/ecc/bls24-317/kzg/kzg_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/kzg/marshal.go b/ecc/bls24-317/kzg/marshal.go
index 6816b2f119..f631b5c6ca 100644
--- a/ecc/bls24-317/kzg/marshal.go
+++ b/ecc/bls24-317/kzg/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/kzg/utils.go b/ecc/bls24-317/kzg/utils.go
index 898c7b3463..35d6154bb3 100644
--- a/ecc/bls24-317/kzg/utils.go
+++ b/ecc/bls24-317/kzg/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/marshal.go b/ecc/bls24-317/marshal.go
index 763eb62c94..3b2203b685 100644
--- a/ecc/bls24-317/marshal.go
+++ b/ecc/bls24-317/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/marshal_test.go b/ecc/bls24-317/marshal_test.go
index 0322fefb3b..fdc5ab5883 100644
--- a/ecc/bls24-317/marshal_test.go
+++ b/ecc/bls24-317/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/multiexp.go b/ecc/bls24-317/multiexp.go
index bf2504ddb5..a0321ad092 100644
--- a/ecc/bls24-317/multiexp.go
+++ b/ecc/bls24-317/multiexp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/multiexp_affine.go b/ecc/bls24-317/multiexp_affine.go
index 976580c294..6d2459a1c9 100644
--- a/ecc/bls24-317/multiexp_affine.go
+++ b/ecc/bls24-317/multiexp_affine.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/multiexp_jacobian.go b/ecc/bls24-317/multiexp_jacobian.go
index c0a5fbc7d4..f86d71d812 100644
--- a/ecc/bls24-317/multiexp_jacobian.go
+++ b/ecc/bls24-317/multiexp_jacobian.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/multiexp_test.go b/ecc/bls24-317/multiexp_test.go
index 767ab56c23..abd7e15109 100644
--- a/ecc/bls24-317/multiexp_test.go
+++ b/ecc/bls24-317/multiexp_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/pairing_test.go b/ecc/bls24-317/pairing_test.go
index 0d7fa6d740..b0e45be37c 100644
--- a/ecc/bls24-317/pairing_test.go
+++ b/ecc/bls24-317/pairing_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/shplonk/doc.go b/ecc/bls24-317/shplonk/doc.go
index 0367893999..d63c7a3ddf 100644
--- a/ecc/bls24-317/shplonk/doc.go
+++ b/ecc/bls24-317/shplonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/shplonk/example_test.go b/ecc/bls24-317/shplonk/example_test.go
index 3ecd80e281..c824a4b96d 100644
--- a/ecc/bls24-317/shplonk/example_test.go
+++ b/ecc/bls24-317/shplonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/shplonk/marshal.go b/ecc/bls24-317/shplonk/marshal.go
index 2345e8da9d..733d7b082f 100644
--- a/ecc/bls24-317/shplonk/marshal.go
+++ b/ecc/bls24-317/shplonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/shplonk/shplonk.go b/ecc/bls24-317/shplonk/shplonk.go
index f63bcc9dca..f949b5f196 100644
--- a/ecc/bls24-317/shplonk/shplonk.go
+++ b/ecc/bls24-317/shplonk/shplonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/shplonk/shplonk_test.go b/ecc/bls24-317/shplonk/shplonk_test.go
index 5f5eb5b05d..97dddd2de4 100644
--- a/ecc/bls24-317/shplonk/shplonk_test.go
+++ b/ecc/bls24-317/shplonk/shplonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/twistededwards/curve.go b/ecc/bls24-317/twistededwards/curve.go
index 952c388d69..e7da422c9d 100644
--- a/ecc/bls24-317/twistededwards/curve.go
+++ b/ecc/bls24-317/twistededwards/curve.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/twistededwards/doc.go b/ecc/bls24-317/twistededwards/doc.go
index e50b5bc91c..e9ac2d624c 100644
--- a/ecc/bls24-317/twistededwards/doc.go
+++ b/ecc/bls24-317/twistededwards/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/twistededwards/eddsa/doc.go b/ecc/bls24-317/twistededwards/eddsa/doc.go
index babd5b23ed..e5b9f85686 100644
--- a/ecc/bls24-317/twistededwards/eddsa/doc.go
+++ b/ecc/bls24-317/twistededwards/eddsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/twistededwards/eddsa/eddsa.go b/ecc/bls24-317/twistededwards/eddsa/eddsa.go
index f3fe4f8f88..b299102475 100644
--- a/ecc/bls24-317/twistededwards/eddsa/eddsa.go
+++ b/ecc/bls24-317/twistededwards/eddsa/eddsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/twistededwards/eddsa/eddsa_test.go b/ecc/bls24-317/twistededwards/eddsa/eddsa_test.go
index dc56916881..909c078fd7 100644
--- a/ecc/bls24-317/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bls24-317/twistededwards/eddsa/eddsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/twistededwards/eddsa/marshal.go b/ecc/bls24-317/twistededwards/eddsa/marshal.go
index c5f2a6e909..c148504fda 100644
--- a/ecc/bls24-317/twistededwards/eddsa/marshal.go
+++ b/ecc/bls24-317/twistededwards/eddsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/twistededwards/point.go b/ecc/bls24-317/twistededwards/point.go
index 26312f97f1..128c78b2bd 100644
--- a/ecc/bls24-317/twistededwards/point.go
+++ b/ecc/bls24-317/twistededwards/point.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bls24-317/twistededwards/point_test.go b/ecc/bls24-317/twistededwards/point_test.go
index 2019c5809e..15cabd72de 100644
--- a/ecc/bls24-317/twistededwards/point_test.go
+++ b/ecc/bls24-317/twistededwards/point_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/ecdsa/doc.go b/ecc/bn254/ecdsa/doc.go
index 0d2265c25a..2f9a655c22 100644
--- a/ecc/bn254/ecdsa/doc.go
+++ b/ecc/bn254/ecdsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/ecdsa/ecdsa.go b/ecc/bn254/ecdsa/ecdsa.go
index fbdd78ca48..963784e5ff 100644
--- a/ecc/bn254/ecdsa/ecdsa.go
+++ b/ecc/bn254/ecdsa/ecdsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/ecdsa/ecdsa_test.go b/ecc/bn254/ecdsa/ecdsa_test.go
index 086ae3c7ed..f5593addca 100644
--- a/ecc/bn254/ecdsa/ecdsa_test.go
+++ b/ecc/bn254/ecdsa/ecdsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/ecdsa/marshal.go b/ecc/bn254/ecdsa/marshal.go
index bc3aecbd7c..ec405a2f17 100644
--- a/ecc/bn254/ecdsa/marshal.go
+++ b/ecc/bn254/ecdsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/ecdsa/marshal_test.go b/ecc/bn254/ecdsa/marshal_test.go
index 24508e4011..d4bc699ab7 100644
--- a/ecc/bn254/ecdsa/marshal_test.go
+++ b/ecc/bn254/ecdsa/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fflonk/doc.go b/ecc/bn254/fflonk/doc.go
index 67a8094e35..a2506720a8 100644
--- a/ecc/bn254/fflonk/doc.go
+++ b/ecc/bn254/fflonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fflonk/example_test.go b/ecc/bn254/fflonk/example_test.go
index 96c7f30f76..89e1cbe722 100644
--- a/ecc/bn254/fflonk/example_test.go
+++ b/ecc/bn254/fflonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fflonk/fflonk.go b/ecc/bn254/fflonk/fflonk.go
index 2e0498b0f3..5ffdd232ff 100644
--- a/ecc/bn254/fflonk/fflonk.go
+++ b/ecc/bn254/fflonk/fflonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fflonk/fflonk_test.go b/ecc/bn254/fflonk/fflonk_test.go
index c22fea4f11..1a39b3a8b8 100644
--- a/ecc/bn254/fflonk/fflonk_test.go
+++ b/ecc/bn254/fflonk/fflonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fflonk/marshal.go b/ecc/bn254/fflonk/marshal.go
index c80e3c776d..1caa3238bd 100644
--- a/ecc/bn254/fflonk/marshal.go
+++ b/ecc/bn254/fflonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/arith.go b/ecc/bn254/fp/arith.go
index bb63552f5a..5c9905de80 100644
--- a/ecc/bn254/fp/arith.go
+++ b/ecc/bn254/fp/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/asm_adx.go b/ecc/bn254/fp/asm_adx.go
index 75e92992fe..8d85a11345 100644
--- a/ecc/bn254/fp/asm_adx.go
+++ b/ecc/bn254/fp/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/asm_avx.go b/ecc/bn254/fp/asm_avx.go
index aa233664d0..45e1ab3f0d 100644
--- a/ecc/bn254/fp/asm_avx.go
+++ b/ecc/bn254/fp/asm_avx.go
@@ -1,6 +1,6 @@
 //go:build !noavx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/asm_noadx.go b/ecc/bn254/fp/asm_noadx.go
index 304dfb7209..75ca96d775 100644
--- a/ecc/bn254/fp/asm_noadx.go
+++ b/ecc/bn254/fp/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/asm_noavx.go b/ecc/bn254/fp/asm_noavx.go
index 900dedbe8b..01f2011925 100644
--- a/ecc/bn254/fp/asm_noavx.go
+++ b/ecc/bn254/fp/asm_noavx.go
@@ -1,6 +1,6 @@
 //go:build noavx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/doc.go b/ecc/bn254/fp/doc.go
index 478c1f24dd..0a37ea68ec 100644
--- a/ecc/bn254/fp/doc.go
+++ b/ecc/bn254/fp/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/element.go b/ecc/bn254/fp/element.go
index ed963e2d50..44aaa929bc 100644
--- a/ecc/bn254/fp/element.go
+++ b/ecc/bn254/fp/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/element_amd64.go b/ecc/bn254/fp/element_amd64.go
index 9cee062e5b..1a6e1cf5eb 100644
--- a/ecc/bn254/fp/element_amd64.go
+++ b/ecc/bn254/fp/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/element_amd64.s b/ecc/bn254/fp/element_amd64.s
index a7c6ffae66..41c54b1aa6 100644
--- a/ecc/bn254/fp/element_amd64.s
+++ b/ecc/bn254/fp/element_amd64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/element_arm64.go b/ecc/bn254/fp/element_arm64.go
index ed26d2b3d9..e27faa8f54 100644
--- a/ecc/bn254/fp/element_arm64.go
+++ b/ecc/bn254/fp/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/element_arm64.s b/ecc/bn254/fp/element_arm64.s
index ef16eaba35..0668975118 100644
--- a/ecc/bn254/fp/element_arm64.s
+++ b/ecc/bn254/fp/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/element_exp.go b/ecc/bn254/fp/element_exp.go
index 38eb2749af..a1f9c2a492 100644
--- a/ecc/bn254/fp/element_exp.go
+++ b/ecc/bn254/fp/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/element_purego.go b/ecc/bn254/fp/element_purego.go
index 861b453dfd..69565d890b 100644
--- a/ecc/bn254/fp/element_purego.go
+++ b/ecc/bn254/fp/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/element_test.go b/ecc/bn254/fp/element_test.go
index 4b2af9d309..4fd5a6a70d 100644
--- a/ecc/bn254/fp/element_test.go
+++ b/ecc/bn254/fp/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/hash_to_field/doc.go b/ecc/bn254/fp/hash_to_field/doc.go
index 113b4e6e69..ab058501c5 100644
--- a/ecc/bn254/fp/hash_to_field/doc.go
+++ b/ecc/bn254/fp/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/hash_to_field/hash_to_field.go b/ecc/bn254/fp/hash_to_field/hash_to_field.go
index f7b035d633..9a67fefa43 100644
--- a/ecc/bn254/fp/hash_to_field/hash_to_field.go
+++ b/ecc/bn254/fp/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/hash_to_field/hash_to_field_test.go b/ecc/bn254/fp/hash_to_field/hash_to_field_test.go
index ba809d498b..97cc2b3e97 100644
--- a/ecc/bn254/fp/hash_to_field/hash_to_field_test.go
+++ b/ecc/bn254/fp/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/vector.go b/ecc/bn254/fp/vector.go
index ef60ed4b45..5dfc17ebbc 100644
--- a/ecc/bn254/fp/vector.go
+++ b/ecc/bn254/fp/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/vector_amd64.go b/ecc/bn254/fp/vector_amd64.go
index 9e05e6b2f3..26cdca4517 100644
--- a/ecc/bn254/fp/vector_amd64.go
+++ b/ecc/bn254/fp/vector_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/vector_purego.go b/ecc/bn254/fp/vector_purego.go
index 6adeb1a8a2..98343052a2 100644
--- a/ecc/bn254/fp/vector_purego.go
+++ b/ecc/bn254/fp/vector_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || !amd64
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fp/vector_test.go b/ecc/bn254/fp/vector_test.go
index e7185486cf..5f78812dc6 100644
--- a/ecc/bn254/fp/vector_test.go
+++ b/ecc/bn254/fp/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/arith.go b/ecc/bn254/fr/arith.go
index dbba8a9ae4..8dbae56e32 100644
--- a/ecc/bn254/fr/arith.go
+++ b/ecc/bn254/fr/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/asm_adx.go b/ecc/bn254/fr/asm_adx.go
index 9b970335f1..52421cc159 100644
--- a/ecc/bn254/fr/asm_adx.go
+++ b/ecc/bn254/fr/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/asm_avx.go b/ecc/bn254/fr/asm_avx.go
index 2a0a166ed4..f89a44926d 100644
--- a/ecc/bn254/fr/asm_avx.go
+++ b/ecc/bn254/fr/asm_avx.go
@@ -1,6 +1,6 @@
 //go:build !noavx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/asm_noadx.go b/ecc/bn254/fr/asm_noadx.go
index 96741014f2..9c9c9dab5d 100644
--- a/ecc/bn254/fr/asm_noadx.go
+++ b/ecc/bn254/fr/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/asm_noavx.go b/ecc/bn254/fr/asm_noavx.go
index 3cb6968fb8..ae86f75e7f 100644
--- a/ecc/bn254/fr/asm_noavx.go
+++ b/ecc/bn254/fr/asm_noavx.go
@@ -1,6 +1,6 @@
 //go:build noavx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/doc.go b/ecc/bn254/fr/doc.go
index 0f4414a3a5..49b9df511a 100644
--- a/ecc/bn254/fr/doc.go
+++ b/ecc/bn254/fr/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/element.go b/ecc/bn254/fr/element.go
index b34c9b59ba..a8f372c092 100644
--- a/ecc/bn254/fr/element.go
+++ b/ecc/bn254/fr/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/element_amd64.go b/ecc/bn254/fr/element_amd64.go
index 4c3f2a8567..7e76a943a1 100644
--- a/ecc/bn254/fr/element_amd64.go
+++ b/ecc/bn254/fr/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/element_amd64.s b/ecc/bn254/fr/element_amd64.s
index a7c6ffae66..41c54b1aa6 100644
--- a/ecc/bn254/fr/element_amd64.s
+++ b/ecc/bn254/fr/element_amd64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/element_arm64.go b/ecc/bn254/fr/element_arm64.go
index 2277914932..ebcd02f492 100644
--- a/ecc/bn254/fr/element_arm64.go
+++ b/ecc/bn254/fr/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/element_arm64.s b/ecc/bn254/fr/element_arm64.s
index ef16eaba35..0668975118 100644
--- a/ecc/bn254/fr/element_arm64.s
+++ b/ecc/bn254/fr/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/element_exp.go b/ecc/bn254/fr/element_exp.go
index 6e87fa4f7e..28b8506cf4 100644
--- a/ecc/bn254/fr/element_exp.go
+++ b/ecc/bn254/fr/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/element_purego.go b/ecc/bn254/fr/element_purego.go
index 70529c5ec8..8b6bab2e09 100644
--- a/ecc/bn254/fr/element_purego.go
+++ b/ecc/bn254/fr/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/element_test.go b/ecc/bn254/fr/element_test.go
index 642d30347d..7811fc3b70 100644
--- a/ecc/bn254/fr/element_test.go
+++ b/ecc/bn254/fr/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/fft/bitreverse.go b/ecc/bn254/fr/fft/bitreverse.go
index 1299286f68..e8964eaaf3 100644
--- a/ecc/bn254/fr/fft/bitreverse.go
+++ b/ecc/bn254/fr/fft/bitreverse.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/fft/bitreverse_test.go b/ecc/bn254/fr/fft/bitreverse_test.go
index 28c14b4936..5ee59d2068 100644
--- a/ecc/bn254/fr/fft/bitreverse_test.go
+++ b/ecc/bn254/fr/fft/bitreverse_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/fft/doc.go b/ecc/bn254/fr/fft/doc.go
index 4cce0f9779..8176d8e77a 100644
--- a/ecc/bn254/fr/fft/doc.go
+++ b/ecc/bn254/fr/fft/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/fft/domain.go b/ecc/bn254/fr/fft/domain.go
index cf4c08e7c4..6280b881eb 100644
--- a/ecc/bn254/fr/fft/domain.go
+++ b/ecc/bn254/fr/fft/domain.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/fft/domain_test.go b/ecc/bn254/fr/fft/domain_test.go
index e445d3cc12..7049120e6a 100644
--- a/ecc/bn254/fr/fft/domain_test.go
+++ b/ecc/bn254/fr/fft/domain_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/fft/fft.go b/ecc/bn254/fr/fft/fft.go
index 5b65603a62..2d75394897 100644
--- a/ecc/bn254/fr/fft/fft.go
+++ b/ecc/bn254/fr/fft/fft.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/fft/fft_test.go b/ecc/bn254/fr/fft/fft_test.go
index 758a257721..89237d314b 100644
--- a/ecc/bn254/fr/fft/fft_test.go
+++ b/ecc/bn254/fr/fft/fft_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/fft/options.go b/ecc/bn254/fr/fft/options.go
index 9656a9e5d9..ae1c9b40f5 100644
--- a/ecc/bn254/fr/fft/options.go
+++ b/ecc/bn254/fr/fft/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/fri/doc.go b/ecc/bn254/fr/fri/doc.go
index cea69fc79a..164ee83268 100644
--- a/ecc/bn254/fr/fri/doc.go
+++ b/ecc/bn254/fr/fri/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/fri/fri.go b/ecc/bn254/fr/fri/fri.go
index f4443969ae..f67873cac2 100644
--- a/ecc/bn254/fr/fri/fri.go
+++ b/ecc/bn254/fr/fri/fri.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/fri/fri_test.go b/ecc/bn254/fr/fri/fri_test.go
index 9092076f81..9f3343a32a 100644
--- a/ecc/bn254/fr/fri/fri_test.go
+++ b/ecc/bn254/fr/fri/fri_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/generator.go b/ecc/bn254/fr/generator.go
index 7997c96216..085998e5c5 100644
--- a/ecc/bn254/fr/generator.go
+++ b/ecc/bn254/fr/generator.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/gkr/gkr.go b/ecc/bn254/fr/gkr/gkr.go
index 696f2e095e..5f6c5b4362 100644
--- a/ecc/bn254/fr/gkr/gkr.go
+++ b/ecc/bn254/fr/gkr/gkr.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/gkr/gkr_test.go b/ecc/bn254/fr/gkr/gkr_test.go
index cfd06a0aa7..72cb355421 100644
--- a/ecc/bn254/fr/gkr/gkr_test.go
+++ b/ecc/bn254/fr/gkr/gkr_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/hash_to_field/doc.go b/ecc/bn254/fr/hash_to_field/doc.go
index cf89740488..6d48d0f9fe 100644
--- a/ecc/bn254/fr/hash_to_field/doc.go
+++ b/ecc/bn254/fr/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/hash_to_field/hash_to_field.go b/ecc/bn254/fr/hash_to_field/hash_to_field.go
index 6753b391a1..99af302dbf 100644
--- a/ecc/bn254/fr/hash_to_field/hash_to_field.go
+++ b/ecc/bn254/fr/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/hash_to_field/hash_to_field_test.go b/ecc/bn254/fr/hash_to_field/hash_to_field_test.go
index 37e7db2dad..12c44d288d 100644
--- a/ecc/bn254/fr/hash_to_field/hash_to_field_test.go
+++ b/ecc/bn254/fr/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/iop/doc.go b/ecc/bn254/fr/iop/doc.go
index 2ef06dfe1a..6c9a441cc1 100644
--- a/ecc/bn254/fr/iop/doc.go
+++ b/ecc/bn254/fr/iop/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/iop/expressions.go b/ecc/bn254/fr/iop/expressions.go
index 57b95b2d6d..a8bbfd5014 100644
--- a/ecc/bn254/fr/iop/expressions.go
+++ b/ecc/bn254/fr/iop/expressions.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/iop/expressions_test.go b/ecc/bn254/fr/iop/expressions_test.go
index 29a2a7ef10..b7072ffc23 100644
--- a/ecc/bn254/fr/iop/expressions_test.go
+++ b/ecc/bn254/fr/iop/expressions_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/iop/polynomial.go b/ecc/bn254/fr/iop/polynomial.go
index d5e1e0ad4f..04866d7fd6 100644
--- a/ecc/bn254/fr/iop/polynomial.go
+++ b/ecc/bn254/fr/iop/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/iop/polynomial_test.go b/ecc/bn254/fr/iop/polynomial_test.go
index b716b83912..57f7cc0620 100644
--- a/ecc/bn254/fr/iop/polynomial_test.go
+++ b/ecc/bn254/fr/iop/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/iop/quotient.go b/ecc/bn254/fr/iop/quotient.go
index 89056e1d12..6cb20d32ac 100644
--- a/ecc/bn254/fr/iop/quotient.go
+++ b/ecc/bn254/fr/iop/quotient.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/iop/quotient_test.go b/ecc/bn254/fr/iop/quotient_test.go
index c9df5e2971..1767068ba4 100644
--- a/ecc/bn254/fr/iop/quotient_test.go
+++ b/ecc/bn254/fr/iop/quotient_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/iop/ratios.go b/ecc/bn254/fr/iop/ratios.go
index 1239a2ccf1..20bb7a761e 100644
--- a/ecc/bn254/fr/iop/ratios.go
+++ b/ecc/bn254/fr/iop/ratios.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/iop/ratios_test.go b/ecc/bn254/fr/iop/ratios_test.go
index e7c8659ec1..af3350a5ca 100644
--- a/ecc/bn254/fr/iop/ratios_test.go
+++ b/ecc/bn254/fr/iop/ratios_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/iop/utils.go b/ecc/bn254/fr/iop/utils.go
index 674bb93184..04134eec44 100644
--- a/ecc/bn254/fr/iop/utils.go
+++ b/ecc/bn254/fr/iop/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/mimc/doc.go b/ecc/bn254/fr/mimc/doc.go
index 900b977185..946e0dafaa 100644
--- a/ecc/bn254/fr/mimc/doc.go
+++ b/ecc/bn254/fr/mimc/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/mimc/mimc.go b/ecc/bn254/fr/mimc/mimc.go
index f7fde2955e..91f260e3cd 100644
--- a/ecc/bn254/fr/mimc/mimc.go
+++ b/ecc/bn254/fr/mimc/mimc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/mimc/mimc_test.go b/ecc/bn254/fr/mimc/mimc_test.go
index 1c0a7e4c5f..71607747d8 100644
--- a/ecc/bn254/fr/mimc/mimc_test.go
+++ b/ecc/bn254/fr/mimc/mimc_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/mimc/options.go b/ecc/bn254/fr/mimc/options.go
index ad4e60060e..19c825f9c8 100644
--- a/ecc/bn254/fr/mimc/options.go
+++ b/ecc/bn254/fr/mimc/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/pedersen/doc.go b/ecc/bn254/fr/pedersen/doc.go
index 2e24034936..dff1285d0e 100644
--- a/ecc/bn254/fr/pedersen/doc.go
+++ b/ecc/bn254/fr/pedersen/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/pedersen/example_test.go b/ecc/bn254/fr/pedersen/example_test.go
index e31c8c6449..bd81d20fa3 100644
--- a/ecc/bn254/fr/pedersen/example_test.go
+++ b/ecc/bn254/fr/pedersen/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/pedersen/pedersen.go b/ecc/bn254/fr/pedersen/pedersen.go
index 9b4e645cee..ec973971cb 100644
--- a/ecc/bn254/fr/pedersen/pedersen.go
+++ b/ecc/bn254/fr/pedersen/pedersen.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/pedersen/pedersen_test.go b/ecc/bn254/fr/pedersen/pedersen_test.go
index 1c72af2a1e..27585e8911 100644
--- a/ecc/bn254/fr/pedersen/pedersen_test.go
+++ b/ecc/bn254/fr/pedersen/pedersen_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/permutation/doc.go b/ecc/bn254/fr/permutation/doc.go
index e24cd82923..4f2ea7b2e4 100644
--- a/ecc/bn254/fr/permutation/doc.go
+++ b/ecc/bn254/fr/permutation/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/permutation/permutation.go b/ecc/bn254/fr/permutation/permutation.go
index 7bc72f1ff6..cc0a44efc1 100644
--- a/ecc/bn254/fr/permutation/permutation.go
+++ b/ecc/bn254/fr/permutation/permutation.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/permutation/permutation_test.go b/ecc/bn254/fr/permutation/permutation_test.go
index 33924e26ee..28b7ac1567 100644
--- a/ecc/bn254/fr/permutation/permutation_test.go
+++ b/ecc/bn254/fr/permutation/permutation_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/plookup/doc.go b/ecc/bn254/fr/plookup/doc.go
index 7a02c59719..5507122fab 100644
--- a/ecc/bn254/fr/plookup/doc.go
+++ b/ecc/bn254/fr/plookup/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/plookup/plookup_test.go b/ecc/bn254/fr/plookup/plookup_test.go
index e91a4ded4e..124a4d285f 100644
--- a/ecc/bn254/fr/plookup/plookup_test.go
+++ b/ecc/bn254/fr/plookup/plookup_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/plookup/table.go b/ecc/bn254/fr/plookup/table.go
index 15728734c2..25faf46e06 100644
--- a/ecc/bn254/fr/plookup/table.go
+++ b/ecc/bn254/fr/plookup/table.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/plookup/vector.go b/ecc/bn254/fr/plookup/vector.go
index c1494d3f9a..a041bd151f 100644
--- a/ecc/bn254/fr/plookup/vector.go
+++ b/ecc/bn254/fr/plookup/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/polynomial/doc.go b/ecc/bn254/fr/polynomial/doc.go
index fd96328e8f..ead3b5cba5 100644
--- a/ecc/bn254/fr/polynomial/doc.go
+++ b/ecc/bn254/fr/polynomial/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/polynomial/multilin.go b/ecc/bn254/fr/polynomial/multilin.go
index 3399187752..63c3d9b391 100644
--- a/ecc/bn254/fr/polynomial/multilin.go
+++ b/ecc/bn254/fr/polynomial/multilin.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/polynomial/multilin_test.go b/ecc/bn254/fr/polynomial/multilin_test.go
index 7ce598505a..f091925d17 100644
--- a/ecc/bn254/fr/polynomial/multilin_test.go
+++ b/ecc/bn254/fr/polynomial/multilin_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/polynomial/polynomial.go b/ecc/bn254/fr/polynomial/polynomial.go
index 0b463ffab8..ef43bb7718 100644
--- a/ecc/bn254/fr/polynomial/polynomial.go
+++ b/ecc/bn254/fr/polynomial/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/polynomial/polynomial_test.go b/ecc/bn254/fr/polynomial/polynomial_test.go
index 76fad6fd40..32467ef247 100644
--- a/ecc/bn254/fr/polynomial/polynomial_test.go
+++ b/ecc/bn254/fr/polynomial/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/polynomial/pool.go b/ecc/bn254/fr/polynomial/pool.go
index ada08b72e8..baabae0ed8 100644
--- a/ecc/bn254/fr/polynomial/pool.go
+++ b/ecc/bn254/fr/polynomial/pool.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/poseidon2/poseidon2.go b/ecc/bn254/fr/poseidon2/poseidon2.go
index b781f9bb46..bf5384f4ce 100644
--- a/ecc/bn254/fr/poseidon2/poseidon2.go
+++ b/ecc/bn254/fr/poseidon2/poseidon2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/poseidon2/poseidon2_test.go b/ecc/bn254/fr/poseidon2/poseidon2_test.go
index eb3c7c78e3..712f04accf 100644
--- a/ecc/bn254/fr/poseidon2/poseidon2_test.go
+++ b/ecc/bn254/fr/poseidon2/poseidon2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/sis/sis_fft.go b/ecc/bn254/fr/sis/sis_fft.go
index 2ea3c6f4e7..05cded5aa0 100644
--- a/ecc/bn254/fr/sis/sis_fft.go
+++ b/ecc/bn254/fr/sis/sis_fft.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/sumcheck/sumcheck.go b/ecc/bn254/fr/sumcheck/sumcheck.go
index a44078c499..89b7d9b8e3 100644
--- a/ecc/bn254/fr/sumcheck/sumcheck.go
+++ b/ecc/bn254/fr/sumcheck/sumcheck.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/sumcheck/sumcheck_test.go b/ecc/bn254/fr/sumcheck/sumcheck_test.go
index 4e50495ac8..563ca3d283 100644
--- a/ecc/bn254/fr/sumcheck/sumcheck_test.go
+++ b/ecc/bn254/fr/sumcheck/sumcheck_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/test_vector_utils/test_vector_utils.go b/ecc/bn254/fr/test_vector_utils/test_vector_utils.go
index 581dd25889..be73caa596 100644
--- a/ecc/bn254/fr/test_vector_utils/test_vector_utils.go
+++ b/ecc/bn254/fr/test_vector_utils/test_vector_utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/vector.go b/ecc/bn254/fr/vector.go
index 4654b1b2d3..7792a6f73b 100644
--- a/ecc/bn254/fr/vector.go
+++ b/ecc/bn254/fr/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/vector_amd64.go b/ecc/bn254/fr/vector_amd64.go
index a7dcec3b25..e3565da46a 100644
--- a/ecc/bn254/fr/vector_amd64.go
+++ b/ecc/bn254/fr/vector_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/vector_purego.go b/ecc/bn254/fr/vector_purego.go
index db43e73504..6608e394c7 100644
--- a/ecc/bn254/fr/vector_purego.go
+++ b/ecc/bn254/fr/vector_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || !amd64
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/vector_test.go b/ecc/bn254/fr/vector_test.go
index f6179e7824..88c4ef318f 100644
--- a/ecc/bn254/fr/vector_test.go
+++ b/ecc/bn254/fr/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/g1.go b/ecc/bn254/g1.go
index b10c129683..f9df8cde99 100644
--- a/ecc/bn254/g1.go
+++ b/ecc/bn254/g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/g1_test.go b/ecc/bn254/g1_test.go
index 1e95f6a6b5..a489fec091 100644
--- a/ecc/bn254/g1_test.go
+++ b/ecc/bn254/g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/g2.go b/ecc/bn254/g2.go
index b89ec2f626..daa22174b3 100644
--- a/ecc/bn254/g2.go
+++ b/ecc/bn254/g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/g2_test.go b/ecc/bn254/g2_test.go
index e1b5a712b5..eb6b671642 100644
--- a/ecc/bn254/g2_test.go
+++ b/ecc/bn254/g2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/hash_to_g1.go b/ecc/bn254/hash_to_g1.go
index bbc18d42b3..f59cf92b54 100644
--- a/ecc/bn254/hash_to_g1.go
+++ b/ecc/bn254/hash_to_g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/hash_to_g1_test.go b/ecc/bn254/hash_to_g1_test.go
index e5915f4ab0..7134af210d 100644
--- a/ecc/bn254/hash_to_g1_test.go
+++ b/ecc/bn254/hash_to_g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/hash_to_g2.go b/ecc/bn254/hash_to_g2.go
index 9c6cd9230e..c036c79126 100644
--- a/ecc/bn254/hash_to_g2.go
+++ b/ecc/bn254/hash_to_g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/hash_to_g2_test.go b/ecc/bn254/hash_to_g2_test.go
index 6b21f48a9d..4eec69c15f 100644
--- a/ecc/bn254/hash_to_g2_test.go
+++ b/ecc/bn254/hash_to_g2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/internal/fptower/asm.go b/ecc/bn254/internal/fptower/asm.go
index 7d64458b6c..c08e8f1574 100644
--- a/ecc/bn254/internal/fptower/asm.go
+++ b/ecc/bn254/internal/fptower/asm.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/internal/fptower/asm_noadx.go b/ecc/bn254/internal/fptower/asm_noadx.go
index 28588f65a0..1dc20b4991 100644
--- a/ecc/bn254/internal/fptower/asm_noadx.go
+++ b/ecc/bn254/internal/fptower/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/internal/fptower/e12.go b/ecc/bn254/internal/fptower/e12.go
index 043a8a4c85..1af2de4375 100644
--- a/ecc/bn254/internal/fptower/e12.go
+++ b/ecc/bn254/internal/fptower/e12.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/internal/fptower/e12_test.go b/ecc/bn254/internal/fptower/e12_test.go
index ab1bc05a1a..f813ca5817 100644
--- a/ecc/bn254/internal/fptower/e12_test.go
+++ b/ecc/bn254/internal/fptower/e12_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/internal/fptower/e2.go b/ecc/bn254/internal/fptower/e2.go
index b0532223db..23f6f99a76 100644
--- a/ecc/bn254/internal/fptower/e2.go
+++ b/ecc/bn254/internal/fptower/e2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/internal/fptower/e2_amd64.go b/ecc/bn254/internal/fptower/e2_amd64.go
index c885a81a61..17873820c3 100644
--- a/ecc/bn254/internal/fptower/e2_amd64.go
+++ b/ecc/bn254/internal/fptower/e2_amd64.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/internal/fptower/e2_amd64.s b/ecc/bn254/internal/fptower/e2_amd64.s
index f7d030d9dd..6806565b52 100644
--- a/ecc/bn254/internal/fptower/e2_amd64.s
+++ b/ecc/bn254/internal/fptower/e2_amd64.s
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 #include "textflag.h"
diff --git a/ecc/bn254/internal/fptower/e2_fallback.go b/ecc/bn254/internal/fptower/e2_fallback.go
index 3dff96dcea..7a2461ec53 100644
--- a/ecc/bn254/internal/fptower/e2_fallback.go
+++ b/ecc/bn254/internal/fptower/e2_fallback.go
@@ -1,6 +1,6 @@
 //go:build !amd64
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/internal/fptower/e2_test.go b/ecc/bn254/internal/fptower/e2_test.go
index c28bfae171..f47f9d37f7 100644
--- a/ecc/bn254/internal/fptower/e2_test.go
+++ b/ecc/bn254/internal/fptower/e2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/internal/fptower/e6.go b/ecc/bn254/internal/fptower/e6.go
index a3bd71a6cc..13fdfdd297 100644
--- a/ecc/bn254/internal/fptower/e6.go
+++ b/ecc/bn254/internal/fptower/e6.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/internal/fptower/e6_test.go b/ecc/bn254/internal/fptower/e6_test.go
index a81a5daa05..e270720898 100644
--- a/ecc/bn254/internal/fptower/e6_test.go
+++ b/ecc/bn254/internal/fptower/e6_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/kzg/doc.go b/ecc/bn254/kzg/doc.go
index 226614bbdf..3a86419c48 100644
--- a/ecc/bn254/kzg/doc.go
+++ b/ecc/bn254/kzg/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/kzg/kzg.go b/ecc/bn254/kzg/kzg.go
index 7ebc1c0627..0751568f2f 100644
--- a/ecc/bn254/kzg/kzg.go
+++ b/ecc/bn254/kzg/kzg.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/kzg/kzg_test.go b/ecc/bn254/kzg/kzg_test.go
index e6fdcc7d58..11f1ded97e 100644
--- a/ecc/bn254/kzg/kzg_test.go
+++ b/ecc/bn254/kzg/kzg_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/kzg/marshal.go b/ecc/bn254/kzg/marshal.go
index 3d7137a9a4..060bfda945 100644
--- a/ecc/bn254/kzg/marshal.go
+++ b/ecc/bn254/kzg/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/kzg/utils.go b/ecc/bn254/kzg/utils.go
index 5f28c5b78e..1e8415ce86 100644
--- a/ecc/bn254/kzg/utils.go
+++ b/ecc/bn254/kzg/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/marshal.go b/ecc/bn254/marshal.go
index ea09bfbef0..1e8b554a98 100644
--- a/ecc/bn254/marshal.go
+++ b/ecc/bn254/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/marshal_test.go b/ecc/bn254/marshal_test.go
index 96978d256d..503084e36f 100644
--- a/ecc/bn254/marshal_test.go
+++ b/ecc/bn254/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/multiexp.go b/ecc/bn254/multiexp.go
index a9fc27c81b..9bb0a8d486 100644
--- a/ecc/bn254/multiexp.go
+++ b/ecc/bn254/multiexp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/multiexp_affine.go b/ecc/bn254/multiexp_affine.go
index 7d060d3d03..0e198cbe82 100644
--- a/ecc/bn254/multiexp_affine.go
+++ b/ecc/bn254/multiexp_affine.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/multiexp_jacobian.go b/ecc/bn254/multiexp_jacobian.go
index 4205b5620f..b13a9ddce0 100644
--- a/ecc/bn254/multiexp_jacobian.go
+++ b/ecc/bn254/multiexp_jacobian.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/multiexp_test.go b/ecc/bn254/multiexp_test.go
index fb69e1db39..7e5691fce1 100644
--- a/ecc/bn254/multiexp_test.go
+++ b/ecc/bn254/multiexp_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/pairing_test.go b/ecc/bn254/pairing_test.go
index abc290e42c..9c60164560 100644
--- a/ecc/bn254/pairing_test.go
+++ b/ecc/bn254/pairing_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/shplonk/doc.go b/ecc/bn254/shplonk/doc.go
index 0367893999..d63c7a3ddf 100644
--- a/ecc/bn254/shplonk/doc.go
+++ b/ecc/bn254/shplonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/shplonk/example_test.go b/ecc/bn254/shplonk/example_test.go
index 29fb75ad14..55e959b386 100644
--- a/ecc/bn254/shplonk/example_test.go
+++ b/ecc/bn254/shplonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/shplonk/marshal.go b/ecc/bn254/shplonk/marshal.go
index 006769c68f..a6d046b52e 100644
--- a/ecc/bn254/shplonk/marshal.go
+++ b/ecc/bn254/shplonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/shplonk/shplonk.go b/ecc/bn254/shplonk/shplonk.go
index c732722145..bc05913e1a 100644
--- a/ecc/bn254/shplonk/shplonk.go
+++ b/ecc/bn254/shplonk/shplonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/shplonk/shplonk_test.go b/ecc/bn254/shplonk/shplonk_test.go
index fd2be5987d..ae0131670b 100644
--- a/ecc/bn254/shplonk/shplonk_test.go
+++ b/ecc/bn254/shplonk/shplonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/twistededwards/curve.go b/ecc/bn254/twistededwards/curve.go
index 2721974834..9fa1693a8d 100644
--- a/ecc/bn254/twistededwards/curve.go
+++ b/ecc/bn254/twistededwards/curve.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/twistededwards/doc.go b/ecc/bn254/twistededwards/doc.go
index 032ff269fe..ccc927f106 100644
--- a/ecc/bn254/twistededwards/doc.go
+++ b/ecc/bn254/twistededwards/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/twistededwards/eddsa/doc.go b/ecc/bn254/twistededwards/eddsa/doc.go
index 12eebe5d29..9e6645f93a 100644
--- a/ecc/bn254/twistededwards/eddsa/doc.go
+++ b/ecc/bn254/twistededwards/eddsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/twistededwards/eddsa/eddsa.go b/ecc/bn254/twistededwards/eddsa/eddsa.go
index fc1de34203..398b913c7e 100644
--- a/ecc/bn254/twistededwards/eddsa/eddsa.go
+++ b/ecc/bn254/twistededwards/eddsa/eddsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/twistededwards/eddsa/eddsa_test.go b/ecc/bn254/twistededwards/eddsa/eddsa_test.go
index f817340864..178062b4d5 100644
--- a/ecc/bn254/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bn254/twistededwards/eddsa/eddsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/twistededwards/eddsa/marshal.go b/ecc/bn254/twistededwards/eddsa/marshal.go
index 4ab1f0b542..9bf8024f73 100644
--- a/ecc/bn254/twistededwards/eddsa/marshal.go
+++ b/ecc/bn254/twistededwards/eddsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/twistededwards/point.go b/ecc/bn254/twistededwards/point.go
index c231cfa9e3..865c0ed7ca 100644
--- a/ecc/bn254/twistededwards/point.go
+++ b/ecc/bn254/twistededwards/point.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/twistededwards/point_test.go b/ecc/bn254/twistededwards/point_test.go
index 767e56a70b..b873b1b925 100644
--- a/ecc/bn254/twistededwards/point_test.go
+++ b/ecc/bn254/twistededwards/point_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/ecdsa/doc.go b/ecc/bw6-633/ecdsa/doc.go
index 933c753ea7..b772ff6860 100644
--- a/ecc/bw6-633/ecdsa/doc.go
+++ b/ecc/bw6-633/ecdsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/ecdsa/ecdsa.go b/ecc/bw6-633/ecdsa/ecdsa.go
index 24b909289d..60ee765771 100644
--- a/ecc/bw6-633/ecdsa/ecdsa.go
+++ b/ecc/bw6-633/ecdsa/ecdsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/ecdsa/ecdsa_test.go b/ecc/bw6-633/ecdsa/ecdsa_test.go
index f4090a3077..a27bd4eb07 100644
--- a/ecc/bw6-633/ecdsa/ecdsa_test.go
+++ b/ecc/bw6-633/ecdsa/ecdsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/ecdsa/marshal.go b/ecc/bw6-633/ecdsa/marshal.go
index 0a348be708..61a8df4842 100644
--- a/ecc/bw6-633/ecdsa/marshal.go
+++ b/ecc/bw6-633/ecdsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/ecdsa/marshal_test.go b/ecc/bw6-633/ecdsa/marshal_test.go
index c49a56e6c7..b5e84da2d3 100644
--- a/ecc/bw6-633/ecdsa/marshal_test.go
+++ b/ecc/bw6-633/ecdsa/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fflonk/doc.go b/ecc/bw6-633/fflonk/doc.go
index 67a8094e35..a2506720a8 100644
--- a/ecc/bw6-633/fflonk/doc.go
+++ b/ecc/bw6-633/fflonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fflonk/example_test.go b/ecc/bw6-633/fflonk/example_test.go
index 2dfc9617b4..518d47d91e 100644
--- a/ecc/bw6-633/fflonk/example_test.go
+++ b/ecc/bw6-633/fflonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fflonk/fflonk.go b/ecc/bw6-633/fflonk/fflonk.go
index eee6f4e6df..f1c961134f 100644
--- a/ecc/bw6-633/fflonk/fflonk.go
+++ b/ecc/bw6-633/fflonk/fflonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fflonk/fflonk_test.go b/ecc/bw6-633/fflonk/fflonk_test.go
index fa5630cf9b..19b75c2744 100644
--- a/ecc/bw6-633/fflonk/fflonk_test.go
+++ b/ecc/bw6-633/fflonk/fflonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fflonk/marshal.go b/ecc/bw6-633/fflonk/marshal.go
index 63c27aec6e..40178d222e 100644
--- a/ecc/bw6-633/fflonk/marshal.go
+++ b/ecc/bw6-633/fflonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/arith.go b/ecc/bw6-633/fp/arith.go
index bb63552f5a..5c9905de80 100644
--- a/ecc/bw6-633/fp/arith.go
+++ b/ecc/bw6-633/fp/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/asm_adx.go b/ecc/bw6-633/fp/asm_adx.go
index 75e92992fe..8d85a11345 100644
--- a/ecc/bw6-633/fp/asm_adx.go
+++ b/ecc/bw6-633/fp/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/asm_noadx.go b/ecc/bw6-633/fp/asm_noadx.go
index 304dfb7209..75ca96d775 100644
--- a/ecc/bw6-633/fp/asm_noadx.go
+++ b/ecc/bw6-633/fp/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/doc.go b/ecc/bw6-633/fp/doc.go
index acb2269c30..4d20983606 100644
--- a/ecc/bw6-633/fp/doc.go
+++ b/ecc/bw6-633/fp/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/element.go b/ecc/bw6-633/fp/element.go
index f096126d09..e1cb5a8210 100644
--- a/ecc/bw6-633/fp/element.go
+++ b/ecc/bw6-633/fp/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/element_amd64.go b/ecc/bw6-633/fp/element_amd64.go
index 9cee062e5b..1a6e1cf5eb 100644
--- a/ecc/bw6-633/fp/element_amd64.go
+++ b/ecc/bw6-633/fp/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/element_amd64.s b/ecc/bw6-633/fp/element_amd64.s
index 76df6b685b..184a5c5df9 100644
--- a/ecc/bw6-633/fp/element_amd64.s
+++ b/ecc/bw6-633/fp/element_amd64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/element_arm64.go b/ecc/bw6-633/fp/element_arm64.go
index d0af52deaa..6790fb82b3 100644
--- a/ecc/bw6-633/fp/element_arm64.go
+++ b/ecc/bw6-633/fp/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/element_arm64.s b/ecc/bw6-633/fp/element_arm64.s
index 39f3d76ae2..8348d75def 100644
--- a/ecc/bw6-633/fp/element_arm64.s
+++ b/ecc/bw6-633/fp/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/element_exp.go b/ecc/bw6-633/fp/element_exp.go
index 21eef1d6c2..01be3cbb82 100644
--- a/ecc/bw6-633/fp/element_exp.go
+++ b/ecc/bw6-633/fp/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/element_purego.go b/ecc/bw6-633/fp/element_purego.go
index 40e6af52e0..0bf06ee060 100644
--- a/ecc/bw6-633/fp/element_purego.go
+++ b/ecc/bw6-633/fp/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/element_test.go b/ecc/bw6-633/fp/element_test.go
index 5ece775b31..501d0347ed 100644
--- a/ecc/bw6-633/fp/element_test.go
+++ b/ecc/bw6-633/fp/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/hash_to_field/doc.go b/ecc/bw6-633/fp/hash_to_field/doc.go
index fc145559ad..6dd0d88b06 100644
--- a/ecc/bw6-633/fp/hash_to_field/doc.go
+++ b/ecc/bw6-633/fp/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/hash_to_field/hash_to_field.go b/ecc/bw6-633/fp/hash_to_field/hash_to_field.go
index d5d745d725..2dd5ad4418 100644
--- a/ecc/bw6-633/fp/hash_to_field/hash_to_field.go
+++ b/ecc/bw6-633/fp/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/hash_to_field/hash_to_field_test.go b/ecc/bw6-633/fp/hash_to_field/hash_to_field_test.go
index 5f660415c4..d45ba7ad3a 100644
--- a/ecc/bw6-633/fp/hash_to_field/hash_to_field_test.go
+++ b/ecc/bw6-633/fp/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/vector.go b/ecc/bw6-633/fp/vector.go
index 58c3692973..c8a70cc86b 100644
--- a/ecc/bw6-633/fp/vector.go
+++ b/ecc/bw6-633/fp/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/vector_purego.go b/ecc/bw6-633/fp/vector_purego.go
index 0cda361871..85670501df 100644
--- a/ecc/bw6-633/fp/vector_purego.go
+++ b/ecc/bw6-633/fp/vector_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fp/vector_test.go b/ecc/bw6-633/fp/vector_test.go
index 3b2aa63de7..175e09b7d5 100644
--- a/ecc/bw6-633/fp/vector_test.go
+++ b/ecc/bw6-633/fp/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/arith.go b/ecc/bw6-633/fr/arith.go
index dbba8a9ae4..8dbae56e32 100644
--- a/ecc/bw6-633/fr/arith.go
+++ b/ecc/bw6-633/fr/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/asm_adx.go b/ecc/bw6-633/fr/asm_adx.go
index 9b970335f1..52421cc159 100644
--- a/ecc/bw6-633/fr/asm_adx.go
+++ b/ecc/bw6-633/fr/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/asm_noadx.go b/ecc/bw6-633/fr/asm_noadx.go
index 96741014f2..9c9c9dab5d 100644
--- a/ecc/bw6-633/fr/asm_noadx.go
+++ b/ecc/bw6-633/fr/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/doc.go b/ecc/bw6-633/fr/doc.go
index af16db2498..3d074bb89d 100644
--- a/ecc/bw6-633/fr/doc.go
+++ b/ecc/bw6-633/fr/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/element.go b/ecc/bw6-633/fr/element.go
index 7dfdf5e88e..286f0cbc97 100644
--- a/ecc/bw6-633/fr/element.go
+++ b/ecc/bw6-633/fr/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/element_amd64.go b/ecc/bw6-633/fr/element_amd64.go
index 4c3f2a8567..7e76a943a1 100644
--- a/ecc/bw6-633/fr/element_amd64.go
+++ b/ecc/bw6-633/fr/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/element_amd64.s b/ecc/bw6-633/fr/element_amd64.s
index 0f7e0b89ff..be272d59ae 100644
--- a/ecc/bw6-633/fr/element_amd64.s
+++ b/ecc/bw6-633/fr/element_amd64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/element_exp.go b/ecc/bw6-633/fr/element_exp.go
index 7a9e0ec902..a2e28c9122 100644
--- a/ecc/bw6-633/fr/element_exp.go
+++ b/ecc/bw6-633/fr/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/element_purego.go b/ecc/bw6-633/fr/element_purego.go
index 93d2bcac2d..08da5bd7f8 100644
--- a/ecc/bw6-633/fr/element_purego.go
+++ b/ecc/bw6-633/fr/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || !amd64
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/element_test.go b/ecc/bw6-633/fr/element_test.go
index b9f7e8709d..f9a47b70bc 100644
--- a/ecc/bw6-633/fr/element_test.go
+++ b/ecc/bw6-633/fr/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/fft/bitreverse.go b/ecc/bw6-633/fr/fft/bitreverse.go
index d0c374f9b8..539ba6603f 100644
--- a/ecc/bw6-633/fr/fft/bitreverse.go
+++ b/ecc/bw6-633/fr/fft/bitreverse.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/fft/bitreverse_test.go b/ecc/bw6-633/fr/fft/bitreverse_test.go
index 1d94a1c6c6..3e15ff3a59 100644
--- a/ecc/bw6-633/fr/fft/bitreverse_test.go
+++ b/ecc/bw6-633/fr/fft/bitreverse_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/fft/doc.go b/ecc/bw6-633/fr/fft/doc.go
index 4cce0f9779..8176d8e77a 100644
--- a/ecc/bw6-633/fr/fft/doc.go
+++ b/ecc/bw6-633/fr/fft/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/fft/domain.go b/ecc/bw6-633/fr/fft/domain.go
index a37f3d80f8..40c0cc1e85 100644
--- a/ecc/bw6-633/fr/fft/domain.go
+++ b/ecc/bw6-633/fr/fft/domain.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/fft/domain_test.go b/ecc/bw6-633/fr/fft/domain_test.go
index e445d3cc12..7049120e6a 100644
--- a/ecc/bw6-633/fr/fft/domain_test.go
+++ b/ecc/bw6-633/fr/fft/domain_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/fft/fft.go b/ecc/bw6-633/fr/fft/fft.go
index 24c93b2c24..591372477d 100644
--- a/ecc/bw6-633/fr/fft/fft.go
+++ b/ecc/bw6-633/fr/fft/fft.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/fft/fft_test.go b/ecc/bw6-633/fr/fft/fft_test.go
index f4cce97c61..e4ce874e62 100644
--- a/ecc/bw6-633/fr/fft/fft_test.go
+++ b/ecc/bw6-633/fr/fft/fft_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/fft/options.go b/ecc/bw6-633/fr/fft/options.go
index 44dd664d89..6b4552ec29 100644
--- a/ecc/bw6-633/fr/fft/options.go
+++ b/ecc/bw6-633/fr/fft/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/fri/doc.go b/ecc/bw6-633/fr/fri/doc.go
index cea69fc79a..164ee83268 100644
--- a/ecc/bw6-633/fr/fri/doc.go
+++ b/ecc/bw6-633/fr/fri/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/fri/fri.go b/ecc/bw6-633/fr/fri/fri.go
index 225b98655a..f54979425a 100644
--- a/ecc/bw6-633/fr/fri/fri.go
+++ b/ecc/bw6-633/fr/fri/fri.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/fri/fri_test.go b/ecc/bw6-633/fr/fri/fri_test.go
index 27719d6a22..2b055f0752 100644
--- a/ecc/bw6-633/fr/fri/fri_test.go
+++ b/ecc/bw6-633/fr/fri/fri_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/generator.go b/ecc/bw6-633/fr/generator.go
index f7491984c9..175ac4f7e0 100644
--- a/ecc/bw6-633/fr/generator.go
+++ b/ecc/bw6-633/fr/generator.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/gkr/gkr.go b/ecc/bw6-633/fr/gkr/gkr.go
index 7229501364..e601da382c 100644
--- a/ecc/bw6-633/fr/gkr/gkr.go
+++ b/ecc/bw6-633/fr/gkr/gkr.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/gkr/gkr_test.go b/ecc/bw6-633/fr/gkr/gkr_test.go
index 5316f63c01..9979f3d6b7 100644
--- a/ecc/bw6-633/fr/gkr/gkr_test.go
+++ b/ecc/bw6-633/fr/gkr/gkr_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/hash_to_field/doc.go b/ecc/bw6-633/fr/hash_to_field/doc.go
index bf75dbff35..7d8c3fd8f9 100644
--- a/ecc/bw6-633/fr/hash_to_field/doc.go
+++ b/ecc/bw6-633/fr/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/hash_to_field/hash_to_field.go b/ecc/bw6-633/fr/hash_to_field/hash_to_field.go
index e8f300e1cb..0e3cb26595 100644
--- a/ecc/bw6-633/fr/hash_to_field/hash_to_field.go
+++ b/ecc/bw6-633/fr/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/hash_to_field/hash_to_field_test.go b/ecc/bw6-633/fr/hash_to_field/hash_to_field_test.go
index 2beeea14db..730fda2588 100644
--- a/ecc/bw6-633/fr/hash_to_field/hash_to_field_test.go
+++ b/ecc/bw6-633/fr/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/iop/doc.go b/ecc/bw6-633/fr/iop/doc.go
index 2ef06dfe1a..6c9a441cc1 100644
--- a/ecc/bw6-633/fr/iop/doc.go
+++ b/ecc/bw6-633/fr/iop/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/iop/expressions.go b/ecc/bw6-633/fr/iop/expressions.go
index 08c735962f..17e29b4d94 100644
--- a/ecc/bw6-633/fr/iop/expressions.go
+++ b/ecc/bw6-633/fr/iop/expressions.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/iop/expressions_test.go b/ecc/bw6-633/fr/iop/expressions_test.go
index 309b60bd44..42e224825a 100644
--- a/ecc/bw6-633/fr/iop/expressions_test.go
+++ b/ecc/bw6-633/fr/iop/expressions_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/iop/polynomial.go b/ecc/bw6-633/fr/iop/polynomial.go
index 354007c795..4637f28502 100644
--- a/ecc/bw6-633/fr/iop/polynomial.go
+++ b/ecc/bw6-633/fr/iop/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/iop/polynomial_test.go b/ecc/bw6-633/fr/iop/polynomial_test.go
index 584ec9c043..148c47a6a9 100644
--- a/ecc/bw6-633/fr/iop/polynomial_test.go
+++ b/ecc/bw6-633/fr/iop/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/iop/quotient.go b/ecc/bw6-633/fr/iop/quotient.go
index 7344abd32b..c354f1bdf5 100644
--- a/ecc/bw6-633/fr/iop/quotient.go
+++ b/ecc/bw6-633/fr/iop/quotient.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/iop/quotient_test.go b/ecc/bw6-633/fr/iop/quotient_test.go
index 629f0bf29f..199939773e 100644
--- a/ecc/bw6-633/fr/iop/quotient_test.go
+++ b/ecc/bw6-633/fr/iop/quotient_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/iop/ratios.go b/ecc/bw6-633/fr/iop/ratios.go
index 97150f3f34..5751ecfa42 100644
--- a/ecc/bw6-633/fr/iop/ratios.go
+++ b/ecc/bw6-633/fr/iop/ratios.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/iop/ratios_test.go b/ecc/bw6-633/fr/iop/ratios_test.go
index 1d6860c47b..4fc59db382 100644
--- a/ecc/bw6-633/fr/iop/ratios_test.go
+++ b/ecc/bw6-633/fr/iop/ratios_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/iop/utils.go b/ecc/bw6-633/fr/iop/utils.go
index db5e837c70..f7584b55dc 100644
--- a/ecc/bw6-633/fr/iop/utils.go
+++ b/ecc/bw6-633/fr/iop/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/mimc/doc.go b/ecc/bw6-633/fr/mimc/doc.go
index 900b977185..946e0dafaa 100644
--- a/ecc/bw6-633/fr/mimc/doc.go
+++ b/ecc/bw6-633/fr/mimc/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/mimc/mimc.go b/ecc/bw6-633/fr/mimc/mimc.go
index f9665cf347..1245152b83 100644
--- a/ecc/bw6-633/fr/mimc/mimc.go
+++ b/ecc/bw6-633/fr/mimc/mimc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/mimc/mimc_test.go b/ecc/bw6-633/fr/mimc/mimc_test.go
index f896dd8e3b..0ca3ed3718 100644
--- a/ecc/bw6-633/fr/mimc/mimc_test.go
+++ b/ecc/bw6-633/fr/mimc/mimc_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/mimc/options.go b/ecc/bw6-633/fr/mimc/options.go
index 9a6b28e3e3..527294027f 100644
--- a/ecc/bw6-633/fr/mimc/options.go
+++ b/ecc/bw6-633/fr/mimc/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/pedersen/doc.go b/ecc/bw6-633/fr/pedersen/doc.go
index 2e24034936..dff1285d0e 100644
--- a/ecc/bw6-633/fr/pedersen/doc.go
+++ b/ecc/bw6-633/fr/pedersen/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/pedersen/example_test.go b/ecc/bw6-633/fr/pedersen/example_test.go
index c4a36efcc9..18e8deb8f5 100644
--- a/ecc/bw6-633/fr/pedersen/example_test.go
+++ b/ecc/bw6-633/fr/pedersen/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/pedersen/pedersen.go b/ecc/bw6-633/fr/pedersen/pedersen.go
index ac20e55e77..0f3484ee3b 100644
--- a/ecc/bw6-633/fr/pedersen/pedersen.go
+++ b/ecc/bw6-633/fr/pedersen/pedersen.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/pedersen/pedersen_test.go b/ecc/bw6-633/fr/pedersen/pedersen_test.go
index 3c263657c3..179ed13630 100644
--- a/ecc/bw6-633/fr/pedersen/pedersen_test.go
+++ b/ecc/bw6-633/fr/pedersen/pedersen_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/permutation/doc.go b/ecc/bw6-633/fr/permutation/doc.go
index e24cd82923..4f2ea7b2e4 100644
--- a/ecc/bw6-633/fr/permutation/doc.go
+++ b/ecc/bw6-633/fr/permutation/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/permutation/permutation.go b/ecc/bw6-633/fr/permutation/permutation.go
index 938ff17aed..909c84c4c9 100644
--- a/ecc/bw6-633/fr/permutation/permutation.go
+++ b/ecc/bw6-633/fr/permutation/permutation.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/permutation/permutation_test.go b/ecc/bw6-633/fr/permutation/permutation_test.go
index 1d7a73d5b5..d32b29140b 100644
--- a/ecc/bw6-633/fr/permutation/permutation_test.go
+++ b/ecc/bw6-633/fr/permutation/permutation_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/plookup/doc.go b/ecc/bw6-633/fr/plookup/doc.go
index 7a02c59719..5507122fab 100644
--- a/ecc/bw6-633/fr/plookup/doc.go
+++ b/ecc/bw6-633/fr/plookup/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/plookup/plookup_test.go b/ecc/bw6-633/fr/plookup/plookup_test.go
index f081d33d5c..3262ed4b62 100644
--- a/ecc/bw6-633/fr/plookup/plookup_test.go
+++ b/ecc/bw6-633/fr/plookup/plookup_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/plookup/table.go b/ecc/bw6-633/fr/plookup/table.go
index 221a50cfd3..bd2f298b7f 100644
--- a/ecc/bw6-633/fr/plookup/table.go
+++ b/ecc/bw6-633/fr/plookup/table.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/plookup/vector.go b/ecc/bw6-633/fr/plookup/vector.go
index e3a3351e8f..c97914376e 100644
--- a/ecc/bw6-633/fr/plookup/vector.go
+++ b/ecc/bw6-633/fr/plookup/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/polynomial/doc.go b/ecc/bw6-633/fr/polynomial/doc.go
index fd96328e8f..ead3b5cba5 100644
--- a/ecc/bw6-633/fr/polynomial/doc.go
+++ b/ecc/bw6-633/fr/polynomial/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/polynomial/multilin.go b/ecc/bw6-633/fr/polynomial/multilin.go
index a271c88575..ed03f6d040 100644
--- a/ecc/bw6-633/fr/polynomial/multilin.go
+++ b/ecc/bw6-633/fr/polynomial/multilin.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/polynomial/multilin_test.go b/ecc/bw6-633/fr/polynomial/multilin_test.go
index 7b722b4c1f..32b504ecad 100644
--- a/ecc/bw6-633/fr/polynomial/multilin_test.go
+++ b/ecc/bw6-633/fr/polynomial/multilin_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/polynomial/polynomial.go b/ecc/bw6-633/fr/polynomial/polynomial.go
index 1c3ff26dfd..b34a991846 100644
--- a/ecc/bw6-633/fr/polynomial/polynomial.go
+++ b/ecc/bw6-633/fr/polynomial/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/polynomial/polynomial_test.go b/ecc/bw6-633/fr/polynomial/polynomial_test.go
index 5b1d24b09e..4eef7d1691 100644
--- a/ecc/bw6-633/fr/polynomial/polynomial_test.go
+++ b/ecc/bw6-633/fr/polynomial/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/polynomial/pool.go b/ecc/bw6-633/fr/polynomial/pool.go
index 6382c3ea48..5355ecd214 100644
--- a/ecc/bw6-633/fr/polynomial/pool.go
+++ b/ecc/bw6-633/fr/polynomial/pool.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/poseidon2/poseidon2.go b/ecc/bw6-633/fr/poseidon2/poseidon2.go
index c4a9ccc8eb..0a3c894a71 100644
--- a/ecc/bw6-633/fr/poseidon2/poseidon2.go
+++ b/ecc/bw6-633/fr/poseidon2/poseidon2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/poseidon2/poseidon2_test.go b/ecc/bw6-633/fr/poseidon2/poseidon2_test.go
index b1e8913fd5..3effc4fc52 100644
--- a/ecc/bw6-633/fr/poseidon2/poseidon2_test.go
+++ b/ecc/bw6-633/fr/poseidon2/poseidon2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/sumcheck/sumcheck.go b/ecc/bw6-633/fr/sumcheck/sumcheck.go
index 4c063b2476..46a4f1dfc5 100644
--- a/ecc/bw6-633/fr/sumcheck/sumcheck.go
+++ b/ecc/bw6-633/fr/sumcheck/sumcheck.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/sumcheck/sumcheck_test.go b/ecc/bw6-633/fr/sumcheck/sumcheck_test.go
index 1abeb3ea5b..b214ea2661 100644
--- a/ecc/bw6-633/fr/sumcheck/sumcheck_test.go
+++ b/ecc/bw6-633/fr/sumcheck/sumcheck_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/test_vector_utils/test_vector_utils.go b/ecc/bw6-633/fr/test_vector_utils/test_vector_utils.go
index fda1206bc2..11599a323d 100644
--- a/ecc/bw6-633/fr/test_vector_utils/test_vector_utils.go
+++ b/ecc/bw6-633/fr/test_vector_utils/test_vector_utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/vector.go b/ecc/bw6-633/fr/vector.go
index 53e5e4e49c..f0face44d9 100644
--- a/ecc/bw6-633/fr/vector.go
+++ b/ecc/bw6-633/fr/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/vector_purego.go b/ecc/bw6-633/fr/vector_purego.go
index c26ef9f1bb..1898ab6bb9 100644
--- a/ecc/bw6-633/fr/vector_purego.go
+++ b/ecc/bw6-633/fr/vector_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/fr/vector_test.go b/ecc/bw6-633/fr/vector_test.go
index 22e0d1bb90..e22c71595c 100644
--- a/ecc/bw6-633/fr/vector_test.go
+++ b/ecc/bw6-633/fr/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/g1.go b/ecc/bw6-633/g1.go
index 62917937bc..a74d47e075 100644
--- a/ecc/bw6-633/g1.go
+++ b/ecc/bw6-633/g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/g1_test.go b/ecc/bw6-633/g1_test.go
index ad2ec5789a..59d10ffea9 100644
--- a/ecc/bw6-633/g1_test.go
+++ b/ecc/bw6-633/g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/g2.go b/ecc/bw6-633/g2.go
index bb5972f107..a61d10e955 100644
--- a/ecc/bw6-633/g2.go
+++ b/ecc/bw6-633/g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/g2_test.go b/ecc/bw6-633/g2_test.go
index c36bcdbbe7..0d3ca63171 100644
--- a/ecc/bw6-633/g2_test.go
+++ b/ecc/bw6-633/g2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/hash_to_g1.go b/ecc/bw6-633/hash_to_g1.go
index 7e2a7bb8da..0d39ca178f 100644
--- a/ecc/bw6-633/hash_to_g1.go
+++ b/ecc/bw6-633/hash_to_g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/hash_to_g1_test.go b/ecc/bw6-633/hash_to_g1_test.go
index bcd21cb91d..57685d3f8c 100644
--- a/ecc/bw6-633/hash_to_g1_test.go
+++ b/ecc/bw6-633/hash_to_g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/hash_to_g2.go b/ecc/bw6-633/hash_to_g2.go
index b08e142909..a9f2295f42 100644
--- a/ecc/bw6-633/hash_to_g2.go
+++ b/ecc/bw6-633/hash_to_g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/hash_to_g2_test.go b/ecc/bw6-633/hash_to_g2_test.go
index 57fdc4b5b4..a3303c46ca 100644
--- a/ecc/bw6-633/hash_to_g2_test.go
+++ b/ecc/bw6-633/hash_to_g2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/kzg/doc.go b/ecc/bw6-633/kzg/doc.go
index 226614bbdf..3a86419c48 100644
--- a/ecc/bw6-633/kzg/doc.go
+++ b/ecc/bw6-633/kzg/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/kzg/kzg.go b/ecc/bw6-633/kzg/kzg.go
index bc27742827..5bcbe36beb 100644
--- a/ecc/bw6-633/kzg/kzg.go
+++ b/ecc/bw6-633/kzg/kzg.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/kzg/kzg_test.go b/ecc/bw6-633/kzg/kzg_test.go
index 995877b769..7743844159 100644
--- a/ecc/bw6-633/kzg/kzg_test.go
+++ b/ecc/bw6-633/kzg/kzg_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/kzg/marshal.go b/ecc/bw6-633/kzg/marshal.go
index f14c91a860..1ba36b4ca5 100644
--- a/ecc/bw6-633/kzg/marshal.go
+++ b/ecc/bw6-633/kzg/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/kzg/utils.go b/ecc/bw6-633/kzg/utils.go
index 1ead3e7c2e..95757be34a 100644
--- a/ecc/bw6-633/kzg/utils.go
+++ b/ecc/bw6-633/kzg/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/marshal.go b/ecc/bw6-633/marshal.go
index 2463435468..ebe98e33a9 100644
--- a/ecc/bw6-633/marshal.go
+++ b/ecc/bw6-633/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/marshal_test.go b/ecc/bw6-633/marshal_test.go
index 9e44f97d3b..d226b1da0d 100644
--- a/ecc/bw6-633/marshal_test.go
+++ b/ecc/bw6-633/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/multiexp.go b/ecc/bw6-633/multiexp.go
index 7bbf91d315..744b983cc1 100644
--- a/ecc/bw6-633/multiexp.go
+++ b/ecc/bw6-633/multiexp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/multiexp_affine.go b/ecc/bw6-633/multiexp_affine.go
index d36e5040fa..be9e4d2c0c 100644
--- a/ecc/bw6-633/multiexp_affine.go
+++ b/ecc/bw6-633/multiexp_affine.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/multiexp_jacobian.go b/ecc/bw6-633/multiexp_jacobian.go
index f3caa67025..e66ed66468 100644
--- a/ecc/bw6-633/multiexp_jacobian.go
+++ b/ecc/bw6-633/multiexp_jacobian.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/multiexp_test.go b/ecc/bw6-633/multiexp_test.go
index c8e312de6a..6174052332 100644
--- a/ecc/bw6-633/multiexp_test.go
+++ b/ecc/bw6-633/multiexp_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/pairing_test.go b/ecc/bw6-633/pairing_test.go
index a878c0e50f..e2c5673d19 100644
--- a/ecc/bw6-633/pairing_test.go
+++ b/ecc/bw6-633/pairing_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/shplonk/doc.go b/ecc/bw6-633/shplonk/doc.go
index 0367893999..d63c7a3ddf 100644
--- a/ecc/bw6-633/shplonk/doc.go
+++ b/ecc/bw6-633/shplonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/shplonk/example_test.go b/ecc/bw6-633/shplonk/example_test.go
index 57471ea4fb..7a7b39ecd2 100644
--- a/ecc/bw6-633/shplonk/example_test.go
+++ b/ecc/bw6-633/shplonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/shplonk/marshal.go b/ecc/bw6-633/shplonk/marshal.go
index abd3918e85..04964c4a28 100644
--- a/ecc/bw6-633/shplonk/marshal.go
+++ b/ecc/bw6-633/shplonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/shplonk/shplonk.go b/ecc/bw6-633/shplonk/shplonk.go
index 1b41c3adcd..db15afaf8c 100644
--- a/ecc/bw6-633/shplonk/shplonk.go
+++ b/ecc/bw6-633/shplonk/shplonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/shplonk/shplonk_test.go b/ecc/bw6-633/shplonk/shplonk_test.go
index bd6fa2f81b..eb1324b673 100644
--- a/ecc/bw6-633/shplonk/shplonk_test.go
+++ b/ecc/bw6-633/shplonk/shplonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/twistededwards/curve.go b/ecc/bw6-633/twistededwards/curve.go
index a5bd1b94f9..d92a2d51d7 100644
--- a/ecc/bw6-633/twistededwards/curve.go
+++ b/ecc/bw6-633/twistededwards/curve.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/twistededwards/doc.go b/ecc/bw6-633/twistededwards/doc.go
index 59833f0b37..c72c0f8276 100644
--- a/ecc/bw6-633/twistededwards/doc.go
+++ b/ecc/bw6-633/twistededwards/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/twistededwards/eddsa/doc.go b/ecc/bw6-633/twistededwards/eddsa/doc.go
index a92c9947a3..300e0ea4a4 100644
--- a/ecc/bw6-633/twistededwards/eddsa/doc.go
+++ b/ecc/bw6-633/twistededwards/eddsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/twistededwards/eddsa/eddsa.go b/ecc/bw6-633/twistededwards/eddsa/eddsa.go
index fca1faee82..c4efc85729 100644
--- a/ecc/bw6-633/twistededwards/eddsa/eddsa.go
+++ b/ecc/bw6-633/twistededwards/eddsa/eddsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/twistededwards/eddsa/eddsa_test.go b/ecc/bw6-633/twistededwards/eddsa/eddsa_test.go
index 6ffff698d8..0d3658c265 100644
--- a/ecc/bw6-633/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bw6-633/twistededwards/eddsa/eddsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/twistededwards/eddsa/marshal.go b/ecc/bw6-633/twistededwards/eddsa/marshal.go
index c0d4f05feb..bc182446f0 100644
--- a/ecc/bw6-633/twistededwards/eddsa/marshal.go
+++ b/ecc/bw6-633/twistededwards/eddsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/twistededwards/point.go b/ecc/bw6-633/twistededwards/point.go
index f7a76239f3..69ceff8294 100644
--- a/ecc/bw6-633/twistededwards/point.go
+++ b/ecc/bw6-633/twistededwards/point.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-633/twistededwards/point_test.go b/ecc/bw6-633/twistededwards/point_test.go
index 7182cdd32d..94feb5b742 100644
--- a/ecc/bw6-633/twistededwards/point_test.go
+++ b/ecc/bw6-633/twistededwards/point_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/ecdsa/doc.go b/ecc/bw6-761/ecdsa/doc.go
index dd72153183..b3ba7e94f8 100644
--- a/ecc/bw6-761/ecdsa/doc.go
+++ b/ecc/bw6-761/ecdsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/ecdsa/ecdsa.go b/ecc/bw6-761/ecdsa/ecdsa.go
index f452ce2164..204cfe7422 100644
--- a/ecc/bw6-761/ecdsa/ecdsa.go
+++ b/ecc/bw6-761/ecdsa/ecdsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/ecdsa/ecdsa_test.go b/ecc/bw6-761/ecdsa/ecdsa_test.go
index d44c6052ae..fc7b4508c9 100644
--- a/ecc/bw6-761/ecdsa/ecdsa_test.go
+++ b/ecc/bw6-761/ecdsa/ecdsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/ecdsa/marshal.go b/ecc/bw6-761/ecdsa/marshal.go
index aab61d03ab..ba89271b28 100644
--- a/ecc/bw6-761/ecdsa/marshal.go
+++ b/ecc/bw6-761/ecdsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/ecdsa/marshal_test.go b/ecc/bw6-761/ecdsa/marshal_test.go
index d0632664ad..30beeff34c 100644
--- a/ecc/bw6-761/ecdsa/marshal_test.go
+++ b/ecc/bw6-761/ecdsa/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fflonk/doc.go b/ecc/bw6-761/fflonk/doc.go
index 67a8094e35..a2506720a8 100644
--- a/ecc/bw6-761/fflonk/doc.go
+++ b/ecc/bw6-761/fflonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fflonk/example_test.go b/ecc/bw6-761/fflonk/example_test.go
index 22c353e4be..58396cc184 100644
--- a/ecc/bw6-761/fflonk/example_test.go
+++ b/ecc/bw6-761/fflonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fflonk/fflonk.go b/ecc/bw6-761/fflonk/fflonk.go
index 1339da3844..5c2d6df6ac 100644
--- a/ecc/bw6-761/fflonk/fflonk.go
+++ b/ecc/bw6-761/fflonk/fflonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fflonk/fflonk_test.go b/ecc/bw6-761/fflonk/fflonk_test.go
index 371b281037..2ce034eccc 100644
--- a/ecc/bw6-761/fflonk/fflonk_test.go
+++ b/ecc/bw6-761/fflonk/fflonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fflonk/marshal.go b/ecc/bw6-761/fflonk/marshal.go
index 29ab15ab97..896b852017 100644
--- a/ecc/bw6-761/fflonk/marshal.go
+++ b/ecc/bw6-761/fflonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/arith.go b/ecc/bw6-761/fp/arith.go
index bb63552f5a..5c9905de80 100644
--- a/ecc/bw6-761/fp/arith.go
+++ b/ecc/bw6-761/fp/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/asm_adx.go b/ecc/bw6-761/fp/asm_adx.go
index 75e92992fe..8d85a11345 100644
--- a/ecc/bw6-761/fp/asm_adx.go
+++ b/ecc/bw6-761/fp/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/asm_noadx.go b/ecc/bw6-761/fp/asm_noadx.go
index 304dfb7209..75ca96d775 100644
--- a/ecc/bw6-761/fp/asm_noadx.go
+++ b/ecc/bw6-761/fp/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/doc.go b/ecc/bw6-761/fp/doc.go
index 8b1c7f5d5e..cee098cd3c 100644
--- a/ecc/bw6-761/fp/doc.go
+++ b/ecc/bw6-761/fp/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/element.go b/ecc/bw6-761/fp/element.go
index 4083df4699..b42b76e5a0 100644
--- a/ecc/bw6-761/fp/element.go
+++ b/ecc/bw6-761/fp/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/element_amd64.go b/ecc/bw6-761/fp/element_amd64.go
index 9cee062e5b..1a6e1cf5eb 100644
--- a/ecc/bw6-761/fp/element_amd64.go
+++ b/ecc/bw6-761/fp/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/element_amd64.s b/ecc/bw6-761/fp/element_amd64.s
index c50306bc8d..e9198f66d7 100644
--- a/ecc/bw6-761/fp/element_amd64.s
+++ b/ecc/bw6-761/fp/element_amd64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/element_arm64.go b/ecc/bw6-761/fp/element_arm64.go
index 665fc7bf74..8807731d93 100644
--- a/ecc/bw6-761/fp/element_arm64.go
+++ b/ecc/bw6-761/fp/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/element_arm64.s b/ecc/bw6-761/fp/element_arm64.s
index e6d61fb12e..5993cf0acd 100644
--- a/ecc/bw6-761/fp/element_arm64.s
+++ b/ecc/bw6-761/fp/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/element_exp.go b/ecc/bw6-761/fp/element_exp.go
index f017426d0f..c34a91fd20 100644
--- a/ecc/bw6-761/fp/element_exp.go
+++ b/ecc/bw6-761/fp/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/element_purego.go b/ecc/bw6-761/fp/element_purego.go
index 27bbd3ea4f..8c78ab1700 100644
--- a/ecc/bw6-761/fp/element_purego.go
+++ b/ecc/bw6-761/fp/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/element_test.go b/ecc/bw6-761/fp/element_test.go
index 57f420e1e9..337daf352a 100644
--- a/ecc/bw6-761/fp/element_test.go
+++ b/ecc/bw6-761/fp/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/hash_to_field/doc.go b/ecc/bw6-761/fp/hash_to_field/doc.go
index 9f9a0f60b2..e8b5e3effc 100644
--- a/ecc/bw6-761/fp/hash_to_field/doc.go
+++ b/ecc/bw6-761/fp/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/hash_to_field/hash_to_field.go b/ecc/bw6-761/fp/hash_to_field/hash_to_field.go
index ca34259946..76bd8b7395 100644
--- a/ecc/bw6-761/fp/hash_to_field/hash_to_field.go
+++ b/ecc/bw6-761/fp/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/hash_to_field/hash_to_field_test.go b/ecc/bw6-761/fp/hash_to_field/hash_to_field_test.go
index cc1be00fb8..0bc6ce1dba 100644
--- a/ecc/bw6-761/fp/hash_to_field/hash_to_field_test.go
+++ b/ecc/bw6-761/fp/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/vector.go b/ecc/bw6-761/fp/vector.go
index e312aebc6e..98af7be4d0 100644
--- a/ecc/bw6-761/fp/vector.go
+++ b/ecc/bw6-761/fp/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/vector_purego.go b/ecc/bw6-761/fp/vector_purego.go
index 0cda361871..85670501df 100644
--- a/ecc/bw6-761/fp/vector_purego.go
+++ b/ecc/bw6-761/fp/vector_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fp/vector_test.go b/ecc/bw6-761/fp/vector_test.go
index d1765ba9bc..daf6f3091d 100644
--- a/ecc/bw6-761/fp/vector_test.go
+++ b/ecc/bw6-761/fp/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/arith.go b/ecc/bw6-761/fr/arith.go
index dbba8a9ae4..8dbae56e32 100644
--- a/ecc/bw6-761/fr/arith.go
+++ b/ecc/bw6-761/fr/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/asm_adx.go b/ecc/bw6-761/fr/asm_adx.go
index 9b970335f1..52421cc159 100644
--- a/ecc/bw6-761/fr/asm_adx.go
+++ b/ecc/bw6-761/fr/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/asm_noadx.go b/ecc/bw6-761/fr/asm_noadx.go
index 96741014f2..9c9c9dab5d 100644
--- a/ecc/bw6-761/fr/asm_noadx.go
+++ b/ecc/bw6-761/fr/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/doc.go b/ecc/bw6-761/fr/doc.go
index d7af83c91e..4c02e1f3ac 100644
--- a/ecc/bw6-761/fr/doc.go
+++ b/ecc/bw6-761/fr/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/element.go b/ecc/bw6-761/fr/element.go
index 4775e29561..71d980d3cc 100644
--- a/ecc/bw6-761/fr/element.go
+++ b/ecc/bw6-761/fr/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/element_amd64.go b/ecc/bw6-761/fr/element_amd64.go
index 4c3f2a8567..7e76a943a1 100644
--- a/ecc/bw6-761/fr/element_amd64.go
+++ b/ecc/bw6-761/fr/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/element_amd64.s b/ecc/bw6-761/fr/element_amd64.s
index 719aecfbe9..db64f3a580 100644
--- a/ecc/bw6-761/fr/element_amd64.s
+++ b/ecc/bw6-761/fr/element_amd64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/element_arm64.go b/ecc/bw6-761/fr/element_arm64.go
index cde9727044..cc1b3bca42 100644
--- a/ecc/bw6-761/fr/element_arm64.go
+++ b/ecc/bw6-761/fr/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/element_arm64.s b/ecc/bw6-761/fr/element_arm64.s
index b4dfd1612c..b656459e76 100644
--- a/ecc/bw6-761/fr/element_arm64.s
+++ b/ecc/bw6-761/fr/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/element_exp.go b/ecc/bw6-761/fr/element_exp.go
index 73a46afaf0..ec0acd1a5e 100644
--- a/ecc/bw6-761/fr/element_exp.go
+++ b/ecc/bw6-761/fr/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/element_purego.go b/ecc/bw6-761/fr/element_purego.go
index c4ef27e9a3..2c60f3c457 100644
--- a/ecc/bw6-761/fr/element_purego.go
+++ b/ecc/bw6-761/fr/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/element_test.go b/ecc/bw6-761/fr/element_test.go
index a01d11c9e7..02bccefcc0 100644
--- a/ecc/bw6-761/fr/element_test.go
+++ b/ecc/bw6-761/fr/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/fft/bitreverse.go b/ecc/bw6-761/fr/fft/bitreverse.go
index 408320f032..8033d021ae 100644
--- a/ecc/bw6-761/fr/fft/bitreverse.go
+++ b/ecc/bw6-761/fr/fft/bitreverse.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/fft/bitreverse_test.go b/ecc/bw6-761/fr/fft/bitreverse_test.go
index 0206f2e5d2..4c1002cc8f 100644
--- a/ecc/bw6-761/fr/fft/bitreverse_test.go
+++ b/ecc/bw6-761/fr/fft/bitreverse_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/fft/doc.go b/ecc/bw6-761/fr/fft/doc.go
index 4cce0f9779..8176d8e77a 100644
--- a/ecc/bw6-761/fr/fft/doc.go
+++ b/ecc/bw6-761/fr/fft/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/fft/domain.go b/ecc/bw6-761/fr/fft/domain.go
index 189b5b1984..c9c1c217ef 100644
--- a/ecc/bw6-761/fr/fft/domain.go
+++ b/ecc/bw6-761/fr/fft/domain.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/fft/domain_test.go b/ecc/bw6-761/fr/fft/domain_test.go
index e445d3cc12..7049120e6a 100644
--- a/ecc/bw6-761/fr/fft/domain_test.go
+++ b/ecc/bw6-761/fr/fft/domain_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/fft/fft.go b/ecc/bw6-761/fr/fft/fft.go
index 85b35a0639..196949dd57 100644
--- a/ecc/bw6-761/fr/fft/fft.go
+++ b/ecc/bw6-761/fr/fft/fft.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/fft/fft_test.go b/ecc/bw6-761/fr/fft/fft_test.go
index 81d4945ef2..cf7b941e6a 100644
--- a/ecc/bw6-761/fr/fft/fft_test.go
+++ b/ecc/bw6-761/fr/fft/fft_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/fft/options.go b/ecc/bw6-761/fr/fft/options.go
index a0fdb41944..0ccbce8ba5 100644
--- a/ecc/bw6-761/fr/fft/options.go
+++ b/ecc/bw6-761/fr/fft/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/fri/doc.go b/ecc/bw6-761/fr/fri/doc.go
index cea69fc79a..164ee83268 100644
--- a/ecc/bw6-761/fr/fri/doc.go
+++ b/ecc/bw6-761/fr/fri/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/fri/fri.go b/ecc/bw6-761/fr/fri/fri.go
index 9dce380ab0..92112258a6 100644
--- a/ecc/bw6-761/fr/fri/fri.go
+++ b/ecc/bw6-761/fr/fri/fri.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/fri/fri_test.go b/ecc/bw6-761/fr/fri/fri_test.go
index d3907b4fc7..cf562814be 100644
--- a/ecc/bw6-761/fr/fri/fri_test.go
+++ b/ecc/bw6-761/fr/fri/fri_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/generator.go b/ecc/bw6-761/fr/generator.go
index ffa85ae746..93b137c58e 100644
--- a/ecc/bw6-761/fr/generator.go
+++ b/ecc/bw6-761/fr/generator.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/gkr/gkr.go b/ecc/bw6-761/fr/gkr/gkr.go
index 3c58a7ae97..79044fb834 100644
--- a/ecc/bw6-761/fr/gkr/gkr.go
+++ b/ecc/bw6-761/fr/gkr/gkr.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/gkr/gkr_test.go b/ecc/bw6-761/fr/gkr/gkr_test.go
index 1922eff6d8..40ee3b212a 100644
--- a/ecc/bw6-761/fr/gkr/gkr_test.go
+++ b/ecc/bw6-761/fr/gkr/gkr_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/hash_to_field/doc.go b/ecc/bw6-761/fr/hash_to_field/doc.go
index 504fadf149..365beb1a9b 100644
--- a/ecc/bw6-761/fr/hash_to_field/doc.go
+++ b/ecc/bw6-761/fr/hash_to_field/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/hash_to_field/hash_to_field.go b/ecc/bw6-761/fr/hash_to_field/hash_to_field.go
index d941e2468b..5b90695845 100644
--- a/ecc/bw6-761/fr/hash_to_field/hash_to_field.go
+++ b/ecc/bw6-761/fr/hash_to_field/hash_to_field.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/hash_to_field/hash_to_field_test.go b/ecc/bw6-761/fr/hash_to_field/hash_to_field_test.go
index aa92379465..0a4b220c99 100644
--- a/ecc/bw6-761/fr/hash_to_field/hash_to_field_test.go
+++ b/ecc/bw6-761/fr/hash_to_field/hash_to_field_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/iop/doc.go b/ecc/bw6-761/fr/iop/doc.go
index 2ef06dfe1a..6c9a441cc1 100644
--- a/ecc/bw6-761/fr/iop/doc.go
+++ b/ecc/bw6-761/fr/iop/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/iop/expressions.go b/ecc/bw6-761/fr/iop/expressions.go
index 3941e95266..5aa08577e6 100644
--- a/ecc/bw6-761/fr/iop/expressions.go
+++ b/ecc/bw6-761/fr/iop/expressions.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/iop/expressions_test.go b/ecc/bw6-761/fr/iop/expressions_test.go
index 4874d59d49..35bbc888e9 100644
--- a/ecc/bw6-761/fr/iop/expressions_test.go
+++ b/ecc/bw6-761/fr/iop/expressions_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/iop/polynomial.go b/ecc/bw6-761/fr/iop/polynomial.go
index 94fbb2d751..46e1330497 100644
--- a/ecc/bw6-761/fr/iop/polynomial.go
+++ b/ecc/bw6-761/fr/iop/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/iop/polynomial_test.go b/ecc/bw6-761/fr/iop/polynomial_test.go
index b04551d9a6..dd5f91ddb8 100644
--- a/ecc/bw6-761/fr/iop/polynomial_test.go
+++ b/ecc/bw6-761/fr/iop/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/iop/quotient.go b/ecc/bw6-761/fr/iop/quotient.go
index 6329b85400..38b26a488e 100644
--- a/ecc/bw6-761/fr/iop/quotient.go
+++ b/ecc/bw6-761/fr/iop/quotient.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/iop/quotient_test.go b/ecc/bw6-761/fr/iop/quotient_test.go
index e3fc8147ec..7d0dda3570 100644
--- a/ecc/bw6-761/fr/iop/quotient_test.go
+++ b/ecc/bw6-761/fr/iop/quotient_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/iop/ratios.go b/ecc/bw6-761/fr/iop/ratios.go
index c130c0ab53..c8e52bf540 100644
--- a/ecc/bw6-761/fr/iop/ratios.go
+++ b/ecc/bw6-761/fr/iop/ratios.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/iop/ratios_test.go b/ecc/bw6-761/fr/iop/ratios_test.go
index 259b0e65fe..7f10a33abc 100644
--- a/ecc/bw6-761/fr/iop/ratios_test.go
+++ b/ecc/bw6-761/fr/iop/ratios_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/iop/utils.go b/ecc/bw6-761/fr/iop/utils.go
index eaf19d9f8e..993d7de514 100644
--- a/ecc/bw6-761/fr/iop/utils.go
+++ b/ecc/bw6-761/fr/iop/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/mimc/doc.go b/ecc/bw6-761/fr/mimc/doc.go
index 900b977185..946e0dafaa 100644
--- a/ecc/bw6-761/fr/mimc/doc.go
+++ b/ecc/bw6-761/fr/mimc/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/mimc/mimc.go b/ecc/bw6-761/fr/mimc/mimc.go
index c77a4a9698..d341995043 100644
--- a/ecc/bw6-761/fr/mimc/mimc.go
+++ b/ecc/bw6-761/fr/mimc/mimc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/mimc/mimc_test.go b/ecc/bw6-761/fr/mimc/mimc_test.go
index f40411068f..cb91d9c60d 100644
--- a/ecc/bw6-761/fr/mimc/mimc_test.go
+++ b/ecc/bw6-761/fr/mimc/mimc_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/mimc/options.go b/ecc/bw6-761/fr/mimc/options.go
index 67bf8506da..03cbf15e1f 100644
--- a/ecc/bw6-761/fr/mimc/options.go
+++ b/ecc/bw6-761/fr/mimc/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/pedersen/doc.go b/ecc/bw6-761/fr/pedersen/doc.go
index 2e24034936..dff1285d0e 100644
--- a/ecc/bw6-761/fr/pedersen/doc.go
+++ b/ecc/bw6-761/fr/pedersen/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/pedersen/example_test.go b/ecc/bw6-761/fr/pedersen/example_test.go
index 6cfdf9cc00..0685ea9c22 100644
--- a/ecc/bw6-761/fr/pedersen/example_test.go
+++ b/ecc/bw6-761/fr/pedersen/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/pedersen/pedersen.go b/ecc/bw6-761/fr/pedersen/pedersen.go
index 78204513eb..50918d61e3 100644
--- a/ecc/bw6-761/fr/pedersen/pedersen.go
+++ b/ecc/bw6-761/fr/pedersen/pedersen.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/pedersen/pedersen_test.go b/ecc/bw6-761/fr/pedersen/pedersen_test.go
index 95dcadf528..dfb2560239 100644
--- a/ecc/bw6-761/fr/pedersen/pedersen_test.go
+++ b/ecc/bw6-761/fr/pedersen/pedersen_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/permutation/doc.go b/ecc/bw6-761/fr/permutation/doc.go
index e24cd82923..4f2ea7b2e4 100644
--- a/ecc/bw6-761/fr/permutation/doc.go
+++ b/ecc/bw6-761/fr/permutation/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/permutation/permutation.go b/ecc/bw6-761/fr/permutation/permutation.go
index 9360d623f3..6ad7944071 100644
--- a/ecc/bw6-761/fr/permutation/permutation.go
+++ b/ecc/bw6-761/fr/permutation/permutation.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/permutation/permutation_test.go b/ecc/bw6-761/fr/permutation/permutation_test.go
index b06266ee8b..64538e5f94 100644
--- a/ecc/bw6-761/fr/permutation/permutation_test.go
+++ b/ecc/bw6-761/fr/permutation/permutation_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/plookup/doc.go b/ecc/bw6-761/fr/plookup/doc.go
index 7a02c59719..5507122fab 100644
--- a/ecc/bw6-761/fr/plookup/doc.go
+++ b/ecc/bw6-761/fr/plookup/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/plookup/plookup_test.go b/ecc/bw6-761/fr/plookup/plookup_test.go
index ba1c843af1..f7c43e775e 100644
--- a/ecc/bw6-761/fr/plookup/plookup_test.go
+++ b/ecc/bw6-761/fr/plookup/plookup_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/plookup/table.go b/ecc/bw6-761/fr/plookup/table.go
index 1215d39f9d..6bcfb1e3ba 100644
--- a/ecc/bw6-761/fr/plookup/table.go
+++ b/ecc/bw6-761/fr/plookup/table.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/plookup/vector.go b/ecc/bw6-761/fr/plookup/vector.go
index f403607365..caf7f1a94d 100644
--- a/ecc/bw6-761/fr/plookup/vector.go
+++ b/ecc/bw6-761/fr/plookup/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/polynomial/doc.go b/ecc/bw6-761/fr/polynomial/doc.go
index fd96328e8f..ead3b5cba5 100644
--- a/ecc/bw6-761/fr/polynomial/doc.go
+++ b/ecc/bw6-761/fr/polynomial/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/polynomial/multilin.go b/ecc/bw6-761/fr/polynomial/multilin.go
index bb658ae1a3..45a33b0a95 100644
--- a/ecc/bw6-761/fr/polynomial/multilin.go
+++ b/ecc/bw6-761/fr/polynomial/multilin.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/polynomial/multilin_test.go b/ecc/bw6-761/fr/polynomial/multilin_test.go
index 128f6197be..e2457e2964 100644
--- a/ecc/bw6-761/fr/polynomial/multilin_test.go
+++ b/ecc/bw6-761/fr/polynomial/multilin_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/polynomial/polynomial.go b/ecc/bw6-761/fr/polynomial/polynomial.go
index a889bcb3b3..d2f01750ee 100644
--- a/ecc/bw6-761/fr/polynomial/polynomial.go
+++ b/ecc/bw6-761/fr/polynomial/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/polynomial/polynomial_test.go b/ecc/bw6-761/fr/polynomial/polynomial_test.go
index db01a6842c..fa453440e6 100644
--- a/ecc/bw6-761/fr/polynomial/polynomial_test.go
+++ b/ecc/bw6-761/fr/polynomial/polynomial_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/polynomial/pool.go b/ecc/bw6-761/fr/polynomial/pool.go
index b4c31a88b9..f0385da896 100644
--- a/ecc/bw6-761/fr/polynomial/pool.go
+++ b/ecc/bw6-761/fr/polynomial/pool.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/poseidon2/poseidon2.go b/ecc/bw6-761/fr/poseidon2/poseidon2.go
index 2034e38169..ee8d45dd41 100644
--- a/ecc/bw6-761/fr/poseidon2/poseidon2.go
+++ b/ecc/bw6-761/fr/poseidon2/poseidon2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/poseidon2/poseidon2_test.go b/ecc/bw6-761/fr/poseidon2/poseidon2_test.go
index cd88f8b7b5..f615ff8dfc 100644
--- a/ecc/bw6-761/fr/poseidon2/poseidon2_test.go
+++ b/ecc/bw6-761/fr/poseidon2/poseidon2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/sumcheck/sumcheck.go b/ecc/bw6-761/fr/sumcheck/sumcheck.go
index 511c685a4d..779fbe7fe6 100644
--- a/ecc/bw6-761/fr/sumcheck/sumcheck.go
+++ b/ecc/bw6-761/fr/sumcheck/sumcheck.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/sumcheck/sumcheck_test.go b/ecc/bw6-761/fr/sumcheck/sumcheck_test.go
index 40cfd15538..875d82578c 100644
--- a/ecc/bw6-761/fr/sumcheck/sumcheck_test.go
+++ b/ecc/bw6-761/fr/sumcheck/sumcheck_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/test_vector_utils/test_vector_utils.go b/ecc/bw6-761/fr/test_vector_utils/test_vector_utils.go
index 27ac283790..26530db603 100644
--- a/ecc/bw6-761/fr/test_vector_utils/test_vector_utils.go
+++ b/ecc/bw6-761/fr/test_vector_utils/test_vector_utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/vector.go b/ecc/bw6-761/fr/vector.go
index 3a2f40c1d1..25413b1ee1 100644
--- a/ecc/bw6-761/fr/vector.go
+++ b/ecc/bw6-761/fr/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/vector_purego.go b/ecc/bw6-761/fr/vector_purego.go
index c26ef9f1bb..1898ab6bb9 100644
--- a/ecc/bw6-761/fr/vector_purego.go
+++ b/ecc/bw6-761/fr/vector_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/fr/vector_test.go b/ecc/bw6-761/fr/vector_test.go
index 7d0a4162b1..868a27f1eb 100644
--- a/ecc/bw6-761/fr/vector_test.go
+++ b/ecc/bw6-761/fr/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/g1.go b/ecc/bw6-761/g1.go
index 8ac167f52e..bafa63903d 100644
--- a/ecc/bw6-761/g1.go
+++ b/ecc/bw6-761/g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/g1_test.go b/ecc/bw6-761/g1_test.go
index 6446bb30b9..fd81b0ffef 100644
--- a/ecc/bw6-761/g1_test.go
+++ b/ecc/bw6-761/g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/g2.go b/ecc/bw6-761/g2.go
index 608503f6c6..680833bd15 100644
--- a/ecc/bw6-761/g2.go
+++ b/ecc/bw6-761/g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/g2_test.go b/ecc/bw6-761/g2_test.go
index 108d220cf7..92555681ba 100644
--- a/ecc/bw6-761/g2_test.go
+++ b/ecc/bw6-761/g2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/hash_to_g1.go b/ecc/bw6-761/hash_to_g1.go
index 52491a7ebb..1ac6d27eb4 100644
--- a/ecc/bw6-761/hash_to_g1.go
+++ b/ecc/bw6-761/hash_to_g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/hash_to_g1_test.go b/ecc/bw6-761/hash_to_g1_test.go
index 20a5d4dee5..ee36dccfa4 100644
--- a/ecc/bw6-761/hash_to_g1_test.go
+++ b/ecc/bw6-761/hash_to_g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/hash_to_g2.go b/ecc/bw6-761/hash_to_g2.go
index 6450a5be75..eb082b6a42 100644
--- a/ecc/bw6-761/hash_to_g2.go
+++ b/ecc/bw6-761/hash_to_g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/hash_to_g2_test.go b/ecc/bw6-761/hash_to_g2_test.go
index daa6c09bb6..7743f0a4d4 100644
--- a/ecc/bw6-761/hash_to_g2_test.go
+++ b/ecc/bw6-761/hash_to_g2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/kzg/doc.go b/ecc/bw6-761/kzg/doc.go
index 226614bbdf..3a86419c48 100644
--- a/ecc/bw6-761/kzg/doc.go
+++ b/ecc/bw6-761/kzg/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/kzg/kzg.go b/ecc/bw6-761/kzg/kzg.go
index f19397ef7a..df19891f91 100644
--- a/ecc/bw6-761/kzg/kzg.go
+++ b/ecc/bw6-761/kzg/kzg.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/kzg/kzg_test.go b/ecc/bw6-761/kzg/kzg_test.go
index d67540bd20..25e5f16e9b 100644
--- a/ecc/bw6-761/kzg/kzg_test.go
+++ b/ecc/bw6-761/kzg/kzg_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/kzg/marshal.go b/ecc/bw6-761/kzg/marshal.go
index 7aa04b5c73..54ab8473cd 100644
--- a/ecc/bw6-761/kzg/marshal.go
+++ b/ecc/bw6-761/kzg/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/kzg/utils.go b/ecc/bw6-761/kzg/utils.go
index 42f8b42efb..503561d6af 100644
--- a/ecc/bw6-761/kzg/utils.go
+++ b/ecc/bw6-761/kzg/utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/marshal.go b/ecc/bw6-761/marshal.go
index a173dd35e2..5591e29177 100644
--- a/ecc/bw6-761/marshal.go
+++ b/ecc/bw6-761/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/marshal_test.go b/ecc/bw6-761/marshal_test.go
index dde2f26b31..288dbff181 100644
--- a/ecc/bw6-761/marshal_test.go
+++ b/ecc/bw6-761/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/multiexp.go b/ecc/bw6-761/multiexp.go
index 507e7fa553..a1b9bcec23 100644
--- a/ecc/bw6-761/multiexp.go
+++ b/ecc/bw6-761/multiexp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/multiexp_affine.go b/ecc/bw6-761/multiexp_affine.go
index 45826af9a8..4c3de055e8 100644
--- a/ecc/bw6-761/multiexp_affine.go
+++ b/ecc/bw6-761/multiexp_affine.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/multiexp_jacobian.go b/ecc/bw6-761/multiexp_jacobian.go
index 482a290b98..d1a01de831 100644
--- a/ecc/bw6-761/multiexp_jacobian.go
+++ b/ecc/bw6-761/multiexp_jacobian.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/multiexp_test.go b/ecc/bw6-761/multiexp_test.go
index 1afb6c9f68..2f2b2a7f58 100644
--- a/ecc/bw6-761/multiexp_test.go
+++ b/ecc/bw6-761/multiexp_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/pairing_test.go b/ecc/bw6-761/pairing_test.go
index c1e639aa8d..c5ce8e89a5 100644
--- a/ecc/bw6-761/pairing_test.go
+++ b/ecc/bw6-761/pairing_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/shplonk/doc.go b/ecc/bw6-761/shplonk/doc.go
index 0367893999..d63c7a3ddf 100644
--- a/ecc/bw6-761/shplonk/doc.go
+++ b/ecc/bw6-761/shplonk/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/shplonk/example_test.go b/ecc/bw6-761/shplonk/example_test.go
index 1f4faf86ab..e40803da56 100644
--- a/ecc/bw6-761/shplonk/example_test.go
+++ b/ecc/bw6-761/shplonk/example_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/shplonk/marshal.go b/ecc/bw6-761/shplonk/marshal.go
index 1a12fe4d48..c3ab5ad686 100644
--- a/ecc/bw6-761/shplonk/marshal.go
+++ b/ecc/bw6-761/shplonk/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/shplonk/shplonk.go b/ecc/bw6-761/shplonk/shplonk.go
index 7ad9e04699..33b82305b5 100644
--- a/ecc/bw6-761/shplonk/shplonk.go
+++ b/ecc/bw6-761/shplonk/shplonk.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/shplonk/shplonk_test.go b/ecc/bw6-761/shplonk/shplonk_test.go
index 4c0fe50bbf..3a12b64b31 100644
--- a/ecc/bw6-761/shplonk/shplonk_test.go
+++ b/ecc/bw6-761/shplonk/shplonk_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/twistededwards/curve.go b/ecc/bw6-761/twistededwards/curve.go
index 96b2881ed2..fb1ce97a2e 100644
--- a/ecc/bw6-761/twistededwards/curve.go
+++ b/ecc/bw6-761/twistededwards/curve.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/twistededwards/doc.go b/ecc/bw6-761/twistededwards/doc.go
index 1b90b6805f..b1d3f819be 100644
--- a/ecc/bw6-761/twistededwards/doc.go
+++ b/ecc/bw6-761/twistededwards/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/twistededwards/eddsa/doc.go b/ecc/bw6-761/twistededwards/eddsa/doc.go
index ae819082e3..00d3d8663d 100644
--- a/ecc/bw6-761/twistededwards/eddsa/doc.go
+++ b/ecc/bw6-761/twistededwards/eddsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/twistededwards/eddsa/eddsa.go b/ecc/bw6-761/twistededwards/eddsa/eddsa.go
index 89ce193349..ae6c3631ba 100644
--- a/ecc/bw6-761/twistededwards/eddsa/eddsa.go
+++ b/ecc/bw6-761/twistededwards/eddsa/eddsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/twistededwards/eddsa/eddsa_test.go b/ecc/bw6-761/twistededwards/eddsa/eddsa_test.go
index 905eca2e21..ae703a13b1 100644
--- a/ecc/bw6-761/twistededwards/eddsa/eddsa_test.go
+++ b/ecc/bw6-761/twistededwards/eddsa/eddsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/twistededwards/eddsa/marshal.go b/ecc/bw6-761/twistededwards/eddsa/marshal.go
index 403e372609..7d8259083f 100644
--- a/ecc/bw6-761/twistededwards/eddsa/marshal.go
+++ b/ecc/bw6-761/twistededwards/eddsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/twistededwards/point.go b/ecc/bw6-761/twistededwards/point.go
index 09af947b1f..8ed10042c0 100644
--- a/ecc/bw6-761/twistededwards/point.go
+++ b/ecc/bw6-761/twistededwards/point.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bw6-761/twistededwards/point_test.go b/ecc/bw6-761/twistededwards/point_test.go
index 86a3737c0d..6cbbee6eef 100644
--- a/ecc/bw6-761/twistededwards/point_test.go
+++ b/ecc/bw6-761/twistededwards/point_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/ecdsa/doc.go b/ecc/secp256k1/ecdsa/doc.go
index 4bc6e71746..9fc3777dcb 100644
--- a/ecc/secp256k1/ecdsa/doc.go
+++ b/ecc/secp256k1/ecdsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/ecdsa/ecdsa.go b/ecc/secp256k1/ecdsa/ecdsa.go
index b3ec2524a4..e4912e98a5 100644
--- a/ecc/secp256k1/ecdsa/ecdsa.go
+++ b/ecc/secp256k1/ecdsa/ecdsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/ecdsa/ecdsa_test.go b/ecc/secp256k1/ecdsa/ecdsa_test.go
index 7170cafd24..15d6336f88 100644
--- a/ecc/secp256k1/ecdsa/ecdsa_test.go
+++ b/ecc/secp256k1/ecdsa/ecdsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/ecdsa/marshal.go b/ecc/secp256k1/ecdsa/marshal.go
index b82b22ddc1..49791fc5f5 100644
--- a/ecc/secp256k1/ecdsa/marshal.go
+++ b/ecc/secp256k1/ecdsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/ecdsa/marshal_test.go b/ecc/secp256k1/ecdsa/marshal_test.go
index 872b7f9a18..b3f72255fd 100644
--- a/ecc/secp256k1/ecdsa/marshal_test.go
+++ b/ecc/secp256k1/ecdsa/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fp/arith.go b/ecc/secp256k1/fp/arith.go
index bb63552f5a..5c9905de80 100644
--- a/ecc/secp256k1/fp/arith.go
+++ b/ecc/secp256k1/fp/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fp/doc.go b/ecc/secp256k1/fp/doc.go
index a7dfcff36c..c433d81b9c 100644
--- a/ecc/secp256k1/fp/doc.go
+++ b/ecc/secp256k1/fp/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fp/element.go b/ecc/secp256k1/fp/element.go
index 1fe3541a37..9c5f79500b 100644
--- a/ecc/secp256k1/fp/element.go
+++ b/ecc/secp256k1/fp/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fp/element_exp.go b/ecc/secp256k1/fp/element_exp.go
index 9acdd2b69e..73e05e9e85 100644
--- a/ecc/secp256k1/fp/element_exp.go
+++ b/ecc/secp256k1/fp/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fp/element_purego.go b/ecc/secp256k1/fp/element_purego.go
index 7a22c54175..5650ed6925 100644
--- a/ecc/secp256k1/fp/element_purego.go
+++ b/ecc/secp256k1/fp/element_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fp/element_test.go b/ecc/secp256k1/fp/element_test.go
index 5ef370d1f1..f704b379c3 100644
--- a/ecc/secp256k1/fp/element_test.go
+++ b/ecc/secp256k1/fp/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fp/vector.go b/ecc/secp256k1/fp/vector.go
index ef60ed4b45..5dfc17ebbc 100644
--- a/ecc/secp256k1/fp/vector.go
+++ b/ecc/secp256k1/fp/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fp/vector_purego.go b/ecc/secp256k1/fp/vector_purego.go
index 0cda361871..85670501df 100644
--- a/ecc/secp256k1/fp/vector_purego.go
+++ b/ecc/secp256k1/fp/vector_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fp/vector_test.go b/ecc/secp256k1/fp/vector_test.go
index e7185486cf..5f78812dc6 100644
--- a/ecc/secp256k1/fp/vector_test.go
+++ b/ecc/secp256k1/fp/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fr/arith.go b/ecc/secp256k1/fr/arith.go
index dbba8a9ae4..8dbae56e32 100644
--- a/ecc/secp256k1/fr/arith.go
+++ b/ecc/secp256k1/fr/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fr/doc.go b/ecc/secp256k1/fr/doc.go
index 5a59e09001..28bfa2f221 100644
--- a/ecc/secp256k1/fr/doc.go
+++ b/ecc/secp256k1/fr/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fr/element.go b/ecc/secp256k1/fr/element.go
index 1bf4a7c491..9f20f3b412 100644
--- a/ecc/secp256k1/fr/element.go
+++ b/ecc/secp256k1/fr/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fr/element_exp.go b/ecc/secp256k1/fr/element_exp.go
index d508eb812d..b157fe1b3a 100644
--- a/ecc/secp256k1/fr/element_exp.go
+++ b/ecc/secp256k1/fr/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fr/element_purego.go b/ecc/secp256k1/fr/element_purego.go
index bdd8a849bb..32720596b7 100644
--- a/ecc/secp256k1/fr/element_purego.go
+++ b/ecc/secp256k1/fr/element_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fr/element_test.go b/ecc/secp256k1/fr/element_test.go
index dc51dce70d..cfe60baf69 100644
--- a/ecc/secp256k1/fr/element_test.go
+++ b/ecc/secp256k1/fr/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fr/vector.go b/ecc/secp256k1/fr/vector.go
index 4654b1b2d3..7792a6f73b 100644
--- a/ecc/secp256k1/fr/vector.go
+++ b/ecc/secp256k1/fr/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fr/vector_purego.go b/ecc/secp256k1/fr/vector_purego.go
index c26ef9f1bb..1898ab6bb9 100644
--- a/ecc/secp256k1/fr/vector_purego.go
+++ b/ecc/secp256k1/fr/vector_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/fr/vector_test.go b/ecc/secp256k1/fr/vector_test.go
index f6179e7824..88c4ef318f 100644
--- a/ecc/secp256k1/fr/vector_test.go
+++ b/ecc/secp256k1/fr/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/g1.go b/ecc/secp256k1/g1.go
index e6aa66e1df..ec71d32950 100644
--- a/ecc/secp256k1/g1.go
+++ b/ecc/secp256k1/g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/g1_test.go b/ecc/secp256k1/g1_test.go
index d2050c04c6..aee07c9487 100644
--- a/ecc/secp256k1/g1_test.go
+++ b/ecc/secp256k1/g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/hash_to_g1.go b/ecc/secp256k1/hash_to_g1.go
index 4d0fc63aba..13824a0622 100644
--- a/ecc/secp256k1/hash_to_g1.go
+++ b/ecc/secp256k1/hash_to_g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/hash_to_g1_test.go b/ecc/secp256k1/hash_to_g1_test.go
index 6e41450a0b..e4426b2e5b 100644
--- a/ecc/secp256k1/hash_to_g1_test.go
+++ b/ecc/secp256k1/hash_to_g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/multiexp.go b/ecc/secp256k1/multiexp.go
index 10338357df..38ddd80e0c 100644
--- a/ecc/secp256k1/multiexp.go
+++ b/ecc/secp256k1/multiexp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/multiexp_affine.go b/ecc/secp256k1/multiexp_affine.go
index be8577bfa5..05ecf0abad 100644
--- a/ecc/secp256k1/multiexp_affine.go
+++ b/ecc/secp256k1/multiexp_affine.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/multiexp_jacobian.go b/ecc/secp256k1/multiexp_jacobian.go
index a328744139..8a81395d62 100644
--- a/ecc/secp256k1/multiexp_jacobian.go
+++ b/ecc/secp256k1/multiexp_jacobian.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/secp256k1/multiexp_test.go b/ecc/secp256k1/multiexp_test.go
index 2d7881abe0..b31c58a925 100644
--- a/ecc/secp256k1/multiexp_test.go
+++ b/ecc/secp256k1/multiexp_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/ecdsa/doc.go b/ecc/stark-curve/ecdsa/doc.go
index 6674a4ab62..aec8d9bce9 100644
--- a/ecc/stark-curve/ecdsa/doc.go
+++ b/ecc/stark-curve/ecdsa/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/ecdsa/ecdsa.go b/ecc/stark-curve/ecdsa/ecdsa.go
index 589562b345..645ecb4797 100644
--- a/ecc/stark-curve/ecdsa/ecdsa.go
+++ b/ecc/stark-curve/ecdsa/ecdsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/ecdsa/ecdsa_test.go b/ecc/stark-curve/ecdsa/ecdsa_test.go
index 61021d83c3..d9809f2102 100644
--- a/ecc/stark-curve/ecdsa/ecdsa_test.go
+++ b/ecc/stark-curve/ecdsa/ecdsa_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/ecdsa/marshal.go b/ecc/stark-curve/ecdsa/marshal.go
index 26d82b5a55..c82c8b3448 100644
--- a/ecc/stark-curve/ecdsa/marshal.go
+++ b/ecc/stark-curve/ecdsa/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/ecdsa/marshal_test.go b/ecc/stark-curve/ecdsa/marshal_test.go
index 4429e18851..d285fd0587 100644
--- a/ecc/stark-curve/ecdsa/marshal_test.go
+++ b/ecc/stark-curve/ecdsa/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/arith.go b/ecc/stark-curve/fp/arith.go
index bb63552f5a..5c9905de80 100644
--- a/ecc/stark-curve/fp/arith.go
+++ b/ecc/stark-curve/fp/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/asm_adx.go b/ecc/stark-curve/fp/asm_adx.go
index 75e92992fe..8d85a11345 100644
--- a/ecc/stark-curve/fp/asm_adx.go
+++ b/ecc/stark-curve/fp/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/asm_avx.go b/ecc/stark-curve/fp/asm_avx.go
index aa233664d0..45e1ab3f0d 100644
--- a/ecc/stark-curve/fp/asm_avx.go
+++ b/ecc/stark-curve/fp/asm_avx.go
@@ -1,6 +1,6 @@
 //go:build !noavx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/asm_noadx.go b/ecc/stark-curve/fp/asm_noadx.go
index 304dfb7209..75ca96d775 100644
--- a/ecc/stark-curve/fp/asm_noadx.go
+++ b/ecc/stark-curve/fp/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/asm_noavx.go b/ecc/stark-curve/fp/asm_noavx.go
index 900dedbe8b..01f2011925 100644
--- a/ecc/stark-curve/fp/asm_noavx.go
+++ b/ecc/stark-curve/fp/asm_noavx.go
@@ -1,6 +1,6 @@
 //go:build noavx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/doc.go b/ecc/stark-curve/fp/doc.go
index b789d5224d..7cd4629d41 100644
--- a/ecc/stark-curve/fp/doc.go
+++ b/ecc/stark-curve/fp/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/element.go b/ecc/stark-curve/fp/element.go
index 2e0a60ca6f..6e911a9281 100644
--- a/ecc/stark-curve/fp/element.go
+++ b/ecc/stark-curve/fp/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/element_amd64.go b/ecc/stark-curve/fp/element_amd64.go
index 9cee062e5b..1a6e1cf5eb 100644
--- a/ecc/stark-curve/fp/element_amd64.go
+++ b/ecc/stark-curve/fp/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/element_amd64.s b/ecc/stark-curve/fp/element_amd64.s
index a7c6ffae66..41c54b1aa6 100644
--- a/ecc/stark-curve/fp/element_amd64.s
+++ b/ecc/stark-curve/fp/element_amd64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/element_arm64.go b/ecc/stark-curve/fp/element_arm64.go
index 3ed880d74f..11feaf7fe4 100644
--- a/ecc/stark-curve/fp/element_arm64.go
+++ b/ecc/stark-curve/fp/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/element_arm64.s b/ecc/stark-curve/fp/element_arm64.s
index ef16eaba35..0668975118 100644
--- a/ecc/stark-curve/fp/element_arm64.s
+++ b/ecc/stark-curve/fp/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/element_exp.go b/ecc/stark-curve/fp/element_exp.go
index 69e57afa05..b89f66850b 100644
--- a/ecc/stark-curve/fp/element_exp.go
+++ b/ecc/stark-curve/fp/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/element_purego.go b/ecc/stark-curve/fp/element_purego.go
index 425a7d564b..bfbebf9634 100644
--- a/ecc/stark-curve/fp/element_purego.go
+++ b/ecc/stark-curve/fp/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/element_test.go b/ecc/stark-curve/fp/element_test.go
index 2c47d8604b..3fbd8544a0 100644
--- a/ecc/stark-curve/fp/element_test.go
+++ b/ecc/stark-curve/fp/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/vector.go b/ecc/stark-curve/fp/vector.go
index ef60ed4b45..5dfc17ebbc 100644
--- a/ecc/stark-curve/fp/vector.go
+++ b/ecc/stark-curve/fp/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/vector_amd64.go b/ecc/stark-curve/fp/vector_amd64.go
index 9e05e6b2f3..26cdca4517 100644
--- a/ecc/stark-curve/fp/vector_amd64.go
+++ b/ecc/stark-curve/fp/vector_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/vector_purego.go b/ecc/stark-curve/fp/vector_purego.go
index 6adeb1a8a2..98343052a2 100644
--- a/ecc/stark-curve/fp/vector_purego.go
+++ b/ecc/stark-curve/fp/vector_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || !amd64
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fp/vector_test.go b/ecc/stark-curve/fp/vector_test.go
index e7185486cf..5f78812dc6 100644
--- a/ecc/stark-curve/fp/vector_test.go
+++ b/ecc/stark-curve/fp/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/arith.go b/ecc/stark-curve/fr/arith.go
index dbba8a9ae4..8dbae56e32 100644
--- a/ecc/stark-curve/fr/arith.go
+++ b/ecc/stark-curve/fr/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/asm_adx.go b/ecc/stark-curve/fr/asm_adx.go
index 9b970335f1..52421cc159 100644
--- a/ecc/stark-curve/fr/asm_adx.go
+++ b/ecc/stark-curve/fr/asm_adx.go
@@ -1,6 +1,6 @@
 //go:build !noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/asm_avx.go b/ecc/stark-curve/fr/asm_avx.go
index 2a0a166ed4..f89a44926d 100644
--- a/ecc/stark-curve/fr/asm_avx.go
+++ b/ecc/stark-curve/fr/asm_avx.go
@@ -1,6 +1,6 @@
 //go:build !noavx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/asm_noadx.go b/ecc/stark-curve/fr/asm_noadx.go
index 96741014f2..9c9c9dab5d 100644
--- a/ecc/stark-curve/fr/asm_noadx.go
+++ b/ecc/stark-curve/fr/asm_noadx.go
@@ -1,6 +1,6 @@
 //go:build noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/asm_noavx.go b/ecc/stark-curve/fr/asm_noavx.go
index 3cb6968fb8..ae86f75e7f 100644
--- a/ecc/stark-curve/fr/asm_noavx.go
+++ b/ecc/stark-curve/fr/asm_noavx.go
@@ -1,6 +1,6 @@
 //go:build noavx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/doc.go b/ecc/stark-curve/fr/doc.go
index 483d069817..fc4940028a 100644
--- a/ecc/stark-curve/fr/doc.go
+++ b/ecc/stark-curve/fr/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/element.go b/ecc/stark-curve/fr/element.go
index 4e9fec24b4..c9d96f98b4 100644
--- a/ecc/stark-curve/fr/element.go
+++ b/ecc/stark-curve/fr/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/element_amd64.go b/ecc/stark-curve/fr/element_amd64.go
index 4c3f2a8567..7e76a943a1 100644
--- a/ecc/stark-curve/fr/element_amd64.go
+++ b/ecc/stark-curve/fr/element_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/element_amd64.s b/ecc/stark-curve/fr/element_amd64.s
index a7c6ffae66..41c54b1aa6 100644
--- a/ecc/stark-curve/fr/element_amd64.s
+++ b/ecc/stark-curve/fr/element_amd64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/element_arm64.go b/ecc/stark-curve/fr/element_arm64.go
index 8e2641ede7..8b7428b3e2 100644
--- a/ecc/stark-curve/fr/element_arm64.go
+++ b/ecc/stark-curve/fr/element_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/element_arm64.s b/ecc/stark-curve/fr/element_arm64.s
index ef16eaba35..0668975118 100644
--- a/ecc/stark-curve/fr/element_arm64.s
+++ b/ecc/stark-curve/fr/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/element_purego.go b/ecc/stark-curve/fr/element_purego.go
index ebd6bca369..a0cbe29f1c 100644
--- a/ecc/stark-curve/fr/element_purego.go
+++ b/ecc/stark-curve/fr/element_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/element_test.go b/ecc/stark-curve/fr/element_test.go
index d217e25816..b493866d21 100644
--- a/ecc/stark-curve/fr/element_test.go
+++ b/ecc/stark-curve/fr/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/vector.go b/ecc/stark-curve/fr/vector.go
index 4654b1b2d3..7792a6f73b 100644
--- a/ecc/stark-curve/fr/vector.go
+++ b/ecc/stark-curve/fr/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/vector_amd64.go b/ecc/stark-curve/fr/vector_amd64.go
index a7dcec3b25..e3565da46a 100644
--- a/ecc/stark-curve/fr/vector_amd64.go
+++ b/ecc/stark-curve/fr/vector_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/vector_purego.go b/ecc/stark-curve/fr/vector_purego.go
index db43e73504..6608e394c7 100644
--- a/ecc/stark-curve/fr/vector_purego.go
+++ b/ecc/stark-curve/fr/vector_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || !amd64
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/stark-curve/fr/vector_test.go b/ecc/stark-curve/fr/vector_test.go
index f6179e7824..88c4ef318f 100644
--- a/ecc/stark-curve/fr/vector_test.go
+++ b/ecc/stark-curve/fr/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/fiat-shamir/transcript.go b/fiat-shamir/transcript.go
index b50df0f0da..4e8b4c3a8b 100644
--- a/fiat-shamir/transcript.go
+++ b/fiat-shamir/transcript.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fiatshamir
diff --git a/fiat-shamir/transcript_test.go b/fiat-shamir/transcript_test.go
index 8232b6b90b..7773d7712c 100644
--- a/fiat-shamir/transcript_test.go
+++ b/fiat-shamir/transcript_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fiatshamir
diff --git a/field/babybear/asm_avx.go b/field/babybear/asm_avx.go
index a8a213182a..585a4df090 100644
--- a/field/babybear/asm_avx.go
+++ b/field/babybear/asm_avx.go
@@ -1,6 +1,6 @@
 //go:build !noavx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/asm_noavx.go b/field/babybear/asm_noavx.go
index 00d2951e19..c9c902ec52 100644
--- a/field/babybear/asm_noavx.go
+++ b/field/babybear/asm_noavx.go
@@ -1,6 +1,6 @@
 //go:build noavx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/doc.go b/field/babybear/doc.go
index fc116bd84f..7264e15bcd 100644
--- a/field/babybear/doc.go
+++ b/field/babybear/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/element.go b/field/babybear/element.go
index 7ec0950bab..8fc970bd41 100644
--- a/field/babybear/element.go
+++ b/field/babybear/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/element_amd64.s b/field/babybear/element_amd64.s
index 11676c6f04..7a3efcf7bd 100644
--- a/field/babybear/element_amd64.s
+++ b/field/babybear/element_amd64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/element_exp.go b/field/babybear/element_exp.go
index b536f6ea6e..b252f7997e 100644
--- a/field/babybear/element_exp.go
+++ b/field/babybear/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/element_purego.go b/field/babybear/element_purego.go
index 19fe63b732..d75894d966 100644
--- a/field/babybear/element_purego.go
+++ b/field/babybear/element_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/element_test.go b/field/babybear/element_test.go
index 075793bf10..712978bdbc 100644
--- a/field/babybear/element_test.go
+++ b/field/babybear/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/fft/bitreverse.go b/field/babybear/fft/bitreverse.go
index 164ee25831..e9bc03bd6d 100644
--- a/field/babybear/fft/bitreverse.go
+++ b/field/babybear/fft/bitreverse.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/fft/bitreverse_test.go b/field/babybear/fft/bitreverse_test.go
index ec29679866..8bbf338450 100644
--- a/field/babybear/fft/bitreverse_test.go
+++ b/field/babybear/fft/bitreverse_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/fft/doc.go b/field/babybear/fft/doc.go
index 4cce0f9779..8176d8e77a 100644
--- a/field/babybear/fft/doc.go
+++ b/field/babybear/fft/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/fft/domain.go b/field/babybear/fft/domain.go
index dc0f897185..6f96d7df62 100644
--- a/field/babybear/fft/domain.go
+++ b/field/babybear/fft/domain.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/fft/domain_test.go b/field/babybear/fft/domain_test.go
index e445d3cc12..7049120e6a 100644
--- a/field/babybear/fft/domain_test.go
+++ b/field/babybear/fft/domain_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/fft/fft.go b/field/babybear/fft/fft.go
index bb69c72330..3eb5d70427 100644
--- a/field/babybear/fft/fft.go
+++ b/field/babybear/fft/fft.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/fft/fft_test.go b/field/babybear/fft/fft_test.go
index b8619c1ccf..1e8144a4e0 100644
--- a/field/babybear/fft/fft_test.go
+++ b/field/babybear/fft/fft_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/fft/options.go b/field/babybear/fft/options.go
index ef1ded416b..da964b5c87 100644
--- a/field/babybear/fft/options.go
+++ b/field/babybear/fft/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/generator.go b/field/babybear/generator.go
index 18d6198950..7f0e972561 100644
--- a/field/babybear/generator.go
+++ b/field/babybear/generator.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/sis/sis.go b/field/babybear/sis/sis.go
index d1d2b92c64..d0d0ae505d 100644
--- a/field/babybear/sis/sis.go
+++ b/field/babybear/sis/sis.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/sis/sis_fft.go b/field/babybear/sis/sis_fft.go
index 0b5cc37994..0b30e84b20 100644
--- a/field/babybear/sis/sis_fft.go
+++ b/field/babybear/sis/sis_fft.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/sis/sis_test.go b/field/babybear/sis/sis_test.go
index 5fb044de67..770c02f3e6 100644
--- a/field/babybear/sis/sis_test.go
+++ b/field/babybear/sis/sis_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/vector.go b/field/babybear/vector.go
index dca652c999..491cb8136f 100644
--- a/field/babybear/vector.go
+++ b/field/babybear/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/vector_amd64.go b/field/babybear/vector_amd64.go
index 742b60ce2e..b6d092f7e3 100644
--- a/field/babybear/vector_amd64.go
+++ b/field/babybear/vector_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/vector_purego.go b/field/babybear/vector_purego.go
index 8164830b26..8ddc0dfae5 100644
--- a/field/babybear/vector_purego.go
+++ b/field/babybear/vector_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/vector_test.go b/field/babybear/vector_test.go
index c05be2917f..5068315a2f 100644
--- a/field/babybear/vector_test.go
+++ b/field/babybear/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/generator/asm/amd64/asm_macros.go b/field/generator/asm/amd64/asm_macros.go
index c960713e2d..215a7422c5 100644
--- a/field/generator/asm/amd64/asm_macros.go
+++ b/field/generator/asm/amd64/asm_macros.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package amd64
diff --git a/field/generator/asm/amd64/build.go b/field/generator/asm/amd64/build.go
index a5407b9d14..afc90223f5 100644
--- a/field/generator/asm/amd64/build.go
+++ b/field/generator/asm/amd64/build.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Package amd64 contains syntactic sugar to generate amd64 assembly code
diff --git a/field/generator/asm/amd64/element_butterfly.go b/field/generator/asm/amd64/element_butterfly.go
index 6ada559b9a..0268b92a6f 100644
--- a/field/generator/asm/amd64/element_butterfly.go
+++ b/field/generator/asm/amd64/element_butterfly.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package amd64
diff --git a/field/generator/asm/amd64/element_frommont.go b/field/generator/asm/amd64/element_frommont.go
index dc45d9c8da..9edb592951 100644
--- a/field/generator/asm/amd64/element_frommont.go
+++ b/field/generator/asm/amd64/element_frommont.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package amd64
diff --git a/field/generator/asm/amd64/element_mul.go b/field/generator/asm/amd64/element_mul.go
index 59e3c5064a..80dc012d01 100644
--- a/field/generator/asm/amd64/element_mul.go
+++ b/field/generator/asm/amd64/element_mul.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package amd64
diff --git a/field/generator/asm/amd64/element_mul_constants.go b/field/generator/asm/amd64/element_mul_constants.go
index 99e52dc16f..917042a9df 100644
--- a/field/generator/asm/amd64/element_mul_constants.go
+++ b/field/generator/asm/amd64/element_mul_constants.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package amd64
diff --git a/field/generator/asm/amd64/element_reduce.go b/field/generator/asm/amd64/element_reduce.go
index c443140eba..bf5bd11e09 100644
--- a/field/generator/asm/amd64/element_reduce.go
+++ b/field/generator/asm/amd64/element_reduce.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package amd64
diff --git a/field/generator/asm/amd64/element_vec_4words.go b/field/generator/asm/amd64/element_vec_4words.go
index 14ac51f8ab..012902bd58 100644
--- a/field/generator/asm/amd64/element_vec_4words.go
+++ b/field/generator/asm/amd64/element_vec_4words.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package amd64
diff --git a/field/generator/asm/arm64/element_mul.go b/field/generator/asm/arm64/element_mul.go
index 681e923ad7..d3e26a672d 100644
--- a/field/generator/asm/arm64/element_mul.go
+++ b/field/generator/asm/arm64/element_mul.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package arm64
diff --git a/field/generator/config/field_config.go b/field/generator/config/field_config.go
index 173b678b34..9b523d6c8f 100644
--- a/field/generator/config/field_config.go
+++ b/field/generator/config/field_config.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Package config provides Golang code generation for efficient field arithmetic operations.
diff --git a/field/generator/generator_test.go b/field/generator/generator_test.go
index 95e28701c2..21c46f4e64 100644
--- a/field/generator/generator_test.go
+++ b/field/generator/generator_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package generator
diff --git a/field/goff/cmd/errors.go b/field/goff/cmd/errors.go
index c28c662d49..5d69a8483e 100644
--- a/field/goff/cmd/errors.go
+++ b/field/goff/cmd/errors.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package cmd
diff --git a/field/goff/cmd/root.go b/field/goff/cmd/root.go
index bf2d859fad..bb2a78fab9 100644
--- a/field/goff/cmd/root.go
+++ b/field/goff/cmd/root.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Package cmd is the CLI interface for goff
diff --git a/field/goff/cmd/version.go b/field/goff/cmd/version.go
index 1f32bf574a..e5991ec4eb 100644
--- a/field/goff/cmd/version.go
+++ b/field/goff/cmd/version.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package cmd
diff --git a/field/goff/main.go b/field/goff/main.go
index 0f3884e223..46958922a0 100644
--- a/field/goff/main.go
+++ b/field/goff/main.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Package goff (go finite field) is a library that generates fast field arithmetic code for a given modulus.
diff --git a/field/goldilocks/arith.go b/field/goldilocks/arith.go
index fd46bf62a0..9b15174ee0 100644
--- a/field/goldilocks/arith.go
+++ b/field/goldilocks/arith.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/doc.go b/field/goldilocks/doc.go
index f122fa27df..c188489b77 100644
--- a/field/goldilocks/doc.go
+++ b/field/goldilocks/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/element.go b/field/goldilocks/element.go
index 885ac83488..349928655a 100644
--- a/field/goldilocks/element.go
+++ b/field/goldilocks/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/element_exp.go b/field/goldilocks/element_exp.go
index 676211d6b4..ae197446c3 100644
--- a/field/goldilocks/element_exp.go
+++ b/field/goldilocks/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/element_purego.go b/field/goldilocks/element_purego.go
index 00d536c716..47da790b25 100644
--- a/field/goldilocks/element_purego.go
+++ b/field/goldilocks/element_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/element_test.go b/field/goldilocks/element_test.go
index e940b56092..a7b55702e1 100644
--- a/field/goldilocks/element_test.go
+++ b/field/goldilocks/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/fft/bitreverse.go b/field/goldilocks/fft/bitreverse.go
index 4e0f7bd962..0164e01624 100644
--- a/field/goldilocks/fft/bitreverse.go
+++ b/field/goldilocks/fft/bitreverse.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/fft/bitreverse_test.go b/field/goldilocks/fft/bitreverse_test.go
index 11bb9f440b..6cb814b11e 100644
--- a/field/goldilocks/fft/bitreverse_test.go
+++ b/field/goldilocks/fft/bitreverse_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/fft/doc.go b/field/goldilocks/fft/doc.go
index 4cce0f9779..8176d8e77a 100644
--- a/field/goldilocks/fft/doc.go
+++ b/field/goldilocks/fft/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/fft/domain.go b/field/goldilocks/fft/domain.go
index cbde6c90e3..a6b01a1fa3 100644
--- a/field/goldilocks/fft/domain.go
+++ b/field/goldilocks/fft/domain.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/fft/domain_test.go b/field/goldilocks/fft/domain_test.go
index e445d3cc12..7049120e6a 100644
--- a/field/goldilocks/fft/domain_test.go
+++ b/field/goldilocks/fft/domain_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/fft/fft.go b/field/goldilocks/fft/fft.go
index ab9ff0135c..966f03457a 100644
--- a/field/goldilocks/fft/fft.go
+++ b/field/goldilocks/fft/fft.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/fft/fft_test.go b/field/goldilocks/fft/fft_test.go
index f5d88e02a4..85fda92d12 100644
--- a/field/goldilocks/fft/fft_test.go
+++ b/field/goldilocks/fft/fft_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/fft/options.go b/field/goldilocks/fft/options.go
index 2ebef76ee5..dca1d37633 100644
--- a/field/goldilocks/fft/options.go
+++ b/field/goldilocks/fft/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/generator.go b/field/goldilocks/generator.go
index 799abb8d58..012ddef3a9 100644
--- a/field/goldilocks/generator.go
+++ b/field/goldilocks/generator.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/sis/sis.go b/field/goldilocks/sis/sis.go
index 7dafd5c715..fc773e91e3 100644
--- a/field/goldilocks/sis/sis.go
+++ b/field/goldilocks/sis/sis.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/sis/sis_fft.go b/field/goldilocks/sis/sis_fft.go
index 06691b4c9d..321a84e905 100644
--- a/field/goldilocks/sis/sis_fft.go
+++ b/field/goldilocks/sis/sis_fft.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/sis/sis_test.go b/field/goldilocks/sis/sis_test.go
index ad7c2dc7ac..ad9b370a2e 100644
--- a/field/goldilocks/sis/sis_test.go
+++ b/field/goldilocks/sis/sis_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/vector.go b/field/goldilocks/vector.go
index 32ad268ee5..969158c112 100644
--- a/field/goldilocks/vector.go
+++ b/field/goldilocks/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/vector_purego.go b/field/goldilocks/vector_purego.go
index aadf02c291..d47c24ed5e 100644
--- a/field/goldilocks/vector_purego.go
+++ b/field/goldilocks/vector_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/goldilocks/vector_test.go b/field/goldilocks/vector_test.go
index 96e735c8cd..cdb63d1da5 100644
--- a/field/goldilocks/vector_test.go
+++ b/field/goldilocks/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/asm_avx.go b/field/koalabear/asm_avx.go
index 85e3e37582..ec075d811d 100644
--- a/field/koalabear/asm_avx.go
+++ b/field/koalabear/asm_avx.go
@@ -1,6 +1,6 @@
 //go:build !noavx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/asm_noavx.go b/field/koalabear/asm_noavx.go
index cdd0d205b3..4e0680b25f 100644
--- a/field/koalabear/asm_noavx.go
+++ b/field/koalabear/asm_noavx.go
@@ -1,6 +1,6 @@
 //go:build noavx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/doc.go b/field/koalabear/doc.go
index c102c15c78..b01dba5f88 100644
--- a/field/koalabear/doc.go
+++ b/field/koalabear/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/element.go b/field/koalabear/element.go
index 214d9f5ab1..c18ddf14a7 100644
--- a/field/koalabear/element.go
+++ b/field/koalabear/element.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/element_amd64.s b/field/koalabear/element_amd64.s
index 11676c6f04..7a3efcf7bd 100644
--- a/field/koalabear/element_amd64.s
+++ b/field/koalabear/element_amd64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/element_exp.go b/field/koalabear/element_exp.go
index 3c2a3c72ba..f29b9ae153 100644
--- a/field/koalabear/element_exp.go
+++ b/field/koalabear/element_exp.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/element_purego.go b/field/koalabear/element_purego.go
index 4ede470cca..4e808b511c 100644
--- a/field/koalabear/element_purego.go
+++ b/field/koalabear/element_purego.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/element_test.go b/field/koalabear/element_test.go
index bea2f28ee3..1be1fa52fd 100644
--- a/field/koalabear/element_test.go
+++ b/field/koalabear/element_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/fft/bitreverse.go b/field/koalabear/fft/bitreverse.go
index 5604c76673..72e1a61a8f 100644
--- a/field/koalabear/fft/bitreverse.go
+++ b/field/koalabear/fft/bitreverse.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/fft/bitreverse_test.go b/field/koalabear/fft/bitreverse_test.go
index 732831a20a..79c423d2ba 100644
--- a/field/koalabear/fft/bitreverse_test.go
+++ b/field/koalabear/fft/bitreverse_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/fft/doc.go b/field/koalabear/fft/doc.go
index 4cce0f9779..8176d8e77a 100644
--- a/field/koalabear/fft/doc.go
+++ b/field/koalabear/fft/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/fft/domain.go b/field/koalabear/fft/domain.go
index 7f13919e7b..4bb84176c4 100644
--- a/field/koalabear/fft/domain.go
+++ b/field/koalabear/fft/domain.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/fft/domain_test.go b/field/koalabear/fft/domain_test.go
index e445d3cc12..7049120e6a 100644
--- a/field/koalabear/fft/domain_test.go
+++ b/field/koalabear/fft/domain_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/fft/fft.go b/field/koalabear/fft/fft.go
index 5e63e1954a..157d9e3872 100644
--- a/field/koalabear/fft/fft.go
+++ b/field/koalabear/fft/fft.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/fft/fft_test.go b/field/koalabear/fft/fft_test.go
index 1d447f2bdf..edce30096b 100644
--- a/field/koalabear/fft/fft_test.go
+++ b/field/koalabear/fft/fft_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/fft/options.go b/field/koalabear/fft/options.go
index c146ac1123..e29ff3b6bd 100644
--- a/field/koalabear/fft/options.go
+++ b/field/koalabear/fft/options.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/generator.go b/field/koalabear/generator.go
index dd5bbb97e9..17f80ff949 100644
--- a/field/koalabear/generator.go
+++ b/field/koalabear/generator.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/sis/sis.go b/field/koalabear/sis/sis.go
index a58727b547..81a312f22e 100644
--- a/field/koalabear/sis/sis.go
+++ b/field/koalabear/sis/sis.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/sis/sis_fft.go b/field/koalabear/sis/sis_fft.go
index e0d544f9c8..7706135c9c 100644
--- a/field/koalabear/sis/sis_fft.go
+++ b/field/koalabear/sis/sis_fft.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/sis/sis_test.go b/field/koalabear/sis/sis_test.go
index ca0fb3da68..b66013d77d 100644
--- a/field/koalabear/sis/sis_test.go
+++ b/field/koalabear/sis/sis_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/vector.go b/field/koalabear/vector.go
index 725e065d16..f4dc8789cb 100644
--- a/field/koalabear/vector.go
+++ b/field/koalabear/vector.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/vector_amd64.go b/field/koalabear/vector_amd64.go
index ede9d1afa9..2d63563df0 100644
--- a/field/koalabear/vector_amd64.go
+++ b/field/koalabear/vector_amd64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/vector_purego.go b/field/koalabear/vector_purego.go
index fa9715eaf5..5beca25df2 100644
--- a/field/koalabear/vector_purego.go
+++ b/field/koalabear/vector_purego.go
@@ -1,6 +1,6 @@
 //go:build purego || (!amd64 && !arm64)
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/vector_test.go b/field/koalabear/vector_test.go
index 606366bb0c..ac3ef9fd75 100644
--- a/field/koalabear/vector_test.go
+++ b/field/koalabear/vector_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/hash/hashes.go b/hash/hashes.go
index ee88d158e4..897a8f11fe 100644
--- a/hash/hashes.go
+++ b/hash/hashes.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package hash
diff --git a/internal/generator/gkr/test_vectors/main.go b/internal/generator/gkr/test_vectors/main.go
index 49ddf92414..a279b83ea0 100644
--- a/internal/generator/gkr/test_vectors/main.go
+++ b/internal/generator/gkr/test_vectors/main.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/internal/generator/test_vector_utils/small_rational/gkr/gkr.go b/internal/generator/test_vector_utils/small_rational/gkr/gkr.go
index 73bb280a5a..f551bbad76 100644
--- a/internal/generator/test_vector_utils/small_rational/gkr/gkr.go
+++ b/internal/generator/test_vector_utils/small_rational/gkr/gkr.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/internal/generator/test_vector_utils/small_rational/polynomial/doc.go b/internal/generator/test_vector_utils/small_rational/polynomial/doc.go
index fd96328e8f..ead3b5cba5 100644
--- a/internal/generator/test_vector_utils/small_rational/polynomial/doc.go
+++ b/internal/generator/test_vector_utils/small_rational/polynomial/doc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/internal/generator/test_vector_utils/small_rational/polynomial/multilin.go b/internal/generator/test_vector_utils/small_rational/polynomial/multilin.go
index d3c0edc694..538725ee15 100644
--- a/internal/generator/test_vector_utils/small_rational/polynomial/multilin.go
+++ b/internal/generator/test_vector_utils/small_rational/polynomial/multilin.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/internal/generator/test_vector_utils/small_rational/polynomial/polynomial.go b/internal/generator/test_vector_utils/small_rational/polynomial/polynomial.go
index 6b67eafada..8aaa44e7a2 100644
--- a/internal/generator/test_vector_utils/small_rational/polynomial/polynomial.go
+++ b/internal/generator/test_vector_utils/small_rational/polynomial/polynomial.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/internal/generator/test_vector_utils/small_rational/polynomial/pool.go b/internal/generator/test_vector_utils/small_rational/polynomial/pool.go
index 9dbd98c86c..688b193907 100644
--- a/internal/generator/test_vector_utils/small_rational/polynomial/pool.go
+++ b/internal/generator/test_vector_utils/small_rational/polynomial/pool.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck.go b/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck.go
index e711cbcf2c..eb8e62c99d 100644
--- a/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck.go
+++ b/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck_test.go b/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck_test.go
index 46acdcca1c..ad6f8ac239 100644
--- a/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck_test.go
+++ b/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/internal/generator/test_vector_utils/small_rational/test_vector_utils/test_vector_utils.go b/internal/generator/test_vector_utils/small_rational/test_vector_utils/test_vector_utils.go
index 273e1c537f..9e91fe7c67 100644
--- a/internal/generator/test_vector_utils/small_rational/test_vector_utils/test_vector_utils.go
+++ b/internal/generator/test_vector_utils/small_rational/test_vector_utils/test_vector_utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/internal/generator/tower/asm/amd64/e2.go b/internal/generator/tower/asm/amd64/e2.go
index e61b127ded..e9c98f3fd3 100644
--- a/internal/generator/tower/asm/amd64/e2.go
+++ b/internal/generator/tower/asm/amd64/e2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package amd64
diff --git a/internal/generator/tower/asm/amd64/e2_bls381.go b/internal/generator/tower/asm/amd64/e2_bls381.go
index 54d49c65b2..4a606e550d 100644
--- a/internal/generator/tower/asm/amd64/e2_bls381.go
+++ b/internal/generator/tower/asm/amd64/e2_bls381.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package amd64
diff --git a/internal/generator/tower/asm/amd64/e2_bn254.go b/internal/generator/tower/asm/amd64/e2_bn254.go
index fed9e14a07..72fe75af85 100644
--- a/internal/generator/tower/asm/amd64/e2_bn254.go
+++ b/internal/generator/tower/asm/amd64/e2_bn254.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package amd64
diff --git a/signature/ecdsa/ecdsa.go b/signature/ecdsa/ecdsa.go
index c21fecb8f6..a0fda91d10 100644
--- a/signature/ecdsa/ecdsa.go
+++ b/signature/ecdsa/ecdsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package ecdsa
diff --git a/signature/eddsa/eddsa.go b/signature/eddsa/eddsa.go
index f17589ebb5..aa61935e17 100644
--- a/signature/eddsa/eddsa.go
+++ b/signature/eddsa/eddsa.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package eddsa
diff --git a/signature/signature.go b/signature/signature.go
index 4a378a1d82..eb89dc5024 100644
--- a/signature/signature.go
+++ b/signature/signature.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Package signature defines interfaces for a Signer and a PublicKey similarly to go/crypto standard package.

From fb7ea000b1b09acdd3a6f9e93f0a3d31d8fcf12d Mon Sep 17 00:00:00 2001
From: Gautam Botrel <gautam.botrel@gmail.com>
Date: Tue, 7 Jan 2025 09:55:21 -0600
Subject: [PATCH 113/114] fix: re-ran go generate for field/

---
 field/babybear/element_arm64.s  | 2 +-
 field/babybear/vector_arm64.go  | 2 +-
 field/koalabear/element_arm64.s | 2 +-
 field/koalabear/vector_arm64.go | 2 +-
 4 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/field/babybear/element_arm64.s b/field/babybear/element_arm64.s
index f3ddfa315e..c9f35b30b7 100644
--- a/field/babybear/element_arm64.s
+++ b/field/babybear/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/babybear/vector_arm64.go b/field/babybear/vector_arm64.go
index 3ab1b562ff..25d034036d 100644
--- a/field/babybear/vector_arm64.go
+++ b/field/babybear/vector_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/element_arm64.s b/field/koalabear/element_arm64.s
index f3ddfa315e..c9f35b30b7 100644
--- a/field/koalabear/element_arm64.s
+++ b/field/koalabear/element_arm64.s
@@ -1,6 +1,6 @@
 //go:build  !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/field/koalabear/vector_arm64.go b/field/koalabear/vector_arm64.go
index dd410b2058..a52fae5265 100644
--- a/field/koalabear/vector_arm64.go
+++ b/field/koalabear/vector_arm64.go
@@ -1,6 +1,6 @@
 //go:build !purego
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT

From 779e884dabb38b92e677f4891286637a3d2e5734 Mon Sep 17 00:00:00 2001
From: Youssef El Housni <youssef.housni21@gmail.com>
Date: Wed, 8 Jan 2025 11:54:33 -0500
Subject: [PATCH 114/114] docs: Change copyright year to 2025 (not
 autogenerated)

---
 ecc/bls12-377/fp/element_utils.go                    | 2 +-
 ecc/bls12-377/internal/fptower/e2_bls377.go          | 2 +-
 ecc/bls12-377/internal/fptower/frobenius.go          | 2 +-
 ecc/bls12-377/internal/fptower/parameters.go         | 2 +-
 ecc/bls12-377/pairing.go                             | 2 +-
 ecc/bls12-381/internal/fptower/e2_bls381.go          | 2 +-
 ecc/bls12-381/internal/fptower/e2_bls381_fallback.go | 2 +-
 ecc/bls12-381/internal/fptower/frobenius.go          | 2 +-
 ecc/bls12-381/internal/fptower/parameters.go         | 2 +-
 ecc/bls12-381/pairing.go                             | 2 +-
 ecc/bls24-315/hash_to_g2.go                          | 2 +-
 ecc/bls24-315/internal/fptower/asm.go                | 2 +-
 ecc/bls24-315/internal/fptower/asm_noadx.go          | 2 +-
 ecc/bls24-315/internal/fptower/e12.go                | 2 +-
 ecc/bls24-315/internal/fptower/e12_test.go           | 2 +-
 ecc/bls24-315/internal/fptower/e2.go                 | 2 +-
 ecc/bls24-315/internal/fptower/e24.go                | 2 +-
 ecc/bls24-315/internal/fptower/e24_test.go           | 2 +-
 ecc/bls24-315/internal/fptower/e2_amd64.go           | 2 +-
 ecc/bls24-315/internal/fptower/e2_amd64.s            | 2 +-
 ecc/bls24-315/internal/fptower/e2_bls315.go          | 2 +-
 ecc/bls24-315/internal/fptower/e2_bls315_fallback.go | 2 +-
 ecc/bls24-315/internal/fptower/e2_fallback.go        | 2 +-
 ecc/bls24-315/internal/fptower/e2_test.go            | 2 +-
 ecc/bls24-315/internal/fptower/e4.go                 | 2 +-
 ecc/bls24-315/internal/fptower/e4_bls315.go          | 2 +-
 ecc/bls24-315/internal/fptower/e4_test.go            | 2 +-
 ecc/bls24-315/internal/fptower/frobenius.go          | 2 +-
 ecc/bls24-315/internal/fptower/parameters.go         | 2 +-
 ecc/bls24-315/pairing.go                             | 2 +-
 ecc/bls24-317/hash_to_g2.go                          | 2 +-
 ecc/bls24-317/internal/fptower/asm.go                | 2 +-
 ecc/bls24-317/internal/fptower/asm_noadx.go          | 2 +-
 ecc/bls24-317/internal/fptower/e12.go                | 2 +-
 ecc/bls24-317/internal/fptower/e12_test.go           | 2 +-
 ecc/bls24-317/internal/fptower/e2.go                 | 2 +-
 ecc/bls24-317/internal/fptower/e24.go                | 2 +-
 ecc/bls24-317/internal/fptower/e24_test.go           | 2 +-
 ecc/bls24-317/internal/fptower/e2_amd64.go           | 2 +-
 ecc/bls24-317/internal/fptower/e2_amd64.s            | 2 +-
 ecc/bls24-317/internal/fptower/e2_bls317.go          | 2 +-
 ecc/bls24-317/internal/fptower/e2_fallback.go        | 2 +-
 ecc/bls24-317/internal/fptower/e2_test.go            | 2 +-
 ecc/bls24-317/internal/fptower/e4.go                 | 2 +-
 ecc/bls24-317/internal/fptower/e4_bls315.go          | 2 +-
 ecc/bls24-317/internal/fptower/e4_test.go            | 2 +-
 ecc/bls24-317/internal/fptower/frobenius.go          | 2 +-
 ecc/bls24-317/internal/fptower/parameters.go         | 2 +-
 ecc/bls24-317/pairing.go                             | 2 +-
 ecc/bn254/bn254.go                                   | 2 +-
 ecc/bn254/fr/sis/sis.go                              | 2 +-
 ecc/bn254/fr/sis/sis_test.go                         | 2 +-
 ecc/bn254/fr/tensor-commitment/commitment.go         | 2 +-
 ecc/bn254/fr/tensor-commitment/commitment_test.go    | 2 +-
 ecc/bn254/internal/fptower/e2_bn254.go               | 2 +-
 ecc/bn254/internal/fptower/e2_bn254_fallback.go      | 2 +-
 ecc/bn254/internal/fptower/frobenius.go              | 2 +-
 ecc/bn254/internal/fptower/parameters.go             | 2 +-
 ecc/bn254/pairing.go                                 | 2 +-
 ecc/bw6-633/fp/bw6_utils.go                          | 2 +-
 ecc/bw6-633/internal/fptower/e3.go                   | 2 +-
 ecc/bw6-633/internal/fptower/e6.go                   | 2 +-
 ecc/bw6-633/internal/fptower/e6_test.go              | 2 +-
 ecc/bw6-633/internal/fptower/frobenius.go            | 2 +-
 ecc/bw6-633/internal/fptower/parameters.go           | 2 +-
 ecc/bw6-633/pairing.go                               | 2 +-
 ecc/bw6-761/fp/bw6_utils.go                          | 2 +-
 ecc/bw6-761/internal/fptower/e3.go                   | 2 +-
 ecc/bw6-761/internal/fptower/e6.go                   | 2 +-
 ecc/bw6-761/internal/fptower/e6_test.go              | 2 +-
 ecc/bw6-761/internal/fptower/frobenius.go            | 2 +-
 ecc/bw6-761/internal/fptower/parameters.go           | 2 +-
 ecc/ecc.go                                           | 2 +-
 ecc/secp256k1/marshal.go                             | 2 +-
 ecc/secp256k1/marshal_test.go                        | 2 +-
 ecc/secp256k1/secp256k1.go                           | 2 +-
 ecc/stark-curve/g1.go                                | 2 +-
 ecc/stark-curve/g1_test.go                           | 2 +-
 ecc/stark-curve/hash_to_g1.go                        | 2 +-
 ecc/stark-curve/hash_to_g1_test.go                   | 2 +-
 ecc/stark-curve/marshal.go                           | 2 +-
 ecc/stark-curve/marshal_test.go                      | 2 +-
 ecc/stark-curve/stark_curve.go                       | 2 +-
 83 files changed, 83 insertions(+), 83 deletions(-)

diff --git a/ecc/bls12-377/fp/element_utils.go b/ecc/bls12-377/fp/element_utils.go
index 1e48d7386c..b65d730369 100644
--- a/ecc/bls12-377/fp/element_utils.go
+++ b/ecc/bls12-377/fp/element_utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fp
diff --git a/ecc/bls12-377/internal/fptower/e2_bls377.go b/ecc/bls12-377/internal/fptower/e2_bls377.go
index dcd9ad959e..8e744274f1 100644
--- a/ecc/bls12-377/internal/fptower/e2_bls377.go
+++ b/ecc/bls12-377/internal/fptower/e2_bls377.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls12-377/internal/fptower/frobenius.go b/ecc/bls12-377/internal/fptower/frobenius.go
index 2c1cd967e5..44ca7315bd 100644
--- a/ecc/bls12-377/internal/fptower/frobenius.go
+++ b/ecc/bls12-377/internal/fptower/frobenius.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls12-377/internal/fptower/parameters.go b/ecc/bls12-377/internal/fptower/parameters.go
index 89db97098c..374a13edee 100644
--- a/ecc/bls12-377/internal/fptower/parameters.go
+++ b/ecc/bls12-377/internal/fptower/parameters.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls12-377/pairing.go b/ecc/bls12-377/pairing.go
index 590e3867bb..bdef731e1c 100644
--- a/ecc/bls12-377/pairing.go
+++ b/ecc/bls12-377/pairing.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package bls12377
diff --git a/ecc/bls12-381/internal/fptower/e2_bls381.go b/ecc/bls12-381/internal/fptower/e2_bls381.go
index 9a498801b1..41a36ab355 100644
--- a/ecc/bls12-381/internal/fptower/e2_bls381.go
+++ b/ecc/bls12-381/internal/fptower/e2_bls381.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls12-381/internal/fptower/e2_bls381_fallback.go b/ecc/bls12-381/internal/fptower/e2_bls381_fallback.go
index 34f5eccebb..3e81e3ee1b 100644
--- a/ecc/bls12-381/internal/fptower/e2_bls381_fallback.go
+++ b/ecc/bls12-381/internal/fptower/e2_bls381_fallback.go
@@ -1,7 +1,7 @@
 //go:build !amd64
 // +build !amd64
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls12-381/internal/fptower/frobenius.go b/ecc/bls12-381/internal/fptower/frobenius.go
index a127cd3c8e..5a3bbc0880 100644
--- a/ecc/bls12-381/internal/fptower/frobenius.go
+++ b/ecc/bls12-381/internal/fptower/frobenius.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls12-381/internal/fptower/parameters.go b/ecc/bls12-381/internal/fptower/parameters.go
index 2b225b06fd..798b3a8026 100644
--- a/ecc/bls12-381/internal/fptower/parameters.go
+++ b/ecc/bls12-381/internal/fptower/parameters.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls12-381/pairing.go b/ecc/bls12-381/pairing.go
index 72266a8f39..3379bd25b1 100644
--- a/ecc/bls12-381/pairing.go
+++ b/ecc/bls12-381/pairing.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package bls12381
diff --git a/ecc/bls24-315/hash_to_g2.go b/ecc/bls24-315/hash_to_g2.go
index 5d5c167292..099476baad 100644
--- a/ecc/bls24-315/hash_to_g2.go
+++ b/ecc/bls24-315/hash_to_g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package bls24315
diff --git a/ecc/bls24-315/internal/fptower/asm.go b/ecc/bls24-315/internal/fptower/asm.go
index 5857e743a3..332299aaa4 100644
--- a/ecc/bls24-315/internal/fptower/asm.go
+++ b/ecc/bls24-315/internal/fptower/asm.go
@@ -1,7 +1,7 @@
 //go:build !noadx
 // +build !noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-315/internal/fptower/asm_noadx.go b/ecc/bls24-315/internal/fptower/asm_noadx.go
index 2bd913581d..fe00c44dc3 100644
--- a/ecc/bls24-315/internal/fptower/asm_noadx.go
+++ b/ecc/bls24-315/internal/fptower/asm_noadx.go
@@ -1,7 +1,7 @@
 //go:build noadx
 // +build noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-315/internal/fptower/e12.go b/ecc/bls24-315/internal/fptower/e12.go
index f962123817..5d0a31a0f1 100644
--- a/ecc/bls24-315/internal/fptower/e12.go
+++ b/ecc/bls24-315/internal/fptower/e12.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-315/internal/fptower/e12_test.go b/ecc/bls24-315/internal/fptower/e12_test.go
index d78aa07bb8..fe188ca67b 100644
--- a/ecc/bls24-315/internal/fptower/e12_test.go
+++ b/ecc/bls24-315/internal/fptower/e12_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-315/internal/fptower/e2.go b/ecc/bls24-315/internal/fptower/e2.go
index c6f688d6cb..29286aa464 100644
--- a/ecc/bls24-315/internal/fptower/e2.go
+++ b/ecc/bls24-315/internal/fptower/e2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-315/internal/fptower/e24.go b/ecc/bls24-315/internal/fptower/e24.go
index c5752cc7d6..822bae2bd1 100644
--- a/ecc/bls24-315/internal/fptower/e24.go
+++ b/ecc/bls24-315/internal/fptower/e24.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-315/internal/fptower/e24_test.go b/ecc/bls24-315/internal/fptower/e24_test.go
index 38f7a8e4d9..1204cde092 100644
--- a/ecc/bls24-315/internal/fptower/e24_test.go
+++ b/ecc/bls24-315/internal/fptower/e24_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-315/internal/fptower/e2_amd64.go b/ecc/bls24-315/internal/fptower/e2_amd64.go
index 33d5ad58da..5de4b352ed 100644
--- a/ecc/bls24-315/internal/fptower/e2_amd64.go
+++ b/ecc/bls24-315/internal/fptower/e2_amd64.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-315/internal/fptower/e2_amd64.s b/ecc/bls24-315/internal/fptower/e2_amd64.s
index ec3c5dc2f0..5f7c9d2164 100644
--- a/ecc/bls24-315/internal/fptower/e2_amd64.s
+++ b/ecc/bls24-315/internal/fptower/e2_amd64.s
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 #include "textflag.h"
diff --git a/ecc/bls24-315/internal/fptower/e2_bls315.go b/ecc/bls24-315/internal/fptower/e2_bls315.go
index b3d94df547..dd1b9b2899 100644
--- a/ecc/bls24-315/internal/fptower/e2_bls315.go
+++ b/ecc/bls24-315/internal/fptower/e2_bls315.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-315/internal/fptower/e2_bls315_fallback.go b/ecc/bls24-315/internal/fptower/e2_bls315_fallback.go
index 850899eb4b..d750c8292a 100644
--- a/ecc/bls24-315/internal/fptower/e2_bls315_fallback.go
+++ b/ecc/bls24-315/internal/fptower/e2_bls315_fallback.go
@@ -1,7 +1,7 @@
 //go:build !amd64
 // +build !amd64
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-315/internal/fptower/e2_fallback.go b/ecc/bls24-315/internal/fptower/e2_fallback.go
index 0a0166a0a2..e85d9feea8 100644
--- a/ecc/bls24-315/internal/fptower/e2_fallback.go
+++ b/ecc/bls24-315/internal/fptower/e2_fallback.go
@@ -1,7 +1,7 @@
 //go:build !amd64
 // +build !amd64
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-315/internal/fptower/e2_test.go b/ecc/bls24-315/internal/fptower/e2_test.go
index c6ac7b02fa..8dd156d8e3 100644
--- a/ecc/bls24-315/internal/fptower/e2_test.go
+++ b/ecc/bls24-315/internal/fptower/e2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-315/internal/fptower/e4.go b/ecc/bls24-315/internal/fptower/e4.go
index 20c34ce359..309a866f6d 100644
--- a/ecc/bls24-315/internal/fptower/e4.go
+++ b/ecc/bls24-315/internal/fptower/e4.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-315/internal/fptower/e4_bls315.go b/ecc/bls24-315/internal/fptower/e4_bls315.go
index 3114895f2b..bdf33ee1b4 100644
--- a/ecc/bls24-315/internal/fptower/e4_bls315.go
+++ b/ecc/bls24-315/internal/fptower/e4_bls315.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-315/internal/fptower/e4_test.go b/ecc/bls24-315/internal/fptower/e4_test.go
index 05dcbfbcf2..a094fd03ae 100644
--- a/ecc/bls24-315/internal/fptower/e4_test.go
+++ b/ecc/bls24-315/internal/fptower/e4_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-315/internal/fptower/frobenius.go b/ecc/bls24-315/internal/fptower/frobenius.go
index 623069108c..b2b21b1b3a 100644
--- a/ecc/bls24-315/internal/fptower/frobenius.go
+++ b/ecc/bls24-315/internal/fptower/frobenius.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-315/internal/fptower/parameters.go b/ecc/bls24-315/internal/fptower/parameters.go
index dda047b542..fe44b48e4d 100644
--- a/ecc/bls24-315/internal/fptower/parameters.go
+++ b/ecc/bls24-315/internal/fptower/parameters.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-315/pairing.go b/ecc/bls24-315/pairing.go
index 22c06b72b0..6366a32b5e 100644
--- a/ecc/bls24-315/pairing.go
+++ b/ecc/bls24-315/pairing.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package bls24315
diff --git a/ecc/bls24-317/hash_to_g2.go b/ecc/bls24-317/hash_to_g2.go
index 4b8561997f..aa758ba2ba 100644
--- a/ecc/bls24-317/hash_to_g2.go
+++ b/ecc/bls24-317/hash_to_g2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package bls24317
diff --git a/ecc/bls24-317/internal/fptower/asm.go b/ecc/bls24-317/internal/fptower/asm.go
index 5857e743a3..332299aaa4 100644
--- a/ecc/bls24-317/internal/fptower/asm.go
+++ b/ecc/bls24-317/internal/fptower/asm.go
@@ -1,7 +1,7 @@
 //go:build !noadx
 // +build !noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-317/internal/fptower/asm_noadx.go b/ecc/bls24-317/internal/fptower/asm_noadx.go
index 2bd913581d..fe00c44dc3 100644
--- a/ecc/bls24-317/internal/fptower/asm_noadx.go
+++ b/ecc/bls24-317/internal/fptower/asm_noadx.go
@@ -1,7 +1,7 @@
 //go:build noadx
 // +build noadx
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-317/internal/fptower/e12.go b/ecc/bls24-317/internal/fptower/e12.go
index 2f0f222428..f17241e486 100644
--- a/ecc/bls24-317/internal/fptower/e12.go
+++ b/ecc/bls24-317/internal/fptower/e12.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-317/internal/fptower/e12_test.go b/ecc/bls24-317/internal/fptower/e12_test.go
index 22904788c5..2aaf4b4861 100644
--- a/ecc/bls24-317/internal/fptower/e12_test.go
+++ b/ecc/bls24-317/internal/fptower/e12_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-317/internal/fptower/e2.go b/ecc/bls24-317/internal/fptower/e2.go
index 6fa66f5906..c4bf9b1292 100644
--- a/ecc/bls24-317/internal/fptower/e2.go
+++ b/ecc/bls24-317/internal/fptower/e2.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-317/internal/fptower/e24.go b/ecc/bls24-317/internal/fptower/e24.go
index 44873ed128..c2e0ab6534 100644
--- a/ecc/bls24-317/internal/fptower/e24.go
+++ b/ecc/bls24-317/internal/fptower/e24.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-317/internal/fptower/e24_test.go b/ecc/bls24-317/internal/fptower/e24_test.go
index 93058a9b56..52538b903d 100644
--- a/ecc/bls24-317/internal/fptower/e24_test.go
+++ b/ecc/bls24-317/internal/fptower/e24_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-317/internal/fptower/e2_amd64.go b/ecc/bls24-317/internal/fptower/e2_amd64.go
index 2dd35a29a5..73ad282b7e 100644
--- a/ecc/bls24-317/internal/fptower/e2_amd64.go
+++ b/ecc/bls24-317/internal/fptower/e2_amd64.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-317/internal/fptower/e2_amd64.s b/ecc/bls24-317/internal/fptower/e2_amd64.s
index 1da5dfafd4..e310053e19 100644
--- a/ecc/bls24-317/internal/fptower/e2_amd64.s
+++ b/ecc/bls24-317/internal/fptower/e2_amd64.s
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 #include "textflag.h"
diff --git a/ecc/bls24-317/internal/fptower/e2_bls317.go b/ecc/bls24-317/internal/fptower/e2_bls317.go
index cd1e34f840..5528fba923 100644
--- a/ecc/bls24-317/internal/fptower/e2_bls317.go
+++ b/ecc/bls24-317/internal/fptower/e2_bls317.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-317/internal/fptower/e2_fallback.go b/ecc/bls24-317/internal/fptower/e2_fallback.go
index 0a0166a0a2..e85d9feea8 100644
--- a/ecc/bls24-317/internal/fptower/e2_fallback.go
+++ b/ecc/bls24-317/internal/fptower/e2_fallback.go
@@ -1,7 +1,7 @@
 //go:build !amd64
 // +build !amd64
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-317/internal/fptower/e2_test.go b/ecc/bls24-317/internal/fptower/e2_test.go
index 8238d4735a..d1d5eea1af 100644
--- a/ecc/bls24-317/internal/fptower/e2_test.go
+++ b/ecc/bls24-317/internal/fptower/e2_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-317/internal/fptower/e4.go b/ecc/bls24-317/internal/fptower/e4.go
index 147994de80..141a26a61e 100644
--- a/ecc/bls24-317/internal/fptower/e4.go
+++ b/ecc/bls24-317/internal/fptower/e4.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-317/internal/fptower/e4_bls315.go b/ecc/bls24-317/internal/fptower/e4_bls315.go
index 1afe60a032..31ae8f2b5c 100644
--- a/ecc/bls24-317/internal/fptower/e4_bls315.go
+++ b/ecc/bls24-317/internal/fptower/e4_bls315.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-317/internal/fptower/e4_test.go b/ecc/bls24-317/internal/fptower/e4_test.go
index a2a8c27962..c124e32344 100644
--- a/ecc/bls24-317/internal/fptower/e4_test.go
+++ b/ecc/bls24-317/internal/fptower/e4_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-317/internal/fptower/frobenius.go b/ecc/bls24-317/internal/fptower/frobenius.go
index 53c8cb6071..f4479c1edf 100644
--- a/ecc/bls24-317/internal/fptower/frobenius.go
+++ b/ecc/bls24-317/internal/fptower/frobenius.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-317/internal/fptower/parameters.go b/ecc/bls24-317/internal/fptower/parameters.go
index 23033e8393..63656331c3 100644
--- a/ecc/bls24-317/internal/fptower/parameters.go
+++ b/ecc/bls24-317/internal/fptower/parameters.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bls24-317/pairing.go b/ecc/bls24-317/pairing.go
index 0aa7f19d4e..bbca4ac664 100644
--- a/ecc/bls24-317/pairing.go
+++ b/ecc/bls24-317/pairing.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package bls24317
diff --git a/ecc/bn254/bn254.go b/ecc/bn254/bn254.go
index 87c5ee74b9..a0fa54df7e 100644
--- a/ecc/bn254/bn254.go
+++ b/ecc/bn254/bn254.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Package bn254 efficient elliptic curve, pairing and hash to curve implementation for bn254. This curve appears in
diff --git a/ecc/bn254/fr/sis/sis.go b/ecc/bn254/fr/sis/sis.go
index 5af87d5e1b..cfbd14f057 100644
--- a/ecc/bn254/fr/sis/sis.go
+++ b/ecc/bn254/fr/sis/sis.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/sis/sis_test.go b/ecc/bn254/fr/sis/sis_test.go
index 08431ad778..b37fc8fcf5 100644
--- a/ecc/bn254/fr/sis/sis_test.go
+++ b/ecc/bn254/fr/sis/sis_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Code generated by consensys/gnark-crypto DO NOT EDIT
diff --git a/ecc/bn254/fr/tensor-commitment/commitment.go b/ecc/bn254/fr/tensor-commitment/commitment.go
index 65542c5f40..5ade9a366b 100644
--- a/ecc/bn254/fr/tensor-commitment/commitment.go
+++ b/ecc/bn254/fr/tensor-commitment/commitment.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package tensorcommitment
diff --git a/ecc/bn254/fr/tensor-commitment/commitment_test.go b/ecc/bn254/fr/tensor-commitment/commitment_test.go
index fa5c43299a..d43fb97e36 100644
--- a/ecc/bn254/fr/tensor-commitment/commitment_test.go
+++ b/ecc/bn254/fr/tensor-commitment/commitment_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package tensorcommitment
diff --git a/ecc/bn254/internal/fptower/e2_bn254.go b/ecc/bn254/internal/fptower/e2_bn254.go
index 945fa1c761..ea5152b696 100644
--- a/ecc/bn254/internal/fptower/e2_bn254.go
+++ b/ecc/bn254/internal/fptower/e2_bn254.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bn254/internal/fptower/e2_bn254_fallback.go b/ecc/bn254/internal/fptower/e2_bn254_fallback.go
index ffa25c7e1b..3d58d737a2 100644
--- a/ecc/bn254/internal/fptower/e2_bn254_fallback.go
+++ b/ecc/bn254/internal/fptower/e2_bn254_fallback.go
@@ -1,7 +1,7 @@
 //go:build !amd64
 // +build !amd64
 
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bn254/internal/fptower/frobenius.go b/ecc/bn254/internal/fptower/frobenius.go
index 4cfef6fa14..4aaf9b5d01 100644
--- a/ecc/bn254/internal/fptower/frobenius.go
+++ b/ecc/bn254/internal/fptower/frobenius.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bn254/internal/fptower/parameters.go b/ecc/bn254/internal/fptower/parameters.go
index e6d241b946..2778dd9948 100644
--- a/ecc/bn254/internal/fptower/parameters.go
+++ b/ecc/bn254/internal/fptower/parameters.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bn254/pairing.go b/ecc/bn254/pairing.go
index f0e843fd35..0d9bbcc9f0 100644
--- a/ecc/bn254/pairing.go
+++ b/ecc/bn254/pairing.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package bn254
diff --git a/ecc/bw6-633/fp/bw6_utils.go b/ecc/bw6-633/fp/bw6_utils.go
index a661ec4154..e8225be100 100644
--- a/ecc/bw6-633/fp/bw6_utils.go
+++ b/ecc/bw6-633/fp/bw6_utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fp
diff --git a/ecc/bw6-633/internal/fptower/e3.go b/ecc/bw6-633/internal/fptower/e3.go
index 9f29bcb441..0e8d2f3298 100644
--- a/ecc/bw6-633/internal/fptower/e3.go
+++ b/ecc/bw6-633/internal/fptower/e3.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bw6-633/internal/fptower/e6.go b/ecc/bw6-633/internal/fptower/e6.go
index 8b4e716395..95bf2058c5 100644
--- a/ecc/bw6-633/internal/fptower/e6.go
+++ b/ecc/bw6-633/internal/fptower/e6.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bw6-633/internal/fptower/e6_test.go b/ecc/bw6-633/internal/fptower/e6_test.go
index 9f7c1856f9..ec71878f9d 100644
--- a/ecc/bw6-633/internal/fptower/e6_test.go
+++ b/ecc/bw6-633/internal/fptower/e6_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bw6-633/internal/fptower/frobenius.go b/ecc/bw6-633/internal/fptower/frobenius.go
index 6b5768cacf..2ee56b3644 100644
--- a/ecc/bw6-633/internal/fptower/frobenius.go
+++ b/ecc/bw6-633/internal/fptower/frobenius.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bw6-633/internal/fptower/parameters.go b/ecc/bw6-633/internal/fptower/parameters.go
index ced7fe6967..d2921508fd 100644
--- a/ecc/bw6-633/internal/fptower/parameters.go
+++ b/ecc/bw6-633/internal/fptower/parameters.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bw6-633/pairing.go b/ecc/bw6-633/pairing.go
index 130aec2b80..ede02249d3 100644
--- a/ecc/bw6-633/pairing.go
+++ b/ecc/bw6-633/pairing.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package bw6633
diff --git a/ecc/bw6-761/fp/bw6_utils.go b/ecc/bw6-761/fp/bw6_utils.go
index f1359d951c..1a7efa23e9 100644
--- a/ecc/bw6-761/fp/bw6_utils.go
+++ b/ecc/bw6-761/fp/bw6_utils.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fp
diff --git a/ecc/bw6-761/internal/fptower/e3.go b/ecc/bw6-761/internal/fptower/e3.go
index cd35eac1a3..2385f4c03a 100644
--- a/ecc/bw6-761/internal/fptower/e3.go
+++ b/ecc/bw6-761/internal/fptower/e3.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bw6-761/internal/fptower/e6.go b/ecc/bw6-761/internal/fptower/e6.go
index 84e5ce8160..858ad4c920 100644
--- a/ecc/bw6-761/internal/fptower/e6.go
+++ b/ecc/bw6-761/internal/fptower/e6.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bw6-761/internal/fptower/e6_test.go b/ecc/bw6-761/internal/fptower/e6_test.go
index 3a5f035bd6..6a9309a44a 100644
--- a/ecc/bw6-761/internal/fptower/e6_test.go
+++ b/ecc/bw6-761/internal/fptower/e6_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bw6-761/internal/fptower/frobenius.go b/ecc/bw6-761/internal/fptower/frobenius.go
index 6c158728b9..c4aa7b0a27 100644
--- a/ecc/bw6-761/internal/fptower/frobenius.go
+++ b/ecc/bw6-761/internal/fptower/frobenius.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/bw6-761/internal/fptower/parameters.go b/ecc/bw6-761/internal/fptower/parameters.go
index fdef10fb91..6b4aca2da4 100644
--- a/ecc/bw6-761/internal/fptower/parameters.go
+++ b/ecc/bw6-761/internal/fptower/parameters.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 package fptower
diff --git a/ecc/ecc.go b/ecc/ecc.go
index 5c9b6b2b32..4ce9bd2d10 100644
--- a/ecc/ecc.go
+++ b/ecc/ecc.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Package ecc provides bls12-381, bls12-377, bn254, bw6-761, bls24-315, bls24-317, bw6-633, secp256k1 and stark-curve elliptic curves implementation (+pairing).
diff --git a/ecc/secp256k1/marshal.go b/ecc/secp256k1/marshal.go
index 061e8a5e37..9827861fa6 100644
--- a/ecc/secp256k1/marshal.go
+++ b/ecc/secp256k1/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // FOO
diff --git a/ecc/secp256k1/marshal_test.go b/ecc/secp256k1/marshal_test.go
index c51a86d091..f47cec933a 100644
--- a/ecc/secp256k1/marshal_test.go
+++ b/ecc/secp256k1/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // FOO
diff --git a/ecc/secp256k1/secp256k1.go b/ecc/secp256k1/secp256k1.go
index 7142e75571..6c83776c70 100644
--- a/ecc/secp256k1/secp256k1.go
+++ b/ecc/secp256k1/secp256k1.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Package secp256k1 efficient elliptic curve implementation for secp256k1. This curve is defined in Standards for Efficient Cryptography (SEC) (Certicom Research, http://www.secg.org/sec2-v2.pdf) and appears in the Bitcoin and Ethereum ECDSA signatures.
diff --git a/ecc/stark-curve/g1.go b/ecc/stark-curve/g1.go
index 3e2806a7df..2943d9f886 100644
--- a/ecc/stark-curve/g1.go
+++ b/ecc/stark-curve/g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // FOO
diff --git a/ecc/stark-curve/g1_test.go b/ecc/stark-curve/g1_test.go
index 768d07e76d..a8f703dff7 100644
--- a/ecc/stark-curve/g1_test.go
+++ b/ecc/stark-curve/g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // FOO
diff --git a/ecc/stark-curve/hash_to_g1.go b/ecc/stark-curve/hash_to_g1.go
index 701002df34..a7aa0c63c0 100644
--- a/ecc/stark-curve/hash_to_g1.go
+++ b/ecc/stark-curve/hash_to_g1.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // FOO
diff --git a/ecc/stark-curve/hash_to_g1_test.go b/ecc/stark-curve/hash_to_g1_test.go
index 7473b0d2cd..6fd6a50b3e 100644
--- a/ecc/stark-curve/hash_to_g1_test.go
+++ b/ecc/stark-curve/hash_to_g1_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // FOO
diff --git a/ecc/stark-curve/marshal.go b/ecc/stark-curve/marshal.go
index ab1afc9184..929f6daa20 100644
--- a/ecc/stark-curve/marshal.go
+++ b/ecc/stark-curve/marshal.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // FOO
diff --git a/ecc/stark-curve/marshal_test.go b/ecc/stark-curve/marshal_test.go
index 8e3e502335..5f17ac1a93 100644
--- a/ecc/stark-curve/marshal_test.go
+++ b/ecc/stark-curve/marshal_test.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // FOO
diff --git a/ecc/stark-curve/stark_curve.go b/ecc/stark-curve/stark_curve.go
index 256ad02d03..716337f482 100644
--- a/ecc/stark-curve/stark_curve.go
+++ b/ecc/stark-curve/stark_curve.go
@@ -1,4 +1,4 @@
-// Copyright 2020-2024 Consensys Software Inc.
+// Copyright 2020-2025 Consensys Software Inc.
 // Licensed under the Apache License, Version 2.0. See the LICENSE file for details.
 
 // Package starkcurve efficient elliptic curve implementation for stark_curve. This is curve used in StarkNet: https://docs.starkware.co/starkex/crypto/stark-curve.html.